ABSTRACT
In this review, we survey work that has been carried out in the attempts of biomathematicians to understand the dynamic behaviour of simple bacterial operons starting with the initial work of the 1960's. We concentrate on the simplest of situations, discussing both repressible and inducible systems and then turning to concrete examples related to the biology of the lactose and tryptophan operons. We conclude with a brief discussion of the role of both extrinsic noise and so-called intrinsic noise in the form of translational and/or transcriptional bursting.
Subject(s)
Gene Expression Regulation , Gene Regulatory Networks , Models, Biological , Algorithms , Animals , Humans , Operon , Prokaryotic Cells/physiologyABSTRACT
In this work we introduce a novel approach to study biochemical noise. It comprises a simplification of the master equation of complex reaction schemes (via an adiabatic approximation) and the numerical solution of the reduced master equation. The accuracy of this procedure is tested by comparing its results with analytic solutions (when available) and with Gillespie stochastic simulations. We further employ our approach to study the stochastic expression of a simple gene network, which is subject to negative feedback regulation at the transcriptional level. Special attention is paid to the influence of negative feedback on the amplitude of intrinsic noise, as well as on the relaxation rate of the system probability distribution function to the steady solution. Our results suggest the existence of an optimal feedback strength that maximizes this relaxation rate.
Subject(s)
Algorithms , Gene Expression Regulation/genetics , Models, Genetic , Stochastic Processes , Feedback, Physiological , Gene Regulatory Networks , Proteins/genetics , RNA, Messenger/geneticsABSTRACT
Oscillatory behaviour in the tryptophan operon of an Escherichia coli mutant strain lacking the enzyme-inhibition regulatory mechanism has been observed by Bliss et al. but not confirmed by others. This behaviour could be important from the standpoint of synthetic biology, whose goals include the engineering of intracellular genetic oscillators. This work is devoted to investigating, from a mathematical modelling point of view, the possibility that the trp operon of the E. coli inhibition-free strain expresses cyclically. For that we extend a previously introduced model for the regulatory pathway of the tryptophan operon in Escherichia coli to account for the observed multiplicity and cooperativity of repressor binding sites. Thereafter we investigate the model dynamics using deterministic numeric solutions, stochastic simulations, and analytic studies. Our results suggest that a quasi-periodic behaviour could be observed in the trp operon expression level of single bacteria.
Subject(s)
Escherichia coli/genetics , Operon , Tryptophan/genetics , Models, TheoreticalABSTRACT
In this paper we study the stability of a previously introduced model for the tryptophan operon regulatory pathway. For this, we make use of the second Lyapunov's method. The results obtained for the wild-type and for a couple ofin-silico mutant bacterial strains allow a deeper understanding of the multiplicity of regulatory mechanisms in this operon. In particular, we confirm that enzyme inhibition and transcription attenuation strengthen the system stability, the effect of transcription attenuation being much shorter than that of enzyme inhibition. Furthermore, the analysis here presented provides some insights about how enzyme inhibition affects the system stability.
Subject(s)
Gene Expression Regulation, Bacterial , Models, Genetic , Operon/genetics , Tryptophan/biosynthesis , Algorithms , Anthranilate Synthase/genetics , Anthranilate Synthase/metabolism , Bacteria/genetics , Bacteria/metabolism , Bacterial Proteins/genetics , Down-Regulation/genetics , Mutation , Operator Regions, Genetic/genetics , Repressor Proteins/geneticsABSTRACT
A mathematical model of the tryptophan operon is developed. This model considers all of the system known regulatory mechanisms: repression, transcription attenuation, and feedback enzyme inhibition. Special attention is paid to the estimation of all the model parameters from reported experimental data. The model equations are numerically solved. An analysis of these solutions reveals that transcription attenuation helps to speed up the operon response to nutritional shifts, while enzyme inhibition increases the operon stability.
