Hydrogen bonds and the desolvation cost

Part 4 is about the physics a scoring function is trying to approximate, and it starts with the interaction everyone thinks they understand. The hydrogen bond is worth much less than its reputation suggests, because both partners have to be stripped of water first — and that cost is the real subject of this module.

A donor is a hydrogen attached to an electronegative atom: N-H, O-H, and in special cases S-H. The hydrogen carries a partial positive charge.

An acceptor is an atom with an available lone pair. The cases students miss are worth listing, because they are common in drug molecules:

• Aromatic nitrogen of the pyridine type — a good acceptor. The pyrrole type is not, as module 4 established.
• Sulfur — a weak acceptor, and often ignored entirely by analysis software.
• Fluorine — despite three lone pairs, a very poor acceptor. Organic fluorine essentially does not accept hydrogen bonds, which surprises everyone the first time.
• Weakly acidic C-H — a real, if weak, donor when the carbon is next to something electron-withdrawing. The C-H of an imidazolium, or the C2-H of a triazole, genuinely donates.
• The pi face of an aromatic ring — can accept from an O-H or N-H pointing at it.

The carbonyl oxygen is the best acceptor in ordinary drug chemistry, and the ether oxygen is a much weaker one than its lone pairs suggest.

A hydrogen bond has a preferred geometry, and software applies criteria to decide whether to draw one.

• Distance. Heavy atom to heavy atom, roughly 2.6 to 3.5 Å. Shorter is a clash; longer is not a hydrogen bond.
• Angle at the hydrogen. The D-H⋯A angle wants to be near 180 degrees. Below about 120 the interaction is negligible.
• Angle at the acceptor. Weaker preference, but the hydrogen should approach roughly along a lone pair direction.

Different programmes use different cut-offs, which is why two pieces of software draw different dashed lines on the same complex. A dashed line is not a measurement; it is a claim, made under criteria someone chose.

There is a further complication in a crystal structure: at ordinary resolution the hydrogens are not there. So the angle at the hydrogen cannot be measured at all, only inferred, and which partner is the donor is a chemical judgement rather than an observation. Keep that in mind as you work through the complex below.

In the gas phase, a neutral hydrogen bond is worth roughly 3 to 6 kcal/mol. Charge-assisted ones — where one partner is ionised — can be 10 to 15. Low-barrier hydrogen bonds, where donor and acceptor have matched pKa values and the proton sits between them, can be higher still.

Those numbers are the reason people over-value hydrogen bonds. In water, they are almost entirely cancelled.

This is the concept the module exists for, and it is worth stating slowly.

Before the ligand and the protein meet, both polar groups are already hydrogen bonded — to water. The ligand's carbonyl has water on it. The protein's N-H has water on it. Water is an excellent hydrogen bonding partner: it is small, it is everywhere, and it can donate twice and accept twice.

To form a hydrogen bond with each other, both partners must first let go of their water. That costs roughly what the new bond will pay. So the net contribution is:

net = (bond formed) − (desolvating the donor) − (desolvating the acceptor)

And that difference is frequently close to zero. Sometimes it is negative — a hydrogen bond that costs more to make than it returns. The experimental estimates for the net contribution of a typical neutral hydrogen bond in a binding site cluster around 0 to 1.5 kcal/mol, an order of magnitude below the gas-phase figure.

The desolvation argument tells you where hydrogen bonds are actually worth designing for.

• Displace a badly-solvated water. If the water on the protein's group is in an awkward position and cannot make its full complement of hydrogen bonds, it is cheap to remove — so your ligand's bond is nearly free. Module 17 is entirely about this.
• Charge-assisted bonds. A salt bridge in a buried, low-dielectric pocket can be worth a great deal. Module 16 covers why, and why it can also be worth nothing.
• Networks and cooperativity. Hydrogen bonds in a chain reinforce each other: each one polarises the next. A network is worth more than the sum of its parts.
• Bidentate arrangements. Two hydrogen bonds from one rigid group — as a kinase hinge binder makes to the backbone — cost less entropy than two independent ones, because one binding event fixes both.

The mirror image of the argument, and it is where the penalty is unambiguous.

If your ligand buries a polar atom in the pocket and gives it no partner, you have paid the full desolvation cost and received nothing. Estimates put the penalty for a buried, unpaired, charged group at several kcal/mol — enough to kill an otherwise good compound outright.

This is one of the most reliable things to look for in a docked pose, and one of the things scoring functions handle least well. When you inspect a pose, look for polar atoms that are buried and unpaired. If you find one and the score is good, be suspicious of the score.