Eur. Phys. J. B 76, 167-178 (2010)
https://doi.org/10.1140/epjb/e2010-00200-9

Evolutionary design of oscillatory genetic networks

¹ Department of Physical Chemistry, Fritz Haber Institute of the Max Planck Society, Faradayweg 4-6, 14195 Berlin, Germany
² Department of Mathematics and Life Sciences, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, 739-8526, Japan
³ PRESTO, Japan Science and Technology Agency (JST), 4-1-8 Honcho Kawaguchi, Saitama, Japan
⁴ Research Institute for Mathematical Science, Kyoto University, Kyoto, 606-8502, Japan

Received: 1 March 2010
Revised: 10 May 2010
Published online: 29 June 2010

Abstract

The present study is devoted to the design and statistical investigations of dynamical gene expression networks. In our model problem, we aim to design genetic networks which would exhibit stable periodic oscillations with a prescribed temporal period. While no rational solution of this problem is available, we show that it can be effectively solved by running a computer evolution of the network models. In this process, structural rewiring mutations are applied to the networks with inhibitory interactions between genes and the evolving networks are selected depending on whether, after a mutation, they closer approach the targeted dynamics. We show that, by using this method, networks with required oscillation periods, varying by up to three orders of magnitude, can be constructed by changing the architecture of regulatory connections between the genes. Statistical properties of designed networks, including motif distributions and Laplacian spectra, are considered.