Kernel Functions for Attributed Molecular Graphs – A New Similarity‐Based Approach to ADME Prediction in Classification and Regression

Abstract

Kernel methods, like the well-known Support Vector Machine (SVM), have received growing attention in recent years for designing QSAR models that have a high predictive strength. One of the key concepts of SVMs is the usage of a so-called kernel function, which can be thought of as a special similarity measure. In this paper we consider kernels for molecular structures, which are based on a graph representation of chemical compounds. The similarity score is calculated by computing an optimal assignment of the atoms from one molecule to those of another one, including information on specific chemical properties, membership to a substructure (e.g., aromatic ring, carbonyl group, etc.) and neighborhood for each atom. We show that by using this kernel we can achieve a generalization performance comparable to a classical model with a few descriptors, which are a-priori known to be relevant for the problem, and significantly better results than with and without performing an automatic descriptor selection. For this purpose we investigate ADME classification and regression datasets for predicting bioavailability (Yoshida), Human Intestinal Absorption (HIA), Blood-Brain-Barrier (BBB) penetration and a dataset consisting of four different inhibitor classes (SOL). We further explore the effect of combining our kernel with a problem-dependent descriptor set. We also demonstrate the usefulness of an extension of our method to a reduced graph representation of molecules, in which certain structural features, like, e.g., rings, donors or acceptors, are represented as a single node in the molecular graph.

Genetic programming for human oral bioavailability of drugs

“…Genetic Algorithms were used to select the best molecular descriptors, and Self Organizing Maps (SOMs) were used to collocate the molecule in a bioavailability class. Fröhlich and Wegner recently experimented the use of Kernel methods (SVM) for assessing the problem of bioavailability predictions, basing their approach on the estimation of similarity between different molecules with similar biological behavior [8]. Various kinds of multivariate and Partial Least Square (PLS) regressions, also coupled with recursive partition [2], have been used to give an estimation of oral bioavailability.…”

Chemical Compound Classification With Automatically Mined Structure Patterns

“…The optimal assignment kernel, described by Frölich et al 4 , differs significantly from the marginalized graph kernel. This kernel function first computes the similarity between all vertices in one graph and all vertices in another.…”

“…The edge weights are calculated via a recursive vertex similarity function. We present the equations describing this algorithm in detail, as discussed by Frölich et al 4 . The top-level equation describing the similarity of two molecular graphs is: (1) Where π denotes a permutation of a subset of graph vertices, and m is the number of vertices in the smaller graph.…”

“…The l parameter controls the topological distance within which to consider neighbors of vertices. The R l equation, which recursively computes the similarity between two specific vertices is given by the following equation: (4) Where |v| is the number of neighbors of vertex v, and n k (v) is the set of neighbors of v. The base case for this equation is R 0 , defined by:…”

Two-step hierarchical assignments on molecular graphs

“…The Optimal Assignment Kernel (OAK) [1] is a successful similarity measure, although it is not a valid kernel, since the function is not positive definite [2]. Careful investigations of the assignment on the atom level disclose that the optimal assignment with the Hungarian algorithm may result in topological errors.…”