Chemical Master Equations - A Mathematical Scheme for the Multi-site Phosphorylation Case

Alessandro Borri, Francesco Carravetta, Gabriella Mavelli, Pasquale Palumbo

Abstract

The Chemical Master Equation (CME) provides a fruitful approach for the stochastic description of complex biochemical processes, because it is able to cope with random fluctuations of the chemical agents and to fit the experimental behavior in a more accurate way than deterministic concentration equations. In this work, our attention is focused on modeling and simulation of multisite phosphorylation/dephosphorylation cycles, by using the quasi-steady state approximation of enzymatic kinetics. The CME dynamics is written from the coefficients of the deterministic reaction-rate equations and the stationary distribution is computed explicitly, according to a recently developed realization scheme. Simulations are included to provide a comparison with Monte Carlo methods in terms of computational complexity.

References

  1. Bazzani, A., Castellani, G. C., Giampieri, E., Remondini, D., and Cooper, L. N. (2012). Bistability in the chemical master equation for dual phosphorylation cycles. The Journal of Chemical Physics, 136(23):235102.
  2. Borri, A., Carravetta, F., Mavelli, G., and Palumbo, P. (2013). Some results on the structural properties and the solution of the chemical master equation. In Proceedings of the 2013 American Control Conference (ACC 2013), Washington, DC, USA.
  3. Bullo, F., Cortes, J., and Martinez, S. (2009). Distributed Control of Robotic Networks. Applied Mathematics Series. Princeton.
  4. Carravetta, F. (2011). 2-d-recursive modelling of homogeneous discrete gaussian markov fields. IEEE Transactions on Automatic Control, 56(5):1198-1203.
  5. Castellani, G. C., Bazzani, A., and Cooper, L. N. (2009). Toward a microscopic model of bidirectional synaptic plasticity. Proceedings of the National Academy of Sciences, 106(33):14091-14095.
  6. Castellani, G. C., Quinlan, E. M., Cooper, L. N., and Shouval, H. Z. (2001). A biophysical model of bidirectional synaptic plasticity: Dependence on ampa and nmda receptors. Proceedings of the National Academy of Sciences, 98(22):12772-12777.
  7. Farina, L. and Rinaldi, S. (2000). Positive Linear Systems: Theory and Applications. Pure and Applied Mathematics Series. John Wiley & Sons, Inc.
  8. Gillespie, D. T. (1977). Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chemistry, 81(25):2340-2361.
  9. Mettetal, J. T. and van Oudenaarden, A. (2007). Necessary noise. Science, 317(5837):463-464.
  10. Michaelis, L. and Menten, M. (1913). Kinetics of invertase action. Biochem. Z, 49:333-369.
  11. Munsky, B. and Khammash, M. (2008). The finite state projection approach for the analysis of stochastic noise in gene networks. IEEE Transactions on Automatic Control, 53(Special Issue on Systems Biology):201-214.
  12. Qu, Z., Weiss, J. N., and MacLellan, W. R. (2003). Regulation of the mammalian cell cycle: a model of the g1-to-s transition. American Journal of Physiology - Cell Physiology, 284(2):C349-C364.
  13. Ullah, M. and Wolkenhauer, O. (2011). Stochastic Approaches for Systems Biology. Springer.
  14. Van Kampen, N. G. (2007). Stochastic Processes in Physics and Chemistry, Third Edition. North Holland.
  15. Whitlock, J. R., Heynen, A. J., Shuler, M. G., and Bear, M. F. (2006). Learning induces long-term potentiation in the hippocampus. Science (New York, N.Y.), 313(5790):1093-1097.
Download


Paper Citation


in Harvard Style

Borri A., Carravetta F., Mavelli G. and Palumbo P. (2013). Chemical Master Equations - A Mathematical Scheme for the Multi-site Phosphorylation Case . In Proceedings of the 3rd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: BIOMED, (SIMULTECH 2013) ISBN 978-989-8565-69-3, pages 681-688. DOI: 10.5220/0004632306810688


in Bibtex Style

@conference{biomed13,
author={Alessandro Borri and Francesco Carravetta and Gabriella Mavelli and Pasquale Palumbo},
title={Chemical Master Equations - A Mathematical Scheme for the Multi-site Phosphorylation Case},
booktitle={Proceedings of the 3rd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: BIOMED, (SIMULTECH 2013)},
year={2013},
pages={681-688},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004632306810688},
isbn={978-989-8565-69-3},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 3rd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: BIOMED, (SIMULTECH 2013)
TI - Chemical Master Equations - A Mathematical Scheme for the Multi-site Phosphorylation Case
SN - 978-989-8565-69-3
AU - Borri A.
AU - Carravetta F.
AU - Mavelli G.
AU - Palumbo P.
PY - 2013
SP - 681
EP - 688
DO - 10.5220/0004632306810688