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Figure 3 | BMC Structural Biology

Figure 3

From: ProteinShader: illustrative rendering of macromolecules

Figure 3

Calculation of local coordinate frames and a spline for drawing tubes. (A) The local coordinate frame for α-carbon number i in a polypeptide chain, Cα (i), is calculated relative to the triangle (light green) that it forms with Cα (i-1) and Cα (i+1). The vectors N (Normal; green), B (Binormal; yellow), and T (Tangent; red) are the xyz-axes, respectively, of the local frame (see Local coordinate frames in the text). (B) The column vectors N, B, and T form a matrix that defines a rotation about Cα (i). (C) The tangent vectors and xyz-coordinates of two α-carbons are sufficient to define a parameterized cubic polynomial equation (see Hermite interpolation in the text). The set of cubic polynomials connecting the α-carbons of a polypeptide chain form a spline, which is shown as a curved dotted line in (A). (D) The equation for interpolation between rotations using quaternions (see SLERP in text). (E) An α-helix after selecting Frenet Frames from the Style menu. The α-carbons (small gray spheres) have local frames represented by green, yellow, and red vectors as in (A). The smaller local frames between α-carbons are interpolated by using the Hermite-SLERP algorithm described in the text. (F) The α-helix from (E) after selecting Tubes from the Style menu and Wireframe from the Decorations panel. To draw the tube, a regular polygon defined by 20 vertices in a circle (red) is swept along the spline and rotated into alignment with the xy-plane of each local frame. Connecting vertices between successive positions of the polygon produces the surface of the tube. (G) The α-helix from (F) after Plain is selected from the Decorations menu and the Cartoon Color subpanel is used to color tube segments by amino acid type.

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