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

Engineering a computable epiblast for in silico modeling of developmental toxicity

Developmental hazard evaluation is an important part of assessing chemical risks during pregnancy. Toxicological outcomes from prenatal testing in pregnant animals result from complex chemical-biological interactions, and while New Approach Methods (NAMs) based on in vitro bioactivity profiles of human cells offer promising alternatives to animal testing, most of these assays lack cellular positional information, physical constraints, and regional organization of the intact embryo. Here, we engineered a fully computable model of the embryonic disc in the CompuCell3D.org modeling environment to simulate epithelial-mesenchymal transition (EMT) of epiblast cells and self-organization of mesodermal domains (chordamesoderm, paraxial, lateral plate, posterior/extraembryonic). Mesodermal fate is modeled by synthetic activity of the BMP4-NODAL-WNT signaling axis. Cell position in the epiblast determines timing with respect to EMT for 988 computational cells in the computer model. An autonomous homeobox (Hox) clock hidden in the epiblast is driven by WNT-FGF4-CDX signaling. Executing the model renders a quantitative cell-level computation of mesodermal fate and consequences of perturbation based on known biology. For example, synthetic perturbation of the control network rendered altered phenotypes (cybermorphs) mirroring some aspects of experimental mouse embryology, with electronic knockouts, under-activation (hypermorphs) or over-activation (hypermorphs) particularly affecting the size and specification of the posterior mesoderm. This foundational model is trained on embryology but capable of performing a wide variety of toxicological tasks conversing through anatomical simulation to integrate in vitro chemical bioactivity data with known embryology. It is amenable to quantitative simulation for probabilistic prediction of early developmental toxicity.

ABCD of IA: A multi-scale agent-based model of T cell activation in inflammatory arthritis

Biomaterial-based agents have been demonstrated to regulate the function of immune cells in models of autoimmunity. However, the complexity of the kinetics of immune cell activation can present a challenge in optimizing the dose and frequency of administration. Here, we report a model of autoreactive T cell activation, which are key drivers in autoimmune inflammatory joint disease. The model is termed a multi-scale Agent-Based, Cell-Driven model of Inflammatory Arthritis (ABCD of IA). Using kinetic rate equations and statistical theory, ABCD of IA simulated the activation and presentation of autoantigens by dendritic cells, interactions with cognate T cells and subsequent T cell proliferation in the lymph node and IA-affected joints. The results, validated with in vivo data from the T cell driven SKG mouse model, showed that T cell proliferation strongly correlated with the T cell receptor (TCR) affinity distribution (TCR-ad), with a clear transition state from homeostasis to an inflammatory state. T cell proliferation was strongly dependent on the amount of antigen in antigenic stimulus event (ASE) at low concentrations. On the other hand, inflammation driven by Th17-inducing cytokine mediated T cell phenotype commitment was influenced by the initial level of Th17-inducing cytokines independent of the amount of arthritogenic antigen. The introduction of inhibitory artificial antigen presenting cells (iaAPCs), which locally suppress T cell activation, reduced T cell proliferation in a dose-dependent manner. The findings in this work set up a framework based on theory and modeling to simulate personalized therapeutic strategies in IA.

Incorporating temporal information during feature engineering bolsters emulation of spatio-temporal emergence

MOTIVATION

Emergent biological dynamics derive from the evolution of lower-level spatial and temporal processes. A long-standing challenge for scientists and engineers is identifying simple low-level rules that give rise to complex higher-level dynamics. High-resolution biological data acquisition enables this identification and has evolved at a rapid pace for both experimental and computational approaches. Simultaneously harnessing the resolution and managing the expense of emerging technologies-e.g. live cell imaging, scRNAseq, agent-based models-requires a deeper understanding of how spatial and temporal axes impact biological systems. Effective emulation is a promising solution to manage the expense of increasingly complex high-resolution computational models. In this research, we focus on the emulation of a tumor microenvironment agent-based model to examine the relationship between spatial and temporal environment features, and emergent tumor properties.

RESULTS

Despite significant feature engineering, we find limited predictive capacity of tumor properties from initial system representations. However, incorporating temporal information derived from intermediate simulation states dramatically improves the predictive performance of machine learning models. We train a deep-learning emulator on intermediate simulation states and observe promising enhancements over emulators trained solely on initial conditions. Our results underscore the importance of incorporating temporal information in the evaluation of spatio-temporal emergent behavior. Nevertheless, the emulators exhibit inconsistent performance, suggesting that the underlying model characterizes unique cell populations dynamics that are not easily replaced.

AVAILABILITY AND IMPLEMENTATION

All source codes for the agent-based model, emulation, and analyses are publicly available at the corresponding DOIs: 10.5281/zenodo.10622155, 10.5281/zenodo.10611675, 10.5281/zenodo.10621244, respectively.

Metabolic symbiosis between oxygenated and hypoxic tumour cells: An agent-based modelling study

Deregulated metabolism is one of the hallmarks of cancer. It is well-known that tumour cells tend to metabolize glucose via glycolysis even when oxygen is available and mitochondrial respiration is functional. However, the lower energy efficiency of aerobic glycolysis with respect to mitochondrial respiration makes this behaviour, namely the Warburg effect, counter-intuitive, although it has now been recognized as source of anabolic precursors. On the other hand, there is evidence that oxygenated tumour cells could be fuelled by exogenous lactate produced from glycolysis. We employed a multi-scale approach that integrates multi-agent modelling, diffusion-reaction, stoichiometric equations, and Boolean networks to study metabolic cooperation between hypoxic and oxygenated cells exposed to varying oxygen, nutrient, and inhibitor concentrations. The results show that the cooperation reduces the depletion of environmental glucose, resulting in an overall advantage of using aerobic glycolysis. In addition, the oxygen level was found to be decreased by symbiosis, promoting a further shift towards anaerobic glycolysis. However, the oxygenated and hypoxic populations may gradually reach quasi-equilibrium. A sensitivity analysis using Latin hypercube sampling and partial rank correlation shows that the symbiotic dynamics depends on properties of the specific cell such as the minimum glucose level needed for glycolysis. Our results suggest that strategies that block glucose transporters may be more effective to reduce tumour growth than those blocking lactate intake transporters.

Model design choices impact biological insight: Unpacking the broad landscape of spatial-temporal model development decisions

Computational models enable scientists to understand observed dynamics, uncover rules underlying behaviors, predict experimental outcomes, and generate new hypotheses. There are countless modeling approaches that can be used to characterize biological systems, further multiplied when accounting for the variety of model design choices. Many studies focus on the impact of model parameters on model output and performance; fewer studies investigate the impact of model design choices on biological insight. Here we demonstrate why model design choices should be deliberate and intentional in context of the specific research system and question. In this study, we analyze agnostic and broadly applicable modeling choices at three levels-system, cell, and environment-within the same agent-based modeling framework to interrogate their impact on temporal, spatial, and single-cell emergent dynamics. We identify key considerations when making these modeling choices, including the (i) differences between qualitative vs. quantitative results driven by choices in system representation, (ii) impact of cell-to-cell variability choices on cell-level and temporal trends, and (iii) relationship between emergent outcomes and choices of nutrient dynamics in the environment. This generalizable investigation can help guide the choices made when developing biological models that aim to characterize spatial-temporal dynamics.

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.

From Chaos to Opportunity: Decoding Cancer Heterogeneity for Enhanced Treatment Strategies

Cancer manifests as a multifaceted disease, characterized by aberrant cellular proliferation, survival, migration, and invasion. Tumors exhibit variances across diverse dimensions, encompassing genetic, epigenetic, and transcriptional realms. This heterogeneity poses significant challenges in prognosis and treatment, affording tumors advantages through an increased propensity to accumulate mutations linked to immune system evasion and drug resistance. In this review, we offer insights into tumor heterogeneity as a crucial characteristic of cancer, exploring the difficulties associated with measuring and quantifying such heterogeneity from clinical and biological perspectives. By emphasizing the critical nature of understanding tumor heterogeneity, this work contributes to raising awareness about the importance of developing effective cancer therapies that target this distinct and elusive trait of cancer.

Mathematical models of developmental vascular remodelling: A review

Over the past 40 years, there has been a strong focus on the development of mathematical models of angiogenesis, while developmental remodelling has received little such attention from the mathematical community. Sprouting angiogenesis can be seen as a very crude way of laying out a primitive vessel network (the raw material), while remodelling (understood as pruning of redundant vessels, diameter control, and the establishment of vessel identity and hierarchy) is the key to turning that primitive network into a functional network. This multiscale problem is of prime importance in the development of a functional vasculature. In addition, defective remodelling (either during developmental remodelling or due to a reactivation of the remodelling programme caused by an injury) is associated with a significant number of diseases. In this review, we discuss existing mathematical models of developmental remodelling and explore the important contributions that these models have made to the field of vascular development. These mathematical models are effectively used to investigate and predict vascular development and are able to reproduce experimentally observable results. Moreover, these models provide a useful means of hypothesis generation and can explain the underlying mechanisms driving the observed structural and functional network development. However, developmental vascular remodelling is still a relatively new area in mathematical biology, and many biological questions remain unanswered. In this review, we present the existing modelling paradigms and define the key challenges for the field.

Impact of variability in cell cycle periodicity on cell population dynamics

The cell cycle consists of a series of orchestrated events controlled by molecular sensing and feedback networks that ultimately drive the duplication of total DNA and the subsequent division of a single parent cell into two daughter cells. The ability to block the cell cycle and synchronize cells within the same phase has helped understand factors that control cell cycle progression and the properties of each individual phase. Intriguingly, when cells are released from a synchronized state, they do not maintain synchronized cell division and rapidly become asynchronous. The rate and factors that control cellular desynchronization remain largely unknown. In this study, using a combination of experiments and simulations, we investigate the desynchronization properties in cervical cancer cells (HeLa) starting from the G1/S boundary following double-thymidine block. Propidium iodide (PI) DNA staining was used to perform flow cytometry cell cycle analysis at regular 8 hour intervals, and a custom auto-similarity function to assess the desynchronization and quantify the convergence to an asynchronous state. In parallel, we developed a single-cell phenomenological model the returns the DNA amount across the cell cycle stages and fitted the parameters using experimental data. Simulations of population of cells reveal that the cell cycle desynchronization rate is primarily sensitive to the variability of cell cycle duration within a population. To validate the model prediction, we introduced lipopolysaccharide (LPS) to increase cell cycle noise. Indeed, we observed an increase in cell cycle variability under LPS stimulation in HeLa cells, accompanied with an enhanced rate of cell cycle desynchronization. Our results show that the desynchronization rate of artificially synchronized in-phase cell populations can be used a proxy of the degree of variance in cell cycle periodicity, an underexplored axis in cell cycle research.

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.

Integration of quantitative methods and mathematical approaches for the modeling of cancer cell proliferation dynamics

Physiological processes rely on the control of cell proliferation, and the dysregulation of these processes underlies various pathological conditions, including cancer. Mathematical modeling can provide new insights into the complex regulation of cell proliferation dynamics. In this review, we first examine quantitative experimental approaches for measuring cell proliferation dynamics in vitro and compare the various types of data that can be obtained in these settings. We then explore the toolbox of common mathematical modeling frameworks that can describe cell behavior, dynamics, and interactions of proliferation. We discuss how these wet-laboratory studies may be integrated with different mathematical modeling approaches to aid the interpretation of the results and to enable the prediction of cell behaviors, specifically in the context of cancer.

Machine Learning and Hybrid Methods for Metabolic Pathway Modeling

Computational cell metabolism models seek to provide metabolic explanations of cell behavior under different conditions or following genetic alterations, help in the optimization of in vitro cell growth environments, or predict cellular behavior in vivo and in vitro. In the extremes, mechanistic models can include highly detailed descriptions of a small number of metabolic reactions or an approximate representation of an entire metabolic network. To date, all mechanistic models have required details of individual metabolic reactions, either kinetic parameters or metabolic flux, as well as information about extracellular and intracellular metabolite concentrations. Despite the extensive efforts and the increasing availability of high-quality data, required in vivo data are not available for the majority of known metabolic reactions; thus, mechanistic models are based primarily on ex vivo kinetic measurements and limited flux information. Machine learning approaches provide an alternative for derivation of functional dependencies from existing data. The increasing availability of metabolomic and lipidomic data, with growing feature coverage as well as sample set size, is expected to provide new data options needed for derivation of machine learning models of cell metabolic processes. Moreover, machine learning analysis of longitudinal data can lead to predictive models of cell behaviors over time. Conversely, machine learning models trained on steady-state data can provide descriptive models for the comparison of metabolic states in different environments or disease conditions. Additionally, inclusion of metabolic network knowledge in these analyses can further help in the development of models with limited data.This chapter will explore the application of machine learning to the modeling of cell metabolism. We first provide a theoretical explanation of several machine learning and hybrid mechanistic machine learning methods currently being explored to model metabolism. Next, we introduce several avenues for improving these models with machine learning. Finally, we provide protocols for specific examples of the utilization of machine learning in the development of predictive cell metabolism models using metabolomic data. We describe data preprocessing, approaches for training of machine learning models for both descriptive and predictive models, and the utilization of these models in synthetic and systems biology. Detailed protocols provide a list of software tools and libraries used for these applications, step-by-step modeling protocols, troubleshooting, as well as an overview of existing limitations to these approaches.

Agent-Based Modeling of Microbial Communities

Microbial communities are complex living systems that populate the planet with diverse functions and are increasingly harnessed for practical human needs. To deepen the fundamental understanding of their organization and functioning as well as to facilitate their engineering for applications, mathematical modeling has played an increasingly important role. Agent-based models represent a class of powerful quantitative frameworks for investigating microbial communities because of their individualistic nature in describing cells, mechanistic characterization of molecular and cellular processes, and intrinsic ability to produce emergent system properties. This review presents a comprehensive overview of recent advances in agent-based modeling of microbial communities. It surveys the state-of-the-art algorithms employed to simulate intracellular biomolecular events, single-cell behaviors, intercellular interactions, and interactions between cells and their environments that collectively serve as the driving forces of community behaviors. It also highlights three lines of applications of agent-based modeling, namely, the elucidation of microbial range expansion and colony ecology, the design of synthetic gene circuits and microbial populations for desired behaviors, and the characterization of biofilm formation and dispersal. The review concludes with a discussion of existing challenges, including the computational cost of the modeling, and potential mitigation strategies.

Mapping CAR T-Cell Design Space Using Agent-Based Models

Chimeric antigen receptor (CAR) T-cell therapy shows promise for treating liquid cancers and increasingly for solid tumors as well. While potential design strategies exist to address translational challenges, including the lack of unique tumor antigens and the presence of an immunosuppressive tumor microenvironment, testing all possible design choices in vitro and in vivo is prohibitively expensive, time consuming, and laborious. To address this gap, we extended the modeling framework ARCADE (Agent-based Representation of Cells And Dynamic Environments) to include CAR T-cell agents (CAR T-cell ARCADE, or CARCADE). We conducted in silico experiments to investigate how clinically relevant design choices and inherent tumor features—CAR T-cell dose, CD4⁺:CD8⁺ CAR T-cell ratio, CAR-antigen affinity, cancer and healthy cell antigen expression—individually and collectively impact treatment outcomes. Our analysis revealed that tuning CAR affinity modulates IL-2 production by balancing CAR T-cell proliferation and effector function. It also identified a novel multi-feature tuned treatment strategy for balancing selectivity and efficacy and provided insights into how spatial effects can impact relative treatment performance in different contexts. CARCADE facilitates deeper biological understanding of treatment design and could ultimately enable identification of promising treatment strategies to accelerate solid tumor CAR T-cell design-build-test cycles.

A Novel Hybrid Logic-ODE Modeling Approach to Overcome Knowledge Gaps

Mathematical modeling allows using different formalisms to describe, investigate, and understand biological processes. However, despite the advent of high-throughput experimental techniques, quantitative information is still a challenge when looking for data to calibrate model parameters. Furthermore, quantitative formalisms must cope with stiffness and tractability problems, more so if used to describe multicellular systems. On the other hand, qualitative models may lack the proper granularity to describe the underlying kinetic processes. We propose a hybrid modeling approach that integrates ordinary differential equations and logical formalism to describe distinct biological layers and their communication. We focused on a multicellular system as a case study by applying the hybrid formalism to the well-known Delta-Notch signaling pathway. We used a differential equation model to describe the intracellular pathways while the cell-cell interactions were defined by logic rules. The hybrid approach herein employed allows us to combine the pros of different modeling techniques by overcoming the lack of quantitative information with a qualitative description that discretizes activation and inhibition processes, thus avoiding complexity.

Multiscale modeling in disease

Multiscale computational modeling aims to connect the complex networks of effects at different length and/or time scales. For example, these networks often include intracellular molecular signaling, crosstalk, and other interactions between neighboring cell populations, and higher levels of emergent phenomena across different regions of tissues and among collections of tissues or organs interacting with each other in the whole body. Recent applications of multiscale modeling across intracellular, cellular, and/or tissue levels are highlighted here. These models incorporated the roles of biochemical and biomechanical modulation in processes that are implicated in the mechanisms of several diseases including fibrosis, joint and bone diseases, respiratory infectious diseases, and cancers.

Modular microenvironment components reproduce vascular dynamics de novo in a multi-scale agent-based model

Cells do not exist in isolation; they continuously act within and react to their environment. And this environment is not static; it continuously adapts and responds to cells. Here, we investigate how vascular structure and function impact emergent cell population behavior using an agent-based model (ABM). Our ABM enables researchers to "mix and match" cell agents, subcellular modules, and microenvironment components ranging from simple nutrient sources to complex, realistic vascular architectures that accurately capture hemodynamics. We use this ABM to highlight the bilateral relationship between cells and nearby vasculature, demonstrate the effect of vascular structure on environmental heterogeneity, and emphasize the non-linear, non-intuitive relationship between vascular function and the behavior of cell populations over time. Our ABM is well suited to characterizing in vitro and in vivo studies, with applications from basic science to translational synthetic biology and medicine. The model is freely available at https://github.com/bagherilab/ARCADE. A record of this paper's transparent peer review process is included in the supplemental information.