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Fig. 2 | BMC Structural Biology

Fig. 2

From: The origin of β-strand bending in globular proteins

Fig. 2

Definitions of twist and bend angles for a four-residue short β-strand frame. a Schematic of a six-α-carbon β-strand belt containing three frames. Open circles denoting Cα(i), Cα(i + 1), Cα(i + 2), and Cα(i + 3) represent the frame for which the twist and bend angles are calculated. The small gray circles represent the Cβ carbons. The letters L, M and N denote midpoints between two Cα carbons. The letters P and Q denote midpoints between L and M and between M and N, respectively. The twist angle is defined as the dihedral angle of Cα(i + 1), P, Q, and Cα(i + 2). The bend, θB, is defined by the angle between the two vectors \( \overrightarrow{LM} \) and \( \overrightarrow{MN} \). The point R is the point at which the vector pointing from line \( \overrightarrow{LM} \) to Cα(i + 1) is perpendicular. Vector \( \overrightarrow{u} \) is the projection vector of \( \overrightarrow{MN} \) on the plane that is perpendicular to \( \overrightarrow{LM} \). Note that vector \( \overrightarrow{u} \) is not on the plane containing Cα(i + 1), Cα(i + 2), and Cα(i + 3). (B) Schematic showing the possible signs of the bend angle. The two signs for the RL and UD directions are defined by the quadrant in which vector \( \overrightarrow{u} \) resides. Vector \( \overrightarrow{LM} \) points downward and is perpendicular to the plane of the dashed circle. The rotation angle, θR, (0° < θR < 360°) is defined by the angle between the perpendicular vector \( \overrightarrow{RC\alpha \left(i+1\right)} \) and the projection vector \( \overrightarrow{u} \) of \( \overrightarrow{MN} \) on the plane of the circle

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