ligand efficiency
{{Short description|Measure of a ligand's binding energy per atom}}
Ligand efficiency is a measurement of the binding energy per atom of a ligand to its binding partner, such as a receptor or enzyme.{{cite journal | vauthors = Kuntz ID, Chen K, Sharp KA, Kollman PA | title = The maximal affinity of ligands | journal = Proceedings of the National Academy of Sciences of the United States of America | volume = 96 | issue = 18 | pages = 9997–10002 | date = August 1999 | pmid = 10468550 | pmc = 17830 | doi = 10.1073/pnas.96.18.9997 | doi-access = free | bibcode = 1999PNAS...96.9997K }}
Ligand efficiency is used in drug discovery research programs to assist in narrowing focus to lead compounds with optimal combinations of physicochemical properties and pharmacological properties.{{cite journal | vauthors = Abad-Zapatero C, Metz JT | title = Ligand efficiency indices as guideposts for drug discovery | journal = Drug Discovery Today | volume = 10 | issue = 7 | pages = 464–469 | date = April 2005 | pmid = 15809192 | doi = 10.1016/S1359-6446(05)03386-6 }}
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
where ΔG = −RTlnKi and N is the number of non-hydrogen atoms.{{cite journal | vauthors = Hopkins AL, Groom CR, Alex A | title = Ligand efficiency: a useful metric for lead selection | journal = Drug Discovery Today | volume = 9 | issue = 10 | pages = 430–431 | date = May 2004 | pmid = 15109945 | doi = 10.1016/S1359-6446(04)03069-7 }} It can be transformed to the equation:
:LE = 1.4(−log IC50)/N
Other metrics
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 (LEscale), size independent ligand efficiency (SILE).{{cite journal | vauthors = Shultz MD | title = Setting expectations in molecular optimizations: Strengths and limitations of commonly used composite parameters | journal = Bioorganic & Medicinal Chemistry Letters | volume = 23 | issue = 21 | pages = 5980–5991 | date = November 2013 | pmid = 24018190 | doi = 10.1016/j.bmcl.2013.08.029 }}
Group efficiency (GE) is a metric used to estimate the binding efficiency of groups added to a ligand.{{Cite journal |last=Verdonk |first=Marcel L. |last2=Rees |first2=David C. |date=2008-08-18 |title=Group Efficiency: A Guideline for Hits‐to‐Leads Chemistry |url=https://chemistry-europe.onlinelibrary.wiley.com/doi/10.1002/cmdc.200800132 |journal=ChemMedChem |language=en |volume=3 |issue=8 |pages=1179–1180 |doi=10.1002/cmdc.200800132 |issn=1860-7179}} Unlike ligand efficiency which evaluates the efficiency of the entire molecule, group efficiency measures the relative change of the Gibbs free energy (ΔΔG), caused by addition or modification of groups, normalized by the change in the number heavy atoms in those groups (ΔN), using the equation:
:GE = -(ΔΔG)/ΔN