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Related Experiment Videos

On the equivalence between a commonly used correlation coefficient and a least-squares function.

Diane C Jamrog1, Yin Zhang, George N Phillips

  • 1Department of Computational and Applied Mathematics, Rice University, Houston, Texas, USA. djamrog@alumni.rice.edu

Acta Crystallographica. Section A, Foundations of Crystallography
|April 23, 2004
PubMed
Summary

This study demonstrates the equivalence of two objective functions for molecular replacement (MR) in X-ray crystallography. The correlation coefficient, particularly using structure-factor magnitudes, is predicted to outperform other methods, especially with low-resolution data.

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Area of Science:

  • Crystallography
  • Structural Biology
  • Computational Chemistry

Background:

  • Objective functions are crucial for solving the molecular replacement (MR) problem in X-ray crystallography.
  • Existing methods include correlation coefficient and least-squares functions, but their comparative performance is not fully understood.

Purpose of the Study:

  • To establish the mathematical equivalence between two common objective functions used in MR: the correlation coefficient and the least-squares function.
  • To investigate the impact of data preprocessing (mean subtraction) on this equivalence.
  • To evaluate the performance of different correlation coefficient types (intensities vs. structure-factor magnitudes) in MR.

Main Methods:

  • Mathematical derivation to prove the equivalence of objective functions.

Related Experiment Videos

  • Analysis of objective function behavior based on mean subtraction.
  • Computational testing using the SOMoRe program for molecular replacement at low resolution.

    • Main Results:

    • The correlation coefficient and least-squares functions are shown to be equivalent under certain conditions, particularly near global optima.
    • Equivalence is dependent on whether mean values are subtracted from observed and calculated data.
    • Correlation coefficient using structure-factor magnitudes showed better performance than using intensities, especially with low-resolution data.

    Conclusions:

    • The equivalence of these objective functions simplifies MR problem-solving strategies.
    • Using structure-factor magnitudes in the correlation coefficient is recommended for improved MR, particularly when dealing with low-resolution crystallographic data.