Nonaffine Displacements Encode Collective Conformational Fluctuations in Proteins.

Identifying subtle conformational fluctuations underlying the dynamics of biomacromolecules 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 homogeneous or "affine" deformations of the biopolymer are trivial, biopolymer conformations are complicated by the occurrence of inhomogeneous or "nonaffine" displacements of atoms relative to their positions in the native structure. We show that these displacements encode functionally relevant conformations of macromolecules, and in combination with a formalism based upon time-structured independent component analysis, they 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 nonaffine modes, obtained by projecting out homogeneous fluctuations from the local displacements, are found to be responsible for local structural changes required for transitioning between pairs of macrostates.