Team:USP-Brazil/Model:Stochastic

Stochastic model

Introduction

We want to simulate a cell where is happening all the chemical reactions discribed in the Deterministic Model as a Stochastical Process whose states are determinated by a collection of nine numbers:

\begin{equation} (et, met, X_f,X_{et}, X_{met}, P_f,P_{et}, P_{met}, R) \end{equation} \begin{equation} A \longrightarrow B$ \end{equation} \begin{equation} p(t) = \lambda e^{-\lambda t} \end{equation} These are the only kind of distribution in continuous time which do not have a "memory" that means: \begin{equation} P(X (t+\delta t) = i | X(t) = j and X(u)= l for u < t ) = \end{equation} A larger explanation of that is in Chapter 5 on [1]. \begin{equation} \end{equation} \begin{equation} \end{equation} \begin{equation} \end{equation} \begin{equation} \end{equation} \begin{equation} \end{equation} \begin{equation} \end{equation}

References

[1] Sheldon M. Ross, Stochastic Process, Wiley, New York 1996

[2] Radek Erban, S. Jonathan Chapman, Philip K. Maini: A prac tical guide to stochastic simulations of reaction-diffusion processes , http://arxiv.org/abs/0704.1908

RFP Visibility | Deterministic Model | Stochastic Model