CONSISTENT CALCULATIONS OF PK(A)S OF IONIZABLE RESIDUES IN PROTEINS -SEMIMICROSCOPIC AND MICROSCOPIC APPROACHES

One of the most direct benchmarks for electrostatic models of macromol ecules is provided by the pK(a)'s of ionizable groups in proteins. Obt aining accurate results for such a benchmark presents a major challeng e. Microscopic models involve very large opposing contributions and su ffer from convergence problems. Continuum models that consider the pro tein permanent dipoles as a part of the dielectric constant cannot rep roduce the correct self-energy. Continuum models that treat the local environment in a semi-microscopic way do not take into account consist ently the protein relaxation during the charging process. This work de scribes calculations of pK(a)' s in protein in an accurate yet consist ent way, using the semi-microscopic version of the protein dipoles Lan gevin dipoles (PDLD) model, which treats the protein relaxation in the microscopic framework of the linear response approximation. This appr oach allows one to take into account the protein structural reorganiza tion during formation of charges, thus reducing the problems with the use of the so-called ''protein dielectric constant'', epsilon(p). The model is used in calculations of pK(a)'s of the acidic groups of lysoz yme, and the calculated results are compared to the corresponding resu lts of discretized continuum (DC) studies. It is found that the presen t approach is more consistent than current DC models and also provides improved accuracies. Significant emphasis is given to the self-energy term, which has been painted out in our early works but has been some times overlooked or presented as a small effect. The meaning of the di electric constant epsilon(p) used in DC models is clarified and illust rated, establishing the finding (e.g. King et. al., J. Phys. Chem. 199 1, 95, 4366) that this parameter represents the contributions that are not treated explicitly in the given model, rather than the ''true'' d ielectric constant. It is pointed out that recent suggestions to use l arge epsilon(p) to obtain improved DC results might not be much differ ent than our earlier suggestion to use a large effective dielectric fo r charge-charge interactions. This epsilon(p) reduces the overestimate of charge-charge interactions relative to models that use small epsil on(p) while not considering the protein relaxation explicitly. Unfortu nately, the use of large epsilon(p) does not reproduce consistently th e self-energies of isolated ionized groups in protein interiors. The r ecent interest in taking protein flexibility into account in pK(a) cal culations is addressed. It is pointed out that running MD over protein configurations will not by itself lead to a more consistent value of epsilon(p). It is clarified that a smaller value of epsilon(p), which is not really more (or less) consistent with the physics of the protei ns, will be obtained if one uses our LRA (linear response approximatio n) formulation, generating configurations of both neutral and ionized states of the protein. It is also slated that such studies have been a standard part of our approach for some time. The present model involv es a consecutive running of all-atom MD simulations of solvated protei ns and an automated used of the electrostatic PDLD model. This allows one to move consistently to any level of explicit solvent model, keepi ng an arbitrary number of solvent molecules in an explicit all-atom re presentation, while treating the rest as dipoles. This capacity is use d in examining the microscopic basis of the PDLD models by comparing i ts free energy contributions to those obtained by the all-atom linear response approximation treatment. The agreement appears to be quite en couraging, thus further verifying the microscopic character of the PDL D model. Finally it is reclarified that real continuum models cannot p rovide proper descriptions of charges in protein and that current DC m odels are becoming more and more microscopic in nature.