Richard Fine

On the calculation of electrostatic interactions in proteins

In this paper we present a classical treatment of electrostatic interactions in proteins. The protein is treated as a region of low dielectric constant with spherical charges embedded within it, surrounded by an aqueous solvent of high dielectric constant, which may contain a simple electrolyte. The complete analysis includes the effects of solvent screening, polarization forces, and self energies, which are related to solvation energies. Formulae, and sample calculations of forces and energies, are given for the special case of a spherical protein. Our analysis and model calculations point out that any consistent treatment of electrostatic interactions in proteins should account for the following. Solvent polarization is an important factor in the calculation of pairwise electrostatic interactions. Solvent polarization substantially affects both electrostatic energies and forces acting upon charges. No simple expression for the effective dielectric constant, Deff, can generally be valid, since Deff is a sensitive function of position. Solvent screening of pairwise interactions involving dipolar groups is less effective than the screening of charges. In fact for many interactions involving dipoles, solvent screening can be essentially ignored. The self energy of charges makes a large contribution to the total electrostatic energy of a protein. This must be compensated by specific interactions with other groups in the protein. Strategies for applying our analysis to proteins whose structures are known are discussed.

The effects of solvent screening in quantum mechanical calculations in protein systems

We report on an implementation of quantum mechanical density functional calculations carried out in a dielectric medium. The dielectric medium is introduced by integrating the solution of the Poisson‐Boltzmann equations into the density functional calculation. The calculations are carried out for a simple amide in vacuum, in the field of an ion, and in the ion field in several dielectric environments. The environment was constructed to include a low dielectric interior embedded in a high dielectric continuum of dielectric 80 (corresponding to aqueous solution). The energies and electron densities of formamide in the ion field were calculated at various configurations in this system, including at the low dielectric–high dielectric interface. The systems were designed to simulate situations which are similar to those that occur in proteins (i.e., the protein constitutes the low dielectric medium surrounded by aqueous solution). The system mimics situations in which charges in such proteins located in various regions interact with other parts of the protein and with ligands which mainly bind to the surface.