01741nas a2200181   4500008004100000022001400041245011500055210006900170260007600239300001200315490000700327520100800334653002601342653002701368100002001395700001701415856012701432       2012                        eng d  a0192-865100aNew approximate method for the stochastic simulation of chemical systems: the representative reaction approach0 aNew approximate method for the stochastic simulation of chemical  aCOMMERCE PLACE, 350 MAIN ST, MALDEN 02148, MA USAbWILEY-BLACKWELLcJAN  a276-2850 v333 a<p>We have developed two new approximate methods for stochastically simulating chemical systems. The methods are based on the idea of representing all the reactions in the chemical system by a single reaction, i.e., by the representative reaction approach (RRA). Discussed in the article are the concepts underlying the new methods along with flowchart with all the steps required for their implementation. It is shown that the two RRA methods {with the reaction \$ 2A \textbackslashrightarrow B \$ as the representative reaction (RR)} perform creditably with regard to accuracy and computational efficiency, in comparison to the exact stochastic simulation algorithm (SSA) developed by Gillespie and are able to successfully reproduce at least the first two moments of the probability distribution of each species in the systems studied. As such, the RRA methods represent a promising new approach for stochastically simulating chemical systems. (C) 2011 Wiley Periodicals, Inc. J Comput Chem, 2012</p>10aapproximate algorithm10aStochastic simulations1 aKadam, Shantanu1 aVanka, Kumar  uhttps://library.ncl.res.in/content/new-approximate-method-stochastic-simulation-chemical-systems-representative-reaction-002217nas a2200241   4500008004100000022001400041245014100055210006900196260006700265300001200332490000700344520126700351653002401618653002701642653002401669653002401693653002601717653003701743653002701780100002001807700001701827856013101844       2013                        eng d  a0192-865100aSolving the problem of negative populations in approximate accelerated stochastic simulations using the representative reaction approach0 aSolving the problem of negative populations in approximate accel  a111 RIVER ST, HOBOKEN 07030-5774, NJ USAbWILEY-BLACKWELLcFEB  a394-4040 v343 a<p>Methods based on the stochastic formulation of chemical kinetics have the potential to accurately reproduce the dynamical behavior of various biochemical systems of interest. However, the computational expense makes them impractical for the study of real systems. Attempts to render these methods practical have led to the development of accelerated methods, where the reaction numbers are modeled by Poisson random numbers. However, for certain systems, such methods give rise to physically unrealistic negative numbers for species populations. The methods which make use of binomial variables, in place of Poisson random numbers, have since become popular, and have been partially successful in addressing this problem. In this manuscript, the development of two new computational methods, based on the representative reaction approach (RRA), has been discussed. The new methods endeavor to solve the problem of negative numbers, by making use of tools like the stochastic simulation algorithm and the binomial method, in conjunction with the RRA. It is found that these newly developed methods perform better than other binomial methods used for stochastic simulations, in resolving the problem of negative populations. (C) 2012 Wiley Periodicals, Inc.</p>10aapproximate methods10abinomial distributions10aGillespie algorithm10aKinetic Monte Carlo10aPoisson distributions10arepresentative reaction approach10aStochastic simulations1 aKadam, Shantanu1 aVanka, Kumar  uhttps://library.ncl.res.in/content/solving-problem-negative-populations-approximate-accelerated-stochastic-simulations-using-0