Inverse bifurcation analysis of a model for the mammalian G1/S regulatory module

Authors:
James Lu;Heinz W. Engl;Rainer Machné;Peter Schuster
Affiliations:
Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Linz, Austria;Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Linz, Austria;Theoretical Biochemistry Group, Theoretical Biochemistry Group,, Vienna, Austria;Theoretical Biochemistry Group, Theoretical Biochemistry Group,, Vienna, Austria
Venue:
BIRD'07 Proceedings of the 1st international conference on Bioinformatics research and development
Year:
2007

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Abstract

Given a large, complex ordinary differential equation model of a gene regulatory network, relating its dynamical properties to its network structure is a challenging task. Biologically important questions include: what network components are responsible for the various dynamical behaviors that arise? can the underlying dynamical behavior be essentially attributed to a small number of modules? In this paper, we demonstrate that inverse bifurcation analysis can be used to address such inverse problems.We show that sparsity-promoting regularization strategies, in combination with numerical bifurcation analysis, can be used to identify small sets of "influential" submodules and parameters within a given network. In addition, hierarchical strategies can be used to generate parameter solutions of increasing cardinality of non-zero entries. We apply the proposed methods to analyze a model of the mammalian G1/S regulatory module.