Geometric fluid approximation for general continuous-time Markov chains.

Fluid approximations have seen great success in approximating the macro-scale behaviour of Markov systems with a large number of discrete states. However, these methods rely on the continuous-time Markov chain (CTMC) having a particular population structure which suggests a natural continuous state-space endowed with a dynamics for the approximating process. We construct here a general method based on spectral analysis of the transition matrix of the CTMC, without the need for a population structure.

Unbiased Bayesian inference for population Markov jump processes via random truncations.

We consider continuous time Markovian processes where populations of individual agents interact stochastically according to kinetic rules. Despite the increasing prominence of such models in fields ranging from biology to smart cities, Bayesian inference for such systems remains challenging, as these are continuous time, discrete state systems with potentially infinite state-space. Here we propose a novel efficient algorithm for joint state/parameter posterior sampling in population Markov Jump processes.

A model of flux regulation in the cholesterol biosynthesis pathway: Immune mediated graduated flux reduction versus statin-like led stepped flux reduction.

The cholesterol biosynthesis pathway has recently been shown to play an important role in the innate immune response to viral infection with host protection occurring through a coordinate down regulation of the enzymes catalysing each metabolic step. In contrast, statin based drugs, which form the principle pharmaceutical agents for decreasing the activity of this pathway, target a single enzyme. Here, we build an ordinary differential equation model of the cholesterol biosynthesis pathway in order to investigate how the two regulatory strategies impact upon the behaviour of the pathway.

Formal methods for checking the consistency of biological models.

Formal modeling approaches such as process algebras and Petri nets seek to provide insight into biological processes by using both symbolic and numerical methods to reveal the dynamics of the process under study. These formal approaches differ from classical methods of investigating the dynamics of the process through numerical integration of ODEs because they additionally provide alternative representations which are amenable to discrete-state analysis and logical reasoning. Backed by these additional analysis methods, formal modeling approaches have been able to identify errors in published and widely-cited biological models.

Stochastic properties of the plant circadian clock.

Circadian clocks are gene regulatory networks whose role is to help the organisms to cope with variations in environmental conditions such as the day/night cycle. In this work, we explored the effects of molecular noise in single cells on the behaviour of the circadian clock in the plant model species Arabidopsis thaliana. The computational modelling language Bio-PEPA enabled us to give a stochastic interpretation of an existing deterministic model of the clock, and to easily compare the results obtained via stochastic simulation and via numerical solution of the deterministic model.

Computational models in systems biology.

A report of the 6th International Conference on Computational Methods in Systems Biology, Rostock, Germany, 12-15 October 2008.