Dynamics of gene regulatory networks and their dependence on network topology and quantitative parameters - The case of phage λ

Abstract

Background: Gene regulatory networks can be modelled in various ways depending on the level of detail required and biological questions addressed. One of the earliest formalisms used for modeling is a Boolean network, although these models cannot describe most temporal aspects of a biological system. Differential equation models have also been used to model gene regulatory networks, but these frameworks tend to be too detailed for large models and many quantitative parameters might not be deducible in practice. Hybrid models bridge the gap between these two model classes - these are useful when concentration changes are important while the information about precise concentrations and binding site affinities is partial. Results: In this paper we study the stable behaviours of phage λ via a hybrid system based model. We identify wild type and mutant behaviours that arise for various orderings of binding site affinities. We propose experiments for detecting these behaviours: we suggest several ways of altering binding affinities with either mutations or genome rearrangements to achieve modified behaviours. The feasibility of these experiments is assessed. The interplay between the qualitative aspects of a network, e.g. network topology, and quantitative parameters, e.g. growth and degradation rates of proteins, is demonstrated. We also provide a software for exploring all feasible states of a hybrid system model and identifying all attractors. Conclusions: The behaviours of phage λ are determined mainly by the topology of this network and by the mutual order of binding affinities. Exact affinities and growth and degradation rates of proteins fine tune the system. We show that only two stable behaviours are possible for phage λ if the main constraints of λ switch are preserved - these behaviours correspond to lysis and lysogeny. We identify several variants of both lysis and lysogeny - one wild type and one modified behaviour for each. We elucidate the necessary constraints for binding site affinities to achieve both wild type lysis and lysogeny. Our software is applicable to a wide range of biological models described as a hybrid system.