Agent-based model of angiogenesis simulates capillary sprout initiation in multicellular networks

Multiscale computational model predicts how environmental changes and treatments affect microvascular remodeling in fibrotic disease

Investigating the molecular, cellular, and tissue-level changes caused by disease, and the effects of pharmacological treatments across these biological scales, necessitates the use of multiscale computational modeling in combination with experimentation. Many diseases dynamically alter the tissue microenvironment in ways that trigger microvascular network remodeling, which leads to the expansion or regression of microvessel networks. When microvessels undergo remodeling in idiopathic pulmonary fibrosis (IPF), functional gas exchange is impaired and lung function declines. We integrated a multiscale computational model with independent experiments to investigate how combinations of biomechanical and biochemical cues in IPF alter cell fate decisions leading to microvascular remodeling. Our computational model predicted that extracellular matrix (ECM) stiffening reduced microvessel area, which was accompanied by physical uncoupling of endothelial cell (EC) and pericytes, the cells that comprise microvessels. Nintedanib, an Food and Drug Administration-approved drug for treating IPF, was predicted to further potentiate microvessel regression by decreasing the percentage of quiescent pericytes while increasing the percentage of pericytes undergoing pericyte-myofibroblast transition in high ECM stiffnesses. Importantly, the model suggested that YAP/TAZ inhibition may overcome the deleterious effects of nintedanib by promoting EC-pericyte coupling and maintaining microvessel homeostasis. Overall, our combination of computational and experimental modeling can predict and explain how cell decisions affect tissue changes during disease and in response to treatments.

Multiscale computational model predicts how environmental changes and drug treatments affect microvascular remodeling in fibrotic disease

Investigating the molecular, cellular, and tissue-level changes caused by disease, and the effects of pharmacological treatments across these biological scales, necessitates the use of multiscale computational modeling in combination with experimentation. Many diseases dynamically alter the tissue microenvironment in ways that trigger microvascular network remodeling, which leads to the expansion or regression of microvessel networks. When microvessels undergo remodeling in idiopathic pulmonary fibrosis (IPF), functional gas exchange is impaired due to loss of alveolar structures and lung function declines. Here, we integrated a multiscale computational model with independent experiments to investigate how combinations of biomechanical and biochemical cues in IPF alter cell fate decisions leading to microvascular remodeling. Our computational model predicted that extracellular matrix (ECM) stiffening reduced microvessel area, which was accompanied by physical uncoupling of endothelial cell (ECs) and pericytes, the cells that comprise microvessels. Nintedanib, an FDA-approved drug for treating IPF, was predicted to further potentiate microvessel regression by decreasing the percentage of quiescent pericytes while increasing the percentage of pericytes undergoing pericyte-myofibroblast transition (PMT) in high ECM stiffnesses. Importantly, the model suggested that YAP/TAZ inhibition may overcome the deleterious effects of nintedanib by promoting EC-pericyte coupling and maintaining microvessel homeostasis. Overall, our combination of computational and experimental modeling can explain how cell decisions affect tissue changes during disease and in response to treatments.

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.

In silico optimization of heparin microislands in microporous annealed particle (MAP) hydrogel for endothelial cell migration

Biomaterials capable of generating growth factor gradients have shown success in guiding tissue regeneration, as growth factor gradients are a physiologic driver of cell migration. Of particular importance, a focus on promoting endothelial cell migration is vital to angiogenesis and new tissue formation. Microporous Annealed Particle (MAP) scaffolds represent a unique niche in the field of regenerative biomaterials research as an injectable biomaterial with an open porosity that allows cells to freely migrate independent of material degradation. Recently, we have used the MAP platform to heterogeneously include spatially isolated heparin-modified microgels (heparin microislands) which can sequester growth factors and guide cell migration. In in vitro sprouting angiogenesis assays, we observed a parabolic relationship between the percentage of heparin microislands and cell migration, where 10% heparin microislands had more endothelial cell migration compared to 1% and 100%. Due to the low number of heparin microisland ratios tested, we hypothesize the spacing between microgels can be further optimized. Rather than use purely empirical methods, which are both expensive and time intensive, we believe this challenge represents an opportunity to use computational modeling. Here we present the first agent-based model of a MAP scaffold to optimize the ratio of heparin microislands. Specifically, we develop a two-dimensional model in Hybrid Automata Library (HAL) of endothelial cell migration within the unique MAP scaffold geometry. Finally, we present how our model can accurately predict cell migration trends in vitro, and these studies provide insight on how computational modeling can be used to design particle-based biomaterials. STATEMENT OF SIGNIFICANCE: : While the combination of experimental and computational approaches is increasingly being used to gain a better understanding of cellular processes, their combination in biomaterials development has been relatively limited. Heparin microislands are spatially isolated heparin microgels; when located within a microporous annealed particle (MAP) scaffold, they can sequester and release growth factors. Importantly, we present the first agent-based model of MAP scaffolds to optimize the ratio of heparin microislands within the scaffold to promote endothelial cell migration. We demonstrate this model can accurately predict trends in vitro, thus opening a new avenue of research to aid in the design of MAP scaffolds.

Biologically-Based Mathematical Modeling of Tumor Vasculature and Angiogenesis via Time-Resolved Imaging Data

Tumor-associated vasculature is responsible for the delivery of nutrients, removal of waste, and allowing growth beyond 2-3 mm3. Additionally, the vascular network, which is changing in both space and time, fundamentally influences tumor response to both systemic and radiation therapy. Thus, a robust understanding of vascular dynamics is necessary to accurately predict tumor growth, as well as establish optimal treatment protocols to achieve optimal tumor control. Such a goal requires the intimate integration of both theory and experiment. Quantitative and time-resolved imaging methods have emerged as technologies able to visualize and characterize tumor vascular properties before and during therapy at the tissue and cell scale. Parallel to, but separate from those developments, mathematical modeling techniques have been developed to enable in silico investigations into theoretical tumor and vascular dynamics. In particular, recent efforts have sought to integrate both theory and experiment to enable data-driven mathematical modeling. Such mathematical models are calibrated by data obtained from individual tumor-vascular systems to predict future vascular growth, delivery of systemic agents, and response to radiotherapy. In this review, we discuss experimental techniques for visualizing and quantifying vascular dynamics including magnetic resonance imaging, microfluidic devices, and confocal microscopy. We then focus on the integration of these experimental measures with biologically based mathematical models to generate testable predictions.

On the preservation of vessel bifurcations during flow-mediated angiogenic remodelling

During developmental angiogenesis, endothelial cells respond to shear stress by migrating and remodelling the initially hyperbranched plexus, removing certain vessels whilst maintaining others. In this study, we argue that the key regulator of vessel preservation is cell decision behaviour at bifurcations. At flow-convergent bifurcations where migration paths diverge, cells must finely tune migration along both possible paths if the bifurcation is to persist. Experiments have demonstrated that disrupting the cells’ ability to sense shear or the junction forces transmitted between cells impacts the preservation of bifurcations during the remodelling process. However, how these migratory cues integrate during cell decision making remains poorly understood. Therefore, we present the first agent-based model of endothelial cell flow-mediated migration suitable for interrogating the mechanisms behind bifurcation stability. The model simulates flow in a bifurcated vessel network composed of agents representing endothelial cells arranged into a lumen which migrate against flow. Upon approaching a bifurcation where more than one migration path exists, agents refer to a stochastic bifurcation rule which models the decision cells make as a combination of flow-based and collective-based migratory cues. With this rule, cells favour branches with relatively larger shear stress or cell number. We found that cells must integrate both cues nearly equally to maximise bifurcation stability. In simulations with stable bifurcations, we found competitive oscillations between flow and collective cues, and simulations that lost the bifurcation were unable to maintain these oscillations. The competition between these two cues is haemodynamic in origin, and demonstrates that a natural defence against bifurcation loss during remodelling exists: as vessel lumens narrow due to cell efflux, resistance to flow and shear stress increases, attracting new cells to enter and rescue the vessel from regression. Our work provides theoretical insight into the role of junction force transmission has in stabilising vasculature during remodelling and as an emergent mechanism to avoid functional shunting.

When new blood vessels are created, the endothelial cells that make up these vessels migrate and rearrange in response to blood flow to remodel and optimise the vessel network. An essential part of this process is maintaining the branched structure of the network; however, it is unclear what cues cells consider at regions where vessels branch (i.e., bifurcations). In this research, we present a computer model of cell migration to interrogate the process of preserving bifurcations during remodelling. In this model, cells at bifurcations are influenced by both flow and force transmitted from neighbouring cells. We found that both cues (flow-based and collective-based) must be considered equally in order to preserve branching in the vessel network. In simulations with stable bifurcations, we demonstrated that these cues oscillate: a strong signal in one was accompanied by a weak signal in the other. Furthermore, we found that these cues naturally compete with each other due to the coupling between blood flow and the size of the blood vessels, i.e. larger vessels with more cells produce less flow signals and vice versa. Our research provides insight into how forces transmitted between neighbouring cells stabilise and preserve branching during remodelling, as well as implicates the disruption of this force transmission as a potential mechanism when remodelling goes wrong as in the case of vascular malformation.

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.

A hybrid model of tumor growth and angiogenesis: In silico experiments

Tumor associated angiogenesis is the development of new blood vessels in response to proteins secreted by tumor cells. These new blood vessels allow tumors to continue to grow beyond what the pre-existing vasculature could support. Here, we construct a mathematical model to simulate tumor angiogenesis by considering each endothelial cell as an agent, and allowing the vascular endothelial growth factor (VEGF) and nutrient fields to impact the dynamics and phenotypic transitions of each tumor and endothelial cell. The phenotypes of the endothelial cells (i.e., tip, stalk, and phalanx cells) are selected by the local VEGF field, and govern the migration and growth of vessel sprouts at the cellular level. Over time, these vessels grow and migrate to the tumor, forming anastomotic loops to supply nutrients, while interacting with the tumor through mechanical forces and the consumption of VEGF. The model is able to capture collapsing and breaking of vessels caused by tumor-endothelial cell interactions. This is accomplished through modeling the physical interaction between the vasculature and the tumor, resulting in vessel occlusion and tumor heterogeneity over time due to the stages of response in angiogenesis. Key parameters are identified through a sensitivity analysis based on the Sobol method, establishing which parameters should be the focus of subsequent experimental efforts. During the avascular phase (i.e., before angiogenesis is triggered), the nutrient consumption rate, followed by the rate of nutrient diffusion, yield the greatest influence on the number and distribution of tumor cells. Similarly, the consumption and diffusion of VEGF yield the greatest influence on the endothelial and tumor cell numbers during angiogenesis. In summary, we present a hybrid mathematical approach that characterizes vascular changes via an agent-based model, while treating nutrient and VEGF changes through a continuum model. The model describes the physical interaction between a tumor and the surrounding blood vessels, explicitly allowing the forces of the growing tumor to influence the nutrient delivery of the vasculature.

Blood Vessel Patterning on Retinal Astrocytes Requires Endothelial Flt-1 (VEGFR-1)

Feedback mechanisms are critical components of many pro-angiogenic signaling pathways that keep vessel growth within a functional range. The Vascular Endothelial Growth Factor-A (VEGF-A) pathway utilizes the decoy VEGF-A receptor Flt-1 to provide negative feedback regulation of VEGF-A signaling. In this study, we investigated how the genetic loss of flt-1 differentially affects the branching complexity of vascular networks in tissues despite similar effects on endothelial sprouting. We selectively ablated flt-1 in the post-natal retina and found that maximum induction of flt-1 loss resulted in alterations in endothelial sprouting and filopodial extension, ultimately yielding hyper-branched networks in the absence of changes in retinal astrocyte architecture. The mosaic deletion of flt-1 revealed that sprouting endothelial cells flanked by flt-1-/- regions of vasculature more extensively associated with underlying astrocytes and exhibited aberrant sprouting, independent of the tip cell genotype. Overall, our data support a model in which tissue patterning features, such as retinal astrocytes, integrate with flt-1-regulated angiogenic molecular and cellular mechanisms to yield optimal vessel patterning for a given tissue.

Microvascular bioengineering: a focus on pericytes

Capillaries within the microcirculation are essential for oxygen delivery and nutrient/waste exchange, among other critical functions. Microvascular bioengineering approaches have sought to recapitulate many key features of these capillary networks, with an increasing appreciation for the necessity of incorporating vascular pericytes. Here, we briefly review established and more recent insights into important aspects of pericyte identification and function within the microvasculature. We then consider the importance of including vascular pericytes in various bioengineered microvessel platforms including 3D culturing and microfluidic systems. We also discuss how vascular pericytes are a vital component in the construction of computational models that simulate microcirculation phenomena including angiogenesis, microvascular biomechanics, and kinetics of exchange across the vessel wall. In reviewing these topics, we highlight the notion that incorporating pericytes into microvascular bioengineering applications will increase their utility and accelerate the translation of basic discoveries to clinical solutions for vascular-related pathologies.

Agent-based modeling of morphogenetic systems: Advantages and challenges

The complexity of morphogenesis poses a fundamental challenge to understanding the mechanisms governing the formation of biological patterns and structures. Over the past century, numerous processes have been identified as critically contributing to morphogenetic events, but the interplay between the various components and aspects of pattern formation have been much harder to grasp. The combination of traditional biology with mathematical and computational methods has had a profound effect on our current understanding of morphogenesis and led to significant insights and advancements in the field. In particular, the theoretical concepts of reaction–diffusion systems and positional information, proposed by Alan Turing and Lewis Wolpert, respectively, dramatically influenced our general view of morphogenesis, although typically in isolation from one another. In recent years, agent-based modeling has been emerging as a consolidation and implementation of the two theories within a single framework. Agent-based models (ABMs) are unique in their ability to integrate combinations of heterogeneous processes and investigate their respective dynamics, especially in the context of spatial phenomena. In this review, we highlight the benefits and technical challenges associated with ABMs as tools for examining morphogenetic events. These models display unparalleled flexibility for studying various morphogenetic phenomena at multiple levels and have the important advantage of informing future experimental work, including the targeted engineering of tissues and organs.

Computational Modeling to Quantify the Contributions of VEGFR1, VEGFR2, and Lateral Inhibition in Sprouting Angiogenesis

Sprouting angiogenesis is a necessary process in regeneration and development as well as in tumorigenesis. VEGF-A is the main pro-angiogenic chemoattractant and it can bind to the decoy receptor VEGFR1 or to VEGFR2 to induce sprouting. Active sprout cells express Dll4, which binds to Notch1 on neighboring cells, in turn inhibiting VEGFR2 expression. It is known that the balance between VEGFR2 and VEGFR1 determines tip selection and network architecture, however the quantitative interrelationship of the receptors and their interrelated balances, also with relation to Dll4-Notch1 signaling, remains yet largely unknown. Here, we present an agent-based computer model of sprouting angiogenesis, integrating VEGFR1 and VEGFR2 in a detailed model of cellular signaling. Our model reproduces experimental data on VEGFR1 knockout. We show that soluble VEGFR1 improves the efficiency of angiogenesis by directing sprouts away from existing cells over a wide range of parameters. Our analysis unravels the relevance of the stability of the active notch intracellular domain as a dominating hub in this regulatory network. Our analysis quantitatively dissects the regulatory interactions in sprouting angiogenesis. Because we use a detailed model of intracellular signaling, the results of our analysis are directly linked to biological entities. We provide our computational model and simulation engine for integration in complementary modeling approaches.

Soluble VEGFR1 signaling guides vascular patterns into dense branching morphologies

Vascular patterning is a key process during development and disease. The diffusive decoy receptor sVEGFR1 (sFlt1) is a known regulator of endothelial cell behavior, yet the mechanism by which it controls vascular structure is little understood. We propose computational models to shed light on how vascular patterning is guided by self-organized gradients of the VEGF/sVEGFR1 factors. We demonstrate that a diffusive inhibitor can generate structures with a dense branching morphology in models where the activator elicits directed growth. Inadequate presence of the inhibitor leads to compact growth, while excessive production of the inhibitor blocks expansion and stabilizes existing structures. Model predictions were compared with time-resolved experimental data obtained from endothelial sprout kinetics in fibrin gels. In the presence of inhibitory antibodies against VEGFR1 vascular sprout density increases while the speed of sprout expansion remains unchanged. Thus, the rate of secretion and stability of extracellular sVEGFR1 can modulate vascular sprout density.

Programming Morphogenesis through Systems and Synthetic Biology

Mammalian tissue development is an intricate, spatiotemporal process of self-organization that emerges from gene regulatory networks of differentiating stem cells. A major goal in stem cell biology is to gain a sufficient understanding of gene regulatory networks and cell-cell interactions to enable the reliable and robust engineering of morphogenesis. Here, we review advances in synthetic biology, single cell genomics, and multiscale modeling, which, when synthesized, provide a framework to achieve the ambitious goal of programming morphogenesis in complex tissues and organoids.

The temporal basis of angiogenesis

The process of new blood vessel growth (angiogenesis) is highly dynamic, involving complex coordination of multiple cell types. Though the process must carefully unfold over time to generate functional, well-adapted branching networks, we seldom hear about the time-based properties of angiogenesis, despite timing being central to other areas of biology. Here, we present a novel, time-based formulation of endothelial cell behaviour during angiogenesis and discuss a flurry of our recent, integrated in silico/in vivo studies, put in context to the wider literature, which demonstrate that tissue conditions can locally adapt the timing of collective cell behaviours/decisions to grow different vascular network architectures. A growing array of seemingly unrelated ‘temporal regulators’ have recently been uncovered, including tissue derived factors (e.g. semaphorins or the high levels of VEGF found in cancer) and cellular processes (e.g. asymmetric cell division or filopodia extension) that act to alter the speed of cellular decisions to migrate. We will argue that ‘temporal adaptation’ provides a novel account of organ/disease-specific vascular morphology and reveals ‘timing’ as a new target for therapeutics. We therefore propose and explain a conceptual shift towards a ‘temporal adaptation’ perspective in vascular biology, and indeed other areas of biology where timing remains elusive.

This article is part of the themed issue ‘Systems morphodynamics: understanding the development of tissue hardware’.

Chemoprotection Across the Tumor Border: Cancer Cell Response to Doxorubicin Depends on Stromal Fibroblast Ratios and Interstitial Therapeutic Transport

INTRODUCTION

Increasing evidence suggests that the tumor microenvironment reduces therapeutic delivery and may lead to chemotherapeutic resistance. At tumor borders, drug is convectively transported across a unique microenvironment composed of inverse gradients of stromal and tumor cells. These regions are particularly important to overall survival, as they are often missed through surgical intervention and contain many invading cells, often responsible for metastatic spread. An understanding of how cells in this tumor-border region respond to chemotherapy could begin to elucidate the role of transport and intercellular interactions in relation to chemoresistance. Here we examine the contribution of drug transport and stromal fibroblasts to breast cancer response to doxorubicin using in silico and in vitro models of the tumor-stroma interface.

METHODS

2D culture systems were utilized to determine the effects of modulated ratios of fibroblasts and cancer cells on overall cancer cell viability. A homogenous breast mimetic in vitro 3D collagen I-based hydrogel system, with drug delivered via pressure driven flow (0.5 µm/s), was developed to determine the effects of transport and fibroblasts on doxorubicin treatment efficacy. Using a novel layered tumor bulk-to-stroma transition in vitro 3D hydrogel model, ratios of MDA-MB-231s and fibroblasts were seeded in successive layers creating cellular gradients, yielding insight into region specific cancer cell viability at the tumor border. In silico models, utilizing concentration profiles developed in COMSOL Multiphysics, were optimized for time dependent viability prediction and confirmation of in vitro findings.

RESULTS

In general, the addition of fibroblasts increased viability of cancer cells exposed to doxorubicin, indicating a protective effect of co-culture. More specifically, however, modulating ratios of cancer cells (MDA-MB-231):fibroblasts in 2D co-cultures, to mimic the tumor-stroma transition, resulted in a linear decrease in cancer cell viability from 77% (4:1) to 44% (1:4). Similar trends were seen in the breast-mimetic in vitro 3D collagen I-based homogenous hydrogel system. Our in vitro and in silico tumor border models indicate that MDA-MB-231s at the top of the gel, indicative of the tumor bulk, receive the greatest concentration of drug for the longest time, yet cellular death is lowest in this region. This trend is reversed for MDA-MB-231s alone.

CONCLUSION

Together, our data indicate that fibroblasts are chemoprotective at lower density, resulting in less tumor death in regions of higher chemotherapy concentration. Additionally, chemotherapeutic agent transport properties can modulate this effect.

Dynamic, heterogeneous endothelial Tie2 expression and capillary blood flow during microvascular remodeling

Microvascular endothelial cell heterogeneity and its relationship to hemodynamics remains poorly understood due to a lack of sufficient methods to examine these parameters in vivo at high resolution throughout an angiogenic network. The availability of surrogate markers for functional vascular proteins, such as green fluorescent protein, enables expression in individual cells to be followed over time using confocal microscopy, while photoacoustic microscopy enables dynamic measurement of blood flow across the network with capillary-level resolution. We combined these two non-invasive imaging modalities in order to spatially and temporally analyze biochemical and biomechanical drivers of angiogenesis in murine corneal neovessels. By stimulating corneal angiogenesis with an alkali burn in Tie2-GFP fluorescent-reporter mice, we evaluated how onset of blood flow and surgically-altered blood flow affects Tie2-GFP expression. Our study establishes a novel platform for analyzing heterogeneous blood flow and fluorescent reporter protein expression across a dynamic microvascular network in an adult mammal.

Mathematical and Computational Modeling in Complex Biological Systems

The biological process and molecular functions involved in the cancer progression remain difficult to understand for biologists and clinical doctors. Recent developments in high-throughput technologies urge the systems biology to achieve more precise models for complex diseases. Computational and mathematical models are gradually being used to help us understand the omics data produced by high-throughput experimental techniques. The use of computational models in systems biology allows us to explore the pathogenesis of complex diseases, improve our understanding of the latent molecular mechanisms, and promote treatment strategy optimization and new drug discovery. Currently, it is urgent to bridge the gap between the developments of high-throughput technologies and systemic modeling of the biological process in cancer research. In this review, we firstly studied several typical mathematical modeling approaches of biological systems in different scales and deeply analyzed their characteristics, advantages, applications, and limitations. Next, three potential research directions in systems modeling were summarized. To conclude, this review provides an update of important solutions using computational modeling approaches in systems biology.

Multi-class and multi-scale models of complex biological phenomena

Computational modeling has significantly impacted our ability to analyze vast (and exponentially increasing) quantities of experimental data for a variety of applications, such as drug discovery and disease forecasting. Single-scale, single-class models persist as the most common group of models, but biological complexity often demands more sophisticated approaches. This review surveys modeling approaches that are multi-class (incorporating multiple model types) and/or multi-scale (accounting for multiple spatial or temporal scales) and describes how these models, and combinations thereof, should be used within the context of the problem statement. We end by highlighting agent-based models as an intuitive, modular, and flexible framework within which multi-scale and multi-class models can be implemented.