The impact of temporal sampling resolution on parameter inference for biological transport models

Imaging data has become widely available to study biological systems at various scales, for example the motile behaviour of bacteria or the transport of mRNA, and it has the potential to transform our understanding of key transport mechanisms. Often these imaging studies require us to compare biological species or mutants, and to do this we need to quantitatively characterise their behaviour. Mathematical models offer a quantitative description of a system that enables us to perform this comparison, but to relate these mechanistic mathematical models to imaging data, we need to estimate the parameters of the models. In this work, we study the impact of collecting data at different temporal resolutions on parameter inference for biological transport models by performing exact inference for simple velocity jump process models in a Bayesian framework. This issue is prominent in a host of studies because the majority of imaging technologies place constraints on the frequency with which images can be collected, and the discrete nature of observations can introduce errors into parameter estimates. In this work, we avoid such errors by formulating the velocity jump process model within a hidden states framework. This allows us to obtain estimates of the reorientation rate and noise amplitude for noisy observations of a simple velocity jump process. We demonstrate the sensitivity of these estimates to temporal variations in the sampling resolution and extent of measurement noise. We use our methodology to provide experimental guidelines for researchers aiming to characterise motile behaviour that can be described by a velocity jump process. In particular, we consider how experimental constraints resulting in a trade-off between temporal sampling resolution and observation noise may affect parameter estimates.Comment: Published in PLOS Computational Biolog

Implementing vertex dynamics models of cell populations in biology within a consistent computational framework

The dynamic behaviour of epithelial cell sheets plays a central role during development, growth, disease and wound healing. These processes occur as a result of cell adhesion, migration, division, differentiation and death, and involve multiple processes acting at the cellular and molecular level. Computational models offer a useful means by which to investigate and test hypotheses about these processes, and have played a key role in the study of cell–cell interactions. However, the necessarily complex nature of such models means that it is difficult to make accurate comparison between different models, since it is often impossible to distinguish between differences in behaviour that are due to the underlying model assumptions, and those due to differences in the in silico implementation of the model. In this work, an approach is described for the implementation of vertex dynamics models, a discrete approach that represents each cell by a polygon (or polyhedron) whose vertices may move in response to forces. The implementation is undertaken in a consistent manner within a single open source computational framework, Chaste, which comprises fully tested, industrial-grade software that has been developed using an agile approach. This framework allows one to easily change assumptions regarding force generation and cell rearrangement processes within these models. The versatility and generality of this framework is illustrated using a number of biological examples. In each case we provide full details of all technical aspects of our model implementations, and in some cases provide extensions to make the models more generally applicable

A bioinspired computing approach to model complex systems

The use of models is intrinsic to any scientific activity. In particular, formal/mathematical models provide a relevant tool for scientific investigation. This paper presents a new Membrane Computing based computational paradigm as a framework for modelling processes and real-life phenomena. P systems, devices in Membrane Computing, are not used as a computing paradigm, but rather as a formalism for describing the behaviour of the system to be modelled. They offer an approach to the development of models for biological systems that meets the requirements of a good modelling framework: relevance, understandability, extensibility and computability.Ministerio de Economía y Competitividad TIN2012-3743

Engineering simulations for cancer systems biology

Computer simulation can be used to inform in vivo and in vitro experimentation, enabling rapid, low-cost hypothesis generation and directing experimental design in order to test those hypotheses. In this way, in silico models become a scientific instrument for investigation, and so should be developed to high standards, be carefully calibrated and their findings presented in such that they may be reproduced. Here, we outline a framework that supports developing simulations as scientific instruments, and we select cancer systems biology as an exemplar domain, with a particular focus on cellular signalling models. We consider the challenges of lack of data, incomplete knowledge and modelling in the context of a rapidly changing knowledge base. Our framework comprises a process to clearly separate scientific and engineering concerns in model and simulation development, and an argumentation approach to documenting models for rigorous way of recording assumptions and knowledge gaps. We propose interactive, dynamic visualisation tools to enable the biological community to interact with cellular signalling models directly for experimental design. There is a mismatch in scale between these cellular models and tissue structures that are affected by tumours, and bridging this gap requires substantial computational resource. We present concurrent programming as a technology to link scales without losing important details through model simplification. We discuss the value of combining this technology, interactive visualisation, argumentation and model separation to support development of multi-scale models that represent biologically plausible cells arranged in biologically plausible structures that model cell behaviour, interactions and response to therapeutic interventions

The economic implications of a multiple species approach to bioeconomic modelling : a thesis presented in partial fulfilment of the requirements for the degree of Master of Applied Economics at Massey University, Palmerston North, New Zealand

Human activity frequently leads to the endangerment or extinction of other species. While ecologists study the biological facets of species loss, economics, as the science of understanding people's behaviour, has been charged with investigating the incentives underlying the actions people take that lead to this loss. One approach economists have taken to gain this understanding is to develop models of endangered species that include both economic and biological components, known as bioeconomic models. While ecologists frequently note the importance of modelling entire ecosystems rather than single species, most bioeconomic models in the current literature focus only on a single species. This thesis addresses the economic significance of this assumption through the development of a series of multiple species models and demonstrates, using African Wildlife as an example, the importance of interrelationships and economic values to the survival of endangered species. From these models one can infer the conditions under which a single species model may be appropriate, at least in general terms. If species are independent, and either the opportunity cost of capital or the value of habitat is very low relative to the value of the species in question, then a single species model may yield results similar to that of a multiple species model. In contrast, if species are independent and these additional conditions are not met, a single species model may significantly underestimate both optimal stock levels and land allocation. However, species do not live independently; they interact with species with which they share habitat and, when species interact, the potential for misapplication of the single species framework is even greater. When species compete, the single species framework consistently produces higher stock levels than the multiple species framework, the greater the level of competition the greater the difference. In a predator-prey relationship, the relative values of predator and prey are critical to determining the outcome of the multiple species model. It is demonstrated that the inclusion of at least all economically valuable species in an ecosystem is important when constructing bioeconomic models. Using single species models where multiple species are economically significant could lead to misleading results and ultimately to incorrect policy decisions

Inferring Biological Mechanisms by Data-Based Mathematical Modelling: Compartment-Specific Gene Activation during Sporulation in Bacillus subtilis as a Test Case

Biological functionality arises from the complex interactions of simple components. Emerging behaviour is difficult to recognize with verbal models alone, and mathematical approaches are important. Even few interacting components can give rise to a wide range of different responses, that is, sustained, transient, oscillatory, switch-like responses, depending on the values of the model parameters. A quantitative comparison of model predictions and experiments is therefore important to distinguish between competing hypotheses and to judge whether a certain regulatory behaviour is at all possible and plausible given the observed type and strengths of interactions and the speed of reactions. Here I will review a detailed model for the transcription factor σF, a regulator of cell differentiation during sporulation in Bacillus subtilis. I will focus in particular on the type of conclusions that can be drawn from detailed, carefully validated models of biological signaling networks. For most systems, such detailed experimental information is currently not available, but accumulating biochemical data through technical advances are likely to enable the detailed modelling of an increasing number of pathways. A major challenge will be the linking of such detailed models and their integration into a multiscale framework to enable their analysis in a larger biological context