tuneable resolution as a systems biology approach for multi-scale

Advanced Review

Tuneable resolution as a systemsbiology approach for multi-scale,multi-compartment computationalmodels

Denise E. Kirschner,1∗ C. Anthony Hunt,2 Simeone Marino,1

Mohammad Fallahi-Sichani3 and Jennifer J. Linderman4∗

The use of multi-scale mathematical and computational models to study complexbiological processes is becoming increasingly productive. Multi-scale models spana range of spatial and/or temporal scales and can encompass multi-compartment(e.g., multi-organ) models. Modeling advances are enabling virtual experimentsto explore and answer questions that are problematic to address in the wet-lab.Wet-lab experimental technologies now allow scientists to observe, measure,record, and analyze experiments focusing on different system aspects at a vari-ety of biological scales. We need the technical ability to mirror that same flex-ibility in virtual experiments using multi-scale models. Here we present a newapproach, tuneable resolution, which can begin providing that flexibility. Tune-able resolution involves fine- or coarse-graining existing multi-scale models at theuser’s discretion, allowing adjustment of the level of resolution specific to a ques-tion, an experiment, or a scale of interest. Tuneable resolution expands options forrevising and validating mechanistic multi-scale models, can extend the longevityof multi-scale models, and may increase computational efficiency. The tuneableresolution approach can be applied to many model types, including differentialequation, agent-based, and hybrid models. We demonstrate our tuneable resolu-tion ideas with examples relevant to infectious disease modeling, illustrating keyprinciples at work. © 2014 The Authors. WIREs Systems Biology and Medicine published by WileyPeriodicals, Inc.

How to cite this article:WIREs Syst Biol Med 2014, 6:289–309. doi: 10.1002/wsbm.1270

∗Correspondence to: [email protected], [email protected] of Microbiology and Immunology, University ofMichigan Medical School, Ann Arbor, MI, USA2Department of Bioengineering and Therapeutic Sciences, Univer-sity of California, San Francisco, CA, USA3Department of Systems Biology, Harvard Medical School, Boston,MA, USA4Department of Chemical Engineering, University of Michigan, AnnArbor, MI, USAConflict of interest: The authors have declared no conflicts ofinterest for this article.

INTRODUCTION

Continued advances in biomedical science willrequire more explanatory mathematical and

computational models.1–9 Increasingly these modelsare multi-scale, encompassing processes operating at arange of temporal and spatial scales and perhaps alsobetween multiple compartments (e.g., organs). Thekey goal of multi-scale modeling in medically focusedsystems biology is the generation of models that can

Volume 6, Ju ly/August 2014 289© 2014 The Authors. WIREs Systems Biology and Medicine published by Wiley Periodicals, Inc.This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution inany medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

Advanced Review wires.wiley.com/sysbio

be used to better understand hypothesized mecha-nisms, make predictions, interpret data, suggest newapproaches for therapy, and offer new explanationsfor observed phenomena.

Advances in multi-scale modeling are enablingvirtual experiments to answer questions that can beproblematic to address in a wet-lab.10–15 In wet-labexperiments, advances in technology now allow sci-entists the flexibility to observe, measure, record, andanalyze experiments at a variety of scales. We need thesame capability in our virtual experiments (Figure 1).While virtual experiments cannot replace experimen-tation on living systems, they can be used to create newknowledge and improve explanatory insight. To do so,we develop, explore, and challenge alternative, plausi-ble mechanistic scenarios, including hypotheses withinand across scales. As progress is made, we can increasethe synergy between virtual and wet-lab experiments.Such synergy is expected to be most productive as ourmulti-scale models become increasingly analogous totheir animal model and human counterparts at multi-ple scales, under an expanding variety of interventionscenarios.

One strategy to achieving such flexibility andincreasing the useability of multi-scale models isan approach we term tuneable resolution. Tune-able resolution proposes that multi-scale modelsshould be built with multiple levels of resolution, sothat a fine-grained or coarse-grained version can beemployed with user discretion, allowing adjustmentof the level(s) of resolution specific to a question,an experiment, a particular use, or a change in per-spective or scale of interest. In addition to providing

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FIGURE 1 | Coupled use of wet-lab and virtual experiments. Leftside: Scientific flow of wet-lab experiments from design throughinterpretation. Right side: Scientific flow of virtual experiments fromdesign through interpretation. Two cycles intersect to generatehypotheses to pose and address new questions. Iteration is a keycomponent of this process and involves multiple cycles on either or bothsides.

this flexibility of level of resolution, we argue thata tuneable resolution approach expands options forrevising and validating models and increases modelusability and portability.

We describe our tuneable resolution approachstarting with arguments for, and evolving principlesguiding, its use. We then demonstrate resolution tun-ing in models of the immune response to infection withMycobacterium tuberculosis, the pathogen that causestuberculosis (TB) (Examples 1–3). Despite many dif-ferent and insightful experimental approaches takenover the years, fundamental questions remain aboutTB. In the TB context, virtual experiments pro-vide means and strategies for generating and testinghypotheses about the disease, its mechanisms, andpotential treatments.16

THE ARGUMENT FOR TUNEABLERESOLUTION

Tuneable Resolution Provides FlexibilityRequired to Span Varying Aspectsand Scales of InterestExperiments on living systems often focus on a singleaspect (or feature) and a single scale. Multiple types ofexperiments allow access to information at differentscales. For example, images of diseased lungs provideinformation about the spread of TB, whereas immuneresponses developing in draining lymph nodes (LNs)determine how well infection can be controlled. Weneed the flexibility and technical ability to change anaspect of a multi-scale model on which a new virtualexperiment focuses and, when needed, the observa-tion interval and frequency (Figure 2). We also needto retain essential knowledge when the aspect ofinterest changes, e.g., from signaling networks withinan immune cell to immune cells interacting witheach other. Models built with tuneable resolution canachieve this.

Tuneable Resolution Enables MoreComprehensive Model ValidationWe can improve both explanatory and predictive use-fulness by improving phenotypic overlap between phe-nomena generated by multi-scale models and their realworld counterparts. To do so we must increase thevariety of ways that results from virtual experimentscan either be validated against corresponding wet-labexperiments or be objectively compared to availableknowledge. We improve the scientific usefulness ofmulti-scale models by building trust into simulatedmechanisms using a tuneable resolution approach

290 © 2014 The Authors. WIREs Systems Biology and Medicine published by Wiley Periodicals, Inc. Volume 6, Ju ly/August 2014

WIREs Systems Biology and Medicine Tuneable resolution as a systems biology approach

A2a

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A3A1

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FIGURE 2 | Tuneable resolution approach. Top: An initial model (shown as 3 puzzle pieces) functions within an environment (A1). Fine-graining aportion of the initial model to generate A2a, and subsequently a portion of that latter model to generate A3, adds additional scales of relevance.Progression from A3 to A2b demonstrates re-engineering of the previous scale model (A2a) to reflect knowledge gained at A3. Bottom: An initialmodel is refined to include additional scales of interest in the environment as model development progresses from B1 through B3. Depending on thequestion or aspect, the user choses the appropriate level of resolution.

and multiple validation targets. Trust increases intwo ways: improving in silico-to-wet-lab similari-ties and identifying when, why, and where dissimi-larities occur. We provide examples supporting ourcase that both activities require a tuneable resolutionapproach.

Fine-Graining May Present Strategiesfor Re-engineering to Obtain an ImprovedCoarse-grained ModelThere are many computational and mathematicalconsiderations that emphasize caution when addingfine-grain information to multi-scale models. A tune-able resolution approach argues not only for graduallyand systematically building in additional detail into amodel (as warranted by available data and questionsbeing asked) but also for informing the formulationof a more biologically accurate coarse-grained versionby using information from the fine-grained model.

For example, an original coarse-grained model isdeveloped and, because of further biological ques-tions or additional validation targets, a finer-grainedversion is created (Figure 2, A1 ->A2a ->A3; Figure 2,B1 ->B2 ->B3). Once those questions are answered,the user wishes to return to a simpler representa-tion but that preserves the biological integrity of thesystem (although not necessarily the mathematicalintegrity): a tuneable resolution approach providesa coarse-grained model that has been improved byinsights gained during virtual experiments on thefine-grained model. This process helps one discoverwhat mechanisms must appear in the model, andat what level of detail, to explain correspondingbiological data (Figure 2, A3 ->A2b). Put anotherway, the re-engineered coarse-grained model can bethought of as a ‘model of a model’, i.e., a versionthat retains some, but not all, finer-grained modelbehaviors.

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Tuneable Resolution Can Help IdentifyModel FlawsModels are perpetual works in progress. New insights,from either virtual or wet-lab experiments, can falsifyone or more mechanistic model features, requiringmodel revision. The multiple perspectives offered bymodels capable of tuneable resolution may reducebias and enable identifying the location of a modelflaw, and thus can reduce reengineering required toproduce and validate resulting revised and improvedmodels.

Tuneable Resolution May Help Identifythe Scale Location of a ‘Tipping Point’An overarching goal for biomedical research is dis-covery of new intervention strategies that improvehealth outcomes. For TB, diabetes, cardiovascular dis-eases, and others that are still shrouded in consid-erable uncertainty, the scale location of the tippingpoint for a therapeutic intervention under study canbe unknown and may even vary between individu-als. For example, should a therapy target a specificreceptor–ligand interaction in a specific biologicalorgan, the expansion of a class of T cells, or areboth required but following a coordinated strategy?We envision that virtual experiments using tuneableresolution provide new options for expediting andnarrowing the search. This would arise, e.g., whencreating a new coarse-grained sub-model to replace afine-grained sub-model (Figure 2). Key model mech-anisms that are required to preserve the behaviorobtained with the fine-grained are likely tipping pointsfor the combined multi-scale model behavior. In a non-linear ordinary differential equation (ODE) system,e.g., those necessary preserved behaviors may identifybifurcation parameters that are targets for therapeuticinterventions.

Tuneable Resolution Approaches CanIncrease Computational Speed, ModelUsefulness, and PortabilityMost multi-scale models grow in complexity andscope as researchers add mechanisms and detailto improve agreement and usefulness in interpret-ing experimental data. Consequently, the model canbecome increasingly difficult to work with—moredifficult to debug, to port to other platforms andother users—and the results of virtual experimentsmay become more difficult to interpret. Simulationsmay require significantly longer runtimes. Indeed,some models essentially ‘die’ under their own weight,becoming too complex to be passed on to the next

user. Tuneable resolution approaches, particularlythose emphasizing modularity, model linking, andre-engineering of coarse-grained model versions, canassist in avoiding or reducing these problems.

EVOLVING PRINCIPLES FOR BUILDINGTUNEABLE RESOLUTION MODELS

Resolution Tuning Requires Coupled Useof Coarse- and Fine-Graining MethodsOur model development typically proceeds by firstincluding well-studied and characterized processesknown to have major or first-order effects on sys-tem behavior. Given specific questions to be addressedin virtual experiments, some biological processes maynot require great detail in their description, and so canbe represented in a coarse-grained fashion, e.g., usinga parameter or a simple phenomenological expres-sion. New biological questions or data might laterrequire virtual experiments that have a new focus andnew multi-scale model uses, and that, in turn, mayrequire increased model resolution, or fine-graining,e.g., replacing the parameter or simple phenomeno-logical expression with a sub-model that simulates rel-evant biological processes in greater detail. Addinginformation from multiple length and time scales,while important for simulating phenomena, signifi-cantly increases the complexity of analyses and execu-tion time. Thus it is important to be able to selectively(and possibly automatically) coarse-grain model com-ponents and/or features when needed. Coarse-grainingcan be achieved by replacing a sub-model consistingof several biologically based equations or rules withwisely chosen phenomenological expressions (e.g., aparameter, a function, or a simplified model). Thesechoices may be guided by temporal considerations(e.g., pseudo steady-state assumption), by valida-tion targets, and/or by information obtained duringbuilding and execution of the fine-grained model.Note that there is no single method for coarse- orfine-graining, and strategies vary by field. Variousmodel structures will require different methods anda review of these methods is beyond the scope ofthis article.

Tuneable Resolution Can Be Usedwith Different Multi-Scale Model ConstructsMulti-scale models with similar uses can havedifferent constructs, including ODE, partial dif-ferential equation (PDE), stochastic, object- andagent-based, and hybrid (i.e., models combining dif-ferent constructs).17–26 Consequently there is no singlestrategy for achieving tuneable resolution. Regardless



of construct type, it is important to have the abilityto shift the aspect and/or scale of focus at will. InExamples 1 and 2, we demonstrate tuneable resolutionusing hybrid models that combine nonlinear systemsof ODEs as sub-models that fine-grain mechanismsof an agent-based model (ABM). In addition, organcompartments of interest can be represented usingeither coarse- or fine-grained versions as appropriatefor the particular virtual experiment (Example 3).

Model Linking Is Central toTuneable ResolutionResolution tuning and established multi-resolutionmodeling methods face several similar technical,implementation, computational, and mathematicalissues. Interfacing or linking independent modelcomponents that operate at different temporal orspatial granularities is a prominent example.27–29

Interfacing or linking independent model compo-nents that use different modes of computation (e.g.,agent-based and continuous mathematics) is another.Adjusting the resolution in a model requires explicitconsideration of model linking issues. There areno standard linking methods. Although details arebeyond the scope of this communication, we notethat several groups are developing frameworks tomodularize models to improve model linking with aneye toward efficient modeling.7–9,30–38 For example,the multi-scale modeling platforms CompuCell 3D(www.compucell3d.org), Simmune, and VirtualCell (http://www.ibiblio.org/virtualcell/) all provideapproaches for model linking.39–41

Modularity Becomes Necessary,Even EssentialAnother impediment in the quest for improvedmulti-scale models is that they can become so com-plicated that scientific utility is jeopardized. Thecost to copy, verify, and maintain their operationcan be prohibitive. In addition, considerable spe-cialized expertise and training is needed to conductvirtual experiments using current multi-scale models.Finally, the barrier to independent virtual experimentreplication (as distinct from repetition) becomes toogreat.42–47 Our experience is that because modelvariants identified during virtual experiments employ-ing tuneable resolution are somewhat specialized,they can be easier to share and have shorter learningcurves. There is value to moving in the directionof multi-scale models designed intentionally to bemodular at all scales, where module variants havingthe same biological counterpart but different mecha-nistic granularities can be exchanged with biomimetic

fidelity and confidence both within and between exper-iments. As these modules become more long-lived, ourexpectation is that it will become increasingly easy toreplicate virtual experiments (a standard in science),and that barriers to more widespread use of virtualexperiments will be lowered. Research to improvemodel modularity is an actively expanding activ-ity (http://www.imagwiki.nibib.nih.gov/mediawiki/index.php?title=Main_Page).

Uncertainty and Sensitivity Analyses PlayImportant, and Multiple, Roles inTuneable ResolutionWhen data are not available to determine some modelparameter values, uncertainty and sensitivity analysescan be used to investigate, narrow and define param-eter spaces. Key generalized features of the processare illustrated in Figure 3. The first role for uncer-tainty analysis is to assess the uncertainty in modeloutput that results from uncertainty in parameter val-ues. Common techniques include generalized MonteCarlo methods (e.g., simple random sampling, Latinhypercube sampling).48 Sensitivity analysis is thenused to quantify how parameter uncertainty impactsmodel outcomes and to identify critical model param-eters. Common techniques include generalized corre-lation (e.g., partial rank correlation coefficients) andvariance decomposition methods (e.g., ANOVA, fastFourier transform).48 The second role for uncertaintyand sensitivity analyses in tuneable resolution is toidentify key mechanism features to guide fine-grainingand sub-model development. For example, we canfine-grain a model by adding detail to processes sug-gested by sensitivity analysis as significant or wecan coarse-grain by conflating sets of parametersthat do not have a large impact on model outcome.Most sensitivity analysis techniques supply indicesthat are time-dependent; key regulatory mechanismscan be important only during certain—sometimesnarrow—time intervals. Such time-dependency canalso be exploited to guide when to change resolution inan automated fashion. For example, if sensitivity anal-ysis suggests that a certain mechanism is only impor-tant early, then we can use the fine-grain model versionearly during the virtual experiment and, based on setcriteria, switch to a coarse-grain version thereafter.49

That illustration highlights that tuneable resolutioncan be applied temporally as well as spatially. Finally,we use uncertainty and sensitivity analyses for esti-mating new parameter values when toggling betweencoarse- and fine-grained model versions (i.e., tuneableresolution) to maintain biological fidelity and modelcongruency with regard to key biological features(Figure 3).


http://www.compucell3d.org

http://www.ibiblio.org/virtualcell/

http://www.imagwiki.nibib.nih.gov/mediawiki/index.php?title=Main&uscore;Page


Biologicalsystem

Coarse-grained

(a) (b) (c)

Fine-grained

FIGURE 3 | Comparing the behavior of multi-scale models(determined with virtual experiments) and the behavior of a biologicalsystem (determined with wet-lab experiments). The degree to which amodel captures the biological system is represented by overlap betweenthe model and biological system shapes (purple and yellow, or greenand yellow). The degree to which the fine- and coarse-grained modelspredict the same behavior is represented by overlap between the purpleand green shapes. In order to toggle between the two models tosimulate resolution tuning, acceptable similarities (sufficientcongruency) for the same set of phenomena must be observed. Afterinitial sensitivity and uncertainty analyses, phenomena overlap betweenthe sibling models is typically inadequate, indicating that furtherrefinements are needed, possibly in both models, providing a degree ofcross-model validation (panels a–c). Because the two model versionsare not the same, we should not expect complete overlap across theirfull range of realizations. Hayenga et al.106 provide an instructivedemonstration of achieving congruency between an agent-based and acontinuum-based biomechanical model.

Tuneable Resolution Is Distinguishable fromMulti-Resolution ModelingMulti-resolution modeling refers to building a sin-gle model, a family of models, or both to describethe same phenomena at different levels of resolu-tion, across multiple scales. Multi-resolution model-ing has a rich history in other domains, most notablyconflict and combat modeling50–54 and ecology.55–58

However, two important characteristics distinguishmany of those models from the tuneable resolutionapproach described here. First, multi-resolution mod-eling efforts typically adopt a reductionist, bottom-upapproach, assuming that knowledge, measurements,and data are available to achieve an acceptable degreeof biological validation at the finest grain (Figure 4,right side)59,60; modeling typically begins with math-ematical descriptions of multi-level mechanisms thatare physics-based. Yet, for TB and many other med-ical fields, the fine grain, explanatory, mechanisticknowledge needed to build a classical multi-resolutionmodel is still not available, placing us toward theaqua area of Figure 4. In fact, a primary goal inour research has been to use virtual experiments tofacilitate acquiring this knowledge. We have begunwith rather coarse-grained models, refining them togenerate biomimetic phenomena, and then focused‘downward’ to discover plausible, finer-grained mech-anistic generators to improve insight into the mech-anisms operating at the level above. This process is

what Brenner and Noble describe as the ‘middle out’approach.61

Second, a key use for multi-resolution mod-eling is generating fast and accurate predictions,and the focus is on inductive and deductive reason-ing. Our interest is different: models and methodswere needed to enable mechanistic exploration andsubsequent development of improved explanationsof phenomena7,62–64 including improved phenotypeoverlap (Figure 3). Improving insight requires shift-ing the aspect of focus of new virtual experiments,i.e., resolution tuning, in ways not easily anticipated.Those activities require expanding the range of reason-ing methods used to include analogical65 and abduc-tive reasoning.7,63,64 (Figure 4).

Model Reduction Is Distinguishable fromTuneable ResolutionModel reduction is an approach that has been usedfor coarse-graining models. Although some theoret-ical and ad-hoc methods have been used to reducedifferential equation models,66–68 there is no standardmethod yet available, particularly when dealing withmulti-scale or multiple linked models of different types(e.g., hybrid models). Model reduction is guided pri-marily by mathematical considerations (e.g., singular

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FIGURE 4 | These four spectra inform modeling approaches,characterize how multi-scale models can be used within the largerbiomedical context, and help distinguish our tuneable resolutionapproach from multi-resolution modeling. Locations on the top twospectra characterize the current state of knowledge about biologicalsystems and phenomena of interest. For immune responses totuberculosis (TB) and other diseases, the locations selected typically fallwithin the aqua box. The pink area characterizes systems for whichtrusted, fine-grained explanatory mechanisms are available at thehighest level of resolution needed.



perturbation analysis, nondimensionalization), whileresolution tuning is guided primarily by biologicalconsiderations and questions (e.g., a need to consideras yet unexplored molecular events, or an interest infocusing on another aspect of the system). That said,model reduction and a tuneable resolution approachmay in some cases lead to a similar outcome, even ifmotivated by very different objectives.

EXAMPLE 1: TUNEABLE RESOLUTIONIMPLEMENTED FOR A KEY CYTOKINEIN A MODEL OF A LUNGGRANULOMA IN TB

The key pathologic feature of TB is the formationof granulomas, self-organizing aggregates of immunecells and M. tuberculosis within lungs (Figure 5(a)).Most granulomas are capable of containing bac-terial infection, leading to (in humans) a clinicallylatent infection that may last for years. If, however,granulomas are impaired in function, infection canprogress, granulomas enlarge, and bacteria seednew granulomas; this sequence causes progressivepathology, i.e., active TB disease. How the interplaybetween various biological processes results in differ-ent infection outcomes is not known, but it is clearthat granulomas play a central role. Myriad hostfactors operating within and across length and timescales influence granuloma formation and function

(a)

M

00h00m00s - 200d00h00mContainment, Containment

N

L

(b)

FIGURE 5 | Nonhuman primate and simulated granulomas. (a)Histopathology of a granuloma in a primate infected withMycobacterium tuberculosis at ∼30 weeks post-infection (courtesy ofJoAnne Flynn, University of Pittsburgh). This typical caseous granulomashows central necrosis (N) surrounded by macrophages (M) and anouter cuff of lymphocytes (T cells) (L). (b) Snapshot of a simulated TBgranuloma at 200 days post-infection. Cell types: macrophages(resting-green, activated-blue, infected-orange, and chronicallyinfected-red), effector lymphocytes pro-inflammatory interferon-𝛾(IFN-𝛾) producing T cells-T𝛾 in pink, cytotoxic T cell-Tc in purple,regulatory T cell-Treg in light blue, extracellular bacteria (olive green),vascular sources-gray, necrotic spots (x). The granuloma shown in (b)has a total bacterial load of ∼2× 105 M. tuberculosis, mostlyextracellular, proliferating and located in the necrotic core.

and thus infection outcome. Improved understandingof mechanisms responsible for granuloma dynamics isexpected to lead to new therapeutic strategies. Becausemulti-scale models can simultaneously incorporatehost–pathogen interactions occurring over molecu-lar, cellular, and tissue scales, they are well-suited forexploration of the immune response to M. tuberculosisinfection.

In this example, we demonstrate tuneable res-olution by introducing a multi-scale model of gran-uloma formation and function, fine-graining thatmodel to include molecular-level detail, and thenre-engineering the original model guided by insights‘learned’ from experiments using the fine-grainedversion.

GRANSIM is our ABM describing granulomaformation and function in lungs during M. tuberculo-sis infection and focusing on cellular and tissue scaledynamics69,70 (Figures 5(b) and 6(a)). Immune cells(resting, infected, chronically infected, and activatedmacrophages; regulatory, cytotoxic, and interferon-𝛾(IFN-𝛾)-producing T cells) are represented as discreteagents. Effector molecules [such as IFN-𝛾 and bac-teria (extracellular, intracellular, and nonreplicatingbacteria)] are represented using continuous variables.Each simulation follows granuloma formation andfunction over several hundred days, building overtime to track thousands of individual cells (agents).GRANSIM (and the related models described here)were developed and achieved degrees of validation uti-lizing extensive data from mice and primates. Simu-lated granuloma features map to the wide spectrum ofthose observed in primates, including bacterial con-tainment, clearance (sometimes with extensive inflam-mation), and dissemination.

GRANSIM includes only minimal informa-tion regarding an important pro-inflammatorycytokine, tumor necrosis factor-𝛼 (TNF). TNF isproduced by infected and activated macrophages asa membrane-bound precursor (mTNF) that can becleaved and released as a soluble protein (sTNF).71,72

TNF binding to membrane receptors (TNFR1 andTNFR2) affects the immune response to bacteriathrough several mechanisms, including activationof macrophages to more effectively kill bacteria,induction of chemokine and cytokine expression,and modulation of apoptosis.73–75 In humans andnonhuman primates, TNF neutralization leads toreactivation TB, i.e., the appearance of active diseasewhere it was once latent, due to a failure of granulo-mas to control bacterial replication.76–79 Therefore,TNF availability and activities within granulomasare essential for restricting bacterial growth80 andmaintaining a latent infection.



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FIGURE 6 | Schematic representation of the multi-scale multi-compartment model of the immune response to Mycobacterium tuberculosisinfection. (a) An overview of selected agent-based model (ABM) rules of interaction between host cells, bacteria and lung environment asimplemented in GRANSIM69,70 which focuses on cellular and tissue scale dynamics. (b–d) Molecular-scale tumor necrosis factor (TNF) sub-model thatcan be embedded at three levels of resolution [coarse (b), intermediate (c), fine (d)] in GRANSIM. The molecular-scale model for TNF (c) is describedin Ref 11 and when implemented in the granuloma model is termed GRANSIMTNF (Example 1). The molecular-scale model for NF-𝜅B (d) is describedin Ref 82 and when implemented in the granuloma model is termed GRANSIMTNF-NFKB (Example 2). (e and f) The lymph node (LN) dynamics aredescribed as in Ref 94 at two levels of resolution [coarse (e), fine (f)] (Example 3). Abbreviations: Mycobacterium tuberculosis (Mtb), macrophage(mac), antigen (Ag), chronically infected macrophage (Mci), activated macrophage (Ma), pro-inflammatory IFN-𝛾 producing T cell (T𝛾 ) cytotoxic T cell(Tc), regulatory T cell (Treg), TNF-𝛼 converting enzyme (TACE), TNF receptor types 1 and 2 (TNFR1, TNFR2), membrane and soluble forms of TNF(mTNF, sTNF).

Availability of TNF within granulomas iscontrolled not only by the rate of TNF secretionfrom macrophages and TNF degradation in tissue,but also by receptor binding and trafficking (i.e.,receptor internalization, degradation, recycling, andshedding) processes. Results of uncertainty and sen-sitivity analyses demonstrated the significance ofchanges in TNF availability in granuloma functionduring GRANSIM simulations, highlighting the likelykey role of TNF-related processes in controllingactual infections. GRANSIM, however, does notinclude a representation of the receptor-level pro-cesses believed to control cellular responses and TNFavailability. To improve insight into current theoriesof TNF-related mechanisms and discover new options

for targeting granulomas therapeutically, we incor-porated TNF-related molecular-scale details andmechanisms within GRANSIM, terming the resultingfine-grained version GRANSIMTNF. (Figure 6(c)).11,81

Molecular-scale dynamics of TNF/receptor bind-ing and trafficking processes were represented as asub-model with a nine nonlinear ODE system solvedindividually for each cell agent (i.e., macrophage orT cell), with several thousand agents per simulation.Simultaneously, the solution to the PDE describingTNF diffusion at the cellular scale on the grid is com-puted, thus linking soluble TNF concentrations at thecellular/tissue scales to TNF binding and traffickingevents within individual cells.



TNF activates two major signaling pathways,the caspase-mediated apoptotic and the NF-𝜅B path-ways. In GRANSIMTNF we coarse-grain both thesepathways, linking the outputs solely to bound TNFreceptors (see Example 2 for an option that includesdetail in one of the pathways).11 TNF-induced NF-𝜅Bactivation for each individual macrophage is describedas a Poisson process with a probability that is a func-tion of the NF-𝜅B activation rate constant (kNF-𝜅B),the concentration of TNF-bound cell surface TNFR1complexes [C], and a threshold for those complexes(𝜏NF-𝜅B):

PNF-𝜅B =

{0 ;

[C]< 𝜏NF-𝜅B

1 − e−kNF-𝜅B([C]−𝜏NF-𝜅B)Δt ;[C]≥ 𝜏NF-𝜅B

.

(1)

An NF-𝜅B-activated macrophage secreteschemokines and TNF, and can be activated to killbacteria. The probability of TNF-induced apoptosisfor each individual cell is specified by:

Papopt =

{0 ;

[Ci]< 𝜏apopt

1 − e−kapopt([Ci]−𝜏apopt)Δt ;[Ci]≥ 𝜏apopt

,

(2)Papopt is a function of the apoptosis rate constant(kapopt), internalized TNF-bound TNFR1 complexes[Ci], and a threshold for those complexes (𝜏apopt).Equations (1) and (2) link TNF/receptor binding andinteractions to cellular scale processes.

A key GRANSIMTNF prediction is that solubleTNF gradients form within granulomas. High con-centrations of soluble TNF near the center of thegranuloma give way to lower peripheral concentra-tions. Although the prediction cannot yet be val-idated against wet-lab data, the consequences areprovocative. High central levels of TNF should trig-ger apoptosis of infected macrophages, whereas lowerlevels at the periphery should trigger survival path-ways for T cells, which are needed to fight infection.81

Uncertainty and sensitivity analyses allowed us toidentify how TNF/TNFR binding and traffickingdynamics may control the soluble TNF gradient.11

GRANSIMTNF can also be used to explore effectsof potential pharmacological manipulation of TNFreceptor binding and trafficking.82 For example, theTNFR1 internalization rate constant controls the spa-tial range of TNF action in a simulated granuloma11;TNFR1 internalization kinetics represent a tippingpoint identified by varying model resolution. Smallinternalization rates lead to a greater chance of clear-ance of the infection, but at the expense of exces-sive inflammation due to high TNF concentrations(Figure 7). Virtual experiments suggest that latent

Reducing TNFR1 internalization(Example 1)

orEnhancing NF-κB signalling

(Example 2)

Macrophage activation

Bac

teria

l loa

d

FIGURE 7 | Congruent behaviors achieved from two modelresolutions. The predicted roles of TNF R1 internalization and NF-𝜅Bsignaling in determining granuloma outcomes are shown. Simulationswith GRANSIMTNF (Example 1) show that reducing TNFR1internalization enhances bacterial killing and increases the probabilityof bacterial clearance. However, the increased TNF concentrations thatresult give rise to excessive macrophage activation and increased tissueinflammation. Simulations with GRANSIMTNF-NFKB (Example 2) showthat containment of bacteria is achieved when a balance exists betweenthe NF-𝜅B-mediated bacterial killing activities and the NF-𝜅B-mediatedinflammation. These levels of model resolution are well-suited toexploring potential pharmacological interventions of the signalingpathway. Snapshots of granulomas follow the same color mapping forcells as in Figure 5. The range of behaviors simulated with the tworesolutions shows model congruency (see Figure 3).

TB represents a physiological compromise that avoidsmore destructive outcomes.83

The fine-graining of our base model to includeTNF/TNF receptor binding and trafficking andTNF-driven cell behavior was well-motivated by adesire to understand the important roles that TNFplays in granuloma formation and function. However,when the focus of our virtual experiments shifts toa new system aspect, e.g., the role of a differentcytokine or cell type, or the effect of a TNF knockout,the model may not need extensive detail regardingTNF. Yet we would like to retain what we learnedduring the fine-graining to create GRANSIMTNF.Thus we used a tuneable resolution approach, learn-ing from GRANSIMTNF to re-engineer GRANSIM(Figure 6(b)), at least with respect to TNF. Because ouranalyses demonstrated the importance of the TNFR1internalization to the fine-grained model outcomes,we replaced the nine ODEs describing TNF receptorbinding and trafficking11 with this single ODE:

d[sTNF

]dt

= k′synth −

( [sTNF

][sTNF

]+ Kd1

)kconsumption

(3)



Equation (3) describes the change of solubleTNF concentration within an ABM compartment thatcontains a macrophage or T cell; k′

synthis the rate of

sTNF secretion by the immune cell, and kconsumption isthe apparent rate constant for sTNF consumption (i.e.,by internalization). The factor [sTNF]

[sTNF]+Kd1represents

the sTNF-bound fraction of TNFR1s on membranesof immune cells (assuming a pseudo steady-state).Kd1 is TNFR1 affinity for sTNF. Because the ODEsare being solved for each of the thousands of agents(cells) during simulation, replacing nine ODEs with asingle ODE yields significant computational savings(simulation times, on the order of tens of minutes,are cut roughly in half). Note that because these arestochastic simulations, and because it is also necessaryto run uncertainty and sensitivity analyses, thousandsof simulations are required for full analysis of themodel.

In addition, Eqs (1) and (2) are replaced withequations that rely on the extracellular sTNF concen-tration rather than bound TNFR1 receptors for prob-ability computations:

PNF-𝜅B =⎧⎪⎨⎪⎩

0 ; [sTNF][sTNF]+Kd1

< 𝜏′NF-𝜅B

1 − e−k′

NF-𝜅B

([sTNF]

[sTNF]+Kd1−𝜏′NF-𝜅B

)Δt; [sTNF][sTNF]+Kd1

≥ 𝜏′NF-𝜅B

, (4)

Papopt =⎧⎪⎨⎪⎩

0 ; [sTNF][sTNF]+Kd1

< 𝜏′apopt

1 − e−k′

apopt

([sTNF]

[sTNF]+Kd1−𝜏′apopt

)Δt

; [sTNF][sTNF]+Kd1

≥ 𝜏′apopt

, (5)

where k′NF−𝜅B, k′

apopt, 𝜏′NF−𝜅B, and 𝜏′apopt are modi-fied rate constants and thresholds for TNF-inducedNF-𝜅B activation and apoptosis, respectively. BecauseTNF-induced responses (NF-𝜅B activation and apop-tosis) in immune cells actually result from sTNFbinding to TNFRs on the cell membrane, TNF con-centration thresholds 𝜏′NF−𝜅B and 𝜏′apopt in Eqs (4) and(5) are defined based on [sTNF]/([sTNF]+Kd1). Initialestimates of the values of the new model parameters(k′

synth, kconsumption, k′

NF−𝜅B, k′apopt, 𝜏

′NF−𝜅B, and 𝜏′apopt)

are based on related parameters from GRANSIMTNF.For example, knowing the rate constant for TNFRinternalization and the average number of cell sur-face TNFRs, we estimated a suitable range of valuesfor kconsumption to be on the order of kint 1[TNFR1],where kint1 is the TNFR1 internalization rate con-stant.

The resulting re-engineered GRANSIM now alsopredicts TNF concentration gradients within a granu-loma and lower levels of macrophage activation andinflammation at the periphery of granuloma, improv-ing similarities with experimental data. Dependingon the focus of a virtual experiment, we can nowtoggle between GRANSIMTNF and the re-engineeredGRANSIM (BOX 1), exercising resolution tuning and,in the case of GRANSIM, incorporating informationregarding molecular-level TNF without the computa-tional expense and complexity of the full model.

EXAMPLE 2: TUNEABLE RESOLUTIONIMPLEMENTED FOR NF-𝜿B SIGNALINGIN A MODEL OF A LUNGGRANULOMA IN TB

In Example 1, we introduced GRANSIMTNF, ahybrid multi-scale model (consisting of agent-based,ODE, and PDE models) that simulates the immuneresponses—specifically, granuloma formation andfunction—during infection with M. tuberculosis

(Figure 6(a) and (c)). Although this model capturesreceptor binding and trafficking processes that inpart control TNF availability, it contains limiteddetail regarding the biological mechanisms that deter-mine the relationship between TNF-bound receptorsand cellular responses (Eq. (1)). In this example,we demonstrate tunable resolution, fine-grainingGRANSIMTNF by incorporating additional moleculardetail describing one of the intracellular signal-ing pathways elicited by TNF binding and thenre-engineering GRANSIMTNF to increase biomimeticfidelity.

TNF binding initiates a signaling pathwayleading to translocation of NF-𝜅B into the nucleusand ultimately transcription of target inflammatorygenes. Activation of the NF-𝜅B pathway affectsthe immune response to M. tuberculosis through



(at least) four mechanisms in macrophages: activationto efficiently kill bacteria, induction of chemokinesecretion, induction of cytokine (TNF) expression,and inhibition of apoptosis.73–75,84–87 We wanted touse virtual experiments to explore answers to ques-tions that would require TNF signaling granularitygreater than that in GRANSIMTNF. For example, howdo the dynamics of the TNF-induced NF-𝜅B pathwayinfluence the long-term immune response to bacte-ria? Could targeting the TNF-induced NF-𝜅B pathwayaffect granuloma formation and function? To under-take those virtual experiments we developed a new(and finer-grained) version of GRANSIMTNF, termedGRANSIMTNF-NFKB, containing the enhanced intra-cellular component details illustrated in Figure 6(d).82

Recent cell culture experiments, including thosein88, have identified important molecular mecha-nisms controlling the dynamics of NF-𝜅B signalingat the single-cell level. To explore possible influencesof this pathway in the context of host infection, weincorporated a representation of these dynamics intoour model. Equation (1) was replaced by a set of50 nonlinear ODEs that determine NF-𝜅B signalingdynamics following TNF binding to cell surface TNFreceptors.82,88 Those NF-𝜅B dynamics were thenlinked to the four NF-𝜅B-mediated cell responses inmacrophages listed above. NF-𝜅B-induced expressionof genes corresponding to TNF, different chemokines,a generic inhibitor of apoptosis protein (IAP),89 anda generic macrophage-activating molecule (ACT;representing, for example, proteins involved in mat-uration of phago-lysosomes essential for killingbacteria84) as well as translation of their mRNAtranscripts were represented using ODEs. For TNFand chemokines, ODEs also describe secretion toextracellular spaces. For macrophage activation andinhibition of apoptosis, because these processes arediscrete at the single-cell level, cell behavior wasdescribed by a Poisson process with a probabilitydetermined within each time-step in part by theintracellular concentration of ACT and IAP, similarto Eqs (1) and (2).82 Fine-graining NF-𝜅B dynam-ics has two major effects on how TNF signalingis implemented. First, the higher resolution model(Figure 6(a) and (d)) is able to capture the dynamicsof TNF-induced responses, for example, oscilla-tory expression of chemokines, as explored in.82

It also mathematically uncouples the four differentNF-𝜅B mediated responses, which is appropriateas these processes are regulated by separate mecha-nisms (transcription and translation of distinct genesand mRNA transcripts). Virtual experiments usingGRANSIMTNF-NFKB documented that the dynamics ofTNF-induced NF-𝜅B-mediated responses are critical

to controlling bacterial load, inflammation levels, andgranuloma size82 (Figure 7).

The three model versions, GRANSIM, GRAN-SIMTNF, and GRANSIMTNF-NFKB, correspond to thecoarse-, intermediate-, and fine-grained multi-scalemodel versions shown schematically in Figure 2(panels A1, A2a, and A3, respectively) and ourtuneable resolution implementation is described inBOX 1. Model congruency between two of thoseversions in terms of key biological outcomes isshown schematically in Figure 7 and was obtainedusing uncertainty and sensitivity analysis (Figure 3).Although GRANSIMTNF-NFKB is the most detailedmodel, not all our questions regarding TB granulomaformation and function require this level of detailin the NF-𝜅B pathway. Thus, our next goal wasto re-engineer and improve scientific usefulness ofGRANSIMTNF by drawing on insights gained fromGRANSIMTNF-NFKB (Figure 2, panel A2b).

Analysis of GRANSIMTNF-NFKB simulationsshowed that the timing of NF-𝜅B induced macrophageactivation has a more significant effect on granulomafunction than the timing of other responses, sowe modified GRANSIMTNF to capture the timingeffects for different NF-𝜅B mediated responses in acoarse-grained manner without solving for all reac-tions. The timing of all NF-𝜅B mediated responsesin GRANSIMTNF is controlled by a single param-eter kNF-𝜅B, the NF-𝜅B activation rate constant, asdescribed in Eq. (1). We replaced this parameter withthree independent parameters, kactivation, kchemokine,and kTNF, controlling the timing of each individ-ual NF-𝜅B mediated response separately (kapopt,controlling the rate of apoptosis, already exists inGRANSIMTNF). These parameters control the prob-ability of each NF-𝜅B associated response within asimulation time-step. For example, Eq. (1) is modifiedto describe the probability at which a macrophagebecomes capable of secreting chemokines followingNF-𝜅B activation:

Pchemokine =⎧⎪⎨⎪⎩

0 ;[C]< 𝜏NF-𝜅B

1 − e−kchemokine([C]−𝜏NF-𝜅B)Δt ;[C]≥ 𝜏NF-𝜅B

.

(6)Similar to Example 1, because the ODEs are

being solved for each of the thousands of agents (cells)in the simulation, replacing 50 ODEs determiningNF-𝜅B signaling dynamics with three ODEs yieldssignificant computational savings (simulation times,on the order of several hours, are cut to tens ofminutes). Because these too are stochastic simulations,thousands of simulations are required for uncertaintyand sensitivity analyses.



BOX 1

EXAMPLE TUNEABLE RESOLUTION ALGORITHM

An overview of the algorithm used in simulations of the tuneable resolution multi-scale granuloma modelwith options for including TNF and NF-𝜅B sub-models (GRANSIMTNF and GRANSIMTNF-NFKB) (Examples 1 and2). Rules and parameters for cell and bacteria processes (e.g., cell movement, cell recruitment, bacterialgrowth—Figure 6(a)) are the same for different resolutions of the model.

Simulation start

Set simulation time = T

Grid initialization

Fine

Intermediate

Modelresolution

CoarseChemokine secretion asdescribed for GRANSIM

Chemokine secretionas described GRANSIM

TNF/TNFR dynamics,including TNF expressionas described in Example 1

Diffusion and degradationof soluble molecules

n = n + 1No

No

Yes

Is simulatedtime ≥ T ?

Yes

Cell movements

Simulated time = N.Δt

N = N + 1

Simulation end

Cell recruitments

Extracellular Mtb growth

Cell–cell interactionsand state transitions

Fine Modelresolution

Coarse

Intermediate

TNF-induced NF-κB activationand apoptosis as described in

Example 1, Eqs (1) and (2)

TNF-induced NF-κB activationand apoptosis as described by

Eqs (4) and (5)

TNF-induced apoptosis asdescribed in Example 2

n = 1

Is n.dt = Δt?

Secretion and apparentconsumption of TNF as

described in Eq. (3)

TNF/TNFR and NF-κBsignaling dynamics,

including sercretion ofTNF and chemokines asdescribed in Example 2

N = n = 1

Simulation results from the re-engineeredGRANSIMTNF (Figure 8) show the importance ofkactivation and less significant effects of kchemokineand kTNF on controlling bacteria numbers and the

level of inflammation in tissue. These results alsoshow model congruency between GRANSIMTNFand GRANSIMTNF-NFKB regarding the importanceof the timing of macrophage activation in control of



Increasing macrophageactivation rate constant

Increasing mRNA half-life Increasing mRNA half-life

Total number of bacteria Activated fraction of macrophages

Increasing macrophageactivation rate constant

TNF expression

TNF

“Mod

ified

”in

term

edia

tere

solu

tion

mod

el

Fin

e-gr

aine

dm

odel

Chemokineexpression

Chemokine

Macrophage-activating molecule

Activated fraction ofmacrophages

0.4100 <101000 0.1 0.025

Total number ofbacteria

Bacterial killing

(a) (b)

FIGURE 8 | Refinement of GRANSIMTNF. Using uncertainty and sensitivity analyses and knowledge gained from GRANSIMTNF-NFKB, theintermediate resolution model GRANSIMTNF was improved (top panels). Simulation results are shown for the timing of NF-𝜅B-mediated responses,including macrophage activation to efficiently kill bacteria, TNF expression, and chemokine expression, and their effects on (a) bacteria numbers 200days post-infection and (b) activated fraction of macrophages 50 days post-infection. Bottom panels show results from GRANSIMTNF-NFKB in which thetiming of NF-𝜅B-mediated responses is regulated by their corresponding mRNA stabilities (half-lives). Simulations are run varying the stability ofmRNA transcripts corresponding to macrophage-activating molecules, chemokines, and TNF while maintaining the average extent of the responses atcontainment baseline levels.82 To maintain the average extent of each response as its corresponding mRNA stability is varied, we simultaneously varyanother parameter associated with a process downstream of mRNA translation. Parameters varied to adjust the extent of the three NF-𝜅B mediatedresponses are: TNF secretion rate, chemokine secretion rate, ACT concentration threshold for macrophage activation, and macrophage activation rateconstant. Four values of mRNA half-life were tested in fine-grain simulations: 12 min, 30 min, 1 h, and 3 h. Top panels show results from the modifiedGRANSIMTNF in which the timing of NF-𝜅B-mediated responses is regulated by new parameters kactivation, kchemokine, and kTNF. Four values tested foreach of these three parameters in intermediate resolution simulations are: 1.26× 10−8, 3.97× 10−8, and 1.26× 10−7 and 3.97× 10−7 (#/cell)−1 s−1.All other parameters are kept at their containment (baseline) levels. Simulation results are averaged over 10 repetitions.

granuloma formation and functioning. Depending onthe focus of our virtual experiments regarding TNFand its influence on granuloma dynamics, we can nowtoggle between a re-engineered GRANSIMTNF andGRANSIMTNF-NFKB (BOX 1), exercising resolutiontuning and, in the case of GRANSIMTNF, incor-porating information from molecular-level NF-𝜅Bsimulations without the computational expense andcomplexity of simulating the full model.

EXAMPLE 3: TUNEABLE RESOLUTIONIMPLEMENTED FOR A MULTI-ORGANMODEL OF LUNG GRANULOMAFORMATION AND FUNCTION IN TB

In Examples 1 and 2, the multi-scale models createdadded molecular-scale dynamics to a cellular/tissue

scale model. In this example, we highlight a tuneableresolution approach when fine-graining at the samescale as the original model. Another way to describethis is that we add an additional compartment (organ)to the original model.

Recruitment of immune cells to the lung to par-ticipate in control of infection is a critical event ingranuloma formation during infection with M. tuber-culosis. Recruited cells include T cells, macrophages,and dendritic cells. Effector immune cells such asCD4+ and CD8+ T cells are generated in LNs andmust travel to lungs. The process can take anywherefrom a few days to weeks for persistent pathogenslike M. tuberculosis. Some studies show that an effec-tive protective response to M. tuberculosis can beimpacted by this slow or delayed induction or func-tion of effector cells.90 For example, host–bacteriainteractions can result in a delayed cell migratory



activity or reduced antigen-presenting cell function,at least in macrophages.91–93 In addition, timing ofinitiation of granuloma formation (which is dependenton the recruitment of these effector cells from LNs)can affect capabilities of antigen-presenting cells (suchas macrophages and dendritic cells) to find bacteriaand migrate to draining LNs in a timely manner. Effec-tor T cells are generated, but in most cases it is toolate to allow infection to be cleared. Instead, there iseither a ‘stand-off’ leading to latency or an active infec-tion. Clearly, LN dynamics can have a huge impact onthe immune response to M. tuberculosis infection, andthat is the focus of Example 3.

GRANSIM is low-resolution with respect toLN mechanisms and processes (Figure 6(a) and (e);Examples 1 and 2).11,69,70,83 It captures effectorT cell recruitment into the lung in a simplified way, byspecifying a forcing function with a parameter repre-senting the time of arrival of those cells to the lung.Decisions to recruit cells and what T cell phenotypesto recruit are based on events unfolding duringsimulations. Effector T cell phenotypes are definedbased on their immunological functions: interferon-𝛾(IFN-𝛾)-producing T cells (T𝛾), cytotoxic T cells (TC),and regulatory T cells (Treg). T cell recruitment fromLN to lung is a stochastic event, and occurs at specificsites (vascular sources) on the grid. To mimic thebiological delay in adaptive immunity development inLNs, effector T cell recruitment is enabled only after∼20 days post-infection, which reflects the typical2–4 week post-infection ‘delay’ in mounting adap-tive immunity. Uncertainty and sensitivity analysesshow that simulated granuloma formation is highlydependent on the value of this delay parameter,69,70

motivating a more physiologically realistic treatmentof immune cell recruitment to the lung.

To better represent mechanisms occurring withina LN during granuloma formation, we fine-grainedrecruitment of immune cells from the LN by replacingparameters with an entire physiological compartmentrepresenting a LN94 (Figure 6(f), and schematicallyshown in Figure 2 panels B1 to B2). Doing so allowedus to address questions related to modulation and tim-ing of T cell responses as a function of infection pro-gression within the lung. We mapped a single virtualLN to a collection of several (∼5) lung-draining LNs,the sites of generation of effector T cells. The result-ing multi-organ model, GRANSIM-LN, is hybrid: anABM for the lung compartment (Figure 6(a)) and anonlinear system of ODEs representing phenomenawithin the LN compartment (Figure 6(f)).94 The LNmodel includes mechanisms that represent antigen pre-sentation and T cell priming and differentiation andconsists of 13 ODEs tracking APCs, naïve T cells, and

precursor, and effector CD4+ and CD8+T cells. Effec-tor T cells can leave the LN to migrate to lungs. ThisLN model was developed and calibrated using datafrom M. tuberculosis-infected mice.95

Linking the LN and lung granuloma models toform GRANSIM-LN requires specifying how cellstraffic between the compartments. To represent Tcell recruitment that is based on the level of infectionin the lung, we used the scaled sum of infected andchronically infected macrophage populations in thelung to represent the pool of antigen-presenting cellsthat have potential to migrate to draining LNs. Thebiological behavior to which this maps captures bac-teria in lung causing more antigen-presenting cells toingest them and traffic to LNs. Mathematical scalingis necessary because GRANSIM represents only aportion of the lung, and our LN model representsonly a single draining LN. We also account for delaysthat an antigen-presenting cell can encounter duringuptake, maturation, and migration processes betweenphysiological compartments. The scaled sum of allinfected macrophages in the lung at each time-step isused as the initial condition for the ‘mature dendriticcell’ (the key antigen-presenting cell in our model)equation within the LN. After the dynamics simulatefor that time-step in the LN model, T cells generatedreturn to the lung via blood to participate in the lunginfection model (GRANSIM). T cell fluxes generatedby the LN model are converted into integers andcells are placed on a queue to enter the lung whena source location becomes available. A T cell in thequeue has a fixed lifespan. Its ‘age’ is preserved whenit enters the grid. The process is intended to mimicthe effect of effector T cells circulating through theblood and waiting for signals to extravasate intothe tissue.96 The only recruitment parameter sharedbetween coarse- and fine-grained model versions,GRANSIM and GRANSIM-LN, respectively, is afixed threshold for recruitment of T cells that is basedon the concentration of cytokines and chemokines atthe blood sources, where cells can enter.

Using our fine-grained model, GRANSIM-LN,we can explore possible changes in the efficiencyand magnitude of T cell priming, differentiation,and migration to the lung. We can also capturethe contraction phase of effector T cell fluxes dueto a reduction of antigen-presenting cells migratingto LNs.

GRANSIM-LN experiments demonstrated thatdetectable levels of effector T cells at the site ofinfection occur only above a threshold number ofbacteria in the lung. On the basis of that observa-tion, we re-engineered the original GRANSIM byintroducing a new threshold parameter. When total



bacteria counts in the lung ABM are greater than thisthreshold, T cell recruitment is enabled. To createthis re-engineered GRANSIM, we focused on oneof the most informative proxies for infection in thelung, the total bacteria count. We used measures fromGRANSIM-LN to create a proxy function of totalbacteria versus T cell fluxes from LN to lung. In orderto simulate a large spectrum of granuloma outcomesranging from clearance to dissemination, we varied12 GRANSIM parameters (while fixing the LN modelparameters) and generated 900 different temporalbacteria profiles. We plotted daily bacteria countsversus T cell flux (Figure 9; only T𝛾 fluxes are dis-played). Figure 9(a) shows a clear separation of fluxesas infection progresses. We then fit time-adjusted

functions to the data (Figure 9(b)) and generated animproved GRANSIM (Figure 9(c)).

Thus we have two model versions, in termsof incorporation of LN dynamics, the re-engineeredGRANSIM and the fine-grained GRANSIM-LN; wecan choose the appropriate version for the biologicalaspect of interest. (When needed, we also have aLN ABM that tracks individual cell movements andgeneration of effector T cells within a LN, but itsdetails are beyond the scope of this example.49,97–99

Our tuneable resolution approach gives us theability to toggle easily between different model ver-sions to continually improve explanatory mechanis-tic insights and expand the scope of those insights.That process is illustrated by the data in Figure 10.

Day 0–30

Day 30–60Day 60–200

TotMtb

100100

101

102

TY fl

uxes

103

104

101 102 103 104

(a)Day 0–30

Day 30–60Day 60–200

Time Time

TotMtb100100

101

102

TY fl

uxes

103

104

101 102 103 104

(b)Day 0–30Day 30–60Day 60–200

TotMtb

100100

101

102

TY fl

uxes

103

104

101 102 103 104

(c)

FIGURE 9 | Comparisons of T𝛾 cell fluxes across different model resolutions. T cells that make the cytokine IFN-𝛾 (T𝛾) are shown on the y-axis.The x-axis represents total bacteria count. Each plot displays a total of 900× 200 points. Each point is the combination of total bacteria count and T𝛾cell fluxes at a certain day during a simulated 200-day infection. Different colors correspond to different time intervals. (a) Results using thefine-grained version of T cell recruitment (GRANSIM-LN). (b) The data from (a) with examples of linear and quadratic functions superimposed to fitthe data. (c) Results using the improved coarse-grained model in which the fine-grained fluxes in (a) are approximated using the linear and quadraticfunctions illustrated in (b). For days 0–60, we use linear approximations. For days 60–200 we use quadratic functions. We fit simulated T𝛾 and TC

fluxes separately. In order to cross-validate with fine-grained LN outcome distributions, we truncated the approximations at a certain level of totalbacteria, below which the flux becomes 0. For example after day 30, if bacteria<35, fluxes are set to 0.

Coarse-grained T cell recruitment700

600

500

400

Num

ber

of r

uns

300

200

100

00 200 400

TotMtb

600 800 1000

Fine-grained T cell recruitment500

450

400

350

300

250

Num

ber

of r

uns

200

150

50

100

00 200 400

TotMtb

600 800 1000 1200

Proxy for fine-grained T cell recruitment500

450

400

350

300

250

Num

ber

of r

uns

200

150

50

100

00 200 400

TotMtb

600 800 1000

(a) (b) (c)

FIGURE 10 | Outcome distributions across different model resolutions describing T cell recruitment. Total bacteria count at day 200 is used asproxy for TB outcome (x-axis). Each plot displays the outcome from 900 different parameter combinations resulting from the virtual experimentsdescribed in the text. Each point is the combination of total bacterial count and T𝛾 cell fluxes at 200 days post infection. (a) GRANSIM.(b) GRANSIM-LN. (c) re-engineered GRANSIM.



Results from the re-engineered GRANSIM differ fromthe other resolutions: using the same set of parametervalues shared across versions, it returns more totalbacteria in the range of 0–1000 (Figure 10(a)). Thisdemonstrates that the original GRANSIM formula-tion of T cell recruitment skews the results towardsa more likely resolution of the infection by superim-posing a fixed time for enabling T cell recruitment,as well as continuous unlimited availability of effec-tor T cells, regardless of the level of infection in thelung. This highlights the use of tuneable resolutionto identify a model flaw. Although the re-engineeredGRANSIM (Figure 10(c)) gives more accurate predic-tions, computational efficiency is not affected (we aresolving a single ODE that only occurs in one step of themodel). In other work with a multi-organ model, how-ever, tuneable resolution allowed a 17-fold increase incomputational efficiency.49

DISCUSSION

Systems biologists are leveraging multi-scale model-ing methods to study important biomedical problemsin new ways. These models are exciting and we neednew approaches to help with analyses, expand sci-entific and medical relevance, and promote sharingcapabilities. We argue that developing and buildingmodels with tuneable resolution is a step in that direc-tion. Tuneable resolution begins with a multi-scalemodel in place and strives to make model mechanismsmore explanatory and thus more biomedically rele-vant, while simultaneously making them more useableand understandable. Our approach is applicable notonly for systems that are multi-scale in space (includ-ing multi-organ) and time, but also for models thatare multi-dimensional. In Ref 97, e.g., we develop anABM of the LN that can be used in 2 or 3 dimensions.

Different features of the tuneable resolutionapproach that we describe here have been employedrecently in other contexts. As examples, Gary An usesvariable resolution components within a multi-scalemodel to explore and study the pathogenesis of mul-tiple organ failure.100 An additional model use isenabling dynamic knowledge representation withinthe multi-scale model’s modular architecture. Lam andHunt38 used sequential changes in micro-mechanismresolution to improve explanatory insight into theparadoxical roles of P-glycoprotein, Cyp3A4 enzymes,and sub-cellular microenvironments in determiningtemporal patterns of transport and metabolism ofsaquinavir (an antiretroviral drug) in Caco-2 cellcultures. Focusing on explanatory cell-level mecha-nisms of epithelial cell cystogenesis in cultures, Kimand Hunt101 used resolution tuning to evolve fully

rule-based cell agents into composite counterpartsthat achieved quantitative cross-model validationtargets under normal and dysregulated conditions.Ruiz-Herrero et al. developed a coarse-grained modelof receptor–ligand binding, allowing computation-ally efficient consideration of some spatial aspectsof interactions.102 Tang et al.14,103,104 altered theresolution of different multi-scale model componentsin order to enable dynamic simulation results toachieve quantitative validation targets drawn froma variety of different experimental conditions. It isuseful to view all of these from within the frameworkof tuneable resolution provided here.

A current weakness of the tuneable resolutionapproach is that it is relatively new and in use in onlya few laboratories. It is not yet clear how establishedgood modeling and simulation practices will needto be expanded to cover the new methods. Figure 2serves to highlight an issue for which additionalbest practice guidelines may be needed. During eachtuning exercise, there are frequent opportunities tointroduce bias, artifacts, and/or seed an inscriptionerror7,105 (http://furm.org/glossary.html), which—ifunnoticed—will jeopardize the scientific usefulness ofsubsequent model refinements. The risks are some-what amplified because we are working in the aquaarea of Figure 4, striving to move rightward. Conse-quently, the models are perpetual works in progress.The best strategy is to reinforce adherence to goodmodeling and simulation practices, and that includeskeeping records of tuning protocols, consequences,inferences, decisions, and evidence of feature falsi-fication. The ideal course for model improvement(Figure 3) anticipates incremental tuning to expandboth coarse- and fine-grain model overlap. However,tuning to improve overlap in one ‘direction’ may comeat the cost of reduced consistency in areas previouslycovered. A mitigating strategy is to expand the varietyof qualitative (and, later, quantitative) validationtargets and/or increase the variety of biomimeticconstraints, and confirm through in silico experimen-tation that those targets are still achieved. Doing so,however, places an additional demand on modelerefforts. Because tuning is currently a hands-on activity,considerable time and effort may be required to suc-cessfully complete several tuning cycles, and that canbe considered a shortcoming. A mitigating strategy isto increase modularity at both mechanism descriptionand software levels so that refactoring decreases asexplanatory power increases. The technical challengesfaced when switching between coarse and fine-graincomponents are common to all multi-scale mod-eling efforts and are well understood.7–9,30–38,59,60

Consequently, efficient resolution tuning should


http://furm.org/glossary.html


be a priority requirement at the beginning of aproject because it can influence selection of modelingmethods.

We envision that the most efficient and produc-tive path to more effective and eventually curativetherapeutic intervention strategies for TB and otherdiseases will involve many cycles through the rightside of Figure 1 coupled with the occasional but essen-tial cycle through the left side. The approach can beextended to and beyond clinical trials. We anticipatenew knowledge falsifying some model and/or assump-tion details, requiring feature revision and inclusionof new features. We do not anticipate those future vir-tual experiments, even those requiring virtual patients,to utilize a single, grand, unified multi-scale model,however. Because each virtual experiment will bemotivated by a specific question or hypothesis, itwill, like wet-lab counterparts, focus on just one (orat most a few) aspect of the disease and its con-text. As was the case for Examples 1–3, we expectthe model used to be somewhat individualized (andsomewhat optimized, from an execution perspective)for the particular virtual experiment and its uses:

easily (ideally automatically) assembled from a fam-ily of exchangeable model components, each havingachieved aspect-specific validation targets. Because TBphenomena are multi-scale within and across manyaspects of the disease, we anticipate that many of thosevirtual experiments will require a resolution changeone or more times during execution. Thus, we arguethat having, expanding, and improving that capabilityis essential to achieving important public health out-comes from computational models.

A multi-scale model that has resolution-tuningcapabilities and has earned a degree of credibility pro-vides improved, plausible explanations of how eventsmay coalesce into phenomena within and between bio-logical scales. Such improved insight—improvementin the theory of TB, in our examples—is often infeasi-ble to achieve through wet-lab experimentation alone.The most frequently touted benefit of multi-scalemodeling is improved predictions. We have demon-strated how improved scientific value can be derivedfrom exploring and refining plausible, explanatorymulti-scale mechanisms using a tuneable resolutionapproach.

ACKNOWLEDGMENTS

This work was supported by NIH R01 HL106804 (DEK), R01 GM096040 (JJL), R01 EB012579 (DEK andJJL) and R01 HL 110811 (DEK and JJL).

REFERENCES1. Bokulich A. How scientific models can explain. Syn-

these 2011, 180:33–45.

2. Darden L. Thinking again about biological mecha-nisms. Philos Sci 2008, 75:958–969.

3. Weiskopf DA. Models and mechanisms in psychologi-cal explanation. Synthese 2011, 183:313–338.

4. Craver CF. When mechanistic models explain. Syn-these 2006, 153:355–376.

5. Winther RG. Interweaving categories: styles,paradigms, and models. Stud Hist Philos Sci A2012, 43:628–639.

6. Weisberg M. Simulation and Similarity: Using Modelsto Understand the World (Oxford Studies in Philoso-phy of Science). New York: Oxford University Press;2013.

7. Hunt CA, Ropella GP, Lam T, Tang J, Kim SJ, Engel-berg J, Sheikh-Bahaei S. At the biological model-ing and simulation frontier. Pharm Res 2009, 26:2369–2400.

8. Hunt CA, Ropella GEP. Moving beyond in silico toolsto in silico science in support of drug developmentresearch. Drug Dev Res 2011, 72:153–161.

9. Hunt CA, Kennedy RC, Kim SHJ, Ropella GEP.Agent-based modeling: a systematic assessment of usecases and requirements for enhancing pharmaceuticalresearch and development productivity. WIREs SystBiol Med 2013, 5:461–480. doi: 10.1002/wsbm.1222.

10. de Lara J, Vangheluwe H. AToM(3): a tool formulti-formalism and meta-modelling. Lect NotesComput Sci 2002, 2306:174–188.

11. Fallahi-Sichani M, El-Kebir M, Marino S, KirschnerDE, Linderman JJ. Multiscale computational modelingreveals a critical role for TNF-𝛼 receptor 1 dynamics intuberculosis granuloma formation. J Immunol 2011,186:3472–3483.

12. Han LQ, Hanan J, Gresshoff PM. Computationalcomplementation: a modelling approach to studysignalling mechanisms during legume autoregula-tion of nodulation. PLoS Comput Biol 2010, 6:e1000685.



13. Karalis V, Dokoumetzidis A, Macheras P. A physio-logically based approach for the estimation of recircu-latory parameters. J Pharmacol Exp Ther 2004, 308:198–205.

14. Tang J, Hunt CA. Identifying the rules of engagementenabling leukocyte rolling, activation, and adhesion.PLoS Comput Biol 2010, 6:e1000681.

15. Park S, Ropella GE, Kim SH, Roberts MS, Hunt CA.Computational strategies unravel and trace how liverdisease changes hepatic drug disposition. J PharmacolExp Ther 2009, 328:294–305.

16. Fallahi-Sichani M, Marino S, Flynn JL, LindermanJJ, Kirschner DE. A systems biology approach forunderstanding granuloma formation and function intuberculosis. In: McFadden J, Beste DJV, Kierzek AM,eds. Systems Biology of Tuberculosis. New York, NY:Springer; 2012.

17. Bassingthwaighte JB, Beard DA, Carlson BE, Dash RK,Vinnakota K. Modeling to link regional myocardialwork, metabolism and blood flows. Ann Biomed Eng2012, 40:2379–2398.

18. Beard DA, Neal ML, Tabesh-Saleki N, ThompsonCT, Bassingthwaighte JB, Shimoyama M, Carlson BE.Multiscale modeling and data integration in the virtualphysiological rat project. Ann Biomed Eng 2012,40:2365–2378.

19. Bolser DC, Pitts TE, Morris KF. The use of multiscalesystems biology approaches to facilitate understandingof complex control systems for airway protection.Curr Opin Pharmacol 2011, 11:272–277.

20. Campbell SG, McCulloch AD. Multi-scale computa-tional models of familial hypertrophic cardiomyopa-thy: genotype to phenotype. J R Soc Interface 2011,8:1550–1561.

21. Flamm MH, Diamond SL. Multiscale systems biologyand physics of thrombosis under flow. Ann BiomedEng 2012, 40:2355–2364.

22. Kim E, Stamatelos S, Cebulla J, Bhujwalla ZM, PopelAS, Pathak AP. Multiscale imaging and computationalmodeling of blood flow in the tumor vasculature.Ann Biomed Eng 2012, 40:2425–2441.

23. Politi AZ, Donovan GM, Tawhai MH, SandersonMJ, Lauzon AM, Bates JH, Sneyd J. A multi-scale, spatially distributed model of asthmaticairway hyper-responsiveness. J Theor Biol 2010,266:614–624.

24. Vodovotz Y, Csete M, Bartels J, Chang S, An G.Translational systems biology of inflammation. PLoSComput Biol 2008, 4:e1000014.

25. Walpole J, Papin JA, Peirce SM. Multiscale compu-tational models of complex biological systems. AnnuRev Biomed Eng 2013, 15:137–154.

26. Wang W, King MR. Multiscale modeling of plateletadhesion and thrombus growth. Ann Biomed Eng2012, 40:2345–2354.

27. Coveney PV, Fowler PW. Modelling biological com-plexity: a physical scientist’s perspective. J R Soc Inter-face 2005, 2:267–280.

28. Kirschner D. The multi-scale immune response topathogens: M. tuberculosis as an example. In: FlowerD, Timmis J, eds. In Silico Immunology. New York:Springer; 2007, 289–311.

29. Vlachos DG. A review of multiscale analysis: examplesfrom systems biology, materials engineering, and otherfluid-surface interacting systems. Adv Chem Eng 2005,30:1–61.

30. Alden K, Read M, Timmis J, Andrews PS,Veiga-Fernandes H, Coles M. Spartan: a com-prehensive tool for understanding uncertainty insimulations of biological systems. PLoS Comput Biol2013, 9:e1002916.

31. Bhalla US, Iyengar R. Emergent properties of net-works of biological signaling pathways. Science 1999,283:381–387.

32. Chylek LA, Harris LA, Tung CS, Faeder JR, Lopez CF,Hlavacek WS. Rule-based modeling: a computationalapproach for studying biomolecular site dynamics incell signaling systems. WIREs Syst Biol Med 2014,6:13–36. doi: 10.1002/wsbm.1245.

33. Hlavacek WS, Faeder JR, Blinov ML, Perelson AS,Goldstein B. The complexity of complexes in signaltransduction. Biotechnol Bioeng 2003, 84:783–794.

34. Hlavacek WS, Faeder JR, Blinov ML, PosnerRG, Hucka M, Fontana W. Rules for modelingsignal-transduction systems. Sci STKE 2006:re6.

35. Kholodenko B, Yaffe MB, Kolch W. Computationalapproaches for analyzing information flow in biologi-cal networks. Sci Signal 2012, 5:re1.

36. Marchisio MA, Colaiacovo M, Whitehead E, StellingJ. Modular, rule-based modeling for the design ofeukaryotic synthetic gene circuits. BMC Syst Biol2013, 7:42.

37. Vilar JM, Saiz L. Reliable prediction of complexphenotypes from a modular design in free energyspace: an extensive exploration of the lac operon.ACS Synth Biol 2013, 2:576–586.

38. Lam TN, Hunt CA. Mechanistic insight from in silicopharmacokinetic experiments: roles of P-glycoprotein,Cyp3A4 enzymes, and microenvironments. J Pharma-col Exp Ther 2010, 332:398–412.

39. Angermann BR, Klauschen F, Garcia AD, Prustel T,Zhang F, Germain RN, Meier-Schellersheim M. Com-putational modeling of cellular signaling processesembedded into dynamic spatial contexts. Nat Methods2012, 9:283–289.

40. Andasari V, Roper RT, Swat MH, Chaplain MA. Inte-grating intracellular dynamics using CompuCell3Dand Bionetsolver: applications to multiscale modellingof cancer cell growth and invasion. PLoS One 2012,7:e33726.



41. Meier-Schellersheim M, Xu X, Angermann B, KunkelEJ, Jin T, Germain RN. Key role of local regula-tion in chemosensing revealed by a new molecularinteraction-based modeling method. PLoS ComputBiol 2006, 2:e82.

42. Donoho DL, Maleki A, Shahram M, Rahman IU,Stodden V. Reproducible research in computationalharmonic analysis. Comput Sci Eng 2009, 11:8–18.

43. Fomel S, Hennenfent G. Reproducible computationalexperiments using SCons. In: International Conferenceon Acoustics, Speech, 2007, 1257–1260.

44. Mesirov JP. Accessible reproducible research. Science2010, 327:415–416.

45. Morin A, Urban J, Adams PD, Foster I, Sali A, BakerD, Sliz P. Shining Light into Black Boxes. Science2012, 336:159–160.

46. Peng RD. Reproducible research and biostatistics.Biostatistics 2009, 10:405–408.

47. Stodden V. The scientific method in practice: repro-ducibility in the computational sciences. MIT SloanResearch Paper 4773; 2010, 10

48. Marino S, Hogue IB, Ray CJ, Kirschner DE. A method-ology for performing global uncertainty and sensitiv-ity analysis in systems biology. J Theor Biol 2008,254:178–196.

49. Gong C, Linderman JJ, Kirschner DE. Harnessing theheterogeneity of T cell differentiation fate to fine-tunegeneration of effector and memory T cells. FrontImmunol 2013, 5:57.

50. Davis PK, Hillestad R. Families of models that crosslevels of resolution – issues for design, calibration andmanagement. In: 1993 Winter Simulation ConferenceProceedings, 1993, 1003–1012.

51. Natrajan A, Reynolds PF, Srinivasan S. MRE: a flex-ible approach to multi-resolution modeling. In: 11thWorkshop on Parallel and Distributed Simulation,Proceedings, 1997, 156–163.

52. Bigelow JH, Davis PK. Developing improved meta-models by combining phenomenological reasoningwith statistical methods. Proc Soc Photo Opt Ins 2002,4716:167–180.

53. Davis PK. Exploratory analysis enabled by multires-olultion, multiperspective modeling. In: Proceedings ofthe 2000 Winter Simulation Conference, Vols. 1 and 2,2000, 293–302.

54. Kasputis S, Ng HC. Composable simulations. In: Pro-ceedings of the 2000 Winter Simulation Conference,Vols. 1 and 2, 2000, 1577–1584.

55. Aumann CA. A methodology for developing simula-tion models of complex systems. Ecol Model 2007,202:385–396.

56. Kimmins JP, Blanco JA, Seely B, Welham C, ScoullarK. Complexity in modelling forest ecosystems:How much is enough? Forest Ecol Manage 2008,256:1646–1658.

57. Ratze C, Gillet F, Muller JP, Stoffel K. Simulationmodelling of ecological hierarchies in constructivedynamical systems. Ecol Complex 2007, 4:13–25.

58. Wu JG, David JL. A spatially explicit hierarchicalapproach to modeling complex ecological systems:theory and applications. Ecol Model 2002, 153:7–26.

59. Bassingthwaighte JB, Chizeck HJ, Atlas LE. Strategiesand tactics in multiscale modeling of cell-to-organsystems. Proc IEEE 2006, 94:819–831.

60. Hernandez AI, Le Rolle V, Defontaine A, CarraultG. A multiformalism and multiresolution modellingenvironment: application to the cardiovascular systemand its regulation. Philos Trans R Soc A 2009, 367:4923–4940.

61. Brenner S, Noble D, Sejnowski TJ, Fields RD, Laugh-lin S, Berridge M, Segel ML, Prank K, DolmetschRE. Understanding complex systems: top-down,bottom-up or middleout? In: Bock GG, ed. NovartisFoundation Symposium 239: Complexity in Biolog-ical Information Processing. Chichester, England:John Wiley & Sons; 2001, 150–159.

62. Bokulich A. Explanatory models versus predictivemodels: reduced complexity modeling in geomorphol-ogy. In: Vassilios Karakostos DD, ed. EPSA11 Per-spectives and Foundational Problems in Philosophy ofScience. New York, NY: Springer International Pub-lishing; 2013, 115–128.

63. Viceconti M. A tentative taxonomy for predictivemodels in relation to their falsifiability. Philos TransA Math Phys Eng Sci 2011, 369:4149–4161.

64. Hunt CA, Ropella GE, Lam T, Gewitz AD. Relationalgrounding facilitates development of scientifically use-ful multiscale models. Theor Biol Med Model 2011,8:35.

65. Bartha P. Analogy and analogical reasoning. In: ZaltaEN, ed. The Stanford Encyclopedia of Philosophy.Fall ed. Standford: The Metaphysics Research Lab,Center for the Study of Language and Information;2013. Available at: http://plato.stanford.edu/archives/fall2013/entries/reasoning-analogy/.

66. Conzelmann H, Saez-Rodriguez J, Sauter T, BullingerE, Allgower F, Gilles ED. Reduction of mathe-matical models of signal transduction networks:simulation-based approach applied to EGF receptorsignalling. Syst Biol (Stevenage) 2004, 1:159–169.

67. Maurya MR, Bornheimer SJ, VenkatasubramanianV, Subramaniam S. Reduced-order modelling of bio-chemical networks: application to the GTPase-cyclesignalling module. Syst Biol (Stevenage) 2005, 152:229–242.

68. Maurya MR, Katare S, Patkar PR, Rundell AE,Venkatasubramanian V. A systematic framework forthe design of reduced-order models for signal trans-duction pathways from a control theoretic perspective.Comput Chem Eng 2006, 30:437–452.


http://plato.stanford.edu/archives/fall2013/entries/reasoning-analogy/


69. Segovia-Juarez JL, Ganguli S, Kirschner D. Identifyingcontrol mechanisms of granuloma formation duringM. tuberculosis infection using an agent-based model.J Theor Biol 2004, 231:357–376.

70. Ray JC, Flynn JL, Kirschner DE. Synergy betweenindividual TNF-dependent functions determinesgranuloma performance for controlling Mycobac-terium tuberculosis infection. J Immunol 2009, 182:3706–3717.

71. Flynn JL, Goldstein MM, Chan J, Triebold KJ, PfefferK, Lowenstein CJ, Schreiber R, Mak TW, Bloom BR.Tumor necrosis factor-𝛼 is required in the protectiveimmune response against Mycobacterium tuberculosisin mice. Immunity 1995, 2:561–572.

72. Saunders BM, Briscoe H, Britton WJ. T cell-derivedtumour necrosis factor is essential, but not sufficient,for protection against Mycobacterium tuberculosisinfection. Clin Exp Immunol 2004, 137:279–287.

73. Algood HM, Lin PL, Yankura D, Jones A, ChanJ, Flynn JL. TNF influences chemokine expressionof macrophages in vitro and that of CD11b+ cellsin vivo during Mycobacterium tuberculosis infection.J Immunol 2004, 172:6846–6857.

74. Keane J, Balcewicz-Sablinska MK, Remold HG,Chupp GL, Meek BB, Fenton MJ, Kornfeld H. Infec-tion by Mycobacterium tuberculosis promotes humanalveolar macrophage apoptosis. Infect Immun 1997,65:298–304.

75. Harris J, Hope JC, Keane J. Tumor necrosis fac-tor blockers influence macrophage responses toMycobacterium tuberculosis. J Infect Dis 2008,198:1842–1850.

76. Lin PL, Myers A, Smith L, Bigbee C, Bigbee M,Fuhrman C, Grieser H, Chiosea I, Voitenek NN,Capuano SV, et al. Tumor necrosis factor neutral-ization results in disseminated disease in acute andlatent Mycobacterium tuberculosis infection with nor-mal granuloma structure in a cynomolgus macaquemodel. Arthritis Rheum 2010, 62:340–350.

77. Wallis RS. Infectious complications of tumor necro-sis factor blockade. Curr Opin Infect Dis 2009,22:403–409.

78. Wallis RS, Broder MS, Wong JY, Hanson ME, Been-houwer DO. Granulomatous infectious diseases asso-ciated with tumor necrosis factor antagonists. ClinInfect Dis 2004, 38:1261–1265.

79. Tubach F, Salmon D, Ravaud P, Allanore Y, GoupilleP, Breban M, Pallot-Prades B, Pouplin S, Sacchi A,Chichemanian RM, et al. Risk of tuberculosis is higherwith anti-tumor necrosis factor monoclonal antibodytherapy than with soluble tumor necrosis factor recep-tor therapy: the three-year prospective French researchaxed on tolerance of biotherapies registry. ArthritisRheum 2009, 60:1884–1894.

80. Lin PL, Plessner HL, Voitenok NN, Flynn JL. Tumornecrosis factor and tuberculosis. J Investig DermatolSymp Proc 2007, 12:22–25.

81. Fallahi-Sichani M, Schaller MA, Kirschner DE, KunkelSL, Linderman JJ. Identification of key processesthat control tumor necrosis factor availability in atuberculosis granuloma. PLoS Comput Biol 2010,6:e1000778.

82. Fallahi-Sichani M, Flynn JL, Linderman JJ, KirschnerDE. Differential risk of tuberculosis reactivationamong anti-TNF therapies is due to drug bindingkinetics and permeability. J Immunol 2012, 188:3169–3178.

83. Cilfone NA, Perry CR, Kirschner DE, LindermanJJ. Multi-scale modeling predicts a balance of tumornecrosis factor-𝛼 and interleukin-10 controls the gran-uloma environment during Mycobacterium tuberculo-sis infection. PLoS One 2013, 8:e68680.

84. Gutierrez MG, Mishra BB, Jordao L, Elliott E,Anes E, Griffiths G. NF-𝜅B activation controlsphagolysosome fusion-mediated killing of mycobac-teria by macrophages. J Immunol 2008, 181:2651–2663.

85. Mosser DM, Edwards JP. Exploring the full spectrumof macrophage activation. Nat Rev Immunol 2008,8:958–969.

86. Beg AA, Baltimore D. An essential role for NF-𝜅B inpreventing TNF-𝛼-induced cell death. Science 1996,274:782–784.

87. Van Antwerp DJ, Martin SJ, Kafri T, Green DR,Verma IM. Suppression of TNF-𝛼-induced apoptosisby NF-𝜅B. Science 1996, 274:787–789.

88. Tay S, Hughey JJ, Lee TK, Lipniacki T, Quake SR,Covert MW. Single-cell NF-𝜅B dynamics reveal dig-ital activation and analogue information processing.Nature 2010, 466:267–271.

89. Karin M, Lin A. NF-𝜅B at the crossroads of life anddeath. Nat Immunol 2002, 3:221–227.

90. Chackerian AA, Alt JM, Perera TV, Dascher CC,Behar SM. Dissemination of Mycobacterium tubercu-losis is influenced by host factors and precedes theinitiation of T-cell immunity. Infect Immun 2002,70:4501–4509.

91. Chang ST, Linderman JJ, Kirschner DE. Multiplemechanisms allow Mycobacterium tuberculosis tocontinuously inhibit MHC class II-mediated antigenpresentation by macrophages. Proc Natl Acad Sci USA2005, 102:4530–4535.

92. Giacomini E, Iona E, Ferroni L, Miettinen M, Fat-torini L, Orefici G, Julkunen I, Coccia EM. Infectionof human macrophages and dendritic cells withMycobacterium tuberculosis induces a differentialcytokine gene expression that modulates T cellresponse. J Immunol 2001, 166:7033–7041.

93. Hickman SP, Chan J, Salgame P. Mycobacteriumtuberculosis induces differential cytokine productionfrom dendritic cells and macrophages with divergenteffects on naive T cell polarization. J Immunol 2002,168:4636–4642.



94. Marino S, El-Kebir M, Kirschner D. A hybridmulti-compartment model of granuloma formationand T cell priming in tuberculosis. J Theor Biol 2011,280:50–62.

95. Marino S, Myers A, Flynn JL, Kirschner DE. TNFand IL-10 are major factors in modulation of thephagocytic cell environment in lung and lymph nodein tuberculosis: a next-generation two-compartmentalmodel. J Theor Biol 2010, 265:586–598.

96. Garcia-Ramallo E, Marques T, Prats N, Beleta J,Kunkel SL, Godessart N. Resident cell chemokineexpression serves as the major mechanism for leuko-cyte recruitment during local inflammation. J Immunol2002, 169:6467–6473.

97. Gong C, Mattila JT, Miller M, Flynn JL, Linderman JJ,Kirschner D. Predicting lymph node output efficiencyusing systems biology. J Theor Biol 2013, 335C:169–184.

98. Linderman JJ, Riggs T, Pande M, Miller M, Marino S,Kirschner DE. Characterizing the dynamics of CD4+T cell priming within a lymph node. J Immunol 2010,184:2873–2885.

99. Riggs T, Walts A, Perry N, Bickle L, Lynch JN,Myers A, Flynn J, Linderman JJ, Miller MJ, KirschnerDE. A comparison of random vs. chemotaxis-drivencontacts of T cells with dendritic cells during repertoirescanning. J Theor Biol 2008, 250:732–751.

100. An G. Introduction of an agent-based multi-scale mod-ular architecture for dynamic knowledge representa-tion of acute inflammation. Theor Biol Med Model2008, 5:11.

101. Kim SH, Hunt CA. Composite cell agent model ofepithelial culture in vitro. In: Proceedings of the 2011Workshop on Agent-Directed Simulation. Society forComputer Simulation International, 2011, 45–51.

102. Ruiz-Herrero T, Estrada J, Guantes R, Miguez DG.A tunable coarse-grained model for ligand-receptorinteraction. PLoS Comput Biol 2013, 9:e1003274.

103. Tang J, Ley KF, Hunt CA. Dynamics of in silicoleukocyte rolling, activation, and adhesion. BMC SystBiol 2007, 1:14.

104. Tang J, Fernandez-Garcia I, Vijayakumar S,Martinez-Ruis H, Illa-Bochaca I, Nguyen DH, MaoJH, Costes SV, Barcellos-Hoff MH. Irradiation ofjuvenile, but not adult, mammary gland increasesstem cell self-renewal and estrogen receptor negativetumors. Stem Cells 2014, 32:649–661.

105. Smith BC. On the Origin of Objects. Cambridge: MITPress; 1996.

106. Hayenga H, Thorne B, Peirce S, Humphrey J. Ensuringcongruency in multiscale modeling: towards linkingagent based and continuum biomechanical modelsof arterial adaptation. Ann Biomed Eng 2011, 39:2669–2682.


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