22 March - 26 March 2010

Isaac Newton Institute for Mathematical Sciences, Cambridge, UK

**Workshop Organisers:** Takis Konstantopoulos (*Heriot-Watt*) and Kavita Ramanan (*Brown University*).

**Workshop Programme Committee:** Vivek Borkar (*Tata Institute of Fundamental Research*), Serguei Foss (*Heriot-Watt University*), Peter Glynn (*Stanford*),

Bruce Hajek (*University of Illinois*), Frank Kelly (*Cambridge*), P.R. Kumar (*University of Illinois*), Tom Kurtz (*University of Wisconsin-Madison*), Jean Mairesse (*LIAFA*), Philippe Robert (*INRIA*), John Tsitsiklis (*MIT*) and Ruth Williams (*University of California, San Diego*)

in association with the Newton Institute programme

Stochastic Processes in Communication Sciences (11 January to 2 July 2010) Participants | Application | Accommodation and CostTitle: Simulation methods for stochastically modeled chemical reaction networks

While exact simulation methods exist for discrete-stochastic models of biochemical reaction networks, they are oftentimes too inefficient for use because the number of computations scales linearly with the number of reaction events; thus, approximate algorithms have been developed. However, stochastically modeled reaction networks often have "natural scales" and it is crucial that these be accounted for when developing and analyzing numerical approximation methods. I will show that conducting such a non-standard error analysis leads to fundamentally different conclusions than previous analyses. Another option for approximating discrete-stochastic models of chemical reaction networks is to use a diffusion approximation. However, even in the regimes where such an approximation is preferable to the discrete numerical approximation methods, it is now necessary to approximate the diffusion process. In the second portion of my talk I will show how the special structure of chemical reaction networks can be utilized to develop an efficient and easy to implement method that is second order accurate in the weak sense for such diffusion processes.

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