Optimal Strategy for Rapid Proteome Re-Arrangements in Bacterial Populations

Abstract

When a bacterial population is subjected to environmental change, its proteome must be re-arranged for resumption of rapid growth. Upon recurrent environmental changes, rapid proteome responses are required for high average growth rate and fitness value, suggesting high selection pressure for rapid proteome re-arrangements in response to environmental changes. What, then, is the best gene expression strategy for rapid proteome change among bacteria?Here, we demonstrate that the optimal solution to the adaptation problem is to direct all gene expression to synthesis of the proteins in the currently rate limiting set of pathways. The result is obtained by reformulating proteome dynamics in terms of flow-coupled networks in which the rate limiting protein components determine the growth rate. This approach provides a universal frame work for the description of the whole proteome and its adaptation to changing external conditions. It also makes it possible to identify optimal solutions to the adaptation problem, which can be experimentally validated. Under optimal conditions the intrinsically non-linear dynamics of these networks becomes simple and linear with respect to the components of the proteome, while the complex dynamics of the concentrations of the signal molecules requires non-linear mathematics: that what is controlled obeys very simple dynamics while the control systems remain non-linear and complex. This allows for simple, analytical solutions to previously intractable dynamic problems. We are therefore optimistic that the present work, focused on the fitness value of bacterial populations, will contribute to quantitative integration of bacterial physiology and population genetics.