Stochastic Analysis of a Simple Gene System for the Synthesis of a Protein Using the Gillespie Methods
Journal Title: Revista Cuarzo - Year 2018, Vol 24, Issue 1
Abstract
In most cases where it is required to describe a biological network, a system of coupled differential equations is proposed, which is then solved by numerical methods. However, when a single value in a steady state does not predict the behavior of the total population, it is essential that the repre-sentation model describes the distribution of states within a system. The algorithm proposed by Gillespie in 1998 consists of the description of a specific phenomenon using stochastic tools, where the behavior of the master probability equation is predicted by means of the Monte Carlo simula-tion. The author proposes two mathematical approaches to resolution: the first reaction method and the direct method. The purpose of this research was to compare the results of these approaches by focusing on the differences between the results when analyzing the network using a classical deter-ministic method and the two stochastic methods of Gillespie, using a simple gene model for protein synthesis, represented in a Petri simple network proposed by Goss and Peccoud in 1998. Finally, perform a sensitivity analysis to the stochastic model with the null hypothesis test. The results ob-tained show that the population does not behave uniformly, so it is pertinent and recommendable to use the Gillespie method for this system and similar systems; additionally, it is corroborated that the direct method is more computationally demanding, and the null hypothesis test concludes that the final number of proteins if affected by variations in kinetic parameters.
Authors and Affiliations
Clavijo Buriticá, D. , Mejía Bohórquez, B. , Rojas, L. , & Sáenz Castro, H.
Keywords
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- EP ID EP694624
- DOI https://doi.org/10.26752/cuarzo.v24.n1.350
- Views 139
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