Delays in gene networks result from the sequential nature of protein assembly. However, it is unclear how models of gene networks that use delays should be modified when considering time-dependent changes in temperature. This is important, as delay is often used in models of genetic oscillators that can be entrained by periodic fluctuations in temperature. Here, we analytically derive the time dependence of delay distributions in response to time-varying temperature changes. We find that the resulting time-varying delay is nonlinearly dependent on parameters of the time-varying temperature such as amplitude and frequency, therefore, applying an Arrhenius scaling may result in erroneous conclusions. We use these results to examine a model of a synthetic gene oscillator with temperature compensation. We show that temperature entrainment follows from the same mechanism that results in temperature compensation. Under a common Arrhenius scaling alone, the frequency of the oscillator is sensitive to changes in the mean temperature but robust to changes in the frequency of a periodically time-varying temperature. When a mechanism for temperature compensation is included in the model, however, we show that the oscillator is entrained by periodically varying temperature even when maintaining insensitivity to the mean temperature.

中文翻译：

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时变温度对遗传网络延迟的影响。

基因网络的延迟是由于蛋白质装配的顺序性造成的。但是，尚不清楚在考虑温度随时间的变化时，应如何修改使用延迟的基因网络模型。这很重要，因为延迟通常在遗传振荡器的模型中使用，而周期性的温度波动可能会拖延这种延迟。在这里，我们通过分析推导响应温度随时间变化的延迟分布的时间依赖性。我们发现，产生的时变延迟与时变温度的参数（例如幅度和频率）非线性相关，因此，应用Arrhenius缩放可能会得出错误的结论。我们使用这些结果来检查具有温度补偿的合成基因振荡器的模型。我们显示温度夹带遵循导致温度补偿的相同机制。仅在常见的Arrhenius标度下，振荡器的频率对平均温度的变化敏感，但对周期性时变温度的频率变化却很稳定。然而，当模型中包括温度补偿机制时，我们表明，即使保持对平均温度的敏感性，振荡器也会受到周期性变化温度的影响。