Strategies for efficient numerical implementation of hybrid multi-scale agent-based models to describe biological systems

Optimizing Solid Tumor Treatment with Antibody-drug Conjugates Using Agent-Based Modeling: Considering the Role of a Carrier Dose and Payload Class

INTRODUCTION

Antibody-drug conjugates (ADCs) show significant clinical efficacy in the treatment of solid tumors, but a major limitation to their success is poor intratumoral distribution. Adding a carrier dose improves both distribution and overall drug efficacy of ADCs, but the optimal carrier dose has not been outlined for different payload classes.

OBJECTIVE

In this work, we study two carrier dose regimens: 1) matching payload potency to cellular delivery but potentially not reaching cells farther away from blood vessels, or 2) dosing to tumor saturation but risking a reduction in cell killing from a lower amount of payload delivered per cell.

METHODS

We use a validated computational model to test four different payloads conjugated to trastuzumab to determine the optimal carrier dose as a function of target expression, ADC dose, and payload potency.

RESULTS

We find that dosing to tumor saturation is more efficacious than matching payload potency to cellular delivery for all payloads because the increase in the number of cells targeted by the ADC outweighs the loss in cell killing on targeted cells. An important exception exists if the carrier dose reduces the payload uptake per cell to the point where all cell killing is lost. Likewise, receptor downregulation can mitigate the benefits of a carrier dose.

CONCLUSIONS

Because tumor saturation and in vitro potency can be measured early in ADC design, these results provide insight into maximizing ADC efficacy and demonstrate the benefits of using simulation to guide ADC design.

In silico agent-based modeling approach to characterize multiple in vitro tuberculosis infection models

In vitro models of Mycobacterium tuberculosis (Mtb) infection are a valuable tool for examining host-pathogen interactions and screening drugs. With the development of more complex in vitro models, there is a need for tools to help analyze and integrate data from these models. To this end, we introduce an agent-based model (ABM) representation of the interactions between immune cells and bacteria in an in vitro setting. This in silico model was used to simulate both traditional and spheroid cell culture models by changing the movement rules and initial spatial layout of the cells in accordance with the respective in vitro models. The traditional and spheroid simulations were calibrated to published experimental data in a paired manner, by using the same parameters in both simulations. Within the calibrated simulations, heterogeneous outputs are seen for bacterial count and T cell infiltration into the macrophage core of the spheroid. The simulations also predict that equivalent numbers of activated macrophages do not necessarily result in similar bacterial reductions; that host immune responses can control bacterial growth in both spheroid structure dependent and independent manners; that STAT1 activation is the limiting step in macrophage activation in spheroids; and that drug screening and macrophage activation studies could have different outcomes depending on the in vitro culture used. Future model iterations will be guided by the limitations of the current model, specifically which parts of the output space were harder to reach. This ABM can be used to represent more in vitro Mtb infection models due to its flexible structure, thereby accelerating in vitro discoveries.

Microglial roles in Alzheimer's disease: An agent-based model to elucidate microglial spatiotemporal response to beta-amyloid

Alzheimer's disease (AD) is characterized by beta-amyloid (Aβ) plaques in the brain and widespread neuronal damage. Because of the high drug attrition rates in AD, there is increased interest in characterizing neuroimmune responses to Aβ plaques. In response to AD pathology, microglia are innate phagocytotic immune cells that transition into a neuroprotective state and form barriers around plaques. We seek to understand the role of microglia in modifying Aβ dynamics and barrier formation. To quantify the influence of individual microglia behaviors (activation, chemotaxis, phagocytosis, and proliferation) on plaque size and barrier coverage, we developed an agent-based model to characterize the spatiotemporal interactions between microglia and Aβ. Our model qualitatively reproduces mouse data trends where the fraction of microglia coverage decreases as plaques become larger. In our model, the time to microglial arrival at the plaque boundary is significantly negatively correlated (p < 0.0001) with plaque size, indicating the importance of the time to microglial activation for regulating plaque size. In addition, in silico behavioral knockout simulations show that phagocytosis knockouts have the strongest impact on plaque size, but modest impacts on microglial coverage and activation. In contrast, the chemotaxis knockouts had a strong impact on microglial coverage with a more modest impact on plaque volume and microglial activation. These simulations suggest that phagocytosis, chemotaxis, and replication of activated microglia have complex impacts on plaque volume and coverage, whereas microglial activation remains fairly robust to perturbations of these functions. Thus, our work provides insights into the potential and limitations of targeting microglial activation as a pharmacological strategy for the treatment of AD.

Development and Analysis of Multiscale Models for Tuberculosis: From Molecules to Populations

Although infectious disease dynamics are often analyzed at the macro-scale, increasing numbers of drug-resistant infections highlight the importance of within-host modeling that simultaneously solves across multiple scales to effectively respond to epidemics. We review multiscale modeling approaches for complex, interconnected biological systems and discuss critical steps involved in building, analyzing, and applying such models within the discipline of model credibility. We also present our two tools: CaliPro, for calibrating multiscale models (MSMs) to datasets, and tunable resolution, for fine- and coarse-graining sub-models while retaining insights. We include as an example our work simulating infection with Mycobacterium tuberculosis to demonstrate modeling choices and how predictions are made to generate new insights and test interventions. We discuss some of the current challenges of incorporating novel datasets, rigorously training computational biologists, and increasing the reach of MSMs. We also offer several promising future research directions of incorporating within-host dynamics into applications ranging from combinatorial treatment to epidemic response.

The spatial dynamics of immune response upon virus infection through hybrid dynamical computational model

Introduction

The immune responses play important roles in the course of disease initiation and progression upon virus infection such as SARS-CoV-2. As the tissues consist of spatial structures, the spatial dynamics of immune responses upon viral infection are essential to the outcome of infection.

Methods

A hybrid computational model based on cellular automata coupled with partial differential equations is developed to simulate the spatial patterns and dynamics of the immune responses of tissue upon virus infection with several different immune movement modes.

Results

Various patterns of the distribution of virus particles under different immune strengths and movement modes of immune cells are obtained through the computational models. The results also reveal that the directed immune cell wandering model has a better immunization effect. Several other characteristics, such as the peak level of virus density and onset time and the onset of the diseases, are also checked with different immune and physiological conditions, for example, different immune clearance strengths, and different cell-to-cell transmission rates. Furthermore, by the Lasso analysis, it is identified that the three main parameters had the most impact on the rate of onset time of disease. It is also shown that the cell-to-cell transmission rate has a significant effect and is more important for controlling the diseases than those for the cell-free virus given that the faster cell-to-cell transmission than cell-free transmission the rate of virus release is low.

Discussion

Our model simulates the process of viral and immune response interactions in the alveola repithelial tissues of infected individuals, providing insights into the viral propagation of viruses in two dimensions as well as the influence of immune response patterns and key factors on the course of infection.

Optimizing tuberculosis treatment efficacy: Comparing the standard regimen with Moxifloxacin-containing regimens

Tuberculosis (TB) continues to be one of the deadliest infectious diseases in the world, causing ~1.5 million deaths every year. The World Health Organization initiated an End TB Strategy that aims to reduce TB-related deaths in 2035 by 95%. Recent research goals have focused on discovering more effective and more patient-friendly antibiotic drug regimens to increase patient compliance and decrease emergence of resistant TB. Moxifloxacin is one promising antibiotic that may improve the current standard regimen by shortening treatment time. Clinical trials and in vivo mouse studies suggest that regimens containing moxifloxacin have better bactericidal activity. However, testing every possible combination regimen with moxifloxacin either in vivo or clinically is not feasible due to experimental and clinical limitations. To identify better regimens more systematically, we simulated pharmacokinetics/pharmacodynamics of various regimens (with and without moxifloxacin) to evaluate efficacies, and then compared our predictions to both clinical trials and nonhuman primate studies performed herein. We used GranSim, our well-established hybrid agent-based model that simulates granuloma formation and antibiotic treatment, for this task. In addition, we established a multiple-objective optimization pipeline using GranSim to discover optimized regimens based on treatment objectives of interest, i.e., minimizing total drug dosage and lowering time needed to sterilize granulomas. Our approach can efficiently test many regimens and successfully identify optimal regimens to inform pre-clinical studies or clinical trials and ultimately accelerate the TB regimen discovery process.

Trabecular bone remodeling in the aging mouse: A micro-multiphysics agent-based in silico model using single-cell mechanomics

Bone remodeling is regulated by the interaction between different cells and tissues across many spatial and temporal scales. Notably, in silico models are regarded as powerful tools to further understand the signaling pathways that regulate this intricate spatial cellular interplay. To this end, we have established a 3D multiscale micro-multiphysics agent-based (micro-MPA) in silico model of trabecular bone remodeling using longitudinal in vivo data from the sixth caudal vertebra (CV6) of PolgA(D257A/D257A) mice, a mouse model of premature aging. Our in silico model includes a variety of cells as single agents and receptor-ligand kinetics, mechanomics, diffusion and decay of cytokines which regulate the cells' behavior. We highlighted its capabilities by simulating trabecular bone remodeling in the CV6 of five mice over 4 weeks and we evaluated the static and dynamic morphometry of the trabecular bone microarchitecture. Based on the progression of the average trabecular bone volume fraction (BV/TV), we identified a configuration of the model parameters to simulate homeostatic trabecular bone remodeling, here named basal. Crucially, we also produced anabolic, anti-anabolic, catabolic and anti-catabolic responses with an increase or decrease by one standard deviation in the levels of osteoprotegerin (OPG), receptor activator of nuclear factor kB ligand (RANKL), and sclerostin (Scl) produced by the osteocytes. Our results showed that changes in the levels of OPG and RANKL were positively and negatively correlated with the BV/TV values after 4 weeks in comparison to basal levels, respectively. Conversely, changes in Scl levels produced small fluctuations in BV/TV in comparison to the basal state. From these results, Scl was deemed to be the main driver of equilibrium while RANKL and OPG were shown to be involved in changes in bone volume fraction with potential relevance for age-related bone features. Ultimately, this micro-MPA model provides valuable insights into how cells respond to their local mechanical environment and can help to identify critical pathways affected by degenerative conditions and ageing.

A multiscale hybrid model for exploring the effect of Resolvin D1 on macrophage polarization during acute inflammation

Dysregulated inflammation underlies various diseases. Specialized pro-resolving mediators (SPMs) like Resolvin D1 (RvD1) have been shown to resolve inflammation and halt disease progression. Macrophages, key immune cells that drive inflammation, respond to the presence of RvD1 by polarizing to an anti-inflammatory type (M₂). However, RvD1's mechanisms, roles, and utility are not fully understood. This paper introduces a gene-regulatory network (GRN) model that contains pathways for RvD1 and other SPMs and proinflammatory molecules like lipopolysaccharides. We couple this GRN model to a partial differential equation - agent-based hybrid model using a multiscale framework to simulate an acute inflammatory response with and without the presence of RvD1. We calibrate and validate the model using experimental data from two animal models. The model reproduces the dynamics of key immune components and the effects of RvD1 during acute inflammation. Our results suggest RvD1 can drive macrophage polarization through the G protein-coupled receptor 32 (GRP32) pathway. The presence of RvD1 leads to an earlier and increased M₂ polarization, reduced neutrophil recruitment, and faster apoptotic neutrophil clearance. These results support a body of literature that suggests that RvD1 is a promising candidate for promoting the resolution of acute inflammation. We conclude that once calibrated and validated on human data, the model can identify critical sources of uncertainty, which could be further elucidated in biological experiments and assessed for clinical use.

Individual-Based Modeling of Spatial Dynamics of Chemotactic Microbial Populations

One important direction of synthetic biology is to establish desired spatial structures from microbial populations. Underlying this structural development process are different driving factors, among which bacterial motility and chemotaxis serve as a major force. Here, we present an individual-based, biophysical computational framework for mechanistic and multiscale simulation of the spatiotemporal dynamics of motile and chemotactic microbial populations. The framework integrates cellular movement with spatial population growth, mechanical and chemical cellular interactions, and intracellular molecular kinetics. It is validated by a statistical comparison of single-cell chemotaxis simulations with reported experiments. The framework successfully captures colony range expansion of growing isogenic populations and also reveals chemotaxis-modulated, spatial patterns of a two-species amensal community. Partial differential equation-based models subsequently validate these simulation findings. This study provides a versatile computational tool to uncover the fundamentals of microbial spatial ecology as well as to facilitate the design of synthetic consortia for desired spatial patterns.

A global method for fast simulations of molecular dynamics in multiscale agent-based models of biological tissues

Agent-based models (ABMs) are a natural platform for capturing the multiple time and spatial scales in biological processes. However, these models are computationally expensive, especially when including molecular-level effects. The traditional approach to simulating this type of multiscale ABM is to solve a system of ordinary differential equations for the molecular events per cell. This significantly adds to the computational cost of simulations as the number of agents grows, which contributes to many ABMs being limited to around10 5 cells. We propose an approach that requires the same computational time independent of the number of agents. This speeds up the entire simulation by orders of magnitude, allowing for more thorough explorations of ABMs with even larger numbers of agents. We use two systems to show that the new method strongly agrees with the traditionally used approach. This computational strategy can be applied to a wide range of biological investigations.

An Agent-Based Interpretation of Leukocyte Chemotaxis in Cancer-on-Chip Experiments

The present paper was inspired by recent developments in laboratory experiments within the framework of cancer-on-chip technology, an immune-oncology microfluidic chip aiming at studying the fundamental mechanisms of immunocompetent behavior. We focus on the laboratory setting where cancer is treated with chemotherapy drugs, and in this case, the effects of the treatment administration hypothesized by biologists are: the absence of migration and proliferation of tumor cells, which are dying; the stimulation of the production of chemical substances (annexin); the migration of leukocytes in the direction of higher concentrations of chemicals. Here, following the physiological hypotheses made by biologists on the phenomena occurring in these experiments, we introduce an agent-based model reproducing the dynamics of two cell populations (agents), i.e., tumor cells and leukocytes living in the microfluidic chip environment. Our model aims at proof of concept, demonstrating that the observations of the biological phenomena can be obtained by the model on the basis of the explicit assumptions made. In this framework, close adherence of the computational model to the biological results, as shown in the section devoted to the first calibration of the model with respect to available observations, is successfully accomplished.

Mathematical Modeling of Proliferative Immune Response Initiated by Interactions Between Classical Antigen-Presenting Cells Under Joint Antagonistic IL-2 and IL-4 Signaling

During an adaptive immune response from pathogen invasion, multiple cytokines are produced by various immune cells interacting jointly at the cellular level to mediate several processes. For example, studies have shown that regulation of interleukin-4 (IL-4) correlates with interleukin-2 (IL-2) induced lymphocyte proliferation. This motivates the need to better understand and model the mechanisms driving the dynamic interplay of proliferation of lymphocytes with the complex interaction effects of cytokines during an immune response. To address this challenge, we adopt a hybrid computational approach comprising of continuous, discrete and stochastic non-linear model formulations to predict a system-level immune response as a function of multiple dependent signals and interacting agents including cytokines and targeted immune cells. We propose a hybrid ordinary differential equation-based (ODE) multicellular model system with a stochastic component of antigen microscopic states denoted as Multiscale Multicellular Quantitative Evaluator (MMQE) implemented using MATLAB. MMQE combines well-defined immune response network-based rules and ODE models to capture the complex dynamic interactions between the proliferation levels of different types of communicating lymphocyte agents mediated by joint regulation of IL-2 and IL-4 to predict the emergent global behavior of the system during an immune response. We model the activation of the immune system in terms of different activation protocols of helper T cells by the interplay of independent biological agents of classic antigen-presenting cells (APCs) and their joint activation which is confounded by the exposure time to external pathogens. MMQE quantifies the dynamics of lymphocyte proliferation during pathogen invasion as bivariate distributions of IL-2 and IL-4 concentration levels. Specifically, by varying activation agents such as dendritic cells (DC), B cells and their joint mechanism of activation, we quantify how lymphocyte activation and differentiation protocols boost the immune response against pathogen invasion mediated by a joint downregulation of IL-4 and upregulation of IL-2. We further compare our in-silico results to in-vivo and in-vitro experimental studies for validation. In general, MMQE combines intracellular and extracellular effects from multiple interacting systems into simpler dynamic behaviors for better interpretability. It can be used to aid engineering of anti-infection drugs or optimizing drug combination therapies against several diseases.

A 3D Agent-Based Model of Lung Fibrosis

Understanding the pathophysiology of lung fibrosis is of paramount importance to elaborate targeted and effective therapies. As it onsets, the randomly accumulating extracellular matrix (ECM) breaks the symmetry of the branching lung structure. Interestingly, similar pathways have been reported for both idiopathic pulmonary fibrosis and radiation-induced lung fibrosis (RILF). Individuals suffering from the disease, the worldwide incidence of which is growing, have poor prognosis and a short mean survival time. In this context, mathematical and computational models have the potential to shed light on key underlying pathological mechanisms, shorten the time needed for clinical trials, parallelize hypotheses testing, and improve personalized drug development. Agent-based modeling (ABM) has proven to be a reliable and versatile simulation tool, whose features make it a good candidate for recapitulating emergent behaviors in heterogeneous systems, such as those found at multiple scales in the human body. In this paper, we detail the implementation of a 3D agent-based model of lung fibrosis using a novel simulation platform, namely, BioDynaMo, and prove that it can qualitatively and quantitatively reproduce published results. Furthermore, we provide additional insights on late-fibrosis patterns through ECM density distribution histograms. The model recapitulates key intercellular mechanisms, while cell numbers and types are embodied by alveolar segments that act as agents and are spatially arranged by a custom algorithm. Finally, our model may hold potential for future applications in the context of lung disorders, ranging from RILF (by implementing radiation-induced cell damage mechanisms) to COVID-19 and inflammatory diseases (such as asthma or chronic obstructive pulmonary disease).

A scalable solver for a stochastic, hybrid cellular automaton model of personalized breast cancer therapy

Mathematical modeling and simulation is a promising approach to personalized cancer medicine. Yet, the complexity, heterogeneity and multi-scale nature of cancer pose significant computational challenges. Coupling discrete cell-based models with continuous models using hybrid cellular automata (CA) is a powerful approach for mimicking biological complexity and describing the dynamical exchange of information across different scales. However, when clinically relevant cancer portions are taken into account, such models become computationally very expensive. While efficient parallelization techniques for continuous models exist, their coupling with discrete models, particularly CA, necessitates more elaborate solutions. Building upon FEniCS, a popular and powerful scientific computing platform for solving partial differential equations, we developed parallel algorithms to link stochastic CA with differential equations (https://bitbucket.org/HTasken/cansim). The algorithms minimize the communication between processes that share CA neighborhood values while also allowing for reproducibility during stochastic updates. We demonstrated the potential of our solution on a complex hybrid cellular automaton model of breast cancer treated with combination chemotherapy. On a single-core processor, we obtained nearly linear scaling with an increasing problem size, whereas weak parallel scaling showed moderate growth in solving time relative to increase in problem size. Finally, we applied the algorithm to a problem that is 500 times larger than previous work, allowing us to run personalized therapy simulations based on heterogeneous cell density and tumor perfusion conditions estimated from magnetic resonance imaging data on an unprecedented scale.

Simulating the Selection of Resistant Cells with Bystander Killing and Antibody Coadministration in Heterogeneous Human Epidermal Growth Factor Receptor 2-Positive Tumors

Intratumoral heterogeneity is a leading cause of treatment failure resulting in tumor recurrence. For the antibody-drug conjugate (ADC) ado-trastuzumab emtansine (T-DM1), two major types of resistance include changes in human epidermal growth factor receptor 2 (HER2) expression and reduced payload sensitivity, which is often exacerbated by heterogenous HER2 expression and ADC distribution during treatment. ADCs with bystander payloads, such as trastuzumab-monomethyl auristatin E (T-MMAE), can reach and kill adjacent cells with lower receptor expression that cannot be targeted directly with the ADC. Additionally, coadministration of T-DM1 with its unconjugated antibody, trastuzumab, can improve distribution and minimize heterogeneous delivery. However, the effectiveness of trastuzumab coadministration and ADC bystander killing in heterogenous tumors in reducing the selection of resistant cells is not well understood. Here, we use an agent-based model to predict outcomes with these different regimens. The simulations demonstrate that both T-DM1 and T-MMAE benefit from trastuzumab coadministration for tumors with high average receptor expression (up to 70% and 40% decrease in average tumor volume, respectively), with greater benefit for nonbystander payloads. However, the benefit decreases as receptor expression is reduced, reversing at low concentrations (up to 360% and 430% increase in average tumor volume for T-DM1 and T-MMAE, respectively) for this mechanism that impacts both ADC distribution and efficacy. For tumors with intrinsic payload resistance, coadministration uniformly exhibits better efficacy than ADC monotherapy (50%-70% and 19%-36% decrease in average tumor volume for T-DM1 and T-MMAE, respectively). Finally, we demonstrate that several regimens select for resistant cells at clinical tolerable doses, which highlights the need to pursue other mechanisms of action for durable treatment responses. SIGNIFICANCE STATEMENT: Experimental evidence demonstrates heterogeneity in the distribution of both the antibody-drug conjugate and the target receptor in the tumor microenvironment, which can promote the selection of resistant cells and lead to recurrence. This study quantifies the impact of increasing the antibody dose and utilizing bystander payloads in heterogeneous tumors. Alternative cell-killing mechanisms are needed to avoid enriching resistant cell populations.

A hybrid PDE-ABM model for viral dynamics with application to SARS-CoV-2 and influenza

We propose a hybrid partial differential equation-agent-based (PDE-ABM) model to describe the spatio-temporal viral dynamics in a cell population. The virus concentration is considered as a continuous variable and virus movement is modelled by diffusion, while changes in the states of cells (i.e. healthy, infected, dead) are represented by a stochastic ABM. The two subsystems are intertwined: the probability of an agent getting infected in the ABM depends on the local viral concentration, and the source term of viral production in the PDE is determined by the cells that are infected. We develop a computational tool that allows us to study the hybrid system and the generated spatial patterns in detail. We systematically compare the outputs with a classical ODE system of viral dynamics, and find that the ODE model is a good approximation only if the diffusion coefficient is large. We demonstrate that the model is able to predict SARS-CoV-2 infection dynamics, and replicate the output of in vitro experiments. Applying the model to influenza as well, we can gain insight into why the outcomes of these two infections are different.

The Role of Biofilms, Bacterial Phenotypes, and Innate Immune Response in Mycobacterium avium Colonization to Infection

Mycobacterium avium complex (MAC), is known for colonizing and infecting humans following inhalation of the bacteria. MAC pulmonary disease is notoriously difficult to treat and prone to recurrence. Both the incidence and prevalence MAC pulmonary disease have been increasing globally. MAC is well known to form biofilms in the environment, and in vitro, these biofilms have been shown to aid MAC in epithelial cell invasion, protect MAC from phagocytosis, and cause premature apoptosis in macrophages. In vivo, the system of interactions between MAC, biofilms and host macrophages is complex, difficult to replicate in vitro and in animal models, has not been fully characterized. Here we present a three-dimensional agent-based model of a lung airway to help understand how these interactions evolve in the first 14 days post-bacterial inhalation. We parameterized the model using published data and performed uncertainty analysis to characterize outcomes and parameters' effects on those outcomes. Model results show diverse outcomes, including wide ranges of macrophage recruitment levels, and bacterial loads and phenotype distribution. Though most bacteria are phagocytosed by macrophages and remain intracellular, there are also many simulations in which extracellular bacteria continue to drive the colonization and infection. Initial parameters dictating host immune levels, bacterial loads introduced to the airway, and biofilm conditions have significant and lasting impacts on the course of these results. Additionally, though macrophage recruitment is key for suppressing bacterial loads, there is evidence of significant excess recruitment that fail to impact bacterial numbers. These results highlight a need and identify a path for further exploration into the inhalation events in MAC infection. Early infection dynamics could have lasting impacts on the development of nodular bronchiectatic or fibrocavitary disease as well as inform possible preventative and treatment intervention targeting biofilm-macrophage interactions.

Neutrophil Dynamics Affect Mycobacterium tuberculosis Granuloma Outcomes and Dissemination

Neutrophil infiltration into tuberculous granulomas is often associated with higher bacteria loads and severe disease but the basis for this relationship is not well understood. To better elucidate the connection between neutrophils and pathology in primate systems, we paired data from experimental studies with our next generation computational model GranSim to identify neutrophil-related factors, including neutrophil recruitment, lifespan, and intracellular bacteria numbers, that drive granuloma-level outcomes. We predict mechanisms underlying spatial organization of neutrophils within granulomas and identify how neutrophils contribute to granuloma dissemination. We also performed virtual deletion and depletion of neutrophils within granulomas and found that neutrophils play a nuanced role in determining granuloma outcome, promoting uncontrolled bacterial growth in some and working to contain bacterial growth in others. Here, we present three key results: We show that neutrophils can facilitate local dissemination of granulomas and thereby enable the spread of infection. We suggest that neutrophils influence CFU burden during both innate and adaptive immune responses, implying that they may be targets for therapeutic interventions during later stages of infection. Further, through the use of uncertainty and sensitivity analyses, we predict which neutrophil processes drive granuloma severity and structure.

To Sobol or not to Sobol? The effects of sampling schemes in systems biology applications

Computational and mathematical models in biology rely heavily on the parameters that characterize them. However, robust estimates for their values are typically elusive and thus a large parameter space becomes necessary for model study, particularly to make translationally impactful predictions. Sampling schemes exploring parameter spaces for models are used for a variety of purposes in systems biology, including model calibration and sensitivity analysis. Typically, random sampling is used; however, when models have a high number of unknown parameters or the models are highly complex, computational cost becomes an important factor. This issue can be reduced through the use of efficient sampling schemes such as Latin hypercube sampling (LHS) and Sobol sequences. In this work, we compare and contrast three sampling schemes - random sampling, LHS, and Sobol sequences - for the purposes of performing both parameter sensitivity analysis and model calibration. In addition, we apply these analyses to different types of computational and mathematical models of varying complexity: a simple ODE model, a complex ODE model, and an agent-based model. In general, the sampling scheme had little effect when used for calibration efforts, but when applied to sensitivity analyses, Sobol sequences exhibited faster convergence. While the observed benefit to convergence is relatively small, Sobol sequences are computationally less expensive to compute than LHS samples and also have the benefit of being deterministic, which allows for better reproducibility of results.

A hybrid model connecting regulatory interactions with stem cell divisions in the root

Stem cells give rise to the entirety of cells within an organ. Maintaining stem cell identity and coordinately regulating stem cell divisions is crucial for proper development. In plants, mobile proteins, such as WUSCHEL-RELATED HOMEOBOX 5 (WOX5) and SHORTROOT (SHR), regulate divisions in the root stem cell niche. However, how these proteins coordinately function to establish systemic behaviour is not well understood. We propose a non-cell autonomous role for WOX5 in the cortex endodermis initial (CEI) and identify a regulator, ANGUSTIFOLIA (AN3)/GRF-INTERACTING FACTOR 1, that coordinates CEI divisions. Here, we show with a multi-scale hybrid model integrating ordinary differential equations (ODEs) and agent-based modeling that quiescent center (QC) and CEI divisions have different dynamics. Specifically, by combining continuous models to describe regulatory networks and agent-based rules, we model systemic behaviour, which led us to predict cell-type-specific expression dynamics of SHR, SCARECROW, WOX5, AN3 and CYCLIND6;1, and experimentally validate CEI cell divisions. Conclusively, our results show an interdependency between CEI and QC divisions.

Spatial Organization and Recruitment of Non-Specific T Cells May Limit T Cell-Macrophage Interactions Within Mycobacterium tuberculosis Granulomas

Tuberculosis (TB) is a worldwide health problem; successful interventions such as vaccines and treatment require a 2better understanding of the immune response to infection with Mycobacterium tuberculosis (Mtb). In many infectious diseases, pathogen-specific T cells that are recruited to infection sites are highly responsive and clear infection. Yet in the case of infection with Mtb, most individuals are unable to clear infection leading to either an asymptomatically controlled latent infection (the majority) or active disease (roughly 5%-10% of infections). The hallmark of Mtb infection is the recruitment of immune cells to lungs leading to development of multiple lung granulomas. Non-human primate models of TB indicate that on average <10% of T cells within granulomas are Mtb-responsive in terms of cytokine production. The reason for this reduced responsiveness is unknown and it may be at the core of why humans typically are unable to clear Mtb infection. There are a number of hypotheses as to why this reduced responsiveness may occur, including T cell exhaustion, direct downregulation of antigen presentation by Mtb within infected macrophages, the spatial organization of the granuloma itself, and/or recruitment of non-Mtb-specific T cells to lungs. We use a systems biology approach pairing data and modeling to dissect three of these hypotheses. We find that the structural organization of granulomas as well as recruitment of non-specific T cells likely contribute to reduced responsiveness.

Impact of Force Function Formulations on the Numerical Simulation of Centre-Based Models

Centre-based or cell-centre models are a framework for the computational study of multicellular systems with widespread use in cancer modelling and computational developmental biology. At the core of these models are the numerical method used to update cell positions and the force functions that encode the pairwise mechanical interactions of cells. For the latter, there are multiple choices that could potentially affect both the biological behaviour captured, and the robustness and efficiency of simulation. For example, available open-source software implementations of centre-based models rely on different force functions for their default behaviour and it is not straightforward for a modeller to know if these are interchangeable. Our study addresses this problem and contributes to the understanding of the potential and limitations of three popular force functions from a numerical perspective. We show empirically that choosing the force parameters such that the relaxation time for two cells after cell division is consistent between different force functions results in good agreement of the population radius of a two-dimensional monolayer relaxing mechanically after intense cell proliferation. Furthermore, we report that numerical stability is not sufficient to prevent unphysical cell trajectories following cell division, and consequently, that too large time steps can cause geometrical differences at the population level.

A computational model tracks whole-lung Mycobacterium tuberculosis infection and predicts factors that inhibit dissemination

Mycobacterium tuberculosis (Mtb), the causative infectious agent of tuberculosis (TB), kills more individuals per year than any other infectious agent. Granulomas, the hallmark of Mtb infection, are complex structures that form in lungs, composed of immune cells surrounding bacteria, infected cells, and a caseous necrotic core. While granulomas serve to physically contain and immunologically restrain bacteria growth, some granulomas are unable to control Mtb growth, leading to bacteria and infected cells leaving the granuloma and disseminating, either resulting in additional granuloma formation (local or non-local) or spread to airways or lymph nodes. Dissemination is associated with development of active TB. It is challenging to experimentally address specific mechanisms driving dissemination from TB lung granulomas. Herein, we develop a novel hybrid multi-scale computational model, MultiGran, that tracks Mtb infection within multiple granulomas in an entire lung. MultiGran follows cells, cytokines, and bacterial populations within each lung granuloma throughout the course of infection and is calibrated to multiple non-human primate (NHP) cellular, granuloma, and whole-lung datasets. We show that MultiGran can recapitulate patterns of in vivo local and non-local dissemination, predict likelihood of dissemination, and predict a crucial role for multifunctional CD8+ T cells and macrophage dynamics for preventing dissemination.

Tuberculosis (TB) is caused by infection with Mycobacterium tuberculosis (Mtb) and kills 3 people per minute worldwide. Granulomas, spherical structures composed of immune cells surrounding bacteria, are the hallmark of Mtb infection and sometimes fail to contain the bacteria and disseminate, leading to further granuloma growth within the lung environment. To date, the mechanisms that determine granuloma dissemination events have not been characterized. We present a computational multi-scale model of granuloma formation and dissemination within primate lungs. Our computational model is calibrated to multiple experimental datasets across the cellular, granuloma, and whole-lung scales of non-human primates. We match to both individual granuloma and granuloma-population datasets, predict likelihood of dissemination events, and predict a critical role for multifunctional CD8+ T cells and macrophage-bacteria interactions to prevent infection dissemination.

Multi-scale models of lung fibrosis

The architectural complexity of the lung is crucial to its ability to function as an organ of gas exchange; the branching tree structure of the airways transforms the tracheal cross-section of only a few square centimeters to a blood-gas barrier with a surface area of tens of square meters and a thickness on the order of a micron or less. Connective tissue comprised largely of collagen and elastic fibers provides structural integrity for this intricate and delicate system. Homeostatic maintenance of this connective tissue, via a balance between catabolic and anabolic enzyme-driven processes, is crucial to life. Accordingly, when homeostasis is disrupted by the excessive production of connective tissue, lung function deteriorates rapidly with grave consequences leading to chronic lung conditions such as pulmonary fibrosis. Understanding how pulmonary fibrosis develops and alters the link between lung structure and function is crucial for diagnosis, prognosis, and therapy. Further information gained could help elaborate how the healing process breaks down leading to chronic disease. Our understanding of fibrotic disease is greatly aided by the intersection of wet lab studies and mathematical and computational modeling. In the present review we will discuss how multi-scale modeling has facilitated our understanding of pulmonary fibrotic disease as well as identified opportunities that remain open and have produced techniques that can be incorporated into this field by borrowing approaches from multi-scale models of fibrosis beyond the lung.

Both Pharmacokinetic Variability and Granuloma Heterogeneity Impact the Ability of the First-Line Antibiotics to Sterilize Tuberculosis Granulomas

Tuberculosis (TB) remains as one of the world's deadliest infectious diseases despite the use of standardized antibiotic therapies. Recommended therapy for drug-susceptible TB is up to 6 months of antibiotics. Factors that contribute to lengthy regimens include antibiotic underexposure in lesions due to poor pharmacokinetics (PK) and complex granuloma compositions, but it is difficult to quantify how individual antibiotics are affected by these factors and to what extent these impact treatments. We use our next-generation multi-scale computational model to simulate granuloma formation and function together with antibiotic pharmacokinetics and pharmacodynamics, allowing us to predict conditions leading to granuloma sterilization. In this work, we focus on how PK variability, determined from human PK data, and granuloma heterogeneity each quantitatively impact granuloma sterilization. We focus on treatment with the standard regimen for TB of four first-line antibiotics: isoniazid, rifampin, ethambutol, and pyrazinamide. We find that low levels of antibiotic concentration due to naturally occurring PK variability and complex granulomas leads to longer granuloma sterilization times. Additionally, the ability of antibiotics to distribute in granulomas and kill different subpopulations of bacteria contributes to their specialization in the more efficacious combination therapy. These results can inform strategies to improve antibiotic therapy for TB.

An Agent-Based Systems Pharmacology Model of the Antibody-Drug Conjugate Kadcyla to Predict Efficacy of Different Dosing Regimens

The pharmaceutical industry has invested significantly in antibody-drug conjugates (ADCs) with five FDA-approved therapies and several more showing promise in late-stage clinical trials. The FDA-approved therapeutic Kadcyla (ado-trastuzumab emtansine or T-DM1) can extend the survival of patients with tumors overexpressing HER2. However, tumor histology shows that most T-DM1 localizes perivascularly, but coadministration with its unconjugated form (trastuzumab) improves penetration of the ADC into the tumor and subsequent treatment efficacy. ADC dosing schedule, e.g., dose fractionation, has also been shown to improve tolerability. However, it is still not clear how coadministration with carrier doses impacts efficacy in terms of receptor expression, dosing regimens, and payload potency. Here, we develop a hybrid agent-based model (ABM) to capture ADC and/or antibody delivery and to predict tumor killing and growth kinetics. The results indicate that a carrier dose improves efficacy when the increased number of cells targeted by the ADC outweighs the reduced fractional killing of the targeted cells. The threshold number of payloads per cell required for killing plays a pivotal role in defining this cutoff. Likewise, fractionated dosing lowers ADC efficacy due to lower tissue penetration from a reduced maximum plasma concentration. It is only beneficial when an increase in tolerability from fractionation allows a higher ADC/payload dose that more than compensates for the loss in efficacy from fractionation. Overall, the multiscale model enables detailed depictions of heterogeneous ADC delivery, cancer cell death, and tumor growth to show how carrier dosing impacts efficacy to design the most efficacious regimen.

Agent-based models of inflammation in translational systems biology: A decade later

Agent-based modeling is a rule-based, discrete-event, and spatially explicit computational modeling method that employs computational objects that instantiate the rules and interactions among the individual components ("agents") of system. Agent-based modeling is well suited to translating into a computational model the knowledge generated from basic science research, particularly with respect to translating across scales the mechanisms of cellular behavior into aggregated cell population dynamics manifesting at the tissue and organ level. This capacity has made agent-based modeling an integral method in translational systems biology (TSB), an approach that uses multiscale dynamic computational modeling to explicitly represent disease processes in a clinically relevant fashion. The initial work in the early 2000s using agent-based models (ABMs) in TSB focused on examining acute inflammation and its intersection with wound healing; the decade since has seen vast growth in both the application of agent-based modeling to a wide array of disease processes as well as methodological advancements in the use and analysis of ABM. This report presents an update on an earlier review of ABMs in TSB and presents examples of exciting progress in the modeling of various organs and diseases that involve inflammation. This review also describes developments that integrate the use of ABMs with cutting-edge technologies such as high-performance computing, machine learning, and artificial intelligence, with a view toward the future integration of these methodologies. This article is categorized under: Translational, Genomic, and Systems Medicine > Translational Medicine Models of Systems Properties and Processes > Mechanistic Models Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models Models of Systems Properties and Processes > Organismal Models.

Credibility of In Silico Trial Technologies-A Theoretical Framing

Different research communities have developed various approaches to assess the credibility of predictive models. Each approach usually works well for a specific type of model, and under some epistemic conditions that are normally satisfied within that specific research domain. Some regulatory agencies recently started to consider evidences of safety and efficacy on new medical products obtained using computer modelling and simulation (which is referred to as In Silico Trials); this has raised the attention in the computational medicine research community on the regulatory science aspects of this emerging discipline. But this poses a foundational problem: in the domain of biomedical research the use of computer modelling is relatively recent, without a widely accepted epistemic framing for model credibility. Also, because of the inherent complexity of living organisms, biomedical modellers tend to use a variety of modelling methods, sometimes mixing them in the solution of a single problem. In such context merely adopting credibility approaches developed within other research communities might not be appropriate. In this paper we propose a theoretical framing for assessing the credibility of a predictive models for In Silico Trials, which accounts for the epistemic specificity of this research field and is general enough to be used for different type of models.

Lattice and continuum modelling of a bioactive porous tissue scaffold

A contemporary procedure to grow artificial tissue is to seed cells onto a porous biomaterial scaffold and culture it within a perfusion bioreactor to facilitate the transport of nutrients to growing cells. Typical models of cell growth for tissue engineering applications make use of spatially homogeneous or spatially continuous equations to model cell growth, flow of culture medium, nutrient transport and their interactions. The network structure of the physical porous scaffold is often incorporated through parameters in these models, either phenomenologically or through techniques like mathematical homogenization. We derive a model on a square grid lattice to demonstrate the importance of explicitly modelling the network structure of the porous scaffold and compare results from this model with those from a modified continuum model from the literature. We capture two-way coupling between cell growth and fluid flow by allowing cells to block pores, and by allowing the shear stress of the fluid to affect cell growth and death. We explore a range of parameters for both models and demonstrate quantitative and qualitative differences between predictions from each of these approaches, including spatial pattern formation and local oscillations in cell density present only in the lattice model. These differences suggest that for some parameter regimes, corresponding to specific cell types and scaffold geometries, the lattice model gives qualitatively different model predictions than typical continuum models. Our results inform model selection for bioactive porous tissue scaffolds, aiding in the development of successful tissue engineering experiments and eventually clinically successful technologies.

Data-Driven Model Validation Across Dimensions

Data-driven model validation across dimensions in mathematical and computational biology assumptions are often made (e.g., symmetry) to reduce the problem from three spatial dimensions (3D) to two (2D). However, some experimental datasets, such as cell counts obtained via flow cytometry, represent the entire 3D biological object. For purpose of model calibration and validation, it is sometimes necessary to compare these biological datasets with model outputs. We propose a methodology for scaling 2D model outputs to compare with 3D experimental datasets, and we discuss the application of this methodology to two examples: agent-based models of granuloma formation and skeletal muscle tissue. The accuracy of the method is evaluated in artificially generated scenarios.

The Role of Dimensionality in Understanding Granuloma Formation

Within the first 2-3 months of a Mycobacterium tuberculosis (Mtb) infection, 2-4 mm spherical structures called granulomas develop in the lungs of the infected hosts. These are the hallmark of tuberculosis (TB) infection in humans and non-human primates. A cascade of immunological events occurs in the first 3 months of granuloma formation that likely shapes the outcome of the infection. Understanding the main mechanisms driving granuloma development and function is key to generating treatments and vaccines. In vitro, in vivo, and in silico studies have been performed in the past decades to address the complexity of granuloma dynamics. This study builds on our previous 2D spatio-temporal hybrid computational model of granuloma formation in TB (GranSim) and presents for the first time a more realistic 3D implementation. We use uncertainty and sensitivity analysis techniques to calibrate the new 3D resolution to non-human primate (NHP) experimental data on bacterial levels per granuloma during the first 100 days post infection. Due to the large computational cost associated with running a 3D agent-based model, our major goal is to assess to what extent 2D and 3D simulations differ in predictions for TB granulomas and what can be learned in the context of 3D that is missed in 2D. Our findings suggest that in terms of major mechanisms driving bacterial burden, 2D and 3D models return very similar results. For example, Mtb growth rates and molecular regulation mechanisms are very important both in 2D and 3D, as are cellular movement and modulation of cell recruitment. The main difference we found was that the 3D model is less affected by crowding when cellular recruitment and movement of cells are increased. Overall, we conclude that the use of a 2D resolution in GranSim is warranted when large scale pilot runs are to be performed and if the goal is to determine major mechanisms driving infection outcome (e.g., bacterial load). To comprehensively compare the roles of model dimensionality, further tests and experimental data will be needed to expand our conclusions to molecular scale dynamics and multi-scale resolutions.

A review of inflammatory mechanism in airway diseases

BACKGROUND

Inflammation in the lung is the body's natural response to injury. It acts to remove harmful stimuli such as pathogens, irritants, and damaged cells and initiate the healing process. Acute and chronic pulmonary inflammation are seen in different respiratory diseases such as; acute respiratory distress syndrome, chronic obstructive pulmonary disease (COPD), asthma, and cystic fibrosis (CF).

FINDINGS

In this review, we found that inflammatory response in COPD is determined by the activation of epithelial cells and macrophages in the respiratory tract. Epithelial cells and macrophages discharge transforming growth factor-β (TGF-β), which trigger fibroblast proliferation and tissue remodeling. Asthma leads to airway hyper-responsiveness, obstruction, mucus hyper-production, and airway-wall remodeling. Cytokines, allergens, chemokines, and infectious agents are the main stimuli that activate signaling pathways in epithelial cells in asthma. Mutation of the CF transmembrane conductance regulator (CFTR) gene results in CF. Mutations in CFTR influence the lung epithelial innate immune function that leads to exaggerated and ineffective airway inflammation that fails to abolish pulmonary pathogens. We present mechanistic computational models (based on ordinary differential equations, partial differential equations and agent-based models) that have been applied in studying the complex physiological and pathological mechanisms of chronic inflammation in different airway diseases.

CONCLUSION

The scope of the present review is to explore the inflammatory mechanism in airway diseases and highlight the influence of aging on airways' inflammation mechanism. The main goal of this review is to encourage research collaborations between experimentalist and modelers to promote our understanding of the physiological and pathological mechanisms that control inflammation in different airway diseases.

Modeling the multi-scale mechanisms of macromolecular resource allocation

As microbes face changing environments, they dynamically allocate macromolecular resources to produce a particular phenotypic state. Broad 'omics' data sets have revealed several interesting phenomena regarding how the proteome is allocated under differing conditions, but the functional consequences of these states and how they are achieved remain open questions. Various types of multi-scale mathematical models have been used to elucidate the genetic basis for systems-level adaptations. In this review, we outline several different strategies by which microbes accomplish resource allocation and detail how mathematical models have aided in our understanding of these processes. Ultimately, such modeling efforts have helped elucidate the principles of proteome allocation and hold promise for further discovery.

High-Performance Agent-Based Modeling Applied to Vocal Fold Inflammation and Repair

Fast and accurate computational biology models offer the prospect of accelerating the development of personalized medicine. A tool capable of estimating treatment success can help prevent unnecessary and costly treatments and potential harmful side effects. A novel high-performance Agent-Based Model (ABM) was adopted to simulate and visualize multi-scale complex biological processes arising in vocal fold inflammation and repair. The computational scheme was designed to organize the 3D ABM sub-tasks to fully utilize the resources available on current heterogeneous platforms consisting of multi-core CPUs and many-core GPUs. Subtasks are further parallelized and convolution-based diffusion is used to enhance the performance of the ABM simulation. The scheme was implemented using a client-server protocol allowing the results of each iteration to be analyzed and visualized on the server (i.e., in-situ) while the simulation is running on the same server. The resulting simulation and visualization software enables users to interact with and steer the course of the simulation in real-time as needed. This high-resolution 3D ABM framework was used for a case study of surgical vocal fold injury and repair. The new framework is capable of completing the simulation, visualization and remote result delivery in under 7 s per iteration, where each iteration of the simulation represents 30 min in the real world. The case study model was simulated at the physiological scale of a human vocal fold. This simulation tracks 17 million biological cells as well as a total of 1.7 billion signaling chemical and structural protein data points. The visualization component processes and renders all simulated biological cells and 154 million signaling chemical data points. The proposed high-performance 3D ABM was verified through comparisons with empirical vocal fold data. Representative trends of biomarker predictions in surgically injured vocal folds were observed.

Deletion of TGF-β1 Increases Bacterial Clearance by Cytotoxic T Cells in a Tuberculosis Granuloma Model

Mycobacterium tuberculosis is the pathogenic bacterium that causes tuberculosis (TB), one of the most lethal infectious diseases in the world. The only vaccine against TB is minimally protective, and multi-drug resistant TB necessitates new therapeutics to treat infection. Developing new therapies requires a better understanding of the complex host immune response to infection, including dissecting the processes leading to formation of granulomas, the dense cellular lesions associated with TB. In this work, we pair experimental and computational modeling studies to explore cytokine regulation in the context of TB. We use our next-generation hybrid multi-scale model of granuloma formation (GranSim) to capture molecular, cellular, and tissue scale dynamics of granuloma formation. We identify TGF-β1 as a major inhibitor of cytotoxic T-cell effector function in granulomas. Deletion of TGF-β1 from the system results in improved bacterial clearance and lesion sterilization. We also identify a novel dichotomous regulation of cytotoxic T cells and macrophages by TGF-β1 and IL-10, respectively. These findings suggest that increasing cytotoxic T-cell effector functions may increase bacterial clearance in granulomas and highlight potential new therapeutic targets for treating TB.

The CXCL12/CXCR7 signaling axis, isoforms, circadian rhythms, and tumor cellular composition dictate gradients in tissue

Chemokine CXCL12 gradients drive chemotaxis in a CXCR4-dependent mechanism and have been implicated in cancer metastasis. While CXCL12 gradients are typically studied in organized, defined environments, the tumor microenvironment is disorganized. In vivo, CXCL12 gradients depend on many factors: the number and arrangement of cells secreting and degrading CXCL12, isoform-dependent binding to the extracellular matrix, diffusion, and circadian fluctuations. We developed a computational model of the tumor microenvironment to simulate CXCL12 gradient dynamics in disorganized tissue. There are four major findings from the model. First, CXCL12-β and -γ form higher magnitude (steeper) gradients compared to CXCL12-α. Second, endothelial CXCR7+ cells regulate CXCL12 gradient direction by controlling concentrations near but not far from the vasculature. Third, the magnitude and direction of CXCL12 gradients are dependent on the local composition of secreting and scavenging cells within the tumor. We theorize that "micro-regions" of cellular heterogeneity within the tumor are responsible for forming strong gradients directed into the blood. Fourth, CXCL12 circadian fluctuations influence gradient magnitude but not direction. Our simulations provide predictions for future experiments in animal models. Understanding the generation of CXCL12 gradients is crucial to inhibiting cancer metastasis.

Applying optimization algorithms to tuberculosis antibiotic treatment regimens

Introduction

Tuberculosis (TB), one of the most common infectious diseases, requires treatment with multiple antibiotics taken over at least 6 months. This long treatment often results in poor patient-adherence, which can lead to the emergence of multi-drug resistant TB. New antibiotic treatment strategies are sorely needed. New antibiotics are being developed or repurposed to treat TB, but as there are numerous potential antibiotics, dosing sizes and potential schedules, the regimen design space for new treatments is too large to search exhaustively. Here we propose a method that combines an agent-based multi-scale model capturing TB granuloma formation with algorithms for mathematical optimization to identify optimal TB treatment regimens.

Methods

We define two different single-antibiotic treatments to compare the efficiency and accuracy in predicting optimal treatment regimens of two optimization algorithms: genetic algorithms (GA) and surrogate-assisted optimization through radial basis function (RBF) networks. We also illustrate the use of RBF networks to optimize double-antibiotic treatments.

Results

We found that while GAs can locate optimal treatment regimens more accurately, RBF networks provide a more practical strategy to TB treatment optimization with fewer simulations, and successfully estimated optimal double-antibiotic treatment regimens.

Conclusions

Our results indicate surrogate-assisted optimization can locate optimal TB treatment regimens from a larger set of antibiotics, doses and schedules, and could be applied to solve optimization problems in other areas of research using systems biology approaches. Our findings have important implications for the treatment of diseases like TB that have lengthy protocols or for any disease that requires multiple drugs.

In Situ Visualization for 3D Agent-Based Vocal Fold Inflammation and Repair Simulation

A fast and insightful visualization is essential in modeling biological system behaviors and understanding underlying inter-cellular mechanisms. High fidelity models produce billions of data points per time step, making in situ visualization techniques extremely desirable as they mitigate I/O bottlenecks and provide computational steering capability. In this work, we present a novel high-performance scheme to couple in situ visualization with the simulation of the vocal fold inflammation and repair using little to no extra cost in execution time or computing resources. The visualization component is first optimized with an adaptive sampling scheme to accelerate the rendering process while maintaining the precision of the displayed visual results. Our software employs VirtualGL to perform visualization in situ. The scheme overlaps visualization and simulation, resulting in the optimal utilization of computing resources. This results in an in situ system biology simulation suite capable of remote simulation of 17 million biological cells and 1.2 billion chemical data points, remote visualization of the results, and delivery of visualized frames with aggregated statistics to remote clients in real-time.

Hybrid approach to model the spatial regulation of T cell responses

BACKGROUND

Moving from the molecular and cellular level to a multi-scale systems understanding of immune responses requires the development of novel approaches to integrate knowledge and data from different biological levels into mechanism-based integrative mathematical models. The aim of our study is to present a methodology for a hybrid modelling of immunological processes in their spatial context.

METHODS

A two-level hybrid mathematical model of immune cell migration and interaction integrating cellular and organ levels of regulation for a 2D spatial consideration of idealized secondary lymphoid organs is developed. It considers the population dynamics of antigen-presenting cells, CD4 + and CD8 + T lymphocytes in naive-, proliferation- and differentiated states. Cell division is assumed to be asymmetric and regulated by the extracellular concentration of interleukin-2 (IL-2) and type I interferon (IFN), together controlling the balance between proliferation and differentiation. The cytokine dynamics is described by reaction-diffusion PDEs whereas the intracellular regulation is modelled with a system of ODEs.

RESULTS

The mathematical model has been developed, calibrated and numerically implemented to study various scenarios in the regulation of T cell immune responses to infection, in particular the change in the diffusion coefficient of type I IFN as compared to IL-2. We have shown that a hybrid modelling approach provides an efficient tool to describe and analyze the interplay between spatio-temporal processes in the emergence of abnormal immune response dynamics.

DISCUSSION

Virus persistence in humans is often associated with an exhaustion of T lymphocytes. Many factors can contribute to the development of exhaustion. One of them is associated with a shift from a normal clonal expansion pathway to an altered one characterized by an early terminal differentiation of T cells. We propose that an altered T cell differentiation and proliferation sequence can naturally result from a spatial separation of the signaling events delivered via TCR, IL-2 and type I IFN receptors. Indeed, the spatial overlap of the concentration fields of extracellular IL-2 and IFN in lymph nodes changes dynamically due to different migration patterns of APCs and CD4 + T cells secreting them.

CONCLUSIONS

The proposed hybrid mathematical model of the immune response represents a novel analytical tool to examine challenging issues in the spatio-temporal regulation of cell growth and differentiation, in particular the effect of timing and location of activation signals.

Identifying mechanisms driving formation of granuloma-associated fibrosis during Mycobacterium tuberculosis infection

Mycobacterium tuberculosis (Mtb), the causative agent of tuberculosis (TB), is a pulmonary pathogen of major global concern. A key feature of Mtb infection in primates is the formation of granulomas, dense cellular structures surrounding infected lung tissue. These structures serve as the main site of host-pathogen interaction in TB, and thus to effectively treat TB we must clarify mechanisms of granuloma formation and their function in disease. Fibrotic granulomas are associated with both good and bad disease outcomes. Fibrosis can serve to isolate infected tissue from healthy tissue, but it can also cause difficulty breathing as it leaves scars. Little is known about fibrosis in TB, and data from non-human primates is just beginning to clarify the picture. This work focuses on constructing a hybrid multi-scale model of fibrotic granuloma formation, in order to identify mechanisms driving development of fibrosis in Mtb infected lungs. We combine dynamics of molecular, cellular, and tissue scale models from previously published studies to characterize the formation of two common sub-types of fibrotic granulomas: peripherally fibrotic, with a cuff of collagen surrounding granulomas, and centrally fibrotic, with collagen throughout granulomas. Uncertainty and sensitivity analysis, along with large simulation sets, enable us to identify mechanisms differentiating centrally versus peripherally fibrotic granulomas. These findings suggest that heterogeneous cytokine environments exist within granulomas and may be responsible for driving tissue scale morphologies. Using this model we are primed to better understand the complex structure of granulomas, a necessity for developing successful treatments for TB.

Agent-based modelling in synthetic biology

Biological systems exhibit complex behaviours that emerge at many different levels of organization. These span the regulation of gene expression within single cells to the use of quorum sensing to co-ordinate the action of entire bacterial colonies. Synthetic biology aims to make the engineering of biology easier, offering an opportunity to control natural systems and develop new synthetic systems with useful prescribed behaviours. However, in many cases, it is not understood how individual cells should be programmed to ensure the emergence of a required collective behaviour. Agent-based modelling aims to tackle this problem, offering a framework in which to simulate such systems and explore cellular design rules. In this article, I review the use of agent-based models in synthetic biology, outline the available computational tools, and provide details on recently engineered biological systems that are amenable to this approach. I further highlight the challenges facing this methodology and some of the potential future directions.

A review of computational and mathematical modeling contributions to our understanding of Mycobacterium tuberculosis within-host infection and treatment

Tuberculosis (TB) is an ancient and deadly disease characterized by complex host-pathogen dynamics playing out over multiple time and length scales and physiological compartments. Computational modeling can be used to integrate various types of experimental data and suggest new hypotheses, mechanisms, and therapeutic approaches to TB. Here, we offer a first-time comprehensive review of work on within-host TB models that describe the immune response of the host to infection, including the formation of lung granulomas. The models include systems of ordinary and partial differential equations and agent-based models as well as hybrid and multi-scale models that are combinations of these. Many aspects of M. tuberculosis infection, including host dynamics in the lung (typical site of infection for TB), granuloma formation, roles of cytokine and chemokine dynamics, and bacterial nutrient availability have been explored. Finally, we survey applications of these within-host models to TB therapy and prevention and suggest future directions to impact this global disease.

Building confidence in quantitative systems pharmacology models: An engineer's guide to exploring the rationale in model design and development

This tutorial promotes good practice for exploring the rationale of systems pharmacology models. A safety systems engineering inspired notation approach provides much needed rigor and transparency in development and application of models for therapeutic discovery and design of intervention strategies. Structured arguments over a model's development, underpinning biological knowledge, and analyses of model behaviors are constructed to determine the confidence that a model is fit for the purpose for which it will be applied.

New insights into mammalian signaling pathways using microfluidic pulsatile inputs and mathematical modeling

Temporally modulated input mimics physiology. This chemical communication strategy filters the biochemical noise through entrainment and phase-locking. Under laboratory conditions, it also expands the observability space for downstream responses. A combined approach involving microfluidic pulsatile stimulation and mathematical modeling has led to deciphering of hidden/unknown temporal motifs in several mammalian signaling pathways and has provided mechanistic insights, including how these motifs combine to form distinct band-pass filters and govern fate regulation under dynamic microenvironment. This approach can be utilized to understand signaling circuit architectures and to gain mechanistic insights for several other signaling systems. Potential applications include synthetic biology and biotechnology, in developing pharmaceutical interventions, and in developing lab-on-chip models.

A Multi-Compartment Hybrid Computational Model Predicts Key Roles for Dendritic Cells in Tuberculosis Infection

Tuberculosis (TB) is a world-wide health problem with approximately 2 billion people infected with Mycobacterium tuberculosis (Mtb, the causative bacterium of TB). The pathologic hallmark of Mtb infection in humans and Non-Human Primates (NHPs) is the formation of spherical structures, primarily in lungs, called granulomas. Infection occurs after inhalation of bacteria into lungs, where resident antigen-presenting cells (APCs), take up bacteria and initiate the immune response to Mtb infection. APCs traffic from the site of infection (lung) to lung-draining lymph nodes (LNs) where they prime T cells to recognize Mtb. These T cells, circulating back through blood, migrate back to lungs to perform their immune effector functions. We have previously developed a hybrid agent-based model (ABM, labeled GranSim) describing in silico immune cell, bacterial (Mtb) and molecular behaviors during tuberculosis infection and recently linked that model to operate across three physiological compartments: lung (infection site where granulomas form), lung draining lymph node (LN, site of generation of adaptive immunity) and blood (a measurable compartment). Granuloma formation and function is captured by a spatio-temporal model (i.e., ABM), while LN and blood compartments represent temporal dynamics of the whole body in response to infection and are captured with ordinary differential equations (ODEs). In order to have a more mechanistic representation of APC trafficking from the lung to the lymph node, and to better capture antigen presentation in a draining LN, this current study incorporates the role of dendritic cells (DCs) in a computational fashion into GranSim.

Computational Modeling of Lipid Metabolism in Yeast

Lipid metabolism is essential for all major cell functions and has recently gained increasing attention in research and health studies. However, mathematical modeling by means of classical approaches such as stoichiometric networks and ordinary differential equation systems has not yet provided satisfactory insights, due to the complexity of lipid metabolism characterized by many different species with only slight differences and by promiscuous multifunctional enzymes. Here, we present an object-oriented stochastic model approach as a way to cope with the complex lipid metabolic network. While all lipid species are treated objects in the model, they can be modified by the respective converting reactions based on reaction rules, a hybrid method that integrates benefits of agent-based and classical stochastic simulation. This approach allows to follow the dynamics of all lipid species with different fatty acids, different degrees of saturation and different headgroups over time and to analyze the effect of parameter changes, potential mutations in the catalyzing enzymes or provision of different precursors. Applied to yeast metabolism during one cell cycle period, we could analyze the distribution of all lipids to the various membranes in time-dependent manner. The presented approach allows to efficiently treat the complexity of cellular lipid metabolism and to derive conclusions on the time- and location-dependent distributions of lipid species and their properties such as saturation. It is widely applicable, easily extendable and will provide further insights in healthy and diseased states of cell metabolism.