Multiresolution persistent homology for excessively large biomolecular datasets

Xia, Kelin; Zhao, Zhixiong; Guo, Wei

doi:10.1063/1.4931733

Cited by 41 publications

(50 citation statements)

References 42 publications

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“…In our earlier work, we have introduced computational topological for mathematical modeling and prediction, such as molecular stability prediction, 108 protein folding analysis, 112 and protein bond length prediction. 109 The present work indicates that the combination of machine learning and computational topology will create a new powerful approach topology based mathematical modeling and prediction.…”

Section: Discussionmentioning

confidence: 99%

A topological approach for protein classification

Cang

et al. 2015

Computational and Mathematical Biophysics

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114

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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 ...

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Section: Discussionmentioning

confidence: 99%

A topological approach for protein classification

Cang

et al. 2015

Computational and Mathematical Biophysics

Self Cite

114

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“…With this modification, each feature in the persistence diagram corresponds to a bump in the density f —namely, the local maximum at which it dies. Other work on using persistence in bump hunting can be found in Xia et al ().…”

Section: Methodsmentioning

confidence: 99%

Bump hunting by topological data analysis

Sommerfeld

Heo

Kim

et al. 2017

Stat

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A topological data analysis approach is taken to the challenging problem of finding and validating the statistical significance of local modes in a data set. As with the SIgnificance of the ZERo (SiZer) approach to this problem, statistical inference is performed in a multi-scale way, that is, across bandwidths. The key contribution is a twoparameter approach to the persistent homology representation. For each kernel bandwidth, a sub-level set filtration of the resulting kernel density estimate is computed. Inference based on the resulting persistence diagram indicates statistical significance of modes. It is seen through a simulated example, and by analysis of the famous Hidalgo stamps data, that the new method has more statistical power for finding bumps than SiZer.

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“…60,168 We introduced persistent homology as a quantitative tool for analyzing biomolecular systems. 90,140,158,[162][163][164][165][166] In particular, we introduced one the first topology-based machine learning algorithms for protein classification in 2015. 22 We further introduced element specific persistent homology, i.e., element-induced topology, to deal with massive and diverse bimolecular datasets.…”

Section: Iia2 Challengementioning

confidence: 99%

A review of mathematical representations of biomolecular data

Nguyen

Cang

Wei

2020

Phys. Chem. Chem. Phys.

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Recently, machine learning (ML) has established itself in various worldwide benchmarking competitions in computational biology, including Critical Assessment of Structure Prediction (CASP) and Drug Design Data Resource (D3R) Grand Challenges. However, the intricate structural complexity and high ML dimensionality of biomolecular datasets obstruct the efficient application of ML algorithms in the field. In addition to data and algorithm, an efficient ML machinery for biomolecular predictions must include structural representation as an indispensable component. Mathematical representations that simplify the biomolecular structural complexity and reduce ML dimensionality have emerged as a prime winner in D3R Grand Challenges. This review is devoted to the recent advances in developing low-dimensional and scalable mathematical representations of biomolecules in our laboratory. We discuss three classes of mathematical approaches, including algebraic topology, differential geometry, and graph theory. We elucidate how the physical and biological challenges have guided the evolution and development of these mathematical apparatuses for massive and diverse biomolecular data. We focus the performance analysis on the protein-ligand binding predictions in this review although these methods have had tremendous success in many other applications, such as protein classification, virtual screening, and the predictions of solubility, solvation free energy, toxicity, partition coefficient, protein folding stability changes upon mutation, etc.

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Multiresolution persistent homology for excessively large biomolecular datasets

Cited by 41 publications

References 42 publications

A topological approach for protein classification

A topological approach for protein classification

Bump hunting by topological data analysis

A review of mathematical representations of biomolecular data

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