John A. Rupley

Calorimetric measurements of the heat capacity of the lysozyme-water system have been carried out over the full range of system composition at 25 degrees C. The partial specific heat capacity of the protein in dilute solution is 1.483 +/- 0.009 J K-1 g-1. The heat capacity of the dry protein is 1.26 +/- 0.01 J K-1 g-1. The system heat capacity responds linearly to change in composition from dilute solution to 0.38 g of water per g of protein (h) and is an irregular function at lower water content. The break in the heat capacity function at 0.38 h defines the amount of water needed to develop the equilibrium solution properties of lysozyme as being 300 molecules of water/protein molecule, just sufficient for monolayer coverage. The heat capacity behavior at low water content describes three hydration regions. The most tightly bound water (0-0.07 h), probably principally bound to charged groups, is characterized by a partial specific heat capacity of 2.3 J K-1 g-1, a value close to that for ice. A heat of reaction associated with proton redistribution is reflected in the heat capacity function for the low-hydration region. Between 0.07 and 0.25 h the heat capacity increases strongly, which is understood to reflect the growth of patches of water covering polar and adjacent nonpolar portions of the protein surface. The hydration shell is completed by condensation of solvent over the weak-interacting portions of the surface, in a process displaying a transition heat.

The framework of percolation theory is used to analyze the hydration dependence of the capacitance measured for protein samples of pH 3-10, at frequencies from 10 kHz to 4 MHz. For all samples there is a critical value of the hydration at which the capacitance sharply increases with increase in hydration level. The threshold h(c) = 0.15 g of water per g of protein is independent of pH below pH 9 and shows no solvent deuterium isotope effect. The fractional coverage of the surface at h(c) is in close agreement with the prediction of theory for surface percolation. We view the protonic conduction process described here for low hydration and previously for high hydration as percolative proton transfer along threads of hydrogen-bonded water molecules. A principal element of the percolation picture, which explains the invariance of h(c) to change in pH and solvent, is the sudden appearance of long-range connectivity and infinite clusters at the threshold h(c). The relationship of the protonic conduction threshold to other features of protein hydration is described. The importance of percolative processes for enzyme catalysis and membrane transport is discussed.