Looping dynamics of a flexible chain with internal friction at different degrees of compactness

Abstract

Recently single molecule experiments have shown the importance of internal friction in biopolymer dynamics. Such studies also suggested that the internal friction although independent of solvent viscosity has strong dependence on denaturant concentration. Recent simulations also support such propositions by pointing out weak interactions to be the origin of internal friction in proteins. Here we made an attempt to investigate how a single polymer chain with internal friction undergoes reconfiguration and looping dynamics in a confining potential which accounts for the presence of the denaturant, by using recently proposed "Compacted Rouse with internal friction (CRIF)". We also incorporated the effect of hydrodynamics by extending this further to "Compacted Zimm with internal friction (CZIF)". All the calculations are carried out within the Wilemski Fixmann (WF) framework. By changing the strength of the confinement we mimicked chains with different degrees of compactness at different denaturant concentrations. While compared with experiments our results are found to be in good agreement.

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

“…As expected with ν = 1/2 which corresponds to θ solvent, SDCRIF gives back "compacted Rouse with internal friction (CRIF)" [31], when k c and ξ int both are nonzero. A more realistic situation would be ν = 3/5 corresponding to good solvent.…”

“…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].…”

“…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].…”

“…Next is the inclusion of internal friction which is done similarly as in case of a phantom polymer chain [54]. Further to take care of the denaturant which controls the compactness of the protein a confining harmonic potential with force constant k c is used as is done in a very recent study by the authors [31] and also in the context of diffusing polymers in microconfinements [55] or in case of bubble formation in double stranded DNA [56]. So the novelty of SDCRIF remains in its applicability for a range of solvent quality, The looping dynamics is studied within Wilemski Fixman (WF) framework [13,57] with SDCRIF, assuming the polymer chain to be Gaussian.…”

Rheological consequences of wet and dry friction in a dumbbell model with hydrodynamic interactions and internal viscosity

“…[1][2][3][4] The inclusion of a resistive force proportional to the rate of change of the connector vector between beads in addition to the spring force has been shown to lead to a finite limiting value for the infinite frequency limit of the dynamic viscosity, 3 instantaneous stress jumps at the inception of steady shear flow, 5 and to a shear-rate dependent viscosity. 6,7 More recently, several experimental, [8][9][10][11][12] theoretical [13][14][15][16][17][18][19] and simulation studies [20][21][22][23] have shown that the presence of internal friction modulates conformational changes in a number of different biological contexts. This includes slowing down the process of protein folding, 8 affecting the dynamics of intermolecular interactions in intrinsically disordered proteins, 10,11 and influencing stretching transitions in single biomolecule force spectroscopy.…”