Interpreting SMFRET-Based Calculation of Transition Path Time with Molecular Simulations

Abstract

Folding transition paths are fleeting events that occur when a protein crosses between unfolded and folded states. The ensemble of folding transition paths for a given protein contains a wealth of information regarding the barrier crossing pathways, i.e. the folding mechanism. Due to their typical durations and vanishing equilibrium probability, transition paths are extremely challenging to resolve experimentally. Recent advances in smFRET confer the time resolution necessary to capture at least the duration of these fast transitions (∼10∧(-5)s). However, measuring transition path durations by FRET presents a problem: a maximum likelihood model based on simplifying assumptions must be used to infer the duration because of the relatively low rate of photon detection. Here we use molecular simulation trajectories, in which all information is known to compute simulated photon trajectories with similar mean photon detection rates to those of real experiments. We then determine transition path times by passing the photon trajectory from simulation through a maximum likelihood algorithm identical to that employed for analysis of smFRET data. Specifically, we use a coarse-grained Go-model as an approximate representation of proteins alpha 3D, CspTm and GB1. We compare transition path times directly calculated from a reaction coordinate based on native contacts and transition path times calculated from a likelihood analysis of photon trajectory realizations of molecular simulations. We find that while the likelihood analysis of photon trajectories estimates transition path times within a factor of three of the true transition path time, it systematically underestimates true transition path times due to the oversimplified model of the transition path shape. Seeing as transition path shapes vary across proteins, we propose searching for the most likely transition path time with tunable transition path shape.