Substrate Enzyme-Sequestration in Multisite Protein Phosphorylation - Introducing WCDD M-matrices in designing stationary probability distributions

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• Andreas Petrides, University of Cambridge
• Thursday 24 November 2016, 14:00-15:00
• Cambridge University Engineering Department, LR4.

If you have a question about this talk, please contact Tim Hughes.

Multisite protein phosphorylation has been of great interest to the systems biology community due to its ability to exhibit multistable behaviour. In the presence of excess substrate, ultrasensitivity can be obtained which, when coupled with positive feedback, can result in bistability. In this same regime, Thomson and Gunawardena showed that the number of stable steady states achieved can increase linearly with the number of phosphosites available, without the need of positive feedback. In the regime of excess enzyme, Martins and Swain showed that substrate enzyme sequestration of the fully unphosphorylated and the fully phosphorylated substrates can provide the necessary ultrasensitivity.

We first illustrate that substrate enzyme sequestration can limit the number of steady states calculated for a particular system with large numbers and excess substrate (without positive feedback), giving a sufficient condition relating the sequestration parameters to the rest of the system’s parameters. However, we also show that substrate enzyme sequestration in the low substrate numbers/excess enzyme regime can exhibit multimodality even when there is only one available phosphosite. In fact, we illustrate that substrate enzyme-sequestration can turn monomodality to bimodality in the low substrate number regime in the presence of a single available phosphosite. In this regime, the analysis is naturally placed in the stochastic domain. Therefore, we also present a weakly chained diagonally dominant M-matrix formulation of the Chemical Master Equation, which has the ability to act both as an accurate computational method and as a framework tool in designing stationary probability distributions for systems where the Markov process characterisation is the most applicable. It is suggested that substrate enzyme sequestration might be beneficial in obtaining multimodality in the low substrate numbers/excess enzyme regime, at the expense of limiting the extent of multistability that can be achieved in the large numbers/excess substrate regime.

This talk is part of the CUED Control Group Seminars series.

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