The role of binding thermodynamics in medicinal chemistry optimizations

Background: Ligand binding thermodynamics has been attracted considerable interest in the past decade owing to the recognized relation between binding thermodynamic profile and the physicochemical and druglike properties of compounds. Discussion: • Affinity improvements in drug discovery optimizations can be either enthalpically or entropically driven. In this review the relation between optimization strategies and ligand properties are presented based on the structural and thermodynamic analysis of ligand-protein complex formation. Conclusions: The control of the binding thermodynamic profile is beneficial for the balanced affinity and physicochemical properties of drug candidates and early phase optimization gives more opportunity to this control. Drug discovery optimizations and molecular obesity The objective of drug discovery projects at the preclinical stage is to find compounds with balanced properties that include high affinity towards the target, sufficient specificity and selectivity and advantageous physicochemical and pharmacokinetic profile. The evolution of the chemical starting point to a clinical candidate is a result of a multiparametric optimization process. While increasing the binding affinity is of primary importance in early optimizations the monitoring and improvement of other druglike properties are also part of the optimization process from the outset and they become even dominant with the advance of the optimization. It is well documented [1,2,3] that affinity improvement tends to increase molecular size and lipophilicity, leading to large, hydrophobic compounds, a phenomenon called molecular obesity [4,5]. This type of compound has a greater chance being promiscuous [2,6,7], having low solubility and suboptimal ADMET properties [8]. Therefore, it is of utmost importance to understand the relationship among the various properties to be optimized simultaneously and it has been increasingly recognized that binding thermodynamics (Box 1) may serve as a link among these properties. In addition to its obvious relationship to binding affinity binding thermodynamics impacts other important druglike parameters such as the physicochemical profile, binding selectivity, specificity and promiscuity. It has been demonstrated that enthalpic compunds have typically better profile of physicochemical parameters than that of the high entropy compounds [9]. Freire and coworkers showed that enthalpic compounds have higher chance being selective against off-targets [10]. Compounds binding their targets with higher entropy contributions tend to hit more off-targets compared to those ligands that had enthalpically-driven thermodynamics profile [11]. Thermodynamic investigations might therefore help both in the understanding of interconnecting relations between molecular properties and also in controlling them. Affinity optimization is typically realized by introducing new atoms in the molecule. This process is validated by the observation that the available maximal affinity of ligands toward protein targets increases with increasing ligand size as it was first observed by Kuntz et al. [12] and later for a larger data set by Reynolds et al. [13]. The same trend was also identified using affinities from thermodynamic measurements [14]. This already indicates that care has to be taken in affinity improvements in order to avoid excessive size and lipophilicity increase. At this point, it is appropriate to analyze ligand-protein interactions and the process of complex formation to understand the detailed relationship between ligand size and affinity. Ligand-protein binding is a complex, multistep process that includes the desolvation of the partners, their conformational change and the formation of new interactions between them. An important component of the process is the reorganization of water networks as a consequence of the release of water molecules from the solvation shells of the binding partners. All these steps contribute to the enthalpy and entropy changes that accompany binding and both contributions are affected by the structure of the ligand and the way it binds to the protein. The increasing amount of structural and thermodynamic data makes it possible to analyze how the interactions and the thermodynamic profile depend on various quantities like ligand size, lipophilicity and affinity. This, in turn, allows us better understanding of the evolution of these latter quantities in the course of optimization.  Size-dependence of ligand-protein interactions The interaction of fitting polar groups of the ligand and the protein is potentially highly beneficial and can significantly contribute to the binding free-energy primarily by enthalpic gain [15]. The formation of polar interactions, however, is accompanied by unfavorable contributions that come from the desolvation of the polar groups and the decreased mobility of the interacting moieties. These predominantly entropic unfavorable contributions can only be compensated by the enthalpy gain of polar interactions if the geometrical arrangement of atoms is near to optimal. H-bonds are probably the most important polar interactions and their energy is highly sensitive to the relative positions of the participating atoms. An analysis of the optimal geometry H-bonds (donor-acceptor distance not larger than 3 Å and D-H...A angle is not smaller than 160 °) in ligand-protein complexes of the Protein Data Bank [16] revealed [17] that the average number of such H-bonds is around two even for small molecules having ~15 heavy atoms and the average number does not increase significantly with increasing ligand size. The appearance of optimal geometry H-bonds in complexes of small molecules is in line with the high free-energy gain associated with these H-bonds. Their number, however, does not increase for larger ligands and this finding can be rationalized by the high sensitivity of the Hbonding energy to the geometry of the interacting atoms that prevents the formation of further optimal geometry H-bonds that could beneficially contribute to the binding free-energy. Larger molecules, however, are able to bind with larger free-energy gain as it was discussed above, thus they have to find another way to achieve high affinity. Apolar desolvation appears to be able to contribute favorably to the binding of large molecules. Indeed, correlation was found between the apolar surface area buried upon complex formation and the binding free-energy [18], and their relation suggests 1 kJ/mol free-energy gain upon the burial of 20 Å. The apolar surface area and the corresponding estimated binding free-energy was calculated for ligands in the Protein Data Bank and they are depicted as a function of heavy atom count in Figure 1. The amount of free-energy coming from apolar desolvation for a molecule of 20 heavy atoms is at most 15 kJ/mol according to Figure 1 and it corresponds to the lower limit of the estimated entropy loss upon binding [19]. This suggests that apolar desolvation alone is unable to ensure the binding of small molecules. However, it becomes increasingly important as molecular size increases. Since polar interactions are unable to increase their favorable contribution to binding (see above) it is apolar desolvation that becomes the driving force of ligand-protein binding in the case of large ligands.  Size-dependence of ligand-protein binding thermodynamics As it was discussed above, polar interactions are able to contribute to binding primarily by enthalpic gain while the contribution of apolar desolvation is dominantly entropic. Then the involvement of these effects in the formation of ligand-protein complexes has to be reflected in the thermodynamic profile of the binding. Plotting the average enthalpic and entropic contributions to binding free energy as a function of ligand size (Figure 2) shows the expected trend. Enthalpy dominates for smaller ligands [14,20] in line with the importance of polar interactions for these molecules and entropy becomes dominant for large molecules as a consequence of the increased contribution of apolar desolvation. The desolvation contribution to binding is related to the surface area as it is supported by the correlation between buried apolar surface area and the binding free-energy [18] and also by a model that includes apolar surface area to calculate binding enthalpy [21]. Detailed thermodynamic and structural analyses of the water network and its perturbation by ligands can distinguish water molecules whose repulsion from the binding site is favorable or unfavorable in terms of their contribution to binding free energy and its components [22,23,24,25,26]. Although an assignment of free-energy and its components to water molecules is an approximation it contributes to our understanding of the role of water in ligand binding. It appears that the enthalpic component of water repulsion can be both favorable and unfavorable while the entropic component is basically favorable [26,27,28]. This finding is in agreement with the increasing role of entropy gain for larger ligands. The trend of decreasing enthalpic contribution with increasing ligand size is also observed for the highest affinity compounds. While available affinity increases with ligand size the corresponding enthalpic contribution diminishes for large ligands as it is shown in Figure 3. This plot was generated by assigning the compounds to bins defined by heavy atom counts and the highest pKd is shown for each bin together with the maximal pKH of those compounds of the bin whose affinity is in the top 5% (most enthalpic binders among the top affinity compounds). It appears that small size high affinity compounds are able to bind with favorable enthalpy while the contribution of enthalpy diminishes with increasing ligand size. Large ligands are able to bind with higher affinity by higher entropic contribution. Optimization strategies and binding thermodynamics The basic challenge in affinity improvement from thermodynamics point of view is to overwrite enthalpy-entropy compensation [29]. Optimizations can then be classified as enthalpically and entropically driven; enthalpically driven optimizations achieve this goal by dominantly pKH increase, while pKS increase dominates in entropically driven optimizations. Since pKH can be improved by the introduction of new polar interactions, enthalpically driven optimizations have the advantage to produce improved affinity compounds with balanced physicochemical properties and advantageous pharmacokinetic profile. However, designing new beneficial polar interactions is difficult that makes enthalpically driven optimization challenging [15]. By contrast, entropically driven optimizations increase affinity by improving pKS. This can be achieved by introducing apolar groups into the ligand so that they match the protein binding site and thus primarily increasing favorable entropy by desolvation. Another way to increase pKS is to reduce ligand flexibility typically achieved by applying chain-ring strategies leading to larger, more complex molecules. Both lipophilicity and complexity increase is generally more straightforward than the design of new beneficial polar interactions and thus entropically driven optimizations are easier to realize. However, entropy dominated optimizations are coupled with extensive increase in molecular size and lipophilicity as it is shown by the comparison of these parameters for enthalpy and entropy dominated binders [14,9] and these features adversely affect physicochemical properties and pharmacokinetic profiles (see e.g. refs 1 and 3). Enthalpically driven optimization is preferred over entropically driven optimization, although, as argued above, it is far more difficult to pursue. Moreover, enthalpically driven optimization appears to be more feasible for smaller compounds as it is shown in Figure 2 and Figure 3. This suggests that increasing the enthalpy content of binding is effective in the early stages of the optimization and furthermore that enthalpic starting points are beneficial. Measuring and comparing the binding enthalpy of ligands at decision points like hit and lead selection and monitoring the enthalpy in early optimizations is expected to advantageously affect the quality of optimized compounds. Late stage optimizations often improve potency at the expense of increased binding entropy and tend to produce more complex and more lipophilic compounds. This is illustrated in Figure 4 that shows the average binding enthalpy and entropy as a function of affinity. Low affinity compounds bind enthalpically and the entropic contribution on average is near to zero. The majority of these low affinity compounds are fragments containing not more than 22 heavy atoms and these small polar compounds bind enthalpically as it is discussed later. On the other hand, the thermodynamic profile above pKd=8 starts to be seriously biased towards entropy and this suggests that affinity increase in that range threaten the quality of physicochemical properties and pharmacokinetic profile.  Thermodynamic rationale of fragment based approaches The chemical starting points of fragment-based drug discovery programs are small, low complexity, polar compounds with typically low affinity. Owing to their low affinity, compounds have to be screened at high concentration that requires high solubility. In line with their small size and polarity that allows fragments to form few, good quality polar interactions without significant contribution from apolar desolvation fragment hits typically bind with favorable enthalpy [17,30,31,32,33,34,35] (Figure 5). The few compounds in Figure 5 that bind with unfavorable enthalpy are all anionic species with highly unfavourable desolvation profile. Another factor that affects binding thermodynamics is the rigid body entropy loss that is estimated to be 15-20 kJ/mol [19] and fragments are able to compensate this entropy loss at a lesser extent than larger compounds. It is worth also noting that the perturbation of the water network upon binding although associated with significant contribution to binding thermodynamics [36,37] is less important for fragments than for larger size ligands. Summarizing, fragments have a binding thermodynamic profile characterized by enthalpy domination and this, first, distinguishes them from larger ligands and, second, forms the thermodynamic rationale of fragment based approaches. Fragments are highly appropriate starting points of drug discovery programs as they have already important polar interactions formed with the hot spot of the protein [17] and due to their enthalpic character provide large operational freedom for a balanced optimization. Ligand efficiency indices and binding thermodynamics  Ligand efficiency and enthalpic efficiency Drug discovery optimizations face the challenge of simultaneously improving affinity, selectivity, physicochemical properties and pharmacokinetic profile. Both decision points like hit and lead selection and the optimization process require the complex characterization of compounds in order to compare them. Ligand efficiency indices are appropriate tools for such characterizations since they are composite measures that carry complex information, yet they can be easily obtained. Various efficiency indices have been proposed (Table 1) some of them are more widely accepted and used than others [38,39,40].The most widely used index is ligand efficiency (LE) that expresses the ratio of affinity and ligand size. It was originally defined as [41] although pKd, pKI and pIC50 are often used instead of G (Table 1). It has to be recognized that although LE is the affinity normalized to the number of atoms, its maximal available value does depend on ligand size [13] and this fact biases the comparison of different size ligands. This recognition led to the definition of size-independent ligand efficiency, , whose maximum available value is independent of ligand size [43]. Indeed, it was demonstrated [44] that LE does not exhibit a clear trend in optimizations, while SILE shows a significant increase in successful optimizations and thus it is an effective tool in hit and lead selection and also in monitoring optimizations. The enthalpy content of binding contains information about the type and quality of ligand-protein interaction and this prompted the definition of enthalpic efficiency , where Q is either the number of heavy atoms or the molecular mass [30,45]. An alternative index is specific that measures the enthalpy change relative to the number of polar atoms [30]. The maximal available value of both enthalpic efficiency and specific enthalpic efficiency heavily depend on ligand size and a size-independent version, , was defined [14] for the unbiased comparison of the binding enthalpy content of different sized ligands. Although the available enthalpy may be target dependent it does not affect compound comparison based on SIHE values against the same target as it is typically required in drug discovery optimizations. However, the maximal available binding enthalpy does not change monotonically with ligand size (Supplementary Figure S1) and therefore neither EE nor SIHE is appropriate to compare very small compounds against those having more than 15 heavy atoms. It has to be also noted that a division by the number of heavy atoms have a damping effect and thus both LE and EE cover a decreasing range with increasing heavy atom count. This has the consequence that LE and EE contain less information for large compounds, but size-independent measures, like SILE and SIHE, do not suffer from this deficiency as their definition ensures ligand size independent maximal values (Supplementary Figure S2). This difference between the size dependent and size independent measures is apparent already around the fragment limit of 22 heavy atoms. The calculation of ligand efficiency requires the knowledge of affinity, and the calculation of enthalpic efficiency requires the knowledge of enthalpy. While affinity measurements are part of the standard drug discovery setup thermodynamic measurements are less common and this currently restricts the use of enthalpic indices. It is worth also noting that the decreasing trend of maximal available ligand efficiency (Supplementary Figure S2c) resembles to the trend observed for enthalpic efficiency. The maximal available enthalpy decreases with ligand size [17] and so does the maximal enthalpic efficiency [20]. Since this decrease is not fully compensated by an entropic efficiency increase the maximal available ligand efficiency decreases.  Lipophilic efficiency Lipophicity is an important property of ligands as it affects affinity, selectivity and ADMET properties. Lipophilicity tends to increase in entropically driven drug discovery optimizations and its thermodynamic background was discussed above. Selectivity and specificity typically decrease with increasing lipophilicity [2], while the relationship between lipophilicity and ADMET properties is more complex. Less lipophilic compounds tend be more soluble [46], less impacted by liver metabolism and hepatic clearance [47], and less toxic [48]. On the other hand, however, they show low permeability across biological membranes [49] and highly affected by renal clearance [50]. These observations suggest that lipophilicity has an optimal range to achieve during drug discovery optimizations and this is also supported by the analysis of discovery datasets that identified optimal lipophilicity ranges for oral drugs between 0.8 and 3.2 logP units [51] and between 2 and 3.2 logP units [9]. The narrow range of optimal lipophilicity has serious consequences on both the identification of chemical starting points and on their optimization. Lipophilic indices are designed to control the balance with respect to the lipophilicity and other properties like affinity and size. Definitions of commonly used lipophilic indices are shown in Table 1. Ligand lipophilicity efficiency (LLE), historically the first lipophilic index, was proposed to have target values ~5-7 or larger [2]. These values were recommended on the basis of the clogP~2.5 and potency range~1-10 nM taken as average values for oral drugs. Compounds at hit identification and early optimizations typically do not achieve this LLE range and other lipophilic indices that also include ligand size were proposed. Lipophilicity corrected ligand efficiency (LELP) [1] describes the price of ligand efficiency paid in logP. The target values for LELP were proposed to be between -10 and +10 based on the widely accepted lower limit of ligand efficiency (0.3), and on the lipophilicity range between –3 and +3. LLEAT was proposed to characterize small screening hits, like fragments and it is defined to have a target value (0.3) and dynamic range similar to ligand efficiency (LE) [52]. Lipophilic indices are obtained from calculated logP values, measured affinities and, eventually, measures of ligand size. They do not explicitly include thermodynamic quantities but logP that characterizes lipophilicity is related to the entropic contribution of apolar desolvation upon ligandprotein complex formation, the latter correlating with the apolar surface area buried in the complex [18] (see above). In this respect, lipophilic indices and enthalpic indices are expected to contain overlapping information, the former having the advantage that they can be obtained without thermodynamic measurements. Establishing a relationship between efficiency indices and binding enthalpy would support enthalpic optimization by easily calculated indices. LLE and binding enthalpy was shown to exhibit some association [53] although the relationship observed appear to be system specific and semi-quantitative in the majority of the cases studied. Our experience with multiple LLEH datasets suggests that the correlation is much improved for congeneric compound series. The extent and utility of the relationship between LLE and binding enthalpy merit further studies. Table 2 presents ligand property changes of different types of medicinal chemistry optimizations. Data for successful fragment optimizations leading to clinical candidates and successful lead optimizations leading to marketed drugs are shown together with data of optimizations performed under thermodynamic control. It is instructive to see that thermodynamic optimizations are able to improve potency with a modest increase in molecular size without notable change in logP and this is reflected in an almost constant LELP and an improving LLE. In this way, thermodynamic optimizations produce average property changes that resemble to successful optimizations. Optimization case studies