An algorithm to analyze stability of gene-expression patterns

Abstract

Many problems in the field of computational biology consist of the analysis of so-called gene-expression data. The successful application of approximation and optimization techniques, dynamical systems, algorithms and the utilization of the underlying combinatorial structures lead to a better understanding in that field. For the concrete example of gene-expression data we extend an algorithm, which exploits discrete information. This is lying in extremal points of polyhedra, which grow step by step, up to a possible stopping. We study gene-expression data in time, mathematically model it by a time-continuous system, and time-discretize this system. By our algorithm we compute the regions of stability and instability. We give an motivating introduction from genetics, present biological and mathematical interpretations of (in)stability, point out structural frontiers and give an outlook to future research