Multiscale computational analysis of Xenopus laevis morphogenesis reveals key insights of systems-level behavior

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.

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.

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 immuno-biology for organ transplantation and regenerative medicine

Organ transplantation and regenerative medicine are adopted platforms that provide replacement tissues and organs from natural or engineered sources. Acceptance, tolerance and rejection depend greatly on the proper control of the immune response against graft antigens, motivating the development of immunological and genetical therapies that prevent organ failure. They rely on a complete, or partial, understanding of the immune system. Ultimately, they are innovative technologies that ensure permanent graft tolerance and indefinite graft survival through the modulation of the immune system. Computational immunology has arisen as a tool towards a mechanistic understanding of the biological and physicochemical processes surrounding an immune response. It comprehends theoretical and computational frameworks that simulate immuno-biological systems. The challenge is centered on the multi-scale character of the immune system that spans from atomistic scales, during peptide-epitope and protein interactions, to macroscopic scales, for lymph transport and organ-organ reactions. In this paper, we discuss, from an engineering perspective, the biological processes that are involved during the immune response of organ transplantation. Previous computational efforts, including their characteristics and visible limitations, are described. Finally, future perspectives and challenges are listed to motivate further developments.

Novel multiscale modeling tool applied to Pseudomonas aeruginosa biofilm formation

Multiscale modeling is used to represent biological systems with increasing frequency and success. Multiscale models are often hybrids of different modeling frameworks and programming languages. We present the MATLAB-NetLogo extension (MatNet) as a novel tool for multiscale modeling. We demonstrate the utility of the tool with a multiscale model of Pseudomonas aeruginosa biofilm formation that incorporates both an agent-based model (ABM) and constraint-based metabolic modeling. The hybrid model correctly recapitulates oxygen-limited biofilm metabolic activity and predicts increased growth rate via anaerobic respiration with the addition of nitrate to the growth media. In addition, a genome-wide survey of metabolic mutants and biofilm formation exemplifies the powerful analyses that are enabled by this computational modeling tool.

Computational modeling of interacting VEGF and soluble VEGF receptor concentration gradients

Experimental data indicates that soluble vascular endothelial growth factor (VEGF) receptor 1 (sFlt-1) modulates the guidance cues provided to sprouting blood vessels by VEGF-A. To better delineate the role of sFlt-1 in VEGF signaling, we have developed an experimentally based computational model. This model describes dynamic spatial transport of VEGF, and its binding to receptors Flt-1 and Flk-1, in a mouse embryonic stem cell model of vessel morphogenesis. The model represents the local environment of a single blood vessel. Our simulations predict that blood vessel secretion of sFlt-1 and increased local sFlt-1 sequestration of VEGF results in decreased VEGF–Flk-1 levels on the sprout surface. In addition, the model predicts that sFlt-1 secretion increases the relative gradient of VEGF–Flk-1 along the sprout surface, which could alter endothelial cell perception of directionality cues. We also show that the proximity of neighboring sprouts may alter VEGF gradients, VEGF receptor binding, and the directionality of sprout growth. As sprout distances decrease, the probability that the sprouts will move in divergent directions increases. This model is a useful tool for determining how local sFlt-1 and VEGF gradients contribute to the spatial distribution of VEGF receptor binding, and can be used in conjunction with experimental data to explore how multi-cellular interactions and relationships between local growth factor gradients drive angiogenesis.

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.

Toward a multi-scale computational model of arterial adaptation in hypertension: verification of a multi-cell agent based model

Agent-based models (ABMs) represent a novel approach to study and simulate complex mechano chemo-biological responses at the cellular level. Such models have been used to simulate a variety of emergent responses in the vasculature, including angiogenesis and vasculogenesis. Although not used previously to study large vessel adaptations, we submit that ABMs will prove equally useful in such studies when combined with well-established continuum models to form multi-scale models of tissue-level phenomena. In order to couple agent-based and continuum models, however, there is a need to ensure that each model faithfully represents the best data available at the relevant scale and that there is consistency between models under baseline conditions. Toward this end, we describe the development and verification of an ABM of endothelial and smooth muscle cell responses to mechanical stimuli in a large artery. A refined rule-set is proposed based on a broad literature search, a new scoring system for assigning confidence in the rules, and a parameter sensitivity study. To illustrate the utility of these new methods for rule selection, as well as the consistency achieved with continuum-level models, we simulate the behavior of a mouse aorta during homeostasis and in response to both transient and sustained increases in pressure. The simulated responses depend on the altered cellular production of seven key mitogenic, synthetic, and proteolytic biomolecules, which in turn control the turnover of intramural cells and extracellular matrix. These events are responsible for gross changes in vessel wall morphology. This new ABM is shown to be appropriately stable under homeostatic conditions, insensitive to transient elevations in blood pressure, and responsive to increased intramural wall stress in hypertension.

Activity of the RhoU/Wrch1 GTPase is critical for cranial neural crest cell migration

The neural crest (NC) is a stem cell-like population that arises at the border of neural and non-neural ectoderm. During development, NC undergoes an epithelio-mesenchymal transition (EMT), i.e. loss of epithelial junctions and acquisition of pro-migratory properties, invades the entire embryo and differentiates into a wide diversity of terminal tissues. We have studied the implication of Rho pathways in NC development and previously showed that RhoV is required for cranial neural crest (CNC) cell specification. We show here that the non-canonical Wnt response rhoU/wrch1 gene, closely related to rhoV, is also expressed in CNC cells but at later stages. Using both gain- and loss-of-function experiments, we demonstrate that the level of RhoU expression is critical for CNC cell migration and subsequent differentiation into craniofacial cartilages. In in vitro cultures, RhoU activates pathways that cooperate with PAK1 and Rac1 in epithelial adhesion, cell spreading and directional cell migration. These data support the conclusion that RhoU is an essential regulator of CNC cell migration.

Systems biology of embryogenesis

The development of a complete organism from a single cell involves extraordinarily complex orchestration of biological processes that vary intricately across space and time. Systems biology seeks to describe how all elements of a biological system interact in order to understand, model and ultimately predict aspects of emergent biological processes. Embryogenesis represents an extraordinary opportunity (and challenge) for the application of systems biology. Systems approaches have already been used successfully to study various aspects of development, from complex intracellular networks to four-dimensional models of organogenesis. Going forward, great advancements and discoveries can be expected from systems approaches applied to embryogenesis and developmental biology.

So what do we really mean when we say that systems biology is holistic?

BACKGROUND

An old debate has undergone a resurgence in systems biology: that of reductionism versus holism. At least 35 articles in the systems biology literature since 2003 have touched on this issue. The histories of holism and reductionism in the philosophy of biology are reviewed, and the current debate in systems biology is placed in context.

RESULTS

Inter-theoretic reductionism in the strict sense envisaged by its creators from the 1930s to the 1960s is largely impractical in biology, and was effectively abandoned by the early 1970s in favour of a more piecemeal approach using individual reductive explanations. Classical holism was a stillborn theory of the 1920s, but the term survived in several fields as a loose umbrella designation for various kinds of anti-reductionism which often differ markedly. Several of these different anti-reductionisms are on display in the holistic rhetoric of the recent systems biology literature. This debate also coincides with a time when interesting arguments are being proposed within the philosophy of biology for a new kind of reductionism.

CONCLUSIONS

Engaging more deeply with these issues should sharpen our ideas concerning the philosophy of systems biology and its future best methodology. As with previous decisive moments in the history of biology, only those theories that immediately suggest relatively easy experiments will be winners.

Applications of genome-scale metabolic reconstructions

The availability and utility of genome-scale metabolic reconstructions have exploded since the first genome-scale reconstruction was published a decade ago. Reconstructions have now been built for a wide variety of organisms, and have been used toward five major ends: (1) contextualization of high-throughput data, (2) guidance of metabolic engineering, (3) directing hypothesis-driven discovery, (4) interrogation of multi-species relationships, and (5) network property discovery. In this review, we examine the many uses and future directions of genome-scale metabolic reconstructions, and we highlight trends and opportunities in the field that will make the greatest impact on many fields of biology.

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.

Interpreting endocrine disruption from an integrative biology perspective

The ability of reductionism to advance our understanding of complex biological phenomena is limited. The ecological developmental biology (eco-devo) movement rejects the notion that development is merely the unfolding of a genetic program. Fetal exposure to environmental endocrine disruptors may contribute to the increased incidence of male genital tract malformations, decreased sperm quality, several neoplasms, and altered body weight. Here we discuss problems hindering the study of endocrine disruption (reductionist stance, technically driven research biases, and study of single end points, chemicals and exposure periods). We propose the study of both upward and downward causation and a Systems Biology approach to develop quantitative mathematical models for use in computer simulations that would generate testable predictions. This integrative approach will allow the simultaneous consideration of organismal (systemic) effects and effects on various organ systems. It will promote the identification of similar and unique effects of different endocrine disruptors, and their inter-relationships.

A computational approach to understand in vitro alveolar morphogenesis

Primary human alveolar type II (AT II) epithelial cells maintained in Matrigel cultures form alveolar-like cysts (ALCs) using a cytogenesis mechanism that is different from that of other studied epithelial cell types: neither proliferation nor death is involved. During ALC formation, AT II cells engage simultaneously in fundamentally different, but not fully characterized activities. Mechanisms enabling these activities and the roles they play during different process stages are virtually unknown. Identifying, characterizing, and understanding the activities and mechanisms are essential to achieving deeper insight into this fundamental feature of morphogenesis. That deeper insight is needed to answer important questions. When and how does an AT cell choose to switch from one activity to another? Why does it choose one action rather than another? We report obtaining plausible answers using a rigorous, multi-attribute modeling and simulation approach that leveraged earlier efforts by using new, agent and object-oriented capabilities. We discovered a set of cell-level operating principles that enabled in silico cells to self-organize and generate systemic cystogenesis phenomena that are quantitatively indistinguishable from those observed in vitro. Success required that the cell components be quasi-autonomous. As simulation time advances, each in silico cell autonomously updates its environment information to reclassify its condition. It then uses the axiomatic operating principles to execute just one action for each possible condition. The quasi-autonomous actions of individual in silico cells were sufficient for developing stable cyst-like structures. The results strengthen in silico to in vitro mappings at three levels: mechanisms, behaviors, and operating principles, thereby achieving a degree of validation and enabling answering the questions posed. We suggest that the in silico operating principles presented may have a biological counterpart and that a semiquantitative mapping exists between in silico causal events and in vitro causal events.