Deterministic and stochastic P systems for modelling cellular processes

This paper presents two approaches based on metabolic and stochastic P systems, together with their associated analysis methods, for modelling biological sys- tems and illustrates their use through two case studies.Kingdom's Engineering and Physical Sciences Research Council EP/ E017215/1Biotechnology and Biological Sciences Research Council/United Kingdom BB/D019613/1Biotechnology and Biological Sciences Research Council/United Kingdom BB/F01855X/

Data-driven modelling of biological multi-scale processes

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript we review mathematical modelling approaches used to describe the individual spatial scales and how they are integrated into holistic models. We discuss the relation between spatial and temporal scales and the implication of that on multi-scale modelling. Based upon this overview over state-of-the-art modelling approaches, we formulate key challenges in mathematical and computational modelling of biological multi-scale and multi-physics processes. In particular, we considered the availability of analysis tools for multi-scale models and model-based multi-scale data integration. We provide a compact review of methods for model-based data integration and model-based hypothesis testing. Furthermore, novel approaches and recent trends are discussed, including computation time reduction using reduced order and surrogate models, which contribute to the solution of inference problems. We conclude the manuscript by providing a few ideas for the development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and Multiscale Dynamics (American Scientific Publishers

Parallel implementation of stochastic simulation for large-scale cellular processes

Experimental and theoretical studies have shown the importance of stochastic processes in genetic regulatory networks and cellular processes. Cellular networks and genetic circuits often involve small numbers of key proteins such as transcriptional factors and signaling proteins. In recent years stochastic models have been used successfully for studying noise in biological pathways, and stochastic modelling of biological systems has become a very important research field in computational biology. One of the challenge problems in this field is the reduction of the huge computing time in stochastic simulations. Based on the system of the mitogen-activated protein kinase cascade that is activated by epidermal growth factor, this work give a parallel implementation by using OpenMP and parallelism across the simulation. Special attention is paid to the independence of the generated random numbers in parallel computing, that is a key criterion for the success of stochastic simulations. Numerical results indicate that parallel computers can be used as an efficient tool for simulating the dynamics of large-scale genetic regulatory networks and cellular processes

Modelling biological invasions: individual to population scales at interfaces

Extracting the population level behaviour of biological systems from that of the individual is critical in understanding dynamics across multiple scales and thus has been the subject of numerous investigations. Here, the influence of spatial heterogeneity in such contexts is explored for interfaces with a separation of the length scales characterising the individual and the interface, a situation that can arise in applications involving cellular modelling. As an illustrative example, we consider cell movement between white and grey matter in the brain which may be relevant in considering the invasive dynamics of glioma. We show that while one can safely neglect intrinsic noise, at least when considering glioma cell invasion, profound differences in population behaviours emerge in the presence of interfaces with only subtle alterations in the dynamics at the individual level. Transport driven by local cell sensing generates predictions of cell accumulations along interfaces where cell motility changes. This behaviour is not predicted with the commonly used Fickian diffusion transport model, but can be extracted from preliminary observations of specific cell lines in recent, novel, cryo-imaging. Consequently, these findings suggest a need to consider the impact of individual behaviour, spatial heterogeneity and especially interfaces in experimental and modelling frameworks of cellular dynamics, for instance in the characterisation of glioma cell motility

Ecological Modelling with the Calculus of Wrapped Compartments

The Calculus of Wrapped Compartments is a framework based on stochastic multiset rewriting in a compartmentalised setting originally developed for the modelling and analysis of biological interactions. In this paper, we propose to use this calculus for the description of ecological systems and we provide the modelling guidelines to encode within the calculus some of the main interactions leading ecosystems evolution. As a case study, we model the distribution of height of Croton wagneri, a shrub constituting the endemic predominant species of the dry ecosystem in southern Ecuador. In particular, we consider the plant at different altitude gradients (i.e. at different temperature conditions), to study how it adapts under the effects of global climate change.Comment: A preliminary version of this paper has been presented in CMC13 (LNCS 7762, pp 358-377, 2013

Dynamic model of gene regulation for the lac operon

Gene regulatory network is a collection of DNA which interact with each other and with other matter in the cell. The lac operon is an example of a relatively simple genetic network and is one of the best-studied structures in the Escherichia coli bacteria. In this work we consider a deterministic model of the lac operon with a noise term, representing the stochastic nature of the regulation. The model is written in terms of a system of simultaneous first order differential equations with delays. We investigate an analytical and numerical solution and analyse the range of values for the parameters corresponding to a stable solution

Partial differential equations for self-organization in cellular and developmental biology

Understanding the mechanisms governing and regulating the emergence of structure and heterogeneity within cellular systems, such as the developing embryo, represents a multiscale challenge typifying current integrative biology research, namely, explaining the macroscale behaviour of a system from microscale dynamics. This review will focus upon modelling how cell-based dynamics orchestrate the emergence of higher level structure. After surveying representative biological examples and the models used to describe them, we will assess how developments at the scale of molecular biology have impacted on current theoretical frameworks, and the new modelling opportunities that are emerging as a result. We shall restrict our survey of mathematical approaches to partial differential equations and the tools required for their analysis. We will discuss the gap between the modelling abstraction and biological reality, the challenges this presents and highlight some open problems in the field

Stronger computational modelling of signalling pathways using both continuous and discrete-state methods

Starting from a biochemical signalling pathway model expresses in a process algebra enriched with quantitative information, we automatically derive both continuous-space and discrete-space representations suitable for numerical evaluation. We compare results obtained using approximate stochastic simulation thereby exposing a flaw in the use of the differentiation procedure producing misleading results