Polypeptide Bond Angles

Bond Rotation

• $\varphi$ is the angle of rotation between the $\mathrm{N}$ and $\mathrm{C}{}_{\alpha }$ atoms
• $\psi$ is the angle of rotation between the $\mathrm{C}$ and $\mathrm{C}{}_{\alpha }$ atoms

Mnemonic

• The $\mathrm{C}$ carbonyl, $\mathrm{C}{}_{\alpha }$, $N$, and the carbonyl $\mathrm{O}$ are all coplanar due to conjugation by delocalization of the nitrogen lone pair. This means there is no variable angle of rotation between the $\mathrm{N}$ and carbonyl $\mathrm{C}$
• $\psi$ is a wave function in physics, and the carbonyl $\mathrm{O}$ looks like of like a stick figure’s head, and so this stick figure “waves” his hand, which can only be between the carbonyl $\mathrm{C}$ and $\mathrm{C}{}_{\alpha }$
• $\varphi$ is the Golden Ratio, which is goldeN, corresponding to the angle being between $\mathrm{N}$ and $\mathrm{C}{}_{\alpha }$