🍩 Database of Original & Non-Theoretical Uses of Topology

(found 26 matches in 0.00451s)
  1. Determining Clinically Relevant Features in Cytometry Data Using Persistent Homology (2022)

    Soham Mukherjee, Darren Wethington, Tamal K. Dey, Jayajit Das
    Abstract Cytometry experiments yield high-dimensional point cloud data that is difficult to interpret manually. Boolean gating techniques coupled with comparisons of relative abundances of cellular subsets is the current standard for cytometry data analysis. However, this approach is unable to capture more subtle topological features hidden in data, especially if those features are further masked by data transforms or significant batch effects or donor-to-donor variations in clinical data. We present that persistent homology, a mathematical structure that summarizes the topological features, can distinguish different sources of data, such as from groups of healthy donors or patients, effectively. Analysis of publicly available cytometry data describing non-naïve CD8+ T cells in COVID-19 patients and healthy controls shows that systematic structural differences exist between single cell protein expressions in COVID-19 patients and healthy controls. We identify proteins of interest by a decision-tree based classifier, sample points randomly and compute persistence diagrams from these sampled points. The resulting persistence diagrams identify regions in cytometry datasets of varying density and identify protruded structures such as ‘elbows’. We compute Wasserstein distances between these persistence diagrams for random pairs of healthy controls and COVID-19 patients and find that systematic structural differences exist between COVID-19 patients and healthy controls in the expression data for T-bet, Eomes, and Ki-67. Further analysis shows that expression of T-bet and Eomes are significantly downregulated in COVID-19 patient non-naïve CD8+ T cells compared to healthy controls. This counter-intuitive finding may indicate that canonical effector CD8+ T cells are less prevalent in COVID-19 patients than healthy controls. This method is applicable to any cytometry dataset for discovering novel insights through topological data analysis which may be difficult to ascertain otherwise with a standard gating strategy or existing bioinformatic tools.

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  2. HiDeF: Identifying Persistent Structures in Multiscale ‘Omics Data (2021)

    Fan Zheng, She Zhang, Christopher Churas, Dexter Pratt, Ivet Bahar, Trey Ideker
    Abstract In any ‘omics study, the scale of analysis can dramatically affect the outcome. For instance, when clustering single-cell transcriptomes, is the analysis tuned to discover broad or specific cell types? Likewise, protein communities revealed from protein networks can vary widely in sizes depending on the method. Here, we use the concept of persistent homology, drawn from mathematical topology, to identify robust structures in data at all scales simultaneously. Application to mouse single-cell transcriptomes significantly expands the catalog of identified cell types, while analysis of SARS-COV-2 protein interactions suggests hijacking of WNT. The method, HiDeF, is available via Python and Cytoscape.
  3. Protein-Folding Analysis Using Features Obtained by Persistent Homology (2020)

    Takashi Ichinomiya, Ippei Obayashi, Yasuaki Hiraoka
    Abstract Understanding the protein-folding process is an outstanding issue in biophysics; recent developments in molecular dynamics simulation have provided insights into this phenomenon. However, the large freedom of atomic motion hinders the understanding of this process. In this study, we applied persistent homology, an emerging method to analyze topological features in a data set, to reveal protein-folding dynamics. We developed a new, to our knowledge, method to characterize the protein structure based on persistent homology and applied this method to molecular dynamics simulations of chignolin. Using principle component analysis or nonnegative matrix factorization, our analysis method revealed two stable states and one saddle state, corresponding to the native, misfolded, and transition states, respectively. We also identified an unfolded state with slow dynamics in the reduced space. Our method serves as a promising tool to understand the protein-folding process.
  4. HERMES: Persistent Spectral Graph Software (2020)

    Rui Wang, Rundong Zhao, Emily Ribando-Gros, Jiahui Chen, Yiying Tong, Guo-Wei Wei
    Abstract Persistent homology (PH) is one of the most popular tools in topological data analysis (TDA), while graph theory has had a significant impact on data science. Our earlier work introduced the persistent spectral graph (PSG) theory as a unified multiscale paradigm to encompass TDA and geometric analysis. In PSG theory, families of persistent Laplacians (PLs) corresponding to various topological dimensions are constructed via a filtration to sample a given dataset at multiple scales. The harmonic spectra from the null spaces of PLs offer the same topological invariants, namely persistent Betti numbers, at various dimensions as those provided by PH, while the non-harmonic spectra of PLs give rise to additional geometric analysis of the shape of the data. In this work, we develop an open-source software package, called highly efficient robust multidimensional evolutionary spectra (HERMES), to enable broad applications of PSGs in science, engineering, and technology. To ensure the reliability and robustness of HERMES, we have validated the software with simple geometric shapes and complex datasets from three-dimensional (3D) protein structures. We found that the smallest non-zero eigenvalues are very sensitive to data abnormality.
  5. Evolutionary Homology on Coupled Dynamical Systems With Applications to Protein Flexibility Analysis (2020)

    Zixuan Cang, Elizabeth Munch, Guo-Wei Wei
    Abstract While the spatial topological persistence is naturally constructed from a radius-based filtration, it has hardly been derived from a temporal filtration. Most topological models are designed for the global topology of a given object as a whole. There is no method reported in the literature for the topology of an individual component in an object to the best of our knowledge. For many problems in science and engineering, the topology of an individual component is important for describing its properties. We propose evolutionary homology (EH) constructed via a time evolution-based filtration and topological persistence. Our approach couples a set of dynamical systems or chaotic oscillators by the interactions of a physical system, such as a macromolecule. The interactions are approximated by weighted graph Laplacians. Simplices, simplicial complexes, algebraic groups and topological persistence are defined on the coupled trajectories of the chaotic oscillators. The resulting EH gives rise to time-dependent topological invariants or evolutionary barcodes for an individual component of the physical system, revealing its topology-function relationship. In conjunction with Wasserstein metrics, the proposed EH is applied to protein flexibility analysis, an important problem in computational biophysics. Numerical results for the B-factor prediction of a benchmark set of 364 proteins indicate that the proposed EH outperforms all the other state-of-the-art methods in the field.
  6. PersGNN: Applying Topological Data Analysis and Geometric Deep Learning to Structure-Based Protein Function Prediction (2020)

    Nicolas Swenson, Aditi S. Krishnapriyan, Aydin Buluc, Dmitriy Morozov, Katherine Yelick
    Abstract Understanding protein structure-function relationships is a key challenge in computational biology, with applications across the biotechnology and pharmaceutical industries. While it is known that protein structure directly impacts protein function, many functional prediction tasks use only protein sequence. In this work, we isolate protein structure to make functional annotations for proteins in the Protein Data Bank in order to study the expressiveness of different structure-based prediction schemes. We present PersGNN - an end-to-end trainable deep learning model that combines graph representation learning with topological data analysis to capture a complex set of both local and global structural features. While variations of these techniques have been successfully applied to proteins before, we demonstrate that our hybridized approach, PersGNN, outperforms either method on its own as well as a baseline neural network that learns from the same information. PersGNN achieves a 9.3% boost in area under the precision recall curve (AUPR) compared to the best individual model, as well as high F1 scores across different gene ontology categories, indicating the transferability of this approach.
  7. Atom-Specific Persistent Homology and Its Application to Protein Flexibility Analysis (2020)

    David Bramer, Guo-Wei Wei
    Abstract Recently, persistent homology has had tremendous success in biomolecular data analysis. It works by examining the topological relationship or connectivity of a group of atoms in a molecule at a variety of scales, then rendering a family of topological representations of the molecule. However, persistent homology is rarely employed for the analysis of atomic properties, such as biomolecular flexibility analysis or B-factor prediction. This work introduces atom-specific persistent homology to provide a local atomic level representation of a molecule via a global topological tool. This is achieved through the construction of a pair of conjugated sets of atoms and corresponding conjugated simplicial complexes, as well as conjugated topological spaces. The difference between the topological invariants of the pair of conjugated sets is measured by Bottleneck and Wasserstein metrics and leads to an atom-specific topological representation of individual atomic properties in a molecule. Atom-specific topological features are integrated with various machine learning algorithms, including gradient boosting trees and convolutional neural network for protein thermal fluctuation analysis and B-factor prediction. Extensive numerical results indicate the proposed method provides a powerful topological tool for analyzing and predicting localized information in complex macromolecules.
  8. Weighted Persistent Homology for Osmolyte Molecular Aggregation and Hydrogen-Bonding Network Analysis (2020)

    D. Vijay Anand, Zhenyu Meng, Kelin Xia, Yuguang Mu
    Abstract It has long been observed that trimethylamine N-oxide (TMAO) and urea demonstrate dramatically different properties in a protein folding process. Even with the enormous theoretical and experimental research work on these two osmolytes, various aspects of their underlying mechanisms still remain largely elusive. In this paper, we propose to use the weighted persistent homology to systematically study the osmolytes molecular aggregation and their hydrogen-bonding network from a local topological perspective. We consider two weighted models, i.e., localized persistent homology (LPH) and interactive persistent homology (IPH). Boltzmann persistent entropy (BPE) is proposed to quantitatively characterize the topological features from LPH and IPH, together with persistent Betti number (PBN). More specifically, from the localized persistent homology models, we have found that TMAO and urea have very different local topology. TMAO is found to exhibit a local network structure. With the concentration increase, the circle elements in these networks show a clear increase in their total numbers and a decrease in their relative sizes. In contrast, urea shows two types of local topological patterns, i.e., local clusters around 6 Å and a few global circle elements at around 12 Å. From the interactive persistent homology models, it has been found that our persistent radial distribution function (PRDF) from the global-scale IPH has same physical properties as the traditional radial distribution function. Moreover, PRDFs from the local-scale IPH can also be generated and used to characterize the local interaction information. Other than the clear difference of the first peak value of PRDFs at filtration size 4 Å, TMAO and urea also shows very different behaviors at the second peak region from filtration size 5 Å to 10 Å. These differences are also reflected in the PBNs and BPEs of the local-scale IPH. These localized topological information has never been revealed before. Since graphs can be transferred into simplicial complexes by the clique complex, our weighted persistent homology models can be used in the analysis of various networks and graphs from any molecular structures and aggregation systems.
  9. Hyperparameter Optimization of Topological Features for Machine Learning Applications (2019)

    Francis Motta, Christopher Tralie, Rossella Bedini, Fabiano Bini, Gilberto Bini, Hamed Eramian, Marcio Gameiro, Steve Haase, Hugh Haddox, John Harer, Nick Leiby, Franco Marinozzi, Scott Novotney, Gabe Rocklin, Jed Singer, Devin Strickland, Matt Vaughn
    Abstract This paper describes a general pipeline for generating optimal vector representations of topological features of data for use with machine learning algorithms. This pipeline can be viewed as a costly black-box function defined over a complex configuration space, each point of which specifies both how features are generated and how predictive models are trained on those features. We propose using state-of-the-art Bayesian optimization algorithms to inform the choice of topological vectorization hyperparameters while simultaneously choosing learning model parameters. We demonstrate the need for and effectiveness of this pipeline using two difficult biological learning problems, and illustrate the nontrivial interactions between topological feature generation and learning model hyperparameters.
  10. Representability of Algebraic Topology for Biomolecules in Machine Learning Based Scoring and Virtual Screening (2018)

    Zixuan Cang, Lin Mu, Guo-Wei Wei
    Abstract This work introduces a number of algebraic topology approaches, including multi-component persistent homology, multi-level persistent homology, and electrostatic persistence for the representation, characterization, and description of small molecules and biomolecular complexes. In contrast to the conventional persistent homology, multi-component persistent homology retains critical chemical and biological information during the topological simplification of biomolecular geometric complexity. Multi-level persistent homology enables a tailored topological description of inter- and/or intra-molecular interactions of interest. Electrostatic persistence incorporates partial charge information into topological invariants. These topological methods are paired with Wasserstein distance to characterize similarities between molecules and are further integrated with a variety of machine learning algorithms, including k-nearest neighbors, ensemble of trees, and deep convolutional neural networks, to manifest their descriptive and predictive powers for protein-ligand binding analysis and virtual screening of small molecules. Extensive numerical experiments involving 4,414 protein-ligand complexes from the PDBBind database and 128,374 ligand-target and decoy-target pairs in the DUD database are performed to test respectively the scoring power and the discriminatory power of the proposed topological learning strategies. It is demonstrated that the present topological learning outperforms other existing methods in protein-ligand binding affinity prediction and ligand-decoy discrimination.
  11. The Architecture of the Endoplasmic Reticulum Is Regulated by the Reversible Lipid Modification of the Shaping Protein CLIMP-63 (2018)

    Patrick A. Sandoz, Robin A. Denhardt-Eriksson, Laurence Abrami, Luciano Abriata, Gard Spreemann, Catherine Maclachlan, Sylvia Ho, Béatrice Kunz, Kathryn Hess, Graham Knott, Vassily Hatzimanikatis, F. Gisou van der Goot
    Abstract \textlessh3\textgreaterAbstract\textless/h3\textgreater \textlessp\textgreaterThe endoplasmic reticulum (ER) has a complex morphology generated and maintained by membrane-shaping proteins and membrane energy minimization, though not much is known about how it is regulated. The architecture of this intracellular organelle is balanced between large, thin sheets that are densely packed in the perinuclear region and a connected network of branched, elongated tubules that extend throughout the cytoplasm. Sheet formation is known to involve the cytoskeleton-linking membrane protein 63 (CLIMP-63), though its regulation and the depth of its involvement remain unknown. Here we show that the post-translational modification of CLIMP-63 by the palmitoyltransferase ZDHHC6 controls the relative distribution of CLIMP-63 between the ER and the plasma membrane. By combining data-driven mathematical modeling, predictions, and experimental validation, we found that the attachment of a medium chain fatty acid, so-called S-palmitoylation, to the unique CLIMP-63 cytoplasmic cysteine residue drastically reduces its turnover rate, and thereby controls its abundance. Light microscopy and focused ion beam electron microcopy further revealed that enhanced CLIMP-63 palmitoylation leads to strong ER-sheet proliferation. Altogether, we show that ZDHHC6-mediated S-palmitoylation regulates the cellular localization of CLIMP-63, the morphology of the ER, and the interconversion of ER structural elements in mammalian cells through its action on the CLIMP-63 protein.\textless/p\textgreater\textlessh3\textgreaterSignificance Statement\textless/h3\textgreater \textlessp\textgreaterEukaryotic cells subcompartmentalize their various functions into organelles, the shape of each being specific and necessary for its proper role. However, how these shapes are generated and controlled is poorly understood. The endoplasmic reticulum is the largest membrane-bound intracellular compartment, accounting for more than 50% of all cellular membranes. We found that the shape and quantity of its sheet-like structures are controlled by a specific protein, cytoskeleton-linking membrane protein 63, through the acquisition of a lipid chain attached by an enzyme called ZDHHC6. Thus, by modifying the ZDHHC6 amounts, a cell can control the shape of its ER. The modeling and prediction technique used herein also provides a method for studying the interconnected function of other post-translational modifications in organelles.\textless/p\textgreater
  12. Identification of Topological Network Modules in Perturbed Protein Interaction Networks (2017)

    Mihaela E. Sardiu, Joshua M. Gilmore, Brad Groppe, Laurence Florens, Michael P. Washburn
    Abstract Biological networks consist of functional modules, however detecting and characterizing such modules in networks remains challenging. Perturbing networks is one strategy for identifying modules. Here we used an advanced mathematical approach named topological data analysis (TDA) to interrogate two perturbed networks. In one, we disrupted the S. cerevisiae INO80 protein interaction network by isolating complexes after protein complex components were deleted from the genome. In the second, we reanalyzed previously published data demonstrating the disruption of the human Sin3 network with a histone deacetylase inhibitor. Here we show that disrupted networks contained topological network modules (TNMs) with shared properties that mapped onto distinct locations in networks. We define TMNs as proteins that occupy close network positions depending on their coordinates in a topological space. TNMs provide new insight into networks by capturing proteins from different categories including proteins within a complex, proteins with shared biological functions, and proteins disrupted across networks.
  13. Using Persistent Homology and Dynamical Distances to Analyze Protein Binding (2016)

    Violeta Kovacev-Nikolic, Peter Bubenik, Dragan Nikolić, Giseon Heo
    Abstract Persistent homology captures the evolution of topological features of a model as a parameter changes. The most commonly used summary statistics of persistent homology are the barcode and the persistence diagram. Another summary statistic, the persistence landscape, was recently introduced by Bubenik. It is a functional summary, so it is easy to calculate sample means and variances, and it is straightforward to construct various test statistics. Implementing a permutation test we detect conformational changes between closed and open forms of the maltose-binding protein, a large biomolecule consisting of 370 amino acid residues. Furthermore, persistence landscapes can be applied to machine learning methods. A hyperplane from a support vector machine shows the clear separation between the closed and open proteins conformations. Moreover, because our approach captures dynamical properties of the protein our results may help in identifying residues susceptible to ligand binding; we show that the majority of active site residues and allosteric pathway residues are located in the vicinity of the most persistent loop in the corresponding filtered Vietoris-Rips complex. This finding was not observed in the classical anisotropic network model.
  14. WDR76 Co-Localizes With Heterochromatin Related Proteins and Rapidly Responds to DNA Damage (2016)

    Joshua M. Gilmore, Mihaela E. Sardiu, Brad D. Groppe, Janet L. Thornton, Xingyu Liu, Gerald Dayebgadoh, Charles A. Banks, Brian D. Slaughter, Jay R. Unruh, Jerry L. Workman, Laurence Florens, Michael P. Washburn
    Abstract Proteins that respond to DNA damage play critical roles in normal and diseased states in human biology. Studies have suggested that the S. cerevisiae protein CMR1/YDL156w is associated with histones and is possibly associated with DNA repair and replication processes. Through a quantitative proteomic analysis of affinity purifications here we show that the human homologue of this protein, WDR76, shares multiple protein associations with the histones H2A, H2B, and H4. Furthermore, our quantitative proteomic analysis of WDR76 associated proteins demonstrated links to proteins in the DNA damage response like PARP1 and XRCC5 and heterochromatin related proteins like CBX1, CBX3, and CBX5. Co-immunoprecipitation studies validated these interactions. Next, quantitative imaging studies demonstrated that WDR76 was recruited to laser induced DNA damage immediately after induction, and we compared the recruitment of WDR76 to laser induced DNA damage to known DNA damage proteins like PARP1, XRCC5, and RPA1. In addition, WDR76 co-localizes to puncta with the heterochromatin proteins CBX1 and CBX5, which are also recruited to DNA damage but much less intensely than WDR76. This work demonstrates the chromatin and DNA damage protein associations of WDR76 and demonstrates the rapid response of WDR76 to laser induced DNA damage.
  15. Object-Oriented Persistent Homology (2016)

    Bao Wang, Guo-Wei Wei
    Abstract Persistent homology provides a new approach for the topological simplification of big data via measuring the life time of intrinsic topological features in a filtration process and has found its success in scientific and engineering applications. However, such a success is essentially limited to qualitative data classification and analysis. Indeed, persistent homology has rarely been employed for quantitative modeling and prediction. Additionally, the present persistent homology is a passive tool, rather than a proactive technique, for classification and analysis. In this work, we outline a general protocol to construct object-oriented persistent homology methods. By means of differential geometry theory of surfaces, we construct an objective functional, namely, a surface free energy defined on the data of interest. The minimization of the objective functional leads to a Laplace-Beltrami operator which generates a multiscale representation of the initial data and offers an objective oriented filtration process. The resulting differential geometry based object-oriented persistent homology is able to preserve desirable geometric features in the evolutionary filtration and enhances the corresponding topological persistence. The cubical complex based homology algorithm is employed in the present work to be compatible with the Cartesian representation of the Laplace-Beltrami flow. The proposed Laplace-Beltrami flow based persistent homology method is extensively validated. The consistence between Laplace-Beltrami flow based filtration and Euclidean distance based filtration is confirmed on the Vietoris-Rips complex for a large amount of numerical tests. The convergence and reliability of the present Laplace-Beltrami flow based cubical complex filtration approach are analyzed over various spatial and temporal mesh sizes. The Laplace-Beltrami flow based persistent homology approach is utilized to study the intrinsic topology of proteins and fullerene molecules. Based on a quantitative model which correlates the topological persistence of fullerene central cavity with the total curvature energy of the fullerene structure, the proposed method is used for the prediction of fullerene isomer stability. The efficiency and robustness of the present method are verified by more than 500 fullerene molecules. It is shown that the proposed persistent homology based quantitative model offers good predictions of total curvature energies for ten types of fullerene isomers. The present work offers the first example to design object-oriented persistent homology to enhance or preserve desirable features in the original data during the filtration process and then automatically detect or extract the corresponding topological traits from the data.
  16. Multidimensional Persistence in Biomolecular Data (2015)

    Kelin Xia, Guo-Wei Wei
    Abstract Persistent homology has emerged as a popular technique for the topological simplification of big data, including biomolecular data. Multidimensional persistence bears considerable promise to bridge the gap between geometry and topology. However, its practical and robust construction has been a challenge. We introduce two families of multidimensional persistence, namely pseudo-multidimensional persistence and multiscale multidimensional persistence. The former is generated via the repeated applications of persistent homology filtration to high dimensional data, such as results from molecular dynamics or partial differential equations. The latter is constructed via isotropic and anisotropic scales that create new simiplicial complexes and associated topological spaces. The utility, robustness and efficiency of the proposed topological methods are demonstrated via protein folding, protein flexibility analysis, the topological denoising of cryo-electron microscopy data, and the scale dependence of nano particles. Topological transition between partial folded and unfolded proteins has been observed in multidimensional persistence. The separation between noise topological signatures and molecular topological fingerprints is achieved by the Laplace-Beltrami flow. The multiscale multidimensional persistent homology reveals relative local features in Betti-0 invariants and the relatively global characteristics of Betti-1 and Betti-2 invariants.
  17. A Topological Measurement of Protein Compressibility (2015)

    Marcio Gameiro, Yasuaki Hiraoka, Shunsuke Izumi, Miroslav Kramar, Konstantin Mischaikow, Vidit Nanda
    Abstract In this paper we partially clarify the relation between the compressibility of a protein and its molecular geometric structure. To identify and understand the relevant topological features within a given protein, we model its molecule as an alpha filtration and hence obtain multi-scale insight into the structure of its tunnels and cavities. The persistence diagrams of this alpha filtration capture the sizes and robustness of such tunnels and cavities in a compact and meaningful manner. From these persistence diagrams, we extract a measure of compressibility derived from those topological features whose relevance is suggested by physical and chemical properties. Due to recent advances in combinatorial topology, this measure is efficiently and directly computable from information found in the Protein Data Bank (PDB). Our main result establishes a clear linear correlation between the topological measure and the experimentally-determined compressibility of most proteins for which both PDB information and experimental compressibility data are available. Finally, we establish that both the topological measurement and the linear correlation are stable with respect to small perturbations in the input data, such as those arising from experimental errors in compressibility and X-ray crystallography experiments.
  18. Multiresolution Persistent Homology for Excessively Large Biomolecular Datasets (2015)

    Kelin Xia, Zhixiong Zhao, Guo-Wei Wei
    Abstract Although persistent homology has emerged as a promising tool for the topological simplification of complex data, it is computationally intractable for large datasets. We introduce multiresolution persistent homology to handle excessively large datasets. We match the resolution with the scale of interest so as to represent large scale datasets with appropriate resolution. We utilize flexibility-rigidity index to access the topological connectivity of the data set and define a rigidity density for the filtration analysis. By appropriately tuning the resolution of the rigidity density, we are able to focus the topological lens on the scale of interest. The proposed multiresolution topological analysis is validated by a hexagonal fractal image which has three distinct scales. We further demonstrate the proposed method for extracting topological fingerprints from DNA molecules. In particular, the topological persistence of a virus capsid with 273 780 atoms is successfully analyzed which would otherwise be inaccessible to the normal point cloud method and unreliable by using coarse-grained multiscale persistent homology. The proposed method has also been successfully applied to the protein domain classification, which is the first time that persistent homology is used for practical protein domain analysis, to our knowledge. The proposed multiresolution topological method has potential applications in arbitrary data sets, such as social networks, biological networks, and graphs.
  19. Conserved Abundance and Topological Features in Chromatin-Remodeling Protein Interaction Networks (2015)

    Mihaela E Sardiu, Joshua M Gilmore, Brad D Groppe, Damir Herman, Sreenivasa R Ramisetty, Yong Cai, Jingji Jin, Ronald C Conaway, Joan W Conaway, Laurence Florens, Michael P Washburn
    Abstract Abstract The study of conserved protein interaction networks seeks to better understand the evolution and regulation of protein interactions. Here, we present a quantitative proteomic analysis of 18 orthologous baits from three distinct chromatin-remodeling complexes in Saccharomyces cerevisiae and Homo sapiens. We demonstrate that abundance levels of orthologous proteins correlate strongly between the two organisms and both networks have highly similar topologies. We therefore used the protein abundances in one species to cross-predict missing protein abundance levels in the other species. Lastly, we identified a novel conserved low-abundance subnetwork further demonstrating the value of quantitative analysis of networks.
  20. Persistent Homology Analysis of Protein Structure, Flexibility, and Folding (2014)

    Kelin Xia, Guo-Wei Wei
    Abstract SUMMARYProteins are the most important biomolecules for living organisms. The understanding of protein structure, function, dynamics, and transport is one of the most challenging tasks in biological science. In the present work, persistent homology is, for the first time, introduced for extracting molecular topological fingerprints (MTFs) based on the persistence of molecular topological invariants. MTFs are utilized for protein characterization, identification, and classification. The method of slicing is proposed to track the geometric origin of protein topological invariants. Both all-atom and coarse-grained representations of MTFs are constructed. A new cutoff-like filtration is proposed to shed light on the optimal cutoff distance in elastic network models. On the basis of the correlation between protein compactness, rigidity, and connectivity, we propose an accumulated bar length generated from persistent topological invariants for the quantitative modeling of protein flexibility. To this end, a correlation matrix-based filtration is developed. This approach gives rise to an accurate prediction of the optimal characteristic distance used in protein B-factor analysis. Finally, MTFs are employed to characterize protein topological evolution during protein folding and quantitatively predict the protein folding stability. An excellent consistence between our persistent homology prediction and molecular dynamics simulation is found. This work reveals the topology–function relationship of proteins. Copyright © 2014 John Wiley & Sons, Ltd.