Abstract
A long time ago, Kuhn predicted that long polymers should approach a limit where their global motion is controlled by solvent friction alone, with ruggedness of their energy landscapes having no consequences for their dynamics. In contrast, internal friction effects are important for polymers of modest length. Internal friction in proteins, in particular, affects how fast they fold or find their binding targets and, as such, has attracted much recent attention. Here we explore the molecular origins of internal friction in unfolded proteins using atomistic simulations, coarse-grained models and analytic theory. We show that the characteristic internal friction timescale is directly proportional to the timescale of hindered dihedral rotations within the polypeptide chain, with a proportionality coefficient b that is independent of the chain length. Such chain length independence of b provides experimentally testable evidence that internal friction arises from concerted, crankshaft-like dihedral rearrangements. In accord with phenomenological models of internal friction, we find the global reconfiguration timescale of a polypeptide to be the sum of solvent friction and internal friction timescales. At the same time, the time evolution of inter-monomer distances within polypeptides deviates both from the predictions of those models and from a simple, one-dimensional diffusion model.
Highlights
Protein folding may be justifiably viewed as a finite-size first-order phase transition, with folding kinetics following a classic nucleation mechanism[1, 2]
We showed that the experimental observations of the dynamics of loop formation within both unfolded proteins and single-stranded DNA obey simple, universal relationships derived from polymer theory[23]
In Kuhn’s original argument, the effect of barrier friction on the global relaxation dynamics will become increasingly small as the chain becomes longer, because the barrier friction decreases with the increasing chain length while the hydrodynamic friction increases
Summary
Protein folding may be justifiably viewed as a finite-size first-order phase transition, with folding kinetics following a classic nucleation mechanism[1, 2]. Among interesting questions are whether the unfolded state is in a swollen (coiled) or molten globular state, and in the former case, whether folding is preceded by globular collapse or takes place concomitantly with it Both analytical and numerical models rooted in polymer theory can provide important insights into the nature of dynamics in the unfolded ensemble and into the specific collective processes driving the folding reaction. These approaches are fruitful in addressing kinetic questions, where many prior studies of protein folding assumed either one-dimensional diffusion along some reaction coordinate[8] (which is postulated, equated to an experimental signal, or computed based on an optimality criterion10) or relied on discrete kinetic networks[11,12,13,14], which are often deduced from all-atom simulations. Equation (1) provides a reasonable order-of-magnitude estimate of the reconfiguration time of chemically denatured proteins, but it manifestly underestimates the reconfiguration times of some of the intrinsically disordered proteins or proteins that are unfolded near native conditions[27], presumably because of intra-chain interactions or some other new effects
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