  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 $D_I\propto1/(R_g + R_0)$, where $R_0\sim0.3$ 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.
