Expansion and Internal Friction in Unfolded Protein Chain

Abstract

Similarities in global properties of homopolymers and unfolded proteins provide approaches to mechanistic description of protein folding. Here, hydrodynamic properties and relaxation rates of the unfolded state of carbonmonoxide-liganded cytochrome c (cyt-CO) have been measured using nuclear magnetic resonance and laser photolysis methods. Hydrodynamic radius of the unfolded chain gradually increases as the solvent turns increasingly better, consistent with theory. Curiously, however, the rate of intrachain contact formation also increases with an increasing denaturant concentration, which, by Szabo, Schulten, and Schulten theory for the rate of intramolecular contact formation in a Gaussian polymer, indicates growing intramolecular diffusion. It is argued that diminishing nonbonded atom interactions with increasing denaturant reduces internal friction and, thus, increases the rate of polypeptide relaxation. Qualitative scaling of the extent of unfolding with nonbonded repulsions allows for description of internal friction by a phenomenological model. The degree of nonbonded atom interactions largely determines the extent of internal friction.

Derivation of a Markov state model of the dynamics of a protein-like chain immersed in an implicit solvent

“…One expects that bonding monomers centrallylocated in the chain to experience a greater effective friction than bonding monomers located near the ends due to the greater number of local interactions through which a binding monomer drags its sterically-connected neighbors. In a similar context, the intra-chain diffusion coefficient plays an important role in diffusion-controlled intra-chain reactions such as loop closing or intra-chain catalytic processes in the Rouse, Rouse-Zimm, and other models of polymer dynamics [42][43][44][45][46].…”

Reconfiguration dynamics in folded and intrinsically disordered protein with internal friction: Effect of solvent quality and denaturant

“…As the k c controls the compactness of the polymer, increasing the value of k c should result in the higher degree of internal friction. Since there is no first principle relation between k c and ξ int , we have used an ansatz in our calculation [12,31].…”

“…Thus it can be approximated that the with increase in denaturant concentration [12]. Higher the denaturant concentration lower the internal friction.…”

“…However recent experiments on looping and folding dynamics [7][8][9][10][11][12] in proteins have indicated the non-negligible role of internal friction. In this context it is worth mentioning that loop formation between any two parts of a bio-polymer [13][14][15][16][17][18][19][20][21][22][23][24] is supposedly the primary step of protein folding, DNA cyclization and since internal friction affects looping it is obvious that measurements of folding rates in proteins would predict the importance of solvent independent internal friction as well [25].…”

“…In this context it is worth mentioning that loop formation between any two parts of a bio-polymer [13][14][15][16][17][18][19][20][21][22][23][24] is supposedly the primary step of protein folding, DNA cyclization and since internal friction affects looping it is obvious that measurements of folding rates in proteins would predict the importance of solvent independent internal friction as well [25]. Subsequently not only these recent experiments [11,12,26] on polypeptides and proteins showed internal friction to play a pivotal role in the dynamics but also motivated theoretical chemical physicists to come up with statistical mechanical models for single polymer chain with the inclusion of internal friction [27][28][29][30][31] and apply these models to investigate the loop formation dynamics. Other than model build up there have been attempts to elucidate the origin of internal friction in proteins based on computer simulation studies [32][33][34][35][36][37][38].…”