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Chirality and Stereochemistry

The fundamental property of amino acids exhibiting chirality, dictating the specific spatial arrangement of atoms and influencing protein folding.
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The statement of the theorem

Consider an amino acid residue ii with a stereocenter at the α\alpha-carbon, Cα\mathbf{C}_{\alpha}. The chirality is determined by the spatial arrangement of the four distinct substituents (amino group, carboxyl group, side chain RiR_i, and backbone N\text{N}). The stereochemistry is quantified by the absolute configuration, typically assigned using the Cahn-Ingold-Prelog (CIP) rules, yielding the RR or SS designation. Mathematically, this requires defining the handedness of the local coordinate system (v1,v2,v3)(\mathbf{v}_1, \mathbf{v}_2, \mathbf{v}_3) formed by the bonds emanating from Cα\mathbf{C}_{\alpha}: \n\nChirality=sgn(v1⋅(v2×v3))\text{Chirality} = \text{sgn}(\mathbf{v}_1 \cdot (\mathbf{v}_2 \times \mathbf{v}_3)) \n\nFor biological proteins, the overwhelming preference is for the L-amino acid configuration, corresponding to a specific, consistent sign for this scalar triple product.