Temperature affects all biological processes, such as metabolism, development, population growth and locomotion. The rates of many of these processes in cells, animals and plants, appear to be Arrhenius, that is, they increase exponentially with the inverse of temperature. This is quite remarkable because they are not based on one simple chemical reaction, but rather a huge set of reactions happening on complex and partially known architectures. This poses a fundamental question: how are the multitude of Arrhenius reactions in an organism combined to result in a single Arrhenius rate? The one-rate limiting reaction theory argues that the rate of the entire process is determined by the slowest chemical reaction, which is Arrhenius by definition. However, recent experiments on cell division show that there are large deviations from a single Arrhenius, including non-monotonic behaviors at high temperatures. We present a mathematical description of the relationship between rates and temperature of the cell cycle, which fits with good accuracy the temperature dependence of cell division rates in C. elegans embryos, in the entire range of temperatures. We derive this expression from first principles for a simple oscillatory system of proteins, considered as the fundamental unit of all cell-cycle regulatory networks. We find that two competing mechanisms are responsible for shaping the temperature dependence of the global period of the system.
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