passages: PMC-2704942-sec-22__text
passages: sec
passages: Stochastic models
  Stochasticity inevitably emerges when molecular components are present at low cellular concentrations (McAdams & Arkin, 1997; Kierzek et al., 2001). This physical phenomenon generates noise in synthetic and natural circuits (Paulsson, 2004; Mettetal et al., 2006), and its consequences over the phenotype are starting to be explored (Suel et al., 2006). For example, noise constitutes the driving force behind differentiation in isogenetic colonies (Colman-Lerner et al., 2005). Biological and theoretical studies have aided to delineate the regulatory mechanism by which the cell handles noise efficiently and effectively to carry out its biological functions (Gardner & Collins, 2000; Orrell & Bolouri, 2004; Raser & O'Shea, 2005). From a theoretical point of view, stochastic models are the most challenging but also the most realistic ones: there is a precise counting of how, through individual chemical reactions, the populations of every chemical species change. The milestone to simulate stochastic processes is the Gillespie algorithm (Gillespie, 1992). Because of their analytical and computational complexity, the present models do not surpass a handful of chemical species. Two immediate problems must be solved to model systems with several dozens of genetic components: the systematic determination of kinetic constants and the efficient computation of thousands of chemical stochastic equations (Kuwahara et al., 2006; Sanchez & Kondev, 2008).
  