Reverse-engineering of polynomial dynamical systems

Details Reverse-engineering of polynomial dynamical systems Reverse-engineering of polynomial dynamical systems

2006-05-19

arxiv.org/abs/q-bio/0605032v1

Biology

Quantitative Biology

Quantitative Methods

Scientific paper

Multivariate polynomial dynamical systems over finite fields have been studied in several contexts, including engineering and mathematical biology. An important problem is to construct models of such systems from a partial specification of dynamic properties, e.g., from a collection of state transition measurements. Here, we consider static models, which are directed graphs that represent the causal relationships between system variables, so-called wiring diagrams. This paper contains an algorithm which computes all possible minimal wiring diagrams for a given set of state transition measurements. The paper also contains several statistical measures for model selection. The algorithm uses primary decomposition of monomial ideals as the principal tool. An application to the reverse-engineering of a gene regulatory network is included. The algorithm and the statistical measures are implemented in Macaulay2 and are available from the authors.

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