Dimensions of Denatured Protein Chains from Hydrodynamic Data

The chain length dependence of the intrinsic viscosity and the Stokes radius demonstrates that denatured proteins are not in the “unperturbed” state but rather have nonlocal excluded-volume interactions between residues. Here, we present hydrodynamic calculations on denatured protein chains with N = 16 to 104 residues. Chain conformations were generated by sampling ( φ, ψ ) from those collected from loop regions in the protein structure database. Excluded-volume effects were explicitly accounted for by assigning a hard-sphere diameter d α to the C α atoms. The value of d α for a chain at a given length was adjusted so the experimental intrinsic viscosity is reproduced. This procedure allowed a simultaneous reproduction of the experimental Stokes radii for all the chain lengths studied. The distribution of the end-to-end distance R and its mean square 〈 R 2 〉 were obtained from the sampled chain conformations. When the chain length dependence of the intrinsic viscosity and the Stokes radius is fitted to the Zimm model (which predicts [ η ] M = Φ 〈 R 2 〉 3/2 and R s = K 〈 R 2 〉 1/2 ), the length dependence of the coefficients Φ and K is obtained. The effective bond length b eff [defined via 〈 R 2 〉 = ( N − 1) b eff 2 ] ranges from 5.71 to 8.78 Å, and the distribution of R is nearly Gaussian when N > 30. The value of b eff is extrapolated to increase to 10.6 Å at N = 1000. For any chain, the distance between two interior residues is characterized by a shorter effective bond length than the end-to-end distance.