Viscosity and transient solvent accessibility of Trp-63 in the native conformation of lysozyme

We have measured the rates of isotope exchange at the nitrogen of the indole ring of Trp-63 of lysozyme and of L-tryptophan as a function of solution viscosity. We have used two cosolvents, glycerol and ethylene glycol, to modify the relative viscosity. We have derived the appropriate kinetic equations for the alternative possibilities that the exchange takes place either in solution or in the intact protein matrix. Because we chose to study the proton-catalyzed exchange reaction, the rate of it is not expected to be diffusion-limited. We confirmed this by measuring the exchange from tryptophan. These results and the known effects of glycerol and ethylene glycol on the solvation of indole allow us to predict that if the exchange reaction takes place in a protein matrix the effects of the two cosolvents when compared under isoviscous conditions should be identical. This is what we find for Trp-63 in lysozyme at 15, 20 and 26 degrees C. The slope of the linear plot of log k vs. log relative viscosity is 0.6. This strongly supports a model for conformational fluctuations where transient solvation takes place without major changes in protein folding. The most interesting feature of our findings is the fact that a slow reaction admittedly not diffusion-limited shows, when taking place in a protein matrix, a linear dependence on solution viscosity. We suggest that what we observe is the effect of damping of movement of the side chain expressed as a change in the friction along the reaction coordinate in the corresponding phase space. The presence of such effects stresses the validity and usefulness of Kramers model of rate processes for reactions taking place in a protein matrix. Such behavior is predicted by several of the recently proposed general mechanisms of enzyme catalysis.