Thomson2009 – Unlimited multistability in multisite phosphorylation systems

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Model Identifier
MODEL2002110001
Short description
This model describes a distributive, sequential system with n = 4, which is a simplified example of unlimited multistability in multisite phosphorylation systems. This method can be applied to systems with multiple substrates and enzymes. This model is described in the article: Unlimited multistability in multisite phosphorylation systems. Thomson, Matthew & Gunawardena, Jeremy. (2009). Nature. 460. 274-7. 10.1038/nature08102 (https://www.nature.com/articles/nature08102). Antimony and Tellurium used. Figure 2 of the reference publication has been reproduced. The code files are available on Github (https://github.com/SunnyXu/Unlimited_multistability). The simulation was performed using Spyder for Tellurium 3.7 (http://tellurium.analogmachine.org/).
Format
SBML (L3V1)
Related Publication
  • Unlimited multistability in multisite phosphorylation systems.
  • Thomson M, Gunawardena J
  • Nature , 7/ 2009 , Volume 460 , Issue 7252 , pages: 274-277 , PubMed ID: 19536158
  • Biophysics Program, Harvard University, Cambridge, Massachusetts 02138, USA.
  • Reversible phosphorylation on serine, threonine and tyrosine is the most widely studied posttranslational modification of proteins. The number of phosphorylated sites on a protein (n) shows a significant increase from prokaryotes, with n /= 150 sites. Multisite phosphorylation has many roles 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 (2^n) of phospho-forms and individual phospho-forms may have distinct biological effects. 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 cells 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 x 2^n 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' such as the histone code. 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 processing.
Contributors
Rahuman Sheriff, Jin Xu

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Non-curated

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Model files

multiStability_Jin_Xu.xml Model files: SBML L3V1 representation of Thomson2009 – Unlimited multistability in multisite phosphorylation systems 18.24 KB Preview | Download

Additional files

Fig2a-2.pdf It is generated by code Fig2-a.py, corresponding to the illustration part of Figure 2a in the original paper. 13.23 KB Preview | Download
Fig2-b.py Fig2b.pdf and multiStability.xml are generated by code Fig2-b.py. The simulation was also performed using Spyder for Tellurium 3.7. 2.35 KB Preview | Download
Fig2a-1.pdf It is generated by code Fig2-a.py, corresponding to the main part of Figure 2a in the original paper. 11.06 KB Preview | Download
multiStability.xml It is generated by code Fig2-b.py, which is similar as the model file only without the contributor's information. 16.51 KB Preview | Download
Fig2b.pdf It is generated by code Fig2-b.py, corresponding to the Figure 2b in the original paper. It can be a proof of the model. 54.78 KB Preview | Download
Fig2-a.py Fig2a-1.pdf and Fig2a-2.pdf are generated by code Fig2-a.py, corresponding to the Figure 2a and its illustration in the original paper. The simulation was performed using Spyder for Tellurium 3.7 (http://tellurium.analogmachine.org/). 4.01 KB Preview | Download

  • Model originally submitted by : Jin Xu
  • Submitted: 12-Feb-2020 23:21:59
  • Last Modified: 12-Feb-2020 23:21:59
Revisions
  • Version: 4 public model Download this version
    • Submitted on: 12-Feb-2020 23:21:59
    • Submitted by: Rahuman Sheriff
    • With comment: Edited model metadata online.
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