Agent-based models in translational systems biology

Agent-based modeling in cancer biomedicine: applications and tools for calibration and validation

Computational models are not just appealing because they can simulate and predict the development of biological phenomena across multiple spatial and temporal scales, but also because they can integrate information from well-established in vitro and in vivo models and test new hypotheses in cancer biomedicine. Agent-based models and simulations are especially interesting candidates among computational modeling procedures in cancer research due to the capability to, for instance, recapitulate the dynamics of neoplasia and tumor - host interactions. Yet, the absence of methods to validate the consistency of the results across scales can hinder adoption by turning fine-tuned models into black boxes. This review compiles relevant literature that explores strategies to leverage high-fidelity simulations of multi-scale, or multi-level, cancer models with a focus on verification approached as simulation calibration. We consolidate our review with an outline of modern approaches for agent-based models' validation and provide an ambitious outlook toward rigorous and reliable calibration.

An agent-based modelling framework to study growth mechanisms in EGFR-L858R mutant cell alveolar type II cells

Mutations in the epidermal growth factor receptor (EGFR) are common in non-small cell lung cancer (NSCLC), particularly in never-smoker patients. However, these mutations are not always carcinogenic, and have recently been reported in histologically normal lung tissue from patients with and without lung cancer. To investigate the outcome of EGFR mutation in healthy lung stem cells, we grow murine alveolar type II organoids monoclonally in a three-dimensional Matrigel. Our experiments show that the EGFR-L858R mutation induces a change in organoid structure: mutated organoids display more 'budding', in comparison with non-mutant controls, which are nearly spherical. We perform on-lattice computational simulations, which suggest that this can be explained by the concentration of division among a small number of cells on the surface of the mutated organoids. We are currently unable to distinguish the cell-based mechanisms that lead to this spatial heterogeneity in growth, but suggest a number of future experiments which could be used to do so. We suggest that the likelihood of L858R-fuelled tumorigenesis is affected by whether the mutation arises in a spatial environment that allows the development of these surface protrusions. These data may have implications for cancer prevention strategies and for understanding NSCLC progression.

Integrating multiplexed imaging and multiscale modeling identifies tumor phenotype conversion as a critical component of therapeutic T cell efficacy

Cancer progression is a complex process involving interactions that unfold across molecular, cellular, and tissue scales. These multiscale interactions have been difficult to measure and to simulate. Here, we integrated CODEX multiplexed tissue imaging with multiscale modeling software to model key action points that influence the outcome of T cell therapies with cancer. The initial phenotype of therapeutic T cells influences the ability of T cells to convert tumor cells to an inflammatory, anti-proliferative phenotype. This T cell phenotype could be preserved by structural reprogramming to facilitate continual tumor phenotype conversion and killing. One takeaway is that controlling the rate of cancer phenotype conversion is critical for control of tumor growth. The results suggest new design criteria and patient selection metrics for T cell therapies, call for a rethinking of T cell therapeutic implementation, and provide a foundation for synergistically integrating multiplexed imaging data with multiscale modeling of the cancer-immune interface. A record of this paper's transparent peer review process is included in the supplemental information.

A simple agent-based hybrid model to simulate the biophysics of glioblastoma multiforme cells and the concomitant evolution of the oxygen field

BACKGROUND AND OBJECTIVES

Glioblastoma multiforme (GBM) is one of the most aggressive cancers of the central nervous system. It is characterized by a high mitotic activity and an infiltrative ability of the glioma cells, neovascularization and necrosis. GBM evolution entails the continuous interplay between heterogeneous cell populations, chemotaxis, and physical cues through different scales. In this work, an agent-based hybrid model is proposed to simulate the coupling of the multiscale biological events involved in the GBM invasion, specifically the individual and collective migration of GBM cells and the concurrent evolution of the oxygen field and phenotypic plasticity. An asset of the formulation is that it is conceptually and computationally simple but allows to reproduce the complexity and the progression of the GBM micro-environment at cell and tissue scales simultaneously.

METHODS

The migration is reproduced as the result of the interaction between every single cell and its micro-environment. The behavior of each individual cell is formulated through genotypic variables whereas the cell micro-environment is modeled in terms of the oxygen concentration and the cell density surrounding each cell. The collective behavior is formulated at a cellular scale through a flocking model. The phenotypic plasticity of the cells is induced by the micro-environment conditions, considering five phenotypes.

RESULTS

The model has been contrasted by benchmark problems and experimental tests showing the ability to reproduce different scenarios of glioma cell migration. In all cases, the individual and collective cell migration and the coupled evolution of both the oxygen field and phenotypic plasticity have been properly simulated. This simple formulation allows to mimic the formation of relevant hallmarks of glioblastoma multiforme, such as the necrotic cores, and to reproduce experimental evidences related to the mitotic activity in pseudopalisades.

CONCLUSIONS

In the collective migration, the survival of the clusters prevails at the expense of cell mitosis, regardless of the size of the groups, which delays the formation of necrotic foci and reduces the rate of oxygen consumption.

Integrating Multiplexed Imaging and Multiscale Modeling Identifies Tumor Phenotype Transformation as a Critical Component of Therapeutic T Cell Efficacy

Cancer progression is a complex process involving interactions that unfold across molecular, cellular, and tissue scales. These multiscale interactions have been difficult to measure and to simulate. Here we integrated CODEX multiplexed tissue imaging with multiscale modeling software, to model key action points that influence the outcome of T cell therapies with cancer. The initial phenotype of therapeutic T cells influences the ability of T cells to convert tumor cells to an inflammatory, anti-proliferative phenotype. This T cell phenotype could be preserved by structural reprogramming to facilitate continual tumor phenotype conversion and killing. One takeaway is that controlling the rate of cancer phenotype conversion is critical for control of tumor growth. The results suggest new design criteria and patient selection metrics for T cell therapies, call for a rethinking of T cell therapeutic implementation, and provide a foundation for synergistically integrating multiplexed imaging data with multiscale modeling of the cancer-immune interface.

Digitize your Biology! Modeling multicellular systems through interpretable cell behavior

Cells are fundamental units of life, constantly interacting and evolving as dynamical systems. While recent spatial multi-omics can quantitate individual cells' characteristics and regulatory programs, forecasting their evolution ultimately requires mathematical modeling. We develop a conceptual framework-a cell behavior hypothesis grammar-that uses natural language statements (cell rules) to create mathematical models. This allows us to systematically integrate biological knowledge and multi-omics data to make them computable. We can then perform virtual "thought experiments" that challenge and extend our understanding of multicellular systems, and ultimately generate new testable hypotheses. In this paper, we motivate and describe the grammar, provide a reference implementation, and demonstrate its potential through a series of examples in tumor biology and immunotherapy. Altogether, this approach provides a bridge between biological, clinical, and systems biology researchers for mathematical modeling of biological systems at scale, allowing the community to extrapolate from single-cell characterization to emergent multicellular behavior.

Soliton approximation in continuum models of leader-follower behavior

Complex biological processes involve collective behavior of entities (bacteria, cells, animals) over many length and time scales and can be described by discrete models that track individuals or by continuum models involving densities and fields. We consider hybrid stochastic agent-based models of branching morphogenesis and angiogenesis (new blood vessel creation from preexisting vasculature), which treat cells as individuals that are guided by underlying continuous chemical and/or mechanical fields. In these descriptions, leader (tip) cells emerge from existing branches and follower (stalk) cells build the new sprout in their wake. Vessel branching and fusion (anastomosis) occur as a result of tip and stalk cell dynamics. Coarse graining these hybrid models in appropriate limits produces continuum partial differential equations (PDEs) for endothelial cell densities that are more analytically tractable. While these models differ in nonlinearity, they produce similar equations at leading order when chemotaxis is dominant. We analyze this leading order system in a simple quasi-one-dimensional geometry and show that the numerical solution of the leading order PDE is well described by a soliton wave that evolves from vessel to source. This wave is an attractor for intermediate times until it arrives at the hypoxic region releasing the growth factor. The mathematical techniques used here thus identify common features of discrete and continuum approaches and provide insight into general biological mechanisms governing their collective dynamics.

Agent-based modeling in medical research, virtual baseline generator and change in patients' profile issue

Simulation studies are promising in medical research in particular to improve drug development. For instance, one can aim to develop In Silico Clinical Trial in order to challenge trial's design parameters in terms of feasibility and probability of success of the trial. Approaches based on agent-based models draw on a particularly useful framework to simulate patients evolution. In this paper, an approach based on agent-based modeling is described and discussed in the context of medical research. An R-vine copula model is used to represent the multivariate distribution of the data. A baseline data cohort can then be simulated and execution models can be developed to simulate the evolution of patients. R-vine copula models are very flexible tools which allow researchers to consider different marginal distributions than the ones observed in the data. It is then possible to perform data augmentation to explore a new population by simulating baseline data which are slightly different than those of the original population. A simulation study illustrates the efficiency of copula modeling to generate data according to specific marginal distributions but also highlights difficulties inherent to data augmentation.

Modeling the roles of cohesotaxis, cell-intercalation, and tissue geometry in collective cell migration of Xenopus mesendoderm

Collectively migrating Xenopus mesendoderm cells are arranged into leader and follower rows with distinct adhesive properties and protrusive behaviors. In vivo, leading row mesendoderm cells extend polarized protrusions and migrate along a fibronectin matrix assembled by blastocoel roof cells. Traction stresses generated at the leading row result in the pulling forward of attached follower row cells. Mesendoderm explants removed from embryos provide an experimentally tractable system for characterizing collective cell movements and behaviors, yet the cellular mechanisms responsible for this mode of migration remain elusive. We introduce an agent-based computational model of migrating mesendoderm in the Cellular-Potts computational framework to investigate the relative contributions of multiple parameters specific to the behaviors of leader and follower row cells. Sensitivity analyses identify cohesotaxis, tissue geometry, and cell intercalation as key parameters affecting the migration velocity of collectively migrating cells. The model predicts that cohesotaxis and tissue geometry in combination promote cooperative migration of leader cells resulting in increased migration velocity of the collective. Radial intercalation of cells towards the substrate is an additional mechanism to increase migratory speed of the tissue.

Summary Statement

We present a novel Cellular-Potts model of collective cell migration to investigate the relative roles of cohesotaxis, tissue geometry, and cell intercalation on migration velocity of Xenopus mesendoderm.

Characterizing the Crosstalk Between Programmed Cell Death Pathways in Cytokine Storm With an Agent-Based Model

Background: There is increasing recognition of extensive crosstalk between programmed cell death pathways (PCDPs), such as apoptosis, pyroptosis, and necroptosis, resulting in a highly redundant system responsive to a breadth of potential pathogens. However, because pyroptosis and necroptosis propagate inflammation, these redundancies also present challenges for therapeutic control of dysregulated hyperinflammation seen in cytokine storm (CS) generated organ dysfunction. Hypothesis: We hypothesize that the conversion of existing knowledge regarding apoptosis, pyroptosis, and necroptosis into a computational model can enhance our understanding of the crosstalk between PCDPs via simulation experiments of microbe interactions and experimental interventions. Materials and Methods: Literature regarding apoptosis, pyroptosis, and necroptosis was reviewed and transposed into an agent-based model, the programmed cell death agent-based model (PCDABM). Computational experiments were performed to simulate the activation of various PCDPs as seen by differing microbes, specifically: influenza A virus (IAV), enteropathic Escherichia coli (EPEC), and Salmonella enterica (SE). The potential protective value of PCDP crosstalk was evaluated by silencing either pyroptosis, necroptosis, or both. Computational experiments were also performed simulating the effect of potential therapies blocking tumor necrosis factor (TNF) and interleukin (IL)-1. Results: The PCDABM was implemented in the agent-based modeling toolkit NetLogo. Computational experiments of infection with IAV, EPEC, and SE reproduced cross-activation of PCDPs with effective microbial clearance. Simulations of anti-TNF and anti-IL-1 did not reduce the aggregated amount of inflammation-generated system damage, the surrogate for CS-generated tissue damage. Conclusions: Redundancies have evolved in host PCDPs to maintain protection against a wide range of pathogens. However, these redundancies also challenge attempts at dampening the pathogenic hyperinflammatory state of CS using therapeutic immunomodulation. Integrative simulation models such as the PCDABM can aid in identifying potentially targetable inflection points to mitigate CS while maintaining effective host defense.

Combined mechanistic modeling and machine-learning approaches in systems biology - A systematic literature review

BACKGROUND AND OBJECTIVE

Mechanistic-based Model simulations (MM) are an effective approach commonly employed, for research and learning purposes, to better investigate and understand the inherent behavior of biological systems. Recent advancements in modern technologies and the large availability of omics data allowed the application of Machine Learning (ML) techniques to different research fields, including systems biology. However, the availability of information regarding the analyzed biological context, sufficient experimental data, as well as the degree of computational complexity, represent some of the issues that both MMs and ML techniques could present individually. For this reason, recently, several studies suggest overcoming or significantly reducing these drawbacks by combining the above-mentioned two methods. In the wake of the growing interest in this hybrid analysis approach, with the present review, we want to systematically investigate the studies available in the scientific literature in which both MMs and ML have been combined to explain biological processes at genomics, proteomics, and metabolomics levels, or the behavior of entire cellular populations.

METHODS

Elsevier Scopus®, Clarivate Web of Science™ and National Library of Medicine PubMed® databases were enquired using the queries reported in Table 1, resulting in 350 scientific articles.

RESULTS

Only 14 of the 350 documents returned by the comprehensive search conducted on the three major online databases met our search criteria, i.e. present a hybrid approach consisting of the synergistic combination of MMs and ML to treat a particular aspect of systems biology.

CONCLUSIONS

Despite the recent interest in this methodology, from a careful analysis of the selected papers, it emerged how examples of integration between MMs and ML are already present in systems biology, highlighting the great potential of this hybrid approach to both at micro and macro biological scales.

Modelling the Effect of Matrix Metalloproteinases in Dermal Wound Healing

With over 2 million people in the UK suffering from chronic wounds, understanding the biochemistry and pharmacology that underpins these wounds and wound healing is of high importance. Chronic wounds are characterised by high levels of matrix metalloproteinases (MMPs), which are necessary for the modification of healthy tissue in the healing process. Overexposure of MMPs, however, adversely affects healing of the wound by causing further destruction of the surrounding extracellular matrix. In this work, we propose a mathematical model that focuses on the interaction of MMPs with dermal cells using a system of partial differential equations. Using biologically realistic parameter values, this model gives rise to travelling waves corresponding to a front of healthy cells invading a wound. From the arising travelling wave analysis, we observe that deregulated apoptosis results in the emergence of chronic wounds, characterised by elevated MMP concentrations. We also observe hysteresis effects when both the apoptotic rate and MMP production rate are varied, providing further insight into the management (and potential reversal) of chronic wounds.

Nanoparticle-mediated cancer cell therapy: basic science to clinical applications

Every sixth person in the world dies due to cancer, making it the second leading severe cause of death after cardiovascular diseases. According to WHO, cancer claimed nearly 10 million deaths in 2020. The most common types of cancers reported have been breast (lung, colon and rectum, prostate cases), skin (non-melanoma) and stomach. In addition to surgery, the most widely used traditional types of anti-cancer treatment are radio- and chemotherapy. However, these do not distinguish between normal and malignant cells. Additional treatment methods have evolved over time for early detection and targeted therapy of cancer. However, each method has its limitations and the associated treatment costs are quite high with adverse effects on the quality of life of patients. Use of individual atoms or a cluster of atoms (nanoparticles) can cause a paradigm shift by virtue of providing point of sight sensing and diagnosis of cancer. Nanoparticles (1-100 nm in size) are 1000 times smaller in size than the human cell and endowed with safer relocation capability to attack mechanically and chemically at a precise location which is one avenue that can be used to destroy cancer cells precisely. This review summarises the extant understanding and the work done in this area to pave the way for physicians to accelerate the use of hybrid mode of treatments by leveraging the use of various nanoparticles.

An agent-based model of monocyte differentiation into tumour-associated macrophages in chronic lymphocytic leukemia

Monocyte-derived macrophages help maintain tissue homeostasis and defend the organism against pathogens. In tumors, recent studies have uncovered complex macrophage populations, including tumor-associated macrophages, which support tumorigenesis through cancer hallmarks such as immunosuppression, angiogenesis, or matrix remodeling. In the case of chronic lymphocytic leukemia, these macrophages are known as nurse-like cells (NLCs) and they protect leukemic cells from spontaneous apoptosis, contributing to their chemoresistance. We propose an agent-based model of monocyte differentiation into NLCs upon contact with leukemic B cells in vitro. We performed patient-specific model optimization using cultures of peripheral blood mononuclear cells from patients. Using our model, we were able to reproduce the temporal survival dynamics of cancer cells in a patient-specific manner and to identify patient groups related to distinct macrophage phenotypes. Our results show a potentially important role of phagocytosis in the polarization process of NLCs and in promoting cancer cells' enhanced survival.

Noncovalent antibody catenation on a target surface greatly increases the antigen-binding avidity

Immunoglobulin G (IgG) antibodies are widely used for diagnosis and therapy. Given the unique dimeric structure of IgG, we hypothesized that, by genetically fusing a homodimeric protein (catenator) to the C-terminus of IgG, reversible catenation of antibody molecules could be induced on a surface where target antigen molecules are abundant, and that it could be an effective way to greatly enhance the antigen-binding avidity. A thermodynamic simulation showed that quite low homodimerization affinity of a catenator, e.g. dissociation constant of 100 μM, can enhance nanomolar antigen-binding avidity to a picomolar level, and that the fold enhancement sharply depends on the density of the antigen. In a proof-of-concept experiment where antigen molecules are immobilized on a biosensor tip, the C-terminal fusion of a pair of weakly homodimerizing proteins to three different antibodies enhanced the antigen-binding avidity by at least 110 or 304 folds from the intrinsic binding avidity. Compared with the mother antibody, Obinutuzumab(Y101L) which targets CD20, the same antibody with fused catenators exhibited significantly enhanced binding to SU-DHL5 cells. Together, the homodimerization-induced antibody catenation would be a new powerful approach to improve antibody applications, including the detection of scarce biomarkers and targeted anticancer therapies.

Synergistic Integration Between Machine Learning and Agent-Based Modeling: A Multidisciplinary Review

Agent-based modeling (ABM) involves developing models in which agents make adaptive decisions in a changing environment. Machine-learning (ML) based inference models can improve sequential decision-making by learning agents' behavioral patterns. With the aid of ML, this emerging area can extend traditional agent-based schemes that hardcode agents' behavioral rules into an adaptive model. Even though there are plenty of studies that apply ML in ABMs, the generalized applicable scenarios, frameworks, and procedures for implementations are not well addressed. In this article, we provide a comprehensive review of applying ML in ABM based on four major scenarios, i.e., microagent-level situational awareness learning, microagent-level behavior intervention, macro-ABM-level emulator, and sequential decision-making. For these four scenarios, the related algorithms, frameworks, procedures of implementations, and multidisciplinary applications are thoroughly investigated. We also discuss how ML can improve prediction in ABMs by trading off the variance and bias and how ML can improve the sequential decision-making of microagent and macrolevel policymakers via a mechanism of reinforced behavioral intervention. At the end of this article, future perspectives of applying ML in ABMs are discussed with respect to data acquisition and quality issues, the possible solution of solving the convergence problem of reinforcement learning, interpretable ML applications, and bounded rationality of ABM.

New perspectives into the vaginal microbiome with systems biology

The vaginal microbiome (VMB) is critical to female reproductive health; however, the mechanisms associated with optimal and non-optimal states remain poorly understood due to the complex community structure and dynamic nature. Quantitative systems biology techniques applied to the VMB have improved understanding of community composition and function using primarily statistical methods. In contrast, fewer mechanistic models that use a priori knowledge of VMB features to develop predictive models have been implemented despite their use for microbiomes at other sites, including the gastrointestinal tract. Here, we explore systems biology approaches that have been applied in the VMB, highlighting successful techniques and discussing new directions that hold promise for improving understanding of health and disease.

Development and application of an agent-based model for the simulation of the extravasation process of circulating tumor cells

The primary cause for cancer-related death is metastasis, and although this phenomenon is the hallmark of cancer, it remains poorly understood. Since studies on the underlying mechanisms are still demanding by experimental means prognostic tools based on computer models can be of great value, not only for elucidating metastasis formation but also for assessing the prospective benefits as well as risks of a therapy for patients with advanced cancer. Here, we present an agent-based model (ABM), describing the complete process of platelet-assisted extravasation of circulating tumor cells (CTCs) from the chemoattraction of blood platelets by the CTCs up to the embedding of the CTCs in the epithelial tissue by computational means. From the simulation results, we conclude that the ABM produces results in consistency with experimental observations, which opens new perspectives for the development of computer models for predicting the efficacity of drug-based tumor therapies and assisting precision medicine approaches.

Mathematical modeling of antihypertensive therapy

Hypertension is a multifactorial disease arising from complex pathophysiological pathways. Individual characteristics of patients result in different responses to various classes of antihypertensive medications. Therefore, evaluating the efficacy of therapy based on in silico predictions is an important task. This study is a continuation of research on the modular agent-based model of the cardiovascular and renal systems (presented in the previously published article). In the current work, we included in the model equations simulating the response to antihypertensive therapies with different mechanisms of action. For this, we used the pharmacodynamic effects of the angiotensin II receptor blocker losartan, the calcium channel blocker amlodipine, the angiotensin-converting enzyme inhibitor enalapril, the direct renin inhibitor aliskiren, the thiazide diuretic hydrochlorothiazide, and the β-blocker bisoprolol. We fitted therapy parameters based on known clinical trials for all considered medications, and then tested the model's ability to show reasonable dynamics (expected by clinical observations) after treatment with individual drugs and their dual combinations in a group of virtual patients with hypertension. The extended model paves the way for the next step in personalized medicine that is adapting the model parameters to a real patient and predicting his response to antihypertensive therapy. The model is implemented in the BioUML software and is available at https://gitlab.sirius-web.org/virtual-patient/antihypertensive-treatment-modeling.

Computational cardiac physiology for new modelers: Origins, foundations, and future

Mathematical models of the cardiovascular system have come a long way since they were first introduced in the early 19th century. Driven by a rapid development of experimental techniques, numerical methods, and computer hardware, detailed models that describe physical scales from the molecular level up to organs and organ systems have been derived and used for physiological research. Mathematical and computational models can be seen as condensed and quantitative formulations of extensive physiological knowledge and are used for formulating and testing hypotheses, interpreting and directing experimental research, and have contributed substantially to our understanding of cardiovascular physiology. However, in spite of the strengths of mathematics to precisely describe complex relationships and the obvious need for the mathematical and computational models to be informed by experimental data, there still exist considerable barriers between experimental and computational physiological research. In this review, we present a historical overview of the development of mathematical and computational models in cardiovascular physiology, including the current state of the art. We further argue why a tighter integration is needed between experimental and computational scientists in physiology, and point out important obstacles and challenges that must be overcome in order to fully realize the synergy of experimental and computational physiological research.

Efficient Bayesian inference for stochastic agent-based models

The modelling of many real-world problems relies on computationally heavy simulations of randomly interacting individuals or agents. However, the values of the parameters that underlie the interactions between agents are typically poorly known, and hence they need to be inferred from macroscopic observations of the system. Since statistical inference rests on repeated simulations to sample the parameter space, the high computational expense of these simulations can become a stumbling block. In this paper, we compare two ways to mitigate this issue in a Bayesian setting through the use of machine learning methods: One approach is to construct lightweight surrogate models to substitute the simulations used in inference. Alternatively, one might altogether circumvent the need for Bayesian sampling schemes and directly estimate the posterior distribution. We focus on stochastic simulations that track autonomous agents and present two case studies: tumour growths and the spread of infectious diseases. We demonstrate that good accuracy in inference can be achieved with a relatively small number of simulations, making our machine learning approaches orders of magnitude faster than classical simulation-based methods that rely on sampling the parameter space. However, we find that while some methods generally produce more robust results than others, no algorithm offers a one-size-fits-all solution when attempting to infer model parameters from observations. Instead, one must choose the inference technique with the specific real-world application in mind. The stochastic nature of the considered real-world phenomena poses an additional challenge that can become insurmountable for some approaches. Overall, we find machine learning approaches that create direct inference machines to be promising for real-world applications. We present our findings as general guidelines for modelling practitioners.

Evaluating COVID-19 Exposure Notification Effectiveness With SimAEN: A Simulation Tool Designed for Public Health Decision Making

OBJECTIVES

Exposure notification (EN) supplements traditional contact tracing by using proximity sensors in smartphones to record close contact between persons. This ledger is used to alert persons of potential SARS-CoV-2 exposure, so they can quarantine until their infection status is determined. We describe a model that estimates the impact of EN implementation on reducing the spread of SARS-CoV-2 and on the workload of public health officials, in combination with other key public health interventions such as traditional contact tracing, face mask wearing, and testing.

METHODS

We created an agent-based model, Simulated Automated Exposure Notification (SimAEN), to explore the effectiveness of EN to slow the spread of SARS-CoV-2. We varied selected simulation variables, such as population adoption of EN and EN detector sensitivity configurations, to illustrate the potential effects of EN. We executed 20 simulations with SimAEN for each scenario and derived results for each simulation.

RESULTS

When more sensitive versus more specific EN configurations were compared, the effective reproductive number, R_E, was minimally affected (a decrease <0.03). For scenarios with increasing levels of EN adoption, an increasing number of additional infected persons were identified through EN, and total infection counts in the simulated population decreased; R_E values for this scenario decreased with increasing EN adoption (a decrease of 0.1 to 0.2 depending on the scenario).

CONCLUSIONS

Estimates from SimAEN can help public health officials determine which levels of EN adoption in combination with other public health interventions can maximize prevention of COVID-19 while minimizing unnecessary quarantine in their jurisdiction.

The role of evolutionary game theory in spatial and non-spatial models of the survival of cooperation in cancer: a review

Evolutionary game theory (EGT) is a branch of mathematics which considers populations of individuals interacting with each other to receive pay-offs. An individual’s pay-off is dependent on the strategy of its opponent(s) as well as on its own, and the higher its pay-off, the higher its reproductive fitness. Its offspring generally inherit its interaction strategy, subject to random mutation. Over time, the composition of the population shifts as different strategies spread or are driven extinct. In the last 25 years there has been a flood of interest in applying EGT to cancer modelling, with the aim of explaining how cancerous mutations spread through healthy tissue and how intercellular cooperation persists in tumour-cell populations. This review traces this body of work from theoretical analyses of well-mixed infinite populations through to more realistic spatial models of the development of cooperation between epithelial cells. We also consider work in which EGT has been used to make experimental predictions about the evolution of cancer, and discuss work that remains to be done before EGT can make large-scale contributions to clinical treatment and patient outcomes.

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.

The future of burn care from a complexity science perspective

Healthcare is undergoing a profound technological and digital transformation and has become increasingly complex. It is important for burns professionals and researchers to adapt to these developments which may require new ways of thinking and subsequent new strategies. As Einstein has put it: 'We must learn to see the world anew'. The relatively new scientific discipline "Complexity science" can give more direction to this and is the metaphorical open door that should not go unnoticed in view of the burn care of the future. Complexity sciences studies 'why the whole is more than the sum of the parts'. It studies how multiple separate components interact with each other and their environment and how these interactions lead to 'behavior of the system'. Biological systems are always part of smaller and larger systems and exhibit the behavior of adaptivity, hence the name complex adaptive systems. From the perspective of complexity science, a severe burn injury is an extreme disruption of the 'human body system'. But this disruption also applies to the systems at the organ and cellular level. All these systems follow principles of complex systems. Awareness of the scaling process at multilevel helps to understand and manage the complex situation when dealing with severe burn cases. The aim of this paper is to create awareness of the concept of complexity and to demonstrate the value and possibilities of complexity science methods and tools for the future of burn care through examples from preclinical, clinical, and organizational perspective in burn care.

Translatability and transferability of in silico models: context of use switching to predict the effects of environmental chemicals on the immune system

Immunotoxicity hazard identification of chemicals aims to evaluate the potential for unintended effects of chemical exposure on the immune system. Perfluorinated alkylate substances (PFAS), such as perfluorooctane sulfonate (PFOS) and perfluorooctanoic acid (PFOA), are persistent, globally disseminated environmental contaminants known to be immunotoxic. Elevated PFAS exposure is associated with lower antibody responses to vaccinations in children and in adults. In addition, some studies have reported a correlation between PFAS levels in the body and lower resistance to disease, in other words an increased risk of infections or cancers.

In this context, modelling and simulation platforms could be used to simulate the human immune system with the aim to evaluate the adverse effects that immunotoxicants may have.

Here, we show the conditions under which a mathematical model developed for one purpose and application (e.g., in the pharmaceutical domain) can be successfully translated and transferred to another (e.g., in the chemicals domain) without undergoing significant adaptation. In particular, we demonstrate that the Universal Immune System Simulator was able to simulate the effects of PFAS on the immune system, introducing entities and new interactions that are biologically involved in the phenomenon. This also revealed a potentially exploitable pathway for assessing immunotoxicity through a computational model.

Scar formation from the perspective of complexity science: a new look at the biological system as a whole

A burn wound is a complex systemic disease at multiple levels. Current knowledge of scar formation after burn injury has come from traditional biological and clinical studies. These are normally focused on just a small part of the entire process, which has limited our ability to sufficiently understand the underlying mechanisms and to predict systems behaviour. Scar formation after burn injury is a result of a complex biological system-wound healing. It is a part of a larger whole. In this self-organising system, many components form networks of interactions with each other. These networks of interactions are typically non-linear and change their states dynamically, responding to the environment and showing emergent long-term behaviour. How molecular and cellular data relate to clinical phenomena, especially regarding effective therapies of burn wounds to achieve minimal scarring, is difficult to unravel and comprehend. Complexity science can help bridge this gap by integrating small parts into a larger whole, such that relevant biological mechanisms and data are combined in a computational model to better understand the complexity of the entire biological system. A better understanding of the complex biological system of post-burn scar formation could bring research and treatment regimens to the next level. The aim of this review/position paper is to create more awareness of complexity in scar formation after burn injury by describing the basic principles of complexity science and its potential for burn care professionals.

Multiscale Computational Modeling of Vascular Adaptation: A Systems Biology Approach Using Agent-Based Models

The widespread incidence of cardiovascular diseases and associated mortality and morbidity, along with the advent of powerful computational resources, have fostered an extensive research in computational modeling of vascular pathophysiology field and promoted in-silico models as a support for biomedical research. Given the multiscale nature of biological systems, the integration of phenomena at different spatial and temporal scales has emerged to be essential in capturing mechanobiological mechanisms underlying vascular adaptation processes. In this regard, agent-based models have demonstrated to successfully embed the systems biology principles and capture the emergent behavior of cellular systems under different pathophysiological conditions. Furthermore, through their modular structure, agent-based models are suitable to be integrated with continuum-based models within a multiscale framework that can link the molecular pathways to the cell and tissue levels. This can allow improving existing therapies and/or developing new therapeutic strategies. The present review examines the multiscale computational frameworks of vascular adaptation with an emphasis on the integration of agent-based approaches with continuum models to describe vascular pathophysiology in a systems biology perspective. The state-of-the-art highlights the current gaps and limitations in the field, thus shedding light on new areas to be explored that may become the future research focus. The inclusion of molecular intracellular pathways (e.g., genomics or proteomics) within the multiscale agent-based modeling frameworks will certainly provide a great contribution to the promising personalized medicine. Efforts will be also needed to address the challenges encountered for the verification, uncertainty quantification, calibration and validation of these multiscale frameworks.

Thymic B Cells as a New Player in the Type 1 Diabetes Response

Type 1 diabetes (T1d) results from a sustained autoreactive T and B cell response towards insulin-producing β cells in the islets of Langerhans. The autoreactive nature of the condition has led to many investigations addressing the genetic or cellular changes in primary lymphoid tissues that impairs central tolerance- a key process in the deletion of autoreactive T and B cells during their development. For T cells, these studies have largely focused on medullary thymic epithelial cells (mTECs) critical for the effective negative selection of autoreactive T cells in the thymus. Recently, a new cellular player that impacts positively or negatively on the deletion of autoreactive T cells during their development has come to light, thymic B cells. Normally a small population within the thymus of mouse and man, thymic B cells expand in T1d as well as other autoimmune conditions, reside in thymic ectopic germinal centres and secrete autoantibodies that bind selective mTECs precipitating mTEC death. In this review we will discuss the ontogeny, characteristics and functionality of thymic B cells in healthy and autoimmune settings. Furthermore, we explore how in silico approaches may help decipher the complex cellular interplay of thymic B cells with other cells within the thymic microenvironment leading to new avenues for therapeutic intervention.

An Agent-Based Model of Combination Oncolytic Viral Therapy and Anti-PD-1 Immunotherapy Reveals the Importance of Spatial Location When Treating Glioblastoma

Simple Summary

A combination of oncolytic viral therapy and immunotherapy provides an alternative option to the standard of care for treating the lethal brain tumor glioblastoma (GBM). Although this combination therapy shows promise, there are many unknown questions regarding how the tumor landscape and spatial dosing strategies impact the effectiveness of the treatment. Our study aims to shed light on these questions using a novel spatially explicit computational model of GBM response to treatment. Our results suggest that oncolytic viral dosing in the location of highest tumor cell density leads to substantial tumor size reduction over viral dosing in the center of the tumor. These results can help to inform future clinical trials and more effective treatment strategies for oncolytic viral therapy in GBM patients.

Abstract

Oncolytic viral therapies and immunotherapies are of growing clinical interest due to their selectivity for tumor cells over healthy cells and their immunostimulatory properties. These treatment modalities provide promising alternatives to the standard of care, particularly for cancers with poor prognoses, such as the lethal brain tumor glioblastoma (GBM). However, uncertainty remains regarding optimal dosing strategies, including how the spatial location of viral doses impacts therapeutic efficacy and tumor landscape characteristics that are most conducive to producing an effective immune response. We develop a three-dimensional agent-based model (ABM) of GBM undergoing treatment with a combination of an oncolytic Herpes Simplex Virus and an anti-PD-1 immunotherapy. We use a mechanistic approach to model the interactions between distinct populations of immune cells, incorporating both innate and adaptive immune responses to oncolytic viral therapy and including a mechanism of adaptive immune suppression via the PD-1/PD-L1 checkpoint pathway. We utilize the spatially explicit nature of the ABM to determine optimal viral dosing in both the temporal and spatial contexts. After proposing an adaptive viral dosing strategy that chooses to dose sites at the location of highest tumor cell density, we find that, in most cases, this adaptive strategy produces a more effective treatment outcome than repeatedly dosing in the center of the tumor.

The Use of Artificial Neural Networks to Forecast the Behavior of Agent-Based Models of Pathophysiology: An Example Utilizing an Agent-Based Model of Sepsis

Introduction: Disease states are being characterized at finer and finer levels of resolution via biomarker or gene expression profiles, while at the same time. Machine learning (ML) is increasingly used to analyze and potentially classify or predict the behavior of biological systems based on such characterization. As ML applications are extremely data-intensive, given the relative sparsity of biomedical data sets ML training of artificial neural networks (ANNs) often require the use of synthetic training data. Agent-based models (ABMs) that incorporate known biological mechanisms and their associated stochastic properties are a potential means of generating synthetic data. Herein we present an example of ML used to train an artificial neural network (ANN) as a surrogate system used to predict the time evolution of an ABM focusing on the clinical condition of sepsis. Methods: The disease trajectories for clinical sepsis, in terms of temporal cytokine and phenotypic dynamics, can be interpreted as a random dynamical system. The Innate Immune Response Agent-based Model (IIRABM) is a well-established model that utilizes known cellular and molecular rules to simulate disease trajectories corresponding to clinical sepsis. We have utilized two distinct neural network architectures, Long Short-Term Memory and Multi-Layer Perceptron, to take a time sequence of five measurements of eleven IIRABM simulated serum cytokine concentrations as input and to return both the future cytokine trajectories as well as an aggregate metric representing the patient's state of health. Results: The ANNs predicted model trajectories with the expected amount of error, due to stochasticity in the simulation, and recognizing that the mapping from a specific cytokine profile to a state-of-health is not unique. The Multi-Layer Perceptron neural network, generated predictions with a more accurate forecasted trajectory cone. Discussion: This work serves as a proof-of-concept for the use of ANNs to predict disease progression in sepsis as represented by an ABM. The findings demonstrate that multicellular systems with intrinsic stochasticity can be approximated with an ANN, but that forecasting a specific trajectory of the system requires sequential updating of the system state to provide a rolling forecast horizon.

A Coupled Mechanobiological Model of Muscle Regeneration In Cerebral Palsy

Cerebral palsy is a neuromusculoskeletal disorder associated with muscle weakness, altered muscle architecture, and progressive musculoskeletal symptoms that worsen with age. Pathological changes at the level of the whole muscle have been shown; however, it is unclear why this progression of muscle impairment occurs at the cellular level. The process of muscle regeneration is complex, and the interactions between cells in the muscle milieu should be considered in the context of cerebral palsy. In this work, we built a coupled mechanobiological model of muscle damage and regeneration to explore the process of muscle regeneration in typical and cerebral palsy conditions, and whether a reduced number of satellite cells in the cerebral palsy muscle environment could cause the muscle regeneration cycle to lead to progressive degeneration of muscle. The coupled model consisted of a finite element model of a muscle fiber bundle undergoing eccentric contraction, and an agent-based model of muscle regeneration incorporating satellite cells, inflammatory cells, muscle fibers, extracellular matrix, fibroblasts, and secreted cytokines. Our coupled model simulated damage from eccentric contraction followed by 28 days of regeneration within the muscle. We simulated cyclic damage and regeneration for both cerebral palsy and typically developing muscle milieus. Here we show the nonlinear effects of altered satellite cell numbers on muscle regeneration, where muscle repair is relatively insensitive to satellite cell concentration above a threshold, but relatively sensitive below that threshold. With the coupled model, we show that the fiber bundle geometry undergoes atrophy and fibrosis with too few satellite cells and excess extracellular matrix, representative of the progression of cerebral palsy in muscle. This work uses in silico modeling to demonstrate how muscle degeneration in cerebral palsy may arise from the process of cellular regeneration and a reduced number of satellite cells.

Step-by-step comparison of ordinary differential equation and agent-based approaches to pharmacokinetic-pharmacodynamic models

Mathematical models in oncology aid in the design of drugs and understanding of their mechanisms of action by simulation of drug biodistribution, drug effects, and interaction between tumor and healthy cells. The traditional approach in pharmacometrics is to develop and validate ordinary differential equation models to quantify trends at the population level. In this approach, time‐course of biological measurements is modeled continuously, assuming a homogenous population. Another approach, agent‐based models, focuses on the behavior and fate of biological entities at the individual level, which subsequently could be summarized to reflect the population level. Heterogeneous cell populations and discrete events are simulated, and spatial distribution can be incorporated. In this tutorial, an agent‐based model is presented and compared to an ordinary differential equation model for a tumor efficacy model inhibiting the pERK pathway. We highlight strengths, weaknesses, and opportunities of each approach.

Modelling-informed cell-seeded nerve repair construct designs for treating peripheral nerve injuries

Millions of people worldwide are affected by peripheral nerve injuries (PNI), involving billions of dollars in healthcare costs. Common outcomes for patients include paralysis and loss of sensation, often leading to lifelong pain and disability. Engineered Neural Tissue (EngNT) is being developed as an alternative to the current treatments for large-gap PNIs that show underwhelming functional recovery in many cases. EngNT repair constructs are composed of a stabilised hydrogel cylinder, surrounded by a sheath of material, to mimic the properties of nerve tissue. The technology also enables the spatial seeding of therapeutic cells in the hydrogel to promote nerve regeneration. The identification of mechanisms leading to maximal nerve regeneration and to functional recovery is a central challenge in the design of EngNT repair constructs. Using in vivo experiments in isolation is costly and time-consuming, offering a limited insight on the mechanisms underlying the performance of a given repair construct. To bridge this gap, we derive a cell-solute model and apply it to the case of EngNT repair constructs seeded with therapeutic cells which produce vascular endothelial growth factor (VEGF) under low oxygen conditions to promote vascularisation in the construct. The model comprises a set of coupled non-linear diffusion-reaction equations describing the evolving cell population along with its interactions with oxygen and VEGF fields during the first 24h after transplant into the nerve injury site. This model allows us to evaluate a wide range of repair construct designs (e.g. cell-seeding strategy, sheath material, culture conditions), the idea being that designs performing well over a short timescale could be shortlisted for in vivo trials. In particular, our results suggest that seeding cells beyond a certain density threshold is detrimental regardless of the situation considered, opening new avenues for future nerve tissue engineering.

Verification of an agent-based disease model of human Mycobacterium tuberculosis infection

Agent-based models (ABMs) are a powerful class of computational models widely used to simulate complex phenomena in many different application areas. However, one of the most critical aspects, poorly investigated in the literature, regards an important step of the model credibility assessment: solution verification. This study overcomes this limitation by proposing a general verification framework for ABMs that aims at evaluating the numerical errors associated with the model. A step-by-step procedure, which consists of two main verification studies (deterministic and stochastic model verification), is described in detail and applied to a specific mission critical scenario: the quantification of the numerical approximation error for UISS-TB, an ABM of the human immune system developed to predict the progression of pulmonary tuberculosis. Results provide indications on the possibility to use the proposed model verification workflow to systematically identify and quantify numerical approximation errors associated with UISS-TB and, in general, with any other ABMs.

DAPT: A package enabling distributed automated parameter testing

Modern agent-based models (ABM) and other simulation models require evaluation and testing of many different parameters. Managing that testing for large scale parameter sweeps (grid searches), as well as storing simulation data, requires multiple, potentially customizable steps that may vary across simulations. Furthermore, parameter testing, processing, and analysis are slowed if simulation and processing jobs cannot be shared across teammates or computational resources. While high-performance computing (HPC) has become increasingly available, models can often be tested faster with the use of multiple computers and HPC resources. To address these issues, we created the Distributed Automated Parameter Testing (DAPT) Python package. By hosting parameters in an online (and often free) "database", multiple individuals can run parameter sets simultaneously in a distributed fashion, enabling ad hoc crowdsourcing of computational power. Combining this with a flexible, scriptable tool set, teams can evaluate models and assess their underlying hypotheses quickly. Here, we describe DAPT and provide an example demonstrating its use.

Simulating ATO Mechanism and EGFR Signaling with Fuzzy Logic and Petri Net

Background:

Interactions of many key proteins or genes in signalling pathway have been studied qualitatively in the literature, but only little quantitative information is available.

Objective:

Although much has been done to clarify the biochemistry of transcriptional dynamics in signalling pathway, it remains difficult to find out and predict quantitative responses. The aim of this study is to construct a computational model of epidermal growth factor receptor (EGFR) signalling pathway as one of hallmarks of cancer so as to predict quantitative responses.

Material and Methods:

In this analytical study, we presented a computational model to investigate EGFR signalling pathway. Interaction of Arsenic trioxide (ATO) with EGFR signalling pathway factors has been elicited by systematic search in data bases, as ATO is one of the mysterious chemotherapy agents that control EGFR expression in cancer. ATO has dichotomous manner in vivo, dependent on its concentration. According to fuzzy rules based upon qualitative knowledge and Petri Net, we can construct a quantitative model to describe ATO mechanism in EGFR signalling pathway.

Results:

By Fuzzy Logic models that have the potential to trade with the loss of quantitative information on how different species interact, along with Petri net quantitatively describe the dynamics of EGFR signalling pathway. By this model the dynamic of different factors in EGFR signalling pathway is achieved.

Conclusion:

The use of Fuzzy Logic and PNs in biological network modelling causes a deeper understanding and comprehensive analysis of the biological networks.

Utilizing the Heterogeneity of Clinical Data for Model Refinement and Rule Discovery Through the Application of Genetic Algorithms to Calibrate a High-Dimensional Agent-Based Model of Systemic Inflammation

Introduction: Accounting for biological heterogeneity represents one of the greatest challenges in biomedical research. Dynamic computational and mathematical models can be used to enhance the study and understanding of biological systems, but traditional methods for calibration and validation commonly do not account for the heterogeneity of biological data, which may result in overfitting and brittleness of these models. Herein we propose a machine learning approach that utilizes genetic algorithms (GAs) to calibrate and refine an agent-based model (ABM) of acute systemic inflammation, with a focus on accounting for the heterogeneity seen in a clinical data set, thereby avoiding overfitting and increasing the robustness and potential generalizability of the underlying simulation model. Methods: Agent-based modeling is a frequently used modeling method for multi-scale mechanistic modeling. However, the same properties that make ABMs well suited to representing biological systems also present significant challenges with respect to their construction and calibration, particularly with respect to the selection of potential mechanistic rules and the large number of associated free parameters. We have proposed that machine learning approaches (such as GAs) can be used to more effectively and efficiently deal with rule selection and parameter space characterization; the current work applies GAs to the challenge of calibrating a complex ABM to a specific data set, while preserving biological heterogeneity reflected in the range and variance of the data. This project uses a GA to augment the rule-set for a previously validated ABM of acute systemic inflammation, the Innate Immune Response ABM (IIRABM) to clinical time series data of systemic cytokine levels from a population of burn patients. The genome for the GA is a vector generated from the IIRABM's Model Rule Matrix (MRM), which is a matrix representation of not only the constants/parameters associated with the IIRABM's cytokine interaction rules, but also the existence of rules themselves. Capturing heterogeneity is accomplished by a fitness function that incorporates the sample value range ("error bars") of the clinical data. Results: The GA-enabled parameter space exploration resulted in a set of putative MRM rules and associated parameterizations which closely match the cytokine time course data used to design the fitness function. The number of non-zero elements in the MRM increases significantly as the model parameterizations evolve toward a fitness function minimum, transitioning from a sparse to a dense matrix. This results in a model structure that more closely resembles (at a superficial level) the structure of data generated by a standard differential gene expression experimental study. Conclusion: We present an HPC-enabled machine learning/evolutionary computing approach to calibrate a complex ABM to complex clinical data while preserving biological heterogeneity. The integration of machine learning, HPC, and multi-scale mechanistic modeling provides a pathway forward to more effectively representing the heterogeneity of clinical populations and their data.

Computational Resources and Strategies to Construct Single-Molecule Models of FISH

Currently, the interactions occurring between oligonucleotides and the cellular envelope of bacteria are not fully resolved at the molecular level. Understanding these interactions is essential to gain insights on how to improve the internalization of the tagged oligonucleotides during fluorescence in situ hybridization (FISH). Agent-based modeling (ABM) is a promising in silico tool to dynamically simulate FISH and bring forward new knowledge on this process. Notably, it is important to simulate the whole bacterial cell, including the different layers of the cell envelope, given that the oligonucleotide must cross the envelope to reach its target in the cytosol. In addition, it is also important to characterize other molecules in the cell to best emulate the cell and represent molecular crowding. Here, we review the main information that should be compiled to construct an ABM on FISH and provide a practical example of an oligonucleotide targeting the 23S rRNA of Escherichia coli .

Comparative analysis of continuum angiogenesis models

Although discrete approaches are increasingly employed to model biological phenomena, it remains unclear how complex, population-level behaviours in such frameworks arise from the rules used to represent interactions between individuals. Discrete-to-continuum approaches, which are used to derive systems of coarse-grained equations describing the mean-field dynamics of a microscopic model, can provide insight into such emergent behaviour. Coarse-grained models often contain nonlinear terms that depend on the microscopic rules of the discrete framework, however, and such nonlinearities can make a model difficult to mathematically analyse. By contrast, models developed using phenomenological approaches are typically easier to investigate but have a more obscure connection to the underlying microscopic system. To our knowledge, there has been little work done to compare solutions of phenomenological and coarse-grained models. Here we address this problem in the context of angiogenesis (the creation of new blood vessels from existing vasculature). We compare asymptotic solutions of a classical, phenomenological “snail-trail” model for angiogenesis to solutions of a nonlinear system of partial differential equations (PDEs) derived via a systematic coarse-graining procedure (Pillay et al. in Phys Rev E 95(1):012410, 2017. https://doi.org/10.1103/PhysRevE.95.012410). For distinguished parameter regimes corresponding to chemotaxis-dominated cell movement and low branching rates, both continuum models reduce at leading order to identical PDEs within the domain interior. Numerical and analytical results confirm that pointwise differences between solutions to the two continuum models are small if these conditions hold, and demonstrate how perturbation methods can be used to determine when a phenomenological model provides a good approximation to a more detailed coarse-grained system for the same biological process.

INFEKTA-An agent-based model for transmission of infectious diseases: The COVID-19 case in Bogotá, Colombia

The transmission dynamics of the coronavirus—COVID-19—have challenged humankind at almost every level. Currently, research groups around the globe are trying to figure out such transmission dynamics under special conditions such as separation policies enforced by governments. Mathematical and computational models, like the compartmental model or the agent-based model, are being used for this purpose. This paper proposes an agent-based model, called INFEKTA, for simulating the transmission of infectious diseases, not only the COVID-19, under social distancing policies. INFEKTA combines the transmission dynamic of a specific disease, (according to parameters found in the literature) with demographic information (population density, age, and genre of individuals) of geopolitical regions of the real town or city under study. Agents (virtual persons) can move, according to its mobility routines and the enforced social distancing policy, on a complex network of accessible places defined over an Euclidean space representing the town or city. The transmission dynamics of the COVID-19 under different social distancing policies in Bogotá city, the capital of Colombia, is simulated using INFEKTA with one million virtual persons. A sensitivity analysis of the impact of social distancing policies indicates that it is possible to establish a ‘medium’ (i.e., close 40% of the places) social distancing policy to achieve a significant reduction in the disease transmission.

Optimization of Agent-Based Models Through Coarse-Graining: A Case Study in Microbial Ecology

Optimization and control are important objectives across biology and biomedicine, and mathematical models are a key enabling technology. This paper reports a computational study of model-based multi-objective optimization in the setting of microbial ecology, using agent-based models. This modeling framework is well-suited to the field, but is not amenable to standard control-theoretic approaches. Furthermore, due to computational complexity, simulation-based optimization approaches are often challenging to implement. This paper presents the results of an approach that combines control-dependent coarse-graining with Pareto optimization, applied to two models of multi-species bacterial biofilms. It shows that this approach can be successful for models whose computational complexity prevents effective simulation-based optimization.

An Early Stage Researcher's Primer on Systems Medicine Terminology

Background: Systems Medicine is a novel approach to medicine, that is, an interdisciplinary field that considers the human body as a system, composed of multiple parts and of complex relationships at multiple levels, and further integrated into an environment. Exploring Systems Medicine implies understanding and combining concepts coming from diametral different fields, including medicine, biology, statistics, modeling and simulation, and data science. Such heterogeneity leads to semantic issues, which may slow down implementation and fruitful interaction between these highly diverse fields. Methods: In this review, we collect and explain more than100 terms related to Systems Medicine. These include both modeling and data science terms and basic systems medicine terms, along with some synthetic definitions, examples of applications, and lists of relevant references. Results: This glossary aims at being a first aid kit for the Systems Medicine researcher facing an unfamiliar term, where he/she can get a first understanding of them, and, more importantly, examples and references for digging into the topic.

Beyond the pair approximation: Modeling colonization population dynamics

The process of range expansion (colonization) is one of the basic types of biological dynamics, whereby a species grows and spreads outwards, occupying new territories. Spatial modeling of this process is naturally implemented as a stochastic cellular automaton, with individuals occupying nodes on a rectangular grid, births and deaths occurring probabilistically, and individuals only reproducing onto unoccupied neighboring spots. In this paper we derive several approximations that allow prediction of the expected range expansion dynamics, based on the reproduction and death rates. We derive several approximations, where the cellular automaton is described by a system of ordinary differential equations that preserves correlations among neighboring spots (up to a distance). This methodology allows us to develop accurate approximations of the population size and the expected spatial shape, at a fraction of the computational time required to simulate the original stochastic system. In addition, we provide simple formulas for the steady-state population densities for von Neumann and Moore neighborhoods. Finally, we derive concise approximations for the speed of range expansion in terms of the reproduction and death rates, for both types of neighborhoods. The methodology is generalizable to more complex scenarios, such as different interaction ranges and multiple-species systems.

Spatial considerations in the resolution of inflammation: Elucidating leukocyte interactions via an experimentally-calibrated agent-based model

Many common medical conditions (such as cancer, arthritis, chronic obstructive pulmonary disease (COPD), and others) are associated with inflammation, and even more so when combined with the effects of ageing and multimorbidity. While the inflammatory response varies in different tissue types, under disease and in response to therapeutic interventions, it has common interactions that occur between immune cells and inflammatory mediators. Understanding these underlying inflammatory mechanisms is key in progressing treatments and therapies for numerous inflammatory conditions. It is now considered that constituent mechanisms of the inflammatory response can be actively manipulated in order to drive resolution of inflammatory damage; particularly, those mechanisms related to the pro-inflammatory role of neutrophils and the anti-inflammatory role of macrophages. In this article, we describe the assembly of a hybrid mathematical model in which the spatial spread of inflammatory mediators is described through partial differential equations, and immune cells (neutrophils and macrophages) are described individually via an agent-based modelling approach. We pay close attention to how immune cells chemotax toward pro-inflammatory mediators, presenting a model for cell chemotaxis that is calibrated against experimentally observed cell trajectories in healthy and COPD-affected scenarios. We illustrate how variations in key model parameters can drive the switch from resolution of inflammation to chronic outcomes, and show that aberrant neutrophil chemotaxis can move an otherwise healthy outcome to one of chronicity. Finally, we reflect on our results in the context of the on-going hunt for new therapeutic interventions.

Inflammation is the body’s primary defence to harmful stimuli such as infections, toxins and tissue strain but also underlies a much broader range of conditions, including asthma, arthritis and cancer. The inflammatory response is key in resolving injury to facilitate recovery, and involves a range of interactions between immune cells (leukocytes, neutrophils and macrophages in particular) and inflammatory mediators. Immune cells are recruited from the blood stream in response to injury. Once in tissue, neutrophils release toxins to kill invading agents and resolve damage; however, if not carefully managed by other immune cells (mainly macrophages), their responses can increase inflammation instead of helping to resolve it. We model these interactions in response to damage using a spatial model, examining how a healthy response can prevent localised inflammation from spreading. We pay close attention to how cells migrate toward the damaged area, as many inflammatory conditions are associated with impairment of this process. We calibrate our model against experimentally-observed cell trajectories from healthy patients and patients with chronic obstructive pulmonary disease. We illustrate that a healthy outcome depends strongly upon efficient cell migration and a delicate balance between the pro- and anti-inflammatory effects of neutrophils and macrophages.

Agent-Based Modeling and Simulation in Mathematics and Biology Education

With advances in computing, agent-based models (ABMs) have become a feasible and appealing tool to study biological systems. ABMs are seeing increased incorporation into both the biology and mathematics classrooms as powerful modeling tools to study processes involving substantial amounts of stochasticity, nonlinear interactions, and/or heterogeneous spatial structures. Here we present a brief synopsis of the agent-based modeling approach with an emphasis on its use to simulate biological systems, and provide a discussion of its role and limitations in both the biology and mathematics classrooms.

Integrative Approaches to Cancer Immunotherapy

Cancer immunotherapy aims to arm patients with cancer-fighting immunity. Many new cancer-specific immunotherapeutic drugs have gained approval in the past several years, demonstrating immunotherapy's efficacy and promise as an anticancer modality. Despite these successes, several outstanding questions remain for cancer immunotherapy, including how to make immunotherapy more efficacious in a broader range of cancer types and patients, and how to predict which patients will respond or not respond to therapy. We present a case for integrative systems approaches that will answer these questions. This involves applying mechanistic and statistical modeling, establishing consistent and widely adopted experimental tools to generate systems-level data, and creating sustained mechanisms of support. If implemented, these approaches will lead to major advances in cancer treatment.

Agent-Based Models Predict Emergent Behavior of Heterogeneous Cell Populations in Dynamic Microenvironments

Computational models are most impactful when they explain and characterize biological phenomena that are non-intuitive, unexpected, or difficult to study experimentally. Countless equation-based models have been built for these purposes, but we have yet to realize the extent to which rules-based models offer an intuitive framework that encourages computational and experimental collaboration. We develop ARCADE, a multi-scale agent-based model to interrogate emergent behavior of heterogeneous cell agents within dynamic microenvironments and demonstrate how complexity of intracellular metabolism and signaling modules impacts emergent dynamics. We perform in silico case studies on context, competition, and heterogeneity to demonstrate the utility of our model for gaining computational and experimental insight. Notably, there exist (i) differences in emergent behavior between colony and tissue contexts, (ii) linear, non-linear, and multimodal consequences of parameter variation on competition in simulated co-cultures, and (iii) variable impact of cell and population heterogeneity on emergent outcomes. Our extensible framework is easily modified to explore numerous biological systems, from tumor microenvironments to microbiomes.