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

We consider a phantom chain model of polymer with internal friction in a harmonic confinement and extend it to take care of effects of solvent quality following a mean field approach where an exponent $\nu$ is introduced. The model termed as "Solvent Dependent Compacted Rouse with Internal Friction (SDCRIF)" is then used to calculate the reconfiguration time of a chain that relates to recent F\"{o}rster resonance energy transfer (FRET) studies on folded and intrinsically disordered proteins (IDPs) and can account for the effects of solvent quality as well as the denaturant concentration on the reconfiguration dynamics. Following an ansatz that relates the strength of the harmonic confinement ($k_c$) with the internal friction of the chain ($\xi_{int}$), SDCRIF can convincingly reproduce the experimental data and explain how the denaturant can change the time scale for the internal friction. It can also predict near zero internal friction in case of IDPs. In addition, our calculations show that the looping time as well as the reconfiguration time scales with the chain length $N$ as $\sim N^\alpha$, where $\alpha$ depends weakly on the internal friction but has rather stronger dependence on the solvent quality. In absence of any internal friction, $\alpha=2\nu+1$ and it goes down in presence of internal friction, but looping slows down in general. On the contrary, poorer the solvent, faster the chain reconfigures and forms loop, even though one expects high internal friction in the collapsed state. However, if the internal friction is too high then the looping and reconfiguration dynamics become slow even in poor solvent.