ArticleJournal of computational chemistry2012
A hierarchical algorithm for fast Debye summation with applications to small angle scattering.
Article in Journal of computational chemistry, 2012. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 11 papers.
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Who cites it
11 citing papers in PubMed.
- SuAVE-Scatter: A Module for Integrating Simulations and SAXS/SANS Analyses.Journal of chemical information and modeling · 2026Article
- Small-angle X-ray scattering profile calculation for high-resolution models of biomacromolecules.Journal of applied crystallography · 2025Article
- Article
- WAXSiS: a web server for the calculation of SAXS/WAXS curves based on explicit-solvent molecular dynamics.Nucleic acids research · 2015Article
- Interpretation of solution x-ray scattering by explicit-solvent molecular dynamics.Biophysical journal · 2015Article
- Validating solution ensembles from molecular dynamics simulation by wide-angle X-ray scattering data.Biophysical journal · 2014Article
- Using small angle solution scattering data in Xplor-NIH structure calculations.Progress in nuclear magnetic resonance spectroscopy · 2014Review
- HierarchicalJournal of applied crystallography · 2014Article
- Recovering a representative conformational ensemble from underdetermined macromolecular structural data.Journal of the American Chemical Society · 2013Article
- Accurate SAXS profile computation and its assessment by contrast variation experiments.Biophysical journal · 2013Article
- Reconstruction of SAXS Profiles from Protein Structures.Computational and structural biotechnology journal · 2013Review
Corrections and comments
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Authors and funding
4 authors.
Funding
Abstract
Debye summation, which involves the summation of sinc functions of distances between all pair of atoms in three-dimensional space, arises in computations performed in crystallography, small/wide angle X-ray scattering (SAXS/WAXS), and small angle neutron scattering (SANS). Direct evaluation of Debye summation has quadratic complexity, which results in computational bottleneck when determining crystal properties, or running structure refinement protocols that involve SAXS or SANS, even for moderately sized molecules. We present a fast approximation algorithm that efficiently computes the summation to any prescribed accuracy ε in linear time. The algorithm is similar to the fast multipole method (FMM), and is based on a hierarchical spatial decomposition of the molecule coupled with local harmonic expansions and translation of these expansions. An even more efficient implementation is possible when the scattering profile is all that is required, as in small angle scattering reconstruction (SAS) of macromolecules. We examine the relationship of the proposed algorithm to existing approximate methods for profile computations, and show that these methods may result in inaccurate profile computations, unless an error-bound derived in this article is used. Our theoretical and computational results show orders of magnitude improvement in computation complexity over existing methods, while maintaining prescribed accuracy.
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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.