Universal relation between instantaneous diffusivity and radius of gyration of proteins in aqueous solution

Abstract

Protein conformational fluctuations are highly complex and exhibit long-term correlations. Here, molecular dynamics simulations of small proteins demonstrate that these conformational fluctuations directly affect the protein's instantaneous diffusivity $D_I$. We find that the radius of gyration $R_g$ of the proteins exhibits $1/f$ fluctuations, that are synchronous with the fluctuations of $D_I$. Our analysis demonstrates the validity of the local Stokes-Einstein type relation $D_I\propto 1/(R_g+R_0)$, where $R_0\sim 0.3$ nm is assumed to be a hydration layer around the protein. From the analysis of different protein types with both strong and weak conformational fluctuations the validity of the Stokes-Einstein type relation appears to be a general property.

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