biomolecular swarms - university of...

Biomolecular SwarmsAn Agent-based Model of the Lactose Operon

Christian Jacob ([email protected])Dept. of Computer Science, Faculty of ScienceDept. of Biochemistry & Molecular Biology, Faculty of MedicineUniversity of Calgary, Calgary, Alberta, CANADA

Ian Burleigh ([email protected])Dept. of Computer Science, Faculty of ScienceUniversity of Calgary, Calgary, Alberta, CANADA

Abstract. We present our latest version of a swarm-based, 3-dimensional model ofthe lactose (lac) operon gene regulatory system. The lac operon is a well-understoodgenetic switch capable of self-regulation dependent on the energy source of lactose.Our model includes a 3D visualization which simulates proteins as agents with phys-ical properties that interact with DNA, molecules, and other proteins, incorporatingmany of the important aspects of a genetic regulatory system. Our model utilizes adecentralized swarm approach with multiple agents acting independently—accordingto local interaction rules—to exhibit complex emergent behaviours, which constitutethe externally observable and measurable switching behaviour. 1

Keywords: Agent-based Biological Modelling, Gene Regulatory System, LactoseOperon, Bioinformatics, Simulation, Swarm Intelligence

1. Introduction

Current research in genomics focuses on understanding the genetics ofmodel organisms, such as the bacterium Escherichia coli, the nema-tode Caenorhabditis elegans, and the fruitfly Drosophila melanogaster.Working with these simple biological models helps to elucidate morecomplex processes found in higher order gene networks. Major advancesin systems biology will more and more be enabled by the utilization ofcomputers as an integral research tool, leading to new interdisciplinaryfields within bioinformatics and biological computing. Innovations inagent-based modelling, computer graphics and specialized visualiza-tion technology, such as the CAVEr Automated Virtual Environment,provide biologists with unprecedented tools for research in ‘virtuallaboratories’ (Burleigh et al., 2003). In this paper, we present ourlatest version of a swarm-based, 3D model of the lactose (short: lac)operon, one of the most basic and well-understood biological systems ofgene regulation. Several computer-based models of the lac operon ex-ist, including simple grammar-based approaches (Collado-Vides, 1992),

1 to appear in: Journal of Natural Computing, Kluwer, 2004.

c© 2004 Kluwer Academic Publishers. Printed in the Netherlands.

LAC-Swarms-Final-Print.tex; 18/10/2004; 14:30; p.1

2 Jacob and Burleigh

Functional Hybrid Petri Net models (Matsuno et al., 2001), systemsbased on rewrite rules (Suen and Jacob, 2003), and systems based onlarge sets of differential equations (Tomita et al., 2000).

However, current models of biomolecular systems, such as the lacoperon, still have major shortcomings regarding their usability for bi-ological and medical research. Most models do not explicitly take intoaccount that the measurable and observable dynamics of biomolecu-lar systems result from the interaction of a (usually large) numberof ‘agents’, such as proteins, peptides, signaling molecules or macro-molecules (e.g., DNA). With our agent-based models, simulations andvisualizations that introduce swarm intelligence algorithms into bio-molecular systems, we develop highly visual, adaptive and user-friendlyinnovative research tools, which, we think, will gain a much broaderacceptance in the biological and life sciences research community—thus complementing most of the current, more abstract mathematicaland computational models (Salzberg et al., 1998), (Bower and Bolouri,2001).

In this paper we propose an agent-based model of the lac operonthat incorporates many important gene regulatory aspects of the sys-tem in a spatial, 3-dimensional cell environment, including the moreuniversal processes of transcription and translation. In section 2, wepresent a brief synopsis of the lac operon gene regulatory system asit is commonly understood in biology. In section 3, we discuss ouragent/swarm-based implementation of the lac operon, highlighting themodelled processes and structures. Section 4 gives a step-by-step de-scription of a simulated lac operon switching cycle, which we analyzein more detail in Section 5, showing the validity of our model.

2. The lac Operon: A Gene Regulatory System

An operon is a group of genes located on the DNA of bacteria. JacquesMonod and Francois Jacob first studied the lac operon in the 1960s(Jacob and Monod, 1961). Found in the bacterium Escherichia coli (E.coli), the lac operon paradigm stands as a key finding in genetics, asit constitutes one of the most basic gene regulatory systems known,and is consequently used as a basis for studies of more complex geneticsystems.

The lac operon, in particular, is a gene system that is responsible forconverting the sugar lactose into glucose, a key energy source for thebacterium, and galactose. E. coli is a prokaryotic organism withouta nucleus that is normally found in a lactose-rich environment, suchas the gut of humans. E. coli requires glucose for much of its growth


An Agent-based Gene Regulation Model 3

and has evolved a solution for obtaining glucose from its environmentby converting lactose into glucose and galactose. This conversion isaccomplished through the enzyme β-galactosidase, which is one of theproducts of the lac operon. In the presence of lactose, the lac operonis turned on and hence produces β-galactosidase. When lactose is nolonger present, the lac operon turns itself off and consequently stopsthe production of β-galactosidase, thus conserving cellular resources. Inthis manner, the lac operon is capable of sophisticated self-regulationmainly mediated by the interactions of repressor proteins, lactose, β-galactosidase, and the DNA (Beckwith and Zipser, 1970), (Muller-Hill,1996), (Ptashne and Gann, 2002).

2.1. Self-Regulation of the lac Operon

Gene-based self-regulation is an emergent property resulting from theinteraction of proteins, enzymes, molecules, and DNA. In order to un-derstand how this ‘emergence’ is accomplished through the interactionsof ‘swarms’ of agents (on which our simulation is based), we will de-scribe the lactose operon in much closer detail (Figs. 1 & 2). The maincomponents of the lac operon as a regulatory unit on the bacterial DNAconsists of four genes: lacZ, lacY, lacA, and lacI.

2.1.1. Gene Complex 1: lacZ-Y-AThe lacZ-Y-A genes appear as a single module and are located adjacentto one another on the operon (Fig. 1). A control complex consistingof an operator and a promoter precedes the three genes. The operatorcontrols the expression of these genes. Producing a protein from a givengene is accomplished through RNA polymerase, which reads a sequenceof genes, resulting in the production of their corresponding proteinsthrough the processes of transcription and translation (Section 2.2).

2.1.2. Gene Complex 2: lacIThe lacI gene, the second key module, is located downstream of themain lac complex (Fig. 1). It likewise contains a promoter region, andproduces proteins with the help of RNA polymerase. The lacI geneproduct is known as a repressor, which has the ability to bind to theoperator region and prevent RNA polymerase from reading the lacZ-Y-A genes. Hence, the repressor serves as the basic control mechanismfor the lac operon.



LacI Pi P O LacZ LacY LacA

RNAPolymerase

+ Ribosomes

mRNA

I

No mRNA and no proteins

I

Repressor bindsto operator

Figure 1. After RNA polymerase docks onto Pi, the LacI promoter site, it tran-scribes the LacI gene into its mRNA representation, which is then translated byribosomes into the repressor protein I. This repressor binds to the LacZ-Y-A oper-ator site, which in turn blocks RNA polymerase; hence, none of the three genes areexpressed.

2.1.3. Turning the SwitchWhen lactose enters the cell, the lac operon can turn itself on (Fig. 2).This is accomplished through the binding of lactose to the repressorto form a repressor-lactose complex. Due to conformational changes,the repressor-lactose complex cannot bind to the operator region ofthe lacZ-Y-A genes any more. Consequently, this allows RNA poly-merase to now read lacZ, lacY, and lacA—producing β-galactosidase,lactose permease, and transacetylase, respectively. Among these threegene products, β-galactosidase is the enzyme that converts lactose intoglucose and galactose. Lactose permease enhances the movement oflactose from the outer environment into the cell, whereas transacetylasedoes not seem to play a role in this regulatory system (Ptashne andGann, 2002), (Alberts et al., 1998).

Once lactose is removed from the system, the repressor is, again,free to bind to the operator region and terminate the production of β-galactosidase (Fig. 1). In this manner, the lac operon is able to regulateits own gene products.



LacI Pi P O LacZ LacY LacA

RNAPolymerase

+ Ribosomes

mRNA

I

+ Ribosomes

mRNAs …

YZ A

Conformational change

blocked

Lactose

Figure 2. When lactose enters into the cell, it induces a shape change in the repres-sors that disables them from binding to the operator. Consequently, the LacZ-Y-Agenes are accessible by the RNA polymerase and are expressed as proteins Z, Y, andA.

2.2. Transcription and Translation

Once genes are ‘switched on’, RNA polymerase has access to the en-coding regions of the structural genes on the DNA. The processes oftranscription and translation serve as intermediary steps in order toproduce proteins from a given gene. Transcription is the process of con-verting Deoxyribose Nucleic Acid (DNA) into an intermediate moleculeknown as messenger Ribonucleic Acid (mRNA). The enzyme RNApolymerase is responsible for this particular conversion, which proceedsas follows: (1) RNA polymerase searches along the DNA structure un-til it encounters an appropriate promoter region. (2) Starting at thepromoter region, RNA polymerase begins to synthesize mRNA basedon the genes found adjacent to the promoter. (3) Once transcriptionis complete, the mRNA strand is free to undergo a second conversionprocess (through translation), whereas RNA polymerase reiterates theprocess of transcription.

During translation a protein is synthesized from an mRNA strand.This mRNA-to-protein conversion is achieved through the action ofribosomes and transfer RNA (tRNA) as follows: (1) A ribosome locatesand attaches to a free mRNA strand. (2) The ribosome begins to read



the strand and synthesizes a chain of amino acids with the supportof tRNA. The chain then folds into a 3-dimensional protein structure.Multiple ribosomes can simultaneously read and synthesize proteinsfrom a single mRNA strand. Once translation is complete, the ribosomedetaches from the mRNA strand and releases the newly made protein.

Figure 3. Zooming into a simulated E. coli cell. All intra-cellular interactions areconfined within a spherical cell. The cell wall is being opened while getting closertowards the center of the cell.

3. A Biomolecular Swarm Model

Our computer implementation of the lactose operon model and itsvisualization incorporates a swarm-based approach with a 3D visu-alization (Fig. 3) (Bonabeau et al., 1999). Each individual element inthe simulation is treated as an independent agent governed by simplerules of interaction. Dynamic elements in the system move randomly,executing specific actions when interacting with other agents, which alloperate within the confines of the cell. Each agent follows a set of rulesthat define its actions in the system. As an example, we show a sampleof the behaviour rules of RNA polymerase in Table I.

The simulation system provides each agent with basic services, suchas the ability to move, rotate, and determine the presence and positionof other agents. A scheduler implements time slicing by invoking eachagent’s Iterate method, which executes a specific, context-dependentaction. These actions are based on the agent’s current state, and the



state of other agents in its vicinity. Our simulated agents work in adecentralized fashion with no central control unit to govern the inter-actions of the biomolecular agents.

There are two specific instances where we have restricted the random-walk movements of agents (Allen, 2003) in order to more acuratelycapture agent interactions with the DNA. RNA polymerase has a natu-ral affinity for DNA. Hence, our RNA polymerase agents will randomlymove within a defined area located around the DNA. In addition, re-pressor proteins have a high affinity for the operator region of the lacoperon. Consequently, we direct the repressors towards the operatorregion, while maintaining their random movements.

A swarm-based approach affords a measure of modularity, as agentscan be added and removed from the system, producing different resultseach time the simulation is run. This is in contrast to common modelsof gene regulatory systems that are usually scripted. In addition, com-pletely new agents can be introduced into the simulation. This allowsfor further aspects of the lac operon to be modelled, such as lactosepermease or the CAP activator complex that promotes the productionof β-galactosidase.

3.1. Modelling Circular DNA

We represent the actual encoding of the lactose operon gene as acircular DNA double-helix with its characteristic Watson-Crick com-plementarity pattern (Figs. 4 & 5)1 (Watson and Crick, 1953). DNAconsists of four nucleotide bases: Adenine, Cytosine, Guanine, andThymine. A grouping of three such bases is known as a codon, whichcodes for a specific amino acid, the basic building blocks of proteins.Due to the vast amount of bases that make up the genes involvedin the lac operon, we represent the genetic information as codons.These codons directly correspond to the amino acid composition oftheir associated proteins. We visualize these codons as colour-codedcylindrical sections that make up the DNA strand (Fig. 5).

3.2. Modelling Gene Structures

There are two distinct gene regions in the lac operon: the lacI and thelacZ-lacY-lacA region (compare Section 2.1). For the purposes of thismodel, we have chosen to only model the lacI and lacZ gene regions.The lacY and lacA genes do not greatly impact the understanding

1 The DNA is kept still within the cell. In this model, we do not consider anythermal fluctuation of DNA, such as translation, rotation, or chain flexibility.



Table I. Rules governing the behaviour of RNA polymerase as an example swarm agent.Pseudocode is presented with each state of RNA polymerase outlined. The correspondingbiological actions are described in the right column.

Iterate Pseudo Code Biological State and Action

case state of

FLOATING: /* initial state */if near DNA:attach to nearest DNA codonstate = DOCKED

else:move randomly within the cell

Floating:RNA polymerase is usually found nearDNA and moves about the cell in a ran-dom manner. In this state, RNA poly-merase will attempt to attach itself to thenearest free DNA strand.

DOCKED:if promoter region is reached:state = READY TO TRANSCRIBE

else:move along DNA to next codon

Docked:Once RNA polymerase has docked ontoa free DNA strand, it will begin readingthe DNA.

READY TO TRANSCRIBE:create an empty mRNA moleculestate = TRANSCRIBING

Ready to Transcribe:When a promoter/operator sequence isfound, the RNA polymerase will begin toinitiate transcription.

TRANSCRIBING:if a stop codon is reached:release constructed mRNAstate = DETACHED

else if blocked by a repressor:destroy partial mRNAstate = DETACHED

else:move to the next codonappend codon mRNA

Transcribing: RNA polymerase willtranscribe the DNA sequence into anmRNA molecule. RNA polymerase readseach codon sequentially, and appends anew base to the growing mRNA molecule.This process is completed once RNApolymerase encounters the appropriatestop codon. RNA polymerase will thendetach itself from the DNA.

DETACHED:detach self from DNAmove randomlystate = FLOATING

Detached:Once RNA polymerase has detached fromDNA, it will again resume its randommovement in the cell.

end case



Figure 4. RNA polymerases attach to the DNA and start scanning along a strand.Once a lac operon is identified, the polymerases search for a viable promoter regionto begin transcription.

of the system and are therefore not included in our current model.2

The lacI and lacZ gene regions are labeled appropriately on the model(Fig. 5). In addition, the promoter and operator regions that precedethe lacZ gene are also included. To further clarify the model, the codonnumbering is shown as well, highlighting various aspects of the DNAcoding sequences. Conventional models of DNA include the −10 TATAbox and the −35 TTGACA RNA polymerase recognition sites, relative tothe promoter region.

2 The codons around the two operator sites and the stop codons represent theactual sequences from the E. coli genome. The rest of the circular DNA consists ofrandom codons. Incorporation of the complete lac operon-related genome is possiblein our model and will be part of a next version of our biomolecular simulation systemcurrently under construction.



Figure 5. The operator region and the lacZ gene on the double helix. Each strandis composed of colour-encoded codons. Shown are also the −10 TATA box and the−35 TTGACA RNA polymerase recognition sites. Analogous labels exist for thelacI gene region.

Figure 6. Once transcription is initiated (Fig. 4), RNA polymerases produce mRNAstrands, undergoing translation by multiple ribosomes. The ribosomes construct theamino acid (AA) chains of unfolded proteins (repressors and β-galactosidases) basedon the mRNA codon sequence.



Figure 7. The repressor binds to the operator region of the lac operon and turns itoff. A lactose-repressor complex has formed, preventing the repressor protein frombinding to the operator.

3.3. Modelling Transcription and Translation

RNA polymerase, the initiator of transcription, is represented as adark brown (detached) or pink (attached) sphere (Fig. 4). Once RNApolymerase attaches to a DNA region, it starts scanning along the chainof codons. Transcription occurs once RNA polymerase has encountereda viable promoter region. Genes adjacent to the promoter region aretranscribed into mRNA, represented as a twisted single-strand helix(Fig. 6). Again, we have taken the liberty of representing the mRNAgene material as codons corresponding to the actual nucleotide basesequence. The process of translation occurs once the mRNA strand hasbeen synthesized. Ribosomes attach to a free mRNA strand and beginto synthesize the associated protein. The unfolded protein is shown asa strand of disks. Multiple ribosomes can simultaneously read a singlemRNA strand, as illustrated in Figure 6. Once a chain of amino acids iscompletely synthesized, the ‘unfolded protein’ turns into its associatedprotein, such as a repressor or β-galactosidase. All folded proteins arerepresented as spheres of different sizes and colours, more details ofwhich are described in the following section.



(a) (b)

(c) (d)

(e) (f)

Figure 8. Different stages of the lac operon simulation. (a) RNA polymerase searchesfor a promoter region. (b) RNA polymerases synthesize mRNA molecules. Ribosomessynthesize proteins. (c) Repressors (on the bottom right) around the operator blockRNA polymerase from transcribing the LacZ gene. (d) Lactose is introduced intothe system. (e) Lactose binds to repressors preventing them from blocking RNApolymerase. Three RNA polymerases (on the left) have just started transcribing theLacZ gene. (f) Most of the lactose is split into glucose and galactose.



4. Simulating Gene Regulation

In the case of the lac operon, the two kinds of proteins synthesizedthrough the processes of transcription and translation are repressorproteins and β-galactosidase enzymes (Figs. 7 & 8). Repressors have anatural affinity for the operator region of the lac operon. They attemptto bind to the operator region and physically block transcription of thelacZ gene. This turns the lac operon off. This sequence of events isillustrated in Figure 8(a-c) through snapshots taken during our sim-ulation over 1000 iteration steps. In Figure 8c the operator site issurrounded by a number of repressors, which ensure that the operatoris blocked (almost) all the time, such that no RNA polymerase canproceed past the operator site.3 Therefore, at this stage, the expressionof β-galactosidase is suppressed, whereas repressors are still produced(see the mRNA strands and ribosomes working in the background onthe right half of the DNA).

Once lactose is introduced into the cell (Fig. 8d), two things willhappen. First, repressor-lactose complexes are formed, which cause anybound repressor to be released from the operator site (Fig. 7). This,in turn, enables RNA polymerases to pass beyond the operator andinitiate expression of β-galactosidase. In Fig. 8e, three polymerases havealready started to scan past the operator in the bottom left part of theDNA. Second, each of the produced β-galactosidases will start to breakdown lactose into glucose and galactose (Fig. 8f). As soon as all lactoses,including those bound to any repressor, are broken down, repressors willagain start to attach to the lacZ operator, blocking any further pro-duction of β-galactosidase. All the particles (except RNA polymeraseand ribosomes) in the simulation system have a predefined lifespan,so that if a protein is not constantly expressed, it will eventually bedegraded. Consequently, the simulated cell will finally switch back to astate analogous to Fig. 8c, where only repressors are expressed.

5. Analysis of Simulation Data

During each simulation we protocol the concentrations of all particlesinvolved. Figure 9 shows the concentration graphs obtained from thesimulation illustrated in Figure 8, which ran over 1000 iteration steps.Initially, there are no repressors or β-galacosidases in the system. Al-though the number of repressors increases over the first 200 iterations, it

3 Here the ‘switch-off’ state is an emergent property, resulting from the interac-tions of multiple repressor proteins.



Figure 9. Concentrations of the biomolecular agents of the lactose simulationillustrated in Figure 8.

cannot prevent the production of some β-galactosidase enzymes. How-ever, once the repressor concentration has reached its initial peak, itcompletely blocks the lacZ operator, which stops any further expressionof β-galactosidase (around step 400). Shortly after iteration step 400,lactose is introduced into the cell, which almost immediately triggersthe formation of repressor-lactose complexes. Now that free repressorsare too few to block the operator, after a short delay the numberof β-galacosidases increases, resulting in a rise of both glucose andgalactose. The lifetime of lactose within the cell was set to 350 timesteps, which reduces the lactose concentration to zero shortly beforeiteration step 800. This causes the repressor concentration to build upagain and resume repressing β-galactosidase production, which bringsthe system back to its initial state with a high number of repressorsand no β-galactosidase.



6. Conclusion and Future Work

We have presented a 3D agent-based model of the lac operon gene regu-latory system, including a fast visualization engine. Currently, we workwith both a Java3D and a C++/OpenGL version of our simulations.The model focuses on simulating important aspects of a biomolecu-lar system including basic genetic processes such as transcription andtranslation. We believe that such simulations and visualizations will notonly serve as powerful educational tools, but will also greatly supportbiologists in their understanding of complex gene regulatory systems,and decentralized, massively-parallel biological systems in general.

A decentralized, swarm approach for modelling the lac operon closelyapproximates the way in which biologists view such systems. Althoughour simulations have so far only been tested for a relatively smallnumber of (hundreds of) interacting agents, the system is designedto handle a much larger number of proteins and other cellular en-tities, thus getting closer to more accurate simulations of massively-parallel interaction processes within a cell that involve hundreds ofthousands of particles. The visualization, developed as a 2D projectionon a normal computer screen, is further enhanced through stereoscopic3D in a CAVEr immersive environment (Burleigh et al., 2003). On theother hand, we are also investigating how the number of biomolecularagents actually affects the emergent behaviour patterns, which we ob-serve in our simulations and which can be measured in vivo in wet-labexperiments.

Future work includes integrating additional aspects of the lac operonnot covered in the current model. This includes the CAP Cataboliteactivator complex, that acts as an initiation factor for promoting theproduction of β-galactosidase based on glucose concentrations, andlactose permease, which facilitates the entry of lactose into the cell.Another important step is to tune the model towards experimental dataderived from E. coli wetlab experiments. Our model also enables us toreconstruct other regulatory systems (such as the λ-switch (Ptashneand Gann, 2002) or the repressilator (Elowitz and Leibler, 2000)) andinvestigate general robustness properties of gene regulatory systems.We also plan to incorporate an evolutionary computation engine intothe simulation, such as the Evolvica system (Jacob, 2001). Evolutionof this gene system may lead to interesting and complex behavioursthat can be compared with other gene regulatory systems evolved bynature. On the web site

http://www.cpsc.ucalgary.ca/∼jacob/ESD/LacOperon.



one will find further information about our lactose operon model andother swarm-based models of biological systems, such as the λ-switchand an artificial immune system.

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