Detection of subtle dynamical changes induced by unresolved "conformational coordinates" in single-molecule trajectories via goodness-of-fit tests.

Single-molecule experiments are allowing researchers to track the evolution of a few order parameters characterizing complex biomolecules. At fine temporal resolution, artifacts of unresolved degrees of freedom, for example, those induced by collective molecular motion, often influence the dynamics. Reliably detecting subtle changes in dynamics at the nanoscale can be difficult due to the inherent stochasticity, but such changes can have relevance to understanding complex enzyme kinetics. Surrogate models can be used to summarize the information content in single-molecule time series (containing fluctuations occurring over multiple time scales). The focus in this article is on detecting slow time scale changes through the use of the surrogates. The conditional density, associated with the surrogates, allows one to formulate quantitative hypothesis tests which can detect the influence of unresolved coordinates in cases where the dynamics are modulated subtly. The relevance of quantitative (and appropriate) testing methods to analyze single-molecule time series is discussed and demonstrated. A brief discussion on some merits of using frequentist (versus Bayesian) time series methods to analyze single-molecule data is also presented. Idealized simulations mimicking features relevant to some enzyme systems where an "unresolved conformational coordinate" slowly evolves (1) with inertia and (2) diffusively are studied in the nonstationary (nonergodic) setting; however, the findings are also relevant to experimentally measured time series and stationary signals.