| Abstract: | Exchange-rate probability-density functions (pdf) have been calculated for lysozyme hydrogen-exchange data by numerical Laplace inversion over the temperature range 5–45°C. The smoothest numerical solutions show three broad overlapping peaks. Analysis of the temperature dependence of the cumulative exchange-rate distributions provides the model-independent probability-density function for the activation energies. For the most rapidly exchanging protons, the activation energies are low, consistent with hydroxyl-ion catalysis in the protein–water interface. The second peak of the exchange-rate pdf's contains those protons located in regions of lower motility we call “matrices,” for which exchange rates are limited by gated-diffusion of the hydroxyl-ion catalyst. The most slowly exchanging protons are located on groups forming strong, dense “knot” structures, identified by neutron-diffraction and nmr data as clustered segments of β-sheet with well-organized hydrogen bonding and sections of the internal faces of α-helices. Exchange from knot structures occurs through local disordering with little loss of strength or stability to expose one or more protons at a time for exchange. Knots appear to be responsible for the two-state character of thermal unfolding that occurs by cooperative disruption of the dominant structures of this type. Below about 55°C, all protons exchange from folded states. Contributions to exchange from unfolding processes occur only at temperatures above 55°C. There is a qualitative difference between the two types of structures indicated by the appearance of two and only two enthalpy–entropy compensation patterns. The compensation temperature, Tc, for the matrices is about 470 K; that for the knots, about 360 K. The preservation of rank-order with temperature change is shown to be a consequence of the fact that all exchange rates in the slow and very slow peaks of the pdf lie on one or the other of the two compensation lines. Although the same electrostatic factors are present in all parts of the protein, we have been forced to conclude that given certain necessary geometric possibilities, these factors cooperate to produce the knots. The knots appear to be the most significant structural element in globular proteins responsible for the structural form of the matrix regions and the dynamic behavior of the protein interior. The knots have high density and low permeability to water, hydroxyl ion, etc., and are probably the explanation for the very low compressibilities, the matrices being nearly mechanically transparent. The knots must make some contribution to folded stability, but it is not clear that this contribution is large. Their major thermodynamic function is to establish kinetic stability; that is, to make the activation free energy for unfolding high. The most important factor in the existence of knots appears to be the ease with which hydrogen bonds adapt in length, angle, and strength to local electrostatic conditions. In proteins, as in water, adaptation is cooperative in local groups of hydrogen bonds, and as in water, this cooperation is enhanced by contact with aromatic and aliphatic groups. |
