Iterative projection algorithms in protein crystallography. I. Theory

Abstract

A general class of iterative projection algorithms is described and proposed as a tool for phasing in protein crystallography in order to improve the radius of convergence over that of conventional density-modification algorithms. Their relationship to conventional density modification is described. The common iterative projection algorithms, their convergence properties and their application to protein crystallography are described. These algorithms offer the possibility of protein structure determination starting with only information on the molecular envelope and low-order non-crystallographic symmetry.

The Use of Connected Masks for Reconstructing the Single Particle Image from X-Ray Diffraction Data. III. Maximum-Likelihood Based Strategies to Select Solution of the Phase Problem

“…Основным используемым подходом к практическому использованию избыточности данных, создаваемой наличием в элементарной ячейке большой области нулевых значений электронной плотности, является широкий класс итерационных методов [27][28][29][30][31][32][33]. При удачном выборе параметров метода и стартовой точки эти методы могут приводить к достаточно точным решениям.…”

Iterative projection algorithms for ab initio phasing in virus crystallography

“…For example, for a virus crystal with 5-fold NCS and 40% solvent, the phase problem is overdetermined by a factor of 4. Therefore, it should be possible to determine high resolution phases in virus crystallography with information on only the nature of the 80 NCS, and what is needed is a phasing algorithm that has a sufficiently large radius of convergence to find the solution [17]. Algorithms that have a larger radius of convergence than current electron density modification algorithms are therefore of interest.…”

“…Yet it is well established that the structural redundancy present places considerable constraints on the phases. We have shown recently [17,16] that quite low-order structural redundancy is theoretically sufficient to render the solution to the 75 phase problem unique, i.e. to constrain the phases to their correct values in the absence of any other experimental information.…”

Improving the efficiency of molecular replacement by utilizing a new iterative transform phasing algorithm

“…For medium (close to 50%) solvent content, if noncrystallographic symmetry (NCS) exists, the iterative transform/projection algorithm works well with some initial phase information such as a low-resolution molecular envelope and the position of the non-crystallographic axes (Millane & Lo, 2013;He & Su, 2015;Lo et al, 2015). It works best when the exact position of the non-crystallographic axis is known which is not easily acquired before model building.…”