Harmonicity in slow protein dynamics

The slow dynamics of proteins around its native folded state is usually described by di€usion in a strongly anharmonic potential. In this paper, we try to understand the form and origin of the anharmonicities, with the principal aim of gaining a better understanding of the principal motion types, but also in order to develop more ecient numerical methods for simulating neutron scattering spectra of large proteins. First, we decompose a molecular dynamics (MD) trajectory of 1.5 ns for a C-phycocyanin dimer surrounded by a layer of water into three contributions that we expect to be independent: the global motion of the residues, the rigid-body motion of the sidechains relative to the backbone, and the internal deformations of the sidechains. We show that they are indeed almost independent by verifying the factorization of the incoherent intermediate scattering function. Then, we show that the global residue motions, which include all large-scale backbone motions, can be reproduced by a simple harmonic model which contains two contributions: a short-time vibrational term, described by a standard normal mode calculation in a local minimum, and a long-time di€usive term, described by Brownian motion in an e€ective harmonic potential. The potential and the friction constants were ®tted to the MD data. The major anharmonic contribution to the incoherent intermediate scattering function comes from the rigid-body di€usion of the sidechains. This model can be used to calculate scattering functions for large proteins and for long-time scales very eciently, and thus provides a useful complement to MD simulations, which are best suited for detailed studies on smaller systems or for shorter time scales. Ó 2000 Elsevier Science B.V. All rights reserved.