STOCHDETBIOMODEL

Stochastic and deterministic modelling of biological and biochemical phenomena with applications to circadian rhythms and pattern formation

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 Obiettivo del progetto (Objective)

'Classical deterministic mathematical description of the dynamics of chemical systems becomes invalid if the concentration of an involved chemical species is too low. In this case the noisy behaviour of individual molecules starts to be significant and considerable stochastic effects are observed. The stochastic models may exhibit even qualitatively different behaviour than the corresponding deterministic models. This situation is very typical in biological and biochemical systems. The collective behaviour of social insect, birds, or fish, bacterial chemotaxis, formation of skin patterns and the biochemical processes in living cells, like gene regulatory networks, the cell cycle, and circadian rhythms are examples of processes mathematically modelled by reaction and reaction-diffusion systems, we concentrate on in this project. We aim at general theoretical problems connected with stochastic and deterministic modelling of reaction and reaction-diffusion systems. For example the model reduction, bifurcation analysis of stochastic differential equations, high computational cost of stochastic models, and the interconnection and comparison of deterministic and stochastic approaches. In addition, we will apply the general theory and multipurpose computational tools to specific biochemical and biological systems of circadian rhythms and skin pattern formation. In particular, we will investigate whether the robustness with respect to noise observed in models of circadian rhythms is preserved if spatial aspects -- the diffusion -- is added to the model. Further, based on recent theoretical results, we will analyze the character of spatial patterns in reaction-diffusion systems with unilateral regulation. The unilateral regulation may increase the robustness of the pattern formation mechanisms that are in general very sensitive on proper values of parameters.'

Introduzione (Teaser)

EU funded researchers have derived efficient and analytical computational methods for analysis of systems where there is both molecular reaction and diffusion. They then applied them to modelling of circadian rhythms and skin pattern formation.

Descrizione progetto (Article)

When non-stochastic or deterministic effects such as radiation dose are in play, severity varies with dose up to a threshold value. Classical deterministic mathematical modelling becomes invalid when concentration of a chemical species is low. This is because of 'noise' with stochastic effects, a scenario very common in biological systems.

Stochastic effects occur by chance and are typical in models of cancer and genetic effects. The STOCHDETBIOMODEL (Stochastic and deterministic modelling of biological and biochemical phenomena with applications to circadian rhythms and pattern formation) project investigated theoretical problems connected with stochastic and deterministic modelling of biological systems.

Stochastic modelling is an invaluable tool but problems arise when there are changes in model parameters that lead to a change in model behaviour, bifurcation. Theoretical problems took in model reduction and bifurcation analysis of stochastic differential equations, the high computational cost of stochastic models and interconnection of deterministic and stochastic approaches using tensor-structured parametric analysis (TPA). In particular, the researchers analysed the robustness of the model as applied to circadian rhythms even in instances where diffusion is added to the model.

The analysis of TPA was based on recently proposed low-parametric tensor-structured representations of classical matrices and vectors. TPA has been implemented in Matlab and the codes are available. Furthermore, application to circadian rhythms used introduction of delays to quasi steady state assumptions. This approach yielded a simplified system that accurately agrees with the original system not only qualitatively but also quantitatively. The researchers tailored the correct size of delays for a particular model of circadian rhythms.

The results of the research have been widely disseminated via eight conferences and publication of three peer-reviewed papers. Collaboration between universities from UK, USA and China was very fruitful for all concerned.

As the knowledge base of biological systems widens, there is an increasing need to employ modelling techniques to represent their dynamics. Stochastic and deterministic modelling is applicable to a whole range of phenomena including collective behaviour or insects, movement of bacteria to a chemical stimulus and gene regulatory networks.