Stochastic π-Calculus Modelling of Multisite Phosphorylation Based Signaling: The PHO Pathway in Saccharomyces Cerevisiae

  • Nicola Segata
  • Enrico Blanzieri
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5410)


We propose a stochastic π-calculus modelling approach able to handle the complexity of post-translational signalling and to overcome some limitations of the ordinary differential equations based methods. The model we developed is customizable without a priori assumptions to every multisite phosphorylation regulation. We applied it to the multisite phosphorylation of the Pho4 transcription factor that plays a crucial role in the phosphate starvation signalling in Saccharomyces cerevisiae, using available in vitro experiments for the model tuning and validation. The in silico simulation of the sub-path with the stochastic π-calculus allows quantitative analyses of the kinetic characteristics of the Pho4 phosphorylation, the different phosphorylation dynamics for each site (possibly combined) and the variation of the kinase activity as the reaction goes to completion. One of the predictions indicates that the Pho80-Pho85 kinase activity on the Pho4 substrate is nearly distributive and not semi-processive as previously found analysing only the phosphoform concentrations in vitro. Thanks to the compositionality property of process algebras, we also developed the whole PHO pathway model that gives new suggestions and confirmations about its general behaviour. The potentialities of process calculi-based in silico simulations for biological systems are highlighted and discussed.


Parallel Composition Process Algebra Phosphate Starvation Phosphate Condition PHO5 Promoter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Seet, B., Dikic, I., Zhou, M., Pawson, T., et al.: Reading protein modifications with interaction domains. Nat. Rev. Mol. Cell. Biol. 7, 473–483 (2006)CrossRefGoogle Scholar
  2. 2.
    Yang, X.: Multisite protein modification and intramolecular signaling. Oncogene 24, 1653–1662 (2005)CrossRefGoogle Scholar
  3. 3.
    Seo, J., Lee, K.: Post-translational modifications and their biological functions: proteomic analysis and systematic approaches. J. Biochem. Mol. Biol. 37(1), 35–44 (2004)Google Scholar
  4. 4.
    Gunawardena, J.: Multisite protein phosphorylation makes a good threshold but can be a poor switch. Proc. Natl. Acad. Sci. USA 102(41), 14617–14622 (2005)CrossRefGoogle Scholar
  5. 5.
    Holmberg, C., Tran, S., Eriksson, J., Sistonen, L.: Multisite phosphorylation provides sophisticated regulation of transcription factors. Trends Biochem. Sci. 27(12), 619–627 (2002)CrossRefGoogle Scholar
  6. 6.
    Cohen, P.: The regulation of protein function by multisite phosphorylation–a 25 year update. Trends Biochem. Sci. 25(12), 596–601 (2000)CrossRefGoogle Scholar
  7. 7.
    Mayya, V., Rezual, K., Wu, L., Fong, M., Han, D.: Absolute Quantification of Multisite Phosphorylation by Selective Reaction Monitoring Mass Spectrometry: Determination of Inhibitory Phosphorylation Status of Cyclin-Dependent Kinases. Mol. Cell. Proteomics 5(6), 1146 (2006)CrossRefGoogle Scholar
  8. 8.
    Glinski, M., Weckwerth, W.: Differential Multisite Phosphorylation of the Trehalose-6-phosphate Synthase Gene Family in Arabidopsis thaliana: A Mass Spectrometry-based Process for Multiparallel Peptide Library Phosphorylation Analysis. Mol. Cell. Proteomics 4(10), 1614–1625 (2005)CrossRefGoogle Scholar
  9. 9.
    Jeffery, D., Springer, M., King, D., O’Shea, E.: Multi-site phosphorylation of Pho4 by the cyclin-CDK Pho80-Pho85 is semi-processive with site preference. J. Mol. Biol. 306(5), 997–1010 (2001)CrossRefGoogle Scholar
  10. 10.
    Markevich, N.I., Hoek, J.B., Kholodenko, B.N.: Signaling switches and bistability arising from multisite phosphorylation in protein kinase cascades. J. Cell. Biol. 164(3), 353–359 (2004)CrossRefGoogle Scholar
  11. 11.
    Batchelor, E., Goulian, M.: Robustness and the cycle of phosphorylation and dephosphorylation in a two-component regulatory system. Proc. Natl. Acad. Sci. USA 100(2), 691–696 (2003)CrossRefGoogle Scholar
  12. 12.
    Huang, C., Ferrell Jr., J.: Ultrasensitivity in the mitogen-activated protein kinase cascade. Proc. Natl. Acad. Sci. USA 93, 10078–10083 (1996)CrossRefGoogle Scholar
  13. 13.
    Cateau, H., Tanaka, S.: Kinetic analysis of multisite phosphorylation using analytic solutions to Michaelis-Menten equations. J. Theor. Biol. 217(1), 1–14 (2002)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Regev, A., Silverman, W., Shapiro, E.: Representation and simulation of biochemical processes using the pi-calculus process algebra. Pac. Symp. Biocomput. 459, 70 (2001)Google Scholar
  15. 15.
    Priami, C., Regev, A., Shapiro, E., Silverman, W.: Application of a stochastic name-passing calculus to representation and simulation of molecular processes. Inform. Process. Lett. 80(1), 25–31 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Errampalli, D., Priami, C., Quaglia, P.: A Formal Language for Computational Systems Biology. OMICS 8(4), 370–380 (2004)CrossRefGoogle Scholar
  17. 17.
    Ciocchetta, F., Priami, C., Quaglia, P.: Modeling Kohn Interaction Maps with Beta-Binders: An Example. T. Comp. Sys. Biol. 3 (2005)Google Scholar
  18. 18.
    Lecca, P., Priami, C., Laudanna, C., Constantin, G.: A BioSpi model of lymphocyte-endothelial interactions in inflamed brain venules. Pac. Symp. Biocomput. 521, 32 (2004)Google Scholar
  19. 19.
    Kuttler, C.: Simulating bacterial transcription and translation in a stochastic pi calculus. T. Comp. Sys. Biol. 4220, 113–149 (2006)MathSciNetGoogle Scholar
  20. 20.
    Curti, M., Degano, P., Priami, C., Baldari, C.: Modelling biochemical pathways through enhanced π-calculus. Theor. Comput. Sci. 325(1), 111–140 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Wykoff, D., O’Shea, E.: Phosphate Transport and Sensing in Saccharomyces cerevisiae. Genetics 159(4), 1491–1499 (2001)Google Scholar
  22. 22.
    Phillips, A.: The stochastic Pi machine (SPiM),
  23. 23.
    Gillespie, D.: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81(25), 2340–2361 (1977)CrossRefGoogle Scholar
  24. 24.
    Gregory, P., Barbari, S., Hörz, W.: Transcriptional Control of Phosphate-regulated Genes in Yeast: the Role of Specific Transcription Factors and Chromatin Remodeling Complexes in vivo. Food Technol. Biotechnol. 38, 295–303 (2000)Google Scholar
  25. 25.
    Persson, B., Lagerstedt, J., Pratt, J., Pattison-Granberg, J., Lundh, K., Shokrollahzadeh, S., Lundh, F.: Regulation of phosphate acquisition in Saccharomyces cerevisiae. Curr. Genet. 43(4), 225–244 (2003)CrossRefGoogle Scholar
  26. 26.
    Waters, N., Knight, J., Creasy, C., Bergman, L.: The yeast Pho80–Pho85 cyclin–CDK complex has multiple substrates. Curr. Genet. 46(1), 1–9 (2004)CrossRefGoogle Scholar
  27. 27.
    Carroll, A., O’Shea, E.: Pho85 and signaling environmental conditions. Trends Biochem. Sci. 27, 87–93 (2002)CrossRefGoogle Scholar
  28. 28.
    Komeili, A., O’Shea, E.: Roles of Phosphorylation Sites in Regulating Activity of the Transcription Factor Pho4. Science 284(5416), 977 (1999)CrossRefGoogle Scholar
  29. 29.
    Byrne, M., Miller, N., Springer, M., O’Shea, E.: A distal, high-affinity binding site on the cyclin-CDK substrate Pho4 is important for its phosphorylation and regulation. J. Mol. Biol. 335(1), 57–70 (2004)CrossRefGoogle Scholar
  30. 30.
    Bhoite, L., Allen, J., Garcia, E., Thomas, L., Gregory, I., Voth, W., Whelihan, K., Rolfes, R., Stillman, D.: Mutations in the pho2 (bas2) transcription factor that differentially affect activation with its partner proteins bas1, pho4, and swi5. J. Biol. Chem. 277(40), 37612–37618 (2002)CrossRefGoogle Scholar
  31. 31.
    Rudolph, H., Hinnen, A.: The yeast PHO5 promoter: phosphate-control elements and sequences mediating mRNA start-site selection. Proc. Natl. Acad. Sci. USA 84(5), 1340–1344 (1987)CrossRefGoogle Scholar
  32. 32.
    Barbaric, S., Munsterkotter, M., Goding, C., Horz, W.: Cooperative Pho2-Pho4 interactions at the PHO5 promoter are critical for binding of Pho4 to UASp1 and for efficient transactivation by Pho4 at UASp2. Mol. Cell. Biol. 18(5), 2629–2639 (1998)Google Scholar
  33. 33.
    Barbaric, S., Munsterkotter, M., Svaren, J., Horz, W.: The homeodomain protein Pho2 and the basic-helix-loop-helix protein Pho4 bind DNA cooperatively at the yeast PHO5 promoter. Nucleic Acids Res. 24(22), 4479–4486 (1996)CrossRefGoogle Scholar
  34. 34.
    Kaffman, A., Rank, N., O’Shea, E.: Phosphorylation regulates association of the transcription factor Pho4 with its import receptor Pse1/Kap121. Genes. Dev. 12(17), 2673–2683 (1998)CrossRefGoogle Scholar
  35. 35.
    Kaffman, A., Rank, N., O’Neill, E., Huang, L., O’Shea, E.: The receptor Msn5 exports the phosphorylated transcription factor Pho4 out of the nucleus. Nature 396(6710), 482–486 (1998)CrossRefGoogle Scholar
  36. 36.
    Springer, M., Wykoff, D., Miller, N., O’Shea, E.: Partially phosphorylated pho4 activates transcription of a subset of phosphate-responsive genes. PLoS Biol. 1, 2 (2003)CrossRefGoogle Scholar
  37. 37.
    Ghaemmaghami, S., Huh, W., Bower, K., Howson, R., Belle, A., Dephoure, N., O’Shea, E., Weissman, J.: Global analysis of protein expression in yeast. Nature 425(6959), 737–741 (2003)CrossRefGoogle Scholar
  38. 38.
    Huh, W., Falvo, J., Gerke, L., Carroll, A., Howson, R., Weissman, J., O’Shea, E.: Global analysis of protein localization in budding yeast. Nature 425(6959), 686–691 (2003)CrossRefGoogle Scholar
  39. 39.
    Martinez, P., Zvyagilskaya, R., Allard, P., Persson, B.: Physiological regulation of the derepressible phosphate transporter in Saccharomyces cerevisiae. J. Bacteriol. 180(8), 2253–2256 (1998)Google Scholar
  40. 40.
    Swinnen, E., Rosseels, J., Winderickx, J.: The minimum domain of Pho81 is not sufficient to control the Pho85-Rim15 effector branch involved in phosphate starvation-induced stress responses. Curr. Genet. (2005)Google Scholar
  41. 41.
    Ogawa, N., DeRisi, J., Brown, P.: New Components of a System for Phosphate Accumulation and Polyphosphate Metabolism in Saccharomyces cerevisiae Revealed by Genomic Expression Analysis. Mol. Biol. Cell. 11(12), 4309–4321 (2000)Google Scholar
  42. 42.
    Priami, C., Quaglia, P.: Modelling the dynamics of biosystems. Brief Bioinform. 5(3), 259–269 (2004)CrossRefGoogle Scholar
  43. 43.
    Nestmann, U., Pierce, B.: Decoding Choice Encodings. Information and Computation 163(1), 1–59 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  44. 44.
    Priami, C., Quaglia, P.: Beta binders for biological interactions. In: Danos, V., Schachter, V. (eds.) CMSB 2004. LNCS (LNBI), vol. 3082, pp. 20–33. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  45. 45.
    Degano, P., Prandi, D., Priami, C., Quaglia, P.: Beta-binders for biological quantitative experiments. Proceedings of QAPL 2006 164(3), 101–117 (2006)Google Scholar
  46. 46.
    Priami, C.: Stochastic π-Calculus. The Computer Journal 38(7), 578 (1995)CrossRefGoogle Scholar
  47. 47.
    Bergstra, J., Ponse, A., Smolka, S.: Handbook of Process Algebra. Elsevier Science Inc, New York (2001)zbMATHGoogle Scholar
  48. 48.
    Phillips, A., Cardelli, L.: A correct abstract machine for the stochastic π-calculus. ENTCS. Elsevier, Amsterdam (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Nicola Segata
    • 1
  • Enrico Blanzieri
    • 1
  1. 1.Dipartimento di Ingegneria e Scienza dell’InformazioneUniversity of Trento 

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