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Circadian clocks ubiquitous in life forms ranging bacteria to multi-cellularorganisms, often exhibit intrinsic temperature compensation; the period ofcircadian oscillators is maintained constant over a range of physiologicaltemperatures, despite the expected Arrhenius form for the reaction coefficient.Observations have shown that the amplitude of the oscillation depends on thetemperature but the period does not---this suggests that although not everyreaction step is temperature independent, the total system comprising severalreactions still exhibits compensation. We present a general mechanism for suchtemperature compensation. Consider a system with multiple activation energybarriers for reactions, with a common enzyme shared across several reactionsteps with a higher activation energy. These reaction steps rate-limit thecycle if the temperature is not high. If the total abundance of the enzyme islimited, the amount of free enzyme available to catalyze a specific reactiondecreases as more substrates bind to common enzyme. We show that this change infree enzyme abundance compensate for the Arrhenius-type temperature dependenceof the reaction coefficient. Taking the example of circadian clocks withcyanobacterial proteins KaiABC consisting of several phosphorylation sites, weshow that this temperature compensation mechanisms is indeed valid.Specifically, if the activation energy for phosphorylation is larger than thatfor dephosphorylation, competition for KaiA shared among the phosphorylationreactions leads to temperature compensation. Moreover, taking a simpler model,we demonstrate the generality of the proposed compensation mechanism,suggesting relevance not only to circadian clocks but to other (bio)chemicaloscillators as well.

Generic temperature compensation of biological clocks by autonomous regulation of catalyst concentration