Decoding of Calcium Oscillations by Phosphorylation Cycles: Analytic Results

Experimental studies have demonstrated that Ca2+-regulated proteins are sensitive to the frequency of Ca2+ oscillations, and several mathematical models for specific proteins have provided insight into the mechanisms involved. Because of the large number of Ca2+-regulated proteins in signal transduction, metabolism and gene expression, it is desirable to establish in general terms which molecular properties shape the response to oscillatory Ca2+ signals. Here we address this question by analyzing in detail a model of a prototypical Ca2+-decoding module, consisting of a target protein whose activity is controlled by a Ca2+-activated kinase and the counteracting phosphatase. We show that this module can decode the frequency of Ca2+ oscillations, at constant average Ca2+ signal, provided that the Ca2+ spikes are narrow and the oscillation frequency is sufficiently low—of the order of the phosphatase rate constant or below. Moreover, Ca2+ oscillations activate the target more efficiently than a constant signal when Ca2+ is bound cooperatively and with low affinity. Thus, the rate constants and the Ca2+ affinities of the target-modifying enzymes can be tuned in such a way that the module responds optimally to Ca2+ spikes of a certain amplitude and frequency. Frequency sensitivity is further enhanced when the limited duration of the external stimulus driving Ca2+ signaling is accounted for. Thus, our study identifies molecular parameters that may be involved in establishing the specificity of cellular responses downstream of Ca2+ oscillations.