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 hc = 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 hc 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 hc to change in pH and solvent, is the sudden appearance of long-range connectivity and infinite clusters at the threshold hc. 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.