The surface reactivity of clay minerals remains challenging to characterize because of a duality of adsorption surfaces and mechanisms that does not exist in the case of simple oxide surfaces: edge surfaces of clay minerals have a variable proton surface charge arising from hydroxyl functional groups, whereas basal surfaces have a permanent negative charge arising from isomorphic substitutions. Hence, the relationship between surface charge and surface potential on edge surfaces cannot be described using the Gouy-Chapman relation, because of a spillover of negative electrostatic potential from the basal surface onto the edge surface. While surface complexation models can be modified to account for these features, a predictive fit of experimental data was not possible until recently, because of uncertainty regarding the densities and intrinsic pKa values of edge functional groups. Here, we reexamine this problem in light of new knowledge on intrinsic pKa values obtained over the past decade using ab initio molecular dynamics simulations, and we propose a new formalism to describe edge functional groups. Our simulation results yield reasonable predictions of the best available experimental acid-base titration data.