Robust gene regulation: Deterministic dynamics from asynchronous networks with delay

Abstract

We compare asynchronous vs. synchronous update of discrete dynamical networks and find that a simple time delay in the nodes may induce a reproducible deterministic dynamics even in the case of asynchronous update in random order. In particular we observe that the dynamics under synchronous parallel update can be reproduced accurately under random asynchronous serial update for a large class of networks. This mechanism points at a possible general principle of how computation in gene regulation networks can be kept in a quasi-deterministic ``clockwork mode'' in spite of the absence of a central clock. A delay similar to the one occurring in gene regulation causes synchronization in the model. Stability under asynchronous dynamics disfavors topologies containing loops, comparing well with the observed strong suppression of loops in biological regulatory networks.