Energy landscapes and the bioactive conformation

A molecule is not a structure. It is a distribution over structures, and which member of that distribution binds is usually not the one at the bottom of the well. This module is where the arithmetic of module 6 turns into something that shows up in a binding free energy.

Every combination of torsion angles is a point on a surface, and the surface has minima — resting places — separated by barriers. One minimum is lowest: the global minimum. The others are local minima, real structures that a molecule genuinely spends time in.

Two questions are separate and get confused constantly. How deep a well is decides how much of the population sits in it. How high the barrier around it is decides how fast the molecule gets out. A deep well behind a low barrier is populated and rapidly exchanging; a shallow well behind a high barrier is barely populated but, once entered, long-lived.

The population of a conformer falls exponentially with its energy above the minimum. The constant that sets the scale is RT, and at 310 K — body temperature — RT is about 0.62 kcal/mol.

That single number does a lot of work. Convert it into ratios and keep them:

• 1 kcal/mol up — about 5% of the population. Present, and doing chemistry.
• 2 kcal/mol up — under 1%. Minor, but not negligible if it is the only form that binds.
• 3 kcal/mol up — a few parts per thousand.
• 5 kcal/mol up — essentially absent.

Drag the temperature on the widget below and watch the distribution change. At low temperature everything collapses into the minimum; at high temperature it flattens out. Body temperature sits somewhere in between, which is exactly why a few kcal/mol is the interesting range.

Here is the point of the module. The conformation a ligand adopts when bound — the bioactive conformation — need not be, and often is not, the global minimum.

That should not be surprising. The free molecule in water is optimising its own internal energy and its interactions with water. The bound molecule is optimising its fit to a protein. Those are different problems with different answers.

Survey after survey of crystal structures finds bound ligands sitting somewhere above their computed global minimum. The typical figure is a few kcal/mol — and a few kcal/mol is exactly the range where the estimate is sensitive to which force field you used, whether you modelled solvent, and how thoroughly you searched. Treat any specific number with suspicion; treat the general finding as solid.

The energy a ligand pays to adopt its bound shape is real, and it comes out of the same budget as everything else. Write the binding free energy as a sum and it appears with a positive sign — opposing binding:

ΔG_bind = ΔG_interactions + ΔG_desolvation + ΔG_strain + ΔG_entropy

A ligand that binds in a conformation 3 kcal/mol above its minimum has spent, at a rough estimate, more than two log units of affinity before it makes a single contact — using the 1.36 kcal/mol per log unit figure that module 19 derives properly. That is why rigidifying a ligand into its bioactive shape is such an attractive move.

There is a second cost, and it is about freedom rather than energy.

A flexible molecule in solution is exploring many conformations. Bound, it is in one. That loss of freedom is a loss of entropy, and entropy loss opposes binding — it enters ΔG as −TΔS with ΔS negative, so the product is positive.

The rough working figure is 0.5 to 1 kcal/mol per rotatable bond frozen, though the literature disagrees and the true value depends on how restricted the bond was to begin with. What is not in dispute is the direction: a flexible ligand pays more to bind than a rigid one, for the same set of contacts.

This is the second reason the Veber criteria put a ceiling on rotatable bond count, and it is why fragment-based work prizes rigid starting points.

If strain and entropy both punish flexibility, the obvious move is to build a molecule that is already in its bioactive shape. That is pre-organisation, and it is one of the most reliable ideas in medicinal chemistry.

• Ring closure. Tie two parts of the molecule together so the torsion cannot move. The classic move, and usually the most effective.
• Intramolecular hydrogen bond. A donor and an acceptor positioned to reach each other form a pseudo-ring. This also masks both polar groups, which can improve permeability — the so-called chameleonic behaviour that lets some large molecules cross membranes they have no business crossing.
• Steric locking. An ortho substituent that raises a rotation barrier, exactly as in module 6's biphenyls.
• Macrocyclisation. Closing a large ring restricts many torsions at once. It is how several beyond-Rule-of-Five drugs manage to work at all.

The risk is equally clear: rigidify into the wrong conformation and you lose everything. A flexible ligand that is 10-fold weaker than it could be will still bind; a rigid ligand locked into the wrong shape will not bind at all. Pre-organisation is a bet on knowing the bioactive conformation, and it should be placed only when you do.

Three practical consequences, all of which you will meet again in Part 4.

• Generate enough conformers. If the bioactive conformation is not in your ensemble, no amount of scoring will find it. This is a failure mode that looks like a scoring problem and is not.
• Do not assume the global minimum is the relevant structure. It is a reasonable starting point and nothing more.
• Watch what your energy window excludes. A window of 5 kcal/mol sounds generous; the bioactive conformation of a flexible ligand can sit outside it.