What do molecules do when we are not looking? State sequence analysis for stochastic chemical systems

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.