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

We consider a flexible chain with internal friction in a harmonic confinement and extend it to include the effects of solvent quality at the mean field level by introducing a Flory type exponent ν. The strength of the harmonic confinement (kc) accounts for the denaturant concentration and connects to the internal friction of the chain (ξint) through an ansatz. Our calculated reconfiguration times falling in the range of 5-50 ns are found out to be within 10%-15% of the experimentally measured reconfiguration times of the folded cold shock protein and the intrinsically disordered protein prothymosin α. In addition, our calculations show that the reconfiguration time scales with the chain length N as ∼Nα, where α depends weakly on the internal friction but has rather stronger dependence on the solvent quality. In the absence of any internal friction, α=2ν+1 and it goes down in the presence of internal friction, but chain reconfiguration slows down in general. On the contrary, in a poorer solvent chain reconfiguration and looping become faster even though the internal friction is higher in the collapsed state.