A kinetic analysis of local fluctuations in ubiquitin by combining the LE4PD normal modes and Markov state modeling

Follwowing the conformational selection hypothesis, accurately determining the location and magnitude of fluctuations along a protein’s primary sequence is important in describing its mechanism of binding, so methods describing precisely the fluctuation dynamics of proteins can help reveal their biological function. Here, we model the fluctuation dynamics and kinetics of the protein ubiquitin using a coarse-grained description of the protein’s dynamics, the Langevin Equation for Protein Dynamics (LE4PD), which decomposes the dynamics of a protein into dynamical pathways that explore mode-dependent free-energy surfaces. Using as input to the theory statistics from a molecular dynamics simulation, we calculate the timescales of the slow LE4PD modes using Markov state models.The predicted timescales of these LE4PD modes can be elucidated using the committor function, and a version of the string method is used to extract real-space fluctuations of the protein from the mode representation. We find the dynamics predicted by the slow LE4PD modes correspond to motion in important binding regions of the protein. We also show that the fastest LE4PD modes correspond to localized, conserved fluctuations along the protein’s primary sequence.