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 DI. We find that the radius of gyration Rg of the proteins exhibits 1/f fluctuations that are synchronous with the fluctuations of DI. Our analysis demonstrates the validity of the local Stokes-Einstein-type relation DIa1/(Rg+R0), where R00.3 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.