On the relationship between genomic regulatory element organization and gene regulatory dynamics

In this project we study the relationship between genomic regulatory element organization and gene regulatory dynamics. This paper illustrates an approach to investigating this relationship based on the application of classical nonlinear system analysis techniques to a transcription level, statistical thermodynamical model like that used in Shea & Ackers (1985). Preliminary ideas presented at the ICMCM conference (Wolf & Eeckman, 1998) are developed in this manuscript. We show that, for prokaryotic gene circuits dominated by local promoter control, dynamical system behavior descriptors like the number and stability of equilibrium point steady states and their bifurcation potential can be largely determined from genomic organization (e.g. the number, type, and placement of regulatory protein binding sites). Concepts are illustrated on hypothetical gene regulation systems with one or two genes and varying numbers of regulatory protein binding sites (operators). Gene regulatory systems with a single gene and an arbitrary number of operator sites are shown to be globally stable, with the potential for having multiple equilibrium points and capable of bifurcating. A monomer-controlled gene regulation system with n operator sites is proven to have a maximum of 1+n/2 stable equilibria for even n, and (n+1)/2 for odd n, while a multimer-controlled, n operator site system is shown to have a maximum of 2+n/2 stable equilibria for even n, and (n+3)/2 for odd n. These results are applied to the design of a two-state switch using a gene regulation system with two operator sites. The question "what is the simplest possible gene regulation system capable of acting like a switch?" is answered. The paper ends with an analysis of a two-gene regulation system, the results of which point to the existence of a "soft-switching" mechanism that may account for the "on-off" hypothesized behavior of some gene networks.