Biochemical systems have critical practical applications, in particular to the study of key cellular processes.

In many cases, stochastic cellular dynamics is modelled using jump Markov processes,

whose probability distributions evolve according to the Chemical Master Equation.

These models of biochemical systems depend on a set of kinetic parameters, whose values are sometimes unknown or poorly estimated.

We propose a model reduction technique for the Chemical Master Equation, based on sensitivity analysis.

For sensitivity analysis we apply some existing finite-difference sensitivity estimators, such as the coupled finite-difference or the

coupled random number strategies. The new technique is successfully applied on some complex biochemical networks arising in applications..

The behaviour of the reduced system is in excellent agreement with that of the full system.

This is joint work with S. Ilie.

The Becker-D\"{o}ring model is one of the most popular models to describe aggregation and detachment in the self assembly of molecules.

$C_{r}+C_{s} \begin{array}{c} k_{r}^{+} \\ \rightleftharpoons \\ k_{r+s}^{-} \end{array} C_{r+s} $

Here, $C_{r}$ are the concentrations of a cluster of size r, where r can be referred to as aggregation number and, $r=1,2,3...$ . The ${r}^{th}$ forward reaction rate constant is $k_{r}^{+}$, and $k_{r+s}^{-}$ is the $(r+s)^{st}$ backward reaction rate constant. One of the limitations of the Becker-D\"{o}ring model is that only monomers can attach or detach to a given cluster. The Becker-D\"{o}ring model is extended here to include attachment and detachment of molecules of size two or more in a cluster(s=2,3,... in above equation), one at a time, with the help of a chemical master equation and stochastic approaches. The mean first assembly times of molecules of different sizes based on the extended Becker D\"{o}ring Model will be determined stochastically.