Overview
This section is devoted to present the general ideas of my vision for a more effective drug discovery methodology based on the use of Ligand Efficiency Indices (LEIs) as robust variables to guide drug discovery. I do believe that using a combination of LEIs as optimization variables can direct the drug discovery process in a more objective way. Currently, as illustrated in several of the technical publications presented in this website and through the literature, I proposed the use of at least two LEIs: one related to efficiency per size (or number of atoms) and another related to the binding affinity of the compound on a per ‘polarity’ basis. A table summarizing the specific definitions of LEIs that I am currently exploring is presented below (Table I).
| Table I | |||
| Names, Definitions, and Idealized Reference Values for various definitions of Ligand Efficiencies | |||
| Name | Definition | Example Valuea | Equation |
| LEb | ΔG/NHEA(non-hydrogen atoms) | -0.50b | [1] |
| BEI | p(Ki), p(Kd), or p(IC50)/MW(kiloDa) | 27 | [2] |
| SEI | p(Ki), p(Kd), or p(IC50)/(PSA/100 Å2) | 18 | [3] |
| NSEI | NSEI = -log10 Ki/(NPOL) = pKi/NPOL(N,O) | 1.5 | [4] |
| NBEI | NBEI= -log10 Ki/(NHEA)= pKi/(NHEA) | 0.36 | [5] |
| nBEI | nBEI= -log10[(Ki/NHEA)]; | 10.25 | [6] |
| mBEI | mBEI=-log10[(Ki/MW)] | 11.5 | [7] |
| aReference values and definitions of BEI,SEI adapted from (Abad-Zapatero & Metz, DDT, 2005). Ki or IC50 = 1.0 nM; Molecular Weight = 333 Daltons (or 0.333 KiloDaltons) This value of MW is near the mean value of MW for a large sample of marketed oral drugs. Van der Waals or any other estimate of the Polar Surface Area PSA = 50 Å2 bΔG = -12.4 kcal/mol, ΔG= -RTlnKi, assuming Ki=1.0 nM, T=300° K; [R=1.98 cal/deg.mole (or 8.314 joules/deg.mole)]; NHEA(non-hydrogen atoms) = 25; corresponding to a mean MW/atom of 13.3 Daltons. Hopkins et al (DDT, 2004). NOTE: By definition, for any given compound the ratio of BEI/SEI is equal to 10(PSA/MW). aExample values for the atom-related definitions of LEIs are calculated for each index using the following idealized values (units have been omitted in the table): Ki or IC50 = 1.0 nM; p(Ki)= –log Ki= 9.00; MW=0.333 kDa; NHEA= Number of heavy atoms (non-Hydrogen in the compound)=25; NPOL=Number of polar atoms (N,O) = 6; NOTE: NBEI/NSEI = NPOL(N,O)/NHEA(non-H)= 0.36/1.5 = 6/25 = 0.24; This Table adapted from various publications, in particular, the latest (2010) Drug Discovery Today, Abad-Zapatero et al. Look for further details on these publications. This Table is presented here just for convenience. |
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In addition to providing an efficiency yardstick for the two critical variables of drug discovery (size and polarity), the combination of two complementary LEIs (one of size and one of polarity), these variables permit a representation of Chemico-Biological Space (CBS) in a series of convenient Cartesian planes that I have referred to as ‘AtlasCBS’. A representative example of this concept is shown below (Fig. 1, adapted from Abad-Zapatero et al. DDT, 2010). The image presents a representation in the NSEI,nBEI (x,y; see equations [4] and [6] above, Table I) efficiency plane of the content of the database PDBBind (2007 release). As has been discussed in published papers, the target:ligand pairs (one point in the Cartesian diagram) line up along lines of slope NPOL (number of polar atoms: N, O). The slope of the lines increases counterclockwise with the increase polarity and the radial distance of the points relates to the affinity of the ligand (Ki in this case) towards the target. This type of representation permits a decoupling of the ‘chemical’ (angular) and ‘biological’ (radial) variables and can be considered as a graphical representation of the content of the corresponding database
Within this context, the concept of ‘efficiency Drug Discovery’ (eDD) refers to the idea of using the values of the various LEIs to optimize the drug discovery process. This idea was suggested in a 2007 Expert Opinion Publication below where a decision box was introduced in the decision process guiding drug discovery.
The idea is to select for further optimization during the pre-clinical stage compounds with the largest values of SEI,BEI (or NSEI, nBEI or equivalent). This implies compounds that progressively migrate towards to upper right of the Efficiency Planes, where both variables are optimized. The schematics of this process are illustrated in Fig. 2 (adapted from Abad-Zapatero, 2007).
Of course, many issues are still pending in order to put this schematic diagram into a working ‘algorithm’ to expedite drug discovery. However, I do believe that the combination of the efficiency variables (LEIs) as ‘figures of merit’, with improved algorithms and methods to estimate the affinity constants (Kis or related) and solid predictors of PK can put drug discovery in a more sound and objective path to deliver improved pharmacological entities to patients in a shorter time span.
Let this be our vision for 2011 and beyond. The Atlas CBS tab presents some of the tools that we are developing to realize this vision.
The article in Future Medicinal Chemistry discusses the inclusion of the AtlasCBS framework and the Ligand Efficiency Variables (LEIs) within the context of ‘alternative variables in drug discovery’. It is my belief that the best way proceed is within the framework of Multiple Parameter Optimization (MPO). The article is entitled ‘Alternative variables in drug discovery: promises and challenges’, my co-authors are Edmund Champness and Matthew Segall of Optibrium, Ltd.
This development is another step towards realizing the vision expressed above.