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.     

Agent-based modelling as scientific method: a case study analysing primate social behaviour

A scientific methodology in general should provide two things: first, a means of explanation and, second, a mechanism for improving that explanation. Agent-based modelling (ABM) is a method that facilitates exploring the collective effects of individual action selection. The explanatory force of the model is the extent to which an observed meta-level phenomenon can be accounted for by the behaviour of its micro-level actors. This article demonstrates that this methodology can be applied to the biological sciences; agent-based models, like any other scientific hypotheses, can be tested, critiqued, generalized or specified. We review the state of the art for ABM as a methodology for biology and then present a case study based on the most widely published agent-based model in the biological sciences: Hemelrijk's DomWorld, a model of primate social behaviour. Our analysis shows some significant discrepancies between this model and the behaviour of the macaques, the genus used for our analysis. We also demonstrate that the model is not fragile: its other results are still valid and can be extended to compensate for these problems. This robustness is a standard advantage of experiment-based artificial intelligence modelling techniques over analytic modelling.     

The epitheliome: agent-based modelling of the social behaviour of cells

We have developed a new computational modelling paradigm for predicting the emergent behaviour resulting from the interaction of cells in epithelial tissue. As proof-of-concept, an agent-based model, in which there is a one-to-one correspondence between biological cells and software agents, has been coupled to a simple physical model. Behaviour of the computational model is compared with the growth characteristics of epithelial cells in monolayer culture, using growth media with low and physiological calcium concentrations. Results show a qualitative fit between the growth characteristics produced by the simulation and the in vitro cell models.     

BIO-LGCA: A cellular automaton modelling class for analysing collective cell migration

Collective dynamics in multicellular systems such as biological organs and tissues plays a key role in biological development, regeneration, and pathological conditions. Collective tissue dynamics—understood as population behaviour arising from the interplay of the constituting discrete cells—can be studied with on- and off-lattice agent-based models. However, classical on-lattice agent-based models, also known as cellular automata, fail to replicate key aspects of collective migration, which is a central instance of collective behaviour in multicellular systems. To overcome drawbacks of classical on-lattice models, we introduce an on-lattice, agent-based modelling class for collective cell migration, which we call biological lattice-gas cellular automaton (BIO-LGCA). The BIO-LGCA is characterised by synchronous time updates, and the explicit consideration of individual cell velocities. While rules in classical cellular automata are typically chosen ad hoc, rules for cell-cell and cell-environment interactions in the BIO-LGCA can also be derived from experimental cell migration data or biophysical laws for individual cell migration. We introduce elementary BIO-LGCA models of fundamental cell interactions, which may be combined in a modular fashion to model complex multicellular phenomena. We exemplify the mathematical mean-field analysis of specific BIO-LGCA models, which allows to explain collective behaviour. The first example predicts the formation of clusters in adhesively interacting cells. The second example is based on a novel BIO-LGCA combining adhesive interactions and alignment. For this model, our analysis clarifies the nature of the recently discovered invasion plasticity of breast cancer cells in heterogeneous environments.     

Cellulat: an agent-based intracellular signalling model

The theory of behaviour-based systems (or autonomous agents) constitutes a useful approach for the modelling of intracellular signalling networks. In this sense, a cell can be seen as an adaptive autonomous agent or as a society of such agents, where each can exhibit a particular behaviour depending on its cognitive capabilities. We present an intracellular signalling model obtained by integrating several computational techniques into an agent-based paradigm. Cellulat, the model, takes into account two essential aspects of the intracellular signalling networks: (1) cognitive capacities, which are modelled as the agent abilities to interact with the surrounding medium and (2) a spatial organisation, this last obtained using a shared data structure through which the agents communicate between them. We propose a methodology for the modelling of intracellular signalling pathway using Cellulat and we discuss the goal of a virtual laboratory based on our model and presently under development.     

Comparing Stochastic Differential Equations and Agent-Based Modelling and Simulation for Early-Stage Cancer

There is great potential to be explored regarding the use of agent-based modelling and simulation as an alternative paradigm to investigate early-stage cancer interactions with the immune system. It does not suffer from some limitations of ordinary differential equation models, such as the lack of stochasticity, representation of individual behaviours rather than aggregates and individual memory. In this paper we investigate the potential contribution of agent-based modelling and simulation when contrasted with stochastic versions of ODE models using early-stage cancer examples. We seek answers to the following questions: (1) Does this new stochastic formulation produce similar results to the agent-based version? (2) Can these methods be used interchangeably? (3) Do agent-based models outcomes reveal any benefit when compared to the Gillespie results? To answer these research questions we investigate three well-established mathematical models describing interactions between tumour cells and immune elements. These case studies were re-conceptualised under an agent-based perspective and also converted to the Gillespie algorithm formulation. Our interest in this work, therefore, is to establish a methodological discussion regarding the usability of different simulation approaches, rather than provide further biological insights into the investigated case studies. Our results show that it is possible to obtain equivalent models that implement the same mechanisms; however, the incapacity of the Gillespie algorithm to retain individual memory of past events affects the similarity of some results. Furthermore, the emergent behaviour of ABMS produces extra patters of behaviour in the system, which was not obtained by the Gillespie algorithm.     

Ecosystem engineering as an energy transfer process: a simple agent-based model

Ecosystem engineers are defined as organisms who modulate the availability of resources for themselves and other organisms by physically changing the environment. Ecosystem engineering is a well-recognised ecological interaction, but there is a limited number of general models due to the recent development of the field. Agent-based models are often used to study how organisms respond to changing environments and are suitable for modelling ecosystem engineering. To our knowledge, agent-based methodology has not yet been used to model ecosystem engineering. In this paper, we develop a simple agent-based population dynamics model of ecosystem engineering as an energy transfer process. We apply energy budget approach to conceptually explain how ecosystem engineers transfer energy to the environment and define various types of energy transfers relative to their effects on the engineers and other organisms. We simulate environments with various levels of resource abundance and compare the results of the model without ecosystem engineering agents to the model with ecosystem engineering agents. We find that in environments with higher levels of resources, the presence of ecosystem engineers increases the average carrying capacity and the strength of population fluctuations, while in environments with lower levels of resources, ecosystem engineering mitigates fluctuations, increases average carrying capacity and makes environments more resilient. Finally, we discuss about the further application of agent-based modelling for the theoretical and experimental development of the ecosystem engineering concept.     

Application of Petri net theory for modelling and validation of the sucrose breakdown pathway in the potato tuber

MOTIVATION: Because of the complexity of metabolic networks and their regulation, formal modelling is a useful method to improve the understanding of these systems. An essential step in network modelling is to validate the network model. Petri net theory provides algorithms and methods, which can be applied directly to metabolic network modelling and analysis in order to validate the model. The metabolism between sucrose and starch in the potato tuber is of great research interest. Even if the metabolism is one of the best studied in sink organs, it is not yet fully understood. RESULTS: We provide an approach for model validation of metabolic networks using Petri net theory, which we demonstrate for the sucrose breakdown pathway in the potato tuber. We start with hierarchical modelling of the metabolic network as a Petri net and continue with the analysis of qualitative properties of the network. The results characterize the net structure and give insights into the complex net behaviour.     

A multi-scale mechanobiological model of in-stent restenosis: deciphering the role of matrix metalloproteinase and extracellular matrix changes

Since their first introduction, stents have revolutionised the treatment of atherosclerosis; however, the development of in-stent restenosis still remains the Achilles' heel of stent deployment procedures. Computational modelling can be used as a means to model the biological response of arteries to different stent designs using mechanobiological models, whereby the mechanical environment may be used to dictate the growth and remodelling of vascular cells. Changes occurring within the arterial wall due to stent-induced mechanical injury, specifically changes within the extracellular matrix, have been postulated to be a major cause of activation of vascular smooth muscle cells and the subsequent development of in-stent restenosis. In this study, a mechanistic multi-scale mechanobiological model of in-stent restenosis using finite element models and agent-based modelling is presented, which allows quantitative evaluation of the collagen matrix turnover following stent-induced arterial injury and the subsequent development of in-stent restenosis. The model is specifically used to study the influence of stent deployment diameter and stent strut thickness on the level of in-stent restenosis. The model demonstrates that there exists a direct correlation between the stent deployment diameter and the level of in-stent restenosis. In addition, investigating the influence of stent strut thickness using the mechanobiological model reveals that thicker strut stents induce a higher level of in-stent restenosis due to a higher extent of arterial injury. The presented mechanobiological modelling framework provides a robust platform for testing hypotheses on the mechanisms underlying the development of in-stent restenosis and lends itself for use as a tool for optimisation of the mechanical parameters involved in stent design.     

Modelling Primate Behavioral Ecology

Models play an important role in any mature science because they force us to make explicit our assumptions about how a phenomenon works and allow us to explore the way in which different variables influence a complex biological system. I review the principal kinds of models that could be used to study primate behavior and ecology: linear programming models, systems models, optimality models, stochastic dynamic programming models and agent-based simulation models. Although less use has been made of modelling in primatology than in some other areas of behavioral ecology, there is considerable scope for exploiting the predictive and explanatory power of models in the field.     

A modelling approach towards epidermal homoeostasis control

In order to grasp the features arising from cellular discreteness and individuality, in large parts of cell tissue modelling agent-based models are favoured. The subclass of off-lattice models allows for a physical motivation of the intercellular interaction rules. We apply an improved version of a previously introduced off-lattice agent-based model to the steady-state flow equilibrium of skin. The dynamics of cells is determined by conservative and drag forces, supplemented with delta-correlated random forces. Cellular adjacency is detected by a weighted Delaunay triangulation. The cell cycle time of keratinocytes is controlled by a diffusible substance provided by the dermis. Its concentration is calculated from a diffusion equation with time-dependent boundary conditions and varying diffusion coefficients. The dynamics of a nutrient is also taken into account by a reaction-diffusion equation. It turns out that the analysed control mechanism suffices to explain several characteristics of epidermal homoeostasis formation. In addition, we examine the question of how in silico melanoma with decreased basal adhesion manage to persist within the steady-state flow equilibrium of the skin. Interestingly, even for melanocyte cell cycle times being substantially shorter than for keratinocytes, tiny stochastic effects can lead to completely different outcomes. The results demonstrate that the understanding of initial states of tumour growth can profit significantly from the application of off-lattice agent-based models in computer simulations.     

Introduction. Modelling natural action selection

Action selection is the task of resolving conflicts between competing behavioural alternatives. This theme issue is dedicated to advancing our understanding of the behavioural patterns and neural substrates supporting action selection in animals, including humans. The scope of problems investigated includes: (i) whether biological action selection is optimal (and, if so, what is optimized), (ii) the neural substrates for action selection in the vertebrate brain, (iii) the role of perceptual selection in decision-making, and (iv) the interaction of group and individual action selection. A second aim of this issue is to advance methodological practice with respect to modelling natural action section. A wide variety of computational modelling techniques are therefore employed ranging from formal mathematical approaches through to computational neuroscience, connectionism and agent-based modelling. The research described has broad implications for both natural and artificial sciences. One example, highlighted here, is its application to medical science where models of the neural substrates for action selection are contributing to the understanding of brain disorders such as Parkinson's disease, schizophrenia and attention deficit/hyperactivity disorder.     

Towards mechanistic models of plant organ growth

Modelling and simulation are increasingly used as tools in the study of plant growth and developmental processes. By formulating experimentally obtained knowledge as a system of interacting mathematical equations, it becomes feasible for biologists to gain a mechanistic understanding of the complex behaviour of biological systems. In this review, the modelling tools that are currently available and the progress that has been made to model plant development, based on experimental knowledge, are described. In terms of implementation, it is argued that, for the modelling of plant organ growth, the cellular level should form the cornerstone. It integrates the output of molecular regulatory networks to two processes, cell division and cell expansion, that drive growth and development of the organ. In turn, these cellular processes are controlled at the molecular level by hormone signalling. Therefore, combining a cellular modelling framework with regulatory modules for the regulation of cell division, expansion, and hormone signalling could form the basis of a functional organ growth simulation model. The current state of progress towards this aim is that the regulation of the cell cycle and hormone transport have been modelled extensively and these modules could be integrated. However, much less progress has been made on the modelling of cell expansion, which urgently needs to be addressed. A limitation of the current generation models is that they are largely qualitative. The possibilities to characterize existing and future models more quantitatively will be discussed. Together with experimental methods to measure crucial model parameters, these modelling techniques provide a basis to develop a Systems Biology approach to gain a fundamental insight into the relationship between gene function and whole organ behaviour.     

Kinetic modelling of plant metabolic pathways

This paper provides a review of kinetic modelling of plant metabolic pathways as a tool for analysing their control and regulation. An overview of different modelling strategies is presented, starting with those approaches that only require a knowledge of the network stoichiometry; these are referred to as structural. Flux-balance analysis, metabolic flux analysis using isotope labelling, and elementary mode analysis are briefly mentioned as three representative examples. The main focus of this paper, however, is a discussion of kinetic modelling, which requires, in addition to the stoichiometry, a knowledge of the kinetic properties of the constituent pathway enzymes. The different types of kinetic modelling analysis, namely time-course simulation, steady-state analysis, and metabolic control analysis, are explained in some detail. An overview is presented of strategies for obtaining model parameters, as well as software tools available for simulation of such models. The kinetic modelling approach is exemplified with discussion of three models from the general plant physiology literature. With the aid of kinetic modelling it is possible to perform a control analysis of a plant metabolic system, to identify potential targets for biotechnological manipulation, as well as to ascertain the regulatory importance of different enzymes (including isoforms of the same enzyme) in a pathway. Finally, a framework is presented for extending metabolic models to the whole-plant scale by linking biochemical reactions with diffusion and advective flow through the phloem. Future challenges include explicit modelling of subcellular compartments, as well as the integration of kinetic models on the different levels of the cellular and organizational hierarchy.     

Development of a Three Dimensional Multiscale Computational Model of the Human Epidermis

Transforming Growth Factor (TGF-β1) 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-β1 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-β1. 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-β1 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-β1 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-β1 at the cellular and subcellular level on different keratinocyte populations during epidermal wound healing.     

An agent-based model of group decision making in baboons

We present an agent-based model of the key activities of a troop of chacma baboons (Papio hamadryas ursinus) based on the data collected at De Hoop Nature Reserve in South Africa. We analyse the predictions of the model in terms of how well it is able to duplicate the observed activity patterns of the animals and the relationship between the parameters that control the agent's decision procedure and the model's predictions. At the current stage of model development, we are able to show that across a wide range of decision parameter values, the baboons are able to achieve their energetic and social time requirements. The simulation results also show that decisions concerning movement (group action selection) have the greatest influence on the outcomes. Those cases where the model's predictions fail to agree with the observed activity patterns have highlighted key elements that were missing from the field data, and that would need to be collected in subsequent fieldwork. Based on our experience, we believe group decision making is a fertile field for future research, and agent-based modelling offers considerable scope for understanding group action selection.