Measurement of protein surface shape by solid angles

Abstract Motivation Global protein surface comparison (GPSC) studies have been limited compared to other research works on protein structure alignment/comparison due to lack of real applications associated with GPSC. However, the technology advances in cryo-electron tomography (CET) have made methods to identify proteins from their surface shapes extremely useful. Results In this study, we developed a new method called Farthest point sampling (FPS)-enhanced Triangulation-based Iterative-closest-Point (ICP) (FTIP) for GPSC. We applied it to protein classification using only surface shape information. Our method first extracts a set of feature points from protein surfaces using FPS and then uses a triangulation-based efficient ICP algorithm to align the feature points of the two proteins to be compared. Tested on a benchmark dataset with 2329 proteins using nearest-neighbor classification, FTIP outperformed the state-of-the-art method for GPSC based on 3D Zernike descriptors. Using real and simulated cryo-EM data, we show that FTIP could be applied in the future to address problems in protein identification in CET experiments. Availability and implementation Programs/scripts we developed/used in the study are available at http://ani.stat.fsu.edu/∼yuan/index.fld/FTIP.tar.bz2. Supplementary information Supplementary data are available at Bioinformatics online.

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Potential for Protein Surface Shape Analysis Using Spherical Harmonics and 3D Zernike Descriptors

Cell Biochemistry and Biophysics ◽

10.1007/s12013-009-9051-x ◽

2009 ◽

Vol 54 (1-3) ◽

pp. 23-32 ◽

Cited By ~ 54

Author(s):

Vishwesh Venkatraman ◽

Lee Sael ◽

Daisuke Kihara

Keyword(s):

Shape Analysis ◽

Spherical Harmonics ◽

Surface Shape ◽

Protein Surface

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Dimensions of plane and solid angles and their units in the International System of Units (SI)

Izmeritel`naya Tekhnika ◽

10.32446/0368-1025it.2020-10-26-32 ◽

2020 ◽

pp. 26-32

Author(s):

M. I. Kalinin ◽

L. K. Isaev ◽

F. V. Bulygin

Keyword(s):

Solid Angle ◽

International System ◽

International Committee ◽

Plane Angle ◽

Arc Length ◽

Weights And Measures ◽

International System Of Units ◽

System Of Units ◽

In Series ◽

Solid Angles

The situation that has developed in the International System of Units (SI) as a result of adopting the recommendation of the International Committee of Weights and Measures (CIPM) in 1980, which proposed to consider plane and solid angles as dimensionless derived quantities, is analyzed. It is shown that the basis for such a solution was a misunderstanding of the mathematical formula relating the arc length of a circle with its radius and corresponding central angle, as well as of the expansions of trigonometric functions in series. From the analysis presented in the article, it follows that a plane angle does not depend on any of the SI quantities and should be assigned to the base quantities, and its unit, the radian, should be added to the base SI units. A solid angle, in this case, turns out to be a derived quantity of a plane angle. Its unit, the steradian, is a coherent derived unit equal to the square radian.

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