Accelerated leap methods for simulating discrete stochastic chemical kinetics
Burrage, Kevin, Macnamara, Shev, & Tian, Tianhai (2006) Accelerated leap methods for simulating discrete stochastic chemical kinetics. In Commault, Christian & Marchand, Nicholas (Eds.) Lecture Notes in Control and Information Science: The Second Multidisciplinary International Symposium on Positive Systems : Theory and Applications (POSTA 06), Springer Verlag, France, Grenoble, pp. 359-366.
Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.
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|Item Type:||Conference Paper|
|Subjects:||Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300)|
Australian and New Zealand Standard Research Classification > BIOLOGICAL SCIENCES (060000) > BIOCHEMISTRY AND CELL BIOLOGY (060100) > Systems Biology (060114)
|Divisions:||Past > QUT Faculties & Divisions > Faculty of Science and Technology|
Past > Schools > Mathematical Sciences
|Deposited On:||27 Sep 2011 11:48|
|Last Modified:||27 Sep 2011 11:48|
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