The discovery of new molecular entities with particular desired properties is the key objective of much of chemistry research. Finding such lead molecules can be highly difficult, even with the assistance of combinatorial chemistry and high-throughput screening given the enormous number of potential small molecule structures. If a single molecular scaffold has N substituent sites with S distinct functional groups, the total number of possible compounds is S^N. A common practice is to employ quantitative structure-activity relationship (QSAR) methods [1] to computationally predict the biological properties of the library compounds. Existing methods for constructing predictive QSAR models involve three basic steps: (1) assaying the properties of a training set of molecules, (2) selection of physical/chemical descriptors to relate the small molecule structures to the measured properties, (3) identification of mathematical functions that quantitatively relate the molecular descriptor to the properties.

We introduce a new strategy to enable efficient substituent reordering and descriptor-free property estimation. This approach casts substituent reordering as a special high-dimensional rearrangement clustering problem, eliminating the need for functional approximation and enhancing computational efficiency. We first introduce an objective function that provides a measure of the smoothness of the compound property space. Three methods have been developed to identify the best substituent orderings given this measure. Deterministic optimization approaches based on mixed-integer linear programming can provide guaranteed convergence to the optimal substituent ordering. The application of a genetic algorithm, a stochastic optimization approach, provides good quality solutions which are frequently close to the optimal solution. Heuristic approaches, such as random row and column swapping, have the potential to quickly identify good solutions to this problem. For problems with certain structure, the problem can be formulated with an ordering independent function and addressed by sorting algorithms.

These methods are applied to a sparsely sampled data set of inhibition values of unknown compounds provided by Pfizer Inc. The overall goal is to identify the most compounds with the highest inhibition. The utility of the approach can be evaluated by randomly selecting a subset of the compound library values, identifying the best substituent ordering, and applying a local interpolation based synthesis strategy to create expected property values. A significant percent of the top 50 unsampled compounds, sorted by their expected property values, exhibit high inhibition values. This method identified 12 (24%) compounds that provide greater than 90% inhibition and 20 (40%) compounds that yield greater than 80% inhibition. The prediction represents a significant enrichment beyond the random selection of unsampled compounds above 90% inhibition (1%) and above 80% inhibition (2.8%).

[1] R. Perkins, H. Fang, W. Tong, and W. Welsh. Quantitative structure-activity relationship methods: Perspectives on drug discovery and toxicology. Environ Toxicol and Chem, 22:1666-1679, 2003.

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