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- Kernel methods for virtual screening (2009)
- We investigate the utility of modern kernel-based machine learning methods for ligand-based virtual screening. In particular, we introduce a new graph kernel based on iterative graph similarity and optimal assignments, apply kernel principle component analysis to projection error-based novelty detection, and discover a new selective agonist of the peroxisome proliferator-activated receptor gamma using Gaussian process regression. Virtual screening, the computational ranking of compounds with respect to a predicted property, is a cheminformatics problem relevant to the hit generation phase of drug development. Its ligand-based variant relies on the similarity principle, which states that (structurally) similar compounds tend to have similar properties. We describe the kernel-based machine learning approach to ligand-based virtual screening; in this, we stress the role of molecular representations, including the (dis)similarity measures defined on them, investigate effects in high-dimensional chemical descriptor spaces and their consequences for similarity-based approaches, review literature recommendations on retrospective virtual screening, and present an example workflow. Graph kernels are formal similarity measures that are defined directly on graphs, such as the annotated molecular structure graph, and correspond to inner products. We review graph kernels, in particular those based on random walks, subgraphs, and optimal vertex assignments. Combining the latter with an iterative graph similarity scheme, we develop the iterative similarity optimal assignment graph kernel, give an iterative algorithm for its computation, prove convergence of the algorithm and the uniqueness of the solution, and provide an upper bound on the number of iterations necessary to achieve a desired precision. In a retrospective virtual screening study, our kernel consistently improved performance over chemical descriptors as well as other optimal assignment graph kernels. Chemical data sets often lie on manifolds of lower dimensionality than the embedding chemical descriptor space. Dimensionality reduction methods try to identify these manifolds, effectively providing descriptive models of the data. For spectral methods based on kernel principle component analysis, the projection error is a quantitative measure of how well new samples are described by such models. This can be used for the identification of compounds structurally dissimilar to the training samples, leading to projection error-based novelty detection for virtual screening using only positive samples. We provide proof of principle by using principle component analysis to learn the concept of fatty acids. The peroxisome proliferator-activated receptor (PPAR) is a nuclear transcription factor that regulates lipid and glucose metabolism, playing a crucial role in the development of type 2 diabetes and dyslipidemia. We establish a Gaussian process regression model for PPAR gamma agonists using a combination of chemical descriptors and the iterative similarity optimal assignment kernel via multiple kernel learning. Screening of a vendor library and subsequent testing of 15 selected compounds in a cell-based transactivation assay resulted in 4 active compounds. One compound, a natural product with cyclobutane scaffold, is a full selective PPAR gamma agonist (EC50 = 10 +/- 0.2 muM, inactive on PPAR alpha and PPAR beta/delta at 10 muM). The study delivered a novel PPAR gamma agonist, de-orphanized a natural bioactive product, and, hints at the natural product origins of pharmacophore patterns in synthetic ligands.

- Molecular similarity for machine learning in drug development : poster presentation (2008)
- Poster presentation In pharmaceutical research and drug development, machine learning methods play an important role in virtual screening and ADME/Tox prediction. For the application of such methods, a formal measure of similarity between molecules is essential. Such a measure, in turn, depends on the underlying molecular representation. Input samples have traditionally been modeled as vectors. Consequently, molecules are represented to machine learning algorithms in a vectorized form using molecular descriptors. While this approach is straightforward, it has its shortcomings. Amongst others, the interpretation of the learned model can be difficult, e.g. when using fingerprints or hashing. Structured representations of the input constitute an alternative to vector based representations, a trend in machine learning over the last years. For molecules, there is a rich choice of such representations. Popular examples include the molecular graph, molecular shape and the electrostatic field. We have developed a molecular similarity measure defined directly on the (annotated) molecular graph, a long-standing established topological model for molecules. It is based on the concepts of optimal atom assignments and iterative graph similarity. In the latter, two atoms are considered similar if their neighbors are similar. This recursive definition leads to a non-linear system of equations. We show how to iteratively solve these equations and give bounds on the computational complexity of the procedure. Advantages of our similarity measure include interpretability (atoms of two molecules are assigned to each other, each pair with a score expressing local similarity; this can be visualized to show similar regions of two molecules and the degree of their similarity) and the possibility to introduce knowledge about the target where available. We retrospectively tested our similarity measure using support vector machines for virtual screening on several pharmaceutical and toxicological datasets, with encouraging results. Prospective studies are under way.

- Kernel learning for ligand-based virtual screening:discovery of a new PPARgamma agonist (2010)
- Poster presentation at 5th German Conference on Cheminformatics: 23. CIC-Workshop Goslar, Germany. 8-10 November 2009 We demonstrate the theoretical and practical application of modern kernel-based machine learning methods to ligand-based virtual screening by successful prospective screening for novel agonists of the peroxisome proliferator-activated receptor gamma (PPARgamma) [1]. PPARgamma is a nuclear receptor involved in lipid and glucose metabolism, and related to type-2 diabetes and dyslipidemia. Applied methods included a graph kernel designed for molecular similarity analysis [2], kernel principle component analysis [3], multiple kernel learning [4], and, Gaussian process regression [5]. In the machine learning approach to ligand-based virtual screening, one uses the similarity principle [6] to identify potentially active compounds based on their similarity to known reference ligands. Kernel-based machine learning [7] uses the "kernel trick", a systematic approach to the derivation of non-linear versions of linear algorithms like separating hyperplanes and regression. Prerequisites for kernel learning are similarity measures with the mathematical property of positive semidefiniteness (kernels). The iterative similarity optimal assignment graph kernel (ISOAK) [2] is defined directly on the annotated structure graph, and was designed specifically for the comparison of small molecules. In our virtual screening study, its use improved results, e.g., in principle component analysis-based visualization and Gaussian process regression. Following a thorough retrospective validation using a data set of 176 published PPARgamma agonists [8], we screened a vendor library for novel agonists. Subsequent testing of 15 compounds in a cell-based transactivation assay [9] yielded four active compounds. The most interesting hit, a natural product derivative with cyclobutane scaffold, is a full selective PPARgamma agonist (EC50 = 10 ± 0.2 microM, inactive on PPARalpha and PPARbeta/delta at 10 microM). We demonstrate how the interplay of several modern kernel-based machine learning approaches can successfully improve ligand-based virtual screening results.

- Virtual screening for PPAR-gamma ligands using the ISOAK molecular graph kernel and gaussian processes (2009)
- For a virtual screening study, we introduce a combination of machine learning techniques, employing a graph kernel, Gaussian process regression and clustered cross-validation. The aim was to find ligands of peroxisome-proliferator activated receptor gamma (PPAR-y). The receptors in the PPAR family belong to the steroid-thyroid-retinoid superfamily of nuclear receptors and act as transcription factors. They play a role in the regulation of lipid and glucose metabolism in vertebrates and are linked to various human processes and diseases [1]. For this study, we used a dataset of 176 PPAR-y agonists published by Ruecker et al [2]. Gaussian process (GP) models can provide a confidence estimate for each individual prediction, thereby allowing to assess which compounds are inside of the model's domain of applicability. This feature is useful in virtual screening, where a large fraction of the tested compounds may be outside of the model's domain of applicability. In cheminformatics, GPs have been applied to different classification and regression tasks using either radial basis function or rational quadratic kernels based on vectorial descriptors [4,5]. We used a graph kernel based on iterative similarity and optimal assignments (ISOAK, [3]) for non-linear Bayesian regression with Gaussian process priors (GP regression, [4]). A number of kernel-based learning algorithms (including GPs) are capable of multiple kernel learning [5], which allows combining heterogeneous information by using multiple kernels at the same time. In this work, we combined rational quadratic kernels for vectorial molecular descriptors (MOE2D, CATS2D and Ghose-Crippen fragment descriptors) with the ISOAK graph kernel. We evaluated our methodology in different ranking and regression settings. Ranking performance was assessed using the number of false positives within the top k predicted compounds. Predicted compounds were ranked based on both predicted binding affinity and the confidence in each prediction. In the regression setting, we employed standard loss functions like mean absolute error (MEA) and root mean squared error. The established linear ridge regression (LRR) and support vector regression (SVR) algorithms served as baseline methods. In addition to standard test/training splits and cross-validation, we used a clustered cross-validation strategy where clusters of compounds are left out when constructing training sets. This results in less optimistic results, but has the advantage of favouring more robust and potentially extrapolation-capable algorithms than standard training/test splits and normal cross-validation. In the regression setting, both GP and SVR models performed well, yielding MAEs as low as 0.66 +- 0.08 log units (clustered CV) and 0.51 +- 0.3 log units (normal CV). In the ranking setting, GPs slightly outperform SVR (0.21 +- 0.09 log units vs. 0.3 +- 0.08 log units). In conclusion, Gaussian process regression using simultaneously – via multiple kernel learning – the ISOAK molecular graph kernel and the rational quadratic kernel (with standard molecular descriptors) performs excellent in retrospective evaluation. A prospective evaluation study is currently in progress.

- DOGS: reaction-driven de novo design of bioactive compounds (2012)
- We present a computational method for the reaction-based de novo design of drug-like molecules. The software DOGS (Design of Genuine Structures) features a ligand-based strategy for automated ‘in silico’ assembly of potentially novel bioactive compounds. The quality of the designed compounds is assessed by a graph kernel method measuring their similarity to known bioactive reference ligands in terms of structural and pharmacophoric features. We implemented a deterministic compound construction procedure that explicitly considers compound synthesizability, based on a compilation of 25'144 readily available synthetic building blocks and 58 established reaction principles. This enables the software to suggest a synthesis route for each designed compound. Two prospective case studies are presented together with details on the algorithm and its implementation. De novo designed ligand candidates for the human histamine H4 receptor and γ-secretase were synthesized as suggested by the software. The computational approach proved to be suitable for scaffold-hopping from known ligands to novel chemotypes, and for generating bioactive molecules with drug-like properties.

- Spherical harmonics coeffcients for ligand-based virtual screening of cyclooxygenase inhibitors (2011)
- Background: Molecular descriptors are essential for many applications in computational chemistry, such as ligand-based similarity searching. Spherical harmonics have previously been suggested as comprehensive descriptors of molecular structure and properties. We investigate a spherical harmonics descriptor for shape-based virtual screening. Methodology/Principal Findings: We introduce and validate a partially rotation-invariant three-dimensional molecular shape descriptor based on the norm of spherical harmonics expansion coefficients. Using this molecular representation, we parameterize molecular surfaces, i.e., isosurfaces of spatial molecular property distributions. We validate the shape descriptor in a comprehensive retrospective virtual screening experiment. In a prospective study, we virtually screen a large compound library for cyclooxygenase inhibitors, using a self-organizing map as a pre-filter and the shape descriptor for candidate prioritization. Conclusions/Significance: 12 compounds were tested in vitro for direct enzyme inhibition and in a whole blood assay. Active compounds containing a triazole scaffold were identified as direct cyclooxygenase-1 inhibitors. This outcome corroborates the usefulness of spherical harmonics for representation of molecular shape in virtual screening of large compound collections. The combination of pharmacophore and shape-based filtering of screening candidates proved to be a straightforward approach to finding novel bioactive chemotypes with minimal experimental effort.