Probing the Viscosity Dependence of Rate: Internal Friction or the Lack of Friction?

Deviation from the Kramers' inverse viscosity dependence of rate, k ∝ 1/η, is often attributed to the presence of internal friction in proteins after Ansari et al. in 1992 showed that the folding rate could fit k ∝ 1/(η + σ) where σ is considered the internal friction. Several experimental and computational studies thereafter used fits to Ansari's equation or extrapolated the rate to η = 0 to estimate the internal friction in proteins and attributed its origin to various internal interactions such as ruggedness, dihedral rotation, and salt bridges. Here, we show that the above method to calculate the internal friction is incorrect since the rate in a simple model system without any internal friction yields a nonzero σ. Further investigation reveals that σ correlates with the relative deviation from Kramers' rate at different viscosities, where the deviation itself is caused due to the absence of full solvent friction rather than the presence of internal friction.