The mechanisms of electrostatically driven adsorption of proteins on charged surfaces are studied with a new theoretical framework. The acid-base behavior, charge distribution, and electrostatic contributions to the thermodynamic properties of the proteins are modeled in the presence of a charged surface. The method is validated against experimental titration curves and apparent pK(a)s. The theory predicts that electrostatic interactions favor the adsorption of proteins at their isoelectric points on charged surfaces despite the fact that the protein has no net charge in solution. Two known mechanisms explain adsorption under these conditions: (i) charge regulation (the charge of the protein changes due to the presence of the surface) and (ii) charge patches (the protein orients to place charged amino acids near opposite surface charges). This work shows that both mechanisms contribute to adsorption at low ionic strengths, whereas only the charge-patch mechanism operates at high ionic strength. Interestingly, the contribution of charge regulation is insensitive to protein orientation under all conditions, which validates the use of constant-charge simulations to determine the most stable orientation of adsorbed proteins. The present study also shows that the charged surface can induce large shifts in the apparent pK(a)s of individual amino acids in adsorbed proteins. Our conclusions are valid for all proteins studied in this work (lysozyme, alpha-amylase, ribonuclease A, and beta-lactoglobulin), as well as for proteins that are not isoelectric but have instead a net charge in solution of the same sign as the surface charge, i.e. the problem of protein adsorption on the "wrong side" of the isoelectric point.