Abstract
The detailed behavior of many molecular processes in the cell, such as protein folding, protein complex assembly, and gene regulation, transcription and translation, can often be accurately captured by stochastic chemical kinetic models. We investigate a novel computational problem involving these models – that of finding the most-probable sequence of reactions that connects two or more states of the system observed at different times. We describe an efficient method for computing the probability of a given reaction sequence, but argue that computing most-probable reaction sequences is EXPSPACE-hard. We develop exact (exhaustive) and approximate algorithms for finding most-probable reaction sequences. We evaluate these methods on test problems relating to a recently-proposed stochastic model of folding of the Trp-cage peptide. Our results provide new computational tools for analyzing stochastic chemical models, and demonstrate their utility in illuminating the behavior of real-world systems.
Highlights
We have detailed knowledge about the chemical interactions or transformations in which various biomolecules participate
We have demonstrated the potential utility of the problem formulation by analyzing a stochastic model of peptide folding
One might, in a similar fashion, study most-probable sequences of transcription factor-DNA binding events that lead to gene activation or most-probable sequences of protein-protein interaction events in protein complex assembly
Summary
We have detailed knowledge about the chemical interactions or transformations in which various biomolecules participate. Real-time fluorescence microscopy allows us to see single molecules moving and interacting (Nie et al, 1995; Sekar and Periasamy, 2003) When studying such interactions at single-cell or even single-molecule levels, mass-action chemical kinetics can be either misleading or inapplicable. In such cases, dynamics are more accurately represented by stochastic chemical kinetic models (SCKMs) (Gardiner, 2004; Van Kampen, 2008). Dynamics are more accurately represented by stochastic chemical kinetic models (SCKMs) (Gardiner, 2004; Van Kampen, 2008) These models define a chemical system in terms of the types of molecules or molecular configurations that are possible, the types of chemical interactions or transformations that may occur, and the state-dependent probabilities with which they occur. SCKMs are often used, for example, to model stochastic thermodynamic switching between different configurations of a protein (Marinelli et al, 2009), to model the opening and closing of ion channels (Ball and Rice, 1992), and to study the sources of noise in gene expression (Swain et al, 2002; Thattai and van Oudenaarden, 2001)
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