Journal: Journal of structural biology

Article Title: Deducing the Symmetry of Helical Assemblies: Applications to Membrane Proteins

doi: 10.1016/j.jsb.2016.05.011

Figure Lengend Snippet: Relationship between a planar, 2D lattice and a helical assembly. (A) The surface of a helical assembly is composed of a planar lattice, which is characterized by unit cell axes a (blue) and b (green) and the intervening angle γ. The horizontal axis corresponds to the circumference of a cylinder, which can be measured either with azimuthal coordinates (ϕ=0–360°) or a linear dimension (0–2πr, r is the radius) and is depicted as a vector extending from one point in the lattice to another. These two points coincide when the assembly is rolled into a cylinder. The vertical axis corresponds to the longitudinal axis of the cylinder, which has a linear dimension. (B) The same lattice as in A, but rolled up into a cylinder. The solid blue and green lines correspond to those in A and follow a helical path around the surface of the cylinder. Each of these lines belongs to a helical family, which are drawn as parallel, dotted lines in A. The start numbers for each family correspond to the number of parallel lines that cross the circumferential vector, which in this case are 10 for the green helices and 9 for the blue helices. The Bessel orders for these helical families are therefore −9 and 10, with the sign reflecting the handedness of the helices. (C) Mock diffraction pattern from the planar lattice in A showing the principal (1,0) and (0,1) reflections. This pattern of reflections is consistent with Bragg’s law that describes how the lattice lines drawn in A generates this diffraction pattern. (D) Mock diffraction pattern from the helical lattice in B. Each discrete reflection in C generates a Bessel function, depicted as series of three amplitude peaks drawn in black. In addition, the helix generates mirror symmetry about the meridional axis (Z), resulting from the superposition of near and far sides of the assembly. This mirror symmetry gives rise to the amplitude peaks drawn in grey. Together, the black and grey amplitudes constitute a layer line. The rise dz and the azimuthal angle dϕ are shown in panel A, which characterize a one-start helix running through all of the points in the lattice. This one-start helix has a pitch, indicated on the right in panel A, and the distance between the corresponding layer line (with a Bessel order of one) and the equator will equal the reciprocal of this pitch. Such a one-start helix is sometimes referred to as a "genetic helix" and is useful for iterative real-space helical reconstruction methods.

Article Snippet: Using 2D lattice parameters to evaluate indexing schemes Knowledge of the 2D lattice dimensions within the membrane plane can help establish the correct helical indexing scheme by predicting the diameter of the helical assembly ( Unwin et al., 1988 ).

Techniques: Plasmid Preparation

Journal: Journal of structural biology

Article Title: Deducing the Symmetry of Helical Assemblies: Applications to Membrane Proteins

doi: 10.1016/j.jsb.2016.05.011

Figure Lengend Snippet: Deducing helical symmetry from a 2D surface lattice. (A) The 2D array represents the crystalline lattice of the protein at the surface of the helical assembly; in the case of membrane proteins such as Bor1p and OmpF, this surface corresponds to the membrane plane. A vector representing the circumference of a helical assembly has been drawn from an arbitrary origin (star) to the (−10,9) coordinate in the array (red triangle). (B) After reorienting the circumferential vector to the equatorial plane (horizontal) and delimiting the azimuthal extent of the array (vertical lines), the start number for 30 helical families can be evaluated by the number of times the parallel lines cross the circumferential vector (cf. green and blue lines in Fig. 1A). The helical families that are shown run perpendicular to the a and b vectors and therefore correspond to the (1,0) and (0,1) layer lines. In this case, the chosen circumferential vector generates start numbers of −10 and 9, respectively. (C) The 2D lattice is the same as in A based on the underlying assumption that all the helical assemblies are built from the same lattice. However, the circumferential vector is drawn to the (−10,8) coordinate (yellow triangle) in order to generate a different helical symmetry. (D) The corresponding helical lattice generates start numbers of −10 and 8 for the (1,0) and (0,1) layer lines, respectively.

Article Snippet: Using 2D lattice parameters to evaluate indexing schemes Knowledge of the 2D lattice dimensions within the membrane plane can help establish the correct helical indexing scheme by predicting the diameter of the helical assembly ( Unwin et al., 1988 ).

Techniques: Membrane, Plasmid Preparation