Research Article: Noncrystallographic symmetry-constrained map obtained by direct density optimization

Date Published: February 01, 2020

Publisher: International Union of Crystallography

Author(s): Masato Yoshimura, Nai-Chi Chen, Hong-Hsiang Guan, Phimonphan Chuankhayan, Chien-Chih Lin, Atsushi Nakagawa, Chun-Jung Chen.


A noncrystallographic symmetry-constrained map obtained by direct density optimization is efficient and equivalent to a noncrystallographic symmetry-averaging map. Using the noncrystallographic symmetry-constrained map, the structure of a T = 1 Penaeus vannamei nodavirus shell-domain subviral particle was newly determined by including twinned data.

Partial Text

The molecular-averaging method in real space coupled with solvent flattening is powerful in phase determination or phase improvement in protein crystallography. In the structure determination of icosahedral viruses, noncrystallographic symmetry (NCS) averaging with phase extension is a common procedure for phase improvement after initial calculations based on molecular replacement (MR) using a density map from a cryo-electron microscope, a similar structural model or initial experimental phases from isomorphous replacement or anomalous dispersion (Arnold et al., 1987 ▸). Under the special conditions that the envelope or icosahedral matrices are given with sufficient precision and the degrees of freedom of the density are sufficiently small, i.e. a lower crystallographic free fraction, the map can be built ab initio (Yoshimura et al., 2016 ▸). Since early in the 1970s, molecular averaging has been performed with iterative calculations of Fourier transformation (FT) and inverse FT between real and inverse space (Buehner et al., 1974 ▸; Bricogne, 1976 ▸). Many applications and results using iterative molecular-averaging methods have been reviewed by Kleywegt & Read (1997 ▸).

The use of NCS is powerful for phasing or phase improvement. NCS has been used as an averaging method in real space. We propose an NCS-constrained map with a new method of direct density optimization (DDO). Whereas the NCS-constrained map is equivalent to an NCS-averaging map, the DDO method requires no Fourier synthesis that calculates a map from Fobs and its phases. To perform DDO, we used unrestrained refinement in REFMAC5 while imposing NCS constraints, and applied this method to a new structure of T = 1 PvNV-Sd. With the condition that the crystallo­graphic ff is sufficiently small, an interpretable map was obtained and the structure of T = 1 PvNV-Sd was subsequently solved. We further demonstrate the application of the DDO method to other T = 1 PvNV-Sd data sets that were twinned, in which the DDO method has no difficulty in generating the NCS-constrained map. A comparison of the NCS-constrained map with DDO and the map from DM, which uses the averaging method, shows no critical difference except that the DDO map produces more complete density at the molecular boundary. Compared with the result of REFMAC5 restrained refinement, the NCS-constrained map with DDO can easily remove the bias from the initial model with the same effort. By making the convergence radius large in future developments, the method will be more powerful for the solution of structures with a large number of NCS including twinned data.




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