Attraction between Charged Groups (Salt Linkages).

Fixed positive and negative charges attract each other strongly. Consider a carboxylate ion in contact with–NH3 + or with an ion of calcium:

From the van der Waals radii of Table 2-1 and the ionic crystal radius of Ca2+ of 0.10 nm, we can estimate an approximate distance between the centers of positive and negative charge of 0.25 nm in both cases. It is of interest to apply Coulomb’s law to compute the force F between two charged particles which are almost in contact. Let us choose a distance of 0.40 nm.

In this equation r is the distance in meters, q and q’ are the charges in coulombs (one electronic charge = 1.6021 x 10–19 coulombs), ε is the dielectric constant, and F is the force in newtons (N). The force per mole is NF where N is Avogadro’s number.
An uncertainty in this kind of calculation is in the dielectric constant ε, which is 1.0 for a vacuum, about 2 for hydrocarbons, and 78.5 for water at 25°C. If ε is taken as 2, the force for r = 0.40 nm is 4.3 x 1014 N/mol. The force would be twice as great for the Ca2+ – COO– case. To move two single charges further apart by just 0.01 nm would require 4.3 kJ/mol, a substantial amount of energy. However, if the dielectric constant were that of water, this would be reduced almost 40-fold and the electrostatic force would not be highly significant in binding. It is extremely difficult to assign a dielectric constant for use in the interior of proteins. For charges spaced far apart within proteins the effective dielectric constant is usually as high as 30–60. For closely spaced charges in hydrophobic niches it may be as low as 2–4.
A calculation that is often made is the work required to remove completely two charges from a given distance apart (e.g., 0.40 nm) to an infinite distance.

If ε = 2, this amounts to 174 kJ/mol for single charges at a distance of 0.40 nm; 69 kJ/mol at 1 nm; and only 6.9 kJ/mol at 10 nm, the distance across a cell membrane. We see that very large forces exist between closely spaced charges.
Electrostatic forces are of great significance in interactions between molecules and in the induction of changes in conformations of molecules. For example, attraction between –COO– and –NH3 + groups occurs in interactions between proteins. Calcium ions often interact with carboxylate groups, the doubly charged Ca2+ bridging between two carboxylate or other polar groups. This occurs in carbohydrates such as agarose, converting solutions of these molecules into rigid gels. Individual macromolecules as well as cell surfaces usually carry a net negative charge at neutral pH. This causes the surfaces to repel each other. However, at a certain distance of separation the van der Waals attractive forces will balance the electrostatic repulsion. Protruding hydrophobic groups may then interact and may“tether” bacteria or other particles at a fixed distance, often ~5 nm, from a cell surface.