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Cytosolic calcium plays a crucial role as a second messenger in cellular signalling. Various cell types, including hepatocytes, display Ca2 ‘ oscillations when stimulated by an extracellular signal. However, the biological relevance of this temporal organization remains unclear. In this paper, we investigate theoretically the e!ect of Ca2 ‘ oscillations on a particular example of cell regulation: the phosphorylation}dephosphorylation cycle controlling the activation of glyco-gen phosphorylase in hepatocytes. By modelling periodic sinusoidal variations in the intracel-lular Ca2 ‘ concentration, we show that Ca2 ‘ oscillations reduce the threshold for the activation of the enzyme. Furthermore, as the activation of a given enzyme depends on the kinetics of its phosphorylation}dephosphorylation cycle, speci"city can be encoded by the oscillation frequency. Finally, using a model for signal-induced Ca2 ‘ oscillations based on Ca2‘-induced Ca2 ‘ release, we show that realistic Ca2 ‘ oscillations can potentiate the response to a hormonal stimulation. These results indicate that Ca2 ‘ oscillations in hepa-tocytes could contribute to increase the e$ciency and speci"city of cellular signalling, as shown experimentally for gene expression in lymphocytes (Dolmetsch et al., 1998). ( 2000 Academic Pres