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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...
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HermiteFit: fast-fitting atomic structures into a low-resolution density map using three-dimensional orthogonal

Georgy Derevyanko1, Sergei Grudinin2

  • 1Institute of Complex Systems (ICS-6), Forschungszentrum Jülich, Jülich, Germany.

Acta Crystallographica. Section D, Biological Crystallography
|August 2, 2014
PubMed
Summary

HermiteFit is a new algorithm for fitting protein structures into electron density maps. It uses Hermite functions to accelerate rotation, improving efficiency for structural biology.

Keywords:
Cryo-EMHermite orthogonal polynomialsHermiteFitdensity fittingfast Fourier transformspherical harmonics

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Area of Science:

  • Structural biology
  • Computational biology
  • Biophysics

Background:

  • Fitting atomic models into low-resolution cryo-EM density maps is crucial for structural biology.
  • Existing methods can be computationally intensive, particularly for large datasets or complex structures.

Purpose of the Study:

  • To present HermiteFit, a novel algorithm for accelerated protein structure fitting into electron density maps.
  • To introduce efficient algorithms for density rotation and coefficient conversion within the Hermite basis.
  • To provide an analytical method for calculating the crystallographic R factor in the Hermite basis.

Main Methods:

  • Developed a novel algorithm, HermiteFit, utilizing three-dimensional orthogonal Hermite functions for accelerated rotation of electron density Fourier images.
  • Implemented algorithms for density rotation and coefficient conversion between Hermite and Fourier bases.
  • Employed cross-correlation and Laplacian-filtered cross-correlation as fitting criteria, noting the simplified form of the Laplacian filter in the Hermite basis.

Main Results:

  • Demonstrated the efficiency of HermiteFit in fitting protein structures to low-resolution electron density maps.
  • Presented an analytical method for computing the crystallographic R factor to assess Hermite basis density encoding quality.
  • Validated HermiteFit through two examples, showing competitive or superior efficiency compared to ADP_EM and colores.

Conclusions:

  • HermiteFit offers an efficient and validated approach for protein structure fitting into electron density maps.
  • The use of Hermite functions provides computational advantages for rotation and analysis.
  • The algorithm is made publicly available, facilitating its adoption in structural biology research.