Combining LE4PD Normal Modes and Markov State Modeling to Elucidate the Fluctuation Dynamics of Ubiquitin

Abstract

Local fluctuations are important for protein binding and molecular recognition because they provide conformational states that can be trapped through a conformational selection mechanism of binding. Thus, an accurate characterization of local fluctuations can be important for modeling the mechanisms leading to the biological activity of a protein. In this presentation we quantify the fluctuation dynamics of the regulatory protein ubiquitin and propose a novel theoretical approach to modelling its fluctuations. A coarse-grained, diffusive, mode-dependent description of the protein's fluctuation dynamics is accomplished using the Langevin Equation for Protein Dynamics (LE4PD); this equation decomposes the dynamics of a protein, modeled through a molecular dynamics (MD) simulation, into dynamical pathways that explore mode-dependent free energy surfaces. Using as input to the theory a one-microsecond, atomistic MD simulation, we calculate the time scales of the slow, high-amplitude fluctuations by modeling the kinetics of barrier crossing in the two-dimensional free-energy surfaces using a Markov state model (MSM) approach. We find that the LE4PD predicts slow fluctuations in three biologically significant binding regions in ubiquitin: the C-terminal tail, the Lys11 loop, and the 50 s loop. The combination of the LE4PD modes with the MSM analysis can provide useful information on the role of fluctuations in the process of molecular recognition regulating the biological activity of ubiquitin, with the LE4PD modes describing the location and magnitude of high-amplitude conformational changes and the MSM giving the associated timescales.