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Stochastic hybrid modeling and parameter identification of genetic networks


E. Cinquemani


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. This has led many researchers to apply already existing hybrid systems tools to the study of biochemical networks. 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 parameter 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. Next, parameter identification is addressed under the assumption that the genetic interaction pattern is known. To exploit the structure of the model, we build on the idea of matching local model statistics at several locations in the state space to empirical statistics drawn from convenient portions of the dataset. This allows us to establish an identification procedure that performs separate estimation of several unknown parameters by numerical solution of simple optimization problems. The procedure can cope with irregularly sampled observations and, to a certain extent, with partial state observations. The computational complexity of the algorithm grows linearly in the size of the dataset and quadratically in the dimension of the state space. Unlike clustering-based hybrid identification algorithms, whose complexity growth is typically exponential, our procedure is therefore applicable to fairly large genetic network models. Numerical results on synthetically generated data support the validity of our method and will also be presented.


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