A Commentary on the Topological Chirality and Achirality of Molecules

The concept of topological chirality is traced from its historic origins to its present-day connection to chemistry. In contrast to geometrical chirality, the topological chirality of molecules depends on models of bonding and is not directly tied to experimentally observable chirality phenomena. Nevertheless, studies dealing with the topological chirality and achirality of molecular graphs have played a significant role in an area where chemistry and topology intersect. »Insofem sich die Sátze der Mathematik auf die Wirklichkeit beziehen, sind sie nicht sicher, und insofern sie sicher sind, beziehen sie sich nicht auf die Wirklichkeit«. Albert Einstein (1921

Nonactin and the Coupe du Roi

The macrolide antibiotic nonactin is the first example of a natural product with S4 symmetry. It is now pointed out that the synthesis of nonactin by dimerization-cyclization of (-)-nonactyl- (+ )-nonactic acid, reported by Ulrich Schmidt in 1975, is also the first example of a chemical combination of two homochiral molecules to give an achiral product

Ovarian Teratoma Masquerading as a CSF Pseudocyst in a Female with a Ventriculoperitoneal Shunt

Background. In today's fast-paced and high-acuity emergency departments, clinicians are often compelled to triage cases so rapidly that a differential diagnosis consistent with the history and physical examination is not comprehensive. Case Report. This case report describes the unexpected finding of a cystic ovarian neoplasm in a young female with an abdominal mass and a ventriculoperitoneal shunt, initially diagnosed as a cerebrospinal fluid pseudocyst. We use this case to illustrate that the astute clinician must always synthesize a diagnosis from all data sources and not to rely on initial radiographic evaluations. Conclusions. This remarkable case demonstrates that all differential diagnoses must be entertained in order to rapidly and accurately diagnose a patient with a cystic abdominal mass

Chiral symmetry breaking via crystallization of the glycine and \alpha-amino acid system: a mathematical model

We introduce and numerically solve a mathematical model of the experimentally established mechanisms responsible for the symmetry breaking transition observed in the chiral crystallization experiments reported by I. Weissbuch, L. Addadi, L. Leiserowitz and M. Lahav, J. Am. Chem. Soc. 110 (1988), 561-567. The mathematical model is based on five basic processes: (1) The formation of achiral glycine clusters in solution, (2) The nucleation of oriented glycine crystals at the air/water interface in the presence of hydrophobic amino acids, (3) A kinetic orienting effect which inhibits crystal growth, (4) The enantioselective occlusion of the amino acids from solution, and (5) The growth of oriented host glycine crystals at the interface. We translate these processes into differential rate equations. We first study the model with the orienting process (2) without (3) and then combine both allowing us to make detailed comparisons of both orienting effects which actually act in unison in the experiment. Numerical results indicate that the model can yield a high percentage orientation of the mixed crystals at the interface and the consequent resolution of the initially racemic mixture of amino acids in solution. The model thus leads to separation of enantiomeric territories, the generation and amplification of optical activity by enantioselective occlusion of chiral additives through chiral surfaces of glycine crystals

Topological Chirality of Minimally Colored Kuratowski Graphs

We prove that topological chirality in a K3 3 graph requires a minimum of two non-adjacent colored edges, while topological chirality in a K5 graph requires a minimum of three colored edges that form an open path

Knotted Structures in Chemistry, Biochemistry, and Molecular Biology

The term »knot« in the mathematical sense, as a closed curve in 3-space that does not intersect itself but that cannot be embedded in the plane without intersections, has been used to describe a wide variety of molecular structures - except in the protein literature, where it has been used to describe structural motifs that are neither closed knots in the above sense nor even knots in the everyday sense. We argue in this paper that description of these motifs as »knots« constitutes »improper« use of scientific terminology, and we propose a definition of »molecular knot«. »Ne faites grace à aucune denomination impropre. Ceux qui savent déjà, entendront toujours; ceux qui ne savent pas encore, entendront plutòt

Spiral Galaxies as Enantiomers: Chirality, an Underlying Feature in Chemistry and Astrophysics

Spiral galaxies are axi-symmetric objects showing 2D-chirality when projected onto a plane. Features in common with tetrahedral molecules are pointed out, in particular the existence of a preferred chiral modality for genetic galaxies as in aminoacids and sugars. Environmental effects can influence the intrinsic chirality of originally isolated stellar systems so that a progressive loss of chirality is recognised in the Hubble morphological sequence of galaxies.Comment: 17 pages, 4 figure

3,9-Dibromo-5,7-dihydro­dibenzo[c,e]oxepine

The title compound, C14H10Br2O, is a biphenyl derivative containing a –CH2—O—CH2– bridge in the 2,2′-position. The compound displays a twisted conformation with the two benzene rings making a dihedral angle of 45.02 (5)°, while the central seven-membered ring is in a boat conformation. The mol­ecule lies on a crystallographic twofold axis of symmetry passing through the O atom and bis­ecting the 1,1′ C—C bond

Chiral polymerization: symmetry breaking and entropy production in closed systems

We solve numerically a kinetic model of chiral polymerization in systems closed to matter and energy flow, paying special emphasis to its ability to amplify the small initial enantiomeric excesses due to the internal and unavoidable statistical fluctuations. The reaction steps are assumed to be reversible, implying a thermodynamic constraint among some of the rate constants. Absolute asymmetric synthesis is achieved in this scheme. The system can persist for long times in quasi- stationary chiral asymmetric states before racemizing. Strong inhibition leads to long-period chiral oscillations in the enantiomeric excesses of the longest homopolymer chains. We also calculate the entropy production {\sigma} per unit volume and show that {\sigma} increases to a peak value either before or in the vicinity of the chiral symmetry breaking transition