Iterative phase retrieval in macromolecular crystal diffraction using the gradients of intensities

Iterative phase retrieval (IPR) offers a model-independent route to crystallographic structure determination but is fundamentally limited by the sampling of the diffraction pattern at Bragg positions. Consequently, conventional IPR methods typically rely on a high solvent fraction (>70%) to sufficiently constrain the solution, a condition met by only a small fraction of protein crystals. This work investigates a magnitude-and-gradient IPR algorithm that overcomes this undersampling barrier by exploiting the local intensity gradients ∇Iq observable in the diffraction patterns of finite crystals. By incorporating the gradients of the molecular transform alongside Bragg intensities, the phase problem is converted from an underdetermined system of equations to one that is overdetermined by a factor of two. Tests on simulated diffraction data for proteins in space group P1 demonstrate that the algorithm successfully reconstructs electron densities across a wide range of solvent fractions, including densely packed crystals where standard algorithms fail. Furthermore, the approach proves robust under experimentally relevant conditions, tolerating significant Poissonian noise and the loss of low-resolution terms due to a beamstop when coupled with approximate real-space support constraints. These results indicate that leveraging the fine structure of Bragg peaks at coherent X-ray sources can significantly extend the applicability of ab initio phasing.

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Subjects

iterative phase retrieiterative phase retrieval

ab initio phasing

macromolecular crystallography

nanocrystals

DDC Class

539: Matter; Molecular Physics; Atomic and Nuclear physics; Radiation; Quantum Physics

519: Applied Mathematics, Probabilities

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https://creativecommons.org/licenses/by/4.0/

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publishedVersion

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te5167.pdf

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