Intrinsic pKas of ionizable residues in proteins: an explicit solvent calculation for lysozyme.

Molecular dynamics simulations of triclinic hen egg white lysozyme in aqueous solution were performed to calculate the intrinsic pKas of 14 ionizable residues. An all-atom model was used for both solvent and solute, and a single 180 ps simulation in conjunction with a Gaussian fluctuation analysis method was used. An advantage of the Gaussian fluctuation method is that it only requires a single simulation of the system in a reference state to calculate all the pKas in the protein, in contrast to multiple simulations for the free energy perturbation method. pKint shifts with respect to reference titratable residues were evaluated and compared to results obtained using a finite difference Poisson-Boltzmann (FDPB) method with a continuum solvent model; overall agreement with the direction of the shifts was generally observed, though the magnitude of the shifts was typically larger with the explicit solvent model. The contribution of the first solvation shell to the total charging free energies of the titratable groups was explicitly evaluated and found to be significant. Dielectric shielding between pairs of titratable groups was examined and found to be smaller than expected. The effect of the approximations used to treat the long-range interactions on the pKint shifts is discussed.

Molecular mechanics and electrostatic effects.

Continuum solvent models predict a quadratic charge dependence (linear response) of the free energy of a system of charged solutes. The relation between this prediction and the structure of the solvation shell around the solutes is discussed. Studies of the derivative of the free energy with respect to the charges for different reference states are shown to be a convenient way of testing the linear response assumption without resorting to the standard free energy perturbation method. We illustrate this with a system of two oppositely charged ions in aqueous solution, where nonlinearities are observed before the full charging process is completed. Since molecular mechanics (MM) simulations preserve the full nonlinearity of the problem, they are well suited to the investigation of the conditions under which linear response accurately reflects the behavior of the system. The error when using linear response theory to calculate the free energies of charging is estimated to be as large as 10-20%.