Abstract
Many biomolecular systems depend on orderly sequences of chemical transformations or reactions. Yet, the dynamics of single molecules or small-copy-number molecular systems are significantly stochastic. Here, we propose state sequence analysis—a new approach for predicting or visualizing the behaviour of stochastic molecular systems by computing maximum probability state sequences, based on initial conditions or boundary conditions. We demonstrate this approach by analysing the acquisition of drug-resistance mutations in the human immunodeficiency virus genome, which depends on rare events occurring on the time scale of years, and the stochastic opening and closing behaviour of a single sodium ion channel, which occurs on the time scale of milliseconds. In both cases, we find that our approach yields novel insights into the stochastic dynamical behaviour of these systems, including insights that are not correctly reproduced in standard time-discretization approaches to trajectory analysis.
Highlights
Stochasticity is a well-documented phenomenon in biomolecular systems
We demonstrate the value of state sequence analysis as an investigative tool by analysing the evolution of drug resistance in human immunodeficiency virus (HIV) (§2.3) and stochastic ion channel dynamics (§2.4)
We proposed state sequence analysis, an approach to investigating stochastic continuous-time discrete-state systems by computing maximum probability state sequences
Summary
Stochasticity is a well-documented phenomenon in biomolecular systems. Advances in microscopy techniques and elegant experiments have revealed inherent stochasticity in the expression of genes and the localization of their products [1,2,3]. There has been an explosion of work on stochasticity in gene expression over the past decade [4,5,6,7]. The signalling pathways that allow cells to sense and react to their environments are subject to molecular stochasticity. At an entirely different time scale, we observe stochastic mutations to the DNA, either within an individual or at the species level. Such mutations enable evolution, and phylogenetic modelling and inference are often based on probabilistic formalisms [12,13]. Apparently stochastic behaviour is observed at many levels of organization, including the stochastic opening and closing behaviour of single ion channels, which became clear with the advent of single-channel patch clamp current recordings [14,15]
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