Hidden markov model for competitive binding and chain elongation

Many chemical systems of interest consist of sets of reactions that contain iterated sequences that elongate a molecular chain. For example, such sets of reactions are commonly found in the transcription of DNA or the translation of RNA. However, there are competitive reactions that can prematurely terminate the chain-elongation process. A hidden Markov method appropriate for modeling chains of reactions with competitive processes (i.e., premature chain termination) is developed. The method is an extension of a hidden Markov model suggested by Gibson and Bruck (J. Phys. Chem. A 2000, 104, 1876). The equivalence between results using this method and results from simulation of a system employing the full set of reactions will be demonstrated (Gillespie, D. T. Markov Processes: An Introduction for Physical Scientists; Academic: San Diego, CA, 1992). Examples of its use are shown for several test problems. As an example of a practical application, a comparison among results for a model of terminal modification of ligand-aggregated receptors (Hlavacek, W.; Redondo, A.; Wofsy, C.; Goldstein, B. Bull. Math. Biol. 2002, 64, 887) simulated by ordinary differential equations, the full set of reactions, and the hidden Markov method are shown.