Feedback Regulation in the Lactose Operon: A Mathematical Modeling Study and Comparison with Experimental Data

Yıldırım, Necmettin; Mackey, Michael C.

doi:10.1016/s0006-3495(03)70013-7

Cited by 191 publications

(245 citation statements)

References 55 publications

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“…ref. 41 and references therein). It could be a dominant source of large deterministic variability, as in the case of circadian rhythms (26,27), or it can play a supportive role as a mechanism that amplifies the effects of random fluctuations.…”

Section: Discussionmentioning

confidence: 99%

Delay-induced stochastic oscillations in gene regulation

Bratsun

Volfson

Tsimring

et al. 2005

Proc. Natl. Acad. Sci. U.S.A.

513

487

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The small number of reactant molecules involved in gene regulation can lead to significant fluctuations in intracellular mRNA and protein concentrations, and there have been numerous recent studies devoted to the consequences of such noise at the regulatory level. Theoretical and computational work on stochastic gene expression has tended to focus on instantaneous transcriptional and translational events, whereas the role of realistic delay times in these stochastic processes has received little attention. Here, we explore the combined effects of time delay and intrinsic noise on gene regulation. Beginning with a set of biochemical reactions, some of which are delayed, we deduce a truncated master equation for the reactive system and derive an analytical expression for the correlation function and power spectrum. We develop a generalized Gillespie algorithm that accounts for the non-Markovian properties of random biochemical events with delay and compare our analytical findings with simulations. We show how time delay in gene expression can cause a system to be oscillatory even when its deterministic counterpart exhibits no oscillations. We demonstrate how such delay-induced instabilities can compromise the ability of a negative feedback loop to reduce the deleterious effects of noise. Given the prevalence of negative feedback in gene regulation, our findings may lead to new insights related to expression variability at the whole-genome scale.master equation ͉ stochastic delay equations ͉ noise ͉ time delay ͉ systems biology T here is considerable experimental evidence that noise can play a major role in gene regulation (1-10). These fluctuations can arise from either intrinsic sources, which are related to the small numbers of reactant biomolecules, or extrinsic sources, which are attributable to a noisy cellular environment. Although the importance of fluctuations in gene regulation was stressed Ͼ30 years ago (11), recent experimental advances have renewed interest in the stochastic modeling of the biochemical reactions that underlie gene regulatory networks (12-16). The most typical approaches are the utilization of the Gillespie algorithms (17)(18)(19)(20), the direct analysis of the master equation, or the development of simplified descriptions based on the Fokker-Planck or Langevin equations (see ref. 21 for a review). A common thread in many of these approaches has been to consider intrinsic noise as the dominant source of variability in gene expression.One major difficulty often encountered in the analysis of gene regulatory networks is the vast separation of time scales between what are typically the fast reactions (dimerization, protein-DNA binding͞unbinding) and the slow reactions (transcription, translation, degradation). There have been many studies devoted to the development of reduced descriptions of these systems using the idea of quasiequilibrium for the fast processes compared with the slow dynamics (cf. ref. 22 and references therein). These approaches have thus far implicitly assumed that all...

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Section: Discussionmentioning

confidence: 99%

Delay-induced stochastic oscillations in gene regulation

Bratsun

Volfson

Tsimring

et al. 2005

Proc. Natl. Acad. Sci. U.S.A.

513

487

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“…This kind of transcriptional regulation appears, for example, in bacterial uptake and utilization systems, whereby enzyme expression is controlled by metabolite-responsive transcription factors ( Figure 1B), e.g. the lactose operon [8,9], and also in aminoacid biosynthesis, e.g. the tryptophan operon [10] and arginine synthesis [11].…”

Section: Generic Model For An Unbranched Metabolic Network Under Tranmentioning

confidence: 99%

“…A widely studied instance of this type of regulatory structure is the lac operon, with a range of mathematical models developed in the literature (see [8,9] and the references therein). For our purposes, a simplified description of the lac operon in the form of the generic model in (1)-(2) can be constructed by (see Figure 10) setting s 0 =lactose (extracellular), s 1 =lactose (internal), and s 2 =allolactose, with the enzymes defined by e 0 =permease (coded by lacY ), and e 1 = β-galactosidase (coded by lacZ ).…”

Section: Regulation Via An Operon: Substrate-induced Bifurcationsmentioning

confidence: 99%

“…One-to-all regulatory motifs are also referred to as "single input modules" and were identified as one of the building blocks in genome-wide bacterial networks [7]. Metabolic networks under one-to-all transcriptional regulation appear in uptake and utilization/biosynthesis systems, whereby enzyme expression is controlled by intracellular metabolites, as in the case of the lactose operon [8,9], and amino acid biosynthesis, e.g. the tryptophan operon [10] and the arginine synthesis network [11].…”

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confidence: 99%

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Multistability and oscillations in genetic control of metabolism

Oyarzún

Chaves²,

Hoff-Hoffmeyer-Zlotnik³

2012

Journal of Theoretical Biology

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Genetic control of enzyme activity drives metabolic adaptations to environmental changes, and therefore the feedback interaction between gene expression and metabolism is essential to cell fitness. In this paper we develop a new formalism to detect the equilibrium regimes of an unbranched metabolic network under transcriptional feedback from one metabolite. Our results indicate that one-to-all transcriptional feedback can induce a wide range of metabolic phenotypes, including mono-, multistability and oscillatory behavior. The analysis is based on the use of switch-like models for transcriptional control and the exploitation of the time scale separation between metabolic and genetic dynamics. For any combination of activation and repression feedback loops, we derive conditions for the emergence of a specific phenotype in terms of genetic parameters such as enzyme expression rates and regulatory thresholds. We find that metabolic oscillations can emerge under uniform thresholds and, in the case of operoncontrolled networks, the analysis reveals how nutrient-induced bistability and oscillations can emerge as a consequence of the transcriptional feedback.

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“…Our starting point is a model of the lactose system due to Yildirim and Mackey [1], [9], adapted to the use of thiomethyl galactosidase (TMG) as inducer. Briefly, the mRNA (M ) transcribed from the lactose operon is translated into three different gene products, among them permease (P ) and β-galactosidase (B).…”

Section: A Deterministic Continuous Modelmentioning

confidence: 99%

Controlling biological systems: the lactose regulation system of Escherichia coli

Julius

Halász

Kumar

et al. 2007

2007 American Control Conference

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In this paper we present a comprehensive framework for abstraction and controller design for a biological system. The first half of the paper concerns modeling and model abstraction of the system. Most models in systems biology are deterministic models with ordinary differential equations in the concentration variables. We present a stochastic hybrid model of the lactose regulation system of E. coli bacteria that capture important phenomena which cannot be described by continuous deterministic models. We then show that the resulting stochastic hybrid model can be abstracted into a much simpler model, a two-state continuous time Markov chain.The second half of the paper discusses controller design for a specific architecture. The architecture consists of measurement of a global quantity in a colony of bacteria as an output feedback, and manipulation of global environmental variables as control actuation. We show that controller design can be performed on the abstracted (Markov chain) model and implementation on the real model yields the desired result. Abstract-In this paper we present a comprehensive framework for abstraction and controller design for a biological system. The first half of the paper concerns modeling and model abstraction of the system. Most models in systems biology are deterministic models with ordinary differential equations in the concentration variables. We present a stochastic hybrid model of the lactose regulation system of E. coli bacteria that capture important phenomena which cannot be described by continuous deterministic models. We then show that the resulting stochastic hybrid model can be abstracted into a much simpler model, a two-state continuous time Markov chain. Disciplines Engineering | Mechanical EngineeringThe second half of the paper discusses controller design for a specific architecture. The architecture consists of measurement of a global quantity in a colony of bacteria as an output feedback, and manipulation of global environmental variables as control actuation. We show that controller design can be performed on the abstracted (Markov chain) model and implementation on the real model yields the desired result. I. INTRODUCTIONIn this paper we present a framework that consists of modeling, abstraction and control of a biological system, namely, the lactose regulation system of the Escherichia coli bacteria. The conceptual idea behind the paper is captured in Figure 1. Roughly speaking, the paper can be divided into two parts. The first part corresponds to the lower half of the hourglass in Figure 1, that discusses modeling of the lac regulation system as a stochastic hybrid system. The model presented in this paper is a slight modification of the one presented in our earlier work [1]. We also discuss how the stochastic hybrid model can be abstracted into a two-state continuous time Markov chain, and demonstrate how this abstraction is consistent with the macroscopic behavior of a colony of bacteria.The second part of the paper pertains to the upper half of the ...

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Feedback Regulation in the Lactose Operon: A Mathematical Modeling Study and Comparison with Experimental Data

Cited by 191 publications

References 55 publications

Delay-induced stochastic oscillations in gene regulation

Delay-induced stochastic oscillations in gene regulation

Multistability and oscillations in genetic control of metabolism

Controlling biological systems: the lactose regulation system of Escherichia coli

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