Iterative projection algorithms in protein crystallography. II. Application

Abstract

Iterative projection algorithms (IPAs) are a promising tool for protein crystallographic phase determination. Although related to traditional density-modification algorithms, IPAs have better convergence properties, and, as a result, can effectively overcome the phase problem given modest levels of structural redundancy. This is illustrated by applying IPAs to determine the electron densities of two protein crystals with fourfold non-crystallographic symmetry, starting with only the experimental diffraction amplitudes, a low-resolution molecular envelope and the position of the non-crystallographic axes. The algorithm returns electron densities that are sufficiently accurate for model building, allowing automated recovery of the known structures. This study indicates that IPAs should find routine application in protein crystallography, being capable of reconstructing electron densities starting with very little initial phase information.

Iterative projection algorithms for ab initio phasing in virus crystallography

“…(4) at iteration n, and its Fourier transform, are used. We use the R-factor (R), mean phase error (Φ), and map correlation coefficient (C) [12] to monitor convergence [17,10].…”

“…Liu et al (2012) [8] and He and Su (2015) [7] have applied the HIO algorithm with a solvent flatness constraint to a number 155 of solved proteins with high (> 65%) solvent content. Recently, Lo et al (2015) [10] applied the difference map algorithm to two solved protein structures with lower (∼50%) solvent content by incorporating a NCS constraint. Here we describe in detail application of the difference map algorithm to ab initio phasing of a previously solved icosahedral virus using the experimental diffraction data, 160 and starting with only a spherical shell envelope.…”

“…Each of these methods can present difficulties, however, and the resulting phases may not be accurate enough to produce an interpretable electron density map. The method of molecular replacement requires knowledge of a related structure, and there- 10 fore is not useful for the determination of novel structures.…”

Resolution Dependence of an Ab Initio Phasing Method in Protein X-ray Crystallography

“…Despite the existence of good physical methods for phasing the X-ray reflections of a protein crystal, direct phasing remains a challenging theoretical problem. Iterative projection algorithms have been widely used for phase retrieval [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17].…”

“…For crystals with high solvent content or with adequate non-crystallographic symmetry (NCS), it has been demonstrated that direct phasing is possible [10,12,13]. Completely ab initio phasing using an iterative algorithm has been reported [13].…”