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Unlimited multistability in multisite phosphorylation systems

Nature volume 460, pages 274–277 (2009)Cite this article

Abstract

Reversible phosphorylation on serine, threonine and tyrosine is the most widely studied posttranslational modification of proteins1,2. The number of phosphorylated sites on a protein (n) shows a significant increase from prokaryotes, with n ≤ 7 sites, to eukaryotes, with examples having n ≥ 150 sites3. Multisite phosphorylation has many roles4,5 and site conservation indicates that increasing numbers of sites cannot be due merely to promiscuous phosphorylation. A substrate with n sites has an exponential number (2n) of phospho-forms and individual phospho-forms may have distinct biological effects6,7. The distribution of these phospho-forms and how this distribution is regulated have remained unknown. Here we show that, when kinase and phosphatase act in opposition on a multisite substrate, the system can exhibit distinct stable phospho-form distributions at steady state and that the maximum number of such distributions increases with n. Whereas some stable distributions are focused on a single phospho-form, others are more diffuse, giving the phospho-proteome the potential to behave as a fluid regulatory network able to encode information and flexibly respond to varying demands. Such plasticity may underlie complex information processing in eukaryotic cells8 and suggests a functional advantage in having many sites. Our results follow from the unusual geometry of the steady-state phospho-form concentrations, which we show to constitute a rational algebraic curve, irrespective of n. We thereby reduce the complexity of calculating steady states from simulating 3 × 2n differential equations to solving two algebraic equations, while treating parameters symbolically. We anticipate that these methods can be extended to systems with multiple substrates and multiple enzymes catalysing different modifications, as found in posttranslational modification ‘codes’9 such as the histone code10,11. Whereas simulations struggle with exponentially increasing molecular complexity, mathematical methods of the kind developed here can provide a new language in which to articulate the principles of cellular information processing12.

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Figure 1: General model of multisite phosphorylation with substrate S having n sites, kinase E and phosphatase F.
Figure 2: Multistability for an n = 4 distributive, sequential system, as in Fig. 3a .
Figure 3: Multistability by kinetic trapping.
Figure 4: Switching between stable states.

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Acknowledgements

This work was supported in part by the NIH under grant R01-GM081578. We thank A. Manrai for scientific discussions, R. Ward for editorial help and HMS RITG for support with cluster computing. We acknowledge the encouragement of the late Stephen Thomson (1946–2006) and Charles Gunawardena (1929–2007).

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Authors and Affiliations

  1. Biophysics Program, Harvard University, Cambridge, Massachusetts 02138, USA,

    Matthew Thomson

  2. Department of Systems Biology, Harvard Medical School, Boston, Massachusetts 02115, USA,

    Jeremy Gunawardena

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  1. Matthew Thomson
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Corresponding author

Correspondence to Jeremy Gunawardena.

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Thomson, M., Gunawardena, J. Unlimited multistability in multisite phosphorylation systems. Nature 460, 274–277 (2009). https://doi.org/10.1038/nature08102

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