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• W2918138906 abstract "Stochastic simulation methods are frequently used to study the behavior of cellular control systems modeled as continuous-time discrete-space Markov processes (CTMC). Compared to the most frequently used deterministic model, the reaction rate equations, the mesoscopic stochastic description can capture effects from intrinsic noise on the behavior of the networks [1, 8, 25, 26, 29]. In the discrete mesoscopic model the state of the system is the copy number of the different chemical species and the reactions are usually assumed to take place in a well-stirred reaction volume. The chemical master equation is the governing equation for the probability density, and for small to medium sized systems it can be solved by direct, deterministic methods [10, 11, 15, 21, 24, 28]. For larger models however, exact or approximate kinetic Monte Carlo methods [17, 18] are frequently used to generate realizations of the stochastic process. Many different hybrid and multiscale methods have also emerged that deal with the typical stiffness of biochemical reactions networks in different ways, see [2, 6, 19, 22, 23, 27] for examples. Many processes inside the living cell can not be expected to be explained in a well-stirred context. The natural macroscopic model is the reaction-diffusion equation which has the same limitations as the reaction rate equations. By discretizing space with small subvolumes it is possible to model the reaction-diffusion process by a CTMC within the same formalism as for the well-stirred case. A diffusion event is now modeled as a first order reaction from a subvolume to an adjacent one and the state of the system is the number of molecules of each species in each subvolume. The corresponding master equation is called the reactiondiffusion master equation (RDME) and due to the very high dimensionality it cannot be solved by deterministic methods for realistic problem sizes. The RDME has been used to study biochemical systems in [7, 14]. Here the next subvolume method (NSM) [7], an extension of Gibson and Bruck’s next reaction method (NRM) [16], was suggested as an efficient method for realizing sample trajectories. An implementation on a structured Cartesian grid is freely available in the software MesoRD [20]. The method was extended to unstructured meshes in [12] by making connections to the finite element method (FEM). This has several advantages, the most notable one being the" @default.
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• W2918138906 date "2009-02-17" @default.
• W2918138906 modified "2023-09-26" @default.
• W2918138906 title "URDME v. 1.1: User's manual" @default.
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