In our initial paper reporting the Surflex QMOD (Quantitative MODeling) method for ligand-based binding affinity prediction, we showed accurate scaffold-independent affinity predictions on a particularly challenging structure-activity data set [1
]. Using just 20 ligands of two relatively rigid scaffolds, accurate predictions were made on 35 molecules from related series as well as on 17 compounds of widely varying structural types. This was done by construction of a physical binding site made up of molecular fragments (a “pocketmol”) such that the maximally active pose of each training ligand (measured using the Surflex-Dock scoring function) yielded a score close to the experimental pKd
. New molecules were flexibly fit into the pocket, and the maximal score was the predicted pKd
, with the corresponding pose being the prediction of binding mode.
illustrates the process on a set of CDK2 inhibitors in a recently published modeling study [2
]. The process begins with structures and activities, develops a rough hypothesis for relative alignments of ligands (many per ligand), generates a diverse set of possible binding pocket fragments, and finally selects and refines a set of optimal fragments. Optimality describes both the fit of the model to binding activity data as well as the fit of ligands into the model: the model itself defines the preferred binding modes of the ligands. Building such models requires a method for model derivation where the objects to be modeled have multiple possible instantiations and where choice among these is dependent on the evolving model. The Compass method was the first to make an iterative refinement paradigm that addressed this problem [3
], and a formalization of this early work, termed multiple-instance learning [6
], has found applications in many areas of machine learning. We have also used it in scoring function development for molecular docking [7
FIGURE 1 Derivation of a pocketmol. Panel A: A 3D similarity-based alignment hypothesis of active ligands. B: Each training ligand is aligned to the hypothesis, resulting in 100–200 initial poses. C: Each training ligand has many poses, resulting in uncertainty (more ...)
There were four chief limitations of the initial QMOD approach. First, results for only a single target were shown, albeit a challenging one. Second, the computational approach to identifying pocket probe subsets (step E from ), was somewhat brittle, and, more importantly, required specification of a single preferred pose for each training ligand rather than choosing automatically from among the pool of many that exist for each ligand. Third, solutions to the pocket induction problem for a given set of training molecules are numerous, but we did not present a general method for model selection. Fourth, while we showed the relationship of our induced physical model to a modeled structure of 5HT1a, we were unable to make a direct comparison to a specific and relevant experimentally determined crystal structure of the target. This paper addresses all of these limitations as well as examining the theoretical basis for the superiority of physically sensible models over purely empirical QSAR approaches.
Most QSAR approaches derive a mathematical relationship between molecular descriptors and activity that is only tangentially related to the physical process of ligand binding. The implications of these limitations on model predictivity were highlighted by Johnson [10
], focusing on the logical fallacy of assigning causality to correlated variables. In particular, it was suggested that “Reliable prediction of future compounds requires that the model have some basis in physical reality.” There are two central limitations of most QSAR approaches relating to this issue of physicality. First, most QSAR methods make an implicit assumption that the effects of substituent changes at different positions on the same scaffold will be strictly additive
, which is not physically realistic. Second, many such methods do not depend on a prediction of ligand binding mode, and even for those that do, the “predicted” ligand binding mode does not
generally depend on the model or its parameters, which is also non-physical. All non-3D approaches share the second limitation (since they do not depend on molecular alignment at all), and those that are linear functions of molecular descriptors generally share the first. The most widely used approaches for 3D QSAR (CoMFA and related variants [11
]) have both limitations. Multi-point quantitative pharmacophoric methods can theoretically address both issues [15
], but they lack physically realistic detail in hydrophobic binding pocket shape. In a historical sense, the present work is also related to the pseudoreceptor concept, which addresses aspects of both limitations. This work includes that of Snyder and Rao [16
], further refinements including Vedani [17
], and the work of Zbinden with Vedani on PrGen [18
]. See Tanrikulu and Schneider [19
] for a review and the initial report of the QMOD approach for additional discussion [1
shows that the first assumption is false and illustrates why making ligand poses dependent on models might offer a means to avoid the assumption in the first place. The four muscarinic antagonists shown were synthesized as part of the same effort for developing a treatment for urinary incontinence [20
]. While two single changes from the parent compound yielded improvements over a full log unit in Kd
, the combination of the two changes was worse
than either of the singly substituted compounds. One simple physical explanation, that the pocket is too small to fit the largest of the four compounds easily, is beyond
the explanatory capability of many QSAR methods. This represents an anti
-additive effect. Generalizing this issue further, consider the case of a rigid protein and a ligand whose substituents have minor effects on ligand conformational energetics. The best possible outcome in the case of two separately favored substituents on a common scaffold is that their combined effect is exactly additive in pKd
. However, for this to be true, the two derivative with single substituents must have the same preference for the position of the central scaffold when bound to the protein. In general, this is not to be expected; even small changes in substitution pattern yield some variation in scaffold alignment. Non-additive behavior is a natural and common consequence of the physical interplay between ligand variants and a protein binding site. The ability to model and predict such effects is a natural by-product of the Surflex-QMOD approach, since it constructs a physical binding pocket that is analogous to a protein active site.
FIGURE 2 Four muscarinic antagonists whose activity pattern shows a strong non-additive effect. A change from the furan to 3-phenyl or to the benzofuran yielded a significant improvement in Kd. However, combining the two changes yielded a compound with poorer (more ...)
This paper reports improvements to the QMOD technique and expands the set of validation cases to include a typical QSAR data set and a more challenging one. The former consisted of 80 congeneric CDK2 inhibitors, split between 30 for training and 50 for testing. This set offered the ability to consider the relationship between induced models and experimentally determined protein binding pocket structure. The latter consisted of 25 muscarinic antagonists, split between 22 for training and 3 for testing the highly non-additive structure-activity effect shown in . For the CDK2 set, the primary model showed a mean error of prediction of 0.4 log units (approx. 0.5 kcal/mol), and highly significant rank correlations were obtained (Kendall’s Tau 0.77, p
0.01, by permutation analysis). Of the top 10 predicted test ligands, 7 of the bona fide
top 10 were identified (p
0.01, by exact binomial). One surprising aspect of model-building for CDK2 was that models that were congruent to the active site were not
significantly more predictive than those that were not. However, this was true only for molecules within the chemical series used for model construction. When considering a diverse set of CDK2 inhibitors, the more geometrically accurate model was more predictive. For the muscarinic case, the primary model accurately ranked the potencies of the three substituted furans shown in .
The methods and results presented here by no means represent a “solution” to the 3D QSAR problem. However, the Surflex-QMOD approach can be seen to be both a practical and theoretical improvement upon the status quo in a field built historically upon correlative analysis that has been premised on non-causative observations.