The Symmetry Landscape of Molecules: From Cosmic Molecular Symmetry to Biological Asymmetry

Molecular symmetry governs numerous physical and chemical properties, but its statistical distribution across biological molecular systems remains insufficiently explored. We compare the symmetry landscape of biological molecules with that previously established for molecules constituting the TMC-1, Orion KL, and IRC + 10216 molecular clouds. The comparison reveals a pronounced contrast: symmetry dominates among molecules detected in molecular clouds, whereas asymmetry dominates among biological molecules. Interstellar and circumstellar molecular corpora are rich in linear, axially symmetric, and mirror-symmetric species, while biological corpora are dominated by the asymmetric point group C1. Exact molecular point groups and symmetry elements were analyzed for a 50-molecule biological pilot corpus, normal human plasma, normal human urine, and the principal molecular constituents of poliovirus. Species- and concentration-weighted point-group probabilities were considered, and their diversity was quantified using the Shannon entropy, normalized Shannon entropy, and Simpson diversity number D2. The predominance of C1 in biological systems reflects the extensive use of chiral building blocks, stereogenic centers, and chemically nonequivalent functional groups required for molecular recognition and biochemical specificity. Concentration weighting modifies but does not universally reverse this tendency: normal human plasma remains predominantly asymmetric, whereas normal urine becomes abundance-dominated by C2v symmetry because of the exceptionally high concentration of urea. Poliovirus represents the limiting molecular case: all principal chemically defined constituents, VP1, VP2, VP3, VP4, VPg, and genomic RNA, belong to C1, yielding zero point-group entropy and D2 = 1. Nevertheless, repeated asymmetric capsid proteins self-assemble into a shell possessing approximate proper icosahedral symmetry. Thus, the transition from cosmic molecular matter to biological molecular organization is accompanied by extensive molecular symmetry breaking, while high symmetry may re-emerge at the supramolecular level through the ordered assembly of asymmetric components.