Computing Reaction Rates in Bio-molecular Systems Using Discrete Macro-states
We discuss different techniques to calculate reaction rates in biomolecular systems. We first review historically the first approaches based on reactive flux, which make certain simplifying assumptions in order to derive relatively simple formulas to estimate rates. Then we discuss a series of methods that attempt to do a more direct calculation based on path sampling, and related techniques such as transition interface sampling, forward flux sampling, and milestoning. Another set of approaches is based on the concept of metastability and includes techniques like conformational dynamics and recently developed methods such as Markov state models that are based on these concepts. Some recent methods attempt to combine the macro-state division of space used in Markov state models with transition path sampling in order to deal with systems exhibiting long memory, for which Markovian models are not sufficiently accurate. Such methods include weighted ensemble Brownian dynamics and non-equilibrium umbrella sampling. Finally, we include a numerical analysis of Markov state models to understand systematic and statistical errors and their behavior, along with some numerical benchmarks to illustrate the results.