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Title: Multiscale Persistent Functions for Biomolecular Structure Characterization

Abstract

Here in this paper, we introduce multiscale persistent functions for biomolecular structure characterization. The essential idea is to combine our multiscale rigidity functions (MRFs) with persistent homology analysis, so as to construct a series of multiscale persistent functions, particularly multiscale persistent entropies, for structure characterization. To clarify the fundamental idea of our method, the multiscale persistent entropy (MPE) model is discussed in great detail. Mathematically, unlike the previous persistent entropy (Chintakunta et al. in Pattern Recognit 48(2):391–401, 2015; Merelli et al. in Entropy 17(10):6872–6892, 2015; Rucco et al. in: Proceedings of ECCS 2014, Springer, pp 117–128, 2016), a special resolution parameter is incorporated into our model. Various scales can be achieved by tuning its value. Physically, our MPE can be used in conformational entropy evaluation. More specifically, it is found that our method incorporates in it a natural classification scheme. This is achieved through a density filtration of an MRF built from angular distributions. To further validate our model, a systematical comparison with the traditional entropy evaluation model is done. Additionally, it is found that our model is able to preserve the intrinsic topological features of biomolecular data much better than traditional approaches, particularly for resolutions in the intermediate range.more » Moreover, by comparing with traditional entropies from various grid sizes, bond angle-based methods and a persistent homology-based support vector machine method (Cang et al. in Mol Based Math Biol 3:140–162, 2015), we find that our MPE method gives the best results in terms of average true positive rate in a classic protein structure classification test. More interestingly, all-alpha and all-beta protein classes can be clearly separated from each other with zero error only in our model. Finally, a special protein structure index (PSI) is proposed, for the first time, to describe the “regularity” of protein structures. Basically, a protein structure is deemed as regular if it has a consistent and orderly configuration. Our PSI model is tested on a database of 110 proteins; we find that structures with larger portions of loops and intrinsically disorder regions are always associated with larger PSI, meaning an irregular configuration, while proteins with larger portions of secondary structures, i.e., alpha-helix or beta-sheet, have smaller PSI. Essentially, PSI can be used to describe the “regularity” information in any systems.« less

Authors:
ORCiD logo [1];  [2]; ORCiD logo [3]
  1. Nanyang Technological University (Singapore). Division of Mathematical Sciences, School of Physical, Mathematical Sciences and School of Biological Sciences
  2. Central China Normal University, Wuhan (China). Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Division
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1415197
DOE Contract Number:  
AC05-00OR22725
Resource Type:
Journal Article
Resource Relation:
Journal Name: Bulletin of Mathematical Biology; Journal Volume: 80; Journal Issue: 1
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 59 BASIC BIOLOGICAL SCIENCES; Conformational entropy (CE); Persistent entropy; Multiscale rigidity function (MRF); Multiscale persistent function (MPF); Multiscale persistent entropy (MPE); Protein structure; Persistent homology

Citation Formats

Xia, Kelin, Li, Zhiming, and Mu, Lin. Multiscale Persistent Functions for Biomolecular Structure Characterization. United States: N. p., 2017. Web. doi:10.1007/s11538-017-0362-6.
Xia, Kelin, Li, Zhiming, & Mu, Lin. Multiscale Persistent Functions for Biomolecular Structure Characterization. United States. doi:10.1007/s11538-017-0362-6.
Xia, Kelin, Li, Zhiming, and Mu, Lin. Thu . "Multiscale Persistent Functions for Biomolecular Structure Characterization". United States. doi:10.1007/s11538-017-0362-6.
@article{osti_1415197,
title = {Multiscale Persistent Functions for Biomolecular Structure Characterization},
author = {Xia, Kelin and Li, Zhiming and Mu, Lin},
abstractNote = {Here in this paper, we introduce multiscale persistent functions for biomolecular structure characterization. The essential idea is to combine our multiscale rigidity functions (MRFs) with persistent homology analysis, so as to construct a series of multiscale persistent functions, particularly multiscale persistent entropies, for structure characterization. To clarify the fundamental idea of our method, the multiscale persistent entropy (MPE) model is discussed in great detail. Mathematically, unlike the previous persistent entropy (Chintakunta et al. in Pattern Recognit 48(2):391–401, 2015; Merelli et al. in Entropy 17(10):6872–6892, 2015; Rucco et al. in: Proceedings of ECCS 2014, Springer, pp 117–128, 2016), a special resolution parameter is incorporated into our model. Various scales can be achieved by tuning its value. Physically, our MPE can be used in conformational entropy evaluation. More specifically, it is found that our method incorporates in it a natural classification scheme. This is achieved through a density filtration of an MRF built from angular distributions. To further validate our model, a systematical comparison with the traditional entropy evaluation model is done. Additionally, it is found that our model is able to preserve the intrinsic topological features of biomolecular data much better than traditional approaches, particularly for resolutions in the intermediate range. Moreover, by comparing with traditional entropies from various grid sizes, bond angle-based methods and a persistent homology-based support vector machine method (Cang et al. in Mol Based Math Biol 3:140–162, 2015), we find that our MPE method gives the best results in terms of average true positive rate in a classic protein structure classification test. More interestingly, all-alpha and all-beta protein classes can be clearly separated from each other with zero error only in our model. Finally, a special protein structure index (PSI) is proposed, for the first time, to describe the “regularity” of protein structures. Basically, a protein structure is deemed as regular if it has a consistent and orderly configuration. Our PSI model is tested on a database of 110 proteins; we find that structures with larger portions of loops and intrinsically disorder regions are always associated with larger PSI, meaning an irregular configuration, while proteins with larger portions of secondary structures, i.e., alpha-helix or beta-sheet, have smaller PSI. Essentially, PSI can be used to describe the “regularity” information in any systems.},
doi = {10.1007/s11538-017-0362-6},
journal = {Bulletin of Mathematical Biology},
number = 1,
volume = 80,
place = {United States},
year = {Thu Nov 02 00:00:00 EDT 2017},
month = {Thu Nov 02 00:00:00 EDT 2017}
}