About 30% of all proteins in any eukaryotic cell are thought to be phosphorylated at any time and many of these substrates have multiple phosphorylation sites. A single substrate molecule with n sites has 2^n states and a population of N such molecules has (2^n)^N states. How do the kinases and phosphatases collectively determine which states appear in the population? I will review earlier work on this problem for n = 1 by Chock and Stadtman and Goldbeter and Koshland and for n = 2 by Ferrell et al and then discuss some recent calculations for arbitrary values of n. These suggest that more elaborate regulatory mechanisms are necessary for large numbers of phosphorylation sites and I will mention some potential elaborations in the light of recent work on the transcription factors NFAT1 and Pho4.
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