Mathematically, ligand efficiency (LE) can be defined as the ratio of Gibbs free energy (ΔG) to the number of non-hydrogen atoms of the compound:
- LE = (ΔG)/N
- LE = 1.4(-logIC50)/N
Some suggest that better metrics for ligand efficiency are percentage/potency efficiency index (PEI), binding efficiency index (BEI) and surface-binding efficiency index (SEI) because they are easier to calculate and take into account the differences between elements in different rows of the periodic table. It is important to note that PEI is a relative measure for comparing compounds tested in the same conditions (e.g. a single-point assay) and are not comparable at different inhibitor concentrations. Also for BEI and SEI, similar measurements must be used (e.g. always using pKi).
- PEI = (% inhibition at a given compound concentration as fraction: 0 – 1.0) / (molecular weight, kDa)
- BEI = (pKi, pKd, or pIC50) / (molecular weight, kDa)
- SEI = (pKi, pKd, or pIC50) / (PSA/100 Å)
where pKi, pKd and pIC50 is defined as -log(Ki), -log(Kd), or -log(IC 50), respectively. Ki and IC50 in mol/L.
The authors suggest plotting compounds SEI and BEI on a plane and optimizing compounds towards the diagonal and so optimizing both SEI and BEI which incorporate potency, molecular weight and PSA.
There are other metrics which can be useful during hit to lead optimization: group efficiency (GE), lipophilic efficiency/lipophilic ligand efficiency (LipE/LLE), ligand lipophilicity index (LLEAT) ligand efficiency dependent lipophilicity (LELP), fit quality scaled ligand efficiency (LE_scale), size independent ligand efficiency (SILE).
- I. D. Kuntz, K. Chen, K. A. Sharp, and P. A. Kollman (1999). "The maximal affinity of ligands". Proc Natl Acad Sci U S A. 96 (18): 9997–10002. Bibcode:1999PNAS...96.9997K. doi:10.1073/pnas.96.18.9997. PMC 17830. PMID 10468550.
- Abadzapatero, C; Metz, J (2005). "Ligand efficiency indices as guideposts for drug discovery". Drug Discovery Today 10 (7): 464–469. doi:10.1016/S1359-6446(05)03386-6. PMID 15809192.
- Hopkins, Andrew L.; Groom, Colin R.; Alex, Alexander (2004). "Ligand efficiency: A useful metric for lead selection". Drug Discovery Today 9 (10): 430–431. doi:10.1016/S1359-6446(04)03069-7. PMID 15109945.
- Shultz, Michael D. (2013). "Setting expectations in molecular optimizations: strengths and limitations of commonly used composite parameters". Bioorganic & Medicinal Chemistry Letters 23 (21): 5980–91. doi:10.1016/j.bmcl.2013.08.029. PMID 24018190.