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![[Figure 1]](yt5034fig1mag.jpg)
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Figure 1
A brief graphic summary of the 2-D helical system. On the left, a 2-D lattice wrapping specified by a circumference vector, w = n1a + n2b, is sketched with an example of n1 = 7 and n2 = 4. The 2-D lattice is highlighted in color with the angle γ between the two axes a and b. The lattice lies on the Cartesian xy plane and the axis a lies along the Cartesian x axis. Thus, the axis a in Cartesian coordinates is (a, 0 ,0) and b is (bcosγ, bsinγ, 0). The wrapped helical coordinates (xw, yw, zw) of the Cartesian coordinates (xc, yc, zc) in the 2-D planar system can then be calculated by the helical transformation in terms of the helical axis t (which is perpendicular to w) with the two parameters α and h, twist angle and rise distance, respectively. It is then straightforward to determine the circumferential unit vector wu, the helical radius r and the helical axis t as formulated on the right-hand side of the sketch with the summarized wrapping equations highlighted in color at the bottom. Note that vector (tx, ty, tz) as calculated from wu is also a unit vector. |
![[Figure 1]](yt5034fig1.jpg)
 | STRUCTURAL BIOLOGY |
ISSN: 2059-7983
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