2004 annual report - engineeringoren/scs_msnet/ar2004/bsg-2004.pdf · connects in silico pv outlets...

2004 Annual Report

For: The McLeod Modeling and Simulation Network – M&SNet –of the Society for Modeling and Simulation International

From: The UCSF BioSystems Group

•• http://biosystems.ucsf.edu ••

The activities of the Group over past 12 months are adequately conveyed bythe following, key symposium and meeting presentations made byBioSystem Group members.

C. Anthony Hunt, Glen E.P. Ropella, Michael S. Roberts, and Li Yan, Biomimetic In Silico Devices. ComputationalMethods in Systems Biology, Second International Workshop, CMSB 2004, Paris, France, Proceedings. Lecture Notesin Bioinformatics, Springer (in press). p. 2-9

Mark R. Grant, C. Anthony Hunt, Lan Xia , Jimmie E. Fata, Mina J. Bissell, Modeling Mammary GlandMorphogenesis as a Reaction-Diffusion Process. Proceedings of the 26th Annual International Conference of the IEEEEMBS, San Francisco, CA, USA • September 1-5, 2004. p. 10-13

Jon Tang, C. Anthony Hunt, J. Mellein, and K. Ley, Simulating Leukocyte-Venule Interactions – A Novel Agent-Oriented Approach. ibid. p. 14-17

Li Yan, C. Anthony Hunt, Glen E.P. Ropella and Michael S. Roberts, In Silico Representation of the Liver: ConnectingFunction to Anatomy, Physiology and Heterogeneous Microenvironments. ibid. p. 18-21

Yu Liu, C. Anthony Hunt, Representing Intestinal Drug Transport In Silico: An Agent-Oriented Approach. ibid. p. 22-25

Suman Ganguli and C. Anthony Hunt, The Necessity of a Theory of Biology for Tissue Engineering: Metabolism-Repair Systems. ibid. p. 26-29

Tai Ning Lam and C. Anthony Hunt, Applying Models of Targeted Drug Delivery to Gene Delivery.ibid. p. 30-33

Song Chen, Suman Ganguli, C. Anthony Hunt, An Agent-based Computational Approach for Representing Aspects ofIn Vitro Multi-Cellular Tumor Spheroid Growth. ibid. p. 34-37

Yuanyuan Xiao, C. Anthony Hunt1, Jean Yee Hwa Yang, and Mark R. Segal, A Novel Stepwise NormalizationMethod for Two-Channel cDNA Microarrays. ibid. p. 38-41

BioDEVS: System-Oriented, Multi-Agent, Modeling & Simulation Framework Sunwoo Park, Glen E. P. Ropella,and C. Anthony Hunt Multiscale Computational Modeling for Biomedical Research, Workshop, 25 - 27 March2004, University of California, San Diego, La Jolla, CA <http://nbcr.ucsd.edu/multiscale.htm> Poster p. 42

C. Anthony Hunt and Glen E. P. Ropella, A Decentralization Method For Modeling The Multiple Levels ofOrganization and Function Within Liver, BISTI 2003 Symposium, "Digital Biology: The Emerging Paradigm,"November 6-7, 2003, Natcher Conference Center, National Institutes of Health, Bethesda, Maryland. Poster p. 43

Presented at CMSB ’04 (www.biopathways.org/CMSB04/), May 26-26, Paris, FranceIn Press: Lecture Notes in Bioinformatics (LNBI)

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Biomimetic In Silico Devices

C. Anthony Hunt1,3, Glen E.P. Ropella1, Michael S. Roberts2, and Li Yan3

1 Dept. of Biopharmaceutical Sciences, Biosystems Group,University of California, San Francisco, CA 94143-0446, [email protected]; [email protected]

http://biosystems.ucsf.edu2 Department of Medicine, University of Queensland, Princess Alexandra

Hospital, Woolloongabba, Q 4102 [email protected]

http://www.som.uq.edu.au/som/Research/therapeutics.shtml3 Joint UCSF/UC Berkeley Bioengineering Graduate Program

[email protected]://socrates.berkeley.edu/~lyan/

Abstract. We introduce biomimetic in silico devices, and means for validationalong with methods for testing and refining them. The devices are constructedfrom adaptable software components designed to map logically to biologicalcomponents at multiple levels of resolution. In this report we focus on the liver;the goal is to validate components that mimic features of the lobule (the hepaticprimary functional unit) and dynamic aspects of liver behavior, structure, andfunction. An assembly of lobule-mimetic devices represents an in silico liver.We validate against outflow profiles for sucrose administered as a bolus toisolated, perfused rat livers. Acceptable in silico profiles are experimentallyindistinguishable from those of the in situ referent. This new technology isintended to provide powerful new tools for challenging our understanding ofhow biological functional units function in vivo.

1 Introduction

Cells of the same type in the same tissue can experience different environments, and asa consequence exhibit quite different gene expression patterns [1]. This is just one ofthe problems faced when modeling biological systems at multiple levels of resolution.Network detail learned from experiments on isolated cells in vitro may not map directlyto the tissue level. Reflecting on this reality, Noble rejects the reductionist bottom-upand the traditional top-down modeling and simulation approaches [2]. He makes thecase for a “middle-out” strategy that focuses on the “functional level between genes andhigher level function” [3], and calls for new ideas and new approaches to help move thefield to the next level. The new class of biological analogue models presented here,which we refer to as biomimetic in silico devices (hereafter, devices), is an answer tothat call. The devices are designed to generate biomimetic behaviors and are constructedfrom software components that map logically to biological components at multiplelevels of resolution. The focus here is the liver. The data used for validation areoutflow profiles from experiments on isolated, perfused rat livers (hereafter, perfusedlivers) given bolus doses of compounds of interest [4, 5]. Acceptable devices arehepato-mimetic in that they generate in silico outflow profiles that are experimentallyindistinguishable from those of the in situ referent.


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2 Device Design

2.1 Modeling Approach and Biological Data

Rather than the traditional inductive, analytic modeling approach, we used aconstructive approach based in part on ideas and concepts from several sources,including compositional modeling [6]. We focus more on the aspects of structure andbehavior that give rise to the data. We deconstruct the system into biologicallyrecognizable components and processes that can be represented as software objects,agents, messages, and events. Next, we reconstruct using those objects within asoftware medium that handles probabilistic events, and can represent dynamic spatialheterogeneity. The process produces in silico devices [6] capable of biomimeticbehaviors. Of course, these devices are also models. We use device to stress theirmodular, constructive nature, to emphasize the essential properties discussed below, andto distinguish them from traditional equational models.

The devices represent aspects of the anatomic structure and behavior of thefunctional unit of the liver that influences administered compounds. We conduct insilico experiments that follow protocols that mimic the original in situ experimentalprotocols. Because a device is not based on equations, we do not directly fit it to data.We use a Similarity Measure [7] to quantify the similarity between data generated bythe device and data generated by the biological referent. Having completed that level ofvalidation we run simulation experiments to address what-if questions and/or grow thedevice so that it accounts for additional, different data (e.g., perfused liver outflowprofiles of additional compounds and/or hepatic imaging data).

2.2 Properties: Essential and Desired

We create a device from data with as few assumptions as possible, by first buildingand validating a simple, biomimetic device, and then iteratively improving it. Devicesand their components must be reusable, revisable, and easily updatable when criticalnew data becomes available, without having to re-engineer the whole device. Devicecomponents, like their biological referents, need to be sufficiently flexible andadaptable to be useful in a variety of research contexts. They should be able tofunction at multiple levels of resolution, from molecule to organ. In addition, deviceand components must logically map to their biological counterparts. Spatialheterogeneity is a quintessential characteristic of organisms at each organizationallevel. So, it is essential that device components be capable of representing thatheterogeneity at different levels of resolution as required by the problem. Finally,hepatic processes, drug disposition, and pharmacokinetic processes are characterizedby probabilistic events. So, our biomimetic devices are exclusively event driven andmost events can be probabilistic. These properties are deemed essential in partbecause they are expected to make this new technology easily accessible and useful toa majority of biomedical researchers.

2.3 Histological and Physiological Considerations

Changes in the architecture of hepatic fluid flow are associated with several diseasestates, and such alterations can influence a drug’s disposition. These considerations


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suggest that a device must have a flexible means of representing that architecture atwhatever level of detail is needed. We use directed graphs, with objects placed at graphnodes, to represent that architecture. Because the lobule is the primary structural andfunctional unit of the rat liver [8], the device must have a component that maps directlyto the lobule. Hereafter refer to that component as a LOBULE1.

Hepatocytes exhibit location-specific properties within lobules,including location-dependentexpression of drug metabolizingenzymes [1]. Such intralobularheterogeneity requires that aLOBULE be capable of easily ex-hibiting heterogeneity and zona-tion when such properties arerequired. LOBULES must also becapable of representing special-ized cell types, including endo-thelial, Kuppfer, and stellatecells, and their specializedbehaviors in appropriate relativerelationships, when needed, without forcing restructuring or redesign. The blood supplyfor one lobule, illustrated schematically by the cross section in Fig. 1, feeds into severaldozen sinusoids that merge as they feed into the lobule’s central vein (CV). Knownhepatic features that are not needed to account for outflow profiles of the targeted datasets do not have corresponding components within the LOBULES. Examples include aseparate hepatic arterial blood supply, the biliary system, and drug transport systems(into cells and into bile).

2.4 Designing the In Silico Components

Computational Framework. Our devices are constructed within the Swarmframework (www.swarm.org). The methods do not require any particular formalism.But, the experimental framework is always formulated using Partially Ordered Sets;they are a generic way to specify concurrent processes with as few strictures aspossible [9].Directed Graphs. A trace of flow paths within one lobule sketches a network that werepresent by an interconnected, directed graph. Literature data [8] are used to constrainthe accessible graph structures used. We only consider the subset of graphs that hasmore nodes connected to the portal vein tract (PV) (source) and fewer nodes connectedto the CV (exit). Teutsch et al. [8] subdivide the lobule interior into concentric zones.For now, we impose a three-zone structure and require that each zone contain at leastone node and that a shortest path from PV to CV will pass through at least one node andno more than one node per zone. The insert in Fig. 1 illustrates a portion of a graph thatconnects in silico PV outlets to the CV. Graph structure is specified by the number ofnodes in each zone and the number of edges connecting those nodes. Edges are furtheridentified as forming either inter-zone or intra-zone connections. The CV receives

1 When referring to the in silico counterpart of a biological component or process, such as“lobule,” “endothelial cell,” or “partition,” we use SMALL CAPS.

Fig. 1. A schematic of an idealized cross-section of ahepatic lobule showing half an acinus and the direction offlow between the terminal portal vein tract (PV), and thecentral hepatic vein (CV). SS: Sinusoidal Segment


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solute from the last node in each shortest path between PV and CV. Edges specify“flow paths” having zero length and containing no objects. A solute object exiting aparent node is randomly assigned to one of the available outgoing graph edges andappears immediately as input for the downstream child node. Randomly assigned intra-zone connections are allowed but are confined to Zones I and II. We randomly assignnodes to each of the zones so that the number of nodes in each zone is approximatelyproportional to the fraction of the total lobule volume found in that zone.

Sinusoidal Segments and the Fate of Solutes. Agents called sinusoidal segments (SSs)(Fig. 2) are placed at each graph node. There is one PV entrance (effectively coveringthe exterior of the LOBULE) and one CV exit for each LOBULE. A solute object is apassive representation of a chemical as it moves through the in silico environment. ThePV creates solute objects, as dictated by the experimental dosage function, anddistributes them to the SSs in Zone I. A solute object moving through the LOBULErepresents molecules moving through the sinusoids of a lobule, and their behavior isdictated by rules specifying the relationships between solute location, proximity to otherobjects and agents, and the solute's physicochemical properties. Each solute has doseparameters and a scale parameter (molecules per solute object). The relative tendencyof a solute object to move forward within a SS determines the effective flow pressureand this is governed by a parameter called Turbo. If there is no flow pressure (Turbo =0), then solute movement is specified by a simple random walk. Increasing Turbobiases the random walk in the direction of the CV.

We have studied the behaviors of several sinusoidal segment designs and describehere the extensible design currently in use. Simpler designs generate behaviors that failto meet our Similarity Measure criterion. Viewed from the center of perfusate flow outin Fig. 2, a SS is modeled as atube with a rim surrounded byother layers. The tube and rimrepresent the sinusoidal spaceand its immediate borders. Thetube contains a fine-grainedabstract Core space thatrepresents blood flow. Grid A isthe Rim. Grid B is wrappedaround Grid A and represents theendothelial layer. Another fine-grained space (Grid C) iswrapped around Grid B tocollectively represent the Spaceof Disse, hepatocytes, and bilecanaliculi2. If needed,hepatocytes and connected features such as bile canaliculi can be moved to a fourth gridwrapped around Grid C. The properties of locations within each grid can behomogeneous or heterogeneous depending on the specific requirements and theexperimental data. Objects can be assigned to one or more grid points. For example, asubset of Grid B points can represent one or more Kupffer cells. Objects that move

2 Because we are building a normalized model there is no direct coupling between grid points

within the fine-grained space and real measures such as hepatocyte volume or its dimensions inmicrons.

Fig. 2. Schematic of a sinusoidal segment (SS). Threetypes of SS are discussed in the text. One SS is placed ateach node of the directed graph within each LOBULE.


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from a location on a particular grid are subject to one or more lists of rules that arecalled into play at the next step. Within Grid B a parameter controls the size andprevalence of FENESTRATIONS1 and currently 10% of Grid B in each SS is randomlyassigned to FENESTRAE; the remaining 90% represents cells. Similarly, within the gridwhere some locations map to hepatocytes, there is a parameter that controls theirrelative density.

Classes of Sinusoidal Segments and Dynamics Within. To further enable accountingfor sinusoidal heterogeneity, we defined two classes of SSs, SA and SB. Additionalclasses can be specified and used when needed. Relative to SB the SA have a shorter pathlength and a smaller surface-to-volume ratio, whereas the SB have a longer path lengthand a larger surface-to-volume ratio. The circumference of each SS is specified by arandom draw from a bounded uniform distribution. To reflect the observed relativerange of real sinusoid path lengths, SS length is given by a random draw from a gammadistribution having a mean and variance specified by the three gamma functionparameters, a, b, and g.

Solute objects can enter a SS at either the Core or the Rim. At each step thereafteruntil it is METABOLIZED or collected it has several stochastic options, the aggregateproperties of which are arrived at through Monte Carlo simulation. In the Rim or Coreit can move within that space, jump from one space to the other, or exit the SS. From aRim location it can also jump to Grid B or back to the Core. Within Grid B it can movewithin the space, jump back to Grid A or to Grid C. When it encounters anENDOTHELIAL CELL within Grid B it may (depending on its properties) PARTITION intoit. Once inside, it can move about, exit, bind or not. Within Grid C it can move withinthe space or jump back to Grid B. When a HEPATOCYTE is encountered the SOLUTE can(depending on its properties) PARTITION into it or move on. Once inside a HEPATOCYTEit can move about, exit, bind (and possibly get METABOLIZED) or not. Currently allobjects within a HEPATOCYTE that bind can also METABOLIZE. The probability of asolute object being METABOLIZED depends on the object’s properties. OnceMETABOLIZED the object is destroyed. The only other way to exit a SS is from the Core,Rim or into bile (not implemented here). When the SOLUTE exits a SS and enters theCV, its arrival is recorded (corresponding to being collected), and it is destroyed.

2.5 Similarity Measure

The in situ liver perfusion protocol is detailed in [4]. Briefly, a compound of interest isinjected into the entering perfusate of the isolated liver. The entire outflow is collectedat intervals and the fraction of the dose within is determined. The 14C-sucrose outflowprofile contains information only about features of the extracellular environmentswhereas the data for a drug contains information on those features as well as onintracellular environments in that same liver. When the results of in silico and in situexperiments are similar, an expert can inspect the two data sets and offer an opinion onthe degree of their similarity. However, automated model generation and refinementrequires having one or more Similarity Measure (SM) to substitute for the expert’sjudgment. A SM is a function which takes two sets of experimental data and returns anumber as a measure of their similarity [7]. Classical regression approaches do notapply because we are comparing the outputs of two or more experiments.

There are two main contributors to intraindividual variability: methodological andbiological. For replicate experiments in the same liver the coefficient of variation for


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fraction of dose within specific outflow collection intervals typically ranges between 10and 40%. A coefficient of variation can define a continuous interval bounding theexperimental data. Any new set of results that falls within those bounds and hasessentially the same shape is defined as being experimentally indistinguishable. Thesame should hold even if the data comes from an in silico experiment, and that providesthe basis for selecting and evaluating SMs.

The objective of the SM is to help select among device designs, not simply tospecify a device and select among variations on that device. Hence, the successful SMmust target the various features of the outflow profile that correlate with the generativestructures and building blocks inside the device. However, for simplicity in these earlystudies we have assumed that the coefficients of variation of repeat observations withindifferent regions of the curve are the same. In that way we can use a simple intervalSM, which is what we do. A set of in situ outflow profiles, T, is used as training data.From this data, we calculate a distance, D, from a reference that will be the basis for amatch. We then take two outflow profiles and pick one to be the reference profile, Pr.For each observation in Pr, create a lower, Pl, and an upper, Pu, bound by multiplyingthat observation by (1 – D) and (1 + D), respectively. The two curves Pl and Pu are thelower and upper bounds of a band around Pr. The two outflow profiles are deemedsimilar if the second profile, P, stays within the band. The distance D used for sucroseis one standard deviation of the array of relative differences between each repeatobservation and the mean observations at that time. To calculate D for the training set Twe choose experimental data on different subjects that were part of the same protocol[4, 5].

3 In Silico Experimental Results

To begin development of a new device we select an outflow profile and begin theprocess of finding the simplest design, given restrictions: one is that it be comprised ofthe minimum components needed to generate an acceptably similar profile. An initialunrefined parameterization is chosen based on available information. Components areadded according to that initial parameterization. If the behavior of the resulting deviceis not satisfactory, any given piece of the device may be surplused and replaced,modified, or reparameterized with minimal impact on the other components within thedevice. This process continues until the device provides reasonable coverage of thetargeted solution space. Once an acceptable parameterization is found, the parameterspace is searched further [10] for additional solution sets. Bounds for the parameterspace can be specified to indicate solution set regions for which the device validates(i.e., acceptable SM measures are obtained). Subsequently, for a second data set, arepeat of the first experiment or a data set for a second drug, we make only minimaladjustments and additions to the structure of the first device so that the resulting newdevice generates acceptable outflow profiles for both data sets.

The typical in situ outflow profile is an account of on the order of 1015 drugmolecules percolating through several thousand lobules. The typical in silico dose forone run with one LOBULE is on the order of 5,000 drug objects, where each drug objectcan represent a number (≥ 1) of drug molecules. Thus, a resulting single outflow profilewill be very noisy and will be inadequate to represent the referent in situ profile.Another independent run with that same device, parameter settings, and dose willproduce a similar but uniquely different outflow profile. Changing the random numbergenerator seed alters the specifics for all stochastic parameters (e.g., placement of SSs


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on the digraph), thus providing a unique, individual version of the LOBULE, analogous tothe unique differences between two lobules in the same liver. A full in silicoexperiment is one that produces an outflow profile that is sufficiently smooth to use theSM, and typically combines the results from 20 or more independent runs using thesame LOBULE.

One can identify several similar parameterizations that will yield outflow profilesthat are experimentally indistinguishable from each other. That is because there is aregion of device-structure space (model space) that will yield acceptable behaviorsrelative to a specific data set. Sucha region can be viewed as ametaphor for the fact that alllobules are similar but not identical.We currently do not attempt tofully map acceptable regions ofeither model or parameter space.Our goal is simply to locate aregion in each that meets ourobjectives.

Figure 3 shows results fromone parameterization of a LOBULEagainst a perfused liver sucroseoutflow profile. The shaded regionis a band enclosing the meanfraction of dose collected for eachcollection interval. The width ofthe band is ± 1 std about the mean.The filled circles are resultsobtained using the specified deviceparameter vector.

4 Higher and Lower Levels of Resolution

Different regions of a normal liver are indistinguishable. That is generally not the casefor a diseased liver, where some lobules can be damaged or otherwise changed. So, tounderstand and account for such differences we need methods to shift levels ofresolution without loss of information. The following summarizes how we are enablingresolution changes. To represent a whole diseased liver with heterogeneous propertieswe can first connect in parallel four to five different sized lobes, where each is adirected graph having multiple parallel, single node paths connecting portal and hepaticveins nodes (Fig. 4), and agents representing secondary units are placed at those nodes.A lobe is comprised of a large number of these units [8]. Each secondary unit can besimilarly represented by a directed subgraph with LOBULES placed at each of its nodes(insert, Fig. 4). When subcellular networks within CELLS located in Grids B and C areneeded, they may also be treated as directed graphs with nodes representing factors andwith edges representing interactions and influences [11]. Having a mechanism forrealizing networks allows us to replace sub-networks (at any location) with rules-basedsoftware modules.

Fig. 3. An outflow profile for a device parameterized tomatch a sucrose outflow profile. Nodes per Zone: 55,24 and 3 for Zones I, II and III, respectively; totaledges: 60; intra-zone connections: Zone I = 10, Zone II= 8, Zone III = 0; inter-zone connections: IÆII = 14,IÆIII = 4, IIÆIII = 14; SSs: 50% SA and SB; Number ofruns = 100.


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5 Conclusion

We have tested and affirmed the hypothesis thatperfused liver outflow data obtained followingbolus administration of sucrose can, inconjunction with other data, be used to specifyand parameterize a physiologically recognizablehepato-mimetic device that can generate outflowprofiles that are experimentally indistinguishablefrom the original in situ data. Each device isconstructed from software components thatexhibit several essential properties includingbeing designed to map logically to hepaticcomponents at multiple levels of resolution, fromsubcellular to whole organ. This new technologyis intended to provide powerful tools foroptimizing the designs of real experiments. Itwill also help us challenge our understanding ofhow mammalian systems function in normal anddiseased states, and when stressed or confrontedwith interventions.

References1. Roberts, M., Magnusson, B., Burczynski, F., Weiss, M.: Enterohepatic Circulation: Physio-

logical, Pharmacokinetic and Clinical Implications. Clin. Pharmacokinet. 41(2002), 751-902. Noble D.: The Rise of Computational Biology. Nat. Rev. Mol. Cell. Bio. 3 (2002) 460-633. Noble, D.: The Future: Putting Humpty-Dumpty Together Again. Biochem. Soc.

Transact. 31 (2003) 156-84. Roberts, M.S., Anissimov, Y.G.: Modeling of Hepatic Elimination and Organ

Distribution Kinetics with the Extended Convection-Dispersion Model. J. Pharmacokin.Biopharm. 27 (1999) 343-382

5. Hung, D.Y., Chang, P., Weiss, M., Roberts, M.S.: Structure-Hepatic DispositionRelationships for Cationic Drugs in Isolated Perfused Rat Livers: Transmembrane Exchangeand Cytoplasmic Binding Process. J. Pharmacol. Exper. Therap. 297 (2001) 780–89

6. Falkenhainer, B., Forbus, K.D.: Compositional Modeling: Finding the Right Model for theJob. Art. Intel. 51 (1991), 95-143

7. Santini, S., Jain, R.: Similarity Measures, IEEE Tran. Pattern Analysis and MachineIntelligence 21 (1999) 871-83

8. Teutsch, H.F., Schuerfeld, D., Groezinger, E.: Three-Dimensional Reconstruction ofParenchymal Units in the Liver of the Rat. Hepatology 29 (1999) 494-505

9. Burns, A., Davies, G.: Concurrent Programming. Addison-Wesley, Reading, MA (1993) 1-210. Sanchez, S.M., Lucas, T.W.: Exploring the World of Agent-Based Simulations: Simple

Models, Complex Analyses. In: Yücesan, E., Chen, C.-H., Snowdon, J.L., Charnes, C.M.,(eds.): Proceedings of the 2002 Winter Simulation Conference (2002) 116-26

10. Gumucio, J.J., Miller, D.L.: Zonal Hepatic Function: Solute-Hepatocyte InteractionsWithin the Liver Acinus. Prog. Liver Diseases 7 (1982) 17-30

11. Tyson, J.J., Chen, K., Novak, B.: Network Dynamics and Cell Physiology. Nat. Revs.Mol. Cell Biol. 2 (2001) 908-17

Fig. 4. An illustration of thehierarchical structure of an in silicoliver. A lobe is comprised of a networkof secondary units (SEC. UNIT) [8]; they,in turn are comprised of a network oflobules (Lb) as pictured in Fig. 2. PV:Portal vein. CV: Central hepatic vein

Abstract- Mammary ducts are formed through a process of branching morphogenesis. We present results of experiments using a simulation model of this process, and discuss their implications for understanding mammary duct extension and bifurcation. The model is a cellular automaton approximation of a reaction-diffusion process in which matrix metalloproteinases represent the activator, inhibitors of matrix metalloproteinases represent the inhibitor, and growth factors serve as a substrate. We compare results from the simulation model with those from in-vivo experiments as part of an assessment of whether duct extension and bifurcation during morphogenesis may be a consequence of a reaction-diffusion mechanism mediated by MMPs and TIMPs.

Keywords—Branching morphogenesis, simulation,

modeling, mammary gland, extracellular matrix, reaction-diffusion, matrix metalloproteinase, tissue inhibitor of metalloproteinase.

I. INTRODUCTION Branching morphogenesis occurs in the development of a variety of organs, from the trachea in Drosophila to nephrons in the kidney. Patterns in branching morphogenesis have been identified and include branch elongation, tip bifurcation, lateral branching, and anastomosis. Elongation and tip bifurcation both occur during mammary branching morphogenesis. What are the key factors and events? To help answer that question and gain a deeper insight into how such processes can unfold (and be influenced by interventions), we developed a cellular automata (CA) model and used it for experimentation. Here we focus on two classes of factors (defined below): MMPs alter the environment of the developing cells, and TIMPs specifically inhibit them. Our hypothesis is that they can work synergistically as activators and inhibitors in a reaction-diffusion process that can guide and control simulated branching morphogenesis.

II. BIOLOGICAL DETAILS The formation of mammary ducts in the mouse also involves branching morphogenesis. It occurs in several stages, beginning in early development with the formation of the mammary bud at mid-gestation, followed by invasion of the epithelium into the mammary fat pad during puberty. During invasion, a branched ductal network is formed

through a process involving extracellular matrix (ECM) remodeling, duct elongation, and branching. The process is facilitated by crosstalk between the proliferating epithelia and the mammary stroma. It has been demonstrated that mammary branching morphogenesis is influenced by extracellular matrix composition, growth factors, ECM-degrading enzymes including matrix metalloproteinases (MMPs), and tissue inhibitors of MMPs (TIMPs) [1] (Fig. 1). The matrix metalloproteinases catalyze the cleavage of extracellular matrix components, which is required for duct extension. Treatment of mice with broad-spectrum MMP inhibitors inhibits branching and duct elongation [2]. Tissue inhibitors of metalloproteinases serve to regulate the activities of matrix metalloproteinases, inhibiting MMP activity by noncovalent binding. It has been hypothesized that it is the coordinated action of MMPs and TIMPs that give rise to branched growth (Fig. 1B). A number of approaches have been taken to model morphogenesis in biological systems. In particular,

A

B

Fig. 1. A. Representation of branching morphogenesis in the developing mouse mammary gland. Black lines represent ductal cells, with each duct terminated by a terminal end bud, where duct bifurcation occurs. Development of the mature gland involves duct elongation, tip bifurcation, and lateral branching. B. Representation of inhibition of MMP action by TIMP expression.

Modeling Mammary Gland Morphogenesis as a Reaction-Diffusion Process

Mark R. Grant1, C. Anthony Hunt2, Lan Xia3 , Jimmie E. Fata4, Mina J. Bissell4 1Joint UCSF/UCB Bioengineering Graduate Group, The University of California, Berkeley, 2Biosystems Group, Department of

Biopharmaceutical Sciences, The University of California, San Francisco, CA 94143, USA 3Comparative Biochemistry Graduate Group, The University of California, Berkeley, 4Life Sciences Division, Lawrence Berkeley

National Laboratory, University of California, Berkeley

reaction-diffusion systems have been used extensively in modeling pattern formation, including branching morphogenesis [3]. A reaction-diffusion system of the substrate-depletion type was used to model the influence of fibroblast growth factor 1 (FGF1) on the growth of lung epithelial cultures in tissue culture, where FGF1 served the role of the substrate, and cells served as the activator [4]. It has also been demonstrated that a reaction-diffusion system of the activator-inhibitor type is able to give rise to fundamental branching features such as bifurcation and lateral branching [5]. In the case of mammary branching morphogenesis, it is possible that MMPs and TIMPs may be acting as activators and inhibitors, respectively, in a reaction-diffusion process. It is known that MMPs exhibit autocatalytic activation. It is also known that MMP and TIMP expression is often co-localized. And finally, TIMPs are capable of inhibiting MMP activity in a 1:1 stoichiometric ratio. We have implemented a computer simulation of a reaction-diffusion process of branching morphogenesis adapted from the work in [5]. We compare results obtained from in-vivo experiments modulating MMP and TIMP activity with output generated from the simulation in order to explore whether MMPs and TIMPs may be functioning as activators and inhibitors in a reaction-diffusion process.

III. MODELING AND SIMULATION The simulation is implemented as a 2D square grid cellular automata with closed boundaries. Four variables determine the state of each grid position in the cellular automata: matrix metalloproteinases (MMP)1, tissue inhibitor of metalloproteinases (TIMP), growth factor (GF), and duct cells (CELL). The following is a description of each variable and the CA update rules which govern their

1 To avoid confusion, the simulation variables which correspond to biological features are italicized.

behavior. The relationships between the variables are represented visually in Fig. 2, and the rules that govern the CA are summarized in Fig. 3.

A. Metalloproteinases

MMPs are proteases that degrade components of the extracellular matrix, particularly collagen and laminin. Most matrix metalloproteinases are secreted as proenzymes, and through autocatalysis they become activated. It is known that MMPs are selectively expressed around sites of duct elongation, and it has been demonstrated that MMP activity is required for normal mammary gland development [2]. It is also known that growth factors can induce expression of MMPs [6]. The ability of MMP to induce TIMP expression has not been verified in the literature; however, MMP and TIMP expression is often colocalized in-vivo, suggesting such a mechanism may exist. These behaviors are represented and controlled within the model by rules 1, 2, 3, 4, 7, 9, and 11.

B. Tissue Inhibitors of Metalloproteinases Tissue inhibitors of metalloproteinases (TIMPs) are the primary regulators of MMP activity. The TIMPs have also been implicated in mammary branching morphogenesis [7]. One function of TIMPs is to bind to MMPs and inhibit their

Fig. 2. Diagram of the relationships between the variables in the model, adapted from [5]. The dashed arrows are used to indicate whether diffusion occurs. MMP: stands for the variable representing matrix metalloproteinase levels; TIMP: stands for the variable representing tissue inhibitor of metalloproteinase; ECM: stands for the variable representing extracellular matrix; CELL: stands for the variable that indicates the presence of a simulated duct cell; and R: A small random variation in the value of GF.

1. If MMP d TIMP> ⋅ , then MMP c MMP GF= ⋅ ⋅

2. If max

MMP MMP> , then max

MMP MMP=

3. 1 2MMP MMPδ δ⋅= −

4. If 0MMP < , then 0MMP =

5. 3 4TIMP TIMPδ δ⋅= −

6. If 0TIMP < , then 0TIMP = 7. TIMP MMP TIMPγ= ⋅ + 8. TIMP TIMP η= + 9. If MMP ε> , then 1CELL =

10. If 1CELL = , then 1

GF GF GFα β= + − ⋅ , else

0GF GF GFα β= + − ⋅

11. MMP MMP= , TIMP TIMP= , GF GF=

12. ( )0,1GF GF Nρ= +

Fig. 3. The CA transition rules used in the simulation, adapted from [5]. Default parameterizations: α = 0.2, β0 = 0.2, β1 = 1.0, β2 = 1.0, δ1 = 0.9, δ2 = 1.0, δ3 = 0.5, δ4 = 0.5, ρ = 0.01, γ = 0.5, ε = 120, c = 3.0, d = 2.0, MMPmax = 250, grid height = 300, and grid width = 300. Initial GF in every cell was set to 0.75, whereas initial MMP, initial CELL, and initial TIMP in every cell were set to zero. The simulation is triggered using a positive value of MMP placed in the corner of the simulation grid. The distances used for the averaging of Moore neighborhoods in rule 12 were RMMP = 2, RGF = 3, and RTIMP = 6.

protease activity. The inhibitory activity of TIMPs is modeled in rule 1. Regulation of TIMP expression is modeled by rules 6 and 7. In order to imitate experiments in which TIMP is expressed constitutively, rule 8 has been included the model. The diffusion of TIMPs is governed by rule 11. C. Growth Factor

It has been demonstrated in 3D cultures as well as in-vivo that growth factors can influence mammary branching morphogenesis [8]. In addition to growth factors such as epidermal growth factor, hepatocyte growth factor, and fibroblast growth factor, byproducts of extracellular matrix decomposition can stimulate branching. Growth factors are able to diffuse through the mammary fat pad, as indicated by studies of the effects of growth factor implants on duct growth in-vivo [8]. It is also known that growth factors can induce MMP synthesis [4]. Rules 1, 10, and 11 model these behaviors in the simulation. A small stochastic component

is introduced into the model to model in-vivo heterogeneity in the mammary fat pad by rule 12. D. Cell Proliferation Cell proliferation occurs as a consequence of MMP activity. It is known that MMP digestion of ECM components generates growth-promoting fragments; furthermore, MMPs are able to degrade cell-ECM contacts, which can induce an epithelial-to-mesenchymal transition and promote growth. Additionally, degradation of the ECM by MMP activity removes physical constraints on cell growth. These effects are modeled by rule 1. It is also known that growth factor is depleted from the extracellular environment through receptor internalization by cells which bind growth factors. This effect has been observed in-vitro [4], and the process is represented within the model as the differential consumption of growth factor by proliferating cells. This process is controlled by rule 10.

III. MODEL BEHAVIOR PERTURBATION AND COMPARISON WITH EXPERIMENTAL OBSERVATIONS

In order to evaluate whether MMPs and TIMPs may be functioning as activators and inhibitors in morphogenesis, we compare results from published in-vivo experiments with output generated from corresponding changes to the simulation. Specifically we compare the effects of increased TIMP expression and inhibition of MMP activity on maximal duct length. A. Effect of changes in basal TIMP level Transgenic mice overexpressing human TIMP1 have been generated [2]. The TIMP1 transgene was driven by a β-actin promoter, resulting in constitutive expression. The effect of the introduction of TIMP1 is modeled through manipulation of the simulation parameter η . The results are summarized in Fig. 4. B. Effect of changes in MMP autocatalysis parameter

There are 28 known MMP genes in humans. Broad-spectrum MMP inhibitors have been developed which are used to mimic the effect of knocking out all MMP genes. These inhibitors have been used to study the role of MMPs in branching morphogenesis. The effect of these inhibitors is imitated in the simulation by decreasing the value of the simulation parameter c. The results from this analysis are summarized in Fig. 5.

A.

B.

80100120140160180

0 0.5 1 1.5 2 3.5simulation parameter η

dist

ance

C.

0

0.05

0.1

0.15

0 0.5 1 1.5 2 3.5 4simulation parameter η

bifu

rcat

ion

freq

uenc

y

Fig. 4. Effect of increasing basal TIMP level, η, on simulation output. A. Simulation output with default parameter values from Fig. 2, but with

0η = , 2.0η = , 3.5η = , and 4.0η = , from left to right. B. Simulated duct extension distance for different values of η , after 300 steps, measured from the initiation point to the tip of the furthest simulated duct, in points. C. The effect of η on the number of bifurcations per unit distance after 300 steps.

V. DISCUSSION

It has been shown that constitutive expression of TIMP1

in mice inhibited duct extension by approximately 25% compared to w.t. controls [2]. The simulated ducts behave in a similar fashion, with a significant reduction in simulated duct extension in response to increasing the basal level of the TIMP variable by increasing the parameter η (Fig. 3A,B). The parameter η also influences the number of simulated duct bifurcations events per unit distance (Fig. 3C). The effect of TIMP1 expression on the frequency of duct bifurcation events in-vivo has not been measured to our knowledge but such an analysis would be interesting in light of the simulation output.

The effect of broad-spectrum MMP inhibitors on mammary duct development in mice is quite dramatic, more so than the effect of TIMP-1 expression. The inhibitor GM6001 is able to completely block duct elongation during the initial 3 weeks of mamary gland development [2]. Although duct growth eventually occurs, the process is

attenuated by continuous treatment, resulting in a ductal network that is approximately 50% of the size of untreated mice. Reduction in MMP activity is mimicked in the simulation by reducing the value of the parameter c. The simulated ducts respond in a fashion similar to ducts in-vivo, as decreasing values of c result in a slower rate of simulated duct extension (Fig. 4A, B). However, unlike the results from increasing the value of η (Fig. 3C), there was not an apparent reduction in simulated duct bifurcations per unit distance (Fig. 4C). Again, it is not known whether a corresponding effect is observed in-vivo as a consequence of MMP inhibition although this could also be analyzed using existing data from in-vivo experiments.

VI. CONCLUSION

The simulation model of mammary gland morphogenesis described in this report generates qualitative results that are similar to those observed in-vivo, in response to modulation of TIMP and MMP activity. The inhibition of simulated duct extension is consistent with the possibility that MMPs and TIMPs are serving as activators and inhibitors in a reaction-diffusion-like process. Additional quantitative data from in-vivo experiments is needed to test this hypothesis further. Comparison of simulation model behavior and experimental results will be useful in this effort.

REFERENCES [1] B. Wiseman and Z. Werb, "Stromal Effects on Mammary Gland

Development and Breast Cancer", Science, vol. 296, no. 5570, pp. 1046-1049, May 2002.

[2] B. Wiseman, M. D. Sternlicht, L. R. Lund, C. M. Alexander, J. Mott, M. J. Bissell, P. Soloway, S. Itohara, Z. Werb, "Site-specific inductive and inhibitory activities of MMP-2 and MMP-3 orchestrate mammary gland branching morphogenesis", J Cell Biol, vol. 162, no. 6, pp. 1123-1133, Sep. 2003.

[3] A. Turing, "The chemical basis of morphogenesis", Phil. Trans R. Soc., vol. B327, pp. 549-578, 1952.

[4] T. Miura and K. Shiota,, "Depletion of FGF acts as a lateral inhibitory factor in lung branching morphogenesis in vitro", Math Biosci, vol. 156, no. 1-2, pp. 191-206, Mar. 1999.

[5] M. Markus, D. Böhm, M. Schmick, "Simulation of vessel morphogenesis using cellular automata" Math Biosci, vol. 156, no. 1-2, pp. 191-206, Mar. 1999.

[6] S. E. Moon, M. K. Dame, D. R. Remick, J. T. Elder, J. Varani, “Induction of matrix metalloproteinase-1 (MMP-1) during epidermal invasion of the stroma in human skin organ culture: keratinocyte stimulation of fibroblast MMP-1 production”, Br. J. Cancer, vol. 85, no. 10, pp. 1600-1605, Nov. 2001.

[7] J. E. Fata, K. J. Leco, R. A. Moorehead, D. C. Martin, R. Khokha, “Timp-1 is important for epithelial proliferation and branching morphogenesis during mouse mammary development”, Dev. Biol., vol. 211, no. 2, pp. 238-254, Jul. 1999.

[8] M. Simian, Y. Hirai, M. Navre, Z. Werb, A. Lochter, M. J. Bissell, “The interplay of matrix metalloproteinases, morphogens and growth factors is necessary for branching of mammary epithelial cells”, Development, vol. 128, no. 16, pp. 3117-3131, Aug. 2001.

A.

B.

0

50

100

150

200

1.7 2 2.3 2.6 3

simulation parameter c

dist

ance

C.

0

0.05

0.1

0.15

1 2 3 4 5simulation parameter c

bifu

rcat

ion

freq

uenc

y

Fig. 5. Effect of reduction of MMP activation coefficient, c, on simulation output. A. Branching pattern after 300 steps, with c = 3.0, c = 2.3, c = 2.0, and c = 1.7, from left to right. B. Simulated duct extension distance for different values of c, after 300 steps, measured from the initiation point to the tip of the furthest simulated duct in points. C. The effect of c on the number of bifurcations per unit distance after 300 steps.

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Abstract—Leukocyte recruitment into sites of inflammation involves a complex cascade of molecular interactions between the leukocyte and the endothelial cells of the inflamed venule. This report proposes a novel agent-oriented approach for simulating leukocyte-venule interactions during inflammation. We focus on modeling and simulating the initial steps of rolling, activation, and firm adhesion of neutrophils on TNF-α-treated mouse cremaster muscle venules.

Keywords—Adhesion, Agent-Based Model, Endothelium,

Inflammation, Leukocyte, Rolling, Transmigration

I. INTRODUCTION

Leukocyte recruitment into sites of inflammation involves a complex cascade of molecular interactions between the leukocyte and endothelial cells of the inflamed venule. Initial interactions are primarily mediated by the selectin family of receptors and their respective carbohy-drate ligands found on the membranes of both leukocytes and endothelial cells. Selectin-ligand interactions are tran-sient due to the fluid force the leukocyte experiences within the venule. As selectin-ligand bonds are constantly formed at the leading edge of the leukocyte, bonds at the trailing edge are broken, which causes the leukocyte to undergo rolling [1]. Each selectin molecule is believed to have a characteristic rate of bond association and dissociation and thus rolling velocities are different when mediated by different selectin molecules. As leukocytes roll along the venular surface, they can detect chemokines presented on the membrane of activated endothelial cells via chemokine receptors. Upon chemokine detection, intracellular signaling events are triggered that activate the leukocyte. The result is an increased affinity and avidity (clustering) of the integrins, another class of recep-tors found on leukocytes. When in a high affinity state, these integrins are capable of forming strong interactions with endothelial cell adhesion molecules that are believed to enable leukocytes to decrease their rolling velocity and eventually firmly adhere to the vessel wall [2]. In neutrophils, it has also been observed that engagement of the selectins and integrins with their ligands can lead to intracellular signaling events and activate the leukocyte [3]. Once firmly adhered to an endothelial cell, a leukocyte undergoes diapedesis: they apparently crawl between adjacent endothelial cells and into the target tissue. Here, we propose a novel computational approach for simulating the events and interactions described here. We use

an agent-oriented approach and represent this system as a collection of autonomous (software) entities, or agents, making decisions on how to interact with their local environment based on a set of encoded rules. Our initial simulation experiments are designed to represent neutrophil rolling, activation, and firm adhesion on TNF-α-treated mouse cremaster muscle venules.

II. MODEL STRUCTURE The proposed agent-based model contains Ligand, Cell, Membrane, and Space superclasses. The Ligand superclass represents biological molecules that can form bonds with other macromolecules. The Membrane superclass represents cellular membranes. The Cell superclass corresponds to cells within the biological model. Lastly, the Space superclasses provide environments within which the objects can interact. A. Ligand

The Ligand superclass can be broken down into AdhesMolecule, Chemok, and ChemokReceptor subclasses. AdhesMolecule objects represent the behaviors of adhesion molecules such as the selectins, integrins, and cellular adhesion molecules. Each AdhesMolecule object has parameters that are used to calculate a probability that it will form an interaction with its coreceptor AdhesMolecule object. Such parameters include the total number of molecules that the AdhesMolecule object represents, as well as an affinity and avidity value. AdhesMolecules also contain parameters that are used to calculate probabilities that they will break their interaction with their respective LIGAND1. The values for these parameters are dynamic and may change during the course of a simulation to reflect the events that occur in the biological model during cell activation by chemokine detection or by engagement of the selectins and integrins with their ligands. Rules that determine how these parameters will be updated are encoded within the AdhesMolecule objects. Chemok objects represent chemokine signaling molecules, and ChemokReceptors correspond to the chemokine receptors that bind them. Knowledge of which AdhesMolecules are affected upon formation of ChemokReceptor-Chemok LIGAND interactions are encoded within the ChemokReceptors.

1 The same word may be used to refer to a biological molecule, component, or event and the in silico object or event that represents them. In the latter case the word is written using small caps.

Simulating Leukocyte-Venule Interactions – A Novel Agent-Oriented Approach

J. Tang1, C. A. Hunt1,2, J. Mellein2, and K. Ley3 1Joint UCSF/UCB Bioengineering Graduate Group and 2The Biosystems Group, Department of Biopharmaceutical Sciences, The

University of California, San Francisco, CA 94143, USA 3Department of Biomedical Engineering, University of Virginia Health Sciences Center, Charlottesville, VA 22908

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A precondition for any Ligand-Ligand interaction to occur is that the two Ligands in question map to an observed biological receptor-ligand pair. A complete set of such receptor-ligand pair rules will be specified during implementation. B. Cell and Membrane

The two types of Cell classes within our model are the ECell and the Leuk. They represent endothelial cells and leukocytes, respectively. The Membrane class can be subdivided into two subclasses, ECellMem and LeukMem. The LeukMem, which represents the leukocyte membrane, is implemented as a 2-D linked list data structure. As shown in Fig. 1-A, the linked list in the first dimension is circular, and all linked lists in the second dimension are of the same length. Each unit in the secondary linked lists corresponds to a section of the leukocyte membrane. When a Leuk object is created, a unique, corresponding LeukMem object will also be created, which involves randomly choosing items from these secondary linked lists. These chosen items represent locations on the membrane where the Ligands on the Leuk object are exposed to the environment. At each chosen section in the LeukMem, there will be AdhesMolecule and ChemokReceptor objects. Each ECell object has an ECellMem to represent the entire luminal surface of the referent membrane. We simplify our model by assuming that this section is rectangular in shape. As shown in Fig 1-B, it is implemented as a 2-D array. Similar to LeukMem objects, unique ECellMem objects are created for every ECell. Units within the array will be uniquely chosen to indicate where the AdhesMolecule objects are exposed to the environment. At each such location there will be an AdhesMolecule object for each adhesion molecule found on endothelial cells in the biological model. In addition, if the ECell has a Chemok object to present to Leuk objects, it will be positioned at one of these specified locations. D. Space

The first Space subclass is the FreeStreamSpace, which represents the central region of a venule where the free blood stream is located. As shown in Fig. 2, it is implemented as a 1-D array, where each unit corresponds to a particular cross-section of the venule. Each unit will contain information about that particular cross-section, such as pointers to Leuk objects within that region, shear rate, and cross-sectional diameter. In addition, each unit will have a parameter that determines the probability that a Leuk object within that unit will move out of the FreeStreamSpace. The MembraneSpace represents the endothelial cell membrane. As shown in Fig. 2, it is a 2-D grid that is circular in one dimension, and contains ECell objects.

III. MODELING BEHAVIORS A. AdhesMolecule-AdhesMolecule Interactions

From the total number, affinity, and avidity parameters of both the Leuk object and ECell object, a probability that an interaction will form can be calculated. Interaction formation will be Monte Carlo determined. The disengagement of interactions between AdhesMolecules will also be determined in a similar manner. B. Rolling

Leuk-ECell interactions can only occur when the Leuk object is on the MembraneSpace near ECell objects. Leuk objects are placed on the MembraneSpace in an orientation that allows the LeukMem to rotate around its axis of rotation and ROLL on the MembraneSpace in the direction of flow. Only a small rectangular region of the LeukMem will be placed on the MembraneSpace. Leuk AdhesMolecule and ECell AdhesMolecule interactions occur only at overlapping regions of the LeukMem and ECellMem where both have been labeled as locations where AdhesMolecules are exposed to the environment. A Leuk ROLLING event consists of a partial rotation of LeukMem around its axis of rotation and in the direction of flow such that a new column of the linked list is placed on top of the MembraneSpace, while an old one is removed. If there is an overlapping region of LeukMem and ECellMem where both regions have been labeled as locations where AdhesMolecules are exposed to the environment, then all Leuk AdhesMolecules will attempt to form interactions with their respective AdhesMolecule LIGANDS on the ECell. A prerequisite for a ROLLING event to occur is that all AdhesMolecule-AdhesMolecule interactions dissociate at the rear column of the linked list that is removed from the MembraneSpace.

Fig. 1. Illustration our representation of the leukocyte membrane (A) and the luminal endothelial cell membrane (B) in our model.

Fig 2. Illustration of the FreeStreamSpace and the MembraneSpace classes in our model.

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If at any time, a Leuk object is on the MembraneSpace, but a sufficient number of AdhesMolecule-AdhesMolecule interactions are not present, then the Leuk will disengage and move back into the FreeStreamSpace. B. Activation and Firm Adhesion

A Leuk object can encounter a Chemok object with its ChemokReceptors when ROLLING on the MembraneSpace. The Chemok object will be removed and all relevant AdhesMolecule objects at nearby regions on the LeukMem will modify their parameters appropriately. When ROLLING, engagement of AdhesMolecule objects with their LIGANDS can also result in SIGNALS (messages) being sent to relevant and nearby AdhesMolecule objects to modify their parameters in an appropriate manner. FIRM ADHESION will only occur when AdhesMolecule-AdhesMolecule interactions have been formed and will not disengage when they are within the very last column of the LeukMem that is on the MembraneSpace.

IV. MODEL SIMULATION A. Rolling

Our initial simulation experiments explore the parameter space for the ADHESION MOLECULES that participate in the process of NEUTROPHIL ROLLING. These will include the parameters representing the selectin, α4 integrin, and β2 (CD18) integrin adhesion molecules. We use data from intravital microscopy experiments [4-5], which observed neutrophil rolling on cremaster muscle venules in mice that lacked different combinations of the selectin and integrin adhesion molecules after treatment of TNF-α. The first simulated experimental condition is based on short term TNF-α treatment [4]: TNF-α is injected intrascrotally 2 h before the beginning of the intravital microscopic experiment. In the in vivo model, the treatment has been shown to induce E-selectin expression and increase the expression of P-selectin [4]. Mice lacking E-selectin (E-/-), P-selectin (P-/-), L-selectin (L-/-), L- and E- selectin (L/E-/-), E- and P- selectin (E/P-/-), and L- and P-selectin (L/P-/-) were generated by bone marrow transplantation. Experimental observations for these mice are summarized in Table I. E, L, and P-selectin deficient mice were generated, but no rolling was observed for these mice. Under short term TNF-α treatment conditions, it has been shown that the β2 integrins play a cooperative role with E-selectin in mediating slow rolling of neutrophils at velocities below 5 µm/s. To refine the parameter space for these adhesion molecules, we use experimental data from [5]. Neutrophil rolling was observed under the same short term TNF-α treatment conditions, but in wild-type mice (WT) and in mutant mice lacking E-selectin (CD62E-/-), β2 integrins (CD18-/-), or β2 integrins and E-selectin (CD18-/-

CD62E-/-). Observations are summarized in Table II.

The second experimental condition that will be simulated uses longer-term treatment with TNF-α: it is injected intrascrotally 6 h before the beginning of the intravital microscopic experiment. Evidence has shown that the roles of L-selectin and α4 integrin in rolling are different in long term TNF-α treatment than in short term treatment [4]. In E- and P-selectin deficient mice, L-selectin and α4 integrin-dependent rolling is induced after long term TNF-α treatment. L-/-, L/E-/-, L/P-/-, E- and P-selectin deficient (E/P-/-), and E-, L-, and P-selectin deficient (E/L/P-/-) mice were generated by bone marrow transplantation. Table III summarizes observations for this experiment. Parameter vectors for the AdhesMolecules will be identified such that ROLLING behaviors in our model are calibrated to the rolling behaviors observed from these in vivo experiments. B. Activation And Firm Adhesion

The third experimental condition being simulated is aimed at refining parameters so that the model adequately represents the steps of activation and firm adhesion. For this we use experimental data from [6], which tracked individual

TABLE III * HEMODYNAMICS AND MICROVASCULATURE PARAMETERS

FOR BONE MARROW-TRANSPLANTED MICE AFTER LONG TERM TREATMENT WITH TNF-α (6 h)

Mouse Avg. Vessel Diameter

(µm)

Wall Shear Rate (s-1)

Rolling Flux Fraction (%)

Avg. Rolling Velocity (µm/s)

L-/- 36.8 ± 1.1 560 ± 20 1.2 ± 0.3 10.7 ± 1.2 L/E-/- 39.5 ± 1.7 660 ± 30 5.0 ± 1.0 15.2 ± 0.9 L/P-/- 42.6 ± 2.2 590 ± 30 0.9 ± 0.3 4.8 ± 0.4 E/P-/- 43.4 ± 2.0 480 ± 40 0.9 ± 0.2 15.7 ± 1.2 E/L/P-/- 45.1 ± 2.1 540 ± 30 0.4 ± 0.06 13.6 ± 1.2 * Reproduced from [4].

TABLE I * HEMODYNAMICS AND MICROVASCULATURE PARAMETERS FOR BONE MARROW-TRANSPLANTED MICE AFTER SHORT

TERM TREATMENT WITH TNF-α (2 h) Mouse Avg. Vessel

Diameter (µm)

Wall Shear Rate (s-1)

Rolling Flux Fraction (%)


L 37.3 ± 1.4 680 ± 30 10.1 ± 1.7 5.0 ± 0.3 E-/- 40.3 ± 1.4 710 ± 30 48.1 ± 5.5 31.1 ± 0.9 P-/- 40.5 ± 1.7 610 ± 20 11.5 ± 2.2 14.8 ± 0.4 L/E-/- 41.6 ± 1.6 720 ± 20 11.3 ± 1.3 5.9 ± 0.3 L/P-/- 49.1 ± 2.1 730 ± 30 1.3 ± 0.2 3.5 ± 0.2 * Reproduced from [4].

TABLE II ** HEMODYNAMICS AND MICROVASCULATURE PARAMETERS FOR MUTANT MICE AFTER SHORT TERM TREATMENT WITH

TNF-α (2 h) Mouse Avg. Vessel

Diameter (µm) Wall Shear Rate (s-1)


WT 47 ± 2 470 ± 30 6.9 ± 0.2 CD62E-/- 37 ± 1 600 ± 40 21.1 ± 0.5 CD18-/- 43 ± 2 460 ± 30 22.7 ± 0.8 CD18-/-, CD62E-/- 51 ± 2 580 ± 50 50.1 ± 1.4 ** Reproduced from [5].

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neutrophils rolling along a TNF-α-treated mouse cremaster muscle venular tree. Reported cumulative distance versus time profiles are shown in Fig. 3. Values for average velocity and average distance rolled before firm adhesion were calculated for CD18-/-, E-/-, and WT mice. Reported values are shown in Table IV.

V. DISCUSSION We have made many assumptions about the biological system that will need to be iteratively revisited during the course of these studies. For example, our initial in silico experiments use one ECell object that spans the entire MembraneSpace and we assume that the distribution of AdhesMolecules is uniform on the ECellMem. The distribution of adhesion molecules on the surface of the endothelial cells has not been fully characterized, but it is known that it is not uniform [7]. In addition, it has been shown that LFA-1 and Mac-1, the two major β2 integrins involved in neutrophil rolling and firm adhesion, have distinct and cooperative roles [8-9]. Our initial experiments use a simplified model that represents all β2 integrins as a single agent. Our future

models will contain separate agents for each of the β2 integrins and their ligands. Finally, the dynamics of leukocyte activation by chemokine detection and by engagement of selectins and integrins with their ligands is not understood. An issue of debate is whether each chemokine detection event or selectin and integrin-ligand engagement event sends global or local activation signals to the integrins [10]. We are testing the latter hypothesis.

VI. CONCLUSION We present a novel, agent-oriented approach to modeling and simulating leukocyte-venule interactions during inflammation. The leukocyte adhesion cascade involves overlapping and intertwined processes [3]. An advantage of this new approach to modeling and simulation is that it is straightforward to systematically represent non-linear systems, which makes it well suited for studying leukocyte-venule interactions. We anticipate that our models will be able to progressively integrate and organize the knowledge that has amassed on this system, thereby helping us to understand how such a system functions under normal, stressed, and diseased conditions. Furthermore, we anticipate that these new models can provide an in silico environment to help inspire and test novel cellular engineering approaches for creating therapeutics.

REFERENCES [1] A. Tözeren and K. Ley, “How do selectins mediate leukocyte

rolling in venules?,” Biophys J., vol. 63, no. 3, pp. 700-709, Sep. 1992.

[2] R. Alon and S. Fiegelson, “From rolling to arrest on blood vessels: leukocyte tap dancing on endothelial integrin ligands and chemokines at sub-second contacts,” Semin Immunol., vol. 14, no. 2, pp. 93-104, Apr. 2002.

[3] K. Ley, “Integration of inflammatory signals by rolling neutrophils,” Immunol Rev., vol 186, pp. 8-18, Aug. 2002.

[4] U. Jung and K. Ley, “Mice lacking two or all three selectins demonstrate overlapping and distinct functions for each selectin,” J Immunol., vol. 162, no. 11, pp. 6755-6762, Jun. 1999.

[5] S. B. Forlow., et al., “Severe inflammatory defect and reduced viability in CD18 and E-selectin double-mutant mice,” J Clin Invest, vol. 106, no. 12, pp. 1457-1466. Dec. 2000.

[6] E. Kunkel, J. L. Dunne, and K. Ley, “Leukocyte Arrest During Cytokine-Dependent Inflammation in vivo,” J Immunol, vol. 164, no. 6, pp. 3301-3308, Mar. 2000.

[7] E. R. Damiano, et al., “Variation in the velocity, deformation, and adhesion energy density of leukocytes rolling within venules,” Circ Res., vol. 79, no. 6, pp. 1122-1130, Dec. 1996.

[8] J. L. Dunne, et al., “Control of leukocyte rolling velocity in TNF-α-induced inflammation by LFA-1 and Mac-1,” J Immunol, vol. 99, no. 1, pp. 336-341, Jan. 2002.

[9] J. Dunne, et al., “Mac-1, but not LFA-1, uses Intercellular Adhesion Molecule-1 to mediate slow rolling in TNF-α-induced inflammation,” J Immunol, vol. 171, no. 11, pp. 6105-61111. Dec. 2003.

[10] R. Alon, V. Grabovsky, and S. Feigelson, “Chemokine induction of integrin adhesiveness on rolling and arrested leukocytes local signaling events or global stepwise activation?” Microcirculation, vol. 10, no. 3-4, pp. 297-311. Jun. 2003.

Fig 3. Distance-time curves for typical rolling leukocytes. Typical distance-time tracings for individual leukocytes from WT (open circles), CD18-/- (dark circles), and E-/- (triangles) mice. Leukocyte outcome is indicated by arrows: up (detach), down (attach). Reproduced from [6].

TABLE IV * AVERAGE TIME ROLLED, DISTANCE ROLLED,

AND AVERAGE ROLLING VELOCITY Mouse

Genotype Outcome Time

Rolled (s) Distance

Rolled (µm) Avg. Rolling

Velocity (µm/s) WT Adhere 86 ± 18 560 ± 20 10.7 ± 1.2 WT Detach 140 ± 29 660 ± 30 15.2 ± 0.9 CD18-/- Adhere --- --- --- CD18-/- Detach 12 ± 2 270 ± 26 32 ± 7 E -/- Adhere 40 ± 14 280 ± 49 14 ± 2 E-/- Detach 41 ± 3 350 ± 110 11 ± 2

* Reproduced from [6].

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In Silico Representation of the Liver -- Connecting Function to Anatomy,Physiology and Heterogeneous Microenvironments

Li Yan1, C. Anthony Hunt1,2, Glen E.P. Ropella2, and Michael S. Roberts3

1 Joint UCSF/UC Berkeley Bioengineering Graduate Program2 Dept. of Biopharmaceutical Sciences, Biosystems Group, University of California, San Francisco, CA, USA

3 Department of Medicine, University of Queensland, Princess Alexandra Hospital, Woolloongabba, Q 4102 Australia

Abstract—We have built a collection of flexible, hepato-mimetic, in silico components. Some are agent-based. Weassemble them into devices that mimic aspects of anatomicstructures and the behaviors of hepatic lobules (the primaryfunctional unit of the liver) along with aspects of liver function.We validate against outflow profiles for sucrose administeredas a bolus to isolated, perfused rat livers (IPRLs). Acceptablein silico profiles are experimentally indistinguishable fromthose of the in situ referent based on Similarity Measure values.The behavior of these devices is expected to cover expandingportions of the behavior space of real livers and theircomponents. These in silico livers will provide powerful toolsfor understanding how the liver functions in normal anddiseased states, at multiple levels of organization.

Keywords— Drug metabolism, in silico, agent-based,modeling and simulation, computational biology, hepatic.

I. INTRODUCTION

The liver is primarily responsible for the conversion ofxenobiotics and endogenous compounds into more water-soluble, excretable forms. Liver disease alters the hepaticmicrocirculation and can impair the disposition kinetics ofmany drugs. Liver disease also complicates pharmacologi-cal treatments of other diseases, as well as itself, and caninfluence pharmacotherapeutic decisions. Modeling andsimulation helps scientists and medical decision makers pre-dict the likely consequences of various options, and therebymake better decisions. Multiple, different traditional modelshave been developed and validated ([1] and referencestherein). They include well-stirred compartments, the singletube, convection-dispersion, and interconnected tube model.Those models work well in accounting for the specific dataand system conditions to which they are applied. However,they also have limitations, and among them are the following.Because the models are data-centric, considerable knowledgeabout hepatic structure and function are mostly ignored.Model components do not map well to specific biologicalcomponents. In addition, their boundary conditions andparameterizations are restricted to one level of organization.Therefore, it is hard to reuse a model developed for one set ofexperimental conditions (or for one drug) under new circum-stances (or for a different drug). Also, related models on thesame system are hard to plug together.

When we discover something important about thetransport and metabolism of a new set of drugs and wish to

make intelligent decisions based on the likely clinicalimplications, we will need an already existing, validatedmodel into which we can seamlessly import the new data inorder to address the what-if questions of interest. No suchmodels exist. Clearly, new ideas and new approaches areneeded. From what direction should new modeling andsimulations methods approach the biology: from the bottom-up or the top-down? Noble makes the case for a “middle-out” approach that focuses on the “functional level betweengenes and higher level function” [2]. We used such amiddle-out approach in developing the silico liver describedhere. We use data drawn from multiple sources, includingtime series data from perfused liver studies. We focus moreon aspects of the structures and behaviors that give rise tothe data. We test and affirmed the hypothesis that perfusedliver outflow data, in conjunction with other data, can beused to specify and parameterize a novel, physiologicallyrecognizable hepato-mimetic device. Furthermore, thatdevice can generate outflow profiles that are experimentallyindistinguishable from the original in situ data.

II. MODEL DESIGN

A. Histological and Physiological Considerations

The in situ liver perfusion protocol is detailed in [3]. Acompound of interest is injected into the entering perfusate ofthe isolated liver. For each drug outflow profile there is acorresponding sucrose profile and it is the latter that we focuson first [1, 4]. Such profile pairing allows us to use a two-stepfeature extraction procedure for building hepato-mimeticdevices: first, from the sucrose data extract information torepresent the extracellular environment. That process leads tounique parameterizations for 1) vascular and sinusoidalgraphs, 2) the arrangement and attributes of the sinusoids, and3) the extracellular topography within sinusoids. We thenexpand that representation with essential intracellular detailsto account for the outflow data of different drugs.

The lobule is the primary structural and functional unitof the rat liver. Hepatic intralobular heterogeneity is welldocumented [5]. No two lobules are identical. Sinusoidsseparate meshworks of one cell-thick plates made up ofhepatocytes that perform the major metabolic functions ofthe liver. Hepatocytes exhibit location-specific propertieswithin lobules, including location-dependent expression ofdrug metabolizing enzymes [6]. Sinusoids experience

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different flows and have different surface to volume ratioswithin different zones. In addition to hepatocytes, lobulescontain several specialized cell types. Endothelial cells linesinusoids that contain Kuppfer, stellate, and other cell types.

B. In Silico Components: Directed Graphs

A trace of flow within one lobule sketches a networkthat can be represented by an interconnected, directed graph.Such graphs are the core architectural feature of our lobule-mimetic devices (hereafter, LOBULE

1). Teutsch et al. [7]subdivide the lobule interior into concentric zones. Fornow, we impose a three-zone structure on the graph (I, IIand III in Fig. 1) and require that each zone contain at leastone node and that a shortest path from portal vein tract (PV)to central vein (CV) will pass through at least one node andno more than one node per zone. The insert in Fig. 1illustrates a portion of a graph network that connects insilico PV outlets through nodes in Zones I and II and thenthrough one Zone III node to the CV. Graph structure isspecified by the number of nodes in each Zone and thenumber of edges connecting those nodes. Edges are furtheridentified as forming either inter-zone or intra-zoneconnections. Edges specify “flow paths” that have zerolength and contain no objects. A solute object exiting aparent node is randomly assigned to one of the availableoutgoing graph edges and appears immediately as input forthe SS located downstream at the child node. Randomlyassigned intra-zone connections are allowed but areconfined to Zones I and II. Nodes are randomly assigned toeach zone so that the number of nodes in each zone isapproximately proportional to the fraction of the total lobulevolume found in that zone.

C. In Silico Components: Sinusoidal Segments

Agents called sinusoidal segments (SSs) (Fig. 2) areplaced at each graph node. There is one PV entrance(effectively covering the exterior of the LOBULE) and one

1 The same word may be used to refer to a biological molecule, component,or event and the in silico object or event that represents them. In the lattercase the word is written using small caps.

CV exit for each ISL. A solute object is a passiverepresentation of a chemical as it moves through the in silicoenvironment. The PV creates solute objects, as dictated bythe experimental dosage function, and distributes them tothe SSs in Zone I.

Movement of solutes from place to place within a lobule canbe modeled as message passing. A solute object movingthrough the LOBULE represents molecules moving throughthe sinusoids of the lobule, and their behavior is dictated byrules specifying the relationships between SOLUTE location,proximity to other objects and agents, and the solute'sphysicochemical properties. Each S O L U T E has doseparameters (mass, constituents, timing, and catheter effects[1]) and a scale parameter (molecules per solute object).The relative tendency of a SOLUTE to move forward within aSS determines the effective flow pressure and this isgoverned by a parameter called Turbo. If there is no flowpressure (Turbo = 0), then solute movement is specified by asimple random walk. Increasing Turbo biases the randomwalk in the direction of the CV.

Viewed from the center of perfusate flow out in Fig. 2,a SS is modeled as a tube with a rim surrounded by otherlayers. The tube and rim are the sinusoidal space and itsimmediate borders. The tube contains a fine-grainedabstract Core space that represents blood flow. Grid A isthe Rim. Grid B is wrapped around Grid A and representsthe endothelial layer. Another fine-grained space (Grid C)is wrapped around Grid B to collectively represent the Spaceof Disse, hepatocytes, and bile canaliculi. If needed,hepatocytes and connected features such as bile canaliculican be moved to a fourth grid wrapped around Grid C. Theproperties of locations within each grid can be homogeneousor heterogeneous depending on the specific requirementsand the experimental data being considered.

Objects can be assigned to one or more grid points. Forexample, a subset of Grid B points can represent one ormore Kupffer cells. Another subset can map to intracellulargaps and fenestrae for particulate sieving into the Space ofDisse. KUPFFER CELL activity can be added to the list of GridB objects, as they are needed. Objects that move from alocation on a particular grid location are subject to one or

Fig. 2. Schematic of a sinusoidal segment (SS). Two types of SS arediscussed in the text. One SS is placed at each node of the directed graph.

Fig. 1. A schematic of an idealized cross-section of a hepatic lobuleshowing half an acinus and the direction of flow between the terminalportal vein tract (PV), and the central hepatic vein (CV). SS: SinusoidalSegment. The insert is an illustration of a LOBULE and corresponds to aportion of an acinus and a small fraction of a lobule.

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more lists of rules that are called into play at the next step.Within Grid B a parameter controls the size and

prevalence of FENESTRATIONS and currently 10% of Grid Bin each SS is randomly assigned to FENESTRAE; the remaining90% represents cells. Similarly, within the grid where somelocations map to hepatocytes, there is a parameter thatcontrols their relative density.

D. Classes of Sinusoidal Segments (SS)

To further enable accounting for sinusoidal heterogene-ity, including differences in transit time and flow [8], topog-raphic arrangement [9], and the different surface to volumeratios within three zones [5], we defined different classes ofSINUSOID, direct SINUSOID (DirSin) and tortuous SINUSOID

(TortSin). Additional SS classes can be specified and usedwhen needed. Relative to TortSins, the DirSins have a shorterpath length and a smaller surface-to-volume ratio, whereas theTortSins have a longer path length and a larger surface-to-volume ratio. The circumference of each SS is specified by arandom draw from a bounded uniform distribution. To reflectthe observed relative range of real sinusoid path lengths, SSlength is given by a random draw from a gamma distributionhaving a mean and variance specified by the three gammafunction parameters, a, b, and g.

E. Dynamics of Solutes within Sinusoidal Segments

Solute objects can enter a SS at either the Core or theRim. At each step thereafter until it is metabolized orcollected it has several options, most are stochastic. In theRim or Core it can move within that space, jump from onespace to the other, or exit the SS. From a Rim location itcan also jump to Grid B or back to the Core. Within Grid Bit can move within the space, jump back to Grid A or toGrid C. When it encounters an ENDOTHELIAL CELL withinGrid B it may (depending on its properties) partition into it.Once inside, it can move about, exit, bind or not. WithinGrid C it can move within the space or jump back to Grid B.When a HEPATOCYTE is encountered the solute can (depend-ing on its properties) partition into it or move on. Onceinside a HEPATOCYTE it can move about, exit, bind (andpossibly get METABOLIZED) or not. Currently all objectswithin a HEPATOCYTE that bind can also METABOLIZE. Theprobability of a solute object being METABOLIZED depends onthe object’s properties. Once METABOLIZED the object isdestroyed. The only other way to exit a SS is from the Core,Rim or into BILE (not implemented here). When the objectexits a SS and enters the CV, its arrival is recorded (corre-sponding to being collected), and it is destroyed.

III. SIMILARITY MEASURE

Replicate in situ experiments conducted on the sameliver provide similar but not identical solute outflowprofiles. The same is true for experiments on LOBULES.

There are two main contributors to intraindividualvariability: methodological and biological. For replicateexperiments in the same liver the coefficient of variation forfractional solute outflow within specific collection intervalstypically ranges between 10 and 40%. A coefficient ofvariation can define a continuous interval bracketing theexperimental data. A new set of results that falls within thatbracketed range and has essentially the same shape isdefined as being experimentally indistinguishable. Thesame should hold even if the data comes from an in silicoexperiment. There would be no way to determine whether adata set came from an in situ or an in silico experiment.This last observation provides the basis for designing andevaluating a Similarity Measure (SM).

The objective of the SM is to help select among variousmodels of the liver, not simply to assume a model and selectamong variations on that model. Hence, the successful SMtargets the various features of the outflow profile thatcorrelate with the generative structures and building blocksinside the model. Neither an instantaneous, per observation,comparison, nor a whole-curve comparison is ideal becausethe different regions of repeated outflow profiles clearlyshow different variances. For these reasons, a multipleobservation SM seems most warranted. However, forsimplicity in these early stage studies we have assumed thatthe coefficients of variation of repeat observations withindifferent regions of the curve are the same. In that way wecan use a simple interval SM. A set of in situ outflowprofiles, which are generated from different subjectsfollowing the same protocol, is used as training data.Calculate the mean of each time point and use this set ofmeans as reference profile (Pr). For each observation in Pr,create a lower, Pl, and an upper, Pu, bound by multiplyingthat observation by (1 – D) and (1 + D), respectively. Thetwo curves Pl and Pu are the lower and upper bounds of aband around Pr. The two outflow profiles are deemedsimilar if the second profile, P, stays within the band. Thedistance D used for sucrose is one standard deviation of thearray of relative differences between each repeat observationand the mean observations at that time.

IV. IN SILICO EXPERIMENTAL RESULTS

In a normal liver each lobule is functionally similar.Consequently, a model representing the liver using oneaverage lobule or even a portion thereof may be adequate toaccount for a specific drug outflow profile. For the firstoutflow profile we find the simplest LOBULE design, givenrestrictions: one that is comprised of the minimumcomponents needed to generate an acceptably similarprofile. An initial unrefined parameterization is chosenbased on available hepatic physical and anatomicinformation. Components are added according to that initialparameterization. If the behavior of the resulting LOBULE isnot satisfactory, any given piece of the LOBULE may be

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discarded and replaced, or modified or reparameterized withminimal impact on the other components within the device.This process continues until the LOBULE generates outflowprofiles that are experimentally indistinguishable: afteraveraging several runs, the result falls between Pl and P u.Once that parameterization is found, the parameter space issearched further [10, 11] for additional, possibly better-performing, solution sets2.

The typical in situ IPRL outflow profile is an account ofapproximately 1015 drug molecules percolating through sev-eral thousand lobules. The typical in silico dose for one runwith one LOBULE is on the order of 5,000 drug objects,where each drug object can represent a number (≥ 1) of drugmolecules. Thus, a single outflow profile will be very noisyand will be inadequate to represent the referent in situ pro-file. In the latter part of such an outflow profile it isincreasingly possible to encounter a collection intervalduring which no drug objects are collected. Another inde-pendent run using that same LOBULE, parameter settings,and DOSE will produce a similar but uniquely different out-flow profile. Changing the random number generator seedalters the specifics for all stochastic parameters (e.g., place-ment of SSs on the digraph), thus providing a unique, indi-vidual version of the LOBULE, analogous to the uniquedifferences between two lobules in the same liver. One insilico experiment combines the results from 20 or moreindependent runs using the same LOBULE thereby producingan outflow profile that is sufficiently smooth to use the SM.It takes one or more experiments to represent an outflowprofile for an in silico liver. Note that an experimentalresult comprising 20 runs of the LOBULE is analogous toresults one might obtain if one could conduct an in situperfusion experiment on only 4-to-5 liver lobules.

Fig. 3 shows results from one parameterization of aLOBULE against an IPRL sucrose outflow profile. Theshaded region is a band enclosing the mean fraction of dosecollected for each collection interval. The width of the bandis ± 1 std about the mean. The filled circles are resultsobtained using a LOBULE parameter vector that provides anacceptable solution set according to the SM.

V. CONCLUSION AND DISCUSSION

We have tested and affirmed the hypothesis that IPRLoutflow data obtained following bolus administration ofsucrose can, in conjunction with other data, be used tospecify and parameterize a physiologically recognizablehepato-mimetic device, an in silico liver. Furthermore, thatdevice can generate outflow profiles that are experimentallyindistinguishable from the original in situ data. This newtechnology is intended to provide powerful tools foroptimizing the designs of real experiments and for

2 Solution set is the combination of the inputs and parameters that result inthe biomimetic behavior, plus the actual device that is biomimetic.

challenging our understanding for how mammalian systems,such as the liver, function in normal and diseased states,when stressed, or when confronted with interventions.These biomimetic devices are expected to evolve to becomesuitable experiment platform to test hypothesis.

REFERENCES

[1] Roberts MS, and Anissimov YG., “Modeling of HepaticElimination and Organ Distribution Kinetics with the ExtendedConvection-Dispersion Model, ”J Pharmacokin. Biopharm.,vol. 27, no. 4, pp. 343-382, 1999.

[2] Noble D, “The Future: Putting Humpty-Dumpty Together Again,”Biochem. Soc. Transact., vol.31, no.1, pp.156-158, 2003.

[3] Cheung K, Hickman PE, Potter JM, et al. “An Optimized Model forRat Liver Perfusion Studies,” J. Sur. Resh., vol.66, pp. 81–89, 1996.

[4] Hung, D.Y., Chang, P., Weiss, M., Roberts, M.S.: Structure-Hepatic Disposition Relationships for Cationic Drugs in IsolatedPerfused Rat Livers: Transmembrane Exchange andCytoplasmic Binding Process. J. Pharmacol. Exper. Therap.vol.297, pp. 780–89 2001.

[5] Gumucio, J.J., and Miller, D.L., “Zonal Hepatic Function:Solute-Hepatocyte Interactions Within the Liver Acinus,” Prog.Liver Diseases, vol. 7, pp. 17-30, 1982.

[6] Roberts, M.S., Magnusson, B.M., Burczynski, F.J., and Weiss, M.,“Enterohepatic Circulation: Physio-logical, Pharmacokinetic andClinical Implications,” Pharmacokinet, vol.41, pp. 751-790, 2002.

[7] Teutsch, H.F., Schuerfeld, D., and Groezinger, E., “Three-Dimensional Reconstruction of Parenchymal Units in the Liverof the Rat,” Hepatology, vol. 29, pp. 494-505, 1999.

[8] Koo, A., Liang, I.Y., and Cheng, K.K., “The Terminal HepaticMicrocirculation in the Rat,” Quart. J. Exp. Physiol. Cogn. Med., vol. 60, pp. 261-266, 1975.

[9] Miller, D.L., Zanolli, C.S., and Gumucio, J.J., “QuantitativeMorphology of the Sinusoids of the Hepatic Acinus,”Gastroenterology, vol. 76, pp. 965-969, 1979.

[10] Sanchez, S.M., and Lucas, T.W., “Exploring the World ofAgent-Based Simulations: Simple Models, Complex Analyses,”in Proceedings of the 2002 Winter Simulation Conference,Yücesan, E., Chen, C.-H., Snowdon, J.L., and Charnes, C.M.,Ed. 2002, pp. 116-126.

[11] Kleijnen, J.P.C., “Experimental Design for Sensitivity Analysis,Optimization, and Validation of Simulation Models,” SeriesDiscussion Paper No. 1, Research Papers in Economics, Centerfor Economic Research, Tilburg University, 2003.Available: http://econpapers.hhs.se/paper/dgrkubcen/199752.htm

Fig. 3. An outflow profile for an HMD parameterized to match asucrose outflow profile. Nodes per Zone: 55, 24 and 3 for Zones I, IIand III, respectively; total edges: 60; intra-zone connections: Zone I =10, Zone II = 8, Zone III = 0; inter-zone connections: IÆII = 14, IÆIII= 4, IIÆIII = 14; SSs: 50% SA and SB; Number of runs = 100

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Abstract—A prototype Epithelio-Mimetic Device (EMD) was developed and tested. EMD components are designed to map logically to biological components at multiple levels of resolution. Those components are engineered to represent actual components within an in vitro cellular system used to study intestinal drug transport. Our goal is that the behaviors of the EMD closely match observed behaviors of the in vitro systems for a wide variety of drugs. Early stage system verification is achieved. The general patterns of experimental results from the EMD for a set of hypothetical drugs having a variety of physicochemical properties reasonably match observed patterns for a wide range of experimental conditions.

Keywords—Agents, computational biology, drug

transport, modeling, simulation

I. INTRODUCTION

Emerging, advanced computational methods [1] are expected to provide drug development and basic biomedical researchers with improved abilities to make useful predictions and to better understand how the small intestine, and other barriers to drug absorption, function in the presence and absence of various stresses, including disease, at multiple levels of organization. The envisioned methods will improve R&D efficiency. Here we present such a method. It is based on a completely new technology that is comprised in part of new tools for simulating complex biological processes, and a completely new class of biological analogue models that we refer to as biomimetic in silico devices (BISDs). The in silico components of these devices are designed specifically to be assembled into BIDS that represent behaviors of in vitro cellular systems or the intact intestine in vivo. Our approach consists of methods for developing, testing, and refining BISDs, as well as means for early stage system verification and evaluation. Early stage system verification is intended to verify that the BISD and its components perform as anticipated, to characterize their available modes of operation and their performances, and to become suitable objects for scientific experimentation, analogous to in vitro systems that they mimic. The devices are designed to generate behaviors and are constructed from software components that are specifically designed to map logically to biological components at multiple levels of resolution. The objective of this study has been to systematically collect evidence to support the feasibility of a prototype device designed to provide in silico experimental results for known and new compounds that, in time, will be experimentally indistinguishable from results from the current high through-put in vitro cellular systems, such as the industry

standard, the Caco-2 cell line in use for studying intestinal drug absorption and metabolism.

Representing Intestinal Drug Transport In Silico: An Agent-Oriented Approach

Yu Liu1, C. Anthony Hunt1, 2 1UCSF/UCB Joint Graduate Group in Bioengineering, University of California, Berkeley, CA, USA

2Biosystems Group, Department of Biopharmaceutical Sciences, University of California, San Francisco, CA, USA

II. METHODOLOGY

A. The In Vitro Membrane System

The class of BISDs described here is intended to mimic Caco-2 in vitro cell culture system that, in turn, is a biological model taken to represent the mature epithelia lining the villi of the small intestine (Fig. 1). Caco-2 cells are typically grown to confluence (e.g., 21 days) on the microporous membrane insert of the Transwell diffusion cell system, and are then used in drug transport studies (Fig. 2a). The Transwell insert is taken to represent the apical lumen compartment of the small intestine, and the cell culture well (into which the insert fits) represents the basolateral side of the intestine. The structure of our prototype epithelio-mimetic device (EMD), diagrammed in Fig. 2b and discussed more below, mimics the essential features of the Transwell system.

Fig. 1. Small intestine villi structure. The mature epithelia lining the villi are the active absorptive area. The enlargement shows the four processes involved in drug intestinal absorption: 1a: Passive transcellular diffusion; 1b: Passive paracellular diffusion; 1c: Transporter mediated active transcellular transport; and 1d: Transcytosis.

Fig 2. In vitro and in silico experimental devices for the study of intestinal drug transport. (a). Caco-2 in vitro Transwell system. (b). Our prototype epithelio-mimetic device (EMD).

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B. A Constructive Approach to Modeling Our approach to modeling includes some new and

novel features. We use a constructive approach that focuses more on the aspects of biological system structure and behavior that give rise to data. We conceptually deconstruct the system into biologically recognizable components and processes that can be represented as software objects, agents, messages, and events. Next, we reconstruct using these objects within a software medium that handles probabilistic events and message passing, and can represent dynamic spatial heterogeneity. The process makes in silico devices capable of biomimetic behaviors. We use device (rather than model) to stress their modular, constructive nature, to emphasize the essential and desired properties described next, and to distinguish them from traditional equation-based (TEB) models. BISDs are not intended as substitutes or replacements for TEB models. They do not do the same things. We expect that they will dramatically expand the repertoire of modeling and simulation options available to researchers.

C. Essential and Desired Properties

Reaching our goals requires stipulating in advance several essential and desired properties that we believe EMDs need to have. Key among them is the following: EMDs and their components must be reusable, revisable, and easily updateable without having to re-engineer the whole device. Drug interactions with tissue and cell components are characterized by probabilistic events. So, our EMDs are exclusively event driven and most events can be probabilistic. They need to be flexible and adaptable to be useful in a variety of contexts for addressing a broad range of research questions and capable of exhibiting a broad range of behaviors. They should function at multiple levels of resolution, from subcellular to organ. EMD components must logically map to their biological counterparts. A goal is for EMDs to have more in common with in vitro and some ex vivo laboratory models, such as tissue cultures and perfused tissues, than they do with TEB models. So, evolvability is also essential. Spatial heterogeneity is a quintessential characteristic of the intestine at each organizational level. So, it is essential that device components be capable of representing dynamic spatial heterogeneity at different levels of resolution as required by the problem.

D. Epithelio-Mimetic Devices: Design and Function

Our methods depend upon Object-Oriented (software) Design. Objects are instances of classes with both state and behavior. Some objects can be agents. Agents are objects that have the ability to add, remove, and modify events. Philosophically, they are objects that have their own motivation and agenda; they can initiate causal chains, as opposed to just participating in a sequence of events something else initiated. An EMD is an agent whose purpose is to mimic aspects of the behavior in vitro Transwell cell culture devices. Agents can contain spaces, objects and other agents. When representing a biological

system one might use agents to represent a tissue, cells within that tissue, and components within cells, such as macromolecules or networks of molecules.

An EMD has a minimum of five parallel spaces, G1 – G5, as illustrated in Fig. 2b. Components are not introduced into a device unless it is required to solve the current problem or account for current or past data. Each space is currently represented as a N×N 2D grid. G1 represents the apical lumen compartment and the fluid in the Transwell cell culture insert. G2 represents the apical cell membrane and junctions between cells (viewed from the apical side). G4 represents basolateral membrane and junctions between cells (viewed from the basolateral side). G3 represents everything that is intracellular. G5 represents the basolateral compartment and the fluid in the cell culture well. Solutes and drug molecules are represented by mobile objects that can move within and between spaces. Each mobile object is identified by type and has its own identity. In this study each object type represents a specific drug. Each MOLECULE1 type has its own list of properties (applied to each object of that type). In this study the properties list includes three physicochemical properties: MW, pKa, and P (partition coefficient). The list can be reduced or extended to include any number of properties.

The movement of an object is subject to the set of rules2 and those rules can be adjusted based on properties of objects and space they are in. Within each space movement is governed by a simulated diffusion algorithm. Between different spaces, the movement is governed by probabilistic transition rules.

E. Early Stage EMD Verification

Our goal is that when a drug object representing a specific drug such as Alfentanil is placed in G1 its in silico permeability in the EMD will be experimentally indistinguishable from its permeability measured in vitro in a particular experimental system. To accomplish this the grid point properties and the within and between space transition probabilities and rules need to be specified and calibrated so that the behavior of the EMD reasonably matches the accumulated literature evidence. That process requires an iterative sequence of adjustments, experiments, and comparisons. Early stage system verification is achieved when the general patterns of experimental results from the newly constructed EMD for numerous in silico drug objects reasonably match observed patterns for a wide range of actual drugs that cover a wide range of the physicochemical properties of interest.

F. Representing Permeation

When DRUG i is placed in G1 an apparent permeability coefficient can be calculated from the appearance of DRUG in G5 according to PEMD,i =(dQi/ds)/a•c0, where PEMD,i is the 1 The same word may be used to refer to a molecule or event in, or component of, the referent system and the corresponding in silico object or event. In the latter case the word is written using small caps. 2 The rules can be simple or complicate; they may include an equation or depend on the outcome of running a separate model.

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apparent permeability of DRUG i measured in silico, dQi/ds is the incremental change in the number of drug objects in G5 following simulation (time) step ds, a is the area of G2/G4, and c0 is the initial “concentration” of DRUG i in G1 at time step 0. The various parameters and rules of the model, including the transition probabilities, are adjusted over a range of experimental conditions so that for several different DRUGS PEMD ~ {the apparent permeability coefficients measured in vitro} [2]. The in silico studies documented the influence of three interrelated physicochemical properties (lipophilicity, ionization, and molecular size [3]) on DRUG permeability, as well as concentration gradient on the permeation rate. We assume that small (≤ 200 Dalton) water-soluble DRUGS having P (partition coefficient) values less than 2 [4] pass through cell monolayers only by passive paracellular diffusion through aqueous pores. We also assume that transmembrane movement of the unionized fraction (calculated by environmental pH and the DRUG’S pKa) of drug increases with increasing logP (increasing lipophilicity) values up to 2.5~3.5 and declines thereafter [5, 6]. MW is used as the simplified molecular size descriptor and is related to the in silico DIFFUSION COEFFICIENT (DEMD,i): DEMD,i ∝ 1/(MWi)n). In these studies we assume n = 1 in lipoid membrane and 0.6 in aqueous fluid.

III. RESULTS

The following experiments and their results show the general relative patterns for results of experiments conducted using the prototype EMD and numerous DRUGS over the full range of EMD operation and over the full range of the three physicochemical properties of interest. The passive paracellular and transcellular transport of the prototype EMD were evaluated over a wide initial concentration range for two hypothetical drugs, both weak bases with pKa = 6.5. One (DRUG I) is hydrophilic (logP = 0.2) with MW = 150. The other (DRUG II) is a hydrophobic drug (logP = 2) with MW = 500. The in silico pH of G1 and G3 was fixed at 7.4. EMD concentration-time profiles were recorded and the initial rate of DRUG permeation was calculated under sink condition (≤ 10% initial DRUG in G1 is transported into G5). Results are presented in Fig. 3. Higher initial concentrations resulted in larger rates of permeation for both hydrophilic and hydrophobic DRUGS, as expected. Transcellular transport had a higher permeation rate than paracellular transport due to the smaller surface area in paracellular pathway (< 1000 fold) [7].

The rate of intestinal absorption is known to be positively correlated with partition coefficient [8]. Membrane permeability as a function of lipophilicity can exhibit different patterns: linear, hyperbolic, sigmoid and bilinear [3]. A set of sigmoidal relationships result from the additional influence of MW [3, 5]. The EMD was initialized to generate experimental results that reflect those

Fig. 3. Rate of permeation across an in silico EPITHELIA from experiments using the prototype EMD at 12 different initial numbers of DRUGS (representing initial concentration). characteristics. To examine the consequences, the passive permeability of five sets of DRUGS (MW values of 100, 150, 300, 500, and 700) was calculated from EMD experimental results with logP values ranging from very hydrophilic (logP = – 2) to very hydrophobic (logP = 4). For DRUGS with logP < 3.5, a set of sigmoidal curves is observed (Fig. 4). For larger DRUGS, the curves are shifted to lower permeabilities. Four patterns are observed, consistent with the cited literature. DRUGS with small logP values are too hydrophilic to significantly cross cell membranes, so the passive paracellular pathway dominates for the two sets with MW ≤ 150. For more hydrophobic DRUGS paracellular transport is negligible and transcellular permeability is strongly dependent on lipophilicity. For those drugs with 2.5 ≤ logP ≤ 3.5, the expected permeability plateaus are reached. For more hydrophobic DRUGS, permeability decreases with increasing lipophilicity.

Each portion of the human gastrointestinal tract typically has a different pH. In the major absorptive part of small intestine duodenum, pH 6.0 - 6.5 favoring absorption of weak base drugs. We obtained results from EMD experiments for one weak base DRUG Alfentanil with properties (Table I) specified. We changed pH in G1(corresponding to a large variation in the degree of ionization for Alfentanil) and used Monte Carlo simulation for 8 experiments per pH value. Results are shown in Fig. 5. The rescaled permeability obtained in our EMD is in the range of 81.9 to 101.8 × 10-6 cm/sec when the G1 properties correspond to pH 8.0 and the patterns observed are consistent with expectations [9].

IV. DISCUSSION

These results verify that for the conditions tested, the prototype EMD exhibits patterns of drug permeability behavior that are similar to those reported for in vitro

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Fig. 4. Influence of logP and MW on DRUG permeability (logPapp) from experiments using the prototype EMD.

TABLE I PHYSICOCHEMICAL PROPORTIES OF DRUG ALFENTANIL

MW logP a pKa a Papp(10-6cm/sec) b Basic drug Alfentanil 416 2.16 6.5 93.5 a Data from [9]. There is slight difference from those obtained in Chemical Abstract Database, where Alfentanil’s pKa is 7.59, and logP is 2.033. b In Ref [9], 1.2 mM Alfentanil transported across Caco-2 cell monolayers at pH 8.0 at a low stirring rate of 100 rpm. experiments. Additional experiments are underway to further verify that the EMD can generate experimental results that are experimentally indistinguishable from in vitro results for a variety of compounds. These verification studies have focused on passive transport through paracellular and transcellular pathways, the routes for a majority of drugs. However, in the intestine active transport and biotransformation of many important drugs do occur. These processes are part of the body’s robust defense system against potentially harmful xenobiotics. P-glycoprotein, present on apical epithelial membranes, actively transports

Fig 5. In silico pH-dependent transport of a DRUG Alfentanil within the EMD. (a) Simulated permeability has a linear relationship with fraction of un-ionized DRUG. (b) EMD permeability as a function of G1 pH.

xenobiotics out of epithelial cells back into the lumen where they can be degraded by bacteria. CYP3A4, the dominant isoform of cytochrome P450 in epithelial cells, plays an important role in the first pass effect for many drugs. Our EMD is designed to easily add (and remove) components (agents, objects and spaces) that can map to transporters and enzymes to enable such an upgraded EMD to account for an increasing fraction of observed drug transport properties. Subsequently, guided by appropriate data, additional components can be designed and added to account for localized heterogeneous system properties including intracellular transport systems and gene up- and down-regulation.

ACKNOWLEDGMENT We thank Cindy (Song) Chen for helpful software

engineering discussions and the other members of Biosystems Group for their helpful discussions, assistance, and support.

REFERENCES

[1] H. Kitano, “Systems biology: a brief overview.” Science vol.

295, pp. 1662-1664, 2002. [2] P. Artursson and J. Karlsson, “Correlation between oral drug

absorption in humans and apparent drug permeability coefficients in human intestinal epithelia (CACO-2) cells.” Biochem. & Biophy. Res. Comm. vol. 175, no. 3, pp. 880-885, 1991.

[3] G. Camenisch, G. Folkers, H. Waterbeemd, “Reviews of theoretical passive drug absorption models: historical background, recent developments and limitations.” Pharmaceutica Acta Helvetiae, vol. 71, pp. 309-327, 1996.

[4] H. Kalant, and W. H. E. Roschlau, Principles of Medical Pharmacology, Oxford University Press, 1998.

[5] G. Camenisch, J. Alsenz, H. Waterbeemd, G. Folkers, “Estimation of permeability by passive diffusion through Caco-2 cell monolayers using the drugs’ lipophilicity and molecular weight.” Euro. J. Pharma Sci. vol. 6, pp. 313-319, 1998.

[6] P. Wils, A. Warnery, V. Phung-Ba, S. Legrain and D. Scherman, “High lipophilicity decreases drug transport across intestinal epithelia cells.” JPET, vol. 269, no. 2, pp. 654-658, 1994.

[7] P. Artursson, K. Palm, K. Luthman, “Caco-2 cells in experimental and theoretical predictions of drug transport”. Adv. Drug Deliv. Rev. vol. 46, pp. 27-43, 2001.

[8] Y. C. Martin, “A practitioner’s perspective of the role of quantitative structure-activity analysis in medicinal chemistry.” J. Med. Chem. vol. 24, no. 3, pp. 229-237, 1981.

[9] K. Palm, K. Luthman, J. Ros, J. Grasjo, P. Artursson, “Effect of molecular charge on intestinal epithelial drug transport: pH-dependent transport of cationic drugs.” JPET. vol. 291, no. 2, pp. 435-443, 1999.

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The Necessity of a Theory of Biology for Tissue Engineering: Metabolism-Repair Systems

Suman Ganguli and C. Anthony Hunt*

Biosystems Group, Department of Biopharmaceutical Sciences, and The Joint UCSF/UCB Bioengineering Graduate Group The University of California, San Francisco, CA 94143, USA

Abstract—Since there is no widely accepted global theory of biology, tissue engineering and bioengineering lack a theoretical understanding of the systems being engineered. By default, tissue engineering operates with a "reductionist" theoretical approach, inherited from traditional engineering of non-living materials. Long term, that approach is inadequate, since it ignores essential aspects of biology. Metabolism-repair systems are a theoretical framework which explicitly represents two “functional” aspects of living organisms: self-repair and self-replication. Since repair and replication are central to tissue engineering, we advance metabolism-repair systems as a potential theoretical framework for tissue engineering. We present an overview of the framework, and indicate directions to pursue for extending it to the context of tissue engineering. We focus on biological networks, both metabolic and cellular, as one such direction. The construction of these networks, in turn, depends on biological protocols. Together these concepts may help point the way to a global theory of biology appropriate for tissue engineering.

Key Words—Theoretical biology, bioengineering, self-repair and self-replication, metabolism-repair systems

I. INTRODUCTION*

Traditional engineering is based on solid theories of how and why things work as they do. Engineering within the domain of biology presents challenges because there is no widely accepted global theory of biology, even though there are standing theories dealing with aspects of biology, such as the Mendelian theory of particulate inheritance. Without a global theoretical framework, bioengineering efforts move forward principally by trial and error on a foundation that biological systems can be treated as machines. However, current efforts in cell and tissue bioengineering can help motivate development of such a theory, and parallel efforts to develop such a theory should prove synergistic to those bioengineering efforts. Bioengineering will benefit by fostering, working within, and contributing to theory.

In this paper, we attempt to initiate such a synergy by exploring the applicability of a proposed global theoretical framework for biology to tissue engineering. That theory is the metabolism-repair systems formalism, initially developed by the theoretical biologist Robert Rosen.

Rosen’s work contained a strong criticism of reliance on the Newtonian “reductionist” approach to understanding biological systems. The Newtonian approach assumes that any system can be understood (and furthermore, fabricated) by

* Correspondence: [email protected] and/or [email protected]

understanding the physical forces (chemical, mechanical, etc.) acting upon the constituent materials of the system. In other words, any biological system can be “reduced” to its materials and the forces at work on them. Mathematically, this approach translates to the classical formalisms of dynamical systems, differential equations, and input-output systems.1

Heuristically, the Newtonian reductionist approach treats living organisms as being analogous to machines [2]. In particular, the problems of engineering living tissue are approached as analogous to those of engineering machines. Bioengineering in general, and tissue engineering in particular, has proceeded thus far largely by trial and error guided by a reductionist approach. This is natural, since that approach is inherited from traditional engineering, i.e., engineering of non-organic, non-living matter.

The nascent field of “systems biology” is based on the realization that the reductionist approach to biology is limited, and that a systems-level, organizational approach must be adopted [3, 4]. Along these lines, we argue that there are organizational and functional aspects of living tissues that tissue engineering must address in a theoretical manner if it is to move to the next level and begin the serious business of engineering living systems.

The metabolism-repair framework offers a route for doing so. It augments the reductionist “materials-only” approach by explicitly addressing two “functional” activities essential to living organisms: self-repair and self-replication2. Within the metabolism-repair framework, these activities are represented by functions. These functional components are included within and regulated by the theoretical representation of the organism itself. Thus, living organisms are explicitly represented as self-repairing and self-replicating.

We begin by introducing the metabolism-repair framework. Our immediate goal is to begin to translate the concepts of the metabolism-repair formalism to the context of tissue engineering. The metabolism-repair formalism focuses on and is developed within the context of single cell organisms. The theory has not been extended to address the

1 For example, the traditional approach to mathematical modeling of morphogenesis “ assumes that each biological form is the solution to a difficult calculus problem” [1]. The same article quotes a molecular biologist’s experience with this approach: “ Physicists are very dogmatic in saying that everything in these systems can be explained with physics. I cannot believe that.” The point is then made that organisms are organized mainly by their genes, and Drosophila is given as a prime example. 2 Here, the concept of replication is not limited to replication of the cell but extends to replication of any somewhat modular system, such as a mitochondria or an endocytotic vesicle.

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three-dimensional, hierarchical topology essential to most biological domains, including mammals. We indicate a direction for incorporating hierarchical topologies into the metabolism-repair framework, via the concepts of networks and protocols.

II. BACKGROUND

We begin with a brief exposition of the metabolism-repair framework. We refer the reader to [5], [6], [7], and [8] for further details.

Let A represent a set of inputs and B a set of outputs. In the initial context of a single cell, A could represent the set of environments in which a cell operates3, and B the set of cellular metabolic configurations4 [6].

The metabolism of a cell is then represented by a function

f: A → B We let H(A, B) denote the set of all physically and contextually realizable maps between A and B (i.e., those maps satisfying the physicochemical constraints of the materials). Then f is an element of the set H(A, B). We suggest that, given a tissue engineering objective, there exists a minimal subset of f about which the bioengineer should be sufficiently knowledgeable so that s/he can make optimum use of that information during engineering decision making.

At this point the framework represents simply the classical “ materials-only” input-output relationship. The metabolic activity of a living cell, however, must have the means to sustain itself. This need requires and is implemented, in part, by repair activities. Those processes are represented within the formalism by a repair function P. Such a repair function reconstitutes a METABOLISM5 from the members of the set outputs, B. Recall that a METABOLISM is an element of H(A, B). Thus, repair is represented by a function

P: B → H(A, B) Using the notation introduced above, the repair function P is an element of the set of maps H(B, H(A, B)). Here also, we suggest that, given a tissue engineering objective, there exists a minimal subset of P about which the bioengineer should be sufficiently knowledgeable so that s/he can make optimum use of that information during engineering decision making.

The repair function P may be interpreted simply as a representation of the processes employed by the cell to sustain itself as components of its metabolic machinery degrade and need repair. Similarly, however, the repair processes themselves degrade. Rather than invoking an additional entity to repair the repair function, which would

3 These will include “ raw materials” that are taken in from outside the cell plus recycled materials. 4 These will include gene products and the cellular components composed of those products. 5 The definition and use of this term is new. To distinguish it from traditional usage we use small caps.

quite obviously lead to an infinite sequence of repairers, Rosen introduced REPLICATION6 into the framework.

In biology, replication processes allow the cell to replace its repair machinery with a new version. In the metabolism-repair formalism, REPLICATION is a function which takes as input an existing METABOLISM and outputs a new repair map. Thus, REPLICATION is represented by a function

R: H(A, B) → H(B, H(A, B))

Where does the replication function come from? Rosen’s central result was to show that replication arises from the system of metabolism and repair itself. By examining these mappings in the context of Category Theory [9], he showed that, under certain conditions, the replication map R could be identified with an element of the set B. Hence replication does not need to be engineered from outside the system, and the system of metabolism, repair and replication is closed. It is in this sense that the metabolism-repair formalism represents a theory of self-replicating and self-repairing systems.

Here yet again, we suggest that, given a tissue engineering objective, there exists a minimal subset of R about which the bioengineer should be sufficiently knowledgeable so that s/he can make optimum use of that information during engineering decision making.

III. METHODS

Rosen took a strong ontological stance regarding the “ functional” components of REPLICATION and repair in the metabolism-repair framework. He viewed them not as just mathematical constructs, but as representing real and essential aspects of living organisms. We can then ask: if, indeed, biological counterparts for the mathematical mappings do exist, then what are they and where are they?

We propose that the concept of networks may lead to the biological locations of the functional repair and replication components. At the level of the single cell, repair and replication may reside within the metabolic network. This is addressed in the treatments of metabolism-repair systems in [7] and [8], so we do not repeat those observations here. We note, however, that recent analyses of metabolic networks have indicated that, more than the materials that make them up, it may be the structures of the networks that are conserved by evolution [10]. This in itself begins to hint at the importance of “ relational” (versus strictly “ material” ) aspects of biology, which Rosen saw the metabolism-repair framework as addressing [8].

We believe these ideas may be applied toward the task of scaling up the concepts of metabolism-repair systems to address multicellular tissues. Metabolic networks contain an implied intracellular topological component behind replication and repair in the single cell case. Similarly, cellular networks may be an essential dynamic topological component behind replication and repair in the multicellular case. In order for multicellular tissues to have functional repair and replication components, the local repair and replication components of the constituent cells must be

6 As with METABOLISM, the definition and use of this term is new. To distinguish it from traditional usage we use small caps.

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integrated into global repair and replication components for the organism as a whole. We conjecture that this integration is determined by the cellular network’s dynamic topology. Reference [5] contains a sketch of some ideas in this direction, with a brief discussion of cellular metabolism-repair networks. These are mentioned as a direction of future study, with great potential for insight into areas relevant to tissue engineering, such as cellular differentiation. It is a direction that, to our knowledge, has yet to be pursued.

A longer-term program is to extend the metabolism-repair framework to an even wider variety of biological contexts. One avenue for doing so may be to focus on the concept of functional units. The clearest example of a biological functional unit is the single cell. Subcellular organelles may also be identified as functional units. Most relevant to tissue engineering, of course, are multicellular functional units that make up organs, and ultimately organs themselves. In this sense, tissue engineering is involved in the reconstruction of multicellular functional units outside of their original context in vivo. Hence, tissue engineering could benefit from a theory of functional units. The metabolism-repair framework may be the basis of such a theory. The concept of a functional unit is an intuitive one, but it lacks a precise definition. Since the capacities for self-repair and self-replication seem like they are central to functional units, it may be that metabolism-repair systems are a formalism for describing functional units.

Finally, we discuss some potential connections between the ideas discussed above and another recently developed abstraction of biological systems: protocols. Csete and Doyle, in describing aspects of engineering theories that can be applied to complex biological systems [11], focus on the importance of what they call protocols. They define protocols as rules that arise repeatedly in systems as interfaces between “ modules.” As examples of biological protocols, they cite a list of diverse abstractions: gene regulation, signal transduction pathways, cell-mediated activation, and many others.

Any engineered system cannot ignore the relevant protocols. Hence, bioengineering efforts must discover the biological protocols essential to the systems being engineered. This in itself is another important point for consideration by the tissue engineering community.

With respect to the ideas of biological networks mentioned above, however, Csete and Doyle note that the protocols are central to understanding and engineering biological systems in part because they facilitate evolution. Protocols allow existing systems to be cobbled together, thus allowing the evolutionary construction of novel systems. Csete and Doyle call this process “ evolutionary tinkering,” and argue that it is essential to the robustness and modularity of biological systems.

From this, it is possible to see roles for protocols in biological networks. It has been widely observed that biological networks are robust and highly modular (scale-free). Indeed, it has been noted that these aspects of biological networks can be attributed to the fact that they arise from evolutionary tinkering [12]. Thus, protocols may in fact be the mechanisms that allow the evolutionary construction of biological networks.

Returning finally to the repair and replication, we have conjectured that these functions may be located within certain biological networks, whether metabolic or cellular. This indicates that biological protocols play a central role in

constructing these functions. We may go further and speculate that replication and repair are themselves protocols of a sort, but that they are “ meta-protocols.” They are the protocols essential to life, and all other protocols are the ingredients that give rise to replication and repair, via the construction of appropriate networks.

Our premise is that in order to make progress on engineering living tissues, we need a theory of biology. However, in order to make progress in building such a theory, we conversely need ways to test ideas. Computational modeling and simulation methods may be the best available bridge between theory (of metabolism-repair systems, for example) and practice (of bioengineering) [13]. The theoretical frameworks described above are abstract and far removed from the biological reality. For example, to test hypotheses about aspects of the theory, we first need ideas that posit form and location of the repair and replication maps. We can begin to make progress in this direction by developing modeling and simulation techniques where the model components map to the biological system in a natural way, yet also encode aspects of the theoretical framework.

We believe that the envisioned modeling and simulation techniques will have more in common with in vitro model systems than with traditional modeling and simulation methods, in that they will need to be dynamic, flexible, adaptable, and thus capable of capturing multiple aspects of the biological system. They should also be capable of automatic model revision and extension when the simulation system is presented with new data. The Functional Unit Representation Method (FURM) is a step in that direction in that it encompasses many of the concepts discussed above [14]. As its name indicates, FURM focuses on modeling at the level of biological functional units, and initial applications of FURM have represented biological networks. In the future, FURM may serve as a method of discovering and testing biological protocols in silico, and eventually may incorporate prototypes of the repair and replication maps of the metabolism-repair framework.

IV. CONCLUSION

Over 30 years ago, Robert Rosen recognized the applicability of his work to fields such as tissue engineering: “ We may envisage the construction of artificial engineering systems manifesting organizational characteristics of biological organisms. Such attempts have been pursued for a long time, especially in the area of artificial intelligence, the design of artificial biological organs, and so forth, but never in a completely systematic manner” [8].

Tissue engineering has been pursuing such attempts at an ever-accelerating pace. But without a theory of living organisms in place, it will continue to do so in an unsystematic manner. Rosen’s metabolism-repair systems, by treating in a theoretical manner the essential biological processes of self-repair and self-replication, may be a path to a theory of biology useful for tissue engineering.

ACKNOWLEDGMENT

This work was supported in part by funding provided by the

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PhRMA Foundation. We thank the members of the Biosystems Group at UCSF and Glen Ropella of Tempus Dictum, Inc. for helpful discussions.

REFERENCES

[1] A. Cho, “ Life’ s patterns: no need to spell it out?” Science, vol. 303, pp. 782-3, 2004.

[2] G. Bock and J. Goode, eds. The Limits of Reductionism in Biology: Novartis Foundation Symposium 213. Chichester; New York: J. Wiley, 1998.

[3] T. Ideker, T. Galitski, and L. Hood, “ A new approach to decoding life: systems biology,” Ann. Rev. Hum. Genet., vol. 2, pp. 343-372, 2001.

[4] O. Wolkenhauer, “ Systems biology: the reincarnation of systems theory applied in biology?” Brief Bioinform., vol. 2, pp. 258-270, 2001.

[5] J.L. Casti, “ The theory of metabolism-repair systems,” Appl. Math. Comput., vol. 28, pp. 113-154, 1988.

[6] J.L. Casti, “ Biologizing control theory: how to make a control system come alive,” Complexity, vol. 7, no. 4, pp. 10-12, 2002.

[7] J.C. Letelier, G. Marin, and J. Mpodozis, “ Autopoietic and (M,R) systems,” Journal of Theoretical Biology, vol. 222, pp. 261-272, 2003.

[8] R. Rosen, “ Some relational cell models: the metabolism-repair systems,” in Foundations of Mathematical Biology, vol. 2, R. Rosen, ed. New York: Academic Press, 1972, ch. 4, pp. 217-253.

[9] F.W. Lawvere and S.H. Shanuel, Conceptual Mathematics: A First Introduction to Categories, Cambridge University Press, 1997.

[10] Y.I. Wolf, G. Karev, and E.V. Koonin, “ Scale-free networks in biology: new insights into the fundamentals of evolution?” Bioessays, vol. 24, no. 2, pp.105-109, 2002.

[11] M.E. Csete and J.C. Doyle, “ Reverse engineering of biological complexity,” Science, vol. 295, pp. 1664-1669, 2002.

[12] U. Alon, “ Biological networks: the tinkerer as engineer,” Science, vol. 301, pp. 1866-1867, 2003.

[13] D. Noble, “ The rise of computational biology,” Nat. Rev. Mol. Cell Bio., vol. 2, pp. 460-463, 2002.

[14] G.E.P. Ropella and C.A. Hunt, “ Prerequisites for effective experimentation in computational biology,” http://citeseer.ist.psu.edu/575600.html.

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Applying Models of Targeted Drug Delivery to Gene Delivery

Tai Ning Lam and C. Anthony Hunt*

Biosystems Group, Department of Biopharmaceutical Sciences University of California, San Francisco, School of Pharmacy, CA 94143, USA

* Correspondence: [email protected]

Abstract—Gene delivery requires targeted delivery systems. Exploratory simulations using models of targeted drug delivery helps one assess the worthiness of such systems, and helps quantify the expected therapeutic benefits of the systems. The drug targeting index (DTI), a ratio of availabilities, is a measure of pharmacokinetic benefit of the delivery device, based on a combination of a physiologically-based pharmacokinetic model and a single pharmacodynamic Emax model. Pharmacodynamic outcomes are quantified by the degree of separation between the dose-response and dose-toxicity curves (SRT). Simulations are undertaken to investigate the potential linkage of DTI and SRT, a pharmacodynamic outcome. A significant positive linear relationship is found between the DTI and SRT. The relationship can be translated into a minimum pharmacokinetic requirement that can be used to guide making decisions regarding whether or not further pursue the development of a candidate gene-delivery device as a therapeutic agent.

Key Words—Targeted drug delivery, gene delivery, population pharmacokinetics, pharmacodynamic, modeling, simulation, systems biology

I. INTRODUCTION Gene delivery faces intrinsic difficulties: genes or

gene-interfering agents, in form of plasmid, single-stranded or double stranded RNA or DNA, or short oligonucleotides, cannot readily access their target response sites � the nuclei of a specific cell group. Giving a huge dose of free RNA or DNA, and hoping that enough will distribute into target tissues does not work. On one hand, free RNA and DNA cannot freely permeate cellular membranes. On the other hand, free RNA and DNA are rapidly degraded in the circulation. They therefore must be protected by some carrier, or be chemically modified to make them resistant to degradation. Hence, there is a need for targeting. Gene delivery to a specific cell group usually requires targeted delivery devices, such as cationic liposomes or viral vectors. Engineering an efficient delivery system is a must to ensure proper gene delivery, and in turn, expected efficacy. Hence, it is prudent to use models of targeted drug delivery to analyze any candidate gene delivery system and thereby help inform the decision making process involved in development as a therapeutic agent. Failure to identify poor candidate delivery systems will result in a lengthy yet unsuccessful development program, not to mention the burden of the financial loss. Better-informed assessment is critical early in the drug development process.

This study applies a physiologically-based population pharmacokinetic model of targeted drug delivery to gene delivery. The model used [1], provides a pharmacokinetic assessment of the targeting device, namely, the drug targeting index, DTI, which is a ratio of availability of drug in the target response compartment to its corresponding availability at the sites that give rise to toxicity. DTI is conveniently taken as the ratio of area under the concentration-time curves (AUC) or the ratio of drug exposures at the two sites. In the simplest sense, if one assumes steady state delivery, the DTI equals the ratio of the level of drug or transcriptionally active genes at the response site(s) to the corresponding level at the sites of toxicity. It will be shown in this report, that such pharmacokinetic assessments can directly reflect pharmacodynamic consequences and thus can be a good estimate of expected performance in terms of increasing the separation between of dose-response and dose-toxicity curves. These simulation experiments are population-based so as to provide some insight into expected inter-subject variability. That variability can have a have a decisive impact on how likely it is that the device under study functions as intended.

II. METHODS

A. Simulations The physiologically-based pharmacokinetic model is

a simplification of that described earlier [1]. Briefly, the body is represented as two physiologic compartments. For the sake of discussions of gene delivery, the response site is taken as the specific groups of cell to which genes need to be delivered in order to generate the desired pharmacological response. The site of toxicity is conservatively taken as everywhere else in the body. DTI is the ratio of active levels at these two sites. A set of differential equations is solved using the steady state assumption to give concentrations at the two sites in terms of dose (D), blood flows (to response site, Qr, and to the site of toxicity, Qt), extractions at each site (at Er and Et), delivery to each site (to response site, Fr, and to the site of toxicity, Ft) and fu is the uncompromised fraction (for a drug, bound)�the fraction available to generate gene products. The values of Cr and Ct are given by the following equations.

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( )( )[ ]

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)1()1(

)(

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As a first approximation, a simplistic

pharmacodynamic model is used. Briefly, the pharmacological effects follow a single Emax model for the uncompromised level of active species at the response site. The uncompromised fraction (unbound fraction for a drug) is used because Tachibana et al [2] observed that only a small fraction of delivered plasmid can be transported into the nucleus to become available for transcription or interference. Although the pharmacodynamic model oversimplifies the complicated sub-cellular processes, it allows assessment of the overall pharmacodynamic outcomes of the targeted delivery of genes or a drug given a simple steady state concentration. The parameters are apparent maximum effects (of response, Pmax, and of toxicity, Tmax) and apparent concentrations at which half-maximal effect is seen (of response, CP,50, and of toxicity, CT,50). The following equations are used.

50,50,ToxicityResponse

Tt

tmax

Pr

rmax

CfuCfuCT

CfuCfuCP

+×

=+×

=

The simulations are run using a population of N = 1000 hypothetical subjects. The values of each subject�s individual variable are sampled from either a normal or a beta distribution having a specified mean and coefficient of variation. The key summary statistics that give rise to the individual parameters of the population are listed in Table 1.

To quantify pharmacodynamic benefit, each subject is simulated to receive 14 doses, from 0.001 to 20, so as to follow the entire dose-response and dose-toxicity curves. The total separation between the response and toxicity curves (SRT) is a pharmacodynamic assessment of the drug. Graphically, it is the area between the response and toxicity curves, shown as the shaded area in Fig 1. In the

study, it is approximated by summing, over all doses, the difference between response and toxicity at each dose: ∑Dose[(Response - Toxicity)].

B. Derivation

A single Emax expression can represent multiple subcellular processes, if a single Emax model can represent each of them, in turn.

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The effect of exposure is estimated by the area under the effect-time curve (AUE), integrated from time zero to infinity. Effect is represented using the above as an Emax model. Following a bolus dose, in which the concentration falls exponentially, AUE is derived as follows.

⎟⎠

⎞⎜⎝

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Fig. 1. Dose-response and dose-toxicity curves. The shaded area is the total separation of response and toxicity (SRT), and is a measure

of pharmacodynamic benefit.

TABLE 1: SUMMARY STATISTICS OF THE POPULATION N = 1000

Variable Mean Median Std Dev

Blood flow to response site (Qr ) 5.05 5.05 3.00Blood flow to toxic site (Qt) 4978 4974 495Extraction at response site (Er) 0.900 0.987 0.177Extraction at toxic site (Et) 0.896 0.990 0.182Delivery to response site (Fr) 0.0990 0.0972 0.0199Delivery to toxic site (Ft) 0.901 0.903 0.0199Uncompromised fraction (fu) 0.100 0.0768 0.0923Apparent maximum response (Pmax) 100 101 20.4Apparent maximum toxicity (Tmax) 100 101 19.6Apparent concentration for half-maximal response (CP,50) 9.89e-5 9.89e-5 1.97e-5Apparent concentration for half-maximal toxicity (CT,50) 2.00e-3 1.99e-3 4.02e-4

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III. RESULTS

Fig. 2 depicts the relationship between the drug targeting index (DTI) and the separation between the response and toxicity curves (SRT). The pharmacokinetic assessment, i.e., the DTI, is linearly related to the pharmacodynamic assessment, the SRT. The significance of this relationship is that, given a favorable pharmacokinetic profile (e.g., high Fr/Ft in particular) and information supporting that the assumptions are reasonable, one can assert that the targeted drug will perform well in the population, pharmacodynamically, without having to actually test it in the population. The DTI, in turn, is a valuable assessment of worthiness of developing the candidate, targeted drug delivery system, as it provides estimates of the expected pharmacodynamic outcomes, before a clinical trial is run. A candidate drug having a too small a DTI can be confidently dropped from development for the reason that it is not likely to be clinically successful.

It is possible to estimate a minimum DTI requirement to be qualified for further development, if one has a sense of how much separation of response and toxicity is desired in the average patient. Suppose, it is arbitrarily chosen that a minimum separation of 25 units is desired if one assumes there is little toxicity associated for such a �low� dose, then it is a quarter of maximum transcriptional capacity of a gene, which can be a substantial amount. The results of simulations show that at the optimal dose (at which the maximum separation is achieved) one actually obtains only about 15% of the total achievable separation of about 167 units; that translates into a DTI of about 3.8. So, a candidate drug for which DTI = 3.81, can be expected to give a response-toxicity separation of 25 units, at the optimal dose in the average patient. Conversely, if a candidate is observed or estimated to have a DTI of 3.8, then a separation of 25 can be expected in the average patient. The relationship between SRT and DTI is thus translated into a guide for drug development decision making.

IV. DISCUSSION

It is of interest to contrast predictions made using the above over-simplified model with one that is more complicate. Rowland et al[3] proposed a subcompartment analysis at the response site to account for flux between subcompartments. The same concepts as above can be used to represent and simulate intracellular pharmacokinetics and nuclear transport. Kamiya et al [4] and Tachibana et al [2] also proposed simple zero-order or first-order intracellular models for intracellular trafficking of gene and gene expression. So, modeling the subcellular processes with these models will be the next step. These more sophisticated models would be expected to give a more detailed description of the intracellular

1 DTI = 3.8 means that the targeted delivery device successfully delivers approximately 4 fold higher levels to target cells, relative to an intravenous dose of untargeted therapeutic.

processes, and should allow one to generate estimates of the most meaningful mechanistic rate constants that are need for effective delivery devices. However, early in a drug development program little is known about such properties. The above over-simplified model is therefore the logical alternative. It gives a simple assessment of the value or performance of the device, without extensive, costly experimentation or lengthy clinical trials, and therein lies the real advantage of its use.

The subcellcular processes are believed to be quite complicated. Is the above oversimplified pharmacodynamic Emax model, relating effect to intracellular cytoplasmic unbound levels adequate to aid decision making? That question will need to be answered for each individual case in light of available information. If an Emax model is adequate to represent each step in the process, then one global Emax model will be sufficient to represent the entire cascade of events, with the apparent Emax and C50 representing hybrids of the microscopic submodel parameters. The argument being made is consistent with the usual reported pharmacodynamic models in which a series of events, for example, a signal transduction cascade, is modeled by a single pharmacodynamic process. Consequently, a single global pharmacodynamic Emax model is used in this study to represent all of the subcellular processes. However, the parameters of such a model are empirical, not mechanistic, and cannot be used to explain or describe the subprocesses.

A limitation of the above approach is use of the steady state assumption. The simulation predictions are difficult to test experimentally. It is difficult to provide steady state gene delivery to cells in vivo. However, because the time scale for intracellular processes such as gene trafficking and gene expression are slow relative to distribution of drug or therapeutic agents into the cell, as observed by Tachibana et al [2], one can remove the steady-state assumption and, instead, approximate the input of gene as a bolus: assume that the therapeutic agent is given as a short infusion, until intracellular

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

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Fig. 2. The relationship between total SRT (y-axis) and logarithm of DTI (x-axis) is shown. The regression equation is y = 4.08+125*x., R2 = 0.85. The intercept is not statistically significant, and the slope

has a p<0.0001.

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concentration of the loaded delivery device reaches its pharmacokinetic steady state, at which time the infusion is stopped. Now, the pharmacodynamic processes, which are slower, are effectively seeing the therapeutic input as a bolus into the cell. Both observing and simulating the effects, as a function of time, are complicated, thus rendering the simple model less valuable. What can be quantified, however, is an estimation of exposure to the effect, or the area under the effect-time curve (AUE.) To do so, it is assumed that the effect does not depend upon past exposure. Given therapeutic input as a bolus and having the effect represented by a single Emax model means that AUE is a function of C0, the initial concentration and λ, first-order rate constant for elimination of the therapeutic at the effector site. There is still a positive relationship between the DTI, a ratio of C0, and pharmacodynamic outcomes, quantified by ratio of AUEs. The exact relationship between the two, including consideration of the time lag and the dependence upon past exposure, will be the topic of further study.

Jiang et al reported successful gene delivery and expression with naked DNA injected intravenously into tail vein of the mouse without using a delivery device [5]. The limitation of this strategy is that the gene does not need to be delivered to a specific group of cells, and therefore non-specific uptake and expression of the gene by liver cells is sufficient to confer some therapeutic effects. The report also described a typical Emax-shaped dose-response effect of plasmid DNA on IL-10 expression in liver cells. Koh et al compared the delivery of naked IL-10 plasmid DNA versus to that delivered and protected by a biodegradable polymer [6]. The authors argued that the carrier protected the plasmid from being degraded in the circulation and, as a consequence, a larger effective amount of gene is delivered and is available for transcription. The study showed 3 to 5-fold increase in IL-10 expression by the delivery device, thereby validating the concept that improving the availability of gene for the effector increase the response. Finally, Liu et al compared the transfection efficiency of naked DNA versus that delivered by cationic lipids [7]. The studies measured radiolabeled intracellular DNA, and found that delivery by cationic lipids achieved several fold differences between different tissues, thereby supporting the argument above that a minimum fold difference in concentration between target and other tissue is achievable by such delivery devices.

One must not overlook the toxicity profile when developing a gene delivery device as a therapeutic agent. The common toxicity seen in clinical trials were immune reactions against the carrier vehicle, usually viral vectors, inflammation reactions at the tissue where the gene is delivered, is believed to be caused by a number of factors, including infection of viral vectors, and mutagenesis in normal cells into which genes are delivered [8]. One can anticipate that these toxicities are dose-dependent and that a Emax model for toxicity can be adequate. In the presence of observable dose-dependent toxicities, gene and gene delivery devices must be carefully engineered and dosed

so that sufficient of effective genes are delivered to the target cells, while toxicities are minimized.

In conclusion, the present study applies a simple simulation model for targeted drug delivery to gene delivery, and shows that a simple pharmacokinetic assessment of the delivery device, the DTI, is directly related to pharmacodynamic outcome over a range of delivered doses, and so can be used to guide decision making during development of therapeutics.

ACKNOWLEDGMENT

The Biosystems Group and the Pharmaceutical Sciences Pharm. D. Pathway, School of Pharmacy, University of California, San Francisco supported this work. We thank the members of the Biosystems Group for assistance, support, and helpful discussions.

REFERENCES

[1] Hunt CA, MacGregor RD, Siegel RA. Engineering Targeted In Vivo Drug Delivery I. The Physiological and Physicochemical Principles Governing Opportunities and Limitations. Pharm Res 1986; 3(6):333-344.

[2] Tachibana R, Ide N, Shinohara Y, Harashima H, Hunt CA, Kiwada H. An assessment of relative transcriptional availability from nonviral vectors. Int J Pharm. 2004 Feb 11;270(1-2):315-21.

[3] Rowland M, McLachlan A. Pharmacokinetic considerations of regional administration and drug targeting: influence of site of input in target tissue and flux of binding protein. J Pharmacokinet Biopharm. 1996 Aug;24(4):369-87.

[4] Kamiya H, Akita H, Harashima H. Pharmacokinetic and pharmacodynamic considerations in gene therapy. Drug Discov Today. 2003 Nov 1;8(21):990-6.

[5] Jiang J, Yamato E, Miyazaki JI. Intravenous delivery of naked plasmid DNA for in vivo cytokine expression. Biochem. Biophys Res Comm. 2001 289: 1088-1092.

[6] Koh JJ, Kol KS, Lee M, Han S, Park JS and Kim SW. Degradable polymeric carrier for the delivery of IL-10 plasmid DNA to prevent autoimmune insulitis in NOD mice. Gene Therapy (2000) 7, 2099�2104

[7] Liu F, Qi H, Huang L, Liu D. Factors controlling the efficiency of cationic lipid-mediated transfection in vivo via intravenous administration. Gene Therapy (1997) 4, 517�523.

[8] Arguilar LK, Arguilar-Cordova E. Evoluation of a gene delivery clinical trial. Journal of Neuro-oncology. 2003; 65: 307-315.

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Abstract—There have been many efforts to explain and simulate tumor growth with mathematical and computational models. However, none have systematically examined the behaviors of tumor spheroids during growth. The interactions among tumor cells during growth are also not well understood. We have implemented an agent-based computational approach to study the macro- and microbehaviors of avascular tumor spheroids during growth. Our simulations of tumor spheroid growth begin with a single tumor cell in optimal environmental conditions. We observe an initial phase of rapid growth, during which the shape of the collective approximates a spheroid. Subsequently a characteristic layered structure develops, consisting of an outermost proliferating cell layer, an intermediate quiescent cell layer, and a central necrotic core. These behaviors of our in silico spheroids map well to experimental in vitro observations.

Keywords—Agent-Based, Computational, Multicellular,

Tumor Spheroid, in vitro, simulation

I. INTRODUCTION*

In vivo, early stage tumor growth is a complicated process, involving interactions among multiple subprocesses, such as proliferation, quiescence, necrosis, apoptosis, and angiogenesis. Moreover, early stage tumor growth in vivo is very difficult to observe, particularly in the avascular phase. Multicellular tumor spheroids (MTS) are an in vitro model system that has been developed to imitate the early, avascular growth phase of in vivo tumors. Computational models of this process that are able to account for the observed behavior of the in vitro system and allow in silico experimentation could prove valuable.

Both mathematical and computational models have been formulated to simulate MTS growth. Drasdo [1] used a Monte-Carlo approach to model the initial exponential growth phase of avascular tumors. Dormann and Deutsch [2] used a hybrid cellular automaton to simulate avascular tumor growth. Kansal et. al. [3] developed a cellular automaton model of brain tumor growth. Casciari et. al. [4] and Ward and King [5] are examples of differential * Correspondence: [email protected]

equation models have also been developed to study these processes. These models, however, are unable to represent certain aspects of this system well. For example, differential equation models cannot easily represent either the individual and spatial heterogeneity of tumor cells or their adaptive behaviors. Cellular automaton models do not provide for detailed representation of individual tumor cell behavior and state, and lack the flexibility to represent the adaptive behavior of individual tumor cells. In addition, none of these approaches allows the detailed study of nutrient and waste transport through a spheroid.

An Agent-based Computational Approach for Representing Aspects of In Vitro Multi-cellular Tumor Spheroid Growth

Song Chen, Suman Ganguli, C. Anthony Hunt*

Biosystems Group, Department of Biopharmaceutical Sciences The University of California, San Francisco, CA 94143, USA

We believe an agent-based approach is sufficiently flexible to model this system. Agents are software objects that have the ability to add, remove, and modify objects and events. Philosophically, they are objects that have their own motivation and can initiate causal chains, as opposed to simply participating in a sequence of events created elsewhere. Agent-based models are discrete in most dimensions, including time, state, and the rules used to govern agent behaviors. Agent-based models were specifically developed to provide more natural descriptions of complex adaptive systems in various contexts [6].

Detailed descriptions of in vitro multicellular tumor spheroids are provided in [7,8] Briefly, in vitro tumor cells consume oxygen and nutrients and release metabolic byproducts. Under optimal environmental conditions—sufficient oxygen and nutrients and low levels of byproducts—tumor cells undergo mitosis, producing new tumor cells. This cell proliferation leads to an initial exponential growth phase and a multicellular spheroid. As spheroid size radius increases, oxygen and nutrient availability internally is reduced, and metabolic byproducts accumulate within the spheroid. Such conditions are thought to contribute to necrosis of cells near the center of the spheroid. The byproducts of necrosis can be cytotoxic, and their presence can further inhibit tumor cell proliferation. Tumor cells near the surface of the spheroid, on the other hand, can continue to proliferate because of the favorable environmental conditions. Cells located between this outer proliferating layer and the inner necrotic regions become quiescent—environmental conditions are adequate to their survival, but not for proliferation. This dynamic results in the characteristic layered structures of tumor spheroids illustrated in below Fig. 1.

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Fig. 1. Tumor Spheroid Schematic Diagram

II. COMPUTATIONAL APPROACH AND METHODS

Swarm1 is a software library that was designed to facilitate multi-agent simulation by managing many programming tasks common to agent-based models, thus freeing the user to focus on the specific requirements of the simulation. Core Swarm libraries provide vital functions such as object creation, memory allocation, scheduling of activities, and list management. All agents and objects in Swarm can be probed. Once attached the probe can send a message, change a variable, or retrieve values.

We have implemented an agent-based model of multicellular tumor spheroid growth using the Swarm framework. Swarm enables and facilitates the simulation of collections of concurrently interacting agents. Our model contains 4 computational spaces (Fig. 2.): TumorSpace, OxygenSpace, NutrientSpace, InhibitorSpace. Each space is represented as a (toroidal) 2-D square lattice. They overlap as shown below. All factors other than oxygen that contribute to growth and division are lumped together into a class called Nutrients. Similarly, all factors that inhibit growth or that are harmful to tumor cells are grouped into the class Inhibitor. Corresponding objects in each class are designated OXYGEN, NUTRIENT, and INHIBITOR to distinguish them from their biological referents2.

Fig. 2. Schematic representation of overlapping grid spaces 1 See http://www.swarm.org. for further information on Swarm. 2 The same word may be used to refer to molecules, cells, system components, or events in the referent system and to the corresponding objects, agents, or events within the in silico system. In the latter case the word is written using small caps.

TumorSpace contains tumor cell agents. Each location can by occupied by a single agent. OXYGEN, NUTRIENT, and INHIBITOR are integer values at each location in their respective spaces.

Proliferating Cell Layer

Quiescence Cell Layer For simulation of oxygen transport in OxygenSpace, we use Swarm’s built-in diffusion algorithm. Swarm provides a discrete 2nd-order approximation of 2-D diffusion with evaporation. For simulation of NUTRIENT and INHIBITOR transport, we have implemented data structures and algorithms to represent the transport of these quantities along the edges between cells. We call this the EdgeFlow function. The EdgeFlow algorithm is implemented similar to diffusion, except that edges can be “open” or “closed,” and transport occurs only along open edges. This allows us to simulate the heterogeneous transport of these materials through a spheroid in a detailed manner.

Necrotic Core

Tumor cell agents, designated TUMOR AGENTs, have the following internal attributes that, collectively, control their behavior:

• state: proliferating, quiescent, or dead • rates of OXYGEN consumption, NUTRIENT consumption and INHIBITOR production

• OXYGEN minimum and maximum requirements • NUTRIENT minimum and maximum requirements • INHIBITOR minimum and maximum requirements The initial conditions are as follows: Initializing OxygenSpace sets the value of OXYGEN at each location to OC. Initializing NutrientSpace sets the value of NUTRIENT at each location to NC. One TUMOR AGENT in the proliferating state is placed at the center of TumorSpace. The simulation is started. At each time step thereafter, OXYGEN and NUTRIENT values are “replenished” outside the spheroid: for each location in the TumorSpace that neither contains a TUMOR AGENT nor is surrounded by TUMOR AGENTs, the corresponding location in OxygenSpace and NutrientSpace is reset to OC or NC. A list of functional TUMOR AGENTs is maintained, (proliferating or quiescent). At each time step, each TUMOR AGENT in the list caries out the following activities. Consume OXYGEN and NUTRIENT only from the corresponding location in OxygenSpace and NutrientSpace, and release an amount of INHIBITOR to InhibitorSpace, following individual internal rate values. Use resulting OXYGEN, NUTRIENT, and INHIBITOR amounts to determine new TUMOR AGENT state for the next time step.

TumorSpace

OxygenSpace

NutrientSpace

InhibitorSpace

The determination of the TUMOR AGENT state is made as follows: the TUMOR AGENT compares OXYGEN, NUTRIENT, and INHIBITOR values against its internal minimum and maximum requirements. If OXYGEN and NUTRIENT values are greater than the maximum requirements and INHIBITOR value is less than the minimum requirement (representing ideal conditions for the tumor cell), the TUMOR AGENT is proliferating. If any of these values are between the agent’s minimum and maximum levels, the TUMOR AGENT may take

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on the proliferating or quiescent state, with varying probabilities. If either OXYGEN or NUTRIENT is less than the agent’s minimum requirements, or INHIBITOR is greater than the maximum requirement (representing adverse conditions), the agent goes to the dead state with a certain probability. If the new state of the TUMOR AGENT is proliferating, attempt to divide. First, examine the eight neighboring locations in TumorSpace. If any neighboring location is unoccupied, create a new TUMOR AGENT in the proliferating state and place it in the unoccupied location. If no neighboring locations are unoccupied, simply remain in the proliferating state. For every TUMOR AGENT in the necrotic state increment InhibitorSpace in the corresponding location to represent accumulation of toxic necrotic material. During the initial stage of simulation, each TUMOR AGENT represents a single tumor cell. As the spheroid increases in size and fills TumorSpace, a “zoom function” is introduced. This allows a TUMOR AGENT to represent multiple tumor cells without distorting the spheroid shape and behaviors. The numbers of tumor cells a TUMOR AGENT represents increases each time the zoomFunction is applied. This allows the model to simulate larger spheroids, in which the total number of tumor cells may reach 1010, without representing each cell individually, which would be computationally intractable.

III. RESULTS

Following initiation of a simulation (Fig. 3a), TUMOR AGENTs proliferate, taking advantage of the optimal environmental conditions. This results in a spheroid of proliferating TUMOR AGENTs (Fig. 3b). The size of spheroid increases rapidly, which causes OXYGEN and NUTRIENT availability in the interior to decrease and INHIBITOR levels to increase. This results in decreasing gradients of OXYGEN and NUTRIENT and increasing gradient of INHIBITOR, moving from the outer edges towards the center. As a result, the TUMOR AGENTs toward the center become quiescent, and proliferating TUMOR AGENTs are limited to the outer regions (Fig. 3c). Eventually, three layers are formed (Fig. 3d). Conditions in the interior become increasingly adverse, causing transition of TUMOR AGENTs from quiescent to necrotic state and the formation of a “necrotic core.” For initial results and validation of our model, we demonstrate the effects of varying OXYGEN and NUTRIENT supply on spheroid growth. OXYGEN and NUTRIENT supply are determined by the parameters OC and NC (the values to which OXYGEN and NUTRIENT are replenished outside the spheroid). We use Proliferating Fraction as an outcome variable to measure spheroid growth. Proliferating Fraction is defined as the number of proliferating TUMOR AGENTs divided by the total number of TUMOR AGENTs.

(a).

(b)

(c)

(d)

Fig. 3. Tumor growth over time (a) TUMOR AGENTs at initial simulation (scale 1:1) (b) TUMOR AGENTs proliferate and form a spheroid (scale 1:1) (c) quiescent layer forms (scale 1:1) (d) spheroid increases in size, forms layered structure (scale 1:5)

Three sets of values for these parameters were used in experiments: baseline OXYGEN and NUTRIENT supply (PF1), doubled OXYGEN and NUTRIENT supply (PF2), and halved OXYGEN and NUTRIENT supply (PF3). For each set of values, we averaged the results of five simulations. The results are shown in Fig. 4. Fig. 4. shows that the Proliferating Fraction declines over time for each of the three set of parameter values. There is a sharp initial decrease, followed by a stabilization. The results also show that Proliferating Fraction varies with OXYGEN and NUTRIENT supply; greater supply of OXYGEN and NUTRIENT result in higher Proliferating Fractions. We use total number of TUMOR AGENTs to represent spheroid size. Spheroid size rapidly increases in the initial stage of simulation. The rate of increase slows and eventually reaches saturation. Similar to proliferating Fraction, doubling the OXYGEN and NUTRIENT supplies increases total number of TUMOR AGENTs and reducing the supplies to half decreases the total number of TUMOR AGENTs.

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Fig. 4. Proliferating Fraction vs. Time for three different sets of parameter values

III. DISCUSSION

Our model is an initial step towards the goal of

providing a flexible model of multicellular tumor spheroids which will allow for in silico experimentation. At this stage our model dynamically simulates formation and growth of multicellular tumor spheroids based on a small set of simple rules. The observed development of a spatial layered structure simulates in vitro observations, and results concerning major growth indicators, such as those presented above for Proliferating Fraction, are very close to those of in vitro data and results of other computational models [9]. Furthermore, a strength of the agent-based approach is that it enables us to observe the microbehaviors of individual agents and their interactions throughout the entire growth process.

Our model at this stage captures a small subset of the biological complexity involved in tumor spheroid growth. However, our approach provides an easy and effective way to add, modify and remove the various parts of the model: agents, rules, etc. As such, it can serve as a foundation for more detailed models of the various biological processes involved.

IV. CONCLUSION

Substantial progress has been made in various specialized areas of cancer research. The complexity of the disease on both the single cell level as well as the multicellular tumor level has led to the first attempts to describe tumors as complex, dynamic, self-organizing biosystems. To begin to understand the complexity of the system, novel models and simulation methods must be developed, incorporating concepts from many areas such as cancer biology, computer programming techniques, and

mathematical and computational applications. Our work is intended to demonstrate that agent-based modeling can be used to represent certain essential aspects of spheroid growth, and thus can serve as the basis for future in silico models of this complex system.

ACKNOWLEDGMENTS

We thank Glen E.P. Ropella, President, Tempus Dictum, Inc, for his tireless technical advice, and Dr. Amy H. Lin for early contribution to this work. We also thank the members of Biosystems group, Department of Biopharmaceutical Science, UCSF for support, and Ms. Pearl Johnson for administrative assistance.

REFERENCES [1] Drasdo D. “A Monte-Carlo approach to growing solid

nonvascular tumors.” In: G. Beysens and G Forgacs (eds), Dynamical networks in physics and biology, pp 171-185. 1998 Springer, New York.

[2] Dormann S, Deutsch A. “Modeling of self-organized avascular tumor growth with a hybrid cellular automaton.” In Silico Biol. 2002;2(3):393-406.

[3] Kansal AR, Torquato S, Harsh GR IV, Chiocca EA, Deisboeck TS. “Simulated brain tumor growth dynamics using a three dimensional cellular automaton.” J. Theor. Biol. (2000) 203, 367-382.

[4] Casciari JJ, Sotirchos SV, Sutherland RM. “Variations in tumor cell growth rates and metabolism with oxygen concentration, glucose concentration, and extracellular pH.” J Cell Physiol. 1992 May;151(2):386-94.

[5] Ward JP, King JR. “Mathematical modelling of avascular-tumour growth.” IMA J Math Appl Med Biol. 1997 Mar;14(1):39-69.

[6] Bonabeau E. “Agent-based modeling: methods and techniques for simulating human systems.” Proc Natl Acad Sci U S A. 2002 May 14;99 Suppl 3:7280-7.

[7] Hamilton G. “Multicellular spheroids as an in vitro tumor model.” Cancer Lett. 1998 Sep 11;131(1):29-34.

[8] Sutherland RM. “Cell and environment interactions in tumor microregions: the multicell spheroid model.” Science. 1988 Apr 8;240(4849):177-184.

[9] Kansal AR, Torquato S, Harsh GR IV, Chiocca EA, Deisboeck TS. “Simulated brain tumor growth dynamics using a three-dimensional cellular automaton.” J. Theor. Biol. 2000 Apr 21;203(4):367-82.

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1 ofA Novel Stepwise Normalization Method for Two-Channel cDNA Microarrays

Yuanyuan Xiao1,3, C. Anthony Hunt1, Jean Yee Hwa Yang2,3, Mark R. Segal2

1Department of Biopharmaceutical Sciences 2Department of Biostatistics

University of California, San Francisco, CA, USA 3These authors contributed equally

bstract—Microarray experiments contain many sources stematic errors. In order to extract biologically relevant mation from microarray data, normalization needs to be ed to remove such variations. Although a number of alization models have been proposed, it has not been well rched on how to assess model adequacy with respect to bserved data. To tackle this problem, we propose in this r a new stepwise within-slide normalization method, NORM. It is a normalization framework that integrates

us models of different complexities to sequentially detect correct systematic variations associated with spot

sities, print-tips, plates and two-dimensional spatial ts. We demonstrate the utility of STEPNORM on a set of studied cDNA microarray expriment.

eywords—cDNA microarray, normalization

I. INTRODUCTION

icroarray technology enables simultaneous itoring of the expression of thousands of genes ([1]). other measuring technologies, microarray data contain rent systematic measurement errors stemming from tions in labeling, hybridization, spotting or other iological sources ([2]). Normalization procedures, h adjust microarray data to remove such systematic tions, are therefore important for subsequent analysis

either differential expression or gene expression ling. In this paper, we describe a new systematic ise normalization procedure on two-channel cDNA

s and illustrate its usage on a Swirl zebrafish slide. The l experiment is comprised of four replicate idizations that contain 8,448 spots. It was carried out zebrafish as a model organism to study the effect of a

t mutation in the BMP2 gene that affects early lopment in vertebrates. wo-channel microarrays measure relative abundance

xpression of thousands of genes in two mRNA lations. This relative abundance is usually expressed as s, M = log2(R/G), where R and G are the fluorescent sity measurements of the red and green channels. The pronounced systematic variation embodied in the s that does not contribute to differential expression een the two mRNA populations is the imbalance of the n and red dye incorporation. This imbalance is ifested as the dependence of ratios on primarily two rs, the fluorescent intensity (hereafter represented by symbol A) and the spatial heterogeneity (hereafter sented by the symbol S). he A bias can be best illustrated using a MA plot ([3]),

e M is plotted against A (A = log2{\sqrt{RG}}). As the

assumption is that the majority of genes are equally expressed between the two mRNA samples, symmetrical distribution of points around the horizontal M=0 line is expected. Yet frequently we observe linear or nonlinear trend between M and A signaling the undesirable dependence of M on A. An example of nonlinear dependence between M and A is illustrated in Fig. 1a). The spatial heterogeneity (S) originates from different experimental conditions applied on spots from different areas on the slide. There are usually three major sources that contribute to this spatial variation. First, spots on the same slide are divided into different grids, and spots of different grids are printed by different print-tips from the printing robot; the inequality among M from different print-tips is well illustrated in Fig. 1a). Second, spots of different rows of the slide are often of different well plate sources; one can imagine that there may be effects associated with different well plates. Last, the physical condition of the slide itself could also differ region from region. Fig. 1b) reveals such artifacts on a Swirl slide by color-coding the ranks of ratios. It shows that the unnormalized ratios are not uniform, and are higher (yellow) at the middle and lower (blue) around the edges especially in the left-most column. We proceed in the next section to introduce a new stepwise normalization method and then showcase its usage on a Swirl slide in the Result section. The last section concludes with discussion and some observations.

II. METHODOLOGY

Having illustrated the existence of non-biological variations in microarray data, we review a number of

a) b)

Fig. 1. Diagnostic plots for a swirl slide: (a) MA plot with lowess fits for individual print-tip groups. (b) Spatial plot of log ratios. The plot is divided into 16 grids representing the 16 different print-tips. Spots are color coded according to the ranks of the ratios, higher ratios are colored yellow and lower ratios are colored blue.

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popular normalization methods before proposing a new systematic approach to remove such variations. Within-slide intensity bias There are currently three most applied models for the removal of the A bias from ratios. Suppose Normalized ratios are obtained as, Mnorm = M + c. Models differ in determining the correction factor c. Global median shift, the most simplistic method, assumes that c is constant regardless of the intensities of the spots (A), and it merely shifts the median of the ratios to be zero. As a refinement to global normalization, robust linear regression (rlm) recognizes the need of A-dependent correction. It does so by fitting a linear regression model. The correction factor c in this model is therefore a linear function of A. This model is sufficient when the relationship between M and A is approximately linear, but fails to correct any nonlinear relationship between them. Nonlinear methods developed by Yang et al. ([3]) applied the robust scatter-plot smoother lowess to perform a local intensity-dependent normalization; the correction factor c is therefore a nonlinear function of A. Within-slide spatial bias: Print-tip and Plate Models, such as median shift, rlm and lowess, if fitted within each print-tip (PT) or plate (PL), corrects the PT or PL bias. Median shift adjusts ratios within each PL (or PT) to be zero in an effort to correct for existing inequality between such spatial attributes, and it is a robust version of the ANOVA approach proposed by Sellers et al. ([4]). Models rlm and lowess, the latter being the most widely practiced normalization method corrects for the A and PT (or PL) biases simultaneously. Within-slide spatial bias: 2D Spatial Other than print-tip and plate effects, there could be other spatial attributes that contribute to the spatial heterogeneity (see Figure 1b)). Sellers et al. ([4]) applied an ANOVA model to test the effects due to array rows and columns. They treat the row and column effects as categorical variables; hence the spatial heterogeneity is modeled as discreet and non-uniform changes. As a result the model fits a large number of parameters as the size of arrays commonly runs up to about a hundred rows and columns. An alternative approach proposed by Yang et al. ([3]) models the spatial heterogeneity as a smooth trend by treating rows and columns as continuous variables and fitting a two-dimensional lowess curve . So doing requires much fewer parameters than the ANOVA model. Yet another way to model local spatial effects is proposed by Wilson et al. ([5]). The spatial trend in this model is estimated by computing for each spot, the median log ratio over its spatial neighborhood. The size of the smoothing element in the spatial median filter in their article is a 3 X 3 block of spots, although other sizes are also possible. This model is able to correct any local spatial trend, for example, a small streak of artifacts, yet so doing costs a lot more degrees of freedom. We have reviewed several models that could be applied for the elimination of non-biological biases in microarray data. These models differ in their assumptions and

complexities. As biases are slide- and experiment-dependent, different slides may show different intensity and spatial trends. Using one model to correct all biases in a slide or using the same model for different slides exhibiting different biases might not be adequate. A more rigorous scheme that captures the particularities of each slide by assessing quantitatively the adequacy of each model with respect to the observed data is urgently called for. Precisely for this reason, we are proposing a new normalization framework that is stepwise and adaptive in nature. This new method is hereafter called STEPNORM. Fig. 2 illustrates the procedures of STEPNORM using the example of the swirl experiment. It consists of four steps and in each step one bias is targeted for correction. The intensity A bias is usually the major source of variation and is therefore subjected to examination first. After the correction of the A bias, normalized log ratios are subjected to further normalizations based on the existence of spatial biases. As illustrated earlier, there are primarily three types of spatial biases, print-tip (PT), plate (PL) and two-dimensional effects (2D) and they will be tested sequentially. PT is subjected to testing first because the number of print-tips is usually smaller than plates and therefore costs fewer degrees of freedom; furthermore, various research ([4]) has shown the PT effect is usually more dominant than other spatial biases. In each step of our new method, there are a number of competing models of different complexities. The solution to the problem of evaluating several candidate models is to select the model that provides an adequate description of the data while using a minimum number of parameters. Take the example of the first step -- removal of A bias, among the candidate models, median shift is the simplest, estimating only one parameter -- the median; and its effect is correspondingly very limited and probably only suits for data that do not show a significant amount of linear or nonlinear trend between M and A. On the other end of the spectrum is the nonlinear local regression model lowess. Its local fitting nature accommodates corrections for non-linearity, yet doing so requires fitting more parameters and runs the risk of over-fitting. Therefore, the challenge is to select the model that achieves the best balance between goodness of fit and simplicity. One of the most popular methods, taking both data fitting and model complexity into account, is the Bayesian Information Criterion (BIC), which is defined as, BIC = -2log(\hat{L}) + Klog(N) , where \hat{L} is the maximum likelihood, K the number of free parameters in the model and N the sample size. We integrate BIC into STEPNORM as the model selection criterion; the model with the lowest BIC value is considered to the preferred model in each step. Importantly, each step also includes testing a “null” model, which doesn't fit any parameters and represents the scenario that the systematic variation in this step is not statistically significant to warrant any correction.

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Fig.2 STEPNORM procedures for the Swirl experiment

III. RESULTS We illustrate in this section the application of STEPNORM on a Swirl slide. For the correction of the A bias, we have observed that almost all data have some sort of trend between M and A, though to various degrees. To find the most appropriate model for the swirl slide, we compare three models median shift, rlm and lowess. From the inspection of the BIC values in Table 1, it is apparent that lowess is the preferred model, possessing the lowest BIC value of all models. The span parameter we used in lowess is the default value in the loess function in the statistical software R, span = 0.4. The number of free parameters required in the fitting is estimated to be 4.95 from the output of this function, which could also be approximated as follows. This span parameter defines that about 40% of points are used for a local fitting in each moving window. Each fitting here is linear and therefore requires two degrees of freedom. Totally, about 1/0.4X2 = 5 degrees of freedom are needed. The model rlm is a special case of lowess when within each local area the fitting is linear and the span size is set to 1. We have observed good behaviors of lowess for most of the slides that we have analyzed, the Swirl slide being a typical example. The results in Table 1 illustrate that due to the typical high spot density nature of microarray data, the default span parameter in the loess function in R (span = 0.4) is adequate to capture the nonlinear dependence of M on A, and it is also large enough to avoid the over-fitting concern. We proceed next to the removal of the PT bias. Fig. 1a) reveals that before any normalization is carried out intensity trends within print-tips show nonlinear tendencies. Yet,

such nonlinear trends disappeared after the first step correction. Indeed, MA plot with lowess fits within print-tips in Fig. 2c) shows largely vertical shifts and no evident curvature. Appropriately, Table 1 indicates that median shift is a better model than the more complex ones, such as rlm and lowess. The same phenomenon also applies to the PL bias. As a conclusion, this slide shows both PT and PL effects, which could be corrected by a simple median shift. The last step in STEPNORM tests if there are remaining systematic variations associated with spot locations on the slide. Fig. 2g) highlights spots with the highest and lowest 15% pre-normalization ratios and reveals some spatial effects especially in the first and last column on the slide, where high (red spots) and low (green spots) ratios show noticeable separations. Table 1 indicates that lowess is the preferred model to remove such spatial bias. Normalized ratios using the 2D-lowess model is plotted in Fig. 2h) which shows an improved distribution of ratios on the slide.

IV. DISCUSSION

Efficient normalization is crucial for microarray research. It directly influences outcomes of downstream data analyses that could give rise to important biological implication and discoveries. In this paper we have presented a new normalization procedure STEPNORM, which integrates a number of published methodologies under the same framework and assesses their effectiveness via a quantitative criterion. Such a process is applied to each individual slide in an experiment so that data (slide) specificity could be achieved.

Unlike other normalization methods, STEPNORM could avoid data under-fitting or over-fitting as it

STEPWISE NOR

Bias Models

Null median shift

rlm A

lowess Null median shift rlm

PT

lowess Null median shift rlm

PL

lowess Nulls rlm lowess med filter

2D Spatial

ANOVA

TABLE I MALIZATION (SWIRL DATA)

K -2logL (X104) BIC

0 -1.978 -1.978 1 -1.985 -1.984 2 -2.002 -2.008 4.95 -2.016 -2.011 4.95 -2.016 -2.011 4.95+16 -2.117 -2.098 4.95+32 -2.122 -2.089 4.95+79.64 -2.128 -2.051 20.95 -2.116 -2.098 20.95+22 -2.172 -2.133 20.95+44 -2.178 -2.119 20.95+112. -2.098 -2.077 42.95 -2.172 -2.133 42.95+4 -2.172 -2.130 42.95+13.6 -2.185 -2.134 42.95+ -2.105 42.95+183 -2.224 -2.020

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implements both bias detection and removal in the same context. Intensity-dependent bias in ratios are usually the most common and dominant in microarray spot measurements. Very frequently such bias exhibits as a nonlinear trend between M and A, the curvature can be estimated using a suitable robust scatterplot smoother, such as the lowess procedure, which have shown good performance for the adjustment of the A bias for most slides we have analyzed using STEPNORM. However, we have also observed that the A bias is usually a whole-slide phenomenon and doesn't localize within spots related to a specific print-tip or plate. Therefore the current common practice that performs lowess within each print-tip (LPT) to remove the A and S biases simultaneously appears to be over-fitting for most datasets. For slides like the Swirl experiment that have 16 print-tips, LPT estimates about 5 X 6 = 80 parameters when the span size is set at 0.4. On the other hand, the procedure preferred by STEPNORM applies lowess for the removal of whole-slide A bias and then employs a simple median shift among ratios in different print-tips to remove the inequality of ratios among print-tips; So doing estimates only 5 + 16 = 21 parameters.

The BIC criterion is no doubt an important component in the STEPNORM framework. It is chosen for model selection in STEPNORM for two reasons. First, it is quick to compute which makes it more appropriate than other computation-heavy criteria, such as cross-validation (CV), in the application of microarray datasets, which are usually large in size. Second, we have also observed that the

a) b)

c) d)

e) f)

g) h)

Fig. 3 Graphical display of bias before (left column) and after (right column) stepwise normalization. The first row shows MA plots before a) and after b) the removal of the A bias. The second row shows MA plots before c) and after d) the removal of PT bias, with lowess fits for individual print-tips. The third row displays boxplots of M before e) and after d) the removal of PL bias. The last column illustrates image plots of M before g) and h) the removal of 2D-spatial effects highlighting only the top 15% spots in both directions. outcome of applying BIC is largely compatible with that of applying CV (results not shown), which indicates the using BIC gives appropriate and reliable results and it is suitable in the application of microarray normalization.

ACKNOWLEDGMENT J. Q. Author thanks ... .” Sponsor and financial support acknowledgments are placed in the unnumbered footnote on the first page.

REFERENCES [1] J. DeRisi, L. Penland, P. O. Brown, M. L. Bittner, P. S. Meltzer,

M. Ray, Y. Chen, Y. A. Su, and J. M. Trent, “Use of cDNA microarray to analyse gene expression patterns in human cancer,” Nature Genetics, vol. 14, pp. 457-460, 1996.

[2] M. Schena, editor, Microarray Biochip. Eaton, 2000. [3] Y. H. Yang, S. Dudoit, P. Luu, D. M. Lin, V. Peng, J. Ngai, and

T. P. Speed, “Normalization of cDNA microarray data: a robust composite method addressing single and multiple slide systematic variation,” Nucleic Acid Research, 30(4):e15, 2002.

[4] K. F. Sellers, J. Miecznikowski, and W. F. Eddy, “Removal of systematic variation in genetic microarray data,” unpublished

[5] D. L. Wilson, M. J. Buckley, C. A. Helliwell, and I. W. Wilson, “New normalization methods for cDNA microarray data,” Bioinformatics, vol. 19, pp. 1325-1332, 2003.

Sunwoo Park1†, Glen E. P. Ropella1§, and C. Anthony Hunt1,2

1Biosystems Group, Department of Biopharmaceutical Sciences, and 2The Joint UCSF/UCB Bioengineering Program, The University of California, San Francisco, CA†[email protected] §[email protected] [email protected] http://biosystems.ucsf.edu

BioDEVS: System-Oriented, Multi-Agent, Modeling & Simulation Framework

1• It is a new work in-progress• An extension of DEVS• It supports both system-oriented and agent-based modeling and simulation• It provides a set of generic, spatial Devices - N-dimensional homogeneous & heterogeneous spaces - N-dimensional Cellular Automata with neighborhood search support

• It supports visualization & animation of various Biomimetic Devices and support libraries - 1D, 2D and 3D visualization & 4D animation - Extendible to N-Dimensional visualization & animation• It provides a reusable, configurable, and self-evolving BD repository system

OVERVIEW – Formal Specification ofBiomimetic In Silico Devices

BioDEVS:• Elucidates structural, temporal, and behavioral properties of Biomimetic In Silico Devices (hereafter, Biomimetic Devices or BDs) based on a solid mathematical formalism • Systematically and mathematically specifies Biomimetic Devices• Allow constructing scalable and modular multi-level Devices and networks of BDs• Can support hybrid multi-formalism constructions of Biomimetic Devices

Devices Classification: atomic - describes temporal behaviors of a biological system coupled - describes structural relationships and event propagation between components, where each component can be an atomic or coupled BDs

Modular Multi-Level Biomimetic Devices and Their Networks

Both a multi-level BD and networks of BDs can be constructed based on concept of closure-under-coupling*

Couplings between BDs can be established either loosely or tightly, or allowed to evolve over time

Evaluation testing can be done at the individual or aggregate Device level

Network classification:

homogeneous network (e.g., N-dimensional cellular automata)

heterogeneous network (e.g., adaptive grid network )

* Closure-under-coupling is a system property that guarantees aggregation of systems based on their coupling information is also considered as a single system in the same formalism. A coupling specifies one-directional event propagation from an event producer to a set of event consumers.

Repository Management System For Biomimetic Devices

BioDEVS will include a Device Repository Management System to facilitate Device reuse.

Goals:

Provides for Device synthesis and decomposition configuration and reuse of Devices

Facilitates evolvability of Devices

A System-oriented Multi-Agent M&S Framework

BioDEVS:

Integrates system-oriented and multi-agent M&S into a common framework

Agents are software objects that have the ability to add, remove, and modify objects and events

Philosophically, they are objects that have their own motivation and can initiate causal chains, as opposed to just participating in a sequence of events something else initiated

Support Collections of GenericBiomimetic Device Patterns

BioDEVS will support a collection of generic and extendible devices and Device components. Here is an example of such a collection from systems engineering:

Integration with High-Performance Computing Infrastructure

Provides a set of system components for a fully automated simulation environment

Supports various high performance software/hardware configurations

IOENGINEERINGB UCSF & UCB joint graduate group in

Hybrid Systems Construction

Hybrid Systems Constructions Based on: • Closure-under-coupling • Behavioral compatibility • Formalism transformation

Can Have Hybrid BDs at the: • System Level • Formalism Level • Trajectory level (or I/O)

What is DEVS?• A framework for discrete event-oriented modeling and simulation • It provides a sold mathematical formalism based on a set theory• It supports construction of multi-level, hybrid system Biomimetic In Silico Devices (hereafter, Biomimetic Devices or BDs) and networks of Biomimetic Devices

KTGPDE Bond Graph, Acausal

System Dynamics Bond Graph, Causal

DAE Non-Causal Set

DAE Causal Set Transfer Function

DAE Non-Causal Sequence

Scheduling-Hybrid-DAE

Petri Nets

Event Scheduling

Activity Scanning

DTSS

RealtimeDEVS

SymbolicDEVS

BIODEVS

DESS

DEV &DESS

Process InteractionCellular Interaction

DEVS

NeuroDEVS

State Charts

Finite State Automata

PDE: Partial Dif. Eq. KTG: Knotted Trivalent GraphDAE: Dif. Algebraic EquationDESS: Differential Eq. System Specification DTSS: Discrete Time System SpecificationDEVS: Discrete Event System Specification

Sources:1. Hans Vangheluwe. DEVS as a common denominator for multi-formalism hybrid systems modeling. IEEE International Symposium on Computer-Aided Control System Design, pg 129-34, 2000.2. Bernard P. Zeigler, H. Praehofer, and T.G. Kim. Theory of Modeling and Simulation, 2nd. Ed., Academic Press, San Diego, 2000

Formal Specification of CoupledBiomimetic Devices

Describe construction of (hybrid) multi-level BDs and networks of BDsSpecify event flows between Biomimetic Devices Abstract networks of Biomimetic Devices to a single aggregated BD

DEVSa = <Xm, Ym, D, {Md}, {Id}, {Zi,d}> Xm = {(p, v)|p Œ Portsinput, v Œ Xp}, a bag of input events

Ym = {(p, v)|p Œ Portsoutput, v Œ Yp}, a bag of output events

D : A set of component references

Md : A set of DEVS models for each d in DZi,d : i-to-d output event translation function

Zi,d : X Æ Xd, i = N : An external input translation

Zi,d : Y Æ Yd, d = N : An external output translation

Zi,d : Yi Æ Xd, i ¹ N Ÿ d ¹ N : An internal translation

Where,

Portsinput : All input ports of an atomic model

Portsoutput : All output ports of an atomic model

Xp : A bag of input events associated with a port, pYp : A bag of output events associated with a port, p

M1 M2

N

M3

M21 M23

M2

M1

N

M3

M21

M21

ZN,M1 ZM1,M2 ZM1,N

ZM1,M3

ZM1,M3

Formal Specification of Atomic Biomimetic Devices

The Atomic device represents the smallest, unbreakable biological system in the model

It consists of a set of I/O interfaces, behavior functions, and states

DEVSa = <Xm, Ym, S, dext, dint, dcon, l, ta> Xm = {(p, v)|p Œ Portsinput, v Œ Xp}, set of input values

Ym = {(p, v)|p Œ Portsoutput, v Œ Yp}, set of output values

S : set of states

dext = Q ¥ Xb Æ S, external transition function

dint = S Æ S, internal transition function

dcon = Q ¥ Xb Æ S, confluent transition function

l = S Æ Yb, output function

ta = S Æ R•, time advance function

where,

Q = {(s, e)|s Œ S, 0 < e < ta(s)}e: elapsed time since last state transition

0

State Transition Causality

S' = dext((s, e), x)

S' = dint(S)

l(S)

ta(s) S

X

Y

Behavior Causality; an example:

dext((s, e), x)

dcon((s, e), x)

dint(S) l(S)

ta(S) ta(S)

S

X

Y Atomic Coupled

OrdinaryDifferentialEquation

PartialDifferentialEquation

Processing,Queuing, &/orCoordinating

Networks,Collaborations

PhysicalSpace

Stochastic

Multi-AgentSystem

CellularAutomata

Self-OrganizedCriticality

OrganizedIntegrator

Fuzzy Logic

SpikeNeuron

SpikeNeuron

NetworksDiscrete Time/State Chart

Petri NetProcessingNetworks

N-DimensionalCell Space

ReactiveAgent

Source:Bernard P. Zeigler, Brief Introduction to Modeling and Simulation Framework and Discrete Event System Specification (DEVS), UCSF Seminar, September, 2003

Application Layer

BioDEVS Layered Architecture

Modeling Layer

Simulation Layer

Network Infrastructure Layer

PartitionerDeployerActivatorSimulator

MPI/MPP*Grid/ClusterP2P/Internet**

*MPI/MPP: Message Passing Interface/Massive Parallel Processors**P2P/Internet: Peer-to-Peer/Internet

What is BioDEVS? 2

3

4 5

6 7

8

9

10

11

C. Anthony Hunt1,2, Glen E. P. Ropella1, Li Yan2, and Michael S. Roberts3

1Department of Biopharmaceutical Sciences,

2Joint Bioengineering Program, The University of California, San Francisco, CA

3Department of Medicine, University of Queensland, AU

[email protected] http://biosystems.ucsf.edu

A Decentralization Method for Modeling the Multiple Levelsof Organization and Function Within Liver

Figures A & B show results from two different parametrization of the In Silico Liver Articulated Model against the sucrose outflow profile form rat 1. The 3 dashed curves represent the mean ± 1 std. The filled circles in Figs. A & B are results obtained using two of the parameter vectors that provide acceptable solution sets for the specific model. Smoothness of the outflow profile increases with the number of runs. Both ArtModel profiles match the data fairly well according to the Similarity Measure.

For both A & B the No. of nodes/Zone is 28, 16 and 8 for Zones I, II and III, respectively.

Total edges: A = 42, B = 50.

Intra-zone connections: AI = BI = 10, AII = 8, BII = 13, AIII = 0, BIII = 3.

Inter-zone connections: A & B(IÆII) = 14, A & B(IÆIII) = 3, A & B(IIÆIII) = 7.

The percent of total SSs that were SA was increased by 5% for B relative to A.

Number of runs = 100.

ArtModel v[2003-05-27]

Figure C shows results from one parametrization of the Articulated Model against the sucrose outflow profile form a second rat, #2. The 3 curves represent the mean ± 1 std. The filled circles in are results obtained using a parameter vectors that provide an acceptable solution set according to the Similarity Measure.

No. of nodes/Zone is 55, 24 and 3 for Zones I, II and III, respectively.

Total edges: 60.

Intra-zone connections: I = 10, II = 8, III = 0.

Inter-zone connections: IÆII = 14, IÆIII = 4, IIÆIII) = 14.

SSs: 50% SA and SB.

Number of runs = 20.

ArtModel v[2003-07-30]

The relationship between the parameter space and the Articulated Model outflow profiles is nonlinear. There is strong covariance between each of the parameters. The follow describes parameter sensitivity of the results in Fig. C.

Turbo Factor: Changes contribute most to peak height.

SA SS Length: Length of SA influences the position of peak; the larger the value, the later the peak. At the same time, the length of the SA also affects peak height: the smaller the value, the higher the peak.

SA SS Circumference: Larger values increase the peak height and move the tail toward target values.

SB SS Length: Smaller values increase the peak height and similarity score and move the tail below target values. Larger values move the tail above target values.

Maximum of SB Length: Smaller values increase the peak height and give larger similarity scores.

Minimum of SB length: When the maximum length is small (e.g., 15), smaller values (e.g., 5) increase the peak height, lower the tail, and give larger similarity scores. When the maximum of SB length is larger (e.g., 45), further changes do not significantly affect either peak height, tail location, or similarity score. Observations – A & B

The discretization of solute amount causes the variance to increse toward the tail end of the outflow profile where solute amount/interval goes to zero.

We mitigate this effect by combining results from M runs (20-30 (for these experiments) to make one study. By so doing we are representing an in silico rat liver as being comprised of M lobules.

Graph topology within the zone-based architecture is important. Pseudo-random number generators are used to vary topology. Runs were scored and the highest scoring graphs was selected as candidates to be optimized. The rest of the parameter vector was fine-tuned to optimize the ArtModel .

The relationship between the parameter space and ArtModel outflow profiles is nonlinear and, in some cases, redundant. For example, the relationship between the ratio of SA to SB and the connection topology of the graph is complex. Such nonlinearity requires searching on both parameter sub-spaces (e.g., possible graph topologies) and on the whole parameter space. It also demonstrates that the SM being used at present is inadequate.

Similarity MeasureThe Similarity Measure (SM) determines whether or not two experimental data sets (one in vitro, the other in silico) are experimentally indistinguishable, e.g., they both fall within a band of appropriate width.

SM = 1 when in silico results fall completely with the specified band for a set of in vitro data.

Neither an instantaneous nor a whole-curve comparison is appropriate because the features of the in vitro outflow profiles clearly show different variances.

A multiple observation SM is warranted.

For these studies, however, the band width is based on the Global Standard Deviation (std) of each outflow profile data set, and that is calculated as follows.

First, a relative difference is computed on the multiple nominal time series. Then, we pool the normalized data and take the standard deviation.

{ni}i = ({di}i – mi)/mi cvariation = std({ni}i)

The envelope is then defined using:

upperi = mi·(1 + cvariation), loweri = mi·(1 – cvariation).

These bands form the similarity envelope around the outflow profile. The similarity score is then calculated.

The in vitro liver perfusion protocol and experimental data is detailed in Roberts and Anissimov1.

Solute is injected into the entering perfusate of an isolated rat liver. The measured time course of solute outflow contains information about the liver architecture, physiology, and subcellular biochemistry as encountered by the solute – each unique solute "sees" the liver from a unique perspective and "experiences" only specific aspects of the hepatic environment.

We consider ratios and normalized values rather than exact values and units. We use output fraction versus time to compare solution sets.

The initial modeling task is to extract from solute outflow profiles as much information as possible about vascular

structure and architecture of the experimental liver. For that task 14C-sucrose is used because it neither binds significantly to tissues not partitions into cells.

Two in silico models are implemented. The Reference Model is the accepted, reference mathematical model2. It too is a functional unit model, but it is not articulated.

Articulated Model: Parameter vectors are based on experimental data in combination with criteria for likely solutions. Given input parameters and initial conditions the model is run until some stopping criteria are met.

Output is logged over time. Model outflow profiles are identified as being close, or not, to the corresponding in vitro data using a Similarity Measure.

*FURM web site: http://biosystems.ucsf.edu/Researc/furm/index.html

Model Development Goals and GuidelinesDefine a new class of articulated biological simulation models that can achieve a higher level of biological realism because they are event-driven.

Articulated Model (ArtModel) – Composed of components that are easily joined and disconnected, that can represent dynamic spatial heterogeneity at different levels of resolution, and that are replaceable, reusable and easily adaptable to represent other tissues and systems.

Design models and components that they are articulated.

Use a middle-out model design strategy: begin with the primary functional units.

Implement models that represent the hepatic lobule and that can be extended to account for the hepatic disposition of solutes.

Use multiple models to cover more of a systems behavior space. Implement a method for building a multitier, in silico apparatus designed to support iterative experimentation on multiple models.

We refer to this method as FURM: Functional Unit Representation Method*

References1. Roberts MS, and Anissimov YG., Modeling of Hepatic Elimination and Organ Distribution

Kinetics with the Extended Convection-Dispersion Model, J. Pharmacokin. Biopharm. 27(4):343-382, 1999.

2. Hung DY, Chang P, Weiss M, and Roberts MS. Structure-Hepatic Disposition Relationships for Cationic Drugs in Isolated Perfused Rat Livers: Transmembrane Exchange and Cytoplasmic Binding Process. J. Pharmacol. Exper. Therap. 297(2):780–89, 2001.

3. Czarnecki K and Eisenecker U. Generative Programming: Methods, Tools, and Applications. Addison-Wesley, pp. 10, 251-254, 2000.

4. Davis PK. Dealing with complexity: Exploratory Analysis Enabled By Multiresolultion, Mu ltiperspective Modeling, Proceedings of the 2000 Winter Simulation Conference, J. A. Joines, R. R. Barton, K. Kang, and P. A. Fishwick, eds. (PWSC2000), 293-302, 2000.

5. Grinspun E, Krysl P, Schroder P. CHARMS: A Simple Framework for Adaptive Simulation. ACM TOG, 2002 / Proceedings of SIGGRAPH 2002.

Results – A & B

Results – C

A portion of the behavior space of a biological system within an organism.

Laboratory experiments cover only a tiny aspect of a system's behavior. Mathematical models typically over focus on such narrow, well-defined behavior, and they lack flexibility to adapt to represent more of the behavior space. They over-simplify and by so doing can ignore key features of a systems true complex nature. They can also be too inflexible to represent that same aspect of behavior when viewed from a different perspective.

New modeling and simulation methods are needed that are sufficiently flexible and adaptable to cover much larger portions of the behavior space.

To understand how and why biosystems function as they do we need to build (assemble, synthesize) simulation devices, and then iteratively test and refine them.

Scientific Problems, Issues, and Needs 1

The Biological and Medical Problems

The multiple levels of organization within the liver have made informative modeling and simulation difficult.

Drug effects are influenced by functional heterogeneity within levels, which in turn is influenced by the health of the liver.

To link genotype to hepatic phenotype and make better predictions, we need a better understanding of how and why these levels function as they do in health and during disease.

The primary functional unit of the liver is the lobule.

Within lobules there is spatial heterogeneity. Sinusoids contain heterogeneous microenvironments:

different flows,

different topographic arrangements, and

different surface to volume ratios.

Hepatcytes have location dependent phenotypes.

Gene expression within hepatocytes is location dependent.

3The overall project goal is to have one in silico model that can account for the hepatic outflow profiles of any combination of the six drugs and be able to shift to either of two disease states, and in those states also successfully account for the out-flow profiles of the six drugs. To achieve this goal we have design and qre building an In Silico Liver (ISL) that has the following properties:

It decouples the various aspects of functional units.

It builds on a middle-out model design strategy to enable and encourage development of different (multiple) models.

It serves as an example of the new class of generative biological simulation models whose components are easily joined and disconnected and are replaceable and reusable.

It works by decentralizing the modeling process without requiring that all of the data be of a specific type.

It does not require any particular formalism. Rather the experimental framework is formulated using Partially Ordered Sets.

4

6

12

13 14

15

Sinusoidal Segment (SS)

Network Level Chemistry

Primary Unit

Lobule

Sinusoid Networkas Directed Graph

Cell Biology

LIVER

PV AA

Acinus

CV

Zone II

Zone III

Zone IPV

CV

Liver Lobe

ZoneI

Zone II

Zone III

Agent A

Agent B

AgentC

Modular Molecular Networks Agents Represent ModulesWithout Loss of Information

Blood

Grid A

Grid C

Grid BHepatocyte

Flow Endothelial Layer

Space of Disse

IntrahepatocyteAgents

Hepatocyte Layer

Blood "Core"

Currently

Implemented

In Planning

In Planning

Levels of Liver O

rganization, M

odel Resolutio

n & Liver F

unction

The properties of grid points can be homogeneous or heterogeneous – as

illustrated here – depending on the specific requirements and the available data.

To account for sinusoidal heterogeneity (transit times, flow, topography, different surface to volume ratios within zones, etc.), we defined two classes of in silico SSs, SA and SB. The SA have a shorter path length and a smaller surface-to-volume ratio. The SB have a longer path length and a larger surface-to-volume ratio.

Each ArtModel is a directed graph. Each shortest path has either two or three nodes. Either a SA or SB agent is placed at each node. We allow for cross connections between any two adjacent nodes within Zones I and II. The PV and CV are sources and sinks for solutes.

Graphs and Networks Play Key Rolesin This New Class of Models

Messages and events characterize the medium of information flow in biology at all levels. Networks – coherent nodes communicating over quasi-stable paths – can represent that flow. In the In Silico Liver everything is a network because everything happens via messages, from object to object, over a medium that handles events. Both the objects and the medium can be dynamically created, atomic, or composite. Objects can be identified as nodes in a graph

A

B C

This illustrates Adaptive Simulation (see right) at the molecular level. The graph represents a portion of a larger, interconnected molecular network that has three subnetworks, A, B & C. The edges represent quasi-stable paths for information flow as messages and/or events. Having a mechanism for realizing networks allows us to replace sub-networks (at any location) with rules-based software modules. In this illustration each of the three subnetworks is replaced by a rule-based agent.

500 mm

CV

Fr: Teutsch, et al., Hepatology 29, 495, ‘99.

5

5

Flow Chart of Solute (S) OptionsWithin the Articulated Model (ArtModel )

PV CV

PV CV

Secondary Unit To account for disease heterogeneity within the liver we can substitute "diseased" for normal objects (hepato-cytes, SSs, lobules or secon-dary units) at what ever levels of resolution are needed.

A solute object represents molecules moving through the articulated model. In silico, solute behavior is dictated by rules specifying the relationships between solute type, location, and proximity to other objects and agents. Those rules can be specified to take into account the solute's physicochemical properties. D in PV

EnterSinusoid

Rim or Core?Coreenter

Core

RimMoveenterRim

Yes exitCore? Move

No

No Jump 2Rim

Exit?

ESpace

Core

Jump

enterESpace

ESpace

enterSoD

SoD

SSpaceJump

enter EC

Jump

enterHepatocyte

Metabolize

Yes

Yes

No

No

No

StartTimer

Move

Move

Wait

Destroy D

Done

Bind?

ExitEC?

ExitHep?

Yes

NoYes

Yes Yes

No

StartTimer

WaitBind?

TimerOff?

Yes

No

No

Yes

Yes Yes

No

No

Yes

TimerOff?

No

Key AssumptionsFive Primary Assumptions:

1. Physiologically accurate models are necessary to begin fully exploring the liver behavior space.

2. Hepatic vascular structure and the arrangement of lobules within a lobe can be represented by a directed graph.

3. Liver function is an aggregate of lobular function, with the lobule being the primary functional unit.

4. Solute transit times are governed by stochastic interactions between solute and agents inside the vascular structures in combination with perfusion pressure.

5. Outflow for sucrose, but not metabolized or transported solutes, is solely a function of the extracellular (vascular cavity) space and its geometry.

9

Framework of the In Silico Liver– Key Components –

7

10Project Goals and Objectives

Data Mgmt.Module

GMLFile

LobuleSpec.

ParameterMgr.

ExperimentAgent

DataModel

ReferenceModel

ArticulatedModel

Data Mgmt.Module

StatisticalObserverModule

Control

Control

Control

Control

Data

Data

Data

Data

Data

Data

Data

Data

Control

Control

Files &DatabasesData

Flow Link: Path by whichparticles flow

SS

SS

SS

SSSS: Sinusoidal

Segment

SS

SS

SSSS

Flow

Zone IZone II

Zone III

Link

PV:PortalVein

CV:Central

Vein

Illustration of a Vascular Graph Segment– Maps to Lobule –

DosageFunction

Vascular Graph is one Componentof the Articulated Model

Use FURM to iteratively create, execute and analyze model variants in the context of experimental procedur-es and available data.

Follow four fundamental guidelines:

Standardize interfaces to multiparadigm, multimode, and trans-domain models

Use discrete interactions

Enable knowledge discovery by designing for an extended life cycle (so that models will outlast a given research agenda), and

Define observables that will submit to a Similarity Measure.

Aspect Oriented Modeling – Aspect-Oriented Programming3 is used to develop systems where any one usage is likely to exercise only a small portion of the system. Developers focus on separable aspects of the system. We extend these ideas into FURM and refer to the result as Aspect-Oriented Modeling (AOM). AOM assumes that there are many, possibly infinite, similarly plausible models that can adequately describe the referent system and account for the available data4. The researcher iteratively explores and systematically shrinks the space of potential models in search of a set of models that make sense in a given context, e.g., they exhibit sufficient biological realism.

Iterative Modeling – Start with an unrefined model and parametrization. Modify any given piece of the model or reparameterization to improve preformance. This process continues until acceptable coverage of the targeted solution space is obtained. Next, the parameter space is searched. Similarity Measures are specified to identify solutions for which the model validates.

Validation and Verification – A DatModel (data model) is used to represent the biological system. During validation a solution set is compared to the DatModel using a Similarity Measure. Because FURM uses multiple models, verification is defined as comparing one model solution set to another and is a generalization of validation.

Model Granularity – All functionality is captured within FURM in a method or object. Functional granularity defines how composable, adaptive, and scalable the model will be. The articulated model that is fine-grained at all levels. We use three concepts in categorizing functional granularity: fine-grained execution control, fine-grained spatial specificity, the ability to package modules arbitrarily.

Encapsulating Experimental Procedures – We promote sound methodology by following these guidelines:

prefer models that track the perceived characteristics of the referent system

model only the most salient characteristics of the referent;

focus first on a coarse or abstract description of the referent, etc.

To bound any wandering of the process, FURM encapsulates experimental procedures. It establishes the experimental context in which the to-be-implemented models must perform. The experimental procedure consist of measures to be taken on the models, the execution paradigm used, and the reporting requirements for measurements and model execution.

Adaptive Simulation5 – When fine-grained parts of a model (e.g., transporter or signal transduction networks in hepatocytes) minimally influence the particular system property being studied (e.g., metabolism of a solute), we can ignore them or replace them in the simulation (even during a simulation) with alternative components (agents in this example) that roughly approximate their behavior. When attention shifts to behavior where those components have significant influence we can return to using the original parts.

Computational Methods 8

EngineeringDesign, Specs,

Prototype

InductiveModeling

In SilicoDevices

SyntheticModeling

Set UpExperiment

M

RA

MR G

Instantiate

Represent

Paths thru AR space: data

LanguageElements

Experiment

AP

Discover,Find Patterns

Opinion,Decision

Mine paths

Analyzed Data,Patterns

Cogitate

AO

PD RS

L

Generators,Building blocks

Mental model

Actualization

Satisfaction

Representations

2

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0 10 20 30 40 50 60 70 80 90 100 110

Fra

ctio

n

Time, sec.

C

Experimental Procedures

Fra

ctio

nF

ract

ion

Time, sec.

A

B

Model ParametersSinusoidal Segment (SS) circumference (min, max)SS length (a. b, g)Solute Scale (molecules per solute "particle")Solute Dose (mass, constituents, timing)Turbo (effective solute flow pressure)Graph Structure (number of SSs, connections between them)

Fenestrations (size and prevalence)Hepatocyte Relative DensityIntra-Cellular binding agents (min, max)Probability of binding (given coincidence of a solute and binding agent)Probability of being metabolized (given coincidence of solute and enzyme)Mean time solute bount to binding agent

11

Observations – C

2004 annual report - engineeringoren/scs_msnet/ar2004/bsg-2004.pdf · connects in silico pv outlets...

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