Decoding of calcium oscillations by phosphorylation cycles: analytic results

Experimental studies have demonstrated that Ca(2+)-regulated proteins are sensitive to the frequency of Ca(2+) oscillations, and several mathematical models for specific proteins have provided insight into the mechanisms involved. Because of the large number of Ca(2+)-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 Ca(2+) signals. Here we address this question by analyzing in detail a model of a prototypical Ca(2+)-decoding module, consisting of a target protein whose activity is controlled by a Ca(2+)-activated kinase and the counteracting phosphatase. We show that this module can decode the frequency of Ca(2+) oscillations, at constant average Ca(2+) signal, provided that the Ca(2+) spikes are narrow and the oscillation frequency is sufficiently low--of the order of the phosphatase rate constant or below. Moreover, Ca(2+) oscillations activate the target more efficiently than a constant signal when Ca(2+) is bound cooperatively and with low affinity. Thus, the rate constants and the Ca(2+) affinities of the target-modifying enzymes can be tuned in such a way that the module responds optimally to Ca(2+) spikes of a certain amplitude and frequency. Frequency sensitivity is further enhanced when the limited duration of the external stimulus driving Ca(2+) signaling is accounted for. Thus, our study identifies molecular parameters that may be involved in establishing the specificity of cellular responses downstream of Ca(2+) oscillations.