Universal Relation between Instantaneous Diffusivity and Radius of Gyration of Proteins in Aqueous Solution

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 D₈. We find that the radius of gyration R₆ of the proteins exhibits 1/f fluctuations that are synchronous with the fluctuations of D₈. Our analysis demonstrates the validity of the local Stokes-Einstein-type relation D₈∝1/ (R₆+R₀), where R₀∼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.