Agent-based modeling of multicell morphogenic processes during development

A hybrid physics-based and data-driven framework for cellular biological systems: Application to the morphogenesis of organoids

How cells orchestrate their cellular functions remains a crucial question to unravel how they organize in different patterns. We present a framework based on artificial intelligence to advance the understanding of how cell functions are coordinated spatially and temporally in biological systems. It consists of a hybrid physics-based model that integrates both mechanical interactions and cell functions with a data-driven model that regulates the cellular decision-making process through a deep learning algorithm trained on image data metrics. To illustrate our approach, we used data from 3D cultures of murine pancreatic ductal adenocarcinoma cells (PDAC) grown in Matrigel as tumor organoids. Our approach allowed us to find the underlying principles through which cells activate different cell processes to self-organize in different patterns according to the specific microenvironmental conditions. The framework proposed here expands the tools for simulating biological systems at the cellular level, providing a novel perspective to unravel morphogenetic patterns.

A computational modeling approach for predicting multicell spheroid patterns based on signaling-induced differential adhesion

Physiological and pathological processes including embryogenesis and tumorigenesis rely on the ability of individual cells to work collectively to form multicell patterns. In these heterogeneous multicell systems, cell-cell signaling induces differential adhesion between cells that leads to tissue-level patterning. However, the sensitivity of pattern formation to changes in the strengths of signaling or cell adhesion processes is not well understood. Prior work has explored these issues using synthetically engineered heterogeneous multicell spheroid systems, in which cell subpopulations engage in bidirectional intercellular signaling to regulate the expression of different cadherins. While engineered cell systems provide excellent experimental tools to observe pattern formation in cell populations, computational models of these systems may be leveraged to explore more systematically how specific combinations of signaling and adhesion parameters can drive the emergence of unique patterns. We developed and validated two- and three-dimensional agent-based models (ABMs) of spheroid patterning for previously described cells engineered with a bidirectional signaling circuit that regulates N- and P-cadherin expression. Systematic exploration of model predictions, some of which were experimentally validated, revealed how cell seeding parameters, the order of signaling events, probabilities of induced cadherin expression, and homotypic adhesion strengths affect pattern formation. Unsupervised clustering was also used to map combinations of signaling and adhesion parameters to these unique spheroid patterns predicted by the ABM. Finally, we demonstrated how the model may be deployed to design new synthetic cell signaling circuits based on a desired final multicell pattern.

A 3D multi-agent-based model for lumen morphogenesis: the role of the biophysical properties of the extracellular matrix

The correct function of many organs depends on proper lumen morphogenesis, which requires the orchestration of both biological and mechanical aspects. However, how these factors coordinate is not yet fully understood. Here, we focus on the development of a mechanistic model for computationally simulating lumen morphogenesis. In particular, we consider the hydrostatic pressure generated by the cells' fluid secretion as the driving force and the density of the extracellular matrix as regulators of the process. For this purpose, we develop a 3D agent-based-model for lumen morphogenesis that includes cells' fluid secretion and the density of the extracellular matrix. Moreover, this computer-based model considers the variation in the biological behavior of cells in response to the mechanical forces that they sense. Then, we study the formation of the lumen under different-mechanical scenarios and conclude that an increase in the matrix density reduces the lumen volume and hinders lumen morphogenesis. Finally, we show that the model successfully predicts normal lumen morphogenesis when the matrix density is physiological and aberrant multilumen formation when the matrix density is excessive.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s00366-022-01654-1.

From Flatland to Jupiter: Searching for Rules of Interaction Across Biological Scales

In this future-spanning perspective, we examine how an agent based model could be used to define general rules for interactions across biological systems and evolutionary time. To date there have been a number of attempts to simulate the emergence of ecological communities using agent-based models of individuals that have evolving traits. Here we speculate whether it is possible to use this computational modeling to simulate self-organizing systems and, importantly, to decipher universal principles that govern biological interactions. This perspective is a thought exercise, meant to extrapolate from current knowledge to how we may make Jupiter-shot leaps to further advance the biosciences in the 21st century.

Interplay of mesoscale physics and agent-like behaviors in the parallel evolution of aggregative multicellularity

Myxobacteria and dictyostelids are prokaryotic and eukaryotic multicellular lineages, respectively, that after nutrient depletion aggregate and develop into structures called fruiting bodies. The developmental processes and resulting morphological outcomes resemble one another to a remarkable extent despite their independent origins, the evolutionary distance between them and the lack of traceable homology in molecular mechanisms. We hypothesize that the morphological parallelism between the two lineages arises as the consequence of the interplay within multicellular aggregates between generic processes, physical and physicochemical processes operating similarly in living and non-living matter at the mesoscale (~10^-3-10^-1 m) and agent-like behaviors, unique to living systems and characteristic of the constituent cells, considered as autonomous entities acting according to internal rules in a shared environment. Here, we analyze the contributions of generic and agent-like determinants in myxobacteria and dictyostelid development and their roles in the generation of their common traits. Consequent to aggregation, collective cell-cell contacts mediate the emergence of liquid-like properties, making nascent multicellular masses subject to novel patterning and morphogenetic processes. In both lineages, this leads to behaviors such as streaming, rippling, and rounding-up, as seen in non-living fluids. Later the aggregates solidify, leading them to exhibit additional generic properties and motifs. Computational models suggest that the morphological phenotypes of the multicellular masses deviate from the predictions of generic physics due to the contribution of agent-like behaviors of cells such as directed migration, quiescence, and oscillatory signal transduction mediated by responses to external cues. These employ signaling mechanisms that reflect the evolutionary histories of the respective organisms. We propose that the similar developmental trajectories of myxobacteria and dictyostelids are more due to shared generic physical processes in coordination with analogous agent-type behaviors than to convergent evolution under parallel selection regimes. Insights from the biology of these aggregative forms may enable a unified understanding of developmental evolution, including that of animals and plants.

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.

Multi-scale models of lung fibrosis

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

NetLogo agent-based models as tools for understanding the self-organization of cell fate, morphogenesis and collective migration of the zebrafish posterior Lateral Line primordium

Interactions between primordium cells and their environment determines the self-organization of the zebrafish posterior Lateral Line primordium as it migrates under the skin from the ear to the tip of the tail forming and depositing neuromasts to spearhead formation of the posterior Lateral Line sensory system. In this review we describe how the NetLogo agent-based programming environment has been used in our lab to visualize and explore how self-generated chemokine gradients determine collective migration, how the dynamics of Wnt signaling can be used to predict patterns of neuromast deposition, and how previously defined interactions between Wnt and Fgf signaling systems have the potential to determine the periodic formation of center-biased Fgf signaling centers in the wake of a shrinking Wnt system. We also describe how NetLogo was used as a database for storing and visualizing the results of in toto lineage analysis of all cells in the migrating primordium. Together, the models illustrate how this programming environment can be used in diverse ways to integrate what has been learnt from biological experiments about the nature of interactions between cells and their environment, and explore how these interactions could potentially determine emergent patterns of cell fate specification, morphogenesis and collective migration of the zebrafish posterior Lateral Line primordium.

Distinguishing cell shoving mechanisms

Motivated by in vitro time–lapse images of ovarian cancer spheroids inducing mesothelial cell clearance, the traditional agent–based model of cell migration, based on simple volume exclusion, was extended to include the possibility that a cell seeking to move into an occupied location may push the resident cell, and any cells neighbouring it, out of the way to occupy that location. In traditional discrete models of motile cells with volume exclusion such a move would be aborted. We introduce a new shoving mechanism which allows cells to choose the direction to shove cells that expends the least amount of shoving effort (to account for the likely resistance of cells to being pushed). We call this motility rule ‘smart shoving’. We examine whether agent–based simulations of different shoving mechanisms can be distinguished on the basis of single realisations and averages over many realisations. We emphasise the difficulty in distinguishing cell mechanisms from cellular automata simulations based on snap–shots of cell distributions, site–occupancy averages and the evolution of the number of cells of each species averaged over many realisations. This difficulty suggests the need for higher resolution cell tracking.

Automated multi-objective calibration of biological agent-based simulations

Computational agent-based simulation (ABS) is increasingly used to complement laboratory techniques in advancing our understanding of biological systems. Calibration, the identification of parameter values that align simulation with biological behaviours, becomes challenging as increasingly complex biological domains are simulated. Complex domains cannot be characterized by single metrics alone, rendering simulation calibration a fundamentally multi-metric optimization problem that typical calibration techniques cannot handle. Yet calibration is an essential activity in simulation-based science; the baseline calibration forms a control for subsequent experimentation and hence is fundamental in the interpretation of results. Here, we develop and showcase a method, built around multi-objective optimization, for calibrating ABSs against complex target behaviours requiring several metrics (termed objectives) to characterize. Multi-objective calibration (MOC) delivers those sets of parameter values representing optimal trade-offs in simulation performance against each metric, in the form of a Pareto front. We use MOC to calibrate a well-understood immunological simulation against both established a priori and previously unestablished target behaviours. Furthermore, we show that simulation-borne conclusions are broadly, but not entirely, robust to adopting baseline parameter values from different extremes of the Pareto front, highlighting the importance of MOC's identification of numerous calibration solutions. We devise a method for detecting overfitting in a multi-objective context, not previously possible, used to save computational effort by terminating MOC when no improved solutions will be found. MOC can significantly impact biological simulation, adding rigour to and speeding up an otherwise time-consuming calibration process and highlighting inappropriate biological capture by simulations that cannot be well calibrated. As such, it produces more accurate simulations that generate more informative biological predictions.

In Silico and In Vivo Experiments Reveal M-CSF Injections Accelerate Regeneration Following Muscle Laceration

Numerous studies have pharmacologically modulated the muscle milieu in the hopes of promoting muscle regeneration; however, the timing and duration of these interventions are difficult to determine. This study utilized a combination of in silico and in vivo experiments to investigate how inflammation manipulation improves muscle recovery following injury. First, we measured macrophage populations following laceration injury in the rat tibialis anterior (TA). Then we calibrated an agent-based model (ABM) of muscle injury to mimic the observed inflammation profiles. The calibrated ABM was used to simulate macrophage and satellite stem cell (SC) dynamics, and suggested that delivering macrophage colony stimulating factor (M-CSF) prior to injury would promote SC-mediated injury recovery. Next, we performed an experiment wherein 1 day prior to injury, we injected M-CSF into the rat TA muscle. M-CSF increased the number of macrophages during the first 4 days post-injury. Furthermore, treated muscles experienced a swifter increase in the appearance of PAX7⁺ SCs and regenerating muscle fibers. Our study suggests that computational models of muscle injury provide novel insights into cellular dynamics during regeneration, and further, that pharmacologically altering inflammation dynamics prior to injury can accelerate the muscle regeneration process.

Gap Junctional Blockade Stochastically Induces Different Species-Specific Head Anatomies in Genetically Wild-Type Girardia dorotocephala Flatworms

The shape of an animal body plan is constructed from protein components encoded by the genome. However, bioelectric networks composed of many cell types have their own intrinsic dynamics, and can drive distinct morphological outcomes during embryogenesis and regeneration. Planarian flatworms are a popular system for exploring body plan patterning due to their regenerative capacity, but despite considerable molecular information regarding stem cell differentiation and basic axial patterning, very little is known about how distinct head shapes are produced. Here, we show that after decapitation in G. dorotocephala, a transient perturbation of physiological connectivity among cells (using the gap junction blocker octanol) can result in regenerated heads with quite different shapes, stochastically matching other known species of planaria (S. mediterranea, D. japonica, and P. felina). We use morphometric analysis to quantify the ability of physiological network perturbations to induce different species-specific head shapes from the same genome. Moreover, we present a computational agent-based model of cell and physical dynamics during regeneration that quantitatively reproduces the observed shape changes. Morphological alterations induced in a genomically wild-type G. dorotocephala during regeneration include not only the shape of the head but also the morphology of the brain, the characteristic distribution of adult stem cells (neoblasts), and the bioelectric gradients of resting potential within the anterior tissues. Interestingly, the shape change is not permanent; after regeneration is complete, intact animals remodel back to G. dorotocephala-appropriate head shape within several weeks in a secondary phase of remodeling following initial complete regeneration. We present a conceptual model to guide future work to delineate the molecular mechanisms by which bioelectric networks stochastically select among a small set of discrete head morphologies. Taken together, these data and analyses shed light on important physiological modifiers of morphological information in dictating species-specific shape, and reveal them to be a novel instructive input into head patterning in regenerating planaria.

Agent-based computational model investigates muscle-specific responses to disuse-induced atrophy

Skeletal muscle is highly responsive to use. In particular, muscle atrophy attributable to decreased activity is a common problem among the elderly and injured/immobile. However, each muscle does not respond the same way. We developed an agent-based model that generates a tissue-level skeletal muscle response to disuse/immobilization. The model incorporates tissue-specific muscle fiber architecture parameters and simulates changes in muscle fiber size as a result of disuse-induced atrophy that are consistent with published experiments. We created simulations of 49 forelimb and hindlimb muscles of the rat by incorporating eight fiber-type and size parameters to explore how these parameters, which vary widely across muscles, influence sensitivity to disuse-induced atrophy. Of the 49 muscles modeled, the soleus exhibited the greatest atrophy after 14 days of simulated immobilization (51% decrease in fiber size), whereas the extensor digitorum communis atrophied the least (32%). Analysis of these simulations revealed that both fiber-type distribution and fiber-size distribution influence the sensitivity to disuse atrophy even though no single tissue architecture parameter correlated with atrophy rate. Additionally, software agents representing fibroblasts were incorporated into the model to investigate cellular interactions during atrophy. Sensitivity analyses revealed that fibroblast agents have the potential to affect disuse-induced atrophy, albeit with a lesser effect than fiber type and size. In particular, muscle atrophy elevated slightly with increased initial fibroblast population and increased production of TNF-α. Overall, the agent-based model provides a novel framework for investigating both tissue adaptations and cellular interactions in skeletal muscle during atrophy.

Simulating tissue morphogenesis and signaling

During embryonic development tissue morphogenesis and signaling are tightly coupled. It is therefore important to simulate both tissue morphogenesis and signaling simultaneously in in silico models of developmental processes. The resolution of the processes depends on the questions of interest. As part of this chapter we introduce different descriptions of tissue morphogenesi s. In the simplest approximation tissue is a continuous domain and tissue expansion is described according to a predefined function of time (and possibly space). In a slightly more advanced version the expansion speed and direction of the tissue may depend on a signaling variable that evolves on the domain. Both versions will be referred to as "prescribed growth." Alternatively tissue can be regarded as incompressible fluid and can be described with Navier-Stokes equations. Local cell expansion, proliferation, and death are then incorporated by a source term. In other applications the cell boundaries may be important and cell-based models must be introduced. Finally, cells may move within the tissue, a process best described by agent-based models.

Investigating biocomplexity through the agent-based paradigm

Capturing the dynamism that pervades biological systems requires a computational approach that can accommodate both the continuous features of the system environment as well as the flexible and heterogeneous nature of component interactions. This presents a serious challenge for the more traditional mathematical approaches that assume component homogeneity to relate system observables using mathematical equations. While the homogeneity condition does not lead to loss of accuracy while simulating various continua, it fails to offer detailed solutions when applied to systems with dynamically interacting heterogeneous components. As the functionality and architecture of most biological systems is a product of multi-faceted individual interactions at the sub-system level, continuum models rarely offer much beyond qualitative similarity. Agent-based modelling is a class of algorithmic computational approaches that rely on interactions between Turing-complete finite-state machines--or agents--to simulate, from the bottom-up, macroscopic properties of a system. In recognizing the heterogeneity condition, they offer suitable ontologies to the system components being modelled, thereby succeeding where their continuum counterparts tend to struggle. Furthermore, being inherently hierarchical, they are quite amenable to coupling with other computational paradigms. The integration of any agent-based framework with continuum models is arguably the most elegant and precise way of representing biological systems. Although in its nascence, agent-based modelling has been utilized to model biological complexity across a broad range of biological scales (from cells to societies). In this article, we explore the reasons that make agent-based modelling the most precise approach to model biological systems that tend to be non-linear and complex.

A computational model predicting disruption of blood vessel development

Vascular development is a complex process regulated by dynamic biological networks that vary in topology and state across different tissues and developmental stages. Signals regulating de novo blood vessel formation (vasculogenesis) and remodeling (angiogenesis) come from a variety of biological pathways linked to endothelial cell (EC) behavior, extracellular matrix (ECM) remodeling and the local generation of chemokines and growth factors. Simulating these interactions at a systems level requires sufficient biological detail about the relevant molecular pathways and associated cellular behaviors, and tractable computational models that offset mathematical and biological complexity. Here, we describe a novel multicellular agent-based model of vasculogenesis using the CompuCell3D (http://www.compucell3d.org/) modeling environment supplemented with semi-automatic knowledgebase creation. The model incorporates vascular endothelial growth factor signals, pro- and anti-angiogenic inflammatory chemokine signals, and the plasminogen activating system of enzymes and proteases linked to ECM interactions, to simulate nascent EC organization, growth and remodeling. The model was shown to recapitulate stereotypical capillary plexus formation and structural emergence of non-coded cellular behaviors, such as a heterologous bridging phenomenon linking endothelial tip cells together during formation of polygonal endothelial cords. Molecular targets in the computational model were mapped to signatures of vascular disruption derived from in vitro chemical profiling using the EPA's ToxCast high-throughput screening (HTS) dataset. Simulating the HTS data with the cell-agent based model of vascular development predicted adverse effects of a reference anti-angiogenic thalidomide analog, 5HPP-33, on in vitro angiogenesis with respect to both concentration-response and morphological consequences. These findings support the utility of cell agent-based models for simulating a morphogenetic series of events and for the first time demonstrate the applicability of these models for predictive toxicology.

Spatial pattern dynamics of 3D stem cell loss of pluripotency via rules-based computational modeling

Pluripotent embryonic stem cells (ESCs) have the unique ability to differentiate into cells from all germ lineages, making them a potentially robust cell source for regenerative medicine therapies, but difficulties in predicting and controlling ESC differentiation currently limit the development of therapies and applications from such cells. A common approach to induce the differentiation of ESCs in vitro is via the formation of multicellular aggregates known as embryoid bodies (EBs), yet cell fate specification within EBs is generally considered an ill-defined and poorly controlled process. Thus, the objective of this study was to use rules-based cellular modeling to provide insight into which processes influence initial cell fate transitions in 3-dimensional microenvironments. Mouse embryonic stem cells (D3 cell line) were differentiated to examine the temporal and spatial patterns associated with loss of pluripotency as measured through Oct4 expression. Global properties of the multicellular aggregates were accurately recapitulated by a physics-based aggregation simulation when compared to experimentally measured physical parameters of EBs. Oct4 expression patterns were analyzed by confocal microscopy over time and compared to simulated trajectories of EB patterns. The simulations demonstrated that loss of Oct4 can be modeled as a binary process, and that associated patterns can be explained by a set of simple rules that combine baseline stochasticity with intercellular communication. Competing influences between Oct4+ and Oct4- neighbors result in the observed patterns of pluripotency loss within EBs, establishing the utility of rules-based modeling for hypothesis generation of underlying ESC differentiation processes. Importantly, the results indicate that the rules dominate the emergence of patterns independent of EB structure, size, or cell division. In combination with strategies to engineer cellular microenvironments, this type of modeling approach is a powerful tool to predict stem cell behavior under a number of culture conditions that emulate characteristics of 3D stem cell niches.

MOSAIC: a multiscale model of osteogenesis and sprouting angiogenesis with lateral inhibition of endothelial cells

The healing of a fracture depends largely on the development of a new blood vessel network (angiogenesis) in the callus. During angiogenesis tip cells lead the developing sprout in response to extracellular signals, amongst which vascular endothelial growth factor (VEGF) is critical. In order to ensure a correct development of the vasculature, the balance between stalk and tip cell phenotypes must be tightly controlled, which is primarily achieved by the Dll4-Notch1 signaling pathway. This study presents a novel multiscale model of osteogenesis and sprouting angiogenesis, incorporating lateral inhibition of endothelial cells (further denoted MOSAIC model) through Dll4-Notch1 signaling, and applies it to fracture healing. The MOSAIC model correctly predicted the bone regeneration process and recapitulated many experimentally observed aspects of tip cell selection: the salt and pepper pattern seen for cell fates, an increased tip cell density due to the loss of Dll4 and an excessive number of tip cells in high VEGF environments. When VEGF concentration was even further increased, the MOSAIC model predicted the absence of a vascular network and fracture healing, thereby leading to a non-union, which is a direct consequence of the mutual inhibition of neighboring cells through Dll4-Notch1 signaling. This result was not retrieved for a more phenomenological model that only considers extracellular signals for tip cell migration, which illustrates the importance of implementing the actual signaling pathway rather than phenomenological rules. Finally, the MOSAIC model demonstrated the importance of a proper criterion for tip cell selection and the need for experimental data to further explore this. In conclusion, this study demonstrates that the MOSAIC model creates enhanced capabilities for investigating the influence of molecular mechanisms on angiogenesis and its relation to bone formation in a more mechanistic way and across different time and spatial scales.

Modeling the dynamic epigenome: from histone modifications towards self-organizing chromatin

Epigenetic mechanisms play an important role in regulating and stabilizing functional states of living cells. However, in spite of an increasing amount of experimental data, models of transcriptional regulation by epigenetic processes, in particular by histone modifications, are rather rare. In this article, we focus on epigenetic modes of transcriptional regulation based on histone modifications and their potential dynamical interplay with DNA methylation and higher-order chromatin structure. The main purpose of this article is to review recent formal modeling approaches to the dynamics and propagation of histone modifications and to relate them to available experimental data. We evaluate their assumptions with respect to recruitment of relevant modifiers, establishment and processing of modifications, and compare the emerging stability properties and memory effects. Theoretical predictions that await experimental validation are highlighted and potential extensions of these models towards multiscale models of self-organizing chromatin are discussed.

The virtual liver: a multidisciplinary, multilevel challenge for systems biology

The liver is the central metabolic organ in human physiology, with functions that are fundamentally important to the detoxification of xenobiotics (drugs), the maintenance of homeostasis of numerous blood metabolites, and the production of mediators of the acute phase response. Liver toxicity, whether actual or implied is the reason for the failure of a significant proportion of many promising novel medicines that consequently never reach the market, and diseases such as atherosclerosis, diabetes, and fatty liver diseases, that are a major burden on current health resources, are directly linked to functional and structural disorders of the liver. This article presents the concepts and approaches underpinning one of the most exciting and ambitious modeling projects in the field of systems biology and systems medicine. This major multidisciplinary research program is aimed at developing a whole-organ model of the human liver, representing its central physiological functions under normal and pathological conditions The model will be composed of a larger battery of interconnected submodels representing liver anatomy and physiology, integrating processes across hierarchical levels in space, time, and structural organization. In this article, we outline the general architecture of the liver model and present first step taken to reach this ambitious goal.

Ensuring congruency in multiscale modeling: towards linking agent based and continuum biomechanical models of arterial adaptation

There is a need to develop multiscale models of vascular adaptations to understand tissue-level manifestations of cellular level mechanisms. Continuum-based biomechanical models are well suited for relating blood pressures and flows to stress-mediated changes in geometry and properties, but less so for describing underlying mechanobiological processes. Discrete stochastic agent-based models are well suited for representing biological processes at a cellular level, but not for describing tissue-level mechanical changes. We present here a conceptually new approach to facilitate the coupling of continuum and agent-based models. Because of ubiquitous limitations in both the tissue- and cell-level data from which one derives constitutive relations for continuum models and rule-sets for agent-based models, we suggest that model verification should enforce congruency across scales. That is, multiscale model parameters initially determined from data sets representing different scales should be refined, when possible, to ensure that common outputs are consistent. Potential advantages of this approach are illustrated by comparing simulated aortic responses to a sustained increase in blood pressure predicted by continuum and agent-based models both before and after instituting a genetic algorithm to refine 16 objectively bounded model parameters. We show that congruency-based parameter refinement not only yielded increased consistency across scales, it also yielded predictions that are closer to in vivo observations.

Notch signaling in the vasculature

Notch signaling is an evolutionarily conserved, intercellular signaling mechanism that plays myriad roles during vascular development and physiology in vertebrates. These roles include the regulation of arteriovenous specification and differentiation in both endothelial cells and vascular smooth muscle cells, regulation of blood vessel sprouting and branching during normal and pathological angiogenesis, and the physiological responses of vascular smooth muscle cells. Defects in Notch signaling also cause inherited vascular diseases, such as the degenerative vascular disorder cerebral autosomal dominant arteriopathy with subcortical infarcts and leukoencephalopathy. This review summarizes recent studies that highlight the multiple roles the Notch signaling pathway plays during vascular development and physiology.

Characterizing the dynamics of CD4+ T cell priming within a lymph node

Generating adaptive immunity postinfection or immunization requires physical interaction within a lymph node T zone between Ag-bearing dendritic cells (DCs) and rare cognate T cells. Many fundamental questions remain regarding the dynamics of DC-CD4+ T cell interactions leading to priming. For example, it is not known how the production of primed CD4+ T cells relates to the numbers of cognate T cells, Ag-bearing DCs, or peptide-MHCII level on the DC. To address these questions, we developed an agent-based model of a lymph node to examine the relationships among cognate T cell frequency, DC density, parameters characterizing DC-T cell interactions, and the output of primed T cells. We found that the output of primed CD4+ T cells is linearly related to cognate frequency, but nonlinearly related to the number of Ag-bearing DCs present during infection. This addresses the applicability of two photon microscopy studies to understanding actual infection dynamics, because these types of experiments increase the cognate frequency by orders of magnitude compared with physiologic levels. We found a trade-off between the quantity of peptide-major histocompatibility class II on the surface of individual DCs and number of Ag-bearing DCs present in the lymph node in contributing to the production of primed CD4+ T cells. Interestingly, peptide-major histocompatibility class II t(1/2) plays a minor, although still significant, role in determining CD4+ T cell priming, unlike the primary role that has been suggested for CD8+ T cell priming. Finally, we identify several pathogen-targeted mechanisms that, if altered in their efficiency, can significantly effect the generation of primed CD4+ T cells.

Nonlinear diffusion and exclusion processes with contact interactions

Exclusion processes on a regular lattice are used to model many biological and physical systems at a discrete level. The average properties of an exclusion process may be described by a continuum model given by a partial differential equation. We combine a general class of contact interactions with an exclusion process. We determine that many different types of contact interactions at the agent-level always give rise to a nonlinear diffusion equation, with a vast variety of diffusion functions D(C). We find that these functions may be dependent on the chosen lattice and the defined neighborhood of the contact interactions. Mild to moderate contact interaction strength generally results in good agreement between discrete and continuum models, while strong interactions often show discrepancies between the two, particularly when D(C) takes on negative values. We present a measure to predict the goodness of fit between the discrete and continuous model, and thus the validity of the continuum description of a motile, contact-interacting population of agents. This work has implications for modeling cell motility and interpreting cell motility assays, giving the ability to incorporate biologically realistic cell-cell interactions and develop global measures of discrete microscopic data.

At the biological modeling and simulation frontier

We provide a rationale for and describe examples of synthetic modeling and simulation (M&S) of biological systems. We explain how synthetic methods are distinct from familiar inductive methods. Synthetic M&S is a means to better understand the mechanisms that generate normal and disease-related phenomena observed in research, and how compounds of interest interact with them to alter phenomena. An objective is to build better, working hypotheses of plausible mechanisms. A synthetic model is an extant hypothesis: execution produces an observable mechanism and phenomena. Mobile objects representing compounds carry information enabling components to distinguish between them and react accordingly when different compounds are studied simultaneously. We argue that the familiar inductive approaches contribute to the general inefficiencies being experienced by pharmaceutical R&D, and that use of synthetic approaches accelerates and improves R&D decision-making and thus the drug development process. A reason is that synthetic models encourage and facilitate abductive scientific reasoning, a primary means of knowledge creation and creative cognition. When synthetic models are executed, we observe different aspects of knowledge in action from different perspectives. These models can be tuned to reflect differences in experimental conditions and individuals, making translational research more concrete while moving us closer to personalized medicine.

Rule-Based Simulation of Multi-Cellular Biological Systems-A Review of Modeling Techniques

Emergent behaviors of multi-cellular biological systems (MCBS) result from the behaviors of each individual cells and their interactions with other cells and with the environment. Modeling MCBS requires incorporating these complex interactions among the individual cells and the environment. Modeling approaches for MCBS can be grouped into two categories: continuum models and cell-based models. Continuum models usually take the form of partial differential equations, and the model equations provide insight into the relationship among the components in the system. Cell-based models simulate each individual cell behavior and interactions among them enabling the observation of the emergent system behavior. This review focuses on the cell-based models of MCBS, and especially, the technical aspect of the rule-based simulation method for MCBS is reviewed. How to implement the cell behaviors and the interactions with other cells and with the environment into the computational domain is discussed. The cell behaviors reviewed in this paper are division, migration, apoptosis/necrosis, and differentiation. The environmental factors such as extracellular matrix, chemicals, microvasculature, and forces are also discussed. Application examples of these cell behaviors and interactions are presented.

Rule-Based Simulation of Multi-Cellular Biological Systems-A Review of Modeling Techniques

Emergent behaviors of multi-cellular biological systems (MCBS) result from the behaviors of each individual cells and their interactions with other cells and with the environment. Modeling MCBS requires incorporating these complex interactions among the individual cells and the environment. Modeling approaches for MCBS can be grouped into two categories: continuum models and cell-based models. Continuum models usually take the form of partial differential equations, and the model equations provide insight into the relationship among the components in the system. Cell-based models simulate each individual cell behavior and interactions among them enabling the observation of the emergent system behavior. This review focuses on the cell-based models of MCBS, and especially, the technical aspect of the rule-based simulation method for MCBS is reviewed. How to implement the cell behaviors and the interactions with other cells and with the environment into the computational domain is discussed. The cell behaviors reviewed in this paper are division, migration, apoptosis/necrosis, and differentiation. The environmental factors such as extracellular matrix, chemicals, microvasculature, and forces are also discussed. Application examples of these cell behaviors and interactions are presented.

Agent-based model of therapeutic adipose-derived stromal cell trafficking during ischemia predicts ability to roll on P-selectin

Intravenous delivery of human adipose-derived stromal cells (hASCs) is a promising option for the treatment of ischemia. After delivery, hASCs that reside and persist in the injured extravascular space have been shown to aid recovery of tissue perfusion and function, although low rates of incorporation currently limit the safety and efficacy of these therapies. We submit that a better understanding of the trafficking of therapeutic hASCs through the microcirculation is needed to address this and that selective control over their homing (organ- and injury-specific) may be possible by targeting bottlenecks in the homing process. This process, however, is incredibly complex, which merited the use of computational techniques to speed the rate of discovery. We developed a multicell agent-based model (ABM) of hASC trafficking during acute skeletal muscle ischemia, based on over 150 literature-based rules instituted in Netlogo and MatLab software programs. In silico, trafficking phenomena within cell populations emerged as a result of the dynamic interactions between adhesion molecule expression, chemokine secretion, integrin affinity states, hemodynamics and microvascular network architectures. As verification, the model reasonably reproduced key aspects of ischemia and trafficking behavior including increases in wall shear stress, upregulation of key cellular adhesion molecules expressed on injured endothelium, increased secretion of inflammatory chemokines and cytokines, quantified levels of monocyte extravasation in selectin knockouts, and circulating monocyte rolling distances. Successful ABM verification prompted us to conduct a series of systematic knockouts in silico aimed at identifying the most critical parameters mediating hASC trafficking. Simulations predicted the necessity of an unknown selectin-binding molecule to achieve hASC extravasation, in addition to any rolling behavior mediated by hASC surface expression of CD15s, CD34, CD62e, CD62p, or CD65. In vitro experiments confirmed this prediction; a subpopulation of hASCs slowly rolled on immobilized P-selectin at speeds as low as 2 µm/s. Thus, our work led to a fundamentally new understanding of hASC biology, which may have important therapeutic implications.

Ischemic pathologies, such as acute myocardial infarction and peripheral vascular disease, continue to be associated with high morbidities and mortalities. Recently, therapies wherein adult stem cells are injected into the circulation have been shown to increase blood flow and help to restore tissue function following injury. Pre-clinical animal models and human trials have shown successes utilizing this approach, but variable trafficking efficiencies and low incorporation of cells into the injured tissue severely limit effectiveness and may preclude clinical adoption. To address this, we sought to study the complex process of how injected stem cells traffic through the microcirculation and home to sites of injury, in an effort to identify bottlenecks in this process that could be manipulated for therapeutic gain. We developed an agent-based computer model to speed the rate of discovery, and we identified a key cell–cell adhesion interaction that could be targeted to enhance stem cell homing efficiencies during injectable stem cell therapies.

Modeling proliferative tissue growth: a general approach and an avian case study

During development, tissues often undergo rapid physical expansion due to cell proliferation. Continuous and discrete models of one- and two-dimensional tissue growth are developed and applied to observational data of the developing avian gut, where the gut tissue cells undergo dramatic proliferation. The discrete cellular automata model provides results at the level of individual cells that reflect a realistic stochasticity and nonuniformity expected in cellular systems. Averaging the discrete results predicts population-level properties of the system, which match those of the continuous model. This dual approach provides an understanding of the interaction between the individual-level and population-level aspects of a developmental growth process. Both models are applied to a case study involving the developing intestinal tract of a quail embryo. A nonuniform growth model accurately predicts the positions of measurable biological landmarks within the growing tissue. Furthermore, the discrete model provides a framework for modeling the interactions between growing tissues and other biological mechanisms, such as cell motility and proliferation on an expanding tissue.

The development of locomotor kinematics in neonatal rats: an agent-based modeling analysis in group and individual contexts

An agent-based model of infant rat (pup) locomotion and aggregation was developed by modifying a previous model of pup aggregation [Schank, J.C., Alberts, J.R., 2000a. The developmental emergence of coupled activity as cooperative aggregation in rat pups. Proc. R. Soc. London B 267, 2307-2315]. The main difference between the earlier and current models is the incorporation of whole-body kinematics of directional locomotion. Data on locomotion and aggregation are presented for individuals and groups of 7- and 10-day-old pups and the data were used to evolve models (with a genetic algorithm) that fit these data. Aggregation between 7- and 10-day-old pups was considerably different and could be explained by agent-based models, in particular, models with directional-kinematic matrices specifying the probabilities of moving to adjacent cells. The directional kinematics of whole-body movement differed between the two age classes and differed between group and individual contexts for 10-day-old pups. This may indicate a developmental transition (by day 10) to more central control of behavior and the ability to change patterns of movement based on social context. The behavior analyzed with agent-based models may provide a precise way to measure motor and nervous system development in rats and other rodents.