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Stochastic dynamics of genetic regulatory networks: modelling and parameter identification


E. Cinquemani

INRIA Rhone-Alpes

Biochemical network modelling has been mostly developed in terms of either purely continuous or purely discrete dynamics. However, it appears that certain processes are more naturally described by models that feature both continuous evolution and discrete events. In addition, it is being recognized that many biological processes are intrinsically uncertain. For instance, stochastic phenomena appear to be instrumental for certain biochemical processes to induce variability or even to improve robustness. In this talk we shall discuss modelling and identification of genetic networks in a stochastic hybrid framework. A piecewise deterministic model is introduced where the deterministic evolution of protein concentration levels is driven by the random activation and deactivation of gene expression. In turn, gene expression follows the laws of a finite Markov chain whose transition rates depend on the current protein concentrations. In our opinion, this modelling framework provides a tradeoff between accuracy and tractability which is not offered by more complex models and is well suited for genetic network analysis and model identification/validation. Based on this framework, we discuss parameter identification under the assumption that the genetic interaction pattern is known. We present a method for the estimation of the unknown model parameters from protein concentration time profiles. The procedure performs separate estimation of the dynamics of every gene in the network and can cope with sparse and noisy measurements. The computational complexity of the algorithm grows nicely with the size of the problem, which makes it applicable to fairly large genetic network models. Results from numerical experiments on simulated data will be presented to show the estimation performance.


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