اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAccurate implementation of leaping in space: The spatial partitioned-leaping algorithm
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There is a great need for accurate and efficient computational approaches that can account for both the discrete and stochastic nature of chemical interactions as well as spatial inhomogeneities and diffusion. This is particularly true in biology and nanoscale materials science, where the common assumptions of deterministic dynamics and well-mixed reaction volumes often break down. In this article, we present a spatial version of the partitioned-leaping algorithm (PLA), a multiscale accelerated-stochastic simulation approach built upon the tau-leaping framework of Gillespie. We pay special attention to the details of the implementation, particularly as it pertains to the time step calculation procedure. We point out conceptual errors that have been made in this regard in prior implementations of spatial tau-leaping and illustrate the manifestation of these errors through practical examples. Finally, we discuss the fundamental difficulties associated with incorporating efficient exact-stochastic techniques, such as the next-subvolume method, into a spatial-leaping framework and suggest possible solutions.
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Leaping methods show great promise for significantly accelerating stochastic simulations of complex biochemical reaction networks. However, few practical applications of leaping have appeared in the literature to date. Here, we address this issue usi
ng the partitioned leaping algorithm (PLA) [L.A. Harris and P. Clancy, J. Chem. Phys. 125, 144107 (2006)], a recently-introduced multiscale leaping approach. We use the PLA to investigate stochastic effects in two model biochemical reaction networks. The networks that we consider are simple enough so as to be accessible to our intuition but sufficiently complex so as to be generally representative of real biological systems. We demonstrate how the PLA allows us to quantify subtle effects of stochasticity in these systems that would be difficult to ascertain otherwise as well as not-so-subtle behaviors that would strain commonly-used exact stochastic methods. We also illustrate bottlenecks that can hinder the approach and exemplify and discuss possible strategies for overcoming them. Overall, our aim is to aid and motivate future applications of leaping by providing stark illustrations of the benefits of the method while at the same time elucidating obstacles that are often encountered in practice.
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