An integrated agent-mathematical model of the effect of intercellular signalling via the epidermal growth factor receptor on cell proliferation

Modelling the Tumour Microenvironment, but What Exactly Do We Mean by "Model"?

The Oxford English Dictionary includes 17 definitions for the word "model" as a noun and another 11 as a verb. Therefore, context is necessary to understand the meaning of the word model. For instance, "model railways" refer to replicas of railways and trains at a smaller scale and a "model student" refers to an exemplary individual. In some cases, a specific context, like cancer research, may not be sufficient to provide one specific meaning for model. Even if the context is narrowed, specifically, to research related to the tumour microenvironment, "model" can be understood in a wide variety of ways, from an animal model to a mathematical expression. This paper presents a review of different "models" of the tumour microenvironment, as grouped by different definitions of the word into four categories: model organisms, in vitro models, mathematical models and computational models. Then, the frequencies of different meanings of the word "model" related to the tumour microenvironment are measured from numbers of entries in the MEDLINE database of the United States National Library of Medicine at the National Institutes of Health. The frequencies of the main components of the microenvironment and the organ-related cancers modelled are also assessed quantitatively with specific keywords. Whilst animal models, particularly xenografts and mouse models, are the most commonly used "models", the number of these entries has been slowly decreasing. Mathematical models, as well as prognostic and risk models, follow in frequency, and these have been growing in use.

Cell-Seeded Biomaterial Scaffolds: The Urgent Need for Unanswered Accelerated Angiogenesis

One of the most arduous challenges in tissue engineering is neovascularization, without which there is a lack of nutrients delivered to a target tissue. Angiogenesis should be completed at an optimal density and within an appropriate period of time to prevent cell necrosis. Failure to meet this challenge brings about poor functionality for the tissue in comparison with the native tissue, extensively reducing cell viability. Prior studies devoted to angiogenesis have provided researchers with some biomaterial scaffolds and cell choices for angiogenesis. For example, while most current angiogenesis approaches require a variety of stimulatory factors ranging from biomechanical to biomolecular to cellular, some other promising stimulatory factors have been underdeveloped (such as electrical, topographical, and magnetic). When it comes to choosing biomaterial scaffolds in tissue engineering for angiogenesis, key traits rush to mind including biocompatibility, appropriate physical and mechanical properties (adhesion strength, shear stress, and malleability), as well as identifying the appropriate biomaterial in terms of stability and degradation profile, all of which may leave essential trace materials behind adversely influencing angiogenesis. Nevertheless, the selection of the best biomaterial and cells still remains an area of hot dispute as such previous studies have not sufficiently classified, integrated, or compared approaches. To address the aforementioned need, this review article summarizes a variety of natural and synthetic scaffolds including hydrogels that support angiogenesis. Furthermore, we review a variety of cell sources utilized for cell seeding and influential factors used for angiogenesis with a concentrated focus on biomechanical factors, with unique stimulatory factors. Lastly, we provide a bottom-to-up overview of angiogenic biomaterials and cell selection, highlighting parameters that need to be addressed in future studies.

Agent-Based Modeling of Complex Molecular Systems

The seamless integration of laboratory experiments and detailed computational modeling provides an exciting route to uncovering many new insights into complex biological processes. In particular, the development of agent-based modeling using supercomputers has provided new opportunities for highly detailed, validated simulations that provide the researcher with greater understanding of these processes and new directions for investigation. This chapter examines some of the principles behind the powerful computational framework FLAME and its application in a number of different areas with a more detailed look at a particular signaling example involving the NF-κB cascade.

Are melanocortin peptides future therapeutics for cutaneous wound healing?

Cutaneous wound healing is a complex process divided into different phases, that is an inflammatory, proliferative and remodelling phase. During these phases, a variety of resident skin cell types but also cells of the immune system orchestrate the healing process. In the last year, it has been shown that the majority of cutaneous cell types express the melanocortin 1 receptor (MC1R) that binds α-melanocyte-stimulating hormone (α-MSH) with high affinity and elicits pleiotropic biological effects, for example modulation of inflammation and immune responses, cytoprotection, antioxidative defense and collagen turnover. Truncated α-MSH peptides such as Lys-Pro-Val (KPV) as well as derivatives like Lys-d-Pro-Thr (KdPT), the latter containing the amino acid sequence 193-195 of interleukin-1β, have been found to possess anti-inflammatory effects but to lack the pigment-inducing activity of α-MSH. We propose here that such peptides are promising future candidates for the treatment of cutaneous wounds and skin ulcers. Experimental approaches in silico, in vitro, ex vivo and in animal models are outlined. This is followed by an unbiased discussion of the pro and contra arguments of such peptides as future candidates for the therapeutic management of cutaneous wounds and a review of the so-far available data on melanocortin peptides and derivatives in wound healing.

A 3D self-organizing multicellular epidermis model of barrier formation and hydration with realistic cell morphology based on EPISIM

The epidermis and the stratum corneum (SC) as its outermost layer have evolved to protect the body from evaporative water loss to the environment. To morphologically represent the extremely flattened cells of the SC - and thereby the epidermal barrier - in a multicellular computational model, we developed a 3D biomechanical model (BM) based on ellipsoid cell shapes. We integrated the BM in the multicellular modelling and simulation platform EPISIM. We created a cell behavioural model (CBM) with EPISIM encompassing regulatory feedback loops between the epidermal barrier, water loss to the environment, and water and calcium flow within the tissue. This CBM allows a small number of stem cells to initiate self-organizing epidermal stratification, yielding the spontaneous emergence of water and calcium gradients comparable to experimental data. We find that the 3D in silico epidermis attains homeostasis most quickly at high ambient humidity, and once in homeostasis the epidermal barrier robustly buffers changes in humidity. Our model yields an in silico epidermis with a previously unattained realistic morphology, whose cell neighbour topology is validated with experimental data obtained from in vivo images. This work paves the way to computationally investigate how an impaired SC barrier precipitates disease.

Agent-Based Modelling in Multicellular Systems Biology

This chapter aims at discussing the content of multi-agent based simulation (MABS) applied to computational biology i.e., to modelling and simulating biological systems by means of computational models, methodologies, and frameworks. In particular, the adoption of agent-based modelling (ABM) in the field of multicellular systems biology is explored, focussing on the challenging scenarios of developmental biology. After motivating why agent-based abstractions are critical in representing multicellular systems behaviour, MABS is discussed as the source of the most natural and appropriate mechanism for analysing the self-organising behaviour of systems of cells. As a case study, an application of MABS to the development of Drosophila Melanogaster is finally presented, which exploits the ALCHEMIST platform for agent-based simulation.

Sources of variability in cytosolic calcium transients triggered by stimulation of homogeneous uro-epithelial cell monolayers

Epithelial tissue structure is the emergent outcome of the interactions between large numbers of individual cells. Experimental cell biology offers an important tool to unravel these complex interactions, but current methods of analysis tend to be limited to mean field approaches or representation by selected subsets of cells. This may result in bias towards cells that respond in a particular way and/or neglect local, context-specific cell responses. Here, an automated algorithm was applied to examine in detail the individual calcium transients evoked in genetically homogeneous, but asynchronous populations of cultured non-immortalized normal human urothelial cells when subjected to either the global application of an external agonist or a localized scratch wound. The recorded calcium transients were classified automatically according to a set of defined metrics and distinct sub-populations of cells that responded in qualitatively different ways were observed. The nature of this variability in the homogeneous cell population was apportioned to two sources: intrinsic variation in individual cell responses and extrinsic variability due to context-specific factors of the environment, such as spatial heterogeneity. Statistically significant variation in the features of the calcium transients evoked by scratch wounding according to proximity to the wound edge was identified. The manifestation of distinct sub-populations of cells is considered central to the coordination of population-level response resulting in wound closure.

Mosaic gene network modelling identified new regulatory mechanisms in HCV infection

Modelling of gene networks is widely used in systems biology to study the functioning of complex biological systems. Most of the existing mathematical modelling techniques are useful for analysis of well-studied biological processes, for which information on rates of reactions is available. However, complex biological processes such as those determining the phenotypic traits of organisms or pathological disease processes, including pathogen-host interactions, involve complicated cross-talk between interacting networks. Furthermore, the intrinsic details of the interactions between these networks are often missing. In this study, we developed an approach, which we call mosaic network modelling, that allows the combination of independent mathematical models of gene regulatory networks and, thereby, description of complex biological systems. The advantage of this approach is that it allows us to generate the integrated model despite the fact that information on molecular interactions between parts of the model (so-called mosaic fragments) might be missing. To generate a mosaic mathematical model, we used control theory and mathematical models, written in the form of a system of ordinary differential equations (ODEs). In the present study, we investigated the efficiency of this method in modelling the dynamics of more than 10,000 simulated mosaic regulatory networks consisting of two pieces. Analysis revealed that this approach was highly efficient, as the mean deviation of the dynamics of mosaic network elements from the behaviour of the initial parts of the model was less than 10%. It turned out that for construction of the control functional, data on perturbation of one or two vertices of the mosaic piece are sufficient. Further, we used the developed method to construct a mosaic gene regulatory network including hepatitis C virus (HCV) as the first piece and the tumour necrosis factor (TNF)-induced apoptosis and NF-κB induction pathways as the second piece. Thus, the mosaic model integrates the model of HCV subgenomic replicon replication with the model of TNF-induced apoptosis and NF-κB induction. Analysis of the mosaic model revealed that the regulation of TNF-induced signaling by the HCV network is crucially dependent on the RIP1, TRADD, TRAF2, FADD, IKK, IκBα, c-FLIP, and BAR genes. Overall, the developed mosaic gene network modelling approach demonstrated good predictive power and allowed the prediction of new regulatory nodes in HCV action on apoptosis and the NF-κB pathway. Those theoretical predictions could be a basis for further experimental verification.

The modulatory effect of cell–cell contact on the tumourigenic potential of pre-malignant epithelial cells: a computational exploration

Malignant development cannot be attributed alone to genetic changes in a single cell, but occurs as a result of the complex interplay between the failure of cellular regulation mechanisms and the presence of a permissive microenvironment. Although E-cadherin is classified as a 'metastasis suppressor' owing to its role in intercellular adhesion, the observation that it may be downregulated at a premalignant stage is indicative of additional roles in neoplastic development. We have used an agent-based computational model to explore the emergent behaviour resulting from the interaction of single and subpopulations of E-cadherin-compromised cells with unaffected normal epithelial cells within a monolayer environment. We have extended this to investigate the importance of local tissue perturbations in the form of scratch-wounding, or ablation of randomly-dispersed normal cells, on the growth of a single cell exhibiting E-cadherin loss. Our results suggest that the microenvironment with respect to localized cell density and normal/E-cadherin-compromised neighbours is crucial in determining whether an abnormal individual cell proliferates or remains dormant within the monolayer. These predictions raise important questions relating to the propensity for individual mutations to give rise to disease, and future experimental exploration of these will enhance our understanding of a complex, multifactorial pathological process.

Integration of TGF-β- and EGFR-based signaling pathways using an agent-based model of epithelial restitution

Damage to an epithelial surface disrupts its mechanical and immunologic barrier function and exposes underlying tissues to a potentially hostile external environment. Epithelial restitution occurs quickly to reestablish the barrier and comprises a major part of the immediate host response to injured tissue. Pathways involving transforming growth factor beta and activation of epidermal growth factor receptor are both of critical importance, although cross-pathway interactions have been poorly characterized. Agent-based modeling has been showed to be useful in integrating disparate bodies of knowledge and showing the dynamic consequences of pathway structures and cellular population behavior and is used herein to create an in silico analog of an in vitro scratch assay. The In Vitro Scratch Agent-Based Model consists of agents representing individual epithelial cells in a simulated extracellular matrix. Agents sense signals from the damaged environment and produce effector molecules, leading to their healing behavior. The In Vitro Scratch Agent-Based Model qualitatively matched wound healing dynamics when compared against data from traditional experiments. Putative cross-talk mechanisms were then instantiated into the In Vitro Scratch Agent-Based Model and their relative plausibility examined, suggesting interaction at the receptor tyrosine kinase level. This highlights the utility of dynamic knowledge representation in the integration of pathways previously studied in separate contexts.

Understanding the melanocyte distribution in human epidermis: an agent-based computational model approach

The strikingly even color of human skin is maintained by the uniform distribution of melanocytes among keratinocytes in the basal layer of the human epidermis. In this work, we investigated three possible hypotheses on the mechanism by which the melanocytes and keratinocytes organize themselves to generate this pattern. We let the melanocyte migration be aided by (1) negative chemotaxis due to a substance produced by the melanocytes themselves, or (2) positive chemotaxis due to a substance produced by keratinocytes lacking direct physical contact with a melanocyte, or (3) positive chemotaxis due to a substance produced by keratinocytes in a distance-to-melanocytes dependent manner. The three hypotheses were implemented in an agent-based computational model of cellular interactions in the basal layer of the human epidermis. We found that they generate mutually exclusive predictions that can be tested by existing experimental protocols. This model forms a basis for further understanding of the communication between melanocytes and other skin cells in skin homeostasis.

Immature oxidative stress management as a unifying principle in the pathogenesis of necrotizing enterocolitis: insights from an agent-based model

BACKGROUND

Necrotizing enterocolitis (NEC) is a complex disease involving prematurity, enteral feeding, and bacterial effects. We propose that the underlying initial condition in its pathogenesis is reduced ability of the neonatal gut epithelial cells (NGECs) to clear oxidative stress (OS), and that when such a NGEC population is exposed to enteral feeding, the increased metabolic OS tips the population toward apoptosis, inflammation, bacterial activation, and eventual necrosis. The multi-factorial complexity of NEC requires characterization with computational modeling, and herein, we used an agent-based model (ABM) to instantiate and examine our unifying hypothesis of the pathogenesis of NEC.

METHODS

An ABM of the neonatal gut was created with NGEC computational agents incorporating rules for pathways for OS, p53, tight junctions, Toll-like receptor (TLR)-4, nitric oxide, and nuclear factor-kappa beta (NF-κB). The modeled bacteria activated TLR-4 on contact with NGECs. Simulations included parameter sweeps of OS response, response to feeding, addition of bacteria, and alterations in gut mucus production.

RESULTS

The ABM reproduced baseline cellular respiration and clearance of OS. Reduction in OS clearance consistent with clinical NEC led to senescence, apoptosis, or inflammation, with disruption of tight junctions, but rarely to NGEC necrosis. An additional "hit" of bacteria activating TLR-4 potentiated a shift to NGEC necrosis across the entire population. The mucus layer was modeled to limit bacterial-NGEC interactions and reduce this effect, but concomitant apoptosis in the goblet cell population reduced the efficacy of the mucus layer and limited its protective effect in simulated experiments. This finding suggests a means by which increased apoptosis at the cellular population level can lead to a transition to the necrosis outcome.

CONCLUSIONS

Our ABM incorporates known components of NEC and demonstrates that impaired OS management can lead to apoptosis and inflammation of NGECs, rendering the system susceptible to an additional insult involving regionalized mucus barrier failure and TLR-4 activation, which potentiates the necrosis outcome. This type of integrative dynamic knowledge representation can be a useful adjunct to help guide and contextualize research.

Normal morphogenesis of epithelial tissues and progression of epithelial tumors

Epithelial cells organize into various tissue architectures that largely maintain their structure throughout the life of an organism. For decades, the morphogenesis of epithelial tissues has fascinated scientists at the interface of cell, developmental, and molecular biology. Systems biology offers ways to combine knowledge from these disciplines by building integrative models that are quantitative and predictive. Can such models be useful for gaining a deeper understanding of epithelial morphogenesis? Here, we take inventory of some recurring themes in epithelial morphogenesis that systems approaches could strive to capture. Predictive understanding of morphogenesis at the systems level would prove especially valuable for diseases such as cancer, where epithelial tissue architecture is profoundly disrupted.

Modelling complex biological systems using an agent-based approach

Many of the complex systems found in biology are comprised of numerous components, where interactions between individual agents result in the emergence of structures and function, typically in a highly dynamic manner. Often these entities have limited lifetimes but their interactions both with each other and their environment can have profound biological consequences. We will demonstrate how modelling these entities, and their interactions, can lead to a new approach to experimental biology bringing new insights and a deeper understanding of biological systems.

Agent-based dynamic knowledge representation of Pseudomonas aeruginosa virulence activation in the stressed gut: Towards characterizing host-pathogen interactions in gut-derived sepsis

Background

There is a growing realization that alterations in host-pathogen interactions (HPI) can generate disease phenotypes without pathogen invasion. The gut represents a prime region where such HPI can arise and manifest. Under normal conditions intestinal microbial communities maintain a stable, mutually beneficial ecosystem. However, host stress can lead to changes in environmental conditions that shift the nature of the host-microbe dialogue, resulting in escalation of virulence expression, immune activation and ultimately systemic disease. Effective modulation of these dynamics requires the ability to characterize the complexity of the HPI, and dynamic computational modeling can aid in this task. Agent-based modeling is a computational method that is suited to representing spatially diverse, dynamical systems. We propose that dynamic knowledge representation of gut HPI with agent-based modeling will aid in the investigation of the pathogenesis of gut-derived sepsis.

Methodology/Principal Findings

An agent-based model (ABM) of virulence regulation in Pseudomonas aeruginosa was developed by translating bacterial and host cell sense-and-response mechanisms into behavioral rules for computational agents and integrated into a virtual environment representing the host-microbe interface in the gut. The resulting gut milieu ABM (GMABM) was used to: 1) investigate a potential clinically relevant laboratory experimental condition not yet developed - i.e. non-lethal transient segmental intestinal ischemia, 2) examine the sufficiency of existing hypotheses to explain experimental data - i.e. lethality in a model of major surgical insult and stress, and 3) produce behavior to potentially guide future experimental design - i.e. suggested sample points for a potential laboratory model of non-lethal transient intestinal ischemia. Furthermore, hypotheses were generated to explain certain discrepancies between the behaviors of the GMABM and biological experiments, and new investigatory avenues proposed to test those hypotheses.

Conclusions/Significance

Agent-based modeling can account for the spatio-temporal dynamics of an HPI, and, even when carried out with a relatively high degree of abstraction, can be useful in the investigation of system-level consequences of putative mechanisms operating at the individual agent level. We suggest that an integrated and iterative heuristic relationship between computational modeling and more traditional laboratory and clinical investigations, with a focus on identifying useful and sufficient degrees of abstraction, will enhance the efficiency and translational productivity of biomedical research.

T cell responses in lymph nodes

Activation of T cells by antigen-presenting cells (APCs) in lymph nodes (LNs) is a key initiating event in many immune responses. Our understanding of this process has been both improved and complicated in recent years by evidence from techniques such as intravital microscopy that has revealed new levels of dynamism in the interaction of T cells and APCs. In particular, the complex motility of T cells within LNs, and their serial interactions with many APCs, imply that earlier static models of T cell activation need to be updated. Here we review the first attempts to model T cell interactions with APCs in LNs that incorporate simulations of T cell motility, based on experimental observations. We show that lattice-based modeling approaches are the dominant trend in these models, and then chart a possible course for development of these models toward spatially-resolved models of immune responses within LNs.

Computational modeling of epithelial tissues

There is an extensive literature on the computational modeling of epithelial tissues at all levels from subcellular to whole tissue. This review concentrates on behavior at the individual cell to whole tissue level, and particularly on organizational aspects, and provides an indication of where information from other areas, such as the modeling of angiogenesis, is relevant. The skin, and the lining of all of the body cavities (lung, gut, cervix, bladder etc) are epithelial tissues, which in a topological sense are the boundary between inside and outside the body. They are thin sheets of cells (usually of the order of 0.5 mm thick) without extracellular matrix, have a relatively simple structure, and contain few types of cells. They have important barrier, secretory and transport functions, which are essential for the maintenance of life, so homeostasis and wound healing are important aspects of the behavior of epithelial tissues. Carcinomas originate in epithelial tissues.There are essentially two approaches to modeling tissues--to start at the level of the tissue (i.e., a length scale of the order of 1 mm) and develop generalized equations for behavior (a continuum approach); or to start at the level of the cell (i.e., a length scale of the order of 10 µm) and develop tissue behavior as an emergent property of cellular behavior (an individual-based approach). As will be seen, these are not mutually exclusive approaches, and they come in a variety of flavors.

Differential regulation of growth-promoting signalling pathways by E-cadherin

BACKGROUND

Despite the well-documented association between loss of E-cadherin and carcinogenesis, as well as the link between restoration of its expression and suppression of proliferation in carcinoma cells, the ability of E-cadherin to modulate growth-promoting cell signalling in normal epithelial cells is less well understood and frequently contradictory. The potential for E-cadherin to co-ordinate different proliferation-associated signalling pathways has yet to be fully explored.

METHODOLOGY/PRINCIPAL FINDINGS

Using a normal human urothelial (NHU) cell culture system and following a calcium-switch approach, we demonstrate that the stability of NHU cell-cell contacts differentially regulates the Epidermal Growth Factor Receptor (EGFR)/Extracellular Signal-Regulated Kinase (ERK) and Phosphatidylinositol 3-Kinase (PI3-K)/AKT pathways. We show that stable cell contacts down-modulate the EGFR/ERK pathway, whilst inducing PI3-K/AKT activity, which transiently enhances cell growth at low density. Functional inactivation of E-cadherin interferes with the capacity of NHU cells to form stable calcium-mediated contacts, attenuates E-cadherin-mediated PI3-K/AKT induction and enhances NHU cell proliferation by allowing de-repression of the EGFR/ERK pathway and constitutive activation of β-catenin-TCF signalling.

CONCLUSIONS/SIGNIFICANCE

Our findings provide evidence that E-cadherin can differentially and concurrently regulate specific growth-related signalling pathways in a context-specific fashion, with direct, functional consequences for cell proliferation and population growth. Our observations not only reveal a novel, complex role for E-cadherin in normal epithelial cell homeostasis and tissue regeneration, but also provide the basis for a more complete understanding of the consequences of E-cadherin loss on malignant transformation.

In silico design of treatment strategies in wound healing and bone fracture healing

Wound and bone fracture healing are natural repair processes initiated by trauma. Over the last decade, many mathematical models have been established to investigate the healing processes in silico, in addition to ongoing experimental work. In recent days, the focus of the mathematical models has shifted from simulation of the healing process towards simulation of the impaired healing process and the in silico design of treatment strategies. This review describes the most important causes of failure of the wound and bone fracture healing processes and the experimental models and methods used to investigate and treat these impaired healing cases. Furthermore, the mathematical models that are described address these impaired healing cases and investigate various therapeutic scenarios in silico. Examples are provided to illustrate the potential of these in silico experiments. Finally, limitations of the models and the need for and ability of these models to capture patient specificity and variability are discussed.

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.

A copulas approach to neuronal networks models

Simultaneous recordings from groups of neurons request to improve models. To switch from single unit description to multivariate models describing the coding activity of two or more neurons, we propose to use the copula notion. This mathematical object catches the coupling properties and allows a mathematical description of the dependencies between two or more random variables. Its use is here illustrated by means of toy examples and further applications are discussed.

Agent-based simulation of T-cell activation and proliferation within a lymph node

Recent intravital microscopy experiments have revealed the complex behavior of T cells within lymph nodes. Modeling T-cell responses in lymph nodes now requires integration of cell trafficking and motility with the molecular processes involved in T-cell activation. We describe an agent-based model that allows such integration, in which T cells undertake a random walk through a three-dimensional representation of the lymph node paracortex, integrating signals from dendritic cells (DCs), and proliferating in response. The model accommodates simulation of a large number of T cells packed at realistic densities, and includes dynamic cell trafficking that allows the lymph nodes to swell and shrink as the immune response progresses. The results from the model, including the kinetics of cognate T-cell proliferation and release, and the changes in their avidity profile, are similar to those observed in vivo. We therefore propose that this modeling framework is capable of successfully simulating T-cell activation while also accounting for new spatiotemporal knowledge of how T cells and DCs interact. Although some of the parameters used to drive the model are not yet experimentally validated, the model is capable of testing the effects of alternative values for any parameter on the T-cell response. We intend to refine each aspect of the model in collaboration with both theoreticians and experimentalists.

Monte Carlo analysis of an ODE Model of the Sea Urchin Endomesoderm Network

BACKGROUND

Gene Regulatory Networks (GRNs) control the differentiation, specification and function of cells at the genomic level. The levels of interactions within large GRNs are of enormous depth and complexity. Details about many GRNs are emerging, but in most cases it is unknown to what extent they control a given process, i.e. the grade of completeness is uncertain. This uncertainty stems from limited experimental data, which is the main bottleneck for creating detailed dynamical models of cellular processes. Parameter estimation for each node is often infeasible for very large GRNs. We propose a method, based on random parameter estimations through Monte-Carlo simulations to measure completeness grades of GRNs.

RESULTS

We developed a heuristic to assess the completeness of large GRNs, using ODE simulations under different conditions and randomly sampled parameter sets to detect parameter-invariant effects of perturbations. To test this heuristic, we constructed the first ODE model of the whole sea urchin endomesoderm GRN, one of the best studied large GRNs. We find that nearly 48% of the parameter-invariant effects correspond with experimental data, which is 65% of the expected optimal agreement obtained from a submodel for which kinetic parameters were estimated and used for simulations. Randomized versions of the model reproduce only 23.5% of the experimental data.

CONCLUSION

The method described in this paper enables an evaluation of network topologies of GRNs without requiring any parameter values. The benefit of this method is exemplified in the first mathematical analysis of the complete Endomesoderm Network Model. The predictions we provide deliver candidate nodes in the network that are likely to be erroneous or miss unknown connections, which may need additional experiments to improve the network topology. This mathematical model can serve as a scaffold for detailed and more realistic models. We propose that our method can be used to assess a completeness grade of any GRN. This could be especially useful for GRNs involved in human diseases, where often the amount of connectivity is unknown and/or many genes/interactions are missing.

The virtual cell--a candidate co-ordinator for 'middle-out' modelling of biological systems

Understanding the functioning of biological systems depends on tackling complexity spanning spatial scales from genome to organ to whole organism. The basic unit of life, the cell, acts to co-ordinate information received across these scales and processes the myriad of signals to produce an integrated cellular response. Cells interact with and respond to other cells through direct or indirect contact, resulting in emergent structure and function of tissues and organs. Systems biology has traditionally used either a 'top-down' or 'bottom-up' approach. However, neither approach takes account of heterogeneity or 'noise', which is an inherent feature of cellular behaviour and may have significant impact on system level behaviour. We review existing approaches to modelling that use cellular automata or agent-based methodologies, where individual cells are represented as equivalent virtual entities governed by simple rules. These paradigms allow a direct one-to-one mapping between real and virtual cells that can be exploited in terms of acquiring parameters from experimental systems, or for model validation. Such models are inherently extensible and can be integrated with other modelling modalities (e.g. partial or ordinary differential equations) to model multi-scale phenomena. Alternatively, hierarchical agent models may be used to explore the functions of biological systems across temporal and spatial scales. This review examines individual-based models and the application of the paradigm to explore multi-scale phenomena in biology. In so doing, it demonstrates how cellular-based models have begun to play an important role in the development of 'middle-out' models, but with considerable potential for future development.

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.

From pathway to population--a multiscale model of juxtacrine EGFR-MAPK signalling

BACKGROUND

Most mathematical models of biochemical pathways consider either signalling events that take place within a single cell in isolation, or an 'average' cell which is considered to be representative of a cell population. Likewise, experimental measurements are often averaged over populations consisting of hundreds of thousands of cells. This approach ignores the fact that even within a genetically-homogeneous population, local conditions may influence cell signalling and result in phenotypic heterogeneity. We have developed a multi-scale computational model that accounts for emergent heterogeneity arising from the influences of intercellular signalling on individual cells within a population. Our approach was to develop an ODE model of juxtacrine EGFR-ligand activation of the MAPK intracellular pathway and to couple this to an agent-based representation of individual cells in an expanding epithelial cell culture population. This multi-scale, multi-paradigm approach has enabled us to simulate Extracellular signal-regulated kinase (Erk) activation in a population of cells and to examine the consequences of interpretation at a single cell or population-based level using virtual assays.

RESULTS

A model consisting of a single pair of interacting agents predicted very different Erk activation (phosphorylation) profiles, depending on the formation rate and stability of intercellular contacts, with the slow formation of stable contacts resulting in low but sustained activation of Erk, and transient contacts resulting in a transient Erk signal. Extension of this model to a population consisting of hundreds to thousands of interacting virtual cells revealed that the activated Erk profile measured across the entire cell population was very different and may appear to contradict individual cell findings, reflecting heterogeneity in population density across the culture. This prediction was supported by immunolabelling of an epithelial cell population grown in vitro, which confirmed heterogeneity of Erk activation.

CONCLUSION

These results illustrate that mean experimental data obtained from analysing entire cell populations is an oversimplification, and should not be extrapolated to deduce the signal:response paradigm of individual cells. This multi-scale, multi-paradigm approach to biological simulation provides an important conceptual tool in addressing how information may be integrated over multiple scales to predict the behaviour of a biological system.

Validation and discovery from computational biology models

Simulation software is often a fundamental component in systems biology projects and provides a key aspect of the integration of experimental and analytical techniques in the search for greater understanding and prediction of biology at the systems level. It is important that the modelling and analysis software is reliable and that techniques exist for automating the analysis of the vast amounts of data which such simulation environments generate. A rigorous approach to the development of complex modelling software is needed. Such a framework is presented here together with techniques for the automated analysis of such models and a process for the automatic discovery of biological phenomena from large simulation data sets. Illustrations are taken from a major systems biology research project involving the in vitro investigation, modelling and simulation of epithelial tissue.

Simulating non-small cell lung cancer with a multiscale agent-based model

BACKGROUND

The epidermal growth factor receptor (EGFR) is frequently overexpressed in many cancers, including non-small cell lung cancer (NSCLC). In silico modeling is considered to be an increasingly promising tool to add useful insights into the dynamics of the EGFR signal transduction pathway. However, most of the previous modeling work focused on the molecular or the cellular level only, neglecting the crucial feedback between these scales as well as the interaction with the heterogeneous biochemical microenvironment.

RESULTS

We developed a multiscale model for investigating expansion dynamics of NSCLC within a two-dimensional in silico microenvironment. At the molecular level, a specific EGFR-ERK intracellular signal transduction pathway was implemented. Dynamical alterations of these molecules were used to trigger phenotypic changes at the cellular level. Examining the relationship between extrinsic ligand concentrations, intrinsic molecular profiles and microscopic patterns, the results confirmed that increasing the amount of available growth factor leads to a spatially more aggressive cancer system. Moreover, for the cell closest to nutrient abundance, a phase-transition emerges where a minimal increase in extrinsic ligand abolishes the proliferative phenotype altogether.

CONCLUSION

Our in silico results indicate that in NSCLC, in the presence of a strong extrinsic chemotactic stimulus (and depending on the cell's location) downstream EGFR-ERK signaling may be processed more efficiently, thereby yielding a migration-dominant cell phenotype and overall, an accelerated spatio-temporal expansion rate.

Investigation of cellular movement in the prostate epithelium using an agent-based model

Experimental patterns of epithelial cell proliferation in the prostate suggest that cell movement may play an important role in prostate epithelial homeostasis, and genes known to regulate cell movement are commonly mutated or deleted in prostate carcinomas. However, the nature of cell movement within the prostate epithelium remains unknown. Here, the role of cellular movement in the prostate epithelium was explored by developing an agent-based model of the prostate duct. Prostatic adult stem cells, transit amplifying/intermediate cells (TA/ICs), and luminal cells were individually modeled within a three-dimensional reconstruction of a prostate duct. Different movement behaviors for TA/ICs and luminal cells were assessed by their ability to recreate experimental patterns of prostate cell proliferation and epithelial morphology. Strongly directed TA/IC movement toward the distal region of the prostate duct combined with weakly directed luminal cell movement toward the proximal region of the prostate duct was able to best recreate experimental patterns of prostate proliferation and morphology. The effects on cell mobility from abnormalities in PTEN and thymosin beta15 (Tbeta15), genes which are commonly altered in prostate cancer, were simulated in the model. These simulations show that altering prostate stem cell movement can dysregulate epithelial homeostasis and lead to excessive cell growth, suggesting that disruption of cell movement may contribute to prostate carcinogenesis.