International
Tables for
Crystallography
Volume F
Crystallography of biological macromolecules
Edited by M. G. Rossmann and E. Arnold

© International Union of Crystallography 2006
International Tables for Crystallography (2006). Vol. F. ch. 19.5, p. 445   | 1 | 2 |

Section 19.5.3.2. Helical symmetry

R. Chandrasekarana* and G. Stubbsb

aWhistler Center for Carbohydrate Research, Purdue University, West Lafayette, IN 47907, USA, and  bDepartment of Molecular Biology, Vanderbilt University, Nashville, TN 37235, USA
Correspondence e-mail:  chandra@purdue.edu

19.5.3.2. Helical symmetry

| top | pdf |

It is convenient to use cylindrical coordinates to describe helical molecules. In real space we use coordinates (r, φ, z); in reciprocal space (R, ψ, Z). By convention, the z axis is the helix axis and the line [(\varphi = 0, z = 0)] corresponds to the x axis in Cartesian coordinates. The repeat distance along the z axis is c. Within this distance, there are u repeating units in t turns of the helix. If the coordinates of a point in the first repeating unit are (r, φ, z), then applying the helical symmetry gives the coordinates of the corresponding point in the (k + 1)th repeating unit as [(r, \varphi + 2\pi kt/u, z + kc/u)].








































to end of page
to top of page