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Title 1 Multi-scale model of Mycobacterium tuberculosis infection maps metabolite and gene 2 perturbations to granuloma sterilization predictions 3 4 5 Running title 6 Mapping genetic- to granuloma-scales in tuberculosis 7 8 9 Authors 10 Elsje Pienaar1,2, William M. Matern3, Jennifer J. Linderman1, Joel S. Bader#3, Denise E. 11 Kirschner#2 12 1Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan, USA, 2Department of 13 Microbiology and Immunology, University of Michigan Medical School, Ann Arbor, MI, USA, 3Department of 14 Biomedical Engineering and High-Throughput Biology Center, Johns Hopkins University, Baltimore, MD, USA. 15 16 #: Corresponding authors 17 Joel S. Bader: [email protected] 18 Denise E. Kirschner: [email protected] 19 20 21

IAI Accepted Manuscript Posted Online 14 March 2016Infect. Immun. doi:10.1128/IAI.01438-15Copyright © 2016, American Society for Microbiology. All Rights Reserved.

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Abstract 22 Granulomas are a hallmark of tuberculosis. Inside granulomas, the pathogen 23 Mycobacterium tuberculosis (Mtb) may enter a metabolically inactive state that is less 24 susceptible to antibiotics. Understanding Mtb metabolism within granulomas could 25 contribute to reducing the lengthy treatment required for tuberculosis and provide 26 additional targets for new drugs. Two key adaptations of Mtb are: a non-replicating 27 phenotype, and accumulation of lipid inclusions in response to hypoxic conditions. To 28 explore how these adaptations influence granuloma scale outcomes in vivo, we present a 29 multi-scale in silico model of granuloma formation in tuberculosis. The model comprises 30 host-immunity, Mtb metabolism, Mtb growth adaptation to hypoxia, and nutrient diffusion. 31 We calibrate our model to in vivo data from non-human primates and rabbits and apply the 32 model to predict Mtb population dynamics and heterogeneity within granulomas. We find 33 that bacterial populations are highly dynamic throughout infection in response to changing 34 oxygen levels and host-immunity pressures. Our results indicate that a non-replicating 35 phenotype, but not lipid inclusion formation, is important for long-term Mtb survival in 36 granulomas. We use virtual Mtb knockouts to predict both the impact of metabolic enzyme 37 inhibitors and metabolic pathways exploited to overcome inhibition. Results indicate that 38 knockouts whose growth rate is below ~66% of wild-type in a culture medium featuring 39 lipid as the only carbon source, are unable to sustain infections in granulomas. By mapping 40 metabolite and gene-scale perturbations to granuloma-scale outcomes and predicting 41


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mechanisms of sterilization, our method provides a powerful tool for hypothesis testing 42 and guiding experimental searches for novel anti-tuberculosis interventions. 43 44 1. Introduction 45 Tuberculosis (TB), caused by inhalation of the pathogen Mycobacterium tuberculosis (Mtb), 46 is a leading cause of death worldwide (1, 2). The main sites of infection during TB are lung 47 granulomas, dense collections of immune cells and bacteria that develop following 48 infection (3). Understanding Mtb dynamics within granulomas could aid in development of 49 new antibiotic therapies, since Mtb growth rates, heterogeneity and dynamics can affect 50 antibiotic efficacy (3-7). 51 52 Two in vitro-observed adaptations of Mtb, suspected to be important in the ability of Mtb to 53 persist in the host lung, are (1) the adoption of a non-replicating phenotype and (2) the 54 accumulation of lipid inclusions, aggregates of neutral lipids inside bacteria (8-13). Hypoxia 55 is known to be a trigger for the transition to a non-replicating phenotype and the formation 56 of lipid inclusions (9, 12, 14, 15). 57 58 The in vivo role of the non-replicating phenotype remains controversial. It has been 59 suggested that Mtb acquires the non-replicating phenotype in response to stresses present 60 in the host (such as hypoxia), and this phenotype allows Mtb to persist in the presence of 61


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antibiotics (3, 4, 16). Supporting this view, granulomas in a number of animal models of TB 62 are hypoxic (17) and likely contain significant levels of nitric oxide, both of which induce 63 the non-replicating phenotype (9, 12, 14, 15, 18). Slow-growing and non-replicating 64 bacteria have been observed in vivo (19-21), and transcriptional profiles of bacteria in 65 patient sputum samples and of non-replicating bacteria in vitro are similar (22). 66 Nevertheless, direct evidence of non-replicating bacterial sub-populations within 67 granulomas has been challenging to obtain. Furthermore, the chemical makeup of the 68 granuloma microenvironment is heterogeneous (23), as is Mtb gene expression within a 69 single granuloma (24, 25) or over time (25). These results suggest that multiple in vitro 70 stress conditions reflecting distinct granuloma microenvironments may be required to 71 mimic the behavior of bacteria in vivo in different regions or during different stages of 72 infection. 73 74 Lipid inclusions are hypothesized to be a carbon source for Mtb while in its non-replicating 75 state or upon reactivation (14, 26). Inclusions may also be sinks for nutrients, leading to 76 slower bacterial replication rates (6). Mtb lipid inclusions are observed during growth 77 arrest in mouse lung (13) and under in vitro stress conditions (6, 10, 12, 14, 15, 27-29). 78 Bacteria form lipid inclusions by rerouting metabolic carbon fluxes from biomass 79 generation pathways to storage pathways (13). While direct evidence for lipid inclusions in 80 bacteria harbored within granulomas has not been reported, Mtb bacilli in sputum from TB 81


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patients do contain lipid inclusions (22). The impact of inhibiting the utilization of lipid 82 inclusions, via a broad-spectrum lipase inhibitor, has been investigated in vitro (26). 83 Though the inhibitor was shown to prevent regrowth of a hypoxic culture with substantial 84 lipid inclusions, the lipase inhibitor also inhibited bacteria without lipid inclusion during 85 log-phase growth. Thus, the effect of specifically targeting lipid inclusion formation and 86 utilization as a therapy for TB remains unclear (30). 87 88 Mtb remains challenging to study in vivo. Experimental difficulties include the time 89 required for animal models to develop features of TB (e.g. 40 days for necrosis in 90 C3HeB/FeJ mice (31)), complications with isolating sufficient bacterial material for high-91 throughput studies (32), and bacterial genetic redundancy (33) that buffers genetic effects. 92 Additionally, investigations of the role of particular Mtb phenotypes (such as the non-93 replicating phenotype) without a well-defined genetic model can be difficult to interpret. 94 Thus, it is challenging to map in vitro observations and predictions into the in vivo 95 granuloma environment experimentally. Efforts to identify Mtb gene essentiality through in 96 vitro screening of genetic knockout mutants could result in false predictions, if the in vitro 97 conditions are unable to accurately capture intra-granuloma micro-environments and 98 dynamics. For example, knockout mutants can be identified as attenuated in vitro, but 99 result in no attenuation when tested in vivo (what might be termed a “false positive” 100 attenuation prediction, e.g. KO3 in Figure 1). Similarly, mutants could be dismissed as non-101


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attenuated in vitro, but show attenuation in vivo (a “false negative” attenuation prediction, 102 e.g. KO2 in Figure 1). We aim to identify and minimize such false attenuation predictions by 103 mapping in vitro outcomes to in vivo outcomes using a computational model of Mtb 104 infection in granulomas. 105 106 Computational methods can complement experimental systems, especially in the complex 107 granuloma environment. We have established computational models of granuloma 108 formation (34-37) to map host immune mechanisms from the molecular to granuloma 109 scale (34, 35, 38) and to explore new antibiotic treatment strategies (39-41). Other models 110 have predicted hypoxic granuloma regions based on granuloma size (42) or used oxygen 111 and nitric oxide concentrations to determine Mtb growth and predict Mtb dynamics (43). 112 More sophisticated models can incorporate additional features, such as the asymmetrical 113 cell division observed in Mtb (5). 114 115 Direct links between bacterial genetics and metabolism are provided by metabolic 116 reconstructions, which specify the metabolic reactions that are possible given the enzymes 117 encoded by a genome. Flux balance analysis (FBA), a constraint-based model (CBM), uses 118 such reconstructions together with a steady-state assumption for internal metabolite pools 119 to define a feasible space for metabolic fluxes; an optimal flux is typically selected to 120 maximize the flux through a reaction defining the biomass required to create a new cell. 121


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Constraint-based models (CBMs) predict bacterial growth in specific environments. The 122 parameters of these CBMs are generally selected to reproduce bacterial growth rates and 123 known metabolic fluxes (44). CBMs of Mtb include GSMN-TB (45, 46), iNJ661 (47) and 124 more recently sMtb (48), which aimed to merge previous models. 125 126 There are numerous published CBMs that have extended the FBA approach in different 127 ways. Dynamic CBMs describe bacterial growth in changing environments by relaxing the 128 steady state assumption of CBMs and instead assuming pseudo-steady states over short 129 time periods (49, 50) (51, 52). CBMs have been coupled with gene expression data to 130 probe metabolic changes in Mtb in response to hypoxia (53), or with spatial models of 131 competing bacterial species to determine bacterial ecosystem dynamics (54). These types 132 of models provide a mechanism to include detailed bacterial dynamics within the context of 133 a larger simulation representing the host tissue and immune response. 134 135 In this work we present a novel multi-scale computational model (GranSim-CBM) 136 combining for the first time a model of host immunity with a model capturing non-137 replicating Mtb phenotypes, Mtb metabolism, lipid inclusion formation, hypoxia and 138 nutrient limitation in a granuloma. GranSim-CBM is a hybrid model, integrating an agent-139 based model of granuloma formation (GranSim), which we have developed and calibrated 140 to non-human primate (NHP) data (34-37), and a dynamic CBM describing Mtb metabolism 141


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and growth. GranSim-CBM is a multi-scale model spanning metabolic, cellular and tissue 142 scales. We use GranSim-CBM to correlate bacterial growth rates predicted by the CBM alone 143 in specific defined media (“in vitro” outcomes) to growth of Mtb predicted within a 144 granuloma (“in vivo” outcomes). This in vitro to in vivo mapping of Mtb growth 145 characteristics could inform screening strategies for new antibiotics and antibiotic targets 146 (Figure 1). We apply this tool to address four questions: Which bacterial phenotypes 147 emerge over time in granulomas? What roles (if any) might the non-replicating Mtb 148 phenotype and lipid inclusions play during infection? What effects manifest at the 149 granuloma-scale when inhibiting specific metabolic pathways in Mtb? Can we predict the 150 potential of in vitro screening (different media and oxygen levels) to identify useful 151 bacterial metabolic targets for treatment of TB? Answers to these questions may help to 152 guide future experimental studies and drug screening assays. 153 154 2. Methods 155 The methods of GranSim-CBM build on an established framework for tissue-scale 156 simulation with coarse-grained bacterial populations. We discuss the methods required to 157 couple this model to a detailed metabolic model for each bacterial cell, and to introduce 158 metabolic switches to permit non-replicating bacterial phenotypes and lipid reserve 159 accumulation and usage in response to hypoxia. We calibrate our model to experimental 160 NHP and rabbit data and perform sensitivity analysis to determine the parameters most 161


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important to simulated infection outcomes. We group bacteria based on their nutrient 162 conditions to connect bacterial growth to granuloma characteristics, and use virtual 163 knockouts of bacterial metabolic genes to predict in vivo phenotypes and identify metabolic 164 bypasses for bacterial reactions. A summary of methods used in this work is presented in 165 Table 1. 166 167 2.1. Agent-based granuloma model (GranSim) 168 Briefly, GranSim captures molecular, cellular and tissue scale events. At the tissue scale, we 169 include cellular movement based on the chemokine environment on a 2D simulation grid, 170 with granuloma formation as an emergent behavior of the system (Figure 2A). At the 171 cellular scale, we model individual macrophages and T cells, their states (resting, activated, 172 infected or chronically infected for macrophages; and cytotoxic T cells, regulatory T cells or 173 IFN-γ producing T cells) and interactions. At the molecular level, the model accounts for 174 secretion, diffusion, binding and degradation of cytokines and chemokines. The model has 175 been extensively calibrated to NHP data and successfully predicts granuloma outcomes for 176 TNF-α, IL-10 and IFN-γ knockouts (34-41, 55). 177 178 In previous versions of GranSim, we separated bacteria into three subpopulations based on 179 their location (intracellular, replicating extracellular and non-replicating extracellular in 180 caseum). Each subpopulation was represented by continuous values in each grid 181


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compartment or macrophage. This continuous representation has the benefit of simplicity 182 and computational ease for capturing the overall interaction between host and pathogen 183 when probing immunological questions. However, to better address mycobacterial 184 questions in granulomas with heterogeneous Mtb populations (5, 56), we implement here a 185 discrete representation of individual Mtb bacilli. 186 187 In our discrete Mtb model, each bacillus is modeled as an individual ‘agent’, with state 188 variables for biomass (Bi), lipid inclusions (Li) and location (Xi) (intracellular/extracellular) 189 tracked for each bacterium i. Growth rates, generation times, size and lipid inclusion levels 190 are tracked for each bacillus over time. Table 2 describes GranSim rules regarding Mtb 191 growth, division, death, phagocytosis and macrophage bursting for continuous vs. discrete 192 Mtb, with variable and parameter definitions given in Tables 3 and 4 respectively. Host 193 parameters are given in Supplement Table S1. Changing the representation of Mtb in 194 GranSim from continuous variables to individual agents does not affect predicted average 195 CFU trajectories in simulated granulomas (Figure 3A). 196 197 2.2. Capturing nutrient dynamics in GranSim 198 We track distribution and bacterial utilization of three nutrients on the simulation grid: 199 glucose, Triacylglycerol (TAG) (representing fatty acid carbon sources), and oxygen. The 200 metabolic requirements of Mtb have been extensively studied. Intracellular Mtb likely 201


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utilizes a range of host-derived carbon sources and amino acids as nutrient sources, 202 including cholesterol and TAG (57, 58). Additionally, glycolysis under hypoxic conditions 203 leads to the accumulation of toxic by-products (59). Therefore, fatty acids are considered to 204 be a major carbon source of Mtb in vivo. 205 206 Lipids are a carbon source for Mtb in vivo in mice (19) (58), inside macrophages (57, 60), in 207 caseum (61) and as an internal nutrient reserve stored by Mtb under hypoxic stress (12, 208 14, 26). We use TAG to represent fatty acid carbon sources in each of these locations 209 (intracellular, in caseum, and in lipid inclusions). The lipid content of caseum is believed to 210 be due to the accumulation of host cell debris (61). Therefore, in the model, each dying 211 macrophage deposits its TAG onto the grid compartment where it died, making the TAG 212 available to extracellular bacteria. Activated macrophages in GranSim have the ability to 213 heal caseation in the 8 adjacent grid spaces on the 2D grid. When caseation is healed, the 214 TAG levels are reduced to reflect the return of the simulation grid compartment toward a 215 ‘normal lung tissue’ state. 216 217 We model oxygen levels in the granuloma by assuming constant oxygen concentration in 218 the blood (O2,plasma), tracking oxygen permeation onto the grid at a rate p via vascular 219 source grid compartments, diffusion on the grid with diffusivity D, and consumption by 220


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host cells using Michaelis-Menten kinetic parameters Vmax-host and khost. We use reaction-221 diffusion methods described previously (62). 222 223 Within granulomas, less is known about glucose levels than oxygen. Glucose is not believed 224 to be a major carbon source for intracellular Mtb (57), either because glucose is not made 225 available to bacteria in phagosomes or because it is not the preferred carbon source for 226 Mtb in the intracellular environment. Therefore we fix glucose levels available to 227 intracellular Mtb at zero. While a C3 carbon source is likely available to intracellular 228 bacteria (57), the identity of this source is currently unknown and we therefore exclude it 229 from the current model. Extracellular glucose is set to an initial amount at each grid cell 230 (GlcE) and is gradually consumed by Mtb without replenishing. 231 232 2.3. Constraint-based model of Mtb metabolism 233 CBMs describe the relationship between nutrient uptake (e.g. glucose and oxygen), waste 234 export (e.g. CO2), and the production rate of biomaterials for new cells, under the 235 assumption of a steady state for internal metabolite pools (63). A CBM makes predictions 236 about cellular metabolism utilizing the metabolites present, the reactions and 237 corresponding enzymes responsible for metabolic transformations, and the constraints on 238 vi (the flux through reaction i) vilow < vi < viup (Figure 2B). Mathematically, the steady-state 239 assumption is formulated as S⋅ν = 0. Rows of the stoichiometry matrix S correspond to 240


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metabolites, and columns of S correspond to enzyme-catalyzed reactions, active and 241 passive transport, and other uncatalyzed reactions. The row-column entry is the number of 242 metabolite molecules that are reactants (negative sign) or products (positive sign) for the 243 reaction. For metabolic reactions, the flux constraints depend on maximum reaction rates 244 for enzymes. For import of metabolites into the bacterial cell, the rates depend on the 245 properties of transporters and on the extracellular metabolite concentration. As described 246 below, the CBM uses Michaelis-Menten kinetics to model the import fluxes. 247 248 The biomass flux νb is defined as the flux of the reaction: Σiwimi → 1b, where mi is 249 metabolite i, wi is the number of molecules of metabolite i required to build one new cell, 250 and b is the total biomass composition of a new cell. By definition, the growth rate of the 251 cell is νb. 252 253 In conventional CBMs, a standard assumption is that bacteria have evolved to maximize 254 growth rates. Therefore, to compute the growth rate, the maximum value of νb is identified 255 within the feasible space of flux vectors defined by bounds on the fluxes and the steady-256 state assumption. Because the objective function and constraints are linear, an optimal 257 solution may be found efficiently using a linear programming solver. However, Mtb grows 258 more slowly than most bacteria and adjusts its growth rate in response to environmental 259


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cues (9, 12, 14, 15, 18). We therefore adjust the assumption of maximized growth rate by 260 modifying the objective function as described below. 261 262 In this work, we develop a dynamic CBM based on an existing CBM describing Mtb 263 metabolism (45, 46), using the ‘static-optimization approach’ (50). The original model of 264 Mtb metabolism is an updated version of GSMN-TB (45, 46) kindly provided by the authors 265 (Dr. Johnjoe McFadden, personal communication). These updates to the published model 266 include corrections of a few reaction imbalances, changes in the ATP penalties for the 267 biomass function, and inclusion and exclusion of additional reactions based on new data. 268 We chose GSMN-TB over other available metabolic models of Mtb due to its relative 269 simplicity, validated predictions for essential genes in vitro, and inclusion of metabolic 270 reactions we wished to study. Inclusion of the host metabolism in a metabolic model, as in 271 iAB-AMØ-1410-Mt-661, introduces significant complexity to modeling infection as 272 additional parameters for host nutrient uptake and transport to the phagosome must be 273 specified. GSMN-TB is more accurate for in vitro predictions of gene essentiality than 274 iNJ661 (45, 47). Additionally both iNJ661 and its descendant iAB-AMØ-1410-Mt-661 did 275 not include the reactions for synthesizing and catabolizing triacylglycerol (TAG) within the 276 bacterium. Inclusion of these reactions is critical for studying the role of TAG as a storage 277 compound and energy source during infection. Another alternative would be the sMtb 278 model (48), which is a unification of GSMB-TB with iNJ661. A qualitative comparison 279


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between GSMN-TB and sMtb (Supplement Table S2) suggests that they will often give 280 similar results in our granuloma simulations. 281 282 283 We make additional modifications to the existing CBM to enable integration with GranSim. 284 In particular, GSMN-TB includes glycerol as a carbon source, but experiments suggest that 285 Mtb does not utilize glycerol in vivo (64). We therefore exclude the glycerol import reaction 286 from our model. The GSMN-TB model also includes cholesterol metabolism reactions. 287 Cholesterol is metabolized via the methylcitrate cycle and the TCA cycle, generating 288 pyruvate, acetyl-COA and propanoyl-COA (65). Pyruvate can then be converted to acetyl-289 COA by the pyruvate dehydrogenase complex (66) pp467). TAG, a primary component of 290 lipid inclusions (12), is metabolized into odd-length fatty acids and a glycerol molecule. The 291 fatty acids are in turn also metabolized to propanoyl-COA and acetyl-COA via beta-292 oxidation while the glycerol can be metabolized by conversion to pyruvate (66) pp. 429, 293 605. Given these similarities in metabolism, we simplify the model by grouping cholesterol 294 and TAG together as a single effective TAG metabolite; similarly, GranSim represents the 295 local concentration of cholesterol and TAG as a single effective TAG metabolite. 296 297 We rescale the published GSMN-TB biomass function to provide a quantitative match with 298 the biomass of a newly divided cell, rather than an average cell during log-phase growth. 299


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Experimental measurements of an actively growing mycobacterial population found that 300 individual bacilli had a dry weight of 274.5 fg, including cells with partially or fully 301 replicated genomes (67). It was also estimated that each cell contained 1.4 genome copies 302 rather than a single genome copy (67). We therefore define one biomass unit (BU) as equal 303 to 196 fg (274.5 fg/1.4) of dry weight. With this definition, a cell with a biomass of 1 BU 304 corresponds to a nascent daughter cell from a symmetric cell division, and a cell with a 305 biomass of 2 BU is on the cusp of division. We also rescale the GSMN-TB flux uptake units 306 for metabolites from mmol/h-gDW to fmol/h-BU. 307 308 2.4. Switching between Mtb biomass growth and lipid inclusion accumulation in response 309 to hypoxic stress 310 We further modify GSMN-TB to include the accumulation of lipid inclusions in non-311 replicating Mtb, and a mechanism for hypoxic stress to trigger the transition to a non-312 replicating bacterial phenotype that accumulates lipid inclusions. Here we refer to bacteria 313 in low oxygen conditions as non-replicating, to encompass both non-replicating and slowly 314 replicating bacteria (growth rates

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in which both directions are active with no net TAG transport, a small ATP penalty (0.1 320 ATP) is added for TAG transport into the lipid inclusions. The two new transport reactions 321 specifically are transfer of TAG into the lipid inclusions, 1 TAG[c] → 1 TAG[inclusion], with 322 flux νpL; and transfer of TAG from the lipid inclusions back to cytoplasm, 1 TAG[inclusion] + 323 0.1 ATP → 1 TAG[c] + 0.1 ADP + 0.1 P (inorganic phosphate), with flux νcL. The net flux of 324 TAG into the lipid inclusions is defined as νL = νpL – νcL. Each molecule of TAG, when fully 325 metabolized, yields between 364.6 and 489.2 molecules of ATP depending on oxygen level, 326 large compared to the 0.1 molecule penalty. 327 328 As in previous work (13), we consider two FBA objective functions, one under high oxygen 329 that maximizes the biomass growth rate, νb, and the other under hypoxia that maximizes 330 the lipid inclusion accumulation rate, νL (Figure 2B). We introduce a continuous oxygen-331 sensitive switching function η that weighs the two objective functions. The combined 332 objective function Z is 333 Z = ηνb +(1–η)VRνL, (eq. 1) 334 where parameter VR provides a convenient scaling between the two objectives. This 335 parameter is necessary, as the relative importance of one unit of biomass and one unit of 336 lipid inclusions may not be equivalent and would generally be dependent on the particular 337 units chosen. The switching function is 338 η=1/(1 + exp[-s([O2]–h)/h]), (eq. 2) 339


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where [O2] is the oxygen concentration, s determines the sensitivity of the switching 340 (steepness of the sigmoid) and h is the half-saturation concentration of the switch. Oxygen-341 dependent metabolic maintenance costs are calculated using the active/non-replicating 342 switch parameter η (eq. 2) and implemented as a biomass degradation rate d, 343 d = dmin + η(dmax - dmin) (eq. 3) 344 where dmax is the biomass degradation rate in fully aerated replicating Mtb, and dmin is the 345 biomass degradation rate in non-replicating Mtb. Thus, we lower the biomass degradation 346 rate (i.e. maintenance metabolism) in response to lower oxygen availability, allowing us to 347 capture the reduced metabolic requirements for survival in the absence of replication. The 348 original GSMN-TB model instead used a lower bound on ATP hydrolysis to incorporate 349 biomass maintenance costs (45, 46). Our form reflects the decreased maintenance cost in 350 decreasing oxygen concentrations. It also ensures a feasible FBA solution when low 351 nutrients constrain the ATP hydrolysis rate. However, GSMN-TB does not capture 352 metabolism in the absence of oxygen (via anaerobic respiration (69, 70)). This is a 353 limitation of our model though we do not expect it to significantly impact our results, as the 354 metabolism of Mtb is very slow during hypoxia. We expect this very slow bacterial 355 metabolic state to be well approximated by our model, which predicts the total absence of 356 metabolism under anoxic conditions. 357 358 2.5. Coupling CBM to local nutrient resources in GranSim to create a dynamic CBM 359


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To capture the variable nutrient conditions available to Mtb during infection, the upper 360 bounds (viup) for the rates of nutrient uptake (oxygen, glucose, and TAG) are determined by 361 the local nutrient availability provided by GranSim (Figure 2A-B). Four uptake fluxes are 362 constrained: oxygen, glucose, and TAG from the external environment, and re-import of 363 TAG back from the lipid inclusion to the cytoplasm. In each case, constraints are modeled 364 using a Michaelis-Menten functional form with Hill coefficient 1 and two parameters 365 corresponding to the maximum flux, Vmax,i, and the metabolite concentration Ki at half 366 maximum, 367 viup = Vmax,i [N]/(Ki +[N]), (eq. 4) 368 for i corresponding to each of the four constrained import fluxes. For import from the 369 extracellular environment, [N] refers to the local concentration provided by GranSim. For 370 import of TAG from the lipid inclusion, the concentration is computed as Li/Bi. For all four 371 import fluxes, vilow is set to zero. The 8 parameters (Vmax,glc , Vmax,TAG, Vmax,O2, Vmax,L, Kglc, KTAG, KO2, KL) 372 for the 4 import flux upper bounds are selected by fitting to experimental data as described 373 below. 374 375 2.6. Multi-scale dynamics with GranSim-CBM 376 The multi-scale model (Figure 2C) tracks concentrations of three nutrients (oxygen, 377 glucose and TAG) in the granuloma environment as well as internal bacterial lipid 378 inclusions. Available nutrients on the simulation grid are used to determine the upper 379


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bounds for CBM transport fluxes (eq. 4), to switch the CBM objective function between 380 biomass production and lipid inclusion production (eq. 2) and to calculate the biomass 381 degradation rate (eq. 3). The optimal fluxes from the CBM are used in GranSim to update 382 bacterial state variables (biomass, Bi, and lipid inclusions, Li) as well as the environmental 383 nutrient pools in the granuloma (see Supplement Figure S1 for more detail). 384 385 Using the growth rate (νb) and the net lipid inclusion production rate (νL) calculated by the 386 FBA, the ABM updates the state variables for biomass (Bi) and lipid inclusion (Li) for the ith 387 bacterium with time increment Δt: 388 Bi(t+Δt)=(νb– d)Bi(t)Δt+Bi(t) (eq. 5) 389 Li(t+Δt)=(νL)Bi(t)Δt+Li(t) (eq. 6) 390 The biomass degradation rate d represents metabolic maintenance and is scaled by the 391 hypoxia switching function η (eq. 2). 392 393 The biomass of each bacterium is kept between a death threshold, τdeath, and a division 394 threshold, τdiv. If the biomass reaches τdiv, the bacterium divides into two asymmetric 395 daughter bacilli with biomass (1-f) and (1+f) BU (f is the asymmetric division fraction), and 396 lipid inclusions split proportionally. If the biomass falls below τdeath, the bacterium dies 397 and is removed from the simulation. Bacterial survival and replication therefore depends 398


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on a balance between growth rate and biomass degradation rate. In our model, growth rate 399 is determined by oxygen, glucose, TAG and lipid inclusion availability, while biomass 400 degradation rate is determined by oxygen availability via the growth switch parameter (eq. 401 2). Therefore, a shortage in any of these nutrients, (resulting in νb < d), will cause a net loss 402 of biomass, leading to death from starvation (or ‘suffocation’ in the case of lack of oxygen) 403 when biomass falls below τdeath. 404 Lipid inclusions per bacterium are constrained to be below a realistic maximum value 405 (Lmax). If Li(t+Δt) > Lmax then we instead set Li(t+Δt) = Lmax and convert the excess TAG to 406 extracellular TAG to prevent loss of mass. As an alternative, we could have introduced a 407 dynamic upper limit for flux of TAG into the lipid inclusion at greater computational 408 expense. Note that if glucose is being used to produce lipids when lipid inclusion levels 409 reach the maximum then some mass will be lost. We have monitored the amount of lipids 410 lost during a 400-day simulation and found that a negligible amount (~0.01%) of the total 411 TAG molecules present on the grid are lost as a result. 412 413 2.7. Uncertainty and sensitivity analysis 414 Uncertainty analysis (UA) identifies the variation in model outputs caused by uncertainty 415 in model parameters. We previously identified bacterial growth rate as a major contributor 416 to uncertainty in GranSim outputs (36, 71) and therefore investigate the contribution of 417


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individual CBM and bacterial GranSim parameters (Table 4), drivers of bacterial growth 418 rate, to granuloma level outputs in GranSim-CBM. 419 420 We use Latin hypercube sampling (LHS) (72) to uniformly and simultaneously sample 421 multiple parameters within the multi-dimensional parameter space (Table 4). We generate 422 1500 parameter sets. Agent-based models contain both aleatory uncertainty from 423 stochastic variation and epistemic uncertainty from parameter variation. In order to 424 sample aleatory uncertainty, we perform 5 independent replicate simulations for each 425 parameter set. Candidate parameter sets are selected using the following criteria based on 426 single granuloma CFU data from NHP (Figure 3B) (21, 73-75) and oxygen measurements in 427 rabbit granulomas (Figure 3C) (17): 428 ● 5000 < Day 30 total CFU < 100,000 for 4 or 5 out of 5 replicates 429 ● Day 80 total CFU < 10,000 for any of the replicates 430 ● Day 200 total CFU < 2500 for 4 or 5 out of 5 replicates 431 ● (Day 200 total CFU)/(Day 100 total CFU) < 2 for any of the replicates 432 ● Only 1 or 2 out of 5 replicates clear infection before day 200 433 ● 1 mg/L < Day 30 oxygen in the granuloma < 200 mg/L for any of the replicates 434 435 The final parameter set (Table 4) is selected by visual inspection from 5 candidate sets 436 identified by the criteria above. A representative granuloma generated with this parameter 437


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set is shown in Figure 3D, along with the predicted oxygen, TAG and glucose levels within 438 the granuloma. This parameter set captures tissue scale outcomes of TNFα , IL-10 and IFNγ 439 knockouts in mice and NHPs (76-82) (Supplement Figure S2). 440 441 Sensitivity analysis (SA) quantifies the strength of correlation between model parameters 442 and outputs of interest, and therefore can identify the main driving mechanisms in the 443 model for specific outputs. SA is performed by calculating partial ranked correlation 444 coefficients (PRCCs) between model parameters and model outputs (72). We again use LHS 445 to simultaneously vary multiple parameters. While a number of other sensitivity analysis 446 methods are available (83-90), our chosen approach allows global sensitivity analysis, i.e. 447 identifying the contribution of a set of parameters to model outcomes in the context of 448 other parameter variations, instead of local sensitivity analysis, i.e. variation of single 449 parameters against baseline values for other parameters. The method also allows the 450 evaluation of parameter contributions to a large number of model outputs at multiple time 451 points. Using LHS to perform parameter sampling, and performing multiple replications of 452 the stochastic model for each parameter set alleviates the significant computational 453 limitations of large parameter sweeps in conventional sensitivity analyses. Parameter 454 ranges used for the SA (Table 4) are constructed around the final parameter set from the 455 uncertainty analysis described above. We sample the parameter space 1500 times and 456 perform 5 replicates for each parameter set to estimate contributions from both aleatory 457


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and epistemic uncertainty. Parameters are ranked in terms of strength of correlation with 458 model outputs using the z-test. Significant PRCC and z-test results are defined as having p-459 values < 0.01. 460 461 2.8. GranSim-CBM validation 462 As model validation we compare killing of bacteria in our model with in vivo measurements 463 (19, 21). Bacterial killing can be assessed as CFU/CEQ, where CEQ (chromosomal 464 equivalents) is a measure of all bacteria that have been in the granuloma during the entire 465 infection. A low CFU/CEQ fraction indicates effective killing of bacteria by the host (21). We 466 measure this ratio in GranSim-CBM by tracking the cumulative number of bacteria in the 467 simulation, including dead bacteria (38). The median value of CFU/CEQ at 75 days post 468 infection (dpi) is 9x10-3 with 95% confidence interval 7x10-3 to 1x10-2. In comparison, 469 experimental CFU/CEQ ratios from non-human primates (NHP) 77 dpi (21) (rhesus 470 macaque) are on average 2x10-3 with range 1x10-5 to 2x10-1. 471 472 2.9. Hierarchical Clustering of Bacteria 473 In order to explore heterogeneity in the bacterial populations in our simulations, we group 474 bacteria according to their growth rates and locally available nutrients. Growth rates 475 depend on local nutrients (using the CBM) as well as host adaptive immunity (using 476 GranSim). For grouping, we use hierarchical clustering based on Euclidean distances 477


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(Matlab Release 2014b, The MathWorks, Inc., Natick, Massachusetts, United States), 478 standardizing by growth rate and available nutrient levels (oxygen, glucose, TAG, lipid 479 inclusions). Each resulting cluster of bacteria represents a group of bacteria with similar 480 growth rates and nutrient environments. Clustering is performed on a collection of bacteria 481 pooled from multiple time points in a single granuloma, to identify patterns that continue 482 throughout the simulation (temporally) as well as patterns that developed at specific times 483 (spatially). Furthermore, clusters are visualized as a heat map augmented to display model 484 variables not used for clustering (time, CBM fluxes, maintenance metabolism and 485 intracellular/extracellular location). 486 487 2.10. Simulations of lipid inclusion defects and virtual Mtb knockouts 488 Since the non-replicating growth phenotype and lipid inclusion formation appear to be 489 important adaptations of Mtb, these adaptations could be attractive antibiotic targets. To 490 explore the potential effects of inhibiting these two adaptations, we perform additional 491 simulations in which bacteria are unable to enter the non-replicating state or to accumulate 492 lipid inclusions. To allow bacteria to slow their growth but not accumulate lipid inclusions, 493 the hypoxia switch is retained but the maximum lipid inclusion parameter (Lmax) is set to 494 zero. To prevent bacteria from slowing their growth, the half-saturation parameter (h) is 495 set to 1x10–100. 496 497


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Gene deletion mutants (virtual knockouts) are simulated in the CBM by removing the set of 498 reactions requiring the corresponding gene product. Removing reactions shrinks the 499 feasible space. Our approach is appropriate to capture the long-term effect of a deletion; 500 other approaches may be more appropriate for capturing immediate short-term effects 501 (91) or partial inhibition by drugs or other small molecules. 502 503 Of the 759 enzymes in the Mtb metabolic model, 291 block the biomass reaction when 504 removed and are essential within the CBM. Of the remaining 468 enzymes, 277 do not 505 change the CBM when removed because other enzymes catalyze the same reaction and, in 506 the context of GranSim-CBM, are identical to wild-type. The remaining 191 virtual 507 knockouts cause changes in the metabolic network, potentially causing growth defects 508 under certain nutrient conditions. These “attenuated” but not essential mutants are suited 509 for further analysis using GranSim-CBM. We simulate these 191 mutants in the multi-scale 510 model by running GranSim-CBM with the virtual knockout CBMs for 10 replications per 511 mutant. We then test the hypothesis that the 10-simulation mean CFU count at 400 dpi 512 (µKO,i) is identical to the corresponding mean for WT strains. An empirical mean 513 distribution (µWT) for the WT is constructed by performing 100 WT simulations, then 514 generating Nb = 4000 bootstrap samples of 10 simulations selected uniformly with 515 replacement from the 100. The empirical one-sided p-value p for each deletion mutant is 516


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then calculated as the percentile of the observed mean CFU for the knockout strain using 517 the bootstrapped WT distribution, 518 519 p = r/(Nb + 1) 520 521 where r is the rank of µKO,i when included in the 4000 WT boostrap replicates. We corrected 522 for multiple testing of the 191 attenuated mutants using the Benjamini-Hochberg method 523 (92) with a false discovery rate (FDR) constrained to 0.05 or less. Increasing Nb to 10,000 524 did not affect the list of attenuated mutants. The TubercuList database was used to map the 525 gene names (Rv) present in GSMN-TB to their common names (93). 526 527 When enzymes are removed from the Mtb metabolic model, the remaining reactions may 528 have different ranges of permitted fluxes. We use flux variability analysis (FVA) (94) to 529 identify “bypass reactions” for each mutant, defined as those reactions not required for 530 maximum growth in WT but required for maximum growth in the mutant considered. 531 Practically, this is done by considering the range of each flux that could result in maximum 532 growth as calculated by FBA. Those fluxes with ranges that do not contain 0 in the mutant 533 but contain 0 in WT are labeled as bypasses for the removed reaction(s). 534 535 2.11. Efficient implementation of GranSim-CBM 536


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Because most of the FBA reactions are effectively unconstrained, the dynamic CBM 537 optimum depends only on a small number of external variables. For computational ease in 538 the multi-scale model, we exploit this observation and replace linear programming with 539 lookup tables generated using linear programming outside of GranSim-CBM. The values in 540 the lookup tables are used to calculate the optimal flux state for each bacillus. Lookup 541 tables are indexed by five input variables: the growth switch parameter (η), the oxygen 542 import flux upper bound (νO2up), the extracellular glucose import flux upper bound (νglcup), 543 the extracellular TAG import flux upper bound (νTAGup), and the lipid inclusion TAG import 544 flux upper bound (νLup). Note that although η depends on oxygen concentration (and 545 therefore νO2up), the relationship varies with the parameters s and h (eq. 2) as well as Vmax-host 546 and khost.. Therefore, indexing by both η and oxygen import fluxes allows the use of a single 547 lookup table with multiple values of these parameters. Since inputs and table entries are 548 normalized to correspond to a bacillus with a biomass of 1 BU; outputs are then scaled 549 linearly by the actual biomass for each bacterium in GranSim-CBM. Six output variables 550 from the CBM are used to update local variables in GranSim-CBM: the biomass growth rate 551 (vb), the oxygen import flux, the glucose import flux, the extracellular TAG import flux, the 552 lipid inclusion production (vpL) and lipid inclusion usage rate (vcL). As a trade-off between 553 lookup table size and accuracy, the lookup table uses 16 points in each input dimension 554 spaced at equal intervals between a minimum and maximum value, with each of the 165 555 entries then storing the 6 output variables. Multidimensional linear interpolation is used to 556


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calculate outputs between the table entries. The lookup table entries are calculated using 557 the Cobra Toolbox for MATLAB (95), custom MATLAB scripts, and CPLEX for the linear 558 programming optimization [URL: http://www-559 01.ibm.com/software/integration/optimization/cplex-optimizer/]. Computational time to 560 generate one lookup table was approximately 28 hours on Intel E5 8-core (Sandy Bridge) 561 processors. 562 563 GranSim and GranSim-CBM are implemented in C++ with Boost libraries (distributed under 564 the Boost Software License and available at www.boost.org). The graphical user interface 565 (GUI), which allows us to visualize, track, and plot different facets of our simulated 566 granulomas in real time, uses the Qt framework (open-source, distributed under GPL from 567 qt.digia.com). The model can be used with or without GUI visualization and is cross-568 platform (Mac, Linux, Windows). Average run time for GranSim is approximately 10 hours 569 per simulation for 1000 days on Dell 8-core processors. Further details, a model executable 570 and parameter file for GranSim-CBM are available online at 571 http://malthus.micro.med.umich.edu/GranSim/GranSim-CBM/. 572 573 3. Results 574 Our goal is to predict Mtb metabolic influences on bacterial loads within granulomas using 575 our multi-scale computational model, GranSim-CBM (Figure 2), which is calibrated to non-576


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human primate and rabbit data (Figure 3). The model captures interactions between Mtb, 577 host immunity and the nutrient environment within granulomas, including the ability of 578 Mtb to slow its growth and accumulate lipid inclusions in response to hypoxia. This 579 approach enables the mapping of in vitro Mtb growth onto in vivo Mtb survival in 580 granulomas (Figure 1). 581 582 3.1 Infection outcome correlates more strongly with bacterial properties than with 583 environmental properties 584 We identify the key molecular and metabolic scale mechanisms that drive granuloma 585 outcomes using sensitivity analysis. We simultaneously vary multiple GranSim-CBM 586 parameters and test their contributions to variations in granuloma outcomes of interest 587 (e.g. bacterial load and oxygen concentration). We quantify these contributions by 588 calculating the partial rank correlation coefficient (PRCC) between each model parameter 589 and granuloma outcome. Sensitivity analysis reveals (Table 5) that two bacterial 590 parameters, biomass degradation rate (dmax, representing maintenance metabolism of a 591 replicating bacterium) and maximum oxygen reduction (Vmax,O2, the maximum rate at which 592 oxygen is reduced by the bacterium), are the main drivers of most granuloma outcomes. 593 Lower ranked parameters with significant correlations are related to granuloma 594 environment, primarily plasma oxygen concentration (O2,plasma), vascular permeability of 595 oxygen (p) and available TAG per macrophage (TAGI). Overall, these correlations are 596


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similar whether calculated at early time points (< 40 dpi) or late time points (> 200 dpi) in 597 the simulation. Parameters that increased total bacterial load tend to decrease the 598 proportion of intracellular bacteria. These results indicate that oxygen-related bacterial 599 properties, and to a lesser extent environmental properties, are the main 600 molecular/metabolic contributors to granuloma outcomes. 601 602 3.2 Bacterial growth phenotypes in granulomas are dynamic and heterogeneous 603 We characterize Mtb growth phenotypes existing within granulomas for wild-type (WT) 604 strains. Since the model is stochastic, we can capture variability in granuloma outcomes by 605 conducting 100 replicate simulations with the baseline parameter set in Table 4. We 606 examine whether bacteria within a granuloma exist in a non-replicating state. Infection is 607 initialized by placing a single infected macrophage, containing a single bacterium, on the 608 simulation grid. The growth status of each bacillus is investigated using two measures, 609 generation time (time between previous divisions) and instantaneous growth rate 610 (instantaneous flux through the biomass reaction). There is a trend toward increased 611 generation times over the course of infection (Figure 4A), though statistically insignificant 612 after 200 dpi (Supplement Figure S3A), with a maximum generation time of up to 94 days 613 for a few bacteria at 1000 dpi. Most bacteria have shorter generation times, however, and 614 the median generation time of 1.5 days at 20 dpi increases to only 3.7 days at 1000 dpi. The 615 distribution of instantaneous growth rates is bimodal (Figure 4B), reflecting distinct 616


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populations of replicating bacteria with growth rates of ~0.033 hr-1 and non-replicating 617 bacteria with growth rates

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causing them to switch to slow growth due to lack of oxygen. Similarly, a bacterium in 637 cluster 3 (magenta star, dashed line, Figure 5A) is clustered together with other bacteria 638 that encounter medium carbon sources, and high oxygen, resulting in relatively rapid 639 growth. The clustered bacteria are then further characterized (Figure 5B) based on their 640 time point (days post infection), nutrient utilization fluxes (lipid inclusions, TAG, glucose 641 and oxygen), biomass degradation rates, and location (intracellular/extracellular). The 642 example bacterium in cluster 4 (red star, dashed line, Figure 5B) is revealed to be from a 643 later time point, using very little carbon and oxygen, it’s slowed metabolism in reflected in 644 a low biomass degradation rate, and it is extracellular. The example bacterium in cluster 3 645 (magenta star, dashed line, Figure 5B) is shown to be from an earlier time point, with high 646 TAG and oxygen consumption, and high biomass degradation rate, and it is intracellular. 647 648 Bacteria from early time points group together in clusters 1 to 3. Although most bacteria at 649 20 dpi have high available oxygen levels, bacteria in clusters 1 and 2 at 20 dpi have low 650 growth rates (Figure 5A-B) compared to cluster 3. Thus, while different clusters are 651 representative of bacteria during different stages of infection, heterogeneity exists even 652 early on. Clusters 4 to 7 are enriched for bacteria from later time points (Figure 5A,B). 653 Cluster 4 represents bacteria that have slowed their growth in response to low oxygen 654 conditions (as reflected in lower biomass degradation rate). 655 656


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We can also locate each bacterium within the granuloma at each time point (Figure 5C). For 657 example, the bacterium from cluster 4 (red stars, dashed lines, Figure 5A-B) is from 700 dpi 658 in a small group of bacteria in the top right of the granuloma (red star, Figure 5C, 700dpi). 659 The bacterium in cluster 3 (magenta stars, dashed lines, Figure 5A-B) is located along with 660 most other bacteria in cluster 3, in the outer rim of the bacterial population at 20 dpi 661 (magenta star, Figure 5C, 20dpi). Examining the spatial distribution of bacteria from all 662 seven growth clusters within the granuloma over time reveals that clusters 1 and 2, which 663 are limited in available TAG, are located in the innermost part of the granuloma (Figure 664 5C). This suggests that at this early time point the rapid expansion of bacteria is generating 665 a carbon-limited subpopulation of bacteria, leading these bacteria to utilize their lipid 666 inclusions (Figure 5B). Furthermore, the major heterogeneity occurs over time rather than 667 space. Bacterial populations shift from one growth cluster to another, e.g. from mostly 668 clusters 5 and 7 at 300 dpi to mostly cluster 4 at 400 dpi. These results indicate that 669 fluctuations occur within granulomas, with Mtb continually responding to the dynamic 670 granuloma microenvironments by changing their growth rates. 671 672 3.4 Growth phenotype changes reflect granuloma size and bacterial loads 673 To explore how the fluctuations in bacterial growth phenotypes connect to granuloma 674 environmental properties, we examine the total number of bacteria and relative fraction of 675 bacteria within each growth cluster at 20-day intervals for a representative granuloma 676


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(Figure 6A). Note again the differences in predominant growth clusters between early (< 677 100 dpi, clusters 1 to 3) and late (>100 dpi, clusters 4 to 7) time points. After 100 dpi, when 678 CFUs are high, the majority of bacteria are in cluster 7, with sufficient carbon sources and 679 low but not limiting oxygen. When CFUs in the granulomas are low, the majority of bacteria 680 are in cluster 4, with ample carbon sources but growth slowed by hypoxia. These non-681 replicating bacteria can re-enter the replicating state when hypoxia is relieved, as a 682 granuloma shrinks. Reducing hypoxia in granulomas has been suggested as a strategy to re-683 sensitize bacteria to antibiotics (96). The dynamics between bacterial load, granuloma size 684 and bacterial growth clusters are also evident if we examine multiple granulomas at 685 multiple time points between 200 and 1000 dpi (Figure 6B, Supplement Figure S4). Smaller 686 granulomas with high bacterial loads have bacteria mostly in growth cluster 7, while larger 687 granulomas have smaller bacterial loads with majority of bacteria in cluster 4. Bacteria in 688 cluster 5 mostly occupy granulomas with intermediate size and bacterial load. We explore 689 the role of different growth clusters with respect to long-term bacterial survival in 690 granulomas by removing slow growth and lipid accumulation independently. Removing 691 Mtb’s ability to slow its growth, i.e. its ability to enter growth cluster 4 (but not its ability to 692 accumulate lipid inclusions), leads to lower bacterial loads and higher sterilization rates 693 (Figure 6C). These differences can be linked to increased bacterial death from starvation 694 (Figure 6D). Specifically, since growth cluster 4 normally adjusts to lack of oxygen by 695 lowering its maintenance metabolism (Table 6), the increased bacterial death shown in 696


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Figure 6D is due to oxygen levels insufficient to sustain maintenance metabolism. This 697 ‘suffocation’ is in contrast to bacterial death due to a lack of carbon sources (such as 698 conditions encountered by growth clusters 1 and 2 early during infection (Figure 5C, Table 699 6). Collectively these results connect bacterial growth phenotypes to granuloma properties, 700 and show the importance of growth adaptation for long-term survival of Mtb in granulomas. 701 702 3.5 Timing of metabolic enzyme inhibition, early vs. late in infection, influences attenuation 703 To explore the potential of metabolic enzymes as antibiotic targets, we predict the effect of 704 each enzyme’s removal on both growth rate in vitro (using the CBM) and bacterial load in 705 granulomas (using GranSim-CBM). We generate virtual metabolic enzyme knockout 706 mutants (KOs) by systematically removing one enzyme at a time from the metabolic 707 network in the CBM. For in vitro predictions, we consider different culture media as well. 708 709 Of 191 KOs tested, we identify 41 as significantly attenuated (FDR 0.05) relative to WT 710 based on bacterial load within granulomas at 400 dpi (Supplemental Figure S5A,B; 711 Supplement Table S3). These 41 enzymes catalyze 22 distinct reactions, primarily within 712 the electron transport chain: 10 different genes encoding components of the cytochrome c 713 oxidase complex, and 13 genes encoding components of NADH-ubiquinone oxidoreductase. 714 The attenuation predicted for these KOs suggests that they could be potential antibiotic 715 targets. Note that our predictions overestimate the amount of attenuation possible with 716


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antibiotics because antibiotics typically result in only partial inhibition of target enzymes 717 and because antibiotic treatment of TB typically starts well after infection when the patient 718 seeks medical care. 719 720 To test the effect of a knockout occurring mid-infection (at 200 dpi, Figure 7) for the 41 721 KOs identified in the previous analysis. Mid-infection KOs fall broadly into three categories: 722 (1) no attenuation for mid-infection knockouts (Figure 7A), (2) less attenuation for mid-723 infection knockouts than pre-infection knockouts (Figure 7B), and (3) similar attenuation 724 in pre- and mid-infection knockouts (Figure 7C). KOs that fall into categories 2 or 3 (but 725 not category 1) could potentially be good antibiotic targets because they are attenuated if 726 knocked out mid-infection. These results suggest that methods that screen for new antibiotic 727 targets should account for differences between bacterial requirements for survival early vs. 728 late in infection. 729 730 3.6 Metabolic bypass pathways mitigate growth defects in attenuated mutants and may 731 represent auxiliary drug targets 732 What drives the differential attenuation in early vs. late KO mutants? We use the CBM to 733 identify metabolic mechanisms that allow some KO mutants to sustain infection in 734 granulomas. We use flux variability analysis (FVA) to identify bypass reactions activated in 735 response to enzyme knockouts. Of the 41 attenuated mutants identified with GranSim-CBM, 736


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28 were observed to have a non-zero growth rate in lipid only media, and these were 737 mapped to a unique subset of 7 reactions (Table 7). Growth rates of the corresponding 738 mutants range from 30% to 75% of the wild-type growth rate in an in vitro environment 739 with high lipid and high oxygen. At maximum growth rate, the mutants all reduce oxygen at 740 the same rate as the wild-type genotype, indicating that oxygen reduce is the limiting 741 reaction for both wild-type and these mutants. Several mutants require greater TAG 742 import, suggesting less efficient stoichiometry in the conversion of TAG to biomass. 743 Mutants with reduced TAG import relative to wild-type utilize oxygen less efficiently and 744 consequently display significant attenuation. 745 746 To identify the reactions used by the KO mutants to bypass knocked-out enzymes, we can 747 visualize metabolic sub-networks involving knockouts, bypass reactions, and metabolite 748 reactants and products used by these KO mutants to compensate for loss of an enzyme 749 (Figure 7D, Supplement Figures S5 to S12). An electron transfer system example is 750 provided by the knockout of ctaB, which eliminated the activity of the cytochrome bc1 751 protein complex within the cytochrome c system. This function is bypassed by the less 752 efficient cytochrome bd complex, which is not used by the wild-type organism under the 753 same conditions (Figure 7D). This bypass allows the ctaB knockout to persist in 754 granulomas at near WT levels (Figure 7B). These computational results are consistent with 755 recent experimental results using small molecules to poison cytochrome bc1 activity, 756


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resulting in up-regulation of cytochrome bd (97). Similarly, knockout of eno requires a 757 bypass reaction for generation of 3-phosphoglycerate (Supplement Figure S5). Inhibitors of 758 enolases have been reported, including phosphonoacetohydroxamate (98) and ENOblock 759 (99). Our computational results suggest that these inhibitors could be made more effective 760 at inhibiting the growth of Mtb by co-treatment with inhibitors of bypass enzymes encoded 761 by genes such as gap (glyceraldehyde 3-phosphate dehydrogenase) or tpi (triosephosphate 762 isomerase). These results illustrate how FBA can be used to broadly characterize the 763 metabolic defects caused by individual drugs and, potentially, to identify secondary targets 764 required for bypassing chemically or genetically inactivated reactions. 765 766 3.7 Multi-scale analysis reveals in vitro culture media and growth thresholds predictive of Mtb 767 survival in granulomas 768 Mtb mutants that grow well in rich media (high glucose, high TAG, and high oxygen) may 769 have growth restrictions in the depleted environment of an in vivo granuloma. With the aim 770 of identifying in vitro conditions that may predict in vivo readouts (Figure 1), we investigate 771 which in vitro nutrient conditions yield Mtb growth rates that correlate with in silico 772 predicted granuloma outcomes such as bacterial load. 773 774 Growth rates calculated for knockouts in rich media (r = 0.67; p-value < 0.001) and lipid-775 only media (r = 0.73; p-value < 0.0001) are correlated with predicted CFU per granuloma 776


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(Figures 9A,B). Thirteen of the 191 mutants are not predicted to be attenuated in rich 777 media but are attenuated in simulated granulomas (Figure 8A; similar to KO2 in Figure 1). 778 Such false negative attenuation predictions are not present using growth predicted on 779 lipid-only media (Figures 9B). Knockouts conducted at 200 dpi rather than pre-infection 780 also show correlation (r = 0.81; p-value < 0.001) between the lipid-only growth rate for the 781 knockout and the bacterial load in granulomas (Figure 8C). These correlations are not 782 unexpected as a reflection of the model constraint that intracellular bacteria use only TAG, 783 not glucose. However, it is unclear which threshold in growth rates should be used to 784 define attenuation relative to WT growth rate. If the same in vitro growth rate threshold 785 (~85% of WT growth rate) is used to define attenuation in the early (Figure 8B) and late 786 (Figure 8C) knockouts, two late knockout mutants appear attenuated based on lipid media 787 growth rates, but are not attenuated in simulated granulomas (Figure 8C; similar to KO3 in 788 Figure 1). A lower threshold (~66% of WT growth rate) is necessary to predict which 789 mutants are unable to sustain long-term infections (Figure 8C). In other words, KOs with 790 predicted growth rates between ~66 and 85% of WT growth rate are able to sustain but 791 not establish infections within granulomas. 792 These data identify ~66% of WT growth in lipid media as a threshold for predicting in vivo 793 attenuation. 794 795 4. Discussion 796


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A better understanding of the microbiology of TB granulomas could help to identify new 797 antibiotic targets or host-directed therapies (100, 101) that could limit long-term Mtb 798 survival in vivo. We present a multi-scale computational model that maps genetic and 799 metabolic detail at the bacterial scale to in vivo granuloma outcomes such as bacterial load. 800 This model recapitulates tissue-level outcomes observed in vivo (21, 73-75), affording us a 801 first-time tool to track dynamics occurring on bacterial and granuloma scales. 802 803 The view of long-term Mtb survival in a non-replicating state within granulomas suggests a 804 static equilibrium between host and pathogen. However, evidence points to a more 805 dynamic host-pathogen balance (73), with non-sterilized granulomas in latently infected 806 individuals indistinguishable from granulomas in individuals with active TB disease (21, 807 23) based on CFU and on CFU/CEQ where CEQ (chromosomal equivalents) is a measure of 808 all bacteria that have been in the granuloma during the entire infection. Our model 809 supports a dynamic persistence mechanism in which Mtb surviving in long-term 810 granulomas can be actively dividing and continually responding to changing granuloma 811 environments. This would imply that TB is not only a highly heterogeneous infection (102) 812 but, on a granuloma level, also a highly dynamic one. Specifically, our model suggests that 813 the slowly- or non-replicating phenotypes of Mtb preserve the bacterial population in vivo 814 by continuously adapting to dynamic granuloma microenvironments, and we show that 815 removing the ability of bacteria to slow their growth mid-infection impairs their ability to 816


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sustain a long-term infection. Inhibitors of the non-replicating phenotype could potentially 817 improve treatment outcomes, similar to the “shock-and-kill” approach currently being 818 investigated in HIV therapy (103). The role of the non-replicating phenotype in dynamic 819 adaptation could, to some extent, be tested in vitro using dynamic nutrient condition 820 manipulation in chemostats or other culture methods (26, 28) combined with knockouts in 821 genes suspected to be connected to the phenotype (eg relA, dosR). 822 823 Our predicted nutrient conditions encountered by Mtb in granulomas could help guide the 824 environmental conditions used for in vitro drug screens. In vitro drug or drug-target 825 screening assays with slow- or non-replicating Mtb (including starvation, low oxygen, and 826 nitric oxide assays) are typically used to represent in vivo bacterial phenotypes, and there 827 is significant research effort into recreating granuloma-like stress conditions in vitro (3). 828 Even in the absence of a hoped-for granuloma-in-a-dish experimental system, our results 829 suggest the most relevant in vitro experimental systems for predicting granuloma 830 outcomes. Mutant phenotypes in simulated granulomas (“in vivo”) are in greatest 831 concordance with growth rates in simulated lipid-only media (“in vitro”). These results 832 could support new directions for in vitro drug or drug-target screening (57). Our results 833 further identify an attenuation threshold, showing that drugs should result in lipid-only 834 growth rates below 66% of the WT to be able to effectively inhibit bacterial survival in 835 granulomas. Note that this threshold provides an upper limit of growth under inhibition 836


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since our granuloma results are based on complete knockout of the genes whereas novel 837 antibiotics are unlikely to continuously and completely eliminate the enzymatic activity of 838 its target. This granuloma-dependent threshold for mutant attenuation suggests a novel 839 strategy for translating in vitro discoveries into potential new therapies. 840 841 Our model also identifies bypass pathways that are not essential in WT but which are 842 essential for optimal growth of a knockout mutant in the granuloma environment. Bypass 843 pathways could be used to identify secondary targets for combination therapy or potential 844 failure modes for inhibition of metabolic enzymes. Bypass reactions may also suggest novel 845 combinations of drugs with synergistic anti-Mtb activity. 846 847 Computational methods have been successfully applied in the drug discovery pipeline 848 against a number of pathogens (104-106). Genes (and combinations of genes) we identify 849 to be important for in vivo survival can now be tested as potential new drug targets using 850 existing drugs or KO strains in animal models. Combining GranSim-CBM with our existing 851 model of antibiotic distribution and activity in the granuloma (40, 41) could also help 852 elucidate the contributions of bacterial heterogeneity, asymmetric division and growth 853 and lipid inclusion levels to treatment outcomes (5, 107). Such insight can in turn inform 854 new regimens and strategic drug design. 855 856


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Funding information 857 This research used these resources: National Energy Research Scientific Computing Center, 858 which is supported by the Office of Science of the U.S. Department of Energy under Contract 859 No. DE-AC02-05CH11231; and the Extreme Science and Engineering Discovery 860 Environment (XSEDE), which is supported by National Science Foundation grant number 861 ACI-1053575. This research was supported by NIH R01 HL106804 (awarded to DEK), R01 862 EB012579 (awarded to DEK and JJL), R01 HL 110811 (awarded to DEK and JJL), R01 863 HL06786 (awarded to JSB), and R01 HL 1060800 (awarded to JSB and DEK). 864 865 Acknowledgments 866 We thank Dr. Johnjoe McFadden for sharing the updated version of GSMN-TB and Drs. 867 JoAnne Flynn and Petros Karakousis for valuable discussions. Dr. McFadden has asked us to 868 mention that further details of GSMN-TB will be published elsewhere. Thanks to Paul 869 Wolberg and Joseph Waliga for technical and computational support. 870 on March 29, 2021 by guest

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Figure Legends 871 872 Figure 1: Paradigm for predicting in vivo attenuations from in vitro experiments. 873 When screening for Mtb drug targets, mapping in vitro phenotypes of knockout (KO) 874 mutants (bacterial scale) to in vivo outcomes (host tissue scale) is not obvious. Defining 875 attenuated mutants relative to wild-type (WT) growth in vitro can result in incorrect 876 identification of drug targets. For example, KO mutants can be identified as attenuated in 877 vitro, but result in no attenuation when tested in vivo (i.e. false positive attenuation 878 prediction, e.g. KO3). Or mutants could be dismissed as non-attenuated in vitro, but show 879 attenuation in vivo (i.e. false negative attenuation prediction, e.g. KO2). Our model system is 880 capable of bridging in vitro and in vivo outcomes. Results can be used to identify such 881 misclassifications, to guide in vivo screening, and to suggest in vitro screening conditions 882 that are more predictive of in vivo infection outcomes. 883 884 Figure 2: Multi-scale model system bridging metabolic to tissue scale. (A) GranSim, our 885 agent-based model of granuloma formation and function, incorporates host immune 886 functions (see (34-37) for details) as well as bacterial dynamics for the first time on an 887 individual bacterium level. In silico granulomas are an emergent behavior of the system. (B) 888 The flux balance model (CBM) uses a stoichiometric matrix representing the metabolic 889 network of Mtb (45) to predict growth rates based on the bacterial objective function 890


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(growth vs lipid inclusion production) (13). (C) The combination model GranSim-CBM 891 tracks granuloma formation and environmental nutrient conditions (oxygen, TAG and 892 glucose) (left) and uses the CBM to predict growth rates and lipid inclusion formation for 893 each bacterial agent based on its local environment and internal lipid inclusion stores 894 (right). 895 896 Figure 3: GranSim-CBM model calibration to experimental data. (A) Discretization of 897 Mtb in GranSim does not affect bacterial loads in granulomas (CFU: colony forming units) 898 as compared to previous model versions with continuous Mtb representation (35-38, 40, 899 41). (B) GranSim-CBM is calibrated to experimental data from animal models of TB. 900 GranSim-CBM predicted colony-forming units (CFU) per granuloma is calibrated to 901 measurements from the NHP model of TB (21, 73-75). (C) Predicted oxygen concentration 902 in granulomas is calibrated to direct measurements in rabbit granulomas (lower dotted 903 line) and the threshold for PIMO hypoxia stain is shown for reference (upper dotted line). 904 For panels (A-C), solid lines show medians, dashed lines show 95% confidence intervals, 905 N=15. (D) Snapshot of a representative in silico granuloma at 300 dpi, with predicted 906 oxygen, TAG and glucose levels within the granuloma. 907 908 Figure 4: Distributions of bacterial growth over time. (A) Histogram showing the 909 distribution of populations of bacteria by generation time. Bacteria with generation times 910


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longer than 10 days are included in the histogram at 10 days. (B) Histogram showing 911 distribution of bacteria by instantaneous growth rate. Results are averages of 100 replicate 912 simulations with the baseline parameter set in Table 4. 913 914 Figure 5: Hierarchical clustering of bacteria by nutrient conditions and spatial 915 location. (A) Bacteria (columns) from multiple time points from a representative 916 granuloma are hierarchically clustered based on growth rate and lipid inclusions, TAG, 917 glucose and oxygen available in each bacterium’s immediate environment (rows). Each 918 nutrient is standardized to its row average. Clusters are numbered and highlighted with 919 color codes indicated by arrows on the right. Two bacteria are highlighted (red and 920 magenta stars with black dashed lines) as examples discussed in the text. These two 921 bacteria are also used as examples in the discussion of panels B and C. (B) Bacterial clusters 922 from panel A are further characterized by plotting their time point (day), fluxes from the 923 CBM (i.e. optimal uptake fluxes for each nutrient calculated by the CBM based on the 924 available nutrients), maintenance metabolism and cellular location. Values for each output 925 are standardized by row values. (C) Bacteria and their growth clusters are localized within 926 granulomas. Granuloma simulation snapshots are shown in the top row with agent colors 927 corresponding to those in Figure 3D. The example bacteria from panels A and B are located 928 in these granuloma snapshots with stars in the panels for 20 dpi and 700 dpi. Bacterial 929


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growth clusters are shown in the granulomas (bottom row) using color codes of clusters 930 from panels A and B. 931 932 Figure 6: Importance of growth adaptation for long-term survival of Mtb in 933 granulomas. (A) Proportions of bacteria in each growth cluster (7 clusters identified in 934 Figure 5) are quantified every 20 days over the course of infection (right y-axis) and 935 plotted with total CFU (left y-axis). (B) Each pie symbol represents one granuloma (300 936 randomly selected granulomas from a collection of 100 granulomas at different time pts at 937 20 day intervals after 200 dpi). Slices are proportions of bacterial populations within each 938 growth cluster. (C,D) Comparing WT simulations to simulations in which growth 939 adaptation or ability to accumulate lipid inclusions was removed. (C) Time-averaged CFU 940 between 200 and 1000 dpi, and (D) fraction of bacteria that died from starvation by 1000 941 dpi (i.e. biomass < τdeath) for individual granulomas (N = 100). P-values indicate results 942 from Kruskall-Wallis test with Dunn’s correction for multiple comparisons. Lines show 943 means. 944 945 946 Figure 7: Bacterial loads over time for different mutants. Predicted total CFU (median) 947 over time for WT (dash), knockouts from start of infection (black) or mid-infection 948


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knockouts from 200 dpi (gray). Three representative genes are shown (A: tpi/Rv1438, a 949 triosephosphate isomerase which has a role in glycolysis; 950 B: ctaB/Rv1451, a cytochrome C oxidase assembly factor; and C: gap/Rv1436, a probable 951 glyceraldehyde 3-phosphate dehydrogenase (GAPDH) involved in the second phase of 952 glycolysis). N=20 for knockouts, N=100 for WT. (D) Bypass reactions identified by flux 953 variability analysis (FVA). Squares are chemical reactions corresponding to the enzyme 954 label. Metabolites used or produced by any of the depicted reactions are included (teal 955 circles). This diagram shows the reactions eliminated by a gene knockout (black square) 956 and reactions that become “required” (defined as leading to attenuation if removed) in the 957 knockout, but were not required in the WT (green square). Dashed arrows correspond to 958 metabolite usage or production no longer present in the knockout (as the reaction has been 959 removed); solid arrows correspond to reactants of the green bypass reactions. To 960 summarize what can be gleaned from this figure: The protein coded for by ctaB is required 961 for cytochrome bc1 oxidase activity. Thus, a knock-out mutant in ctaB will make use of a 962 bypass flux through cydB, which is part of the less efficient cytochrome bd complex. If cydB 963 was also knocked out (or severely inhibited by drugs) then the model predicts that Mtb 964 would be further attenuated (though not necessarily incapable of growth). Identical results 965 are obtained for knockouts in any genes annotated as required for cytochrome c oxidase 966 activity: ctaB, ctaC, ctaD, ctaE, fixA, fixB, qcrA, qcrB, qcrC, and Rv1456c. 967 968


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Figure 8: Predicting in vivo attenuations from in vitro Mtb growth rates. We implement 969 the paradigm described in Figure 1 by correlating CBM-predicted growth rates and average 970 GranSim-CBM predicted CFU per granuloma. We plot CBM-predicted growth rates for 971 attenuated single gene knockouts in rich media (A) or lipid-only media (B) vs average 972 GranSim-CBM predicted CFU per granuloma when knocked out from the start infection (A, 973 B) or knocked out mid-infection at 200 dpi (C). Scatter plot of mean +/- SEM (N=20) for 974 each knockout and wild-type. Note that the high CFU burden knockouts can be cleanly 975 separated from the low CFU burden knockouts based on the CBM growth rate in lipid-only 976 media, but that timing of the knockout moves the in vitro threshold to the left (arrow in 977 panel C). 978 979


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Tables 980 Table 1: Summary of modeling methods and their application in our multi-scale 981 computational approach 982 Method Description Application Agent-based model (ABM) Stochastic model that describes the behavior of a population of individuals. ABMs consist of an environment, individuals (agents) and rules. Each agent is tracked individually in the environment, and their behavior is determined based on predefined rules and probabilities. Emergent behavior of the system is observed and analyzed. (62, 108, 109)

GranSim describes the behavior of a population of host cells and bacteria in the lung environment based on biological rules. Granuloma formation and function is an emergent behavior of this population of cells. http://malthus.micro.med.umich.edu/GranSim/GranSim-CBM/ (34-37)

Constraint-based model (CBM) Models that determine the possible set of behaviors, or the optimal behavior according to a predefined criterion, of a system within certain constraints, and assuming steady state. Flux balance analysis is a type of CBM that determines the possible set of fluxes through a metabolic network given constraints on enzymatic reactions and nutrient availability. (45, 46), iNJ661 (47) and more recently sMtb (48))

Our CBM determines the optimal flux of metabolites through the Mtb metabolic network, to maximize production of a combination of biomass and lipid inclusions.

Dynamic CBM These CBMs replace the steady-state assumption with a pseudo steady-state assumption to capture changes in the system or the environment over time. Our CBM assumes a pseudo steady-state to capture changes in nutrient micro-environments within the granuloma over time.


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(49, 50) (51, 52) Multi-scale model A model that captures and integrates real-world dynamics at multiple spatial or temporal scales.(62, 108, 110) GranSim-CBM is a multi-scale model that captures dynamics from the metabolic, cellular and tissue scales on time scales spanning minutes to years. Latin hypercube sampling (LHS)

A sampling method that stratifies the sampling space to achieve the same accuracy as random sampling with fewer samples. (72) LHS is used as part of uncertainty and sensitivity analysis, to sample the large parameter space for GranSim-CBM.

Partial rank correlation coefficients (PRCC) PRCC determines the correlation between an input factors and an output, by removing the influence of other simultaneously varying input factors. (72)

PRCC is used during sensitivity analysis to determine the most influential model parameters in determining granuloma level outputs. Hierarchical clustering Hierarchical clustering calculates the difference between individual observations based on a predefined distance metric. Individual observations are then grouped/clustered such that similar observations are collected in a single cluster. (111)

We cluster individual bacteria (observations) based on their growth rate and local nutritional environment.

983 984


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Table 2: GranSim rules for Mtb modeled as continuous variables or individual agents. See 985 Table 3 for variable and parameter definitions. 986 Bacterial event Continuous Mtb Agent MtbGrowth (Intracellular or extracellular)

νb = growth rate Mtb(t+1) = (1+νb)Mtb(t)

νb = growth rate Shuffle MtbList For i = 1 to Mtb(t) Bi(t+1) = (1+νb)Bi(t) If Bi > τdiv Make new Mtb agent Divide Bi and Li into fractions f and (1-f) between two daughter agents Else if Bi < τdeath Mtb agent dies Death (From host mediated killing or lack of nutrients) nrKill = number of Mtb to kill Mtb(t+1) = Mtb(t)-nrKill

nrKill = number of Mtb to killShuffle MtbList Delete 1st ‘nrKill’ Mtb agents on MtbList Disperse a fraction of intracellular Mtb to Moore

fd= fraction to dispersedispMtb = fdMtb(t) dMtb = dispMtb/NM for m = 1 to NM fd = fraction to dispersedispMtb = fdMtb(t) dMtbBase = dispMtb/NM dMtbExtra = mod(dispMtb,NM)


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Neighborhood (When a chronically infected macrophage bursts)

Mtbm(t+1) = Mtbm(t)+dMtb Shuffle MtbListFor m = 1 to dMtbExtra Move 1st ‘dMtbBase+1’ agents in MtbList to compartment m For m=dMtbExtra+1 to NM Move 1st dMtbBase agents in MtbList to compartment m Delete the rest of MtbList Phagocytosis (Move extracellular Mtb to intracellular)

count = nr of Mtb to phagocytose MtbE(t+1) = MtbE(t)-count MtbI(t+1) = MtbI(t)+count

count = nr of Mtb to phagocytoseShuffle MtbEList Move 1st ‘count’ Mtb agents from MtbEList to MtbIList 987 988


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Table 3: Variables used in GranSim-CBM 989 Variables Units Description νb h-1 Growth rate νL h-1 Net lipid inclusion generation rate νpL h-1 Lipid inclusion production rate predicted by CBM νcL h-1 Lipid inclusion consumption rate predicted by CBM d timestep-1 Biomass degradation rate η Switching parameter to calculate objective function and biomass degradation rate MtbXList List of Mtb agents in location X (E: extracellular, I: intracellular) Mtb(t) Number of bacteria as continuous Mtb or in MtbList at timestep t Bi(t) BU Biomass of Mtb agent i at timestep t Li(t) fmol Lipid inclusions of Mtb agent i at timestep t Xi(t) Location of Mtb agent i at timestep t (E: Extracellular; I: Intracellular)


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NM Number of grid compartments in Moore neighborhood (adjacent grid compartments in a 2 dimensional grid). vilow fmol/h.BU Lower limit on import flux for nutrient i. Set to zero. viup fmol/h.BU Upper limit on import flux for nutrient i. Dependent on Vmax,i and Ki. Z Objective function to be optimized by the CBM. A linear combination of νb and νL. *Conversion factors: 10 min/timestep. 1 BU = 196 fg dry weight. 990 991


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Table 4: Parameters used in GranSim-CBM 992 993 Parameter Description Unit Ranges for

uncertainty

analysis Ranges for

sensitivity

analysis Baseline

parameter set τdiv

Biomass division threshold BU 1.7 - 2.5 2τdeath

Biomass death threshold BU 0.2 - 0.6 0.5 f Division fraction 0.25 - 0.5 0.25 - 0.5 0.47 D Diffusivity of oxygen cm2/s 1x10-6 – 1x10-4 7x10-7 –7x10-5 7.3x10-6 O2,plasma Plasma oxygen concentration M 8x10-4 - 1 x10-2 9 x10-5 - 9 x10-3 1x10-3 p Vascular permeability of oxgyen

cm/s 1 x10-6 - 1 x10-4 1 x10-6 - 1 x10-4 1.1 x10-5 Vmax-host Max host cell oxgyen consumption

moles/cell/s 6 x10-18 - 6e-16 1 x10-18 - 1 x10-16

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