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首页> 外文期刊>Journal of Biological Physics >Deterministic Versus Stochastic Models for Circadian Rhythms
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Deterministic Versus Stochastic Models for Circadian Rhythms

机译：昼夜节律的确定性与随机模型

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Circadian rhythms which occur with a period close to 24 h in nearly all living organisms originate from the negative autoregulation of gene expression.Deterministic models based on genetic regulatory processes account for theoccurrence of circadian rhythms in constant environmental conditions (e.g.constant darkness), for entrainment of these rhythms by light-dark cycles, and for their phase-shifting by light pulses. At low numbers of protein and mRNA molecules, it becomes necessary to resort to stochastic simulations to assess the influence of molecular noise on circadian oscillations. We address the effect of molecular noise by considering two stochastic versions of a core model for circadian rhythms. The deterministic version of this core modelwas previously proposed for circadian oscillations of the PER protein in Drosophila and of the FRQ protein in Neurospora. In the first, non-developed version of the stochastic model, we introduce molecular noise without decomposing the deterministic mechanism into detailed reaction steps while in the second, developed version we carry out such a detailed decomposition. Numerical simulations of the two stochastic versions of the model are performed by means of the Gillespie method. We compare the predictions of the deterministic approach with those of the two stochastic models, with respect both to sustained oscillations of the limit cycle type and to the influence of the proximity of a bifurcation point beyond which the system evolves to a stable steady state. The results indicate that robust circadian oscillations can occur even when the numbers of mRNA and nuclear protein involved in the oscillatory mechanism are reduced to a few tens orhundreds, respectively. The non-developed and developed versions of the stochastic model yield largely similar results and provide good agreement with the predictions of the deterministic model for circadian rhythms.
机译：在几乎所有活生物体中，昼夜节律发生的时间都接近24小时，这源于基因表达的负自调控。基于遗传调控过程的确定性模型解释了恒定环境条件（例如恒定的黑暗）下昼夜节律的发生，从而导致了引诱这些节奏的变化是由明暗周期决定的，并且由于光脉冲而使它们发生相移。在蛋白质和mRNA分子数量较少的情况下，有必要诉诸于随机模拟来评估分子噪声对生物钟振荡的影响。我们通过考虑昼夜节律的核心模型的两个随机版本来解决分子噪声的影响。该核心模型的确定性版本先前曾提出用于果蝇中PER蛋白和Neurospora中FRQ蛋白的昼夜节律振荡。在随机模型的第一个非开发版本中，我们在不将确定性机制分解为详细的反应步骤的情况下引入了分子噪声，而在第二个开发的版本中，我们进行了这种详细的分解。该模型的两个随机版本的数值模拟是通过Gillespie方法进行的。我们将确定性方法的预测与两种随机模型的预测相比，在极限循环类型的持续振荡以及分叉点附近的影响（系统超过该分叉点演变成稳定的稳态）方面都进行了比较。结果表明，即使参与振荡机制的mRNA和核蛋白的数量分别减少到几十个或几百个，也可能发生鲁棒的昼夜节律振荡。随机模型的未开发版本和已开发版本产生的结果大致相似，并且与昼夜节律的确定性模型的预测非常吻合。

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