A Numerical Aggregation Algorithm for the Enzyme-Catalyzed Substrate Conversion Hauke Busch 1 , Werner Sandmann 2 , and Verena Wolf 3 1 German Cancer Research Center, D-69120 Heidelberg, Germany h.busch@dkfz.de 2 University of Bamberg, D-96045 Bamberg, Germany werner.sandmann@wiai.uni-bamberg.de 3 University of Mannheim, D-68131 Mannheim, Germany wolf@informatik.uni-mannheim.de Abstract. Computational models of biochemical systems are usually very large, and moreover, if reaction frequencies of different reaction types differ in orders of magnitude, models possess the mathematical property of stiffness, which renders system analysis difficult and often even impossible with traditional methods. Recently, an accelerated stochastic simulation technique based on a system partitioning, the slow- scale stochastic simulation algorithm, has been applied to the enzyme- catalyzed substrate conversion to circumvent the inefficiency of standard stochastic simulation in the presence of stiffness. We propose a numerical algorithm based on a similar partitioning but without resorting to simu- lation. The algorithm exploits the connection to continuous-time Markov chains and decomposes the overall problem to significantly smaller sub- problems that become tractable. Numerical results show enormous effi- ciency improvements relative to accelerated stochastic simulation. Keywords: Biochemical Reactions, Stochastic Model, Markov Chain, Aggregation. 1 Introduction The complexity of living systems has led to a rapidly increasing interest in mod- eling and analysis of biochemically reacting systems. Different types of computa- tional mathematical models exist, where quantitative and temporal relationships are often given in terms of rates and the specific meaning of these rates depends on the chosen model type. Of course, the different model types are intimately related since they represent the same type of system. A comprehensive treatment of computational models can be found in [2]. Models, not only in the context of biochemical systems, are distinguished in terms of their states and state changes (transitions) where a state consists of a collection of variables that sufficiently well represents the relevant 1 parameters 1 Any model is a simplified abstraction of the real system and both suitability of a model and the relevant parameters depend on the scope of the study. C. Priami (Ed.): CMSB 2006, LNBI 4210, pp. 298–311, 2006. c  Springer-Verlag Berlin Heidelberg 2006