# 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.

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#### 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