Best description of forces/ mechanisms that stabilize the interaction between a hydrophobic protein binding pocket and a hydrophobic ligand

Question

This is a more theoretical or definition question that is related to the terms "hydrophobic effect", "hydrophilic interaction", and "van der Waals' forces" (and others I may have missed).

In case I would like to describe a hydrophobic ligand that is binding to a protein binding pocket that has also hydrophobic residues (such as Leucine, valine) that stabilize (or favor) the binding of the ligand. What would be the best description to use to describe the binding?

from this question and from this PNAS paper

Although it seems the definition for these terms is also confusing, generally these terms have the meaning of:

1. hydrophobic effect (the low solubility of hydrophobic solutes in water)
2. hydrophobic interaction or force (the unusually strong attraction of hydrophobic surfaces and groups in water, it is specifically describing the repulsion of water)
3. van der Waal's force (attractions/repulsions between molecules or atoms, other than attractions like ionic attractions, and covalent attractions)

I also know that hydrophobic interaction is stronger than van der Waal's force (vdW). Given the "definition" of the hydrophobic interaction, I assume using this term to describe the interaction between the ligand and protein is not very appropriate because there is no necessary repulsion of the water molecules (that is usually used for forming the protein core). Please correct me if I am wrong.

Therefore vdW seems to be the answer. However, the problem is why the interaction between hydrophobic ligand and the hydrophobic protein surface is favorable? To be more specific, or in other words, whether there will be the same/ similar stability for a hydrophilic ligand to bind?

As also mentioned in this question, there is Deybe force or induced dipole if the ligand is polar or even charged. Should I assume the "stacking" of the London dispersal effect is much greater than Deybe force, although the London dispersal effect is weak if they are alone?

Answer 1

In discussing interactions in a biological context, often the most relevant measure of binding strength is the equilibrium binding constant (or more commonly dissociation constand $K_\mathrm{D}$), which is directly related to the Gibbs energy of binding at a given temperature.

On the other hand, when discussing intermolecular interactions, the focus often is on the enthalpy of binding, or the potential energy (or force) of the interaction at the molecular level.

The hydrophobic effect is described in the context of water as bulk solvent. If you split the Gibbs energy of binding of a hydrophobic ligand into enthalpy and entropy, the enthalpy contribution will be small (a hydrophobic ligand has slightly stronger interactions with water than with the hydrophobic binding pocket). The entropy contribution will drive the value of the binding constant. The hand-waiving explanation is that when a water molecule is at the interface between ligand and bulk water, it loses freedom of orientation because all hydrogen bonds are with the bulk water.

However, the problem is why the interaction between hydrophobic ligand and the hydrophobic protein surface is favorable? To be more specific, or in other words, whether there will be the same/ similar stability for a hydrophilic ligand to bind?

The hydrophobic ligand will have a lower dissociation constant ("tighter" binding) than the hydrophilic ligand. However, the enthalpy of binding will be larger (slightly) for the hydrophilic ligand if it fits snugly into the pocket. Trying to explain the binding constants (Gibbs energy) by just looking at the potential energy (enthalpy) will give an incorrect conclusion.

The distribution between entropic and enthalpic contributions might be different for different binding pockets. From the viewpoint of fitness, it does not matter whether binding is driven by one or the other, as long as the ligand binds. (Here is a paper that shows evidence for hydrophobic interactions driven by enthalpic contribution: https://pubs.acs.org/doi/pdf/10.1021/ct1003077).