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Computer Algebra Approach to Investigating Regulatory Mechanisms in Biochemical Reaction Networks: Application to Tryptophan Operon

Ordinary differential equations are widely used to study dynamics of biochemical reaction networks. Possible regulatory mechanisms in these networks can be investigated by exploring how the system variables (concentration) respond to small changes in parameter values. Mathematically, this can be done by solving the model and sensitivity equations simultaneously. The number of sensitivity equations is a product of the number of variables and parameters. Even for simple networks, the derivations of these equations becomes challenging, if not impossible, when one wants to do it by hand.

In this talk we will explain how to use Computer Algebra Systems, such as Maple, to perform a complete sensitivity analysis for biochemical reaction networks whose dynamics are described by a system of differential equations. In the second part of this talk, we will show how to apply our approach a model developed for the tryptophan operon of E.coli, which is a small genetic network responsible for production of tryptophan when it is not present in the environment.