Abstract
In recent past, experiments and simulations have suggested that apart from the solvent friction, friction arising from the protein itself plays an important role in protein folding by affecting the intra-chain loop formation dynamics. This friction is termed as internal friction in the literature. Using a flexible Gaussian chain with internal friction we analyze the intra-chain reconfiguration and loop formation times for all three topology classes namely end-to-end, end-to-interior and interior-to-interior. In a nutshell, bypassing expensive simulations we show how simple models like that of Rouse and Zimm can support the single molecule experiment and computer simulation results on intra-chain diffusion coefficients, looping time and even can predict the effects of tail length on the looping time.
Highlights
Loop formation between two ends of a polymer chain has extensively been studied by experimentalists and polymer theorists
One of the theoretical models to calculate the loop formation time between two ends of a long chain molecule is due to Wilemski and Fixman (WF).[1]
To calculate the reconfiguration time defined in Eq (4) we first compute the correlation function defined in Eq (5) and put this back in Eq (4)
Summary
Loop formation between two ends of a polymer chain has extensively been studied by experimentalists and polymer theorists. Several studies using single molecule FRET by Schuler’s42,43 group have shown the existence of non-vanishing reconfiguration time of the cold shock protein and spectrin domains even at extrapolated zero viscosity of the solvent They found internal friction to have an additive contribution to the reconfiguration time of unfolded protein. In a more compact situation different parts of a protein are close enough to interact through weak forces such as hydrogen bonds, more likely to undergo intra-chain collisions and contributing more to the internal friction and would result in higher internal friction Based on their experimental observations they proposed a relation between the reconfiguration time τr and the time scale associated with the internal friction τint as follows τr η. It is practically impossible to unentangle the effects of internal friction and excluded volume interactions
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