Team:USP-Brazil/Model:Stochastic

From 2013.igem.org

(Difference between revisions)
Line 13: Line 13:
<h2>Stochastic model</h2>
<h2>Stochastic model</h2>
<h3>Introduction</h3>
<h3>Introduction</h3>
-
<p>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 9 numbers:
+
<p>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:
</p>
</p>
\begin{equation}
\begin{equation}
-
(et, met, X_f,X_{et}, X_{met}, P_f,P_{et}, P_{met}, R)$$
+
(et, met, X_f,X_{et}, X_{met}, P_f,P_{et}, P_{met}, R)
\end{equation}
\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}
 +
 +
 +
 +
 +
 +
 +
 +
 +
<h4 style="color:grey;">References</h4>
<h4 style="color:grey;">References</h4>
<p style="color:grey;">[1] Sheldon M. Ross, Stochastic Process, Wiley, New York 1996 </p>
<p style="color:grey;">[1] Sheldon M. Ross, Stochastic Process, Wiley, New York 1996 </p>
-
<p style="color:grey;">[2] Radek Erban, S. Jonathan Chapman, Philip K. Maini: A prac-
+
<p style="color:grey;">[2] Radek Erban, S. Jonathan Chapman, Philip K. Maini: A prac
tical guide to stochastic simulations of reaction-diffusion processes ,
tical guide to stochastic simulations of reaction-diffusion processes ,
http://arxiv.org/abs/0704.1908</p>
http://arxiv.org/abs/0704.1908</p>

Revision as of 01:25, 28 September 2013

Template:Https://2013.igem.org/Team:USP-Brazil/templateUP

Modelling

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

Template:Https://2013.igem.org/Team:USP-Brazil/templateDOWN

Retrieved from "http://2013.igem.org/Team:USP-Brazil/Model:Stochastic"