The Role of Dimerization in Noise Reduction of Simple Genetic Networks

Bundschuh, Ralf; Hayot, F.; Jayaprakash, C.

doi:10.1006/jtbi.2003.3164

Cited by 86 publications

(81 citation statements)

References 20 publications

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“…Nevertheless, our formulation in Eqs. 1-3 corresponds to the statistically averaged results of more complex models that do include these stochastic effects (18). The advantage of our approach is that it allows us to rapidly elucidate the average behavior of each circuit for all combinations of its parameters.…”

Section: Circuits and Modelsmentioning

confidence: 99%

Nonlinear protein degradation and the function of genetic circuits

Buchler

Gerland

Hwa

2005

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

157

169

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The functions of most genetic circuits require a sufficient degree of cooperativity in the circuit components. Although mechanisms of cooperativity have been studied most extensively in the context of transcriptional initiation control, cooperativity from other processes involved in the operation of the circuits can also play important roles. In this work, we examine a simple kinetic source of cooperativity stemming from the nonlinear degradation of multimeric proteins. Ample experimental evidence suggests that protein subunits can degrade less rapidly when associated in multimeric complexes, an effect we refer to as ''cooperative stability.'' For dimeric transcription factors, this effect leads to a concentration-dependence in the degradation rate because monomers, which are predominant at low concentrations, will be more rapidly degraded. Thus, cooperative stability can effectively widen the accessible range of protein levels in vivo. Through theoretical analysis of two exemplary genetic circuits in bacteria, we show that such an increased range is important for the robust operation of genetic circuits as well as their evolvability. Our calculations demonstrate that a few-fold difference between the degradation rate of monomers and dimers can already enhance the function of these circuits substantially. We discuss molecular mechanisms of cooperative stability and their occurrence in natural or engineered systems. Our results suggest that cooperative stability needs to be considered explicitly and characterized quantitatively in any systematic experimental or theoretical study of gene circuits.amplification ͉ dimerization ͉ bistability ͉ oscillation I t is widely recognized that controlled proteolysis, where the degradation of one protein depends on the presence of another protein in the cell, can play an important regulatory role in genetic circuits (1). Here, we examine another effect of proteolysis that does not involve such regulatory control, but can nevertheless impact the function of genetic circuits in important ways. It is a kinetic, cooperative effect predicated on the following two essential ingredients: (i) the fact that many proteins perform their physiological functions as dimers or higher-order oligomers, and (ii) the tendency for the oligomers to be more stable (to proteolysis) than their monomeric components. This effect, referred to below as ''cooperative stability,'' has been discussed previously in qualitative terms in the context of many well-studied examples in prokaryotes and eukaryotes (1, 2). For example, in the SOS response of Escherichia coli, UmuC degradation is rescued by oligomerization with UmuDЈ 2 (3). Additionally, in Saccharomyces cerevisiae, the dimerization of a1 and ␣2 reduced the degradation rate by as much as 15-fold (4). Possible molecular mechanisms that give rise to cooperative stability include enhanced thermal stability of proteins upon mutual association [because thermal instability correlates with the rate of degradation (5, 6)] and the burial of proteolytic recogni...

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Section: Circuits and Modelsmentioning

confidence: 99%

Nonlinear protein degradation and the function of genetic circuits

Buchler

Gerland

Hwa

2005

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

157

169

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“…As discussed in the appendix, the repressor gal80p, and the structural proteins gal7p and gal10p, all form dimers, which has been shown t o reduce noise in genetic networks [30]. In order to assess the degree of noise reduction, it is convenient to work in terms of the Fano factor, which is the ratio of variance to mean.…”

Section: Dimerization Reduces Intrinsic Noisementioning

confidence: 99%

Evolution of design principles in biochemical networks

et al. 2004

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Computer modelling and simulation are commonly used to analyse engineered systems.Biological systems differ in that they often can not be accurately characterized, so simulations are far from exact. Nonetheless , we argue in this paper that evolution results in recurring, dynamic organizational principles in biological systems, and that simulation can help to identify them and analyse their dynamic properties. As a specific example, we present a dynamic model of the galactose utilization pathway in yeast, and highlight several features of the model that embody such "design principles".

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“…A few studies have also considered variations of this simple model by allowing inhibition or activation by protein dimers. 24,25 In this paper we obtain an exact solution of the master equation for arbitrary free and bound protein degradation rates in non-equilibrium steady-state conditions. For the case of equal bound and free protein degradation rates, our solution differs markedly from the exact solution claimed by Hornos et al; 19 we explicitly show that the difference between the two solutions stems from the fact that the master equations studied in the latter work have no consistent physical interpretation and hence constitute an incorrect description of the biochemical processes at play.…”

Section: Introductionmentioning

confidence: 99%

Steady-state fluctuations of a genetic feedback loop: An exact solution

Grima

Schmidt

Newman³

2012

The Journal of Chemical Physics

129

161

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Genetic feedback loops in cells break detailed balance and involve bimolecular reactions; hence, exact solutions revealing the nature of the stochastic fluctuations in these loops are lacking. We here consider the master equation for a gene regulatory feedback loop: a gene produces protein which then binds to the promoter of the same gene and regulates its expression. The protein degrades in its free and bound forms. This network breaks detailed balance and involves a single bimolecular reaction step. We provide an exact solution of the steady-state master equation for arbitrary values of the parameters, and present simplified solutions for a number of special cases. The full parametric dependence of the analytical non-equilibrium steady-state probability distribution is verified by direct numerical solution of the master equations. For the case where the degradation rate of bound and free protein is the same, our solution is at variance with a previous claim of an exact solution [J. E. M. Hornos, D. Schultz, G. C. P. Innocentini, J. Wang, A. M. Walczak, J. N. Onuchic, and P. G. Wolynes, Phys. Rev. E 72, 051907 (2005), and subsequent studies]. We show explicitly that this is due to an unphysical formulation of the underlying master equation in those studies.

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The Role of Dimerization in Noise Reduction of Simple Genetic Networks

Cited by 86 publications

References 20 publications

Nonlinear protein degradation and the function of genetic circuits

Nonlinear protein degradation and the function of genetic circuits

Evolution of design principles in biochemical networks

Steady-state fluctuations of a genetic feedback loop: An exact solution

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