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Decoding of Calcium Oscillations by Phosphorylation Cycles: Analytic Results

Research Group Modeling of Biological Systems, German Cancer Research Center, Heidelberg, Germany

Correspondence: Address reprint requests to Carlos Salazar, E-mail: c.salazar{at}dkfz-heidelberg.de; or Thomas Höfer, E-mail: t.hoefer{at}dkfz-heidelberg.de.

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.