Benchmarking R packages for Calculation of Persistent Homology.
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ABSTRACT:
SUBMITTER: Somasundaram EV
PROVIDER: S-EPMC8434812 | biostudies-literature | 2021 Jun
REPOSITORIES: biostudies-literature
Publications
Benchmarking R packages for Calculation of Persistent Homology.
Somasundaram Eashwar V EV Brown Shael E SE Litzler Adam A Scott Jacob G JG Wadhwa Raoul R RR
The R journal 20210607 1
Several persistent homology software libraries have been implemented in R. Specifically, the Dionysus, GUDHI, and Ripser libraries have been wrapped by the <b>TDA</b> and <b>TDAstats</b> CRAN packages. These software represent powerful analysis tools that are computationally expensive and, to our knowledge, have not been formally benchmarked. Here, we analyze runtime and memory growth for the 2 R packages and the 3 underlying libraries. We find that datasets with less than 3 dimensions can be ev ...[more]
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Project description: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.
| S-EPMC4685963 | biostudies-literature
Project description:MotivationOver the last decades, vast numbers of sequences were deposited in public databases. Bioinformatics tools allow homology and consequently functional inference for these sequences. New profile-based homology search tools have been introduced, allowing reliable detection of remote homologs, but have not been systematically benchmarked. To provide such a comparison, which can guide bioinformatics workflows, we extend and apply our previously developed benchmark approach to evaluate the 'next generation' of profile-based approaches, including CS-BLAST, HHSEARCH and PHMMER, in comparison with the non-profile based search tools NCBI-BLAST, USEARCH, UBLAST and FASTA.MethodWe generated challenging benchmark datasets based on protein domain architectures within either the PFAM + Clan, SCOP/Superfamily or CATH/Gene3D domain definition schemes. From each dataset, homologous and non-homologous protein pairs were aligned using each tool, and standard performance metrics calculated. We further measured congruence of domain architecture assignments in the three domain databases.ResultsCSBLAST and PHMMER had overall highest accuracy. FASTA, UBLAST and USEARCH showed large trade-offs of accuracy for speed optimization.ConclusionProfile methods are superior at inferring remote homologs but the difference in accuracy between methods is relatively small. PHMMER and CSBLAST stand out with the highest accuracy, yet still at a reasonable computational cost. Additionally, we show that less than 0.1% of Swiss-Prot protein pairs considered homologous by one database are considered non-homologous by another, implying that these classifications represent equivalent underlying biological phenomena, differing mostly in coverage and granularity.Availability and implementationBenchmark datasets and all scripts are placed at (http://sonnhammer.org/download/Homology_benchmark).Contactforslund@embl.deSupplementary informationSupplementary data are available at Bioinformatics online.
| S-EPMC5013910 | biostudies-literature
Project description:Persistent homology, a topological data analysis (TDA) method, is applied to microarray data sets. Although there are a few papers referring to TDA methods in microarray analysis, the usage of persistent homology in the comparison of several weighted gene coexpression networks (WGCN) was not employed before to the very best of our knowledge. We calculate the persistent homology of weighted networks constructed from 38 Arabidopsis microarray data sets to test the relevance and the success of this approach in distinguishing the stress factors. We quantify multiscale topological features of each network using persistent homology and apply a hierarchical clustering algorithm to the distance matrix whose entries are pairwise bottleneck distance between the networks. The immunoresponses to different stress factors are distinguishable by our method. The networks of similar immunoresponses are found to be close with respect to bottleneck distance indicating the similar topological features of WGCNs. This computationally efficient technique analyzing networks provides a quick test for advanced studies.
| S-EPMC6169238 | biostudies-literature
Project description:Relatively little is known about ATP synthase structure in protists, and the investigated ones exhibit divergent structures distinct from yeast or animals. To clarify the subunit composition of ATP synthases across all eukaryotic lineages, we used homology detection techniques and molecular modeling tools to identify an ancestral set of 17 ATP synthase subunits. Most eukaryotes possess an ATP synthase comparable to those of animals and fungi, while some have undergone drastic divergence (e.g., ciliates, myzozoans, euglenozoans). Additionally, a ∼1 billion-year-old gene fusion between ATP synthase stator subunits was identified as a synapomorphy of the SAR (Stramenopila, Alveolata, Rhizaria) supergroup (stramenopile, alveolate, rhizaria). Our comparative approach highlights the persistence of ancestral subunits even amidst major structural changes. We conclude by urging that more ATP synthase structures (e.g., from jakobids, heteroloboseans, stramenopiles, rhizarians) are needed to provide a complete picture of the evolution of the structural diversity of this ancient and essential complex.
| S-EPMC10214729 | biostudies-literature
Project description:In this paper, we systematically review weighted persistent homology (WPH) models and their applications in biomolecular data analysis. Essentially, the weight value, which reflects physical, chemical and biological properties, can be assigned to vertices (atom centers), edges (bonds), or higher order simplexes (cluster of atoms), depending on the biomolecular structure, function, and dynamics properties. Further, we propose the first localized weighted persistent homology (LWPH). Inspired by the great success of element specific persistent homology (ESPH), we do not treat biomolecules as an inseparable system like all previous weighted models, instead we decompose them into a series of local domains, which may be overlapped with each other. The general persistent homology or weighted persistent homology analysis is then applied on each of these local domains. In this way, functional properties, that are embedded in local structures, can be revealed. Our model has been applied to systematically study DNA structures. It has been found that our LWPH based features can be used to successfully discriminate the A-, B-, and Z-types of DNA. More importantly, our LWPH based principal component analysis (PCA) model can identify two configurational states of DNA structures in ion liquid environment, which can be revealed only by the complicated helical coordinate system. The great consistence with the helical-coordinate model demonstrates that our model captures local structure variations so well that it is comparable with geometric models. Moreover, geometric measurements are usually defined in local regions. For instance, the helical-coordinate system is limited to one or two basepairs. However, our LWPH can quantitatively characterize structure information in regions or domains with arbitrary sizes and shapes, where traditional geometrical measurements fail.
| S-EPMC7005716 | biostudies-literature
Project description:G protein-coupled receptors (GPCR) are integral membrane proteins of considerable interest as targets for drug development. GPCR ligand interaction studies often have a starting point with either crystal structures or comparative models. The majority of GPCR do not have experimentally-characterized 3-dimensional structures, so comparative modeling, also called homology modeling, is a good structure-based starting point. Comparative modeling is a widely used method for generating models of proteins with unknown structures by analogy to crystallized proteins that are expected to exhibit structural conservation. Traditionally, comparative modeling template selection is based on global sequence identity and shared function. However high sequence identity localized to the ligand binding pocket may produce better models to examine protein-ligand interactions. This in silico benchmark study examined the performance of a global versus local similarity measure applied to comparative modeling template selection for 6 previously crystallized, class A GCPR (CXCR4, FFAR1, NOP, P2Y12, OPRK, and M1) with the long-term goal of optimizing GPCR ligand identification efforts. Comparative models were generated from templates selected using both global and local similarity measures. Similarity to reference crystal structures was reflected in RMSD values between atom positions throughout the structure or localized to the ligand binding pocket. Overall, models deviated from the reference crystal structure to a similar degree regardless of whether the template was selected using a global or local similarity measure. Ligand docking simulations were performed to assess relative performance in predicting protein-ligand complex structures and interaction networks. Calculated RMSD values between ligand poses from docking simulations and crystal structures indicate that models based on locally selected templates give docked poses that better mimic crystallographic ligand positions than those based on globally-selected templates in five of the six benchmark cases. However, protein model refinement strategies in advance of ligand docking applications are clearly essential as the average RMSD between crystallographic poses and poses docked into local template models was 9.7 Å and typically less than half of the ligand interaction sites are shared between the docked and crystallographic poses. These data support the utilization of local similarity measures to guide template selection in protocols using comparative models to investigate ligand-receptor interactions.
| S-EPMC6449851 | biostudies-literature
Project description: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.
| S-EPMC4592433 | biostudies-literature
Project description:In many scientific and technological contexts, we have only a poor understanding of the structure and details of appropriate mathematical models. We often, therefore, need to compare different models. With available data we can use formal statistical model selection to compare and contrast the ability of different mathematical models to describe such data. There is, however, a lack of rigorous methods to compare different models a priori. Here, we develop and illustrate two such approaches that allow us to compare model structures in a systematic way by representing models as simplicial complexes. Using well-developed concepts from simplicial algebraic topology, we define a distance between models based on their simplicial representations. Employing persistent homology with a flat filtration provides for alternative representations of the models as persistence intervals, which represent model structure, from which the model distances are also obtained. We then expand on this measure of model distance to study the concept of model equivalence to determine the conceptual similarity of models. We apply our methodology for model comparison to demonstrate an equivalence between a positional-information model and a Turing-pattern model from developmental biology, constituting a novel observation for two classes of models that were previously regarded as unrelated.
| S-EPMC8511761 | biostudies-literature
Project description:Persistent homology (PH) is a method used in topological data analysis (TDA) to study qualitative features of data that persist across multiple scales. It is robust to perturbations of input data, independent of dimensions and coordinates, and provides a compact representation of the qualitative features of the input. The computation of PH is an open area with numerous important and fascinating challenges. The field of PH computation is evolving rapidly, and new algorithms and software implementations are being updated and released at a rapid pace. The purposes of our article are to (1) introduce theory and computational methods for PH to a broad range of computational scientists and (2) provide benchmarks of state-of-the-art implementations for the computation of PH. We give a friendly introduction to PH, navigate the pipeline for the computation of PH with an eye towards applications, and use a range of synthetic and real-world data sets to evaluate currently available open-source implementations for the computation of PH. Based on our benchmarking, we indicate which algorithms and implementations are best suited to different types of data sets. In an accompanying tutorial, we provide guidelines for the computation of PH. We make publicly available all scripts that we wrote for the tutorial, and we make available the processed version of the data sets used in the benchmarking.Electronic supplementary materialThe online version of this article (doi:10.1140/epjds/s13688-017-0109-5) contains supplementary material.
| S-EPMC6979512 | biostudies-literature
Project description:G protein-coupled receptors (GPCR) comprise the largest family of membrane proteins and are of considerable interest as targets for drug development. However, many GPCR structures remain unsolved. To address the structural ambiguity of these receptors, computational tools such as homology modeling and loop modeling are often employed to generate predictive receptor structures. Here we combined both methods to benchmark a protocol incorporating homology modeling based on a locally selected template and extracellular loop modeling that additionally evaluates the presence of template ligands during these modeling steps. Ligands were also docked using three docking methods and two pose selection methods to elucidate an optimal ligand pose selection method. Results suggest that local template-based homology models followed by loop modeling produce more accurate and predictive receptor models than models produced without loop modeling, with decreases in average receptor and ligand RMSD of 0.54 Å and 2.91 Å, respectively. Ligand docking results showcased the ability of MOE induced fit docking to produce ligand poses with atom root-mean-square deviation (RMSD) values at least 0.20 Å lower (on average) than the other two methods benchmarked in this study. In addition, pose selection methods (software-based scoring, ligand complementation) selected lower RMSD poses with MOE induced fit docking than either of the other methods (averaging at least 1.57 Å lower), indicating that MOE induced fit docking is most suited for docking into GPCR homology models in our hands. In addition, target receptor models produced with a template ligand present throughout the modeling process most often produced target ligand poses with RMSD values ≤ 4.5 Å and Tanimoto coefficients > 0.6 after selection based on ligand complementation than target receptor models produced in the absence of template ligands. Overall, the findings produced by this study support the use of local template homology modeling in combination with de novo ECL2 modeling in the presence of a ligand from the template crystal structure to generate GPCR models intended to study ligand binding interactions.
| S-EPMC7484324 | biostudies-literature