Regulatory gene networks contain generic modules, like those involving feedback loops, which are essential for the regulation of many biological functions (Guido et al. in Nature 439:856-860, 2006). We consider a class of self-regulated genes which are the building blocks of many regulatory gene networks, and study the steady-state distribution of the associated Gillespie algorithm by providing...

The "Tau-Leap" strategy for stochastic simulations of chemical reaction systems due to Gillespie and co-workers has had considerable impact on various applications. This strategy is reexamined with Chebyshev's inequality for random variables as it provides a rigorous probabilistic basis for a measured τ-leap thus adding significantly to simulation efficiency. It is also shown that existing stra...

We present here a model for multivalent diffusive transport whereby central point-like hub is coupled to multiple feet, which bind complementary sites on two-dimensional landscape. The available number of binding interactions dependent the feet (multivalency) and their allowed distance from (span). Using Monte Carlo simulations that implement Gillespie algorithm, we simulate processes 100 disti...

Autonomous evaluation of computer generated musical pieces remains one of the most challenging open problems in evolutionary music composition. This paper introduces the design of novel mutation and fitness operators for autonomous evolution of human-competitive rhythm accompaniment using genetic algorithm. We propose several fitness operators that autonomously evaluate the quality of generated...

Gillespie’s Stochastic Simulation Algorithm (SSA) is an exact procedure for simulating the evolution of a collection of discrete, interacting entities, such as coalescing aerosol particles or reacting chemical species. The high computational cost of SSA has motivated the development of more efficient variants, such as Tau-Leaping, which sacrifices the exactness of SSA. For models whose interact...

The stochastic simulation algorithm (SSA) is extensively used to simulate biochemical systems. By generating realizations from the probability distribution governing the time evolution of each system, the SSA provides a numerical approach for quantitative estimation of system behavior. A consequence of this approach is the dependence of estimation accuracy on the number of realizations generate...

MOTIVATION Cellular signal transduction involves spatial-temporal dynamics and often stochastic effects due to the low particle abundance of some molecular species. Others can, however, be of high abundances. Such a system can be simulated either with the spatial Gillespie/Stochastic Simulation Algorithm (SSA) or Brownian/Smoluchowski dynamics if space and stochasticity are important. To combin...

In biochemical systems some of the chemical species are present with only small numbers of molecules. In this situation discrete and stochastic simulation approaches are more relevant than continuous and deterministic ones. The fundamental Gillespie’s stochastic simulation algorithm (SSA) accounts for every reaction event, which occurs with a probability determined by the configuration of the s...

In the past five years, there has been significant progress in developing high-speed algorithms for solving the stochastic kinetics of complex biochemical networks. In this section, we briefly survey some of these algorithms. Gillespie proposed a discrete-event Monte Carlo technique for generating approximate solutions to the chemical master equation for the grand probability function. During e...

The nonlinear dynamics of biochemical reactions in a small-sized system on the order of a cell are stochastic. Assuming spatial homogeneity, the populations of n molecular species follow a multi-dimensional birth-and-death process on Z . We introduce the Delbrück–Gillespie process, a continuous-time Markov jump process, whose Kolmogorov forward equation has been known as the chemical master equ...