Overdamped dynamics of folded protein domains within a locally harmonic basin using coarse graining based on a partition of compact flexible clusters.

A coarse-graining method based on the partitioning of atoms into compact flexible clusters is used to formulate the dynamics of the nonequilibrium response of a protein to ligand dissociation. The α-carbon positions are used as the degrees of freedom. The net stiffness between each pair of neighboring α-carbons is calculated for the quasi-static, overdamped regime within the harmonic (quadratic potential energy surface) using the equivalent stiffness matrix of the network of atoms occupying the intervening space within the locally interacting region. This localized approach realizes a divide and conquer strategy that results in a substantial reduction in computational complexity while accurately predicting relaxations under general loading conditions. A close correlation between the shapes and time scales of the relaxation curves of the coarse-grained and all-atom instances of two medium-sized proteins, T4 lysozyme and ferric binding protein (each of which having known apo and holo structures), was observed for the holo to the apo transitions. Furthermore, for both proteins the dominant modes of motion and the decay rates of the temporal relaxation profiles monitoring the separation distance between select amino acid pairs were found to be nearly identical when calculated on the coarse-grained and all-atom scales.