@article { ISI:000298058400005,
	title = {New approximate method for the stochastic simulation of chemical systems: the representative reaction approach},
	journal = {Journal of Computational Chemistry},
	volume = {33},
	number = {3},
	year = {2012},
	month = {JAN},
	pages = {276-285},
	publisher = {WILEY-BLACKWELL},
	address = {COMMERCE PLACE, 350 MAIN ST, MALDEN 02148, MA USA},
	abstract = {<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>},
	keywords = {approximate algorithm, Stochastic simulations},
	issn = {0192-8651},
	doi = {10.1002/jcc.21971},
	author = {Kadam, Shantanu and Vanka, Kumar}
}
@article { ISI:000313985200009,
	title = {Solving the problem of negative populations in approximate accelerated stochastic simulations using the representative reaction approach},
	journal = {Journal of Computational Chemistry},
	volume = {34},
	number = {5},
	year = {2013},
	month = {FEB},
	pages = {394-404},
	publisher = {WILEY-BLACKWELL},
	address = {111 RIVER ST, HOBOKEN 07030-5774, NJ USA},
	abstract = {<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>},
	keywords = {approximate methods, binomial distributions, Gillespie algorithm, Kinetic Monte Carlo, Poisson distributions, representative reaction approach, Stochastic simulations},
	issn = {0192-8651},
	doi = {10.1002/jcc.23158},
	author = {Kadam, Shantanu and Vanka, Kumar}
}
