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.

A Machine Learning Assisted, Label-free, Non-invasive Approach for Somatic Reprogramming in Induced Pluripotent Stem Cell Colony Formation Detection and Prediction.

During cellular reprogramming, the mesenchymal-to-epithelial transition is accompanied by changes in morphology, which occur prior to iPSC colony formation. The current approach for detecting morphological changes associated with reprogramming purely relies on human experiences, which involve intensive amounts of upfront training, human error with limited quality control and batch-to-batch variations. Here, we report a time-lapse-based bright-field imaging analysis system that allows us to implement a label-free, non-invasive approach to measure morphological dynamics. To automatically analyse and determine iPSC colony formation, a machine learning-based classification, segmentation, and statistical modelling system was developed to guide colony selection. The system can detect and monitor the earliest cellular texture changes after the induction of reprogramming in human somatic cells on day 7 from the 20-24 day process. Moreover, after determining the reprogramming process and iPSC colony formation quantitatively, a mathematical model was developed to statistically predict the best iPSC selection phase independent of any other resources. All the computational detection and prediction experiments were evaluated using a validation dataset, and biological verification was performed. These algorithm-detected colonies show no significant differences (Pearson Coefficient) in terms of their biological features compared to the manually processed colonies using standard molecular approaches.

Competition between members of the tribbles pseudokinase protein family shapes their interactions with mitogen activated protein kinase pathways.

Spatio-temporal regulation of intracellular signalling networks is key to normal cellular physiology; dysregulation of which leads to disease. The family of three mammalian tribbles proteins has emerged as an important controller of signalling via regulating the activity of mitogen activated protein kinases (MAPK), the PI3-kinase induced signalling network and E3 ubiquitin ligases. However, the importance of potential redundancy in the action of tribbles and how the differences in affinities for the various binding partners may influence signalling control is currently unclear. We report that tribbles proteins can bind to an overlapping set of MAPK-kinases (MAPKK) in live cells and dictate the localisation of the complexes. Binding studies in transfected cells reveal common regulatory mechanisms and suggest that tribbles and MAPKs may interact with MAPKKs in a competitive manner. Computational modelling of the impact of tribbles on MAPK activation suggests a high sensitivity of this system to changes in tribbles levels, highlighting that these proteins are ideally placed to control the dynamics and balance of activation of concurrent signalling pathways.

Multi-Compartmentalisation in the MAPK Signalling Pathway Contributes to the Emergence of Oscillatory Behaviour and to Ultrasensitivity.

Signal transduction through the Mitogen Activated Protein Kinase (MAPK) pathways is evolutionarily highly conserved. Many cells use these pathways to interpret changes to their environment and respond accordingly. The pathways are central to triggering diverse cellular responses such as survival, apoptosis, differentiation and proliferation. Though the interactions between the different MAPK pathways are complex, nevertheless, they maintain a high level of fidelity and specificity to the original signal. There are numerous theories explaining how fidelity and specificity arise within this complex context; spatio-temporal regulation of the pathways and feedback loops are thought to be very important. This paper presents an agent based computational model addressing multi-compartmentalisation and how this influences the dynamics of MAPK cascade activation. The model suggests that multi-compartmentalisation coupled with periodic MAPK kinase (MAPKK) activation may be critical factors for the emergence of oscillation and ultrasensitivity in the system. Finally, the model also establishes a link between the spatial arrangements of the cascade components and temporal activation mechanisms, and how both contribute to fidelity and specificity of MAPK mediated signalling.

Reducing complexity in an agent based reaction model-Benefits and limitations of simplifications in relation to run time and system level output.

Agent based modelling is a methodology for simulating a variety of systems across a broad spectrum of fields. However, due to the complexity of the systems it is often impossible or impractical to model them at a one to one scale. In this paper we use a simple reaction rate model implemented using the FLAME framework to test the impact of common methods for reducing model complexity such as reducing scale, increasing iteration duration and reducing message overheads. We demonstrate that such approaches can have significant impact on simulation runtime albeit with increasing risk of aberrant system behaviour and errors, as the complexity of the model is reduced.

Computational Modelling of NF-κB Activation by IL-1RI and Its Co-Receptor TILRR, Predicts a Role for Cytoskeletal Sequestration of IκBα in Inflammatory Signalling.

The transcription factor NF-κB (nuclear factor kappa B) is activated by Toll-like receptors and controlled by mechanotransduction and changes in the cytoskeleton. In this study we combine 3-D predictive protein modelling and in vitro experiments with in silico simulations to determine the role of the cytoskeleton in regulation of NF-κB. Simulations used a comprehensive agent-based model of the NF-κB pathway, which includes the type 1 IL-1 receptor (IL-1R1) complex and signalling intermediates, as well as cytoskeletal components. Agent based modelling relies on in silico reproductions of systems through the interactions of its components, and provides a reliable tool in investigations of biological processes, which require spatial considerations and involve complex formation and translocation of regulatory components. We show that our model faithfully reproduces the multiple steps comprising the NF-κB pathway, and provides a framework from which we can explore novel aspects of the system. The analysis, using 3-D predictive protein modelling and in vitro assays, demonstrated that the NF-κB inhibitor, IκBα is sequestered to the actin/spectrin complex within the cytoskeleton of the resting cell, and released during IL-1 stimulation, through a process controlled by the IL-1RI co-receptor TILRR (Toll-like and IL-1 receptor regulator). In silico simulations using the agent-based model predict that the cytoskeletal pool of IκBα is released to adjust signal amplification in relation to input levels. The results suggest that the process provides a mechanism for signal calibration and enables efficient, activation-sensitive regulation of NF-κB and inflammatory responses.

Modelling the Transport of Nanoparticles under Blood Flow using an Agent-based Approach.

Blood-mediated nanoparticle delivery is a new and growing field in the development of therapeutics and diagnostics. Nanoparticle properties such as size, shape and surface chemistry can be controlled to improve their performance in biological systems. This enables modulation of immune system interactions, blood clearance profile and interaction with target cells, thereby aiding effective delivery of cargo within cells or tissues. Their ability to target and enter tissues from the blood is highly dependent on their behaviour under blood flow. Here we have produced an agent-based model of nanoparticle behaviour under blood flow in capillaries. We demonstrate that red blood cells are highly important for effective nanoparticle distribution within capillaries. Furthermore, we use this model to demonstrate how nanoparticle size can selectively target tumour tissue over normal tissue. We demonstrate that the polydispersity of nanoparticle populations is an important consideration in achieving optimal specificity and to avoid off-target effects. In future this model could be used for informing new nanoparticle design and to predict general and specific uptake properties under blood flow.

Agent-based modeling of oxygen-responsive transcription factors in Escherichia coli.

In the presence of oxygen (O2) the model bacterium Escherichia coli is able to conserve energy by aerobic respiration. Two major terminal oxidases are involved in this process - Cyo has a relatively low affinity for O2 but is able to pump protons and hence is energetically efficient; Cyd has a high affinity for O2 but does not pump protons. When E. coli encounters environments with different O2 availabilities, the expression of the genes encoding the alternative terminal oxidases, the cydAB and cyoABCDE operons, are regulated by two O2-responsive transcription factors, ArcA (an indirect O2 sensor) and FNR (a direct O2 sensor). It has been suggested that O2-consumption by the terminal oxidases located at the cytoplasmic membrane significantly affects the activities of ArcA and FNR in the bacterial nucleoid. In this study, an agent-based modeling approach has been taken to spatially simulate the uptake and consumption of O2 by E. coli and the consequent modulation of ArcA and FNR activities based on experimental data obtained from highly controlled chemostat cultures. The molecules of O2, transcription factors and terminal oxidases are treated as individual agents and their behaviors and interactions are imitated in a simulated 3-D E. coli cell. The model implies that there are two barriers that dampen the response of FNR to O2, i.e. consumption of O2 at the membrane by the terminal oxidases and reaction of O2 with cytoplasmic FNR. Analysis of FNR variants suggested that the monomer-dimer transition is the key step in FNR-mediated repression of gene expression.

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.

Challenges and opportunities in a tuberculosis outbreak investigation in southern Mississippi, 2005-2007.

OBJECTIVE: Between December 2005 and November 2007, a cluster of 11 tuberculosis (TB) cases emerged in Jackson County, Mississippi. We investigated the potential sources of disease transmission and epidemiologic links in this cluster to prevent future transmission in the community. MATERIALS AND METHODS: Cases of TB reported in Jackson County from December 2005 to November 2007 having matching genotypes or social links to patients with matching genotypes were included in the investigation. We interviewed patients, reviewed medical records, and performed contact investigations. RESULTS: The combined genotyping and epidemiologic data pointed to ongoing TB transmission in this rural community. A combination of patient-specific and programmatic factors, including substance use, delays in TB diagnosis, nonadherence, and TB program staffing cuts, contributed to this outbreak in the context of the 2004 and 2005 Atlantic hurricane seasons. CONCLUSIONS: To eliminate Mycobacterium tuberculosis transmission in this setting, recommendations for the TB program include enhanced coordination with substance abuse programs, community and provider education, and increased outreach capacity.

Development of a three dimensional multiscale computational model of the human epidermis.

Transforming Growth Factor (TGF-beta1) is a member of the TGF-beta superfamily ligand-receptor network. and plays a crucial role in tissue regeneration. The extensive in vitro and in vivo experimental literature describing its actions nevertheless describe an apparent paradox in that during re-epithelialisation it acts as proliferation inhibitor for keratinocytes. The majority of biological models focus on certain aspects of TGF-beta1 behaviour and no one model provides a comprehensive story of this regulatory factor's action. Accordingly our aim was to develop a computational model to act as a complementary approach to improve our understanding of TGF-beta1. In our previous study, an agent-based model of keratinocyte colony formation in 2D culture was developed. In this study this model was extensively developed into a three dimensional multiscale model of the human epidermis which is comprised of three interacting and integrated layers: (1) an agent-based model which captures the biological rules governing the cells in the human epidermis at the cellular level and includes the rules for injury induced emergent behaviours, (2) a COmplex PAthway SImulator (COPASI) model which simulates the expression and signalling of TGF-beta1 at the sub-cellular level and (3) a mechanical layer embodied by a numerical physical solver responsible for resolving the forces exerted between cells at the multi-cellular level. The integrated model was initially validated by using it to grow a piece of virtual epidermis in 3D and comparing the in virtuo simulations of keratinocyte behaviour and of TGF-beta1 signalling with the extensive research literature describing this key regulatory protein. This research reinforces the idea that computational modelling can be an effective additional tool to aid our understanding of complex systems. In the accompanying paper the model is used to explore hypotheses of the functions of TGF-beta1 at the cellular and subcellular level on different keratinocyte populations during epidermal wound healing.

NIK and IKKbeta interdependence in NF-kappaB signalling--flux analysis of regulation through metabolites.

Activation of the transcription factor NF-kappaB is central to control of immune and inflammatory responses. Cytokine induced activation through the classical or canonical pathway relies on degradation of the inhibitor, IkappaBalpha and regulation by the IKKbeta kinase. In addition, the NF-kappaB is activated through the NF-kappaB-inducing kinase, NIK. Analysis of the IKK/NIK inter-relationship and its impact on NF-kappaB control, were analysed by mathematical modelling, using matrix formalism and stoichiometrically balanced reactions. The analysis considered a range of bio-reactions and core metabolites and their role in relation to kinase activation and in control of specific steps of the NF-kappaB pathway. The model predicts a growth-rate and time-dependent transfer of the primary kinase activity from IKKbeta to NIK. In addition, it suggests that NIK/IKKbeta interdependence is controlled by intermediates of phosphoribosylpyrophosphate (PRPP) within the glycolysis pathway, and thus, identifies a link between specific metabolic events and kinase activation in inflammatory signal transduction. Subsequent in vitro experiments, carried out to validate the impact of IKK/NIK interdependence, confirmed signal amplification at the level of the NF-kappaB/IkappaBalpha complex control in the presence of both kinases. Further, they demonstrate that the induced potentiation is due to synergistic enhancement of relA-dependent activation.

Exploring hypotheses of the actions of TGF-beta1 in epidermal wound healing using a 3D computational multiscale model of the human epidermis.

In vivo and in vitro studies give a paradoxical picture of the actions of the key regulatory factor TGF-beta1 in epidermal wound healing with it stimulating migration of keratinocytes but also inhibiting their proliferation. To try to reconcile these into an easily visualized 3D model of wound healing amenable for experimentation by cell biologists, a multiscale model of the formation of a 3D skin epithelium was established with TGF-beta1 literature-derived rule sets and equations embedded within it. At the cellular level, an agent-based bottom-up model that focuses on individual interacting units (keratinocytes) was used. This was based on literature-derived rules governing keratinocyte behavior and keratinocyte/ECM interactions. The selection of these rule sets is described in detail in this paper. The agent-based model was then linked with a subcellular model of TGF-beta1 production and its action on keratinocytes simulated with a complex pathway simulator. This multiscale model can be run at a cellular level only or at a combined cellular/subcellular level. It was then initially challenged (by wounding) to investigate the behavior of keratinocytes in wound healing at the cellular level. To investigate the possible actions of TGF-beta1, several hypotheses were then explored by deliberately manipulating some of these rule sets at subcellular levels. This exercise readily eliminated some hypotheses and identified a sequence of spatial-temporal actions of TGF-beta1 for normal successful wound healing in an easy-to-follow 3D model. We suggest this multiscale model offers a valuable, easy-to-visualize aid to our understanding of the actions of this key regulator in wound healing, and provides a model that can now be used to explore pathologies of wound healing.

Introducing spatial information into predictive NF-kappaB modelling--an agent-based approach.

Nature is governed by local interactions among lower-level sub-units, whether at the cell, organ, organism, or colony level. Adaptive system behaviour emerges via these interactions, which integrate the activity of the sub-units. To understand the system level it is necessary to understand the underlying local interactions. Successful models of local interactions at different levels of biological organisation, including epithelial tissue and ant colonies, have demonstrated the benefits of such 'agent-based' modelling. Here we present an agent-based approach to modelling a crucial biological system--the intracellular NF-kappaB signalling pathway. The pathway is vital to immune response regulation, and is fundamental to basic survival in a range of species. Alterations in pathway regulation underlie a variety of diseases, including atherosclerosis and arthritis. Our modelling of individual molecules, receptors and genes provides a more comprehensive outline of regulatory network mechanisms than previously possible with equation-based approaches. The method also permits consideration of structural parameters in pathway regulation; here we predict that inhibition of NF-kappaB is directly affected by actin filaments of the cytoskeleton sequestering excess inhibitors, therefore regulating steady-state and feedback behaviour.

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.

Agent based modelling helps in understanding the rules by which fibroblasts support keratinocyte colony formation.

BACKGROUND: Autologous keratincoytes are routinely expanded using irradiated mouse fibroblasts and bovine serum for clinical use. With growing concerns about the safety of these xenobiotic materials, it is desirable to culture keratinocytes in media without animal derived products. An improved understanding of epithelial/mesenchymal interactions could assist in this. METHODOLOGY/PRINCIPAL FINDINGS: A keratincyte/fibroblast o-culture model was developed by extending an agent-based keratinocyte colony formation model to include the response of keratinocytes to both fibroblasts and serum. The model was validated by comparison of the in virtuo and in vitro multicellular behaviour of keratinocytes and fibroblasts in single and co-culture in Greens medium. To test the robustness of the model, several properties of the fibroblasts were changed to investigate their influence on the multicellular morphogenesis of keratinocyes and fibroblasts. The model was then used to generate hypotheses to explore the interactions of both proliferative and growth arrested fibroblasts with keratinocytes. The key predictions arising from the model which were confirmed by in vitro experiments were that 1) the ratio of fibroblasts to keratinocytes would critically influence keratinocyte colony expansion, 2) this ratio needed to be optimum at the beginning of the co-culture, 3) proliferative fibroblasts would be more effective than irradiated cells in expanding keratinocytes and 4) in the presence of an adequate number of fibroblasts, keratinocyte expansion would be independent of serum. CONCLUSIONS: A closely associated computational and biological approach is a powerful tool for understanding complex biological systems such as the interactions between keratinocytes and fibroblasts. The key outcome of this study is the finding that the early addition of a critical ratio of proliferative fibroblasts can give rapid keratinocyte expansion without the use of irradiated mouse fibroblasts and bovine serum.

An integrated systems biology approach to understanding the rules of keratinocyte colony formation.

Closely coupled in vitro and in virtuo models have been used to explore the self-organization of normal human keratinocytes (NHK). Although it can be observed experimentally, we lack the tools to explore many biological rules that govern NHK self-organization. An agent-based computational model was developed, based on rules derived from literature, which predicts the dynamic multicellular morphogenesis of NHK and of a keratinocyte cell line (HaCat cells) under varying extracellular Ca++ concentrations. The model enables in virtuo exploration of the relative importance of biological rules and was used to test hypotheses in virtuo which were subsequently examined in vitro. Results indicated that cell-cell and cell-substrate adhesions were critically important to NHK self-organization. In contrast, cell cycle length and the number of divisions that transit-amplifying cells could undergo proved non-critical to the final organization. Two further hypotheses, to explain the growth behaviour of HaCat cells, were explored in virtuo-an inability to differentiate and a differing sensitivity to extracellular calcium. In vitro experimentation provided some support for both hypotheses. For NHKs, the prediction was made that the position of stem cells would influence the pattern of cell migration post-wounding. This was then confirmed experimentally using a scratch wound model.

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

We have previously developed Epitheliome, a software agent representation of the growth and repair characteristics of epithelial cell populations, where cell behaviour is governed by a number of simple rules. In this paper, we describe how this model has been extended to incorporate an example of a molecular 'mechanism' behind a rule-in this case, how signalling by both endogenous and exogenous ligands of the epidermal growth factor receptor (EGFR) can impact on the proliferation of cell agents. We have developed a mathematical model representing release of endogenous ligand by cells, three-dimensional diffusion of the secreted molecules through a volume of cell culture medium, ligand-receptor binding, and bound receptor internalization and trafficking. Information relating to quantities of molecular species associated with each cell agent is frequently exchanged between the agent and signalling models, and the ratio of bound to free receptors determines cell cycle progression and hence the proliferative behaviour of the cell agents. We have applied this integrated model to examine the effect of plating density on tissue growth via autocrine/paracrine signalling. This predicts that cell growth is dependent on the concentration of exogenous ligand, but where this is limited, then growth becomes dependent on cell density and the availability of endogenous ligand. We have further modified the calcium concentration of the medium to modulate the formation of intercellular bonds between cells and shown that the increased propensity for cells to form colonies in physiological calcium does not result in significantly different patterns of receptor occupancy. In conclusion, our approach demonstrates that by combining agent-based and mathematical modelling paradigms, it is possible to probe the complex feedback relationship between the behaviour of individual cells and their interaction with one another and their environment.

Formal agent-based modelling of intracellular chemical interactions.

Individual-based or agent-based models have proved useful in a variety of different biological contexts. This paper presents an agent-based model using a formal computational modelling approach to model a crucial biological system--the intracellular NF-kappaB signalling pathway. The pathway is vital to immune response regulation, and is fundamental to basic survival in a range of species. Alterations in pathway regulation underlie many diseases, including atherosclerosis and arthritis. Our modelling of individual molecules, receptors and genes provides a more comprehensive outline of regulatory network mechanisms than previously possible with equation-based approaches. The model has been validated with data obtained from single cell experimental analysis.

Insect communication: 'no entry' signal in ant foraging.

Forager ants lay attractive trail pheromones to guide nestmates to food, but the effectiveness of foraging networks might be improved if pheromones could also be used to repel foragers from unrewarding routes. Here we present empirical evidence for such a negative trail pheromone, deployed by Pharaoh's ants (Monomorium pharaonis) as a 'no entry' signal to mark an unrewarding foraging path. This finding constitutes another example of the sophisticated control mechanisms used in self-organized ant colonies.