Object-oriented persistent homology

Wang, Bao; Wei, Guo-Wei

doi:10.1016/j.jcp.2015.10.036

Cited by 54 publications

(58 citation statements)

References 94 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We consider a benchmark test example, a C 60 molecule, to illustrate the ESES performance in loop and cavity generation . Figure depicts C 60 generated at the atomic radius of 0.8 Å for all the Carbon atoms with the probe radius of 0.1 Å.…”

Section: Validationmentioning

confidence: 99%

ESES: Software for Eulerian solvent excluded surface

et al. 2017

Self Cite

View full text Add to dashboard Cite

Solvent excluded surface (SES) is one of the most popular surface definitions in biophysics and molecular biology. In addition to its usage in biomolecular visualization, it has been widely used in implicit solvent models, in which SES is usually immersed in a Cartesian mesh. Therefore, it is important to construct SESs in the Eulerian representation for biophysical modeling and computation. This work describes a software package called Eulerian solvent excluded surface (ESES) for the generation of accurate SESs in Cartesian grids. ESES offers the description of the solvent and solute domains by specifying all the intersection points between the SES and the Cartesian grid lines. Additionally, the interface normal at each intersection point is evaluated. Furthermore, for a given biomolecule, the ESES software not only provides the whole surface area, but also partitions the surface area according to atomic types. Homology theory is utilized to detect topological features, such as loops and cavities, on the complex formed by the SES. The sizes of loops and cavities are measured based on persistent homology with an evolutionary partial differential equation-based filtration. ESES is extensively validated by surface visualization, electrostatic solvation free energy computation, surface area and volume calculations, and loop and cavity detection and their size estimation. We used the Amber PBSA test set in our electrostatic solvation energy, area, and volume validations. Our results are either calibrated by analytical values or compared with those from the MSMS software. © 2017 Wiley Periodicals, Inc.

show abstract

Section: Validationmentioning

confidence: 99%

ESES: Software for Eulerian solvent excluded surface

et al. 2017

Self Cite

View full text Add to dashboard Cite

show abstract

“…Persistent Homology [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55] is a means of topological data analysis. Now let us use an example to show how the topological data analysis methods can overcome the limitations of geometrical methods.…”

Section: Persistent Homologymentioning

confidence: 99%

Topological Data Analysis for the Characterization of Atomic Scale Morphology from Atom Probe Tomography Images

2018

View full text Add to dashboard Cite

Atom probe tomography (APT) represents a revolutionary characterization tool for materials that combine atomic imaging with a time-of-flight (TOF) mass spectrometer to provide direct space three-dimensional, atomic scale resolution images of materials with the chemical identities of hundreds of millions of atoms. It involves the controlled removal of atoms from a specimen's surface by field evaporation and then sequentially analyzing them with a position sensitive detector and TOF mass spectrometer. A paradox in APT is that while on the one hand, it provides an unprecedented level of imaging resolution in three dimensions, it is very difficult to obtain an accurate perspective of morphology or shape outlined by atoms of similar chemistry and microstructure. The origins of this problem are numerous, including incomplete detection of atoms and the complexity of the evaporation fields of atoms at or near interfaces. Hence, unlike scattering techniques such as electron microscopy, interfaces appear diffused, not sharp. This, in turn, makes it challenging to visualize and quantitatively interpret the microstructure at the "meso" scale, where one is interested in the shape and form of the interfaces and their associated chemical gradients. It is here that the application of informatics at the nanoscale and statistical learning methods plays a critical role in both defining the level of uncertainty and helping to make quantitative, statistically objective interpretations where heuristics often dominate. In this chapter, we show how the tools of Topological Data Analysis provide a new and powerful tool in the field of nanoinformatics for materials characterization.

show abstract

“…This structure is constructed by replacing each hexagonal vertex with a smaller hexagon. The coordinates of largest hexagon are set to ( 30], and the grid spacing is chosen as 0.05 in order to capture all the local details in the structure. It is easy to see that the length of the edge is 20.…”

Section: Multiresolution Geometric Analysis Of the Hexagonal Fractal mentioning

confidence: 99%

“…36 We have devised persistent homology to predict the stability of proteins 36 and the curvature energies of fullerene isomers. 30,34 To proactively extract desirable topological traits from complex data, we have introduced objectiveoriented persistent homology based on variational principle. 30 We have also developed multidimensional persistence to better analyze biomolecular data.…”

Section: Introductionmentioning

confidence: 99%

“…30,34 To proactively extract desirable topological traits from complex data, we have introduced objectiveoriented persistent homology based on variational principle. 30 We have also developed multidimensional persistence to better analyze biomolecular data. 37 We have utilized persistent homology to resolve ill-posed inverse problems in cryo-EM structural fitting.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Multiresolution persistent homology for excessively large biomolecular datasets

Xia

Zhao

Guo

2015

The Journal of Chemical Physics

Self Cite

View full text Add to dashboard Cite

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 flexibilityrigidity 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. C 2015 AIP Publishing LLC. [http://dx

show abstract

Object-oriented persistent homology

Cited by 54 publications

References 94 publications

ESES: Software for Eulerian solvent excluded surface

ESES: Software for Eulerian solvent excluded surface

Topological Data Analysis for the Characterization of Atomic Scale Morphology from Atom Probe Tomography Images

Multiresolution persistent homology for excessively large biomolecular datasets

Contact Info

Product

Resources

About