### How does the cell regulate its phosphorylation state?

Jeremy Gunawardena
#### Abstract

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.

#### References

D A Jeffrey et al, *"Multi-site phosphorylation of Pho4 by the cyclin-CDK Pho80-Pho85 is semi-processive with site preference"*, JMB, 306:997-1010, 2001. PubMed.

H Okamura et al, *"Concerted dephosphorylation of the transcription factor NFAT1 induces a conformational switch that regulates transcriptional activity"*, Molecular Cell, 6:539-50, 2000. PubMed.

C Salazar and T Höfer, *"Allosteric regulation of the transcription factor NFAT1 by multiple phosphorylation sites: a mathematical analysis"*, JMB, 327-31-45, 2003. PubMed.