Hydrodynamic, or Stokes, radius of a particle is the radius of a hard sphere that diffuses at the same rate as that particle. When we are considering proteins, they are of course not hard particles, but complex folds of varying compactness and shape. The hydrodynamic radius of a peptide chain can thus vary depending on its folding state. For this reason, when converting hydrodynamic radius to molecular weight we can provide approximate boundaries corresponding to a fully folded, globular peptide in its most compact state, and a fully unfolded chain that has the least compact state.
For the fully folded state the volume of the protein scales with the molecular weight, leading to a relationship of:
Rh ∝ MW1/3
while for unfolded proteins the relationship is approximately:
Rh ∝ MW0.6
The empirically determined curves illustrating these relationships are shown below. The data used for the folded protein series was the collated experimental diffusion measurements in Tyn & Gusek (Prediction of Diffusion Coefficients of Proteins, Biotechnol. Bioeng. 35, 327). For unfolded proteins data from water soluble polymers (polyethyleneglycol, dextran and polyvinylpyrrolidone) in Armstrong, Wenby, Meiselman and Fisher (The Hydrodynamic Radii of Macromolecules and Their Effect on Red Blood Cell Aggregation, Biophys. J., 87, 4259) was used.
We've created a converter to enable you to make this conversion for both folded and unfolded proteins — from hydrodynamic radius to molecular weight or vice versa. Simply choose which state you expect the protein to be in and update the values accordingly: