Modulation of Folding Internal Friction by Local and Global Barrier Heights

Abstract

Recent experiments have revealed an unexpected deviation from a first power dependence of protein relaxation times on solvent viscosity, an effect which has been attributed to “internal friction”. One clear source of internal friction in protein dynamics is the isomerization of dihedral angles. A key outstanding question is whether the global folding barrier height influences the measured internal friction, based on the observation that the folding rates of fast-folding proteins, with smaller folding free energy barriers, tend to exhibit larger internal friction. Here, by studying two alanine-based peptides we find that systematic variation of global folding barrier heights has little effect on the internal friction for folding rates. On the other hand, increasing local torsion angle barriers leads to increased internal friction, which is consistent with solvent memory effects being the origin of the viscosity dependence. Thus, it appears that local torsion transitions determine the viscosity dependence of the diffusion coefficient on the global coordinate, and in turn internal friction effects on the folding rate.

Integrated view of internal friction in unfolded proteins from single-molecule FRET, contact quenching, theory, and simulations

“…Dihedral rearrangements have been implicated as a mechanism of internal friction in protein folding, especially for helical proteins, where such local transitions are particularly important for the dynamics in the transition-state region (24,25). A lack of solvent relaxation on the time scale of dihedral barrier crossing can also result in low sensitivity of dynamics to solvent viscosity, and thus contribute to the signature commonly ascribed to internal friction (20,25). For a fully folded protein, most of the protein atoms are excluded from the solvent, and internal friction can be assumed to result from collisions with other protein atoms instead of solvent molecules (9).…”

“…Based on these studies, different molecular contributions to internal friction have been proposed, including hydrogen bonds (19), nonnative salt bridges (14), concerted dihedral rotations involving crank-shaft motions of the polypeptide backbone (21), and differences in native-state topology (24). Deviations from direct proportionality of relaxation times and solvent viscosity can also be due to inertial effects or solvent memory in dihedral angle hopping (20,25,26).…”

Butane dihedral angle dynamics in water is dominated by internal friction

“…In fact, deviations from a linear dependence have been experimentally observed for some proteins ( 9 ), while for other proteins, no internal friction was detected at all ( 17 ). Even in simulations, where—in contrast to experiments—the water friction can be reduced and a modification of the folding free-energy landscape with changing viscosity can be excluded, the extrapolation down to vanishing solvent friction is not trivial ( 18 – 22 ).…”

“…Previous theoretical approaches to internal friction based on reaction times suffer from the indirect connection between transition times and friction and necessarily rely on various model assumptions ( 18 – 22 ) (not so different from the experimental situation). Direly needed are models which allow to check for the presence of internal friction independently of any theoretical assumptions that relate friction to reaction times, as well as methods to extract friction and memory functions directly from simulations instead of inferring friction effects indirectly from measured reaction times.…”

Quantifying residue-specific conformational dynamics of a highly reactive 29-mer peptide

“…The decrease in Q upon MP01-Gen4 conjugation is significant. In the absence of other factors, the activation energy for diffusive motion of short polymers typically increases with molecular weight, due to increased internal friction 50,51 . Higher activation energies correspond to rougher energy landscapes, which occur when no single configuration adequately satisfies all of the intramolecular interactions necessary to fully stabilize it 52 .…”