Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

The highest reflection intensity in a resolution shell.

Matthias Bochtler1, Grzegorz Chojnowski

  • 1International Institute of Molecular and Cell Biology, ul. Trojdena 4, 02-109 Warsaw, Poland. mbochtler@iimcb.gov.pl

Acta Crystallographica. Section A, Foundations of Crystallography
|February 16, 2007
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

A single viral enzyme drives tRNA-dependent hypermodification of DNA at adenine.

Nature communications·2026
Same author

Etiology of TP53 mutated complex karyotype acute myeloid leukemia.

Leukemia·2025
Same author

gapTrick-structural characterization of protein-protein interactions using AlphaFold.

Bioinformatics (Oxford, England)·2025
Same author

Competition between binding partners of yeast Pex3 affects peroxisome biology.

The FEBS journal·2025
Same author

Introducing the "other" type of DNA methylation.

Science advances·2025
Same author

Activity and structure of human (d)CTP deaminase CDADC1.

Proceedings of the National Academy of Sciences of the United States of America·2025
Same journal

Report of the Executive Committee for 2006.

Acta crystallographica. Section A, Foundations of crystallography·2020
Same journal

Spin line groups.

Acta crystallographica. Section A, Foundations of crystallography·2013
Same journal

Distribution rules of systematic absences on the Conway topograph and their application to powder auto-indexing.

Acta crystallographica. Section A, Foundations of crystallography·2013
Same journal

Platonic solids generate their four-dimensional analogues.

Acta crystallographica. Section A, Foundations of crystallography·2013
Same journal

C70, C80, C90 and carbon nanotubes by breaking of the icosahedral symmetry of C60.

Acta crystallographica. Section A, Foundations of crystallography·2013
Same journal

Comparative study of X-ray charge-density data on CoSb3.

Acta crystallographica. Section A, Foundations of crystallography·2013
See all related articles

The Gumbel-Fisher-Tippett analysis models extreme-value statistics for X-ray diffraction intensities. This provides accurate predictions for reflection intensity distribution in crystals with many atoms.

Area of Science:

  • Crystallography
  • Statistical Mechanics
  • Materials Science

Background:

  • X-ray diffraction is crucial for determining crystal structures.
  • Understanding intensity distribution of reflections is key for accurate structural analysis.
  • Extreme-value statistics offer a framework for analyzing rare events, like strongest reflections.

Purpose of the Study:

  • To apply Gumbel-Fisher-Tippett extreme-value analysis to X-ray diffraction data.
  • To derive and validate formulas for the distribution, expectation value, and standard deviation of the strongest reflection intensity.
  • To assess the applicability of these formulas for both centric and acentric reflections in various crystal structures.

Main Methods:

  • Utilized Gumbel-Fisher-Tippett extreme-value analysis.

Related Experiment Videos

  • Separately analyzed centric and acentric reflections.
  • Measured intensities in units of average reflection intensity.
  • Performed extensive numerical simulations to validate theoretical formulas.

    • Main Results:

    • Derived analytical expressions for the expectation value (mu) and standard deviation (sigma) of the strongest reflection intensity (J) for both centric and acentric reflections.
    • Formulas for acentric reflections: mu = ln n + gamma and sigma = pi/6(1/2).
    • Formulas for centric reflections: mu = 2(ln n + gamma) - ln(pi ln n) and sigma = 2pi/6(1/2) - pi/(6(1/2) ln n).
    • Numerical simulations confirmed the formulas as excellent approximations for random atom configurations and good approximations for real protein crystal structures (2.5-1.0 A resolution).

    Conclusions:

    • The Gumbel-Fisher-Tippett analysis provides accurate statistical models for extreme reflection intensities in X-ray diffraction.
    • The derived formulas are reliable for predicting intensity distributions in crystals with numerous scattering atoms.
    • This approach enhances the interpretation of X-ray diffraction data, particularly for complex crystal structures.