Hydrogen Bond Basicity Prediction for Medicinal Chemistry Design

Article pubs.acs.org/jmc

Hydrogen Bond Basicity Prediction for Medicinal Chemistry Design Peter W. Kenny,* Carlos A. Montanari, Igor M. Prokopczyk, Jean F. R. Ribeiro, and Geraldo Rodrigues Sartori Grupo de Estudos em Química MedicinalNEQUIMED, Instituto de Química de São Carlos, Universidade de São Paulo, Av. Trabalhador Sancarlense, 400, 13560-590 São Carlos, São Paulo, Brazil S Supporting Information *

ABSTRACT: Hydrogen bonding is discussed in the context of medicinal chemistry design. Minimized molecular electrostatic potential (Vmin) is shown to be an effective predictor of hydrogen bond basicity (pKBHX), and predictive models are presented for a number of hydrogen bond acceptor types relevant to medicinal chemistry. The problems posed by the presence of nonequivalent hydrogen bond acceptor sites in molecular structures are addressed by using nonlinear regression to fit measured pKBHX to calculated Vmin. Predictions are made for hydrogen bond basicity of fluorine in situations where relevant experimental measurements are not available. It is shown how predicted pKBHX can be used to provide insight into the nature of bioisosterism and to profile heterocycles. Examples of pKBHX prediction for molecular structures with multiple, nonequivalent hydrogen bond acceptors are presented.

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INTRODUCTION Hydrogen bonding1−6 is a key element of molecular recognition7,8 and is implicated in diverse physicochemical phenomena such as crystal packing,9−11 DNA base-pairing,12,13 protein folding,14−18 and enzyme specificity.19 The cohesiveness of liquid water that drives hydrophobic association20,21 in aqueous media is a consequence of cooperative hydrogen bonds between water molecules. In the pharmaceutical context, hydrogen bonding influences solubility of drugs, both in water and in lipids, and the affinity with which they associate with their targets. Partition coefficients,22,23 especially when measured for the 1-octanol/water system, are widely used in drug discovery, and differences between values measured for a compound in different systems (e.g., cyclohexane/water) reflect the hydrogen-bonding characteristics of the compound.24−30 Hydrogen bond (HB) strength can be quantified by the stability of the 1:1 complex between an HB donor and an HB acceptor in a nonpolar solvent such as tetrachloromethane or 1,1,1-trichloroethane.3,31−34 The 1:1 complex stability measured using a reference HB donor such as 4-fluorophenol31−33 or 4-nitrophenol34 can be used to define scales for HB basicity, and a reference HB acceptor such as 1-methylpyrrolidone can be used to quantify HB acidity in an analogous manner.34 Measured HB basicity (and acidity) can be used to guide molecular design, although there are limitations to how the measurements can be used. First, measurements made for compounds which have nonequivalent HB acceptors cannot, in general, be used to characterize the different HB acceptor sites for a molecular structure, although in some cases35 the individual isomeric 1:1 complexes can be observed. Second, in polar solvents such as water or in ligand-protein complexes, formation of multiple interactions can perturb HB basicity and © 2016 American Chemical Society

acidity of individual acceptors and donors. This is a particular issue for carbonyl oxygen atoms, which are typically associated with two HB acceptor sites, and hydroxyl groups for which an HB donor and acceptor are in close proximity.29,36 Outside narrowly defined structural series, pKa is not an effective predictor of HB acidity or basicity.33,34 This study focuses on the use of molecular electrostatic potential (MEP) minima37 to interpret and predict HB basicity. MEP minima are points in space where the electric field strength vanishes, and the value (Vmin) of MEP at the minimum has been shown to be predictive of HB basicity.37,38 Although HB donors lack analogous MEP maxima, HB acidity can be predicted in an analogous manner using the Vα(r) descriptor which is defined as MEP calculated on the geometric extension of the covalent bond to the HB donor hydrogen.36 MEP calculated on molecular surfaces has also been used39 for prediction of HB basicity and acidity, although it has not been shown that these MEP values are optimal for this purpose. Polarization charge density has been shown to be a useful and effective predictor of both enthalpy and entropy changes associated with HB formation.40 HB strength can be predicted by calculating energies for the HB donor, HB acceptor, and complex, although high-level calculations are usually necessary to obtain useful results.41 Furthermore, the need to sample and minimize the energies of multiple orientations of the HB donor and acceptor typically imposes significant computational costs. It may be helpful to articulate what is meant by the term “design” since one objective of this study is to demystify some Special Issue: Computational Methods for Medicinal Chemistry Received: December 16, 2015 Published: February 12, 2016 4278

DOI: 10.1021/acs.jmedchem.5b01946 J. Med. Chem. 2016, 59, 4278−4288

Journal of Medicinal Chemistry

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increases in pIC50 of 1.9 and >2.2 respectively against cathepsins S and L2.51 One aspect of the drug designer’s job might be summarized as beating water at hydrogen bonding, and the pKBHX value of 0.65 measured33 for water indicates that it is a relatively weak HB acceptor. It should also be noted that contact between polar and nonpolar molecular surfaces is not inherently repulsive as illustrated by the observation52 that gas to hexadecane transfer is slightly more favorable for tetrahydrofuran (ΔG° = −0.84 kcal/mol) than for cyclopentane (ΔG° = −0.72 kcal/mol). As such, it is questionable to invoke “a dual character of the weakly polar sulfonyl groups as a hydrogen bond acceptor and as a hydrophobic group” 7 as a rationale for the existence of intermolecular contacts of this nature in crystal structures. One tactic employed in structure-based design is to identify53,54 unstable water molecules bound to protein that can be readily displaced by ligands but one might also attempt to identify “privileged” arrangements of HB donors and acceptors that cannot easily be mimicked by clusters of water molecules. Much of the value of predicting HB basicity (and acidity) stems from helping medicinal chemists to think about consequences of structural modifications before these have been made or when relevant experimental data are lacking. In this study, we first show how Vmin can be used as a predictor of pKBHX and then use a number of examples to illustrate the scope for exploiting predicted HB basicity in medicinal chemistry design. We refer readers to a selection of reviews32,33 and articles55−63 in which hydrogen bonding is discussed in a medicinal chemistry context.

of the computational methods used in medicinal chemistry. Molecular design may be defined42 as control of behavior of compounds and materials by manipulation of molecular properties. It is not generally feasible to predict all relevant chemical behavior from molecular structure with sufficient accuracy to enable what can be termed36 “prediction-driven molecular design”, and practical design typically requires that some experimental measurements be made. Molecular design is not only about making predictions, and the focus of hypothesisdriven molecular design36,42 is generating the knowledge that is required for making informed decisions. The principal challenge for hypothesis-driven molecular design is to make it as systematic, objective, and efficient as possible, and there is a degree of overlap with statistical molecular design.43 Much medicinal chemistry design, especially in lead optimization, focuses on the effects (e.g., on affinity and aqueous solubility) of structural modifications. In cheminformatic terms this is equivalent to saying that biological activity and physicochemical properties may be perceived in terms of structural relationships between compounds.42,44 Molecular interactions7,8 are of great importance in medicinal chemistry because much of the behavior of a compound is determined by the interactions of its molecules with the environments in which they exist. Although much is known about geometry of molecular interactions, exploiting this knowledge to predict affinity remains challenging. A particular problem is that the contribution of an intermolecular contact to affinity is not, in general, an experimental observable.45 Individual interactions differ in their geometric preferences and, as the number of interactions increases, it becomes progressively more difficult to simultaneously accommodate these preferences. This is the essence of the molecular complexity model46 of Hann et al., and these effects can also be considered in terms of non-additivity of interactions. Zhou and Gilson emphasize the (frequently disregarded) arbitrary nature of the standard state when interpreting molecular recognition phenomena and also highlight pitfalls associated with attempting to distribute affinity between individual molecular recognition elements of the ligand structure.47 In biological systems, molecular recognition occurs in aqueous environments, and this greatly complicates interpretation of molecular interactions.19 Hydrogen-bonding partners need to compensate each other for lost solvation, and this suggests the existence of an optimal ligand charge distribution48 that will maximize affinity for a given protein charge distribution. In terms of hydrogen bonding, we can think of needing to balance36,39 the HB basicity of the acceptor with the HB acidity of the donor to get the most effective interaction, and it may be useful to interpret binding enthalpy49 in these terms. It is commonly believed that HB formation between protein and ligand is of limited scope as a means for increasing affinity, and it has been asserted that “a neutral−neutral hydrogen bond is worth less than 15-fold in binding”.50 We challenge this view on the grounds that it is based on a small body of data, and deletion of a single HB donor or acceptor from a molecular structure has effects other than simply eliminating an intermolecular HB from the association complex. For example, of the atoms in a linker may be able to move more freely in the complex or make more effective hydrophobic contact with the protein once the ligand atom participating in the relevant HB has been eliminated. On a less speculative note, aza-substution of a pyridyl substituent in a cysteine protease inhibitor has been observed to result in

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RESULTS AND DISCUSSION Modeling HB Basicity with Vmin. Many medicinal chemists will be unfamiliar with the MEP minima used to model HB basicity so a good way to start this section is to note that these can be considered to be roughly equivalent to “lone pairs”. The Vmin value at the MEP minimum can be thought of as the “strength”, “intensity”, or “availability” of the “lone pair”. Vmin is a more direct (and less arbitrary) measure than an atomic charge of what an HB donor would “see”. MEP minima typically lie within the van der Waals molecular surface, and computational chemists should be aware that these minima cannot, in general, be reproduced using atom-centered multipoles. When only a single MEP minimum is present in the molecular structure, HB basicity can be modeled38 according to a linear model with intercept A and slope B: pK BHX = A + BVmin

(1)

If two HB acceptor sites are present in the molecular structure, the observed association constant K is simply the sum of the association constants (K1 and K2) for the individual acceptors:33,38 K = K1 + K 2

(2)

There are two simplifying assumptions that can sometimes be made in order to fit measured pKBHX when two HB acceptor sites are present in a molecular structure. First, when the HB acceptors are equivalent (K1 = K2), the measured pKBHX can be corrected statistically and used for fitting as if only a single HB acceptor is present. Second, when one of the HB acceptors is likely to be much stronger than the other (e.g., oxazole), we can neglect the contribution of the weaker acceptor to HB basicity when fitting pKBHX to Vmin. In this scenario, the relevant Vmin values are useful for testing the validity of the assumptions. 4279



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Table 1. Hydrogen Bond Basicity Models for Different Atom Types atom type

QM modela

Nb

Ac

SE(A)d

B/(e/Eh)e

SE(B)(e/Eh)f

RMSEg

SDh

nitrile N nitrile N aromatic N aromatic N imine N Imine N amine N amine N carbonyl O carbonyl O O[n,N;X3]i O[n,N;X3]i O[S,Se]j O[S,Se]j O[N,P,As;X4]k O[N,P,As;X4]k OX2l OX2l fluorine fluorine thiocarbonyl S thiocarbonyl S SX2m SX2m all datan all datan

HF/6-31G** MP2/6-311+G** HF/6-31G** B3LYP/6-311+G** HF/6-31G** MP2/6-311+G** HF/6-31G** MP2/6-311+G** HF/6-31G** MP2/6-31G** HF/6-31G** HF/6-311G** HF/6-31G** M06/6-31G** HF/6-31G** M06/6-311+G** HF/6-31G** HF/6-311+G** HF/6-31G** MP2/6-311+G** HF/6-31G** MP2/6-31G** HF/6-31G** HF/6-311+G** HF/6-31G** HF/6-311+G**

16 16 58 58 22 22 60 60 110 110 8 8 12 12 7 7 47 47 7 7 5 5 12 12 357 357

−2.38 −2.59 −4.31 −3.67 −3.56 −2.72 −2.09 −3.02 −4.05 −3.58 −5.61 −5.65 −4.02 −3.40 −4.34 −4.98 −2.96 −2.84 −1.11 −1.67 −3.70 −2.79 −2.67 −2.68 −3.05 −3.18

0.22 0.14 0.22 0.17 0.40 0.31 0.64 0.60 0.17 0.13 0.43 0.34 0.44 0.33 0.94 0.90 0.31 0.31 0.28 0.24 1.36 0.46 0.18 0.20 0.09 0.09

−36.61 −43.99 −54.79 −56.09 −47.16 −47.96 −33.20 −46.78 −50.24 −59.53 −72.25 −72.71 −52.80 −56.64 −58.66 −72.39 −39.86 −38.71 −19.69 −30.94 −59.50 −56.05 −42.18 −44.39 −43.05 −45.22

2.47 1.79 1.97 1.84 3.38 3.06 5.29 5.69 1.88 1.69 4.19 3.30 4.18 3.76 7.72 8.26 3.51 3.53 4.92 4.77 18.9 7.61 3.32 3.82 0.91 0.93

0.117 0.072 0.163 0.151 0.189 0.177 0.333 0.293 0.231 0.200 0.182 0.142 0.255 0.211 0.494 0.464 0.257 0.271 0.128 0.106 0.282 0.134 0.068 0.073 0.330 0.320

0.460 0.460 0.622 0.622 0.604 0.604 0.428 0.428 0.716 0.716 1.312 1.313 1.027 1.027 1.819 1.819 0.507 0.507 0.200 0.200 0.500 0.500 0.272 0.272 0.866 0.866

a

Quantum mechanical model used for Vmin calculation. bNumber of observations. cIntercept term in eq 1. dStandard error of intercept term in eq 1. Slope term in eq 1. fStandard error of slope term in eq 1. gRoot mean square error. hStandard deviation in pKBHX. iOxygen in nitro or heteroaromatic N-oxide. jOxygen doubly bonded to sulfur or selenium. kOxygen doubly bonded to tetrahedral nitrogen, phosphorus, or arsenic. l Alcohols, ethers, furans, and peroxides. mThiols, thioethers, and disulfides. nExcluding seven compounds in fluorine data subset. e

Oxygen, sulfur, and fluorine atoms are typically associated with two or three MEP minima with comparable Vmin values that are not in general equivalent, and it is not, in general, valid to statistically correct pKBHX in these situations. One solution to the problem of fitting measured pKBHX to comparable, nonequivalent Vmin values is to use nonlinear regression as exemplified by eq 3, in which V1 and V2 are two nonequivalent Vmin values: pK BHX = A + log10(10 BV1 + 10 BV2)

364 measured pKBHX values to address these questions. Each of the protocols used in this study to calculate Vmin consists of a theoretical model and basis set of atom-based functions from which the electron density of the molecule can be constructed. Modeling interactions between electrons is the main challenge in quantum chemistry. The four theoretical models differ in how they achieve this and in their computational cost (which increases with the size of the molecule and number of atombased functions in the basis set). Energy-minimization of molecular structures with quantum mechanical models is more demanding than calculating MEP, and we have used a much less computationally expensive molecular mechanics model for this purpose. We have also created ADD_CENTRE for setting up the starting points for the minimization of MEP, and source code is provided as Supporting Information. A summary of the results of fitting pKBHX to Vmin for different atom types and computational protocols is presented in Table 1, and complete results are provided as Supporting Information. Summary statistics are listed for two protocols for each atom type in Table 1. These are the model derived from the least demanding computational protocol (HF/6‑31G**; see Computational Details) and the best model for the atom type as judged by root-mean-square error (RMSE). In cases where least demanding computational model was found to be optimal, summary statistics for the second best model are also given. For a given atom type, it is valid to use RMSE to rank models because each model is fit using two parameters to identical data. The standard deviation for measured pKBHX is also given for each atom type in Table 1, and this quantity indicates how well

(3)

Although eqs 2 and 3 can be generalized to any number of HB acceptor sites, the pKBHX value measured for a compound with multiple, nonequivalent HB acceptors has no thermodynamic significance.33 Furthermore, the sum of association constants for all isomeric 1:1 complexes is not directly relevant to the solvated state in which all HB acceptors and donors of the solute can interact simultaneously with solvent molecules. HB basicity measurements for compounds with nonequivalent acceptors are only useful if the association constants for individual acceptors can be quantified,35 and this is not generally the case for compounds of interest to medicinal chemists. Predictive models usually represent the only practical means of quantifying HB basicity of individual acceptors in molecular structures of interest to medicinal chemists, although measurements made for structural prototypes are absolutely essential for developing the predictive models. The first objective of this study was to explore the influence of atom type and computational protocol on the performance of Vmin as a predictor of HB basicity, and we used a database of 4280



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Figure 1. Plots of measured versus predicted pKBHX for nitrile nitrogen (A), heteroaromatic nitrogen (B), amines (C), carbonyl oxygen (D), singly connected oxygen bonded to sulfur or selenium (E), and doubly connected oxygen (F). The models depicted in this figure were fit using Vmin values calculated according to HF/6‑31G** protocol (see Computational Details), and each model is specific to its atom type. The same scale has been used for all six plots to illustrate how the range in the data varies with atom type.

Figure 2. Plot of measured versus predicted pKBHX for fluorine (A), and values of pKBHX predicted for structural prototypes (B) using Vmin values calculated using the MP2/6‑311+G** protocol (see Computational Details). pKBHX predicted for 1 is for the compound (measured67 value in parentheses), and the other predicted values of pKBHX are for individual fluorine atoms.

comparable with the standard deviation (0.43; Table 1) for this atom type. Should it be necessary to make the most accurate predictions for a specific atom type then the protocol most appropriate to that atom type can be used. It must be stressed that it would not be valid to invoke these results in support of an assertion that one theoretical model was better than another. Hydrogen Bond Basicity of Fluorine. Fluorine is of great interest in medicinal chemistry, although its properties and behavior are sometimes considered to be enigmatic.65,66 For example, it is a weak HB acceptor when bound to carbon despite being the most electronegative element. However, this might be seen as simply illustrating the importance of charge distribution within, as opposed to between, atoms as a

pKBHX is likely to be predicted by the mean value measured for the relevant atom type. It should be noted that the coefficient of determination (R2), commonly used as a measure of quality of linear models, cannot be used for nonlinear models.64 The models can be used in a number of ways. We would recommend the use of Vmin calculated using the HF/6‑31G** protocol (see Computational Details) as a default for prediction of HB basicity since it is the least computationally demanding of the protocols that were evaluated and performs acceptably across a range of atom types. Plots of measured versus predicted pKBHX are shown for six models derived using this protocol are shown in Figure 1, and it should be apparent that the RMSE value (0.33; Table 1) for the amine nitrogen is 4281



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Figure 3. Predicted pKBHX values for individual hydrogen bond acceptors in oxadiazole and related bioisosteres. Methyl substituent was included to define alignment of bioisosteres and to lock tetrazoles and triazoles into desired tautomer. Measured33 pKBHX values for reference: furan, −0.40; 1,3,5-triazine, 0.38 (statistically corrected); isoxazole, 0.81; oxazole, 1.31; pyridine, 1.86; N-methylimidazole, 2.72.

determinant of interaction potential. Measurements67 of pKBHX have been reported for seven saturated hydrocarbons with one or two fluoro substitutions. The value of pKBHX for 1 (0.48) is noteworthy and can be interpreted in terms of a through-space, repulsive interaction between the electrons associated with the fluorine atoms. The small size and limited range (0.75 log unit) of the training data set make it important to use the best protocol for calculating Vmin which in this case was MP2/ 6‑311+G** (see Computational Details). The fit of of pKBHX to Vmin is shown in Figure 2, and these results are consistent with what has been reported in the literature. The value (−0.5) of pKBHX predicted for 2 suggests that fluorine bonded to aromatic carbon will be, in general, a weaker HB acceptor when bonded to aliphatic carbon. Each fluorine atom in 3 is predicted (pKBHX = −0.6) to be a slightly weaker HB acceptor than the fluorine atom of 2, suggesting that the through-bond interaction between the fluorine atoms outweighs the through-space interaction. The fluorine atom of 2 is associated with two equivalent MEP minima above and below the molecular plane, but the single MEP minimum associated each fluorine atom of 3 lies in the molecular plane. The Vmin calculations can be used to explore the effect of substituting fluorine for hydrogen, and the predicted difference (0.8) in pKBHX between 4 and 5 on a per fluorine atom basis is comparable with the corresponding difference68 (0.6) between fluoromethylbenzene and difluoromethylbenzene measured at −2 °C. All Bioisosteres Are Not Created Equal. Bioisosterism69−72 is an important concept in medicinal chemistry, and computed values of Vmin can provide insight into the nature of bioisosteric relationships. For example, Vmin and Vα(r) were used to compare guanine and adenine bioisosteres from the perspective of DNA base-pairing.36 Meaningful results can sometimes even be obtained for charged systems, and Vmin calculations provide a view of the bioisosteric relationship

between carboxylate and tetrazole anions.36 In some cases, a bioisosteric relationship may be associated with systematic differences in physicochemical properties, and tetrazoles appear to be more highly bound by plasma protein than the corresponding carboxylic acids despite being less lipophilic.73 The bioisosteric relationship between 1,3,4-oxadiazoles and 1,2,4-oxadiazoles has been examined from the perspective of physicochemical properties, and Vmin was used to provide a rationale for experimental observations.57,58 Both studies noted that 1,3,4-oxadiazoles tend to be less lipophilic and more soluble in aqueous media than the corresponding 1,2,4oxadiazoles.57,58 In some cases, lipophilicity prediction software was unable to distinguish regioisomers even when their measured log D values differed by over a unit. Predictions for HB basicity are presented in Figure 3 for oxadiazole regioisomers and some related compounds. Although prototypical structures were used for this generic study of these bioisosteres, structurally elaborated models can easily be used if it is necessary to characterize a bioisosteric relationship in specific structural context. The pKBHX values predicted for 8, 9, and 10 are consistent with the previous studies57,58 in that the nitrogen atoms of the 1,3,4-oxadiazole have greater HB basicity than their regioisomeric equivalents. The predicted pKBHX values for the tetrazole 11 suggest that its hydrogen-bonding profile (and, by implication, its lipophilicity) will be intermediate between the profiles of 8 and 9. The 1,2,3oxadiazoles and 1,2,5-oxadiazoles (12, 13, and 14) are predicted to be even weaker HB acceptors than their 1,2,4oxadiazole equivalents, although the tetrazole bioisostere 15, linked at N1 in this case rather than N2, is predicted to have HB basicity comparable to that of the 1,3,4-oxadiazole 8. Oxazoles and isoxazoles such as 16 and 18 can be mimicked by triazoles (17 and 19) for which the predicted pKBHX values illustrate how triazole isomer and linking position are likely to influence HB basicity. 4282



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Figure 4. Predicted pKBHX values for individual hydrogen bond acceptors in some six-membered heteroaromatic rings. Measured33 pKBHX values for reference: 1,3,5-triazine, 0.38 (statistically corrected); pyrimidine, 1.07 (statistically corrected); pyridazine, 1.65 (statistically corrected); pyridine, 1.86; quinoline, 1.89; isoquinoline, 1.94; 4-dimethylaminopyridine, 2.80.

profile75 heterocycles when relevant physicochemical measurements are unavailable, as can be the case when the heterocycle is uncommon or has an unusual substitution pattern. The heterocycles discussed in this section are shown in Figure 4. One difficulty likely to be encountered when attempting to enhance HB basicity of heteroaromatic nitrogen is that structural modifications that make a nitrogen atom a better HB acceptor will also tend to make it a better proton acceptor with the result that loss of neutral form nullifies any gain in HB basicity. For example, N-methylimidazole (pKBHX = 2.72; pKa = 7.25)33,76 and 4-dimethylaminopyridine (pKBHX = 2.80; pKa = 9.70)33,76 are of comparable HB basicity despite differing significantly in proton basicity. An inference that might be drawn from this observation is that a strong, neutral HB acceptor based on aromatic nitrogen can be more easily accommodated in a five-membered ring than in a six-membered ring. The observation that pyridazine (pKBHX = 1.95; pKa = 2.24)33,76 and pyridine (pKBHX = 1.86; pKa = 5.22)33,76 are of similar HB basicity despite differing significantly in pKa hints at how a strong HB acceptor might be accommodated in a sixmembered aromatic ring without losing it to protonation. While the pKBHX value (2.6) predicted for N1 of 20 approaches that of 4-dimethylaminopyridine, its pKa is expected to be similar to the value of 6.8 reported for 4-aminopyridazine.77 The apparently anomalous HB basicity of pyridazine can be interpreted as due to a through-space interaction and may also be seen as a manifestation of the α effect.78 The results obtained for pyridazine raise the question of what would be observed for the more obscure 1,2,3-triazine79 (21), and the pKBHX values predicted for its nitrogen atoms are all significantly greater than the measured value (0.38; statistically corrected)33 for a single nitrogen atom in the isomeric 1,3,5triazine. Differences in distribution of HB basicity across the three ring nitrogen atoms predicted for 21, 22, and 23 may be of interest, and it is instructive to compare these HB basicity profiles with that of the tetrazole 15.

HB basicity measurements that could have been used to compare 1,2,4-oxadiazoles with their 1,3,4-oxadiazole regioisomers do not appear to have been reported so the calculated Vmin values were particularly useful in these studies. 57,58 Predicted HB basicity can provide useful information even if measurements are available when nonequivalent HB acceptors are present in the molecular structure. The contributions of individual HB acceptors to the overall formation constant can only be measured in certain circumstances, and large differences in HB basicity between individual acceptors make measurement more difficult. The oxadiazole bioisostere studies57,58 highlight a problem faced by users of physicochemical property prediction software. In lead optimization it is particularly important that the effects of structural changes be predicted accurately. Typically, data used to train models are not freely available which makes it impossible to know whether or not chemotypes of interest are adequately represented in training data. Quoted measures of model quality may simply be irrelevant for some chemotypes but users of models are not usually in a position to know if this is the case for specific chemotypes of interest. The oxadiazole bioisostere studies57,58 also show how HB basicity predictions can be used to challenge (and possibly even correct) predictive models. When attempting to control lipophilicity in lead optimization projects it may be helpful to draw a distinction between an increase in HB basicity and an increase in the number of HB acceptors. Heterocyclic Profiles and Through-Space Interactions. Molecular recognition characteristics and physicochemical properties of heterocycles are heavily influenced by HB basicity and acidity. For example, furan (log P = 1.34)74 is more lipophilic than tetrahydrofuran (log P = 0.46),74 but benzene (log P = 2.13)74 is less lipophilic than cyclohexane (log P = 3.44).74 This apparent paradox is easily resolved once it is recognized that the HB basicity of tetrahydrofuran (pKBHX = 1.28)33 is greater than that of furan (pKBHX = −0.40).33 Predicted hydrogen-bonding characteristics can be used to 4283



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Figure 5. Measured log D7.4 and predicted pKBHX for phosphatidylinositol 3-kinase (PI3K) inhibitors.63 Arrows denote changes in log D7.4 associated with the relevant structural transformation. Measured33 pKBHX values for reference: 1,3,5-triazine, 0.38 (statistically corrected); pyrazine, 0.92 (statistically corrected); pyridazine, 1.65 (statistically corrected); pyridine, 1.86; N,N-dimethylacetamide, 2.44 (no statistical correction for number of acceptor sites).

respect to concave regions of the protein molecular surface. Second, compounds capable of presenting these molecular recognition elements might be included in generic fragment screening libraries82 or even designed83 specifically as fragments. It is possible that 20, 22, 23, and 27 would be suitable for crystallographic fragment screening.84 Hydrogen Bond Basicity Predictions for Structurally Elaborated Species. The predicted pKBHX values presented so far in this study were for structurally prototypical compounds and, in this section, we show how Vmin calculations can be applied to molecular structures of the complexity that medicinal chemists typically encounter. HB basicity can often be assessed by consulting compilations33,34 of measured values just as the pKa for an ionizable center in a complex molecular structure can be estimated from the value measured for a structural prototype (e.g., morpholine). However, compilations of measured values are less useful if substitution patterns are complex or HB acceptors are part of an extended π-system. Predicted pKBHX values are presented for five structurally related phosphatidylinositol 3-kinase inhibitors63 in Figure 5. The nitrogen atoms in the benzotriazole and pyrazine rings are predicted to be relatively weak HB acceptors. This reflects the tendency of aza-substitution to weaken HB basicity for

The naphthyridines provide another illustration of how predicted HB basicity can be used to profile heterocycles. One would expect aza-substitution of one ring in a fused heterocyclic system to lead to a reduction in the HB basicity of nitrogen in the other ring, and predicted pKBHX values for five of the isomers are indeed 0.3−0.7 unit lower than the measured values for quinoline (1.89)33 and isoquinoline (1.94).33 The predicted pKBHX (2.5) for the nitrogen atoms of 27 suggests that the HB basicity of this compound will approach that of 4dimethylaminopyridine (pKBHX = 2.80),33 even though it is less basic (pKa = 3.39)80 than pyridine. In this system, the effects of through-space interactions between the HB acceptors of 27 outweigh the effects of through-bond interactions. As noted in the Introduction, molecular structures that can present arrangements of hydrogen-bonding groups that cannot easily be mimicked by clusters of water molecules are of potential interest in drug design. For example, we might conjecture that it would be difficult for a cluster of water molecules to mimic the adjacent, aligned HB acceptors of pyridazine, 21 or 27, especially if an additional restriction that HB donors be absent is also imposed. This line of thinking can be explored in a number of ways. First, one might use these structures as docking probes81 to test complementarity with 4284



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than amide-like. The HB basicity predictions suggest that each carbonyl oxygen atom is associated with two HB acceptor sites. When considering the crystal packing of theophylline, it is important to note that using one acceptor site of a carbonyl oxygen atom will weaken the HB basicity of the other site, and Vmin has been used to examine this effect.29 Alternatively, one might focus on the HB donor/acceptor imbalance in the molecular structure of theophylline and the likelihood that the HB acceptors, although relatively weak, are of comparable strength. Neither of these factors is addressed specifically by Etter’s rules,9 and one might conjecture that either factor could influence the tendency for a compound to crystallize in multiple polymorphic forms.

individual acceptors as well as the likely presence of an intramolecular hydrogen bond between the amino group and N2 of the benzotriazole ring. The effects on lipophilicity of modulating HB basicity of the nitrogen atoms in the nonfused, five-membered ring can be observed, and the log D7.4 measured for 33 (imidazole) is 0.5 unit lower than for 31 (pyrazole). While aza-substitution of 30 to give 32 leads to a marginal increase in lipophilicity, 34, the aza-derivative of 31 is 0.9 unit less lipophilic than the parent compound. The effects of these aza-substitutions on inhibition of PIK3α reflect predicted pKBHX, and the relevant changes in pIC50 are [30 → 32] (ΔpIC50 = −0.1) and [31 → 34] (ΔpIC50 = −0.6). In contrast, inhibitory activity against KDR is more sensitive to aza substitution, and the corresponding changes in pIC50 are [30 → 32] (ΔpIC50 = −0.9) and [31 → 34] (ΔpIC50 = −2.0) for this enzyme.63 The amide carbonyl oxygen atom is predicted to be the strongest HB acceptor for each of five compounds. The values of pKBHX predicted for 30 and 32 indicate an interaction between amide and a nitrogen atom of the heteroaromatic substituent at C4 of the piperidine since the corresponding pKBHX predictions are greater for 30, 32, and 33. There is precedent for interactions like this in that C4-substitution of a piperidine with fluorine leads to a decrease in pKa of 1.9.85 Solid-state chemistry86 of active pharmaceutical ingredients is an important determinant of solubility and dissolution rate, and the existence of polymorphs can complicate development, and even manufacture, of drugs.87 Hydrogen bonding in the solid state is the focus of Etter’s rules,9 the first of which states that “all good proton donors and acceptors are used in hydrogen bonding”. A recent study88 of polymorphism of theophylline prompted the question as to how predicted HB basicity and acidity might provide insight into molecular interactions in the solid state. One assumption made in the study was that the strongest acceptor in theophylline is N9, although HB basicity predictions (Figure 6) suggest that it will actually be a weaker acceptor than either of the carbonyl oxygen atoms. None of the HB acceptors of theophylline are likely to be especially strong indicating that the rings are mutually electron-withdrawing. The pKBHX value (0.5) predicted for of N9 is comparable with the statistically corrected value (0.38)33 measured for 1,3,5-triazine, and the carbonyl groups are predicted to be ketone-like rather

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CONCLUSION We have evaluated Vmin as a predictor of pKBHX across a range of HB acceptor types and used the models to make predictions when measured values are unavailable as is the case for acceptor types such as fluorine bonded to aromatic carbon. We have demonstrated that pKBHX predictions can provide insight into bioisosteric relationships, and the curious case of the isomeric oxadiazoles prompts questions about the value of categorizing atoms and molecular surface as either polar or nonpolar in practical lead optimization. We have shown how that throughspace interactions can be harnessed to increase HB basicity independently of proton basicity and have suggested that certain arrangements of HB acceptors and donors may be “privileged” in the sense that their interaction potential cannot be easily reproduced by clusters of water molecules. We hope to have illustrated how consideration of HB basicity can help medicinal chemists gain a deeper understanding of the properties of the compounds that they seek to optimize.

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COMPUTATIONAL DETAILS

Measured values of pKHXB and were taken from the literature and corrected statistically for the presence in the molecular structure of more than one equivalent acceptor. This data set is provided as Supporting Information, which includes a link to the literature reference for each compound. Molecular structures were encoded as isomeric SMILES,89,90 and a single conformation was generated for each using Omega91,92 and energy-minimized with Szybki93 using the MMFF94S94 force field. Quantum mechanical calculations were performed with Gaussian 09 95 using Hartree−Fock 96 (HF), B3LYP,97,98 M06,99 and MP296,100,101 theoretical models with 631G** and 6-311+G** basis sets.102−105 Dimethylselenoxide and triethylarsine oxide were incompatible with the Omega/Szybki protocol and were energy-minimized at the HF/6‑31G** level using Gaussian 09.95 Coordinates for starting points for MEP minimization were calculated using ADD_CENTRE that was created using the OEChem106 programming toolkit. This software is described in greater detail in the Supporting Information, and source code is also provided. All data analysis was performed using the JMP107 statistical analysis software, and nonlinear fitting was performed according to eq 4, in which V1, V2, and V3 are Vmin values associated with the HB acceptor atom of interest.

pK BHX = A + log10(10 BV1 + 10 BV2 + 10 BV3) Figure 6. Predicted pKBHX values for hydrogen bond acceptor sites of theophylline. Measured33 pKBHX values for reference: 1,3,5-triazine, 0.38 (statistically corrected); isoxazole, 0.81; pyridine, 1.8; Nmethylimidazole, 2.72; propanone, 0.88 (statistically corrected for number of HB acceptor sites); N,N-dimethylacetamide, 2.44 (no statistical correction for number of HB acceptor sites).

(4)

In cases where fewer than three MEP minima were located, dummy minima were created by assigning a value of 1 hartree/elemental charge to V3 and, if necessary, also to V2. Additional details are provided in the Supporting Information. Predictions for pKBHX shown in Figure 2 were made using MP2/6‑311+G** Vmin values, and those in Figures 3, 4, 5, and 6 were made using HF/6‑31G** Vmin values. 4285



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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jmedchem.5b01946. Detailed descriptions of the nonlinear regression, the G09 setup, and the ADD_CENTRE software (PDF) Data used to build the pKBHX models (CSV) Isomeric SMILES strings for molecular structures (CSV) Summary statistics for the full set of pKBHX models (CSV) Source code for the ADD_CENTRE software (TXT)

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AUTHOR INFORMATION

Corresponding Author

* E-mail: [email protected]. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Fundacão de Amparo a Pesquisa do Estado de São Paulo (FAPESP) through the granting award no. 2013/18009-4 for funding to carry out this work. I.M.P., J.F.R.R., and G.R.S. thank FAPESP for scholarships. We are grateful to OpenEye Scientific Software for providing an academic license for software and the three reviewers of the manuscript for their constructive and insightful comments.

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ABBREVIATIONS USED B3LYP, Becke three-parameter exchange functional with Lee− Yang−Parr correlation functional; HF, Hartree−Fock; HB, hydrogen bond; M06, Minnesota 06 functional; MEP, molecular electrostatic potential; MP2, second-order Møller− Plesset perturbation theory; RMSE, root-mean-square error; Vα(r), value of molecular electrostatic potential at distance r from hydrogen on extension of covalent bond to hydrogen; Vmin, value of molecular electrostatic potential at local minimum

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Hydrogen Bond Basicity Prediction for Medicinal Chemistry Design

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