Dispersion Forces and the Molecular Origin of Internal Friction in Protein

Internal friction in macromolecules is one of the curious phenomena that control conformational changes and reaction rates. It is held here that dispersion interactions and London-van der Waals forces between nonbonded atoms are major contributors to internal friction. To demonstrate this, the flipping motion of aromatic rings of F10 and Y97 amino acid residues of cytochrome c has been studied in glycerol/water mixtures by cross relaxation-suppressed exchange nuclear magnetic resonance spectroscopy. The ring-flip rate is highly overdamped by glycerol, but this is not due to the effect of protein-solvent interactions on the Brownian dynamics of the protein, because glycerol cannot penetrate into the protein to slow the internal collective motions. Sound velocity in the protein under matching solvent conditions shows that glycerol exerts its effect by rather smothering the protein interior to produce reduced molecular compressibility and root-mean-square volume fluctuation (δVRMS), implying an increased number of dispersion interactions of nonbonded atoms. Hence, δVRMS can be used as a proxy for internal friction. By using the ansatz that internal friction is related to nonbonded interactions by the equation f(n) = f0 + f1n + f2n(2) + ..., where the variable n is the extent of nonbonded interactions with fi coefficients, the barrier to aromatic ring rotation is found to be flat. Also interesting is the appearance of a turnover region in the δVRMS dependence of the ring-flip rate, suggesting anomalous internal diffusion. We conclude that cohesive forces among nonbonded atoms are major contributors to the molecular origin of internal friction.