Modeling Biological Activities of Chemical Compounds: Kernel Methods for Structure Activity Relationship

The function of enzymes as well as the function of proteins involved in regulatory pathways often implies interactions with small chemical compounds. To understand the function of these proteins as well as for applications such as predicting activity or adverse effects of potential drugs we try here to compute the similarity between chemical compounds using a new similarity function based on the 2D structure of chemical compounds. Small chemical compounds can be represented as undirected labeled graphs (2D structures). Although not perfect, this model representation of molecules has been shown to be related to the biological activity of chemical compounds[3]. Traditionally molecular similarity was computed in two different ways. One way is to find maximal of frequent common subgraphs[1]. This approached generally suffer from its computational complexity. Another approach was to transform graphs into vectors of molecular descriptors and then compare these vectors. This requires the expert choice of adequate molecular descriptors[3]. Here we explore another way to compare chemical compounds using the recently published kernel function for graphs by Kashima et al.[2]. This algorithm allows the direct computation of a similarity value between two graphs as a weighted sum of all common paths (sequences of atoms and bonds) in the two graphs. The path weights are choosen given a random walk probability model on a graph representation of molecules were undirected bonds are replaced by bidirectional edges. The kernel does not require an explicit vectorial representation of molecules. Kernel functions are particularly interesting because they allow the direct computation of multivariate statistical methods like kernel principal component analysis (KPCA), and support vector machines (SVM) on the similarity matrices. Here we apply the graph kernel to two chemoinformatic tasks. Supervised learning for predicting an adverse effect of chemical compounds, and unsupervised learning for compound classification.