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Updated: Feb 28, 2026

Microcrystallography of Protein Crystals and In Cellulo Diffraction
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Direct Phasing of Protein Crystals with Continuous Iterative Projection Algorithms and Refined Envelope

Yang Liu1, Ruijiang Fu1, Wu-Pei Su2

  • 1Department of Physics, School of Physical Science and Technology, Ningbo University, Ningbo 315211, China.

Biomolecules
|February 27, 2026
PubMed
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This summary is machine-generated.

New continuous algorithms and refined molecular envelope reconstruction improve direct phasing for protein crystals, especially those with low solvent content. This enhances accuracy and extends the applicability of crystallographic methods.

Area of Science:

  • Structural biology
  • Crystallography
  • Biophysics

Background:

  • Direct methods offer model-free solutions to the crystallographic phase problem, yielding unbiased atomic structures.
  • Conventional algorithms like Hybrid Input-Output (HIO) struggle with discontinuous density modification and inaccurate molecular envelopes, particularly in crystals with limited solvent content.

Purpose of the Study:

  • To develop improved continuous iterative projection algorithms for smoother density modification.
  • To enhance molecular envelope reconstruction accuracy by accounting for trapped solvent.
  • To extend the applicability of direct phasing methods to challenging protein crystals.

Main Methods:

  • Introduced four continuous iterative projection algorithms with smooth density modification.
Keywords:
continuous density modificationdirect methodsgenetic algorithmhigh solvent contentiterative projection algorithmsmolecular envelope reconstructionphase problemprotein crystallography

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  • Developed a two-step refined reconstruction scheme using Gaussian filters to identify trapped solvent.
  • Integrated a genetic algorithm co-evolution strategy for enhanced performance and convergence.

    • Main Results:

    • The refined envelope scheme significantly increased success rates for both continuous (45.7%) and classical (60.5%) algorithms.
    • Continuous and improved classical algorithms performed comparably to HIO, forming a top-tier group.
    • Genetic algorithm integration boosted success rates 2.5-fold and accelerated convergence.
    • Averaging solutions reduced mean phase error by ~6.83° and yielded models with low RMSD (<0.5 Å).

    Conclusions:

    • Novel continuous algorithms and refined envelope reconstruction enhance direct phasing reliability, particularly for crystals with low solvent content.
    • The integrated framework extends the practical boundaries of direct methods in structural biology.
    • This toolkit addresses challenging phasing cases, improving atomic model accuracy.