Section 22.3.2.3. The concepts of screening, reaction potentials, solvation, dielectric, polarity and polarizability

Application of a classical electrostatic view to macromolecular electrostatics involves a number of useful concepts that describe the physical behaviour. It should first be recognized that the potential at a particular charged atom i includes three physically distinct contributions. The first is the direct or Coulombic potential of j at i. The second is the potential at i generated by the polarization (of a molecule, water and ion atmosphere) induced by j. This is often referred to as the screening potential, since it opposes the direct Coulombic potential. The third arises from the polarization induced by i itself. This is often referred to as the reaction or self-potential, or if solvent is involved, as the solvation potential.

When using models that apply the concept of a dielectric constant (a measure of polarizability) to a macromolecule, it is important to distinguish between polarity and polarizability. Briefly, polarity may be thought of as describing the density of charged and dipolar groups in a particular region. Polarizability, by contrast, refers to the potential for reorganizing charges, orienting dipoles and inducing dipoles. Thus polarizability depends both on the polarity and the freedom of dipoles to reorganize in response to an applied electric field. When a protein is folding or undergoing a large conformational rearrangement, the peptide groups may be quite free to reorient. In the folded protein, these may become spatially organized so as to stabilize another charge or dipole, creating a region with high polarity, but with low polarizability, since there is much less ability to reorient the dipolar groups in response to a new charge or dipole without significant disruption of the structure. Thus, while there is still some discussion about the value and applicability of a protein dielectric constant, it is generally agreed that the interior of a macromolecule is a less polarizable environment compared to solvent. This difference in polarizability has a significant effect on the potential distribution.

Formally charged groups on proteins, particularly the longer side chains on the surface of proteins, Arg, Lys, and to a lesser extent Glu and Asp, have the ability to alter their conformation in response to electrostatic fields. In addition, information about fluctuations about their mean position may need to be included in calculating average properties. Three approaches to modelling protein formal charge movements can be taken. The first is to treat the motions within the dielectric response. In this approach, the protein may be viewed as having a dielectric higher than 2.5–4 in the regions of these charged groups, particularly at the surface, where the concentration and mobility of these groups may give an effective dielectric of 20 or more (Antosiewicz et al., 1994; Simonson & Perahia, 1995; Smith et al., 1993). A second approach is to model the effect of charge motions on the electrostatic quantity of interest explicitly, e.g. with MD simulations (Langsetmo et al., 1991; Wendoloski & Matthew, 1989). This involves generating an ensemble of structures with different atomic charge distributions. The third approach is based on the fact that one is often interested in a specific biological process in which one can evaluate the structure of the protein in states A and B (experimentally or by modelling), and any change in average charge positions is incorporated at the level of different average explicit charge distribution inputs for the calculation, modelling only the electronic, dipolar and salt contributions as the response.

The term `effective' dielectric constant is sometimes used in the literature to describe the strength of interaction between two charges, and . This is defined as the ratio of the observed or calculated interaction strength, U, to that expected between the same two charges in a vacuum: where is the distance between the charges. If the system were completely homogeneous in terms of its electrostatic response and involved no charge rearrangement then would describe the dielectric constant of the medium containing the charges. This is generally never the case: the strength of interaction in a protein system is determined by the net contribution from protein, solvent and ions, so does not give information about the dielectric property of any particular region of space. In fact, in the same system different charge–charge interactions will generally yield different values of . Thus is really no more than its definition – a measure of the strength of interaction – and it cannot be used directly to answer questions about the protein dielectric constant, for example. Rather, it is one of the quantities that one aims to extract from theoretical models to compare with an experiment.