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arXiv 1209.5603q-bio.MN
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转录波动对生化振荡的影响

Transcription fluctuation effects on biochemical oscillations

Ryota Nishino, Takahiro Sakaue, Hiizu Nakanishi

备注：
with Supplementary material
发表信息：
PLoS ONE 8(4) (2013) e60938
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摘要：

生化振荡系统通常由负反馈环和抑制性转录调控组成。与普通的化学系统相比，这种系统具有独特的特征：i）所涉及的分子数量很少，ii）在有限的调控时间尺度下，细胞中通常只有几个基因。由于这些特征引起的波动，系统行为可能与速率方程获得的行为完全不同，因为速率方程忽略了分子波动，因此仅在无限分子数限制下是精确的。Gonze等人（2002）通过引入系统大小的尺度参数$Ω$研究了自由运行的昼夜节律系统上的分子波动。然而，他们只考虑第一种效应，假设基因过程足够快，第二种效应可以忽略不计，但这还没有得到系统的检验。在这项工作中，我们研究了波动效应由于有限的基因调控时间通过引入一个新的尺度参数$τ$，我们采取从基因的核蛋白的解结合时间。我们专注于的情况下，由于小分子数的波动可以忽略不计。在Gonze等人研究的同一系统的模拟中，我们发现该系统对转录调控的波动很敏感，即使调控时间尺度$τ$在30 s左右，振荡周期也在30 min左右波动，甚至小于其昼夜节律周期的1/1000。在小$τ$区域，振荡周期和振幅的分布宽度与$\sqrtτ$成比例，振荡的相关时间与$1/τ$成比例.周期的相对起伏约为振幅的一半，即周期比振幅更稳定。

英文摘要：

Biochemical oscillation systems often consist of negative feedback loops with repressive transcription regulation. Such systems have distinctive characteristics in comparison with ordinary chemical systems: i) the numbers of molecules involved are small, ii) there are typically only a couple of genes in a cell with a finite regulation time scale. Due to the fluctuations caused by these features, the system behavior can be quite different from the one obtained by rate equations, because the rate equations ignore molecular fluctuations and thus are exact only in the infinite molecular number limit. The molecular fluctuations on a free-running circadian system have been studied by Gonze et al. (2002) by introducing a scale parameter $Ω$ for the system size. They consider, however, only the first effect, assuming that the gene process is fast enough for the second effect to be ignored, but this has not been examined systematically yet. In this work, we study fluctuation effects due to the finite gene regulation time by introducing a new scale parameter $τ$, which we take as the unbinding time of a nuclear protein from the gene. We focus on the case where the fluctuations due to small molecular numbers can be ignored. In simulations on the same system studied by Gonze et al., we find the system is sensitive to the fluctuation in the transcription regulation; the period of oscillation fluctuates about 30 min even when the regulation time scale $τ$ is around 30 s, that is even smaller than 1/1000 of its circadian period. We also demonstrate that the distribution width for the oscillation period and the amplitude scales with $\sqrtτ$, and the correlation time of the oscillation scales with $1/τ$ in the small $τ$ regime. The relative fluctuations for the period are about half of that for the amplitude, namely, the periodicity is more stable than the amplitude.

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