The understanding of toxicity is of paramount importance to human health and environmental protection. Quantitative toxicity analysis has become a new standard in the field. This work introduces element specific persistent homology (ESPH), an algebraic topology approach, for quantitative toxicity prediction. ESPH retains crucial chemical information during the topological abstraction of geometric complexity and provides a representation of small molecules that cannot be obtained by any other method. To investigate the representability and predictive power of ESPH for small molecules, ancillary descriptors have also been developed based on physical models. Topological and physical descriptors are paired with advanced machine learning algorithms, such as the deep neural network (DNN), random forest (RF), and gradient boosting decision tree (GBDT), to facilitate their applications to quantitative toxicity predictions. A topology based multitask strategy is proposed to take the advantage of the availability of large data sets while dealing with small data sets. Four benchmark toxicity data sets that involve quantitative measurements are used to validate the proposed approaches. Extensive numerical studies indicate that the proposed topological learning methods are able to outperform the state-of-the-art methods in the literature for quantitative toxicity analysis. Our online server for computing element-specific topological descriptors (ESTDs) is available at http://weilab.math.msu.edu/TopTox/ .

Protein function and dynamics are closely related to its sequence and structure. However prediction of protein function and dynamics from its sequence and structure is still a fundamental challenge in molecular biology. Protein classification, which is typically done through measuring the similarity between proteins based on protein sequence or physical information, serves as a crucial step toward the understanding of protein function and dynamics. Persistent homology is a new branch of algebraic topology that has found its success in the topological data analysis in a variety of disciplines, including molecular biology. The present work explores the potential of using persistent homology as an independent tool for protein classification. To this end, we propose a molecular topological fingerprint based support vector machine (MTF-SVM) classifier. Specifically, we construct machine learning feature vectors solely from protein topological fingerprints, which are topological invariants generated during the filtration process. To validate the present MTF-SVM approach, we consider four types of problems. First, we study protein-drug binding by using the M2 channel protein of influenza A virus. We achieve 96% accuracy in discriminating drug bound and unbound M2 channels. Additionally, we examine the use of MTF-SVM for the classification of hemoglobin molecules in their relaxed and taut forms and obtain about 80% accuracy. The identification of all alpha, all beta, and alpha-beta protein domains is carried out in our next study using 900 proteins. We have found a 85% success in this identification. Finally, we apply the present technique to 55 classification tasks of protein superfamilies over 1357 samples. An average accuracy of 82% is attained. The present study establishes computational topology as an independent and effective alternative for protein classification. I IntroductionProteins are essential building blocks of living organisms. They function as catalyst, structural elements, chemical signals, receptors, etc. The molecular mechanism of protein functions are closely related to their structures. The study of structure-function relationship is the holy grail of biophysics and has attracted enormous effort in the past few decades. The understanding of such a relationship enables us to predict protein functions from structure or amino acid sequence or both, which remains major challenge in molecular biology. Intensive experimental investigation has been carried out to explore the interactions among proteins or proteins with other biomolecules, e.g., DNAs and/or RNAs. In particular, the understanding of protein-drug interactions is of premier importance to human health.A wide variety of theoretical and computational approaches has been proposed to understand the protein structure-function relationship. One class of approaches is biophysical. From the point of view of biophysics, protein structure, function, dynamics and transport are, in general, dictated by protein interactions. Quantum mechanics (QM) is based ...

Advanced mathematics, such as multiscale weighted colored subgraph and element specific persistent homology, and machine learning including deep neural networks were integrated to construct mathematical deep learning models for pose and binding affinity prediction and ranking in the last two D3R Grand Challenges in computer-aided drug design and discovery. D3R Grand Challenge 2 focused on the pose prediction, binding affinity ranking and free energy prediction for Farnesoid X receptor ligands. Our models obtained the top place in absolute free energy prediction for free energy set 1 in stage 2. The latest competition, D3R Grand Challenge 3 (GC3), is considered as the most difficult challenge so far. It has five subchallenges involving Cathepsin S and five other kinase targets, namely VEGFR2, JAK2, p38-α, TIE2, and ABL1. There is a total of 26 official competitive tasks for GC3. Our predictions were ranked 1st in 10 out of these 26 tasks.

Aqueous solubility and partition coefficient are important physical properties of small molecules. Accurate theoretical prediction of aqueous solubility and partition coefficient plays an important role in drug design and discovery. The prediction accuracy depends crucially on molecular descriptors which are typically derived from a theoretical understanding of the chemistry and physics of small molecules. This work introduces an algebraic topology-based method, called element-specific persistent homology (ESPH), as a new representation of small molecules that is entirely different from conventional chemical and/or physical representations. ESPH describes molecular properties in terms of multiscale and multicomponent topological invariants. Such topological representation is systematical, comprehensive, and scalable with respect to molecular size and composition variations. However, it cannot be literally translated into a physical interpretation. Fortunately, it is readily suitable for machine learning methods, rendering topological learning algorithms. Due to the inherent correlation between solubility and partition coefficient, a uniform ESPH representation is developed for both properties, which facilitates multi-task deep neural networks for their simultaneous predictions. This strategy leads to a more accurate prediction of relatively small datasets. A total of six datasets is considered in this work to validate the proposed topological and multitask deep learning approaches. It is demonstrated that the proposed approaches achieve some of the most accurate predictions of aqueous solubility and partition coefficient. Our software is available online at http://weilab.math.msu.edu/TopP-S/. © 2018 Wiley Periodicals, Inc.

Implicit solvent models divide solvation free energies into polar and nonpolar additive contributions, whereas polar and nonpolar interactions are inseparable and nonadditive. We present a feature functional theory (FFT) framework to break this ad hoc division. The essential ideas of FFT are as follows: (i) representability assumption: there exists a microscopic feature vector that can uniquely characterize and distinguish one molecule from another; (ii) feature-function relationship assumption: the macroscopic features, including solvation free energy, of a molecule is a functional of microscopic feature vectors; and (iii) similarity assumption: molecules with similar microscopic features have similar macroscopic properties, such as solvation free energies. Based on these assumptions, solvation free energy prediction is carried out in the following protocol. First, we construct a molecular microscopic feature vector that is efficient in characterizing the solvation process using quantum mechanics and Poisson-Boltzmann theory. Microscopic feature vectors are combined with macroscopic features, that is, physical observable, to form extended feature vectors. Additionally, we partition a solvation dataset into queries according to molecular compositions. Moreover, for each target molecule, we adopt a machine learning algorithm for its nearest neighbor search, based on the selected microscopic feature vectors. Finally, from the extended feature vectors of obtained nearest neighbors, we construct a functional of solvation free energy, which is employed to predict the solvation free energy of the target molecule. The proposed FFT model has been extensively validated via a large dataset of 668 molecules. The leave-one-out test gives an optimal root-mean-square error (RMSE) of 1.05 kcal/mol. FFT predictions of SAMPL0, SAMPL1, SAMPL2, SAMPL3, and SAMPL4 challenge sets deliver the RMSEs of 0.61, 1.86, 1.64, 0.86, and 1.14 kcal/mol, respectively. Using a test set of 94 molecules and its associated training set, the present approach was carefully compared with a classic solvation model based on weighted solvent accessible surface area. © 2017 Wiley Periodicals, Inc.