Principles of Protein Structural Organization - H. Schultz 1982

Interactions Determining Protein Structure
Electrostatic Interactions

Most covalently bonded atoms carry partial charges. Because covalent bonds between Different types of atoms lead to an asymmetric distribution of valence electrons, the majority of atoms in a molecule bear partial charges. The partial charges of Certain amino acid residues are listed in Table 3.3. Since the net charge of a neutral molecule is zero, it can be approximated as a set of dipoles or multipoles. These multipoles interact with one another according to Coulomb's law, as shown in Table 3.4. The interaction energy depends on the dielectric constant k of the surrounding medium. Here we use a value of ε = 4, which is the macroscopic Dielectric Constant of the amide polymer [50]. The dielectric constant for microscopic objects is difficult to calculate, and The values of ε used in calculations can range from 1 to 5 [51].

Examples of electrostatic interactions are given in Table 3.1. An internal (ε = 4) salt bridge between Lys and Asp has a binding energy of approximately 5 kcal/mol. Two carbonyl groups at contact distance R_m exhibit an electrostatic repulsion energy of 0.3 kcal/mol.

Class="center">Table 3.3 Partial charges on the atoms of the polypeptide backbone and three side chains ^a

According to Momany et al. [52], who determined the partial charges of atoms in natural amino acid residues using CNDO/2 calculations (Complete Neglect of Differential Overlap), partial charges have also been derived from ab initio molecular orbital calculations for small molecules [53], as well as from the analysis of X-Ray Diffraction data [54].

Table 3.4 Electrostatic interactions

Electrostatic interactions in Proteins are local in nature. Although calculating electrostatic interactions is essentially a direct application of Coulomb's law to all partial charges, it is very time-consuming due to the large number of atoms in a protein and the long-range nature of electrostatic forces. However, the calculation can be simplified. Since proteins contain no monopoles—that is, free charges (salt bridges are ion pairs or dipoles)—all partial charges form dipoles or multipoles. The interaction between them decreases in proportion to at least the third power of the distance (Table 3.4). Therefore, the effective range of electrostatic interactions is quite small, and energy calculations can be limited to interactions between nearest neighbors.

One might argue that weak long-range interactions could accumulate if dipoles are uniformly oriented, such as the Hydrogen bond dipoles in α-helices and β-sheets. However, in β-sheets, adjacent dipoles are antiparallel, and their fields cancel each other out over long distances; in α-helices, the dipoles are arranged linearly and also compensate for one another, except for the charges at both ends. For this very reason, antiparallel helices are more favorable than parallel ones. Nevertheless, even in this case, THE CONTRIBUTION OF electrostatic interaction is small compared to the total interaction energy between such α-helices.