THEORETICAL MODELING OF ELECTROSTATIC EFFECTS OF TITRATABLE SIDE-CHAIN GROUPS ON PROTEIN CONFORMATION IN A POLAR IONIC SOLUTION .2. PH-INDUCED HELIX-COIL TRANSITION OF POLY(L-LYSINE) IN WATER AND METHANOL IONIC-SOLUTIONS

The helix-coil transition of poly(L-lysine) in water and in methanol solutions of a 1:1 salt is studied as a function of pH. The relative electrostatic free energy between the ionized microstates of poly(L-lysine) is evaluated as the sum of the potentials of mean force (PMF) between pairs of charged lysine residues. The PMFs in the alpha-helical and the statistical-coil conformations in water and in methanol-water solutions were calculated with a continuum electrostatic model based on a numerical solution of the nonlinear Poisson-Boltzmann equation. It was found that the PMFs in a polar solution of a 1:1 salt are strongly dependent on the ionization microstate of the poly(L-lysine). A 24-residue peptide served as a model for the helix to coil transition. An ensemble of 1200 statistical-coil conformations was generated for neutral poly(L-lysine) with the ECEPP/3 program. A representative ensemble of the statistical-coil conformation was then built by constraining the average end-to-end distance of the polymer to fit the experimental value of the characteristic ratio. The dependence of the electrostatic free energy difference between the alpha-helix and the coil state on the pH was calculated with Tanford's equation for equilibrium proton binding by integrating the difference between the titration curves for the two conformational states, The calculations show the following: (i) poly(L-lysine) undergoes the helix to coil transition in a water solution around pH 10.4, where the polymer is 30% charged for the alpha-helical conformation and 40% charged for the statistical-coil state, in good agreement with experimental data; (ii) the characteristics of the helix to coil transition have a small dependence on the concentration of a 1:1 salt in the range of 0.1-0.5 M. The completely charged alpha-helix is stabilized in an aqueous 95% methanol solution relative to that in water solution because the coil state is less stable in methanol, where its polar groups are less solvated than in water solution; this solvation effect dominates even though there is a small increase in electrostatic repulsion between the charged lysine residues in the helical state in methanol solution. The fact that electrostatic repulsion in an aqueous 95% methanol solution is only slightly greater (about 0.1 kcal/mol per residue) than that in water is due to a nonlinear increase of the screening by the mobile ions of a 1:1 salt in methanol, The main conclusions from this study are the following: (i) the presence of a 1:1 salt, even at a low concentration of 0.01 M, is of primary importance in explaining the dependence of proton binding (titration curves) and the conformational stability of poly(L-lysine) on the solvent pH and polarity; (ii) the nonlinear Poisson-Boltzmann equation reproduces the dependence of the electrostatic effects of poly(L-lysine) on the concentration of a 1:1 salt, solvent pH. and polarity correctly.