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Related Concept Videos

Spherical Coordinates01:23

Spherical Coordinates

Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
Surface Area Calculations01:22

Surface Area Calculations

Surface area calculations for a graph z = f(x, y) are fundamental in engineering applications involving curved structures such as satellite dishes. A parabolic dish reflects communication signals efficiently, but engineers must determine its exact curved surface area to estimate coating materials, fabrication costs, and structural requirements. Since the rim of the dish forms a circular boundary, the surface area is calculated over a circular domain in the xy-plane.Parametric Representation of...
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Newman Projections

Different notations are used to represent the three-dimensional structure of molecules on two-dimensional surfaces. One of the most commonly used representations is the dash-wedge formula. The dashed wedges, solid wedges, and the plane lines indicate the groups situated behind the plane, coming out of the plane, and in the plane, respectively.
The organic molecules rotate across the single bonds leading to numerous temporary three-dimensional structures of varying energy known as conformers.
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Learning to draw Fischer projections of molecules and understanding their relevance plays a crucial role in the visual depiction of organic molecules. A Fischer projection is a two-dimensional projection on a planar surface to simplify the three-dimensional wedge–dash representation of molecules. This is especially helpful in the case of molecules with multiple chiral centers that can be difficult to draw. Here, all the bonds of interest are represented as horizontal or vertical lines. While...

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Potential for protein surface shape analysis using spherical harmonics and 3D Zernike descriptors.

Vishwesh Venkatraman1, Lee Sael, Daisuke Kihara

  • 1Department of Biological Sciences, Purdue University, West Lafayette, IN 47907, USA.

Cell Biochemistry and Biophysics
|June 13, 2009
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Summary

Moment-based representations offer efficient molecular structure encoding for large-scale function prediction. Spherical harmonics and 3D Zernike descriptors are key methods for fast screening and molecular comparisons.

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Area of Science:

  • Computational chemistry
  • Structural bioinformatics
  • Cheminformatics

Background:

  • Databases of molecular structures are growing rapidly.
  • Predicting molecular function at scale is challenging.
  • Efficient molecular structure encodings are needed for rapid screening.

Purpose of the Study:

  • To provide an overview of moment-based representations for molecular structure encoding.
  • To focus on spherical harmonics and 3D Zernike descriptors.
  • To highlight applications and recent advances in shape and property-based comparisons.

Main Methods:

  • Review of commonly used moment-based representations.
  • Detailed examination of spherical harmonics and 3D Zernike descriptors.
  • Discussion of global and local comparison methods.

Main Results:

  • Moment-based representations offer compact and nonredundant descriptions of molecular shape and properties.
  • Spherical harmonics and 3D Zernike descriptors provide effective encodings for screening.
  • Recent advances enable advanced shape and property-based comparisons.

Conclusions:

  • Moment-based representations are crucial for large-scale molecular function prediction.
  • Spherical harmonics and 3D Zernike descriptors are valuable tools in cheminformatics.
  • The presented methods facilitate effective molecular comparisons at multiple levels.