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. Author manuscript; available in PMC: 2010 Apr 8.
Published in final edited form as: J Am Chem Soc. 2009 Apr 8;131(13):4854–4865. doi: 10.1021/ja8095224

Figure 9.

Figure 9

A diagram showing the methods by which individual sterol orientation is defined using Euler angles relating molecular axes of the sterol to reference axes of the bilayer as a whole. The reference z axis is defined along the membrane normal, while the reference xy is the plane of the bilayer. A molecular ring axis Z is defined from carbon 13 to 3 along the length of the ring, and a molecular tail axis Z′ is defined from carbon 25 to 17 along the length of the tail. Finally, a ring normal axis X is defined from carbon 10 to 19, outward through the protruding methyl groups. Three Euler angles are then calculated. The sterol ring tilt β is defined as the angle between the reference z-axis and sterol ring Z-axis, the sterol ring twist γ is defined as the angle between the intersection N of the reference xy plane and sterol ring XY plane and the sterol ring X axis, and the sterol tail tilt β′ is defined as the angle between the reference z-axis and sterol tail Z′-axis.