Bacterial gene regulation in diauxic and non-diauxic growth

Abstract

When bacteria are grown in a batch culture containing a mixture of two growth-limiting substrates, they exhibit a rich spectrum of substrate consumption patterns including diauxic growth, simultaneous consumption, and bistable growth. In previous work, we showed that a minimal model accounting only for enzyme induction and dilution captures all the substrate consumption patterns [Narang, A., 1998a. The dynamical analogy between microbial growth on mixtures of substrates and population growth of competing species. Biotechnol. Bioeng. 59, 116-121, Narang, A., 2006. Comparitive analysis of some models of gene regulation in mixed-substrate microbial growth, J. Theor. Biol. 242, 489-501]. In this work, we construct the bifurcation diagram of the minimal model, which shows the substrate consumption pattern at any given set of parameter values. The bifurcation diagram explains several general properties of mixed-substrate growth. (1) In almost all the cases of diauxic growth, the "preferred" substrate is the one that, by itself, supports a higher specific growth rate. In the literature, this property is often attributed to the optimality of regulatory mechanisms. Here, we show that the minimal model, which accounts for induction and growth only, displays the property under fairly general conditions. This suggests that the higher growth rate of the preferred substrate is an intrinsic property of the induction and dilution kinetics. It can be explained mechanistically without appealing to optimality principles. (2) The model explains the phenotypes of various mutants containing lesions in the regions encoding for the operator, repressor, and peripheral enzymes. A particularly striking phenotype is the "reversal of the diauxie" in which the wild-type and mutant strains consume the very same two substrates in opposite order. This phenotype is difficult to explain in terms of molecular mechanisms, such as inducer exclusion or CAP activation, but it turns out to be a natural consequence of the model. We show furthermore that the model is robust. The key property of the model, namely, the competitive dynamics of the enzymes, is preserved even if the model is modified to account for various regulatory mechanisms. Finally, the model has important implications for the problem of size regulation in development. It suggests that protein dilution may be the mechanism coupling patterning and growth.

Optimal parameter settings for information processing in gene regulatory networks

“…This is probably the simplest exam-ple of computing one could imagine. The next step in biological software sophistication is inducer exclusion (Narang, 2006;Narang and Pilyugin, 2007), i.e. the process whereby prokaryotic cells faced with several concurrently available nutrient sources exclusively take up the highest quality one.…”

Models of transcription factor binding: Sensitivity of activation functions to model assumptions

“…Gene activation and TF binding is commonly modeled using differential equation approaches (see for example Murray, 2008;Chu et al, 2008;Narang, 2006;Narang and Pilyugin, 2007;Zhu et al, 2007) or piecewise-linear differential equations (see for example Alon, 2006;Batt et al, 2005). Differential equation models are very convenient from a practical point of view because there is a well developed body of theory to either solve them analytically or at least numerically.…”

Observation of Oscillation in Bacterial Luminescence

“…It is known that when bacteria are grown in a batch culture containing a mixture of two growth-limiting substrates, they show some specific patterns in the growth curve. 10 In addition, a few distinct phases of active growth are observed in a diauxic growth curve.…”