Discrete differential geometry of curves and protein structure

Jack Quine (April 25, 2011)

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Abstract

Differential geometry of curves uses the Frenet-Serret moving frame. A curve can be defined by scalar quantities of curvature and torsion and these quantities are defined by differentiating the frame. Similar techniques can be used for discrete curves formed by sequences of bonded atoms. The frames are related to molecular frames and are useful in finding protein structure from NMR data which gives the orientation of the frames with respect to the magnetic field direction. Curvature and torsion can be related to helical protein secondary structure. We discuss the use of these techniques in solving an alpha helical structure using NMR.