In Silico Physicochemical Parameter Predictions - Molecular

Article pubs.acs.org/molecularpharmaceutics

In Silico Physicochemical Parameter Predictions Mark C. Wenlock* and Patrick Barton AstraZeneca R&D Alderley Park, DMPK, Mereside, Macclesfield, Cheshire, SK10 4TF, United Kingdom ABSTRACT: Drug discovery is a complex process with the aim of discovering efficacious molecules where their potency and selectivity are balanced against ADMET properties to set the appropriate dose and dosing interval. The link between physicochemical properties and molecular structure are well established. The subsequent connections between physicochemical properties and a drug’s biological behavior provide an indirect link back to structure, facilitating the prediction of a biological property as a consequence of a particular molecular manipulation. Due to this understanding, during early drug discovery in vitro physicochemical property assays are commonly performed to eliminate compounds with properties commensurate with high attrition risks. However, the goal is to accurately predict physicochemical properties to prevent the synthesis of high risk compounds and hence minimize wasted drug discovery efforts. This paper will review the relevance to ADMET behaviors of key physicochemical properties, such as ionization, aqueous solubility, hydrogen bonding strength and hydrophobicity, and the in silico methodology for predicting them. KEYWORDS: in silico predictions, pKa, aqueous solubility, hydrogen bonding, hydrophobicity

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INTRODUCTION

Principally drugs are designed with in vivo efficacy in mind, driven by free concentrations of the drug available to the protein target receptor and guided by in vitro potency assays. Bimolecular drug receptor interactions can be influenced by the manipulation of physicochemical properties and favorable contributions to the Gibbs free binding energy can include charged and uncharged hydrogen bond interactions and hydrophobic (entropy driven) interactions (along with salt bridges, charge transfer interactions, and van der Waals forces). Once synthesized, the physicochemical properties of a drug molecule are fixed (with the exception of dissolution that can be manipulated by physical form variations), and in minimizing attrition risks there is invariably a balancing act between features that are good for efficacy and those that give rise to preferential ADMET behavior. Difficulty arises when the properties good for protein affinity conflict with those for ADMET, and the druggability of a particular target needs to be considered when identifying complementary ligands. Pharmacokinetic parameters tend to be influenced by a combination of different physicochemical properties. Oral absorption of a drug is influenced by (and in conjunction with physiological and formulation factors) its molecular size, shape, hydrophobicity, hydrogen bonding potential, ionization (or charge), amphilicity, solubility, diffusivity, and hydrolytic

The aim of drug discovery is to find efficacious molecules where potency and selectivity are balanced against absorption, distribution, metabolism, elimination, and toxicity (ADMET) to set the appropriate dose and dosing interval. From the position where the biological relevance of the target has been established the key question that needs answering is: what is the correct chemical structure for an efficacious and safe candidate drug for the given biological target? Due to the complexity of this multiparameter problem our ability to directly relate a compound’s three-dimensional molecular structure to its human pharmacokinetic profile, in vivo efficacy, or toxicity is extremely limited; consequently extensive experimentation in in vitro and in vivo animal models are necessary to develop this understanding. However, there is increasing knowledge of the relationship between a compound’s bulk physiochemical properties and its biological behavior, in particular its pharmacokinetic properties. The effect of changes to chemical structures to manipulate physicochemical properties is reasonably well understood. An indirect situation exists where physicochemical properties can facilitate the interpretation of an ADMET effect due to a molecular structure cause. In the early stages of drug discovery, an appreciation of a compound’s physicochemical properties such as ionization (pKa), aqueous solubility, hydrogen bonding potential, and hydrophobicity can help the interpretation of its ADMET behavior. Furthermore, the ability to use in silico techniques to predict a virtual compound’s physicochemical properties and hence ADMET behavior can help guide drug discovery efforts into potentially more fruitful areas of chemical space. © XXXX American Chemical Society

Special Issue: Predictive DMPK: In Silico ADME Predictions in Drug Discovery Received: September 21, 2012 Revised: December 27, 2012 Accepted: January 10, 2013

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dx.doi.org/10.1021/mp300537k | Mol. Pharmaceutics XXXX, XXX, XXX−XXX

Molecular Pharmaceutics

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stability.1−4 The pH-partition hypothesis states that nonionized form of an ionizable molecule can permeate across the gastrointestinal tract and the extent of ionization at a particular pH can be estimated from the Henderson−Hasselbalch equation.5,6 This concept oversimplifies a multifaceted process where a drug’s dissolution, solubility, and permeation characteristics are paramount as summarized in the Biopharmaceutics Classification System (BCS) or the Developability Classification System,7,8 hydrophobicity, molecular size, polarity, hydrogen bond counts, and charge being the fundamental parameters that influence solubility and permeation.9−16 The different hepatic metabolizing cytochrome P450 isoenzymes are selective for different types of molecules differentiated by hydrophobicity, charge, and shape.17−20 The extent of biliary clearance is influenced by molecular weight, hydrophobicity, and charge, the latter two implicated in renal clearance along with polarity.21−25 The distribution of unmetabolized drug throughout the body is governed to an extent by the molecule’s charge and hydrophobicity.23,26 The extent of binding to albumin is particular strong for acidic compounds compared to other proteolytic classes for a similar hydrophobicity.27,28 From the perspective of toxicity, a drug’s physicochemical properties can be related to adverse drug reactions due to secondary pharmacology that result from modulating targets other than the primary target. A drug’s hydrophobicity, size, polarity, amphilicity, charge, and electrophilicity are parameters that have been related to cardiovascular toxicity, hepatotoxicty, phospholipidosis, genotoxicity, and phototoxicity effects.29−33 In designing drugs, for druggable protein targets, an appreciation of how the physicochemical properties of a molecule affect its pharmacokinetics and toxicity (as well as its efficacy) is important for minimizing attrition risks. Furthermore an understanding of the structural features that influence such physicochemical properties is fundamental and facilitates in silico predictions of virtual compounds.

(where an approximation is made whereby the activities are replaced with concentrations). ⎛ [H+]aq [Base]aq ⎞ ⎟⎟ pK a = −log10 K a ≈ −log10⎜⎜ ⎝ [Acid]aq ⎠

(1)

In eq 1, for an monoprotic acidic compound the “acid” entity is “HA”, and the “base” (i.e., conjugate base) entity is “A−”, conversely for a monoprotic basic compound the “acid” (i.e., conjugate acid) entity is “BH+” and the “base” entity is “B”. The pKa of a basic compound reflects the ionization constant of the conjugate acid entity. Similar to other equilibrium constants, pKa will vary significantly depending on the temperature of measurement and the ionic strength of the aqueous media; consequently literature pKa data is quoted on two distinct scales: infinite dilution (or “thermodynamic”) scale and the constant ionic strength (or “practical” or “mixed”) scale. These different scales are a consequence of the different experimental techniques used to measure a compound’s pKa; techniques in early drug discovery tend to include potentiometric, spectrophotometric, capillary electrophoresis, and 1H NMR (for ionizations on proteins).37−39 The thermodynamic ionization constant Ktherm for a weak acid HA is defined as a K atherm =

γ − {H+}[A−] {H+}{A−} = A γHA [HA] {HA}

(2)

where γ are activity coefficients. The “practical” or “mixed” ionization constant Kmixed is defined as a K amixed =

{H+}[A−] [HA]

(3)

Equation 2 can be simplified by assuming that γHA equals 1 pK atherm = pK amixed − log γA−

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(4)

Equation 4 highlights the difference between the two ionization scales, and the activity of the anion is calculated using the Debye−Huckel theory

DISCUSSION pKa. pKa is of significance in controlling the ADMET characteristics of a drug and can influence its bulk property effects and specific binding to a protein target receptor.34,35 In understanding the ionization of compounds within an aqueous medium it is important to appreciate the unique hydrogen bonding properties of water that give rise to many anomalous behaviors (e.g., hydrophobic effect, etc.). Chaplin offered the following description: “The hydrogen-bonding properties of water allow it to execute an intricate ballet exchanging partners while retaining complex order”.36 If water’s hydrogen bonding strength was slightly different, then its amphiprotic nature (i.e., its ability to act as both an acid and a base) would change, and it is this autoprotolysis equilibrium of a proton transfer involving a single substance that allows proteins to function and compounds to behave as acids or bases, and so forth. Kw is the autoprotolysis constant for water and at 25 °C, Kw ≈ 1 × 10−14 (pKw = 14) indicative that only a few water molecules are ionized. An acid is a species having the tendency to lose a proton while a base is a species having the tendency to add a proton. Acids and bases only manifest their properties by reacting with bases and acids, respectively. In aqueous media, equilibrium is established whereby an acid compound (HA) reacts with water acting as a base, or a basic compound (B) reacts with water acting as an acid. The ionization constant (Ka) for such an equilibrium is quoted as a pKa and defined by eq 1

−log γA− =

0.5085z 2I1/2 1 + 0.3281aI1/2

(5)

where I is the ionic strength, z is the charge of the ion, and a is a size parameter assumed to be 5 Å; for a A− anion (where I = 0.1) the difference is ∼0.1, for a A2− anion the difference is ∼0.4, and for a A3− anion the difference is ∼0.9. Although the Debye−Huckel activity coefficient calculation is an approximation, it is prudent to be aware of these differences when building in silico models for pKa that are trained on data from different sources especially for complex charged species. Qualitatively, as pKa increases, it implies the acid HA(aq) or the conjugate acid of the base BH+(aq) is more stable than the anion A−(aq) or the base B(aq); the reverse is true when pKa decreases. The molecular effects that influence pKas include inductive, electrostatic, and π-electron-delocalization (“mesomeric”) effects (in addition hydrogen bonding, conformational, and steric factors can also contribute).40 Mesomeric effects can result in very large changes in pKa due to the stabilization of charge via delocalization around π electron systems. At 25 °C at 1 atm, the change in Gibbs free energy, for a 1 unit change in pKa is ∼5.7 kJ·mol−1. The result of this is to make acids and bases appreciably stronger or weaker than seen in saturated systems. Cyclohexylamine has a pKa of ∼10.6, whereas aniline B



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has a pKa of ∼4.7, a difference of 6 log units due to the mesomeric effect.41,42 Within a series of meta- and parasubstituted aromatic or aliphatic/alicyclic molecules the free energy changes are linear and additive and expressed as either a Hammett or Taft equation (eqs 6 and 7):

pK a = pK a0 − ρ(Σσ )

(6)

pK a = pK a0 − ρ*(Σσ *)

(7)

different methodologies for predicting pKa values for protein and small molecules comments that the main limiting factor to improving pKa predictions is the need for large quantities of well-curated data.46 At AstraZeneca (AZ) an ionization formula nomenclature of AxBy is used to systematically categorize compounds and subsequently aid QSAR/QSPR modeling efforts. “A” refers to acidic centers within the molecule that are appreciably ionized at a pH below 11 and x can equal 0, 1, 2, 3, ...; where A1 refers to the most acidic center and A2 the next most acidic, etc. “B” refers to a basic centers that are appreciably ionized at a pH above pH 2, and y can equal 0, 1, 2, 3, ...; where B1 refers to the most basic center and B2 the next basic, etc. Figure 1 shows a plot of ACD pKa v12 predictions for

pK0a is the pKa of the unsubstituted acid or base. ρ and ρ* are constants for a particular aromatic and aliphatic/alicyclic system, and σ (more specifically σmeta and σpara) and σ* are constants for a particular substituent. If pK0a is known along with an estimate of the ρ (or ρ*) value for a particular series, then the pKa of an unknown compound from this series can be estimated by using the σ (or σ*) values for the relevant substituent(s). For benzoic acid the pK0a is ∼4.2, and the ρ value for this series is arbitrarily set to 1 (the σmeta and σpara for a hydrogen substituent is arbitrarily set to 0).40 Hence for benzoic acid its pKa = pK0a . For 4-chlorobenzoic acid the σpara value for the para-chloro substituent is 0.24; hence its pKa is predicted to be ∼4.0. For pyridine the pK0a is ∼5.3, and the ρ value for this series has been established to be ∼5.9. This much higher ρ value indicates that the electronic effect of a given substituent on the pKa of pyridine will be much greater than that on benzoic acid. For 4-chloropyridine its pKa is predicted to be ∼3.9. σmeta and σpara values can be further convoluted into inductive (or field) effects, F, and resonance effects, R. Hence, the effect of substituents on pKa values therefore lead to quantitative descriptors, σmeta, σpara, σ*, F, and R, of electronic effects. These can be used in quantitative structure activity (or property) relationships (QSAR or QSPR), (other electronic descriptors include atomic partial charges, HOMO/LUMO energies, dipole moments, etc.). Drug receptor associations are typically a function of a drug molecule’s hydrophobicity, sterics, electronics, etc. For a given chemical series, practically the difference, ΔpKa, between the pKa of an unsubstituted and substituted version can be used as a descriptor as this will be equivalent to ρ∑σ or ρ*∑σ* and ρ or ρ* although unknown will be by assumption constant for a chemical series. The use of Hammett and Taft equations to predict pKa are more broadly referred to as linear free energy relationships (LFER) and an example of an empirical methodology. Other empirical methods include similarity searching of databases or QSPR. The MoKa (1.2) tool is a notable example of such a method which has been trained on 26 515 pKa values and validated against 5581 pKa values taken from Roche’s in-house library.43 The predictive power of such tools is related to the inclusion within the training set of similar ionizable motifs that represent the molecular effects that influence the compound in question pKa(s). The alternative to these empirical methods are quantum mechanical (QM) calculations.44 A variety of different commercially available pKa estimation packages have recently been compared against each other in two studies.44,45 Although different compound sets were used in the two evaluations (Nicklaus and Liao: 197 pharmaceutical substances; Manchester et al.: 211 druglike compounds) a consensus of the best packages include ACD/pK a v12 (Advanced Chemistry Development, Inc.; LFER), ADME Boxes (Pharma Algorithms, Inc.; QSPR), MoKa (Molecular Discovery, Ltd.; Topological), and Marvin (ChemAxon Ltd.; QSPR) with typically errors >0.4 to ∼1 log unit. A further excellent review, by Crippen et al., of

Figure 1. ACD pKa v12 predictions versus pKa measurements of the basic center for ∼900 AZ proprietary monobasic compounds.

the basic center in a diverse selection of ∼900 AZ proprietary monobases against measurements, and the root-mean-squared error (RMSE) between prediction and measurement for this data set is still 1.45 units. This highlights the need for better QSPR or QM methods of predictions. The assignment of ionization formula is based on experimental data and structural critique as commonly employed measurement techniques (potentiometry, UV, or CEMS) have pH-electrode limitations restricting their dynamic range to 2−11 and extremely strong acidic or basic pKa values such as sulfonic acid or guanidine can be hard to measure. The relevance of some pKa values can be questioned if the pH at which the biological parameter is being modeled is such that a particular center is not appreciably ionized. Bumetanide has three pK a s: A1 = 3.5 (carboxylic acid), A2 = 9.7 (sulphonamide), B1 = 6.1 (aniline):

At pH = 7.4 only A1 is appreciably ionized, and at this pH bumetanide can be approximated to behave as a monoacid (i.e., A1B0). However, if modeling a biological parameter where pH is a variable, such as solubility or absorption throughout the gastrointestinal tract where pH ranges from ∼1.5 to ∼8, then all three pKa values need to be accounted for as the numbers of species present at any pH will vary.47 C



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From a QSAR perspective pKa contains information on electronic effects of different chemical substituents on a particular drug receptor activity; it is also used as a bulk descriptor to estimate the different concentrations of ionized and un-ionized species at a particular pH. The distribution of species for the monoacid benzoic acid is shown in Figure 2. At

The two ionizations in salsalate correspond to well-separated pKa values (>3 units) and can be treated as separate processes, and practically only two species exist in equilibrium at any particular pH: H2A and HA− below pH = 5.5 and HA− and A2− above pH = 5.5). An analogous situation exists for dibasic and zwitterionic (where acidic pKa < basic pKa) compounds with well separated pKas: BH22+ and BH+ exist below a particular pH and BH+ and B above; HABH+ and A−BH+ exist below a particular pH and A−BH+ and A−B exist above. (Note, for such zwitterions the HAB species will be present in solution but to a much lesser extent than the A−BH+ species.) The situation with carbenicillin is significantly different and highlights a critical aspect of attempting to structurally interpret experimental pKa data for multiply charged compounds and any subsequent application of this interpretation to future predictions, see Figure 4. The similarity between the 2 pKas of carbenicillin implies that the ionization of the two acidic groups take place simultaneously. These pKa values are referred to as overlapping and can no longer be assigned to the ionization of a particular functional group. pKa1 is the pH at which 0.5 equivalent of protons are removed from carbenicillin and pKa2 is the pH at which 1.5 equivalent of protons are removed and are referred to as macroscopic pKa values. A macroscopic pKa cannot be assigned to a specific structural feature. As can be seen in Figure 4 between the pH range 2−5 there are four different species that exist in equilibrium. Microscopic pKa values must be determined before the concentration of each monoanion can be determined, and a similar situation exists for certain types of amphoteric compounds where the acidic and basic pKa values are close. Dealing with multiply charged species will be specific to each drug discovery project. At AZ over the last 12 months more than 50% of the compound’s that had a pKa measurement contained more than 1 pKa, see Figure 5. From the perspective of in silico ADME, pKa is generally used to guide the subdivision of compounds into broad classification such as acids, bases, neutrals, or amphoterics, including studies for predicting renal clearance, extent of plasma protein binding, microsomal binding, and volume of distribution.25,27,28,48−50 This assignment is usually made by assessing ionization behavior at pH = 7.4, but this can seem contrived as the strength of the ionization is mostly ignored as a compound may be treated as an acid if it contains an acidic center whose pKa < 7.4 (i.e., it is more than 50% ionized at pH = 7.4) and contains no appreciably ionized basic centers (i.e., none that are where

Figure 2. Species distribution for benzoic acid (monoacid, pKa = 4.2).

any pH there exists, in equilibrium, two species and the percentage of the anionic species, A−, is defined as 100 A−% = (8) 1 + 10 pKa − pH If a biological process is dependent on the concentration of either of these two species, then it will be dictated by pKa and pH. For oral absorption the distribution of these two species will vary across the pH gradient of the gastrointestinal tract (pH range from ∼1.5 to ∼8). For diacids, such as salsalate, three species exist in equilibrium, see Figure 3. The percentage of the anionic species, A2− and HA− are defined as 100 A2 −% = 2 pK a1+ pK a2 − 2pH (9) 1 + 10 + 10 pKa − pH 100

HA−% = 1 + 10

pK a1− pH

2

+ 10 pH − pKa

(10)

Figure 3. Species distribution for salsalate (diacid, pKa1 = 2.9, pKa2 = 8.0). D



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Figure 4. Species distribution for carbenicillin (diacid, pKa1 = 2.6, pKa2 = 3.1).

factors such as pKa, aqueous solubility, hydrophobicity will be influential but in the very early stages of evaluating a new potential drug candidate other key dissolution factors such as salt form, surface area, particle size, crystal form, and dosage form are typically uncharacterized simply due to pragmatic reasons. With respect to determining a compound’s aqueous solubility there are broadly two different experimental methodologies: equilibrium (thermodynamic) or kinetic aqueous solubility assays, typically at 20 °C and pH = 7.4.53,54 The starting form of the compound being one of the main distinguishing features (i.e., solid or DMSO stock) along with the length of time the compound and aqueous buffer are allowed to equilibrate for. Why the legacy development of two different forms of assays? From an AZ early drug discovery perspective there has always been a need for an early indication of solubility issues within a typical buffer system that could affect the design and running of subsequent biological in vitro or in vivo studies that require a minimum aqueous concentration. This can be satisfied using a more highthroughput kinetic aqueous solubility assay. Thermodynamic aqueous solubility assays tend to be lower throughput but, in our experience, less variable. Essentially the kinetic aqueous solubility measurement was poorly predictive of a compound’s thermodynamic aqueous solubility except for those compounds that exceeded the upper limit of the former assay.55 Such an observation has significant implications when in silico predictive models are built because if the RMSE between the observed and the predicted data for a training set is better than the random error and bias associated with the experimental measurement then the model is overfitted and its use questionable. Within the literature there are significant deficiencies in the consistency and reliability of aqueous solubility data for what is a simple experiment and the ability to predict aqueous solubility can be challenging.56 From a basic QSPR perspective it is not unexpected that an inverse linear relationship exists between the logarithm of the aqueous thermodynamic solubility (at pH = 7.4 and 20 °C starting with solid material) and the logarithm of the octan-1-ol/water partition coefficient (i.e., log P). The latter is essentially the

Figure 5. Proteolytic class distribution for AZ compounds with a pKa measurement in the last 12 months.

pKa > 7.4), and a similar but reversed assignment may be applied to classify basic compounds. Such classification may be suitable when studying bulk transfer processes such as passive absorption but not so when modeling drug receptor associations where the anion or cation are orders of magnitude more potent than the neutral form due to a charge reinforced interaction; in this scenario, at pH = 7.4, an acidic pKa = 8.9 or a basic pKa = 5.9 may be important. Therefore in drug discovery, an appreciation of the different proteolytic classes, the relative strengths of the pKa values and their relevance to a particular biological parameter (i.e., constant pH or variable pH) is paramount. From the perspective of designing new compounds the limitation of experimental techniques need to be considered (i.e., macroscopic pKa values, and the reliable detection range) if using measured data to train bespoke LFER, QSPR, or QM methodologies for pKa predictions for novel chemical series. Solubility. The absorption of an oral or dry powder inhaled drug into the systemic circulation requires dissolution of the compound into biological aqueous media.51,52 Physicochemical E



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molecules have high levels of conformational flexibility; furthermore the accuracy of log P predictions can be unacceptably poor.61 An alternative LFER aqueous solubility equation was proposed by Abraham et al. where a compound’s aqueous solubility was related to the following descriptors: molar refractivity, polarizability, hydrogen bond acidity, hydrogen bond basicity, McGowan molecular volume.62 Further complications involved in predicting aqueous solubility is the affect of temperature and in addition for ionizable compounds the affect of pH. Semiempirical models exist for relating the molar solubility of a compound and temperature dependence (expressed as the van’t Hoff enthalpy of solubility) in solvents, although water is more difficult to model than organic solvents and so the extrapolation is less reliable for aqueous solubility data.63 Theoretical equations exist for modeling the ideal affect of pH on solubility for mono-, di-, and triprotic compounds, but examples of sparingly soluble drugs that show deviations from the ideal are known.64 The reliability of using temperature and pH models to extrapolate experimental solubility data measured at 20 °C and pH = 7.4 in a nonbiologically relevant aqueous system, as commonly generated in the very early stages of a drug discovery screening cascades, to 37 °C and the pH range 1.5−8 as might be the case in modeling absorption across the gastrointestinal tract needs to be carefully considered. The purpose of such experimental data is more applicable to the identification of potential solubility issues in subsequent assays. From a design perspective the requirements of an aqueous solubility prediction trained on early screening data is for the model to be able to confidently (i.e., with approximately 80% probability) identify virtual compounds that will have poor aqueous solubility. Hill et al. define low aqueous solubility to be 3 and total PSA < 75 Å2).30 An obvious shortcoming in the application of physicochemical properties to drug discovery for ionizable molecules is that log P is of interest from a compound quality perspective but DMPK tends to focus on measurements of log D7.4. A log P* can be estimated from a log D7.4 and pKa measurement and application of the relevant proteolytic class equation, the asterisk implying an indirect measure of log P. However, where the former is typically measured routinely, pKa measurements are not routine on all compounds, and the use of pKa predictions using generic methodologies can add large errors to a log P* estimate. To address this issue AZ has developed a Pipeline Pilot (Accelrys Inc.) based AutoLogP system that automatically maximizes the log P* data set for proprietary compounds with an experimentally determined log D (at a given pH) and pKa data. The experimenter’s assessment of a compound’s ionization formula (i.e., AxBy, see pKa section above) is critical in the curation of the experimental pKa data as the decision flow logic within Pipeline Pilot will vary for different proteolytic classes. The system has the pragmatic functionality that enables the assignment of a pKa for a constant ionizable group within a common scaffold (or substructure) used within a particular drug discovery chemical series (i.e., where the chemical exploratory changes do not affect the ionization). Thus maximizing the use of experimental pKa data and consequently minimizing the absolute number of compound measurements. Provided that a log D measurement exists and an ionization formula has been assigned, there is a general pattern to the inherent decision flow logic of the AutoLogP system. Do all pKa values exist for the compound as indicated by the ionization formula? If not, check to see if a fragment pKa exists for the chemical series, and use ACD/pKa v12 prediction to estimate whether the ionization is significant to the calculation of log P*. A molecule may have multiple ionizations which are measurable but too weak to affect the log P* calculation; hence an approximation is valid using a more simple proteolytic class equation (e.g., certain A2B0 compounds can be treated as A1B0). Although dependent on the ionization formula in question, an acidic ionization may be ignored if it is predicted to be greater than 8.9 (e.g., phenols), and for such a compound with an ionization formula A1B0 it can be assumed that the log D7.4 measurement is a log P measurement. The value of 8.9 is somewhat conservative but allows for error in the ACD/pKa v12 prediction. Similarly, a value of 5.9 can be used for basic ionizations. The estimation of log P* for certain amphoteric compounds is possible. For

example in the case of A1B1 if the acidic pKa is 5 and the basic pKa is 3, then the compound can be treated as a monoacid (i.e., A1B0). Figure 7 shows a plot of clogP values for AZ proprietary

Figure 7. clogP versus log P* (determined using measured log D7.4 and pKa data) for 1324 AZ proprietary monoacidic (A1B0), monobasic (A0B1), or amphotheric (A1B1) compounds.

compounds against their log P* values, and although there is a significant correlation the RMSE (1.07) is large and equivalent to that shown by Tetko et al.61 There is an assumption that log P* provides a better estimate of an AZ proprietary compound’s lipophilicity than a clogP prediction, and it is implicit that log P* will be a better descriptor in QSAR/QSPR modeling. Predictive models for human PPB are often modeled using lipophilicity descriptors.95 PPB data can be analyzed on a pseudo binding constant scale (K PPB ) by taking the (logarithmic) ratio of the %bound to the %free value.28 The plots between the measured human log KPPB and either log P* or clogP for 373 AZ proprietary monoacidic, monobasic, or amphoteric compounds are shown in Figures 8 and 9. The two correlations are weak, but the former appears better and is illustrative that log P* for AZ proprietary compounds potentially has extra value as a lipophilicity descriptor in subsequent QSAR over the use of clogP. However, log P*

Figure 8. Log P* (determined using measured log D7.4 and pKa data) versus human plasma protein binding for 373 AZ proprietary monoacidic (A1B0), monobasic (A0B1), or amphotheric (A1B1) compounds. H



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potential can facilitate a BCS classification.96 The Rodgers and Rowland methodology predicted tissue distribution for different proteolytic classes using log P and pKas.97 Luker et al. described an in silico methodology for predicting attrition in preclinical toxicology for basic oral drugs, where key descriptors included those that described a molecule’s charge distribution, shape, and hydrogen bonding potential.98 The drug efficiency index (DEI) has been proposed as a useful parameter to optimize ADMET and in vivo efficacy potentials of molecules, and Valko et al. described an in vitro estimate of DEI that uses an estimate of PPB and hydrophobicity.99 These examples are highlighted to further demonstrate the greater focus on the use of physicochemical parameters to understand ADMET and subsequently modulate a drug’s dose.

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Figure 9. clogP versus human plasma protein binding for 373 AZ proprietary monoacidic (A1B0), monobasic (A0B1), or amphotheric (A1B1) compounds.

AUTHOR INFORMATION

Corresponding Author

*Phone: +44 1625 516603. E-mail: mark.wenlock@astrazeneca. com. Notes

The authors declare no competing financial interest.

values require experimental data so from a drug design perspective, where log P is used as a key compound quality parameter, it follows that the “local” in silico QSPR model for this property trained specifically on log P* data may offer complementary and potentially more accurate estimates of intrinsic lipophilicity.

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ABBREVIATIONS USED ADME(T), absorption distribution metabolism elimination (toxicity); AZ, AstraZeneca; BCS, Biopharmaceutics Classification System; clogP, Daylight’s octanol/water partition coefficient; CMC, critical micelle concentration; D, octan-1ol/water distribution coefficient; DEI, drug efficiency index; HBA, hydrogen bond acceptor; HBD, hydrogen bond donor; HOMO, highest occupied molecular orbital; Kα, hydrogen bond donor association constant; Kβ, hydrogen bond acceptor association constant; KPPB, pseudo plasma protein binding constant; LFER, linear free energy relationship; LUMO, lowest unoccupied molecular orbital; MP, melting point; P, octan-1ol/water partition coefficient; pKa, ionization constant; PPB, plasma protein binding; PSA, polar surface area; QM, quantum mechanical; QSAR, quantitative structure activity relationship; QSPR, quantitative structure property relationship; RMSE, root-mean-squared error; Ssolid 0 , intrinsic aqueous solubility of crystalline (solid) compound; SFI, solubility forecast index

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CONCLUSION The rational design of compounds within drug discovery benefits from understanding how a drug’s ADMET behavior is controlled by its molecular structure or, at the very least, influenced by its physicochemical properties. The use of commercial or proprietary in silico models, built using a variety of statistical techniques, for pKa, solubility, and hydrophobicity is routine within the drug discovery. Physicochemical property predictions are often used as descriptors within multivariate QSAR/QSPR models that relate to a particular biological process or more holistically used as broad compound quality criteria. High-quality experimental physicochemical property data should result in improved in silico QSPR models for predicting that parameter and proprietary in silico models of commonly built for this purpose. The log P* parameter is derived from experimental log D data and experimental pKa data or decisions based on predicted pKa data using specific proteolytic class equations. Log P* has been shown to be a better descriptor for understanding human PPB data compared to clogP. It follows that the inclusion of such improved in silico predictions as descriptors in ADMET multivariate QSAR models should confer some degree of advantage within drug discovery, helping to reduce costs and uncertainty as decisions may be more confidently made on virtual structures. The prediction accuracy of these models will be dependent on the applicability domain of the training set compounds to the compounds being predicted. As drug discovery projects explore different chemical areas, the applicability of such models needs to be monitored, and if necessary models should be refined to incorporate information pertaining to new compounds at appropriate intervals. Although there are many examples where physicochemical parameters have been related to ADMET, four further studies are noteworthy. Comer and Box proposed that an appreciation of a molecule’s log P, intrinsic solubility, and hydrogen bonding

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