The effects of time-varying temperature on delayed gene networks

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 timedependent changes in temperature. This is important, as delay is often used in models of genetic oscillators, such as circadian 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 and use these results to examine a model of a synthetic gene oscillator. We demonstrate that, 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 maintaing insensitivity to the mean temperature.