45. Point group symmetry operations such as inversion and mirror plane are not applicable to protein crystals. This is because
(A) Protein molecules assemble in highly ordered fashion.
(B) Protein molecules have handedness.
(C) Protein molecules form a lattice plane that do not diffract X-rays.
(D) Hydrogen atoms in proteins diffract weakly.
Why Mirror Plane and Inversion Symmetry Are Not Present in Protein Crystals
Correct Answer
Option (2): Protein molecules have handedness.
Explanation
Protein crystals obey the principles of crystallography, but unlike many inorganic crystals, they are composed of biological macromolecules that are inherently chiral. Chirality means that a molecule and its mirror image cannot be superimposed on one another. This property, also known as handedness, arises because proteins are built almost exclusively from L-amino acids. As a result, every naturally occurring protein possesses a unique three-dimensional arrangement that lacks mirror symmetry.
Mirror planes and inversion centers are symmetry operations that convert a structure into its mirror image. If either of these symmetry elements were present in a protein crystal, they would transform every protein molecule into its opposite enantiomer. Since protein crystals contain only one chiral form of the molecule, such symmetry operations are incompatible with their molecular structure. Consequently, protein crystals can belong only to those crystallographic point groups and space groups that preserve molecular chirality.
This restriction is known as the chirality restriction in crystallography. Among the 230 crystallographic space groups, only the 65 Sohncke space groups contain symmetry operations that preserve chirality. These groups include translations, rotations, and screw axes but exclude mirror planes, inversion centers, and rotoinversion axes because these operations generate mirror images.
Why Option (1) is Incorrect
Protein molecules do assemble into highly ordered crystalline arrays, and this regular arrangement is essential for X-ray diffraction. However, the ordered packing of molecules does not determine whether mirror planes or inversion centers are allowed. The absence of these symmetry elements is a consequence of molecular chirality rather than crystal order.
Why Option (2) is Correct
Proteins possess handedness because they are constructed from chiral L-amino acids. Mirror reflection or inversion would convert these molecules into their non-superimposable mirror images, which are not present in the crystal. Therefore, symmetry operations that reverse chirality cannot exist in protein crystals. This is the fundamental reason why mirror planes and inversion centers are absent.
Why Option (3) is Incorrect
Protein crystals certainly form regular lattice planes, and these planes are responsible for producing X-ray diffraction patterns according to Bragg’s law. The statement that protein lattice planes do not diffract X-rays is scientifically incorrect. X-ray crystallography itself depends entirely on diffraction from these ordered lattice planes.
Why Option (4) is Incorrect
Hydrogen atoms scatter X-rays much more weakly than heavier atoms because they possess only one electron. Although this affects the visibility of hydrogen atoms in electron density maps, it has no relationship to crystallographic symmetry. Weak hydrogen scattering does not determine whether mirror planes or inversion centers are present in a crystal.
Chirality and Protein Crystal Symmetry
Most biological macromolecules are chiral because they are composed of stereochemically defined building blocks. During crystallization, these molecules retain their handedness and pack in ways that preserve their three-dimensional configuration. As a result, only symmetry operations that maintain chirality are permitted. Rotations, screw axes, and translational symmetry preserve the handedness of a molecule, whereas mirror reflection, inversion, and rotoinversion reverse it and are therefore forbidden.
Symmetry Elements Allowed in Protein Crystals
Protein crystals commonly contain translational symmetry, rotational symmetry, and screw axes. These operations reproduce identical molecules without changing their stereochemistry. In contrast, improper symmetry elements such as mirror planes, inversion centers, and rotoinversion axes are absent because they generate the opposite enantiomer of the protein. This distinction is one of the defining characteristics of crystals formed from chiral biological molecules.
Relationship Between Chirality and Space Groups
Crystallographic space groups describe all possible symmetry arrangements within crystals. Only a subset of these space groups preserves molecular chirality and can therefore accommodate proteins and other chiral biomolecules. These space groups contain exclusively chirality-preserving symmetry operations and exclude all improper symmetry elements that would generate mirror-image structures.
Conclusion
Protein crystals do not contain mirror planes or inversion centers because proteins are intrinsically chiral molecules composed of L-amino acids. These improper symmetry operations would convert a protein into its non-superimposable mirror image, which cannot exist within the same crystal lattice. Therefore, the correct answer is Option (2): Protein molecules have handedness.
