A new method for the analysis of the dynamics of the molecular genetic control systems. I. Description of the method of generalized threshold models.

In the molecular system of coding polymers and metabolites a control subsystem has been singled out that forms controlling variables showing the action of regulatory molecules and a controlled subsystem where, depending on the values of controlling variables controlled variables are formed, i.e. concentrations of DNA, m-RNA, proteins and metabolites. Relationships have been obtained which enable controlling variables to be found. Equations showing the dynamics of molecular genetic control systems' components have been obtained. A method of generalized threshold models that enables kinetic curves to be obtained by pure mathematical means for macromolecular components (DNA, RNA, proteins) of molecular genetic control systems of varying complexity is suggested.     

Cycling expression and cooperative operator interaction in the trp operon of Escherichia coli

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.     

Metabolic design based on a coupled gene expression-metabolic network model of tryptophan production in Escherichia coli

The presumably high potential of a holistic design approach for complex biochemical reaction networks is exemplified here for the network of tryptophan biosynthesis from glucose, a system whose components have been investigated thoroughly before. A dynamic model that combines the behavior of the trp operon gene expression with the metabolic network of central carbon metabolism and tryptophan biosynthesis is investigated. This model is analyzed in terms of metabolic fluxes, metabolic control, and nonlinear optimization. We compare two models for a wild-type strain and another model for a tryptophan producer. An integrated optimization of the whole network leads to a significant increase in tryptophan production rate for all systems under study. This enhancement is well above the increase that can be achieved by an optimization of subsystems. A constant ratio of control coefficients on tryptophan synthesis rate has been identified for the models regarding or disregarding trp operon expression. Although we found some examples where flux control coefficients even contradict the trends of enzyme activity changes in an optimized profile, flux control can be used as an indication for enzymes that have to be taken into account in optimization.     

Markov Chain modeling of pyelonephritis-associated pili expression in uropathogenic Escherichia coli

Pyelonephritis-associated pili (Pap) expression in uropathogenic Escherichia coli is regulated by a complex phase variation mechanism involving the competition between leucine-responsive regulatory protein (Lrp) and DNA adenine methylase (Dam). Population dynamics of pap gene expression has been studied extensively and the detailed molecular mechanism has been largely elucidated, providing sufficient information for mathematical modeling. Although the Gillespie algorithm is suited for modeling of stochastic systems such as the pap operon, it becomes computationally expensive when detailed molecular steps are explicitly modeled in a population. Here we developed a Markov Chain model to simplify the computation. Our model is analytically derived from the molecular mechanism. The model presented here is able to reproduce results presented using the Gillespie method, but since the regulatory information is incorporated before simulation, our model runs more efficiently and allows investigation of additional regulatory features. The model predictions are consistent with experimental data obtained in this work and in the literature. The results show that pap expression in uropathogenic E. coli is initial-state-dependent, as previously reported. However, without environment stimuli, the pap-expressing fraction in a population will reach an equilibrium level after approximately 50-100 generations. The transient time before reaching equilibrium is determined by PapI stability and Lrp and Dam copy numbers per cell. This work demonstrates that the Markov Chain model captures the essence of the complex molecular mechanism and greatly simplifies the computation.     

A simple genetically structured model of trp repressor-operator interactions

A genetically structured mathematical model of the trp operon based on known molecular interactions of aporepressor, corepressor, and inducer is proposed. The model simulates, both qualitatively and quantitatively, the influence of these regulatory species on the extent of repression and expression of cloned gene products. It shows that at low aporepressor concentration, full repression is not possible even with high tryptophan levels, resulting in leaky expression. Calculations based on the model enabled predictions of optimum levels of aporepressor and tryptophan for effective repression and, concurrently, the beta-indoleacrylic acid concentrations required for induction for both low and high plasmid copy number clones. Using the model we attempted to provide explanations for seemingly anomalous and sometimes contradictory observations by researchers when working with the trp promoter. (c) 1993 John Wiley & Sons, Inc.     

Modeling real eukaryotic control gene subnetworks based on generalized threshold models]

Mathematical and computational means are developed that take into consideration the specifics of control processes at the molecular level and allow one to obtain both qualitative and quantitative patterns of gene network dynamics. Using the method of generalized threshold models, models are constructed for the Arabidopsis thaliana flower morphogenesis control subsystem and gene subnetwork controlling the Drosophila melanogaster early ontogeny. The dynamics of these systems are investigated: kinetic curves are computed for molecular components (RNA, proteins), possible modes of functioning and steady states of the nets are revealed and biologically interpreted. The models are shown to be adequate to the real processes. The effectiveness of the generalized threshold model method is evaluated in the analysis of the actual eukaryotic gene networks.     

Dynamic model of Escherichia coli tryptophan operon shows an optimal structural design.

A mathematical model has been developed to study the effect of external tryptophan on the trp operon. The model accounts for the effect of feedback repression by tryptophan through the Hill equation. We demonstrate that the trp operon maintains an intracellular steady-state concentration in a fivefold range irrespective of extracellular conditions. Dynamic behavior of the trp operon corresponding to varying levels of extracellular tryptophan illustrates the adaptive nature of regulation. Depending on the external tryptophan level in the medium, the transient response ranges from a rapid and underdamped to a sluggish and highly overdamped response. To test model fidelity, simulation results are compared with experimental data available in the literature. We further demonstrate the significance of the biological structure of the operon on the overall performance. Our analysis suggests that the tryptophan operon has evolved to a truly optimal design.     

Modeling of Actual Eukaryotic Control Gene Subnetworks Based on the Method of Generalized Threshold Models

Mathematical and computational means are developed that take into consideration the specifics of control processes at the molecular level and allow one to obtain both qualitative and quantitative patterns of gene network dynamics. Using the method of generalized threshold models, models are constructed for the Arabidopsis thalianaflower morphogenesis control subsystem and gene subnetwork controlling the Drosophila melanogasterearly ontogeny. The dynamics of these systems are investigated: kinetic curves are computed for molecular components (RNA, proteins), possible modes of functioning and steady states of the nets are revealed and biologically interpreted. The models are shown to be adequate to the real processes. The effectiveness of the generalized threshold model method is evaluated in the analysis of the actual eukaryotic gene networks.     

Bistable behavior in a model of the lac operon in Escherichia coli with variable growth rate

This work is a continuation from another study previously published in this journal. Both the former and the present works are dedicated to investigating the bistable behavior of the lac operon in Escherichia coli from a mathematical modeling point of view. In the previous article, we developed a detailed mathematical model that accounts for all of the known regulatory mechanisms in this system, and studied the effect of inducing the operon with lactose instead of an artificial inducer. In this article, the model is improved to account, in a more detailed way, for the interaction of the repressor molecules with the three lac operators. A recently discovered cooperative interaction between the CAP molecule (an activator of the lactose operon) and Operator 3 (which influences DNA folding) is also included in this new version of the model. The growth rate dependence on the rate of energy entering the bacteria (in the form of transported glucose molecules and of metabolized lactose molecules) is also considered. A large number of numerical experiments is carried out with this improved model. The results are discussed in regard to the bistable behavior of the lactose operon. Special attention is paid to the effect that a variable growth rate has on the system dynamics.     

The complete nucleotide sequence of the tryptophan operon of Escherichia coli.

The tryptophan (trp) operon of Escherichia coli has become the basic reference structure for studies on tryptophan metabolism. Within the past five years the application of recombinant DNA and sequencing methodologies has permitted the characterization of the structural and functional elements in this gene cluster at the molecular level. In this summary report we present the complete nucleotide sequence for the five structural genes of the trp operon of E. coli together with the internal and flanking regions of regulatory information.     

色氨酸操纵子调控机理详析

色氨酸操纵子是最早被研究的细菌合成代谢调控、基因表达调控的模型之一。其中阻遏蛋白对转录起始的抑制作用、色氨酸作为辅阻遏物的作用以及通过定点突变揭示的弱化作用的分子机制已基本被阐明。此外,色氨酸操纵子RNA结合弱化蛋白、NusA、NusG、TrpY等调节蛋白对细菌色氨酸操纵子弱化作用的调节机制也在近年来得到进一步揭示。特别是在枯草芽孢杆菌中,色氨酸操纵子主要依赖于转录衰减机制调控,包括由色氨酸激活的色氨酸操纵子RNA结合弱化蛋白与新生转录产物结合形成内部终止子,导致5′非翻译区（5′UTR）转录终止。NusA、NusG通过刺激RNA聚合酶在5′UTR的U107和U144位点暂停,释放出RNA聚合酶,最终造成转录终止。不同的是,在U144位点NusA参与的转录弱化机制依赖其发夹结构,且NusA与RNA聚合酶作用促进了RNA结合弱化蛋白与新生转录产物的结合,使转录终止。而NusG是通过与非模板DNA链中的一段富含T碱基序列和RNA聚合酶同时互作,阻止了RNA聚合酶向下游移动,从而引起RNA聚合酶高效停滞。但在细菌操纵子中,绝大多数调节因子参与的弱化机制最终依赖于ρ因子,从而导致多达一半的转录终止事件发生。近年来,随着学科的发展,越来越多关于色氨酸操纵子调节机制新概念被挖掘报道,这也使人类对色氨酸操纵子的表达调控机制的认知愈加详尽。