A two variable delay model for the circadian rhythm of Neurospora crassa

Sriram, K.; Gopinathan, M. S.

doi:10.1016/j.jtbi.2004.04.006

Cited by 63 publications

(51 citation statements)

References 48 publications

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“…Profile of period obtained as a function of the clock protein degradation rate (q p ) in the delay model for circadian oscillations (Scheper et al 1999a,b). ( A minimal delay model for circadian oscillations was proposed by Scheper et al (1999a,b) (see also Sriram & Gopinathan 2004). It consists of two variables, the mRNA (M ) and protein (P) concentrations, and contains a single explicit delay included in the function describing the rate of protein synthesis…”

Section: Extending the Results To Other Models For Circadian Oscillatmentioning

confidence: 99%

Dependence of the period on the rate of protein degradation in minimal models for circadian oscillations

Gérard

Gonze

Goldbeter

2009

Phil. Trans. R. Soc. A.

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Circadian rhythms, which occur spontaneously with a period of about 24 h in a variety of organisms, allow their adaptation to the periodic variations of the environment. These rhythms are generated by a genetic regulatory network involving a negative feedback loop on transcription. Mathematical models based on the negative autoregulation of gene expression by the protein product of a clock gene account for the occurrence of selfsustained circadian oscillations. These models differ by their degree of complexity and, hence, by the number of variables considered. Some of these models can be considered as minimal because they contain a reduced number of biochemical processes and variables capable of producing sustained oscillations. In three of these minimal models, the period of the oscillations significantly changes with the rate of degradation of the clock protein. However, depending on the model considered, the period increases, decreases or passes through a maximum as a function of the protein degradation rate. We clarify the bases for these markedly different results by bringing to light the roles of (i) protein phosphorylation, which is required for protein degradation, and (ii) the velocity and degree of saturation of mRNA and protein degradation. Changes in the parameter values of the more complex of the minimal models can produce the period profiles observed in the other two models. The analysis allows us to reconcile the contradictory predictions for the dependence of the period on the clock protein degradation rate in three minimal models used to describe circadian rhythms.

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Section: Extending the Results To Other Models For Circadian Oscillatmentioning

confidence: 99%

Dependence of the period on the rate of protein degradation in minimal models for circadian oscillations

Gérard

Gonze

Goldbeter

2009

Phil. Trans. R. Soc. A.

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“…They may cause oscillations of mRNA and protein concentrations. However, the process of degradation of both mRNA (Clayton and Shapira 2007) and proteins (Clayton and Shapira 2007;Liu et al 2000;Smolen et al 2001;Sriram and Gopinathan 2004) can also consist of several steps and therefore can be modeled by explicit time delays. Delayed degradation of JAK2 protein in signaling pathways was discussed in Melzner et al (2006).…”

Section: Introductionmentioning

confidence: 99%

Stochastic Models of Gene Expression with Delayed Degradation

et al. 2011

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In many biochemical reactions occurring in living cells, number of various molecules might be low which results in significant stochastic fluctuations. In addition, most reactions are not instantaneous, there exist natural time delays in the evolution of cell states. It is a challenge to develop a systematic and rigorous treatment of stochastic dynamics with time delays and to investigate combined effects of stochasticity and delays in concrete models.We propose a new methodology to deal with time delays in biological systems and apply it to simple models of gene expression with delayed degradation. We show that time delay of protein degradation does not cause oscillations as it was recently argued. It follows from our rigorous analysis that one should look for different mechanisms responsible for oscillations observed in biological experiments.We develop a systematic analytical treatment of stochastic models of time delays. Specifically we take into account that some reactions, for example degradation, are consuming, that is: once molecules start to degrade they cannot be part in other degradation processes. We introduce an auxiliary stochastic process and calculate analytically the variance and the autocorrelation function of the number of protein molecules in stationary states in basic models of delayed protein degradation.

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“…It is widely accepted now that these oscillations are caused by delays in certain elements of gene regulation networks [see recent experimental (24,25) and modeling (26)(27)(28)(29) studies]. It is plausible that the role of time delays in circadian rhythms has come to light because the delays in the corresponding reactions are particularly long (several hours) in comparison with other characteristic times of the system.…”

mentioning

confidence: 99%

Delay-induced stochastic oscillations in gene regulation

Bratsun

Volfson

Tsimring

et al. 2005

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

515

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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A two variable delay model for the circadian rhythm of Neurospora crassa

Cited by 63 publications

References 48 publications

Dependence of the period on the rate of protein degradation in minimal models for circadian oscillations

Dependence of the period on the rate of protein degradation in minimal models for circadian oscillations

Stochastic Models of Gene Expression with Delayed Degradation

Delay-induced stochastic oscillations in gene regulation

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