Inverse bifurcation analysis: application to simple gene systems

Background: Bifurcation analysis has proven to be a powerful method for understanding the qualitative behavior of gene regulatory networks. In addition to the more traditional forward problem of determining the mapping from parameter space to the space of model behavior, the inverse problem of determining model parameters to result in certain desired properties of the bifurcation diagram provides an attractive methodology for addressing important biological problems. These include understanding how the robustness of qualitative behavior arises from system design as well as providing a way to engineer biological networks with qualitative properties. Results: We demonstrate that certain inverse bifurcation problems of biological interest may be cast as optimization problems involving minimal distances of reference parameter sets to bifurcation manifolds. This formulation allows for an iterative solution procedure based on performing a sequence of eigen-system computations and one-parame...

• Type: Journal
• Year: 2006
• Where: ALMOB
• Authors: James Lu, Heinz W. Engl, Peter Schuster
• Keywords: ALMOB 2006, Inverse Bifurcation Problems, Parameters, Qualitative Behavior