Chemical structure modeling with kernel methods

Small molecules that have the ability to alter the biological response of a cell or disease state are of significant interest as drug candidates. One approach to the design of such molecules using kernel methods is through a map of molecules to a feature space induced by a kernel, where the predictions of the molecular properties are made in a linear manner. The forward mapping helps guide the synthesis of new molecules. Another more direct approach is to solve the so-called pre-image problem, i.e., to reconstruct a corresponding molecule (aka pre-image) from its feature space representation. The inverse mapping is of central importance for the design of new molecules with desired properties. In this thesis, we address two problems in drug design: (I) the forward problem of predicting molecular properties, where we propose a new graph kernel that induces a feature space amenable to the prediction of molecular properties, and (II) the inverse problem of designing new molecules that possess properties required for drug candidates, where we develop a population-based Monte Carlo method to solve the pre-image problem for the molecules. Our respective contributions to these problems are summarized as: (I) Forward problem of predicting molecular properties The measurement of molecular similarity is an essential part of predicting molecular properties. Graph kernels provide good similarity measures between molecules. A conventional graph kernel is based on counting common subgraphs of a specific type in molecular graphs. This approach suffers from two primary limitations: (i) only exact subgraph matching is ii considered in the counting operation, and (ii) most of the subgraphs will be less relevant to a given task. In order to address these limitations, we propose a new graph kernel as an extension of the subtree kernel initially proposed by Ramon and Gartner (2003). The proposed kernel tolerates an inexact match between subgraphs by allowing matching between atoms with similar local environments. In addition, the proposed kernel provides a method to assign an importance weight to each subgraph according to the relevance to the task, which is predetermined by a statistical test. These extensions lead to promising improvements in classification and regression tasks for predicting a wide range of pharmaceutical properties from the chemical structure of molecules. (II) Inverse problem of designing new molecules The de novo design of new molecules that yield desired properties has the potential to substantially reduce both the time and cost involved in drug development. Recent developments in graph kernels have enabled us to apply well-established machine learning techniques to molecular data which are internally represented as graphs. However, in order to allow for the design that generates new molecules as a result, it is necessary to solve the pre-image problem for molecules. Unlike the traditional method proposed in Bakir et al. (2004), which is formulated as a nonlinear combinatorial optimization problem, we express the pre-image problem as a sampling problem for molecular graphs. Here, we are not only interested in optimal molecules, but also in near-optimal molecules which are often considered to be good candidates for further chemical synthesis. Therefore, we develop a population-based Monte Carlo method for sampling structurally diversified molecules near the pre-images, which possess good drug-likeness. The key to an efficient sampling method is to use the update of a population by evolutionary operators for the structural alteration of molecules. Furthermore, to penalize non-drug-like molecules, we use the knowledge of drug-likeness commonly considered by medicinal chemists. The effectiveness of the proposed method is iii illustrated through experiments to find corresponding molecules from given image points in a feature space induced by a graph kernel.