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Refinement of macromolecular structures by the maximum-likelihood method.

G N Murshudov1, A A Vagin, E J Dodson

  • 1Chemistry Department, University of York, Heslington, England.

Acta Crystallographica. Section D, Biological Crystallography
|May 1, 1997
PubMed
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This study enhances maximum likelihood methods for macromolecular structures by incorporating prior phase information and experimental uncertainties. Results show maximum-likelihood refinement consistently outperforms traditional least-squares methods.

Area of Science:

  • Structural biology
  • Crystallography
  • Biophysics

Background:

  • Maximum likelihood (ML) is a fundamental statistical method.
  • Refining macromolecular structures requires accurate error estimation.
  • Prior phase information and experimental uncertainties are crucial for accurate structure determination.

Purpose of the Study:

  • To review the mathematical basis of maximum likelihood for macromolecular structures.
  • To extend the likelihood function to include prior phase information and experimental standard uncertainties.
  • To develop and test a method for estimating sigma(A) using 'free' reflections.

Main Methods:

  • Review of maximum likelihood mathematical principles.
  • Extension of the likelihood function to incorporate prior phase information and experimental uncertainties.

Related Experiment Videos

  • Development of a method for estimating sigma(A) using 'free' reflections.
  • Implementation of derived equations in the REFMAC program.

    • Main Results:

    • The extended likelihood function effectively incorporates prior phase information and experimental uncertainties.
    • The method for estimating sigma(A) using 'free' reflections was analyzed.
    • Testing on various proteins demonstrated consistent improvements using the maximum-likelihood residual.
    • Maximum-likelihood refinement yielded superior results compared to least-squares refinement.

    Conclusions:

    • The enhanced maximum likelihood approach provides a more robust method for macromolecular structure refinement.
    • The REFMAC program, incorporating these methods, shows significant advantages over least-squares refinement.
    • Accurate estimation of experimental uncertainties and prior phase information are critical for high-resolution structure determination.