Ligand efficiency metrics

Potency alone will always favour the biggest, greasiest compound in the list. Efficiency metrics ask a different question: how much affinity did you get {{o:per unit of molecule}} — and they exist because the answer to that question predicts what happens next far better than potency does.

LE is binding energy per heavy atom:

LE = −ΔG° / (number of heavy atoms)

It is quoted in kcal/mol per heavy atom, and the rule of thumb is that a useful fragment or lead sits near 0.3 or better. A compound with LE 0.5 is doing a great deal with very little; one with LE 0.15 is large and only moderately potent.

Heavy atom count is the denominator, not molecular weight, for the reason module 12 gave: it measures how much molecule there is without rewarding you for using light atoms.

The metric was devised in the fragment context, and that is where it matters most. A fragment binding at 1 mM sounds hopeless next to a lead binding at 100 nM — but if the fragment has 12 heavy atoms and the lead has 40, the fragment is the more efficient starting point, and growing it is likely to get further than optimising the lead.

LE has a mathematical problem that is worth understanding rather than ignoring. Because ΔG is a logarithmic quantity divided by a linear one, LE is not size-independent: it tends to fall as molecules get larger even when nothing has gone wrong, simply because each additional atom cannot keep contributing at the same rate. Comparing LE between molecules of very different sizes therefore has a built-in bias.

That does not make it useless. It makes it a metric for comparing similarly-sized compounds, and for watching a single series over time — which is how it is mostly used in practice.

LLE is the most useful member of the family and by far the easiest to compute:

LLE = pIC50 (or pK_i, or pK_d) − cLogP

That is all. Potency minus lipophilicity. It asks: how much of your potency did you get for free by making the molecule greasier, and how much did you earn?

The target is LLE ≥ 5, and marketed oral drugs cluster around 5 to 7. A compound with a 10 nM IC50 and cLogP 6 has LLE 2, and is much less attractive than it looks; a compound with a 1 µM IC50 and cLogP 1 has LLE 5, and is a far better starting point.

LLE is the direct answer to the lipophilicity trap of module 9. Adding a greasy group raises potency and raises logP by similar amounts, so LLE stays flat — the metric simply does not reward the move. Only a change that improves potency without adding lipophilicity moves LLE, and those changes are the ones that survive.

• LELP = cLogP / LE. Combines both concerns into one number. Healthy values run roughly −10 to 10; large positive values mean the potency was bought with lipophilicity.
• BEI, binding efficiency index = pIC50 / (MW in kDa). LE's cousin, using molecular weight instead of heavy atom count. Its numbers are much larger — around 20 to 30 for a good compound — and are not comparable to LE.
• SEI, surface efficiency index = pIC50 / (TPSA / 100). Potency per unit of polar surface. Useful alongside BEI: plotting the two against each other separates compounds that are efficient because they are small from those efficient because they are polar.

The family is larger than this and grows steadily. In practice most projects watch LE and LLE and treat the rest as occasionally interesting.

Plot potency against heavy atom count, with lines of constant LE drawn on. Every compound in a programme becomes a point, and the shape of the cloud tells you what the chemists have been doing.

• Moving up and to the right along a line of constant LE — getting more potent by getting bigger, at the same efficiency. Common, and not necessarily wrong, but it has a ceiling: keep going and you leave developable space.
• Moving up at constant size — genuinely better interactions. This is what good optimisation looks like.
• Moving right without moving up — adding atoms that do nothing. Wasted effort, and it should prompt a look at whether the added group has anywhere to go.
• A tight cluster — the series has plateaued. Time for a new scaffold rather than another analogue.

The practical question these metrics were invented to answer: you have a potent, large, lipophilic hit and a weaker, smaller, cleaner one. Which do you take?

Usually the smaller, cleaner one — because optimisation will add weight and lipophilicity, and you want to start with room to spend. The potent, greasy compound may already be at the edge of developable space, so every improvement makes it worse in some other dimension.

Three caveats, because this is a heuristic and not a law:

• Timelines matter. If you need a tool compound next month, take the potent one.
• Efficiency assumes room to grow. If the small compound already fills its pocket, there is nowhere to add anything.
• cLogP is a prediction. LLE inherits every uncertainty in module 9's calculated logP, so a difference of half a unit in LLE is not a difference.