Electrostatics and salt bridges

A salt bridge looks like the strongest thing in a binding site, and sometimes it is worth almost nothing. Whether it is depends on where it sits, and the reason is a number that changes by a factor of twenty between bulk water and a buried pocket.

The energy between two charges follows Coulomb's law: proportional to the product of the charges, inversely proportional to the distance, and inversely proportional to the dielectric constant of whatever sits between them.

The distance dependence is the first thing to notice. Electrostatics falls off as 1/r. Dispersion, from module 15, falls off as 1/r⁶. So electrostatics reaches much further: a charge is felt across a binding site, while a dispersion contact is felt only on touching. That is why long-range electrostatic steering can accelerate association even when it contributes little to the final affinity.

Now the number that makes this module difficult, and interesting.

The dielectric constant measures how well a medium screens charge. For bulk water it is about 80 — water molecules reorient around a charge and largely neutralise its effect at a distance. For the interior of a protein it is nearer 4, because the environment is packed, non-polar and cannot reorient.

The consequence is stark. The same pair of charges at the same distance is worth roughly twenty times more in a buried pocket than in bulk water. A salt bridge on a solvent-exposed surface is worth very little; the same salt bridge buried is worth a great deal.

This is genuinely hard for a scoring function. Most use a distance-dependent dielectric or a single fudged constant, because computing the real one means solving a boundary-value problem over the molecular surface. It is one of the reasons docking scores handle charged ligands badly.

To compute electrostatics you need a charge on every atom. Atoms do not actually have charges — electron density is continuous — so partial atomic charges are a fitted convenience.

Different charge models give different answers for the same atom. Some fit to reproduce the electrostatic potential around the molecule; some partition the electron density between atoms; some use empirical rules. Values for a carbonyl oxygen can differ by several tenths of an electron between models, and the electrostatic energy is proportional to the product of two of them.

The practical point: electrostatic terms in a force field are only meaningful with the charge model they were parameterised against. Mixing charges from one source into a force field fitted with another is a common and quiet error.

A salt bridge is an ion pair — usually a carboxylate against a guanidinium or an ammonium — close enough to interact directly, conventionally within about 4 Å. On the protein side these are aspartate and glutamate for the negative, arginine and lysine for the positive, and histidine when it is protonated.

Two complexes make the point, and they are worth comparing directly.

Notice that the widget will not tell you whether the ligand side is charged. It cannot: that depends on a pKa, which is not in the structure file. Deciding it is your job, and module 10 is where you learnt how.

Charges are not the only electrostatics. A carbonyl has a permanent dipole; so does an amide, a nitrile, a sulfonamide. These interact with each other and with charges, more weakly than ion pairs but at similar range.

The helix dipole is a nice example: the aligned backbone amides of an alpha helix sum to a substantial dipole, and the positive end at the N-terminus is a recognised binding site for phosphate and carboxylate groups.

The counterweight, and it is large.

A charged group in water is surrounded by an ordered, tightly-held solvation shell. Burying it means removing that shell, and the cost is measured in tens of kcal/mol for a bare ion. It is partly compensated by whatever the group meets in the pocket, but the balance is delicate.

Three consequences follow, and they are the practical heart of this module:

• A buried, unpaired charge is close to fatal. You have paid a huge desolvation cost for nothing. This is a stronger version of module 14's buried unpaired polar atom.
• A buried, paired charge can be excellent — but only if the pairing is good. The geometry has to be right, and there is little tolerance.
• This is why charged groups are risky in ligand design. They give large numbers in a scoring function, which computes the favourable term more confidently than the desolvation term, so docking systematically over-rewards charged ligands. If your top-scoring virtual screening hits are all polycationic, that is a known artefact and not a discovery.