Calculations of pH-dependent binding of proteins to biological membranes

Binding of proteins to membranes is often accompanied by titration of ionizable residues and is, therefore, dependent on pH. We present a theoretical treatment and computational approach for predicting absolute, pH-dependent membrane binding free energies. The standard free energy of binding, DeltaG, is defined as -RTln(P(b)/P(f)), where P(b) and P(f) are the amounts of bound and free protein. The apparent pK(a) of binding is the pH value at which P(b) and P(f) are equal. Proteins bind to the membrane in the pH range where DeltaG is negative. The components of the binding free energy are (a) the free energy cost of ionization state changes (DeltaG(ion)), (b) the effective energy of transfer from solvent to the membrane surface, (c) the translational/rotational entropy cost of binding, and (d) an ideal entropy term that depends on the relative volume of the bound and free state and therefore depends on lipid concentration. Calculation of the first term requires determination of pK(a) values in solvent and on the membrane surface. All energies required by the method are obtained from molecular dynamics trajectories on an implicit membrane (IMM1-GC). The method is tested on pentalysine and the helical peptide VEEKS, derived from the membrane-binding domain of phosphocholine cytidylyltransferase. The agreement between the measured and the calculated free energies of binding of pentalysine is good. The extent of membrane binding of VEEKS is, however, underestimated compared to experiment. Calculations of the interaction energy between two VEEKS helices on the membrane suggest that the discrepancy is mainly due to the neglect of protein-protein interactions on the membrane surface.