A Mathematical Model for the Intracellular Circadian Rhythm Generator

Scheper, Tjeerd Olde; Klinkenberg, D.; Pennartz, Cyriel M. A.; Pelt, Jaap van

doi:10.1523/jneurosci.19-01-00040.1999

Cited by 142 publications

(106 citation statements)

References 36 publications

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“…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. Along these lines, it is interesting to note that our model can be used to demonstrate that the ''noise signature'' of a system dominated by delay can be similar to a system dominated by intrinsic noise (Fig.…”

Section: Discussionmentioning

confidence: 99%

“…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.…”

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confidence: 99%

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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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Section: Discussionmentioning

confidence: 99%

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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“…Some modeling of circadian rhythms, including recent efforts [e.g., Scheper et al (1999)], is essentially phenomenological in that little biochemical justification is given for the equations used. However, biochemically realistic models of circadian rhythmicity in Drosophila, which should apply without great modification to mammals, have been developed recently by Goldbeter and coworkers.…”

Section: 2mentioning

confidence: 99%

Modeling Transcriptional Control in Gene Networks—Methods, Recent Results, and Future Directions

Smolen

Baxter

Byrne

2000

Bulletin of Mathematical Biology

280

161

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Mathematical models are useful for providing a framework for integrating data and gaining insights into the static and dynamic behavior of complex biological systems such as networks of interacting genes. We review the dynamic behaviors expected from model gene networks incorporating common biochemical motifs, and we compare current methods for modeling genetic networks. A common modeling technique, based on simply modeling genes as ON-OFF switches, is readily implemented and allows rapid numerical simulations. However, this method may predict dynamic solutions that do not correspond to those seen when systems are modeled with a more detailed method using ordinary differential equations. Until now, the majority of gene network modeling studies have focused on determining the types of dynamics that can be generated by common biochemical motifs such as feedback loops or protein oligomerization. For example, these elements can generate multiple stable states for gene product concentrations, state-dependent responses to stimuli, circadian rhythms and other oscillations, and optimal stimulus frequencies for maximal transcription. In the future, as new experimental techniques increase the ease of characterization of genetic networks, qualitative modeling will need to be supplanted by quantitative models for specific systems.

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“…The parameters k i represent the degradation rate of the corresponding biological entity. Models in the general structure of (1.4) are frequently encountered in the modeling of biological processes such as mitogen-activated protein cascades and circadian rhythm generator, see, e.g., [28][29][30] and [31]. To account for the switchlike phenomena observed in gene regulation, the nonlinear regulation functions are often approximated by Hill functions [32,33].…”

Section: Continuous-time Modelsmentioning

confidence: 99%