A general method for directly phasing diffraction data from high-solvent-content protein crystals

Abstract

A procedure is described for direct phase determination in protein crystallography, applicable to crystals with high solvent content. The procedure requires only the diffraction data and an estimate of the solvent content as input. Direct phase determination is treated as a constraint satisfaction problem, in which an image is sought that is consistent with both the diffraction data and generic constraints on the density distribution in the crystal. The problem is solved using an iterative projection algorithm, the Difference Map algorithm, which has good global convergence properties, and can locate the correct solution without any initial phase information. Computational efficiency is improved by breaking the problem down into two stages; initial approximation of the molecular envelope at low resolution, followed by subsequent phase determination using all of the data. The molecular envelope is continually updated during the phase determination step. At both stages, the algorithm is initiated with many different and random phase sets, which are evolved subject to the constraints. A clustering procedure is used to identify consistent results across multiple runs, which are then averaged to generate consensus envelopes or phase sets. The emergence of highly consistent phase sets is diagnostic of success. The effectiveness of the procedure is demonstrated by application to 42 known structures of solvent fraction 0.60–0.85. The procedure works robustly at intermediate resolutions (1.9–3.5 Å) but is strongly dependent on crystal solvent content, only working routinely with solvent fractions greater than 0.70.

Refining Protein Envelopes with a Transition Region for Enhanced Direct Phasing in Protein Crystallography

“…Direct methods play a crucial role in solving protein crystal structures directly from diffraction data without relying on any prior information, such as heavy-atom derivatives or homology structures [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Traditional direct methods for phasing small-molecule crystals [17][18][19][20][21][22][23][24][25][26][27][28][29] use the triplet relation and the tangent formula [21][22][23], the vive la différence algorithm (VLD) [28], the electron-density modification (EDM) and the difference electrondensity modification (DEDM) [29], etc.…”

“…It is cyclic and easy to implement with a large convergence radius when the crystal has a high solvent content. While the direct method for macromolecule crystals has been successfully tested in retrieving known crystal structures of proteins and viruses [8][9][10][11][12][13][14][15][16], it has not been applied to solve the atomic structure of unknown protein crystals.…”

Direct phasing algorithm for protein crystals with high solvent content using low-resolution diffraction data

“…Over the past decade, significant effort has been devoted to the development of various algorithms for de novo protein structure determination (Uso ´n & Sheldrick, 1999;Dorset, 2000;Miller et al, 2001;Rodrı ´guez et al, 2009;Liu et al, 2012; ISSN 2059-7983 He & Su, 2015;Kingston & Millane, 2022). Direct phase determination using iterative projection algorithms (IPAs; Millane & Lo, 2013;Lo et al, 2015) has shown potential as an effective tool for ab initio phase determination in protein crystallography.…”

A deep learning solution for crystallographic structure determination

“…Fienup (1982) also extended the G-S algorithm to work better in settings similar to X-ray crystallography. Similar methods to that developed by Fienup have occasionally been applied to solve the crystallographic phase problem, but only in special cases where the crystals have very high solvent content (He & Su, 2015;He et al, 2016a;Kingston & Millane, 2022).…”