Non-affine displacements encode collective conformational fluctuations in proteins

Abstract

Identifying subtle conformational fluctuations underlying the dynamics of bio macromolecules is crucial for resolving their free energy landscape. We show that a collective variable, originally proposed for crystalline solids, is able to filter out essential macromolecular motions more efficiently than other approaches. While homogenous or 'affine' deformations of the biopolymer are trivial, biopolymer conformations are complicated by the occurrence of in-homogenous or 'non-affine' displacements of atoms relative to their positions in the native structure. We show that these displacements encode functionally relevant conformations of macromolecule and, in combination with a formalism based upon time-structured independent component analysis, quantitatively resolve the free energy landscape of a number of macromolecules of hierarchical complexity. The kinetics of conformational transitions among the basins can now be mapped within the framework of a Markov state model. The non-affine modes, obtained by projecting out homogenous fluctuations from the local displacements, are found to be responsible for local structural changes required for transitioning between pairs of macro states.