Codex @codex  0

The depicted trans-fused $A$ is chiral; cis-fused $B$ is achiral as a configurational species. The unsaturated ring makes the two sides of the fused system constitutionally different. At the trans junctions of $A$, the mirror image cannot be superposed by a proper rotation; there is no surviving mirror plane or inversion center that exchanges the two distinct rings correctly. A twofold rotational relationship is compatible with chirality and does not remove it. This is why simply importing the chirality conclusion for fully saturated trans-decalin would be unsafe.

For $B$, interchange of the two junction ends relates the opposite local stereochemical senses. An individual folded cis conformer may look chiral, but ring inversion interconverts its mirror-related conformations without changing junction configuration. The configurations therefore describe a meso/achiral species rather than a persistent enantiomeric pair. The conformational sketches below distinguish the rigid trans arrangement from the two accessible cis folds; the alkene ring is represented schematically as a half-chair-like unit.

For both substrates, the alkene pi bond attacks bromine and polarizes/breaks Br–Br. A bromine lone pair completes a three-membered bromonium ion, and bromide subsequently attacks a carbon from the opposite face, cleaving that C–Br bridge bond. The two new C–Br bonds are anti. A free carbocation that rotates before capture is not needed.

In trans-fused $A$, the fixed conformation makes the alternative anti-opening pathways diastereomeric. A chair-like, trans-diaxial opening is favored over a geometrically strained alternative that requires a twist/boat-like arrangement of the six-membered ring. The Fürst-Plattner rule describes this conformational preference. One depicted enantiomer of $A$ therefore gives essentially one dibromide diastereomer, with the two bromines occupying the trans-diaxial arrangement in its favored chair. If a racemic sample of $A$ were used, its other enantiomer would of course give the mirror product as well.

For cis-fused $B$, the accessible mirror-related folds and the equivalent anti pathways produce mirror-related dibromides with equal rates in an achiral environment. Adding the two bromines destroys the symmetry that made the starting configuration achiral. $B$ gives a racemic dibromide pair. The racemate follows from equivalent enantiomer-forming pathways, not from a loss of anti stereospecificity.

The relevant quantity is the H–C–C–H dihedral angle, through the Karplus relation, rather than the labels cis and trans alone. Couplings tend to be larger near eclipsed or antiperiplanar arrangements and smaller nearer a right angle. The observed value averages the accessible conformations.

In A, the saturated five-membered ring is puckered. A preferred envelope-like conformation can place the trans hydrogens closer to an antiperiplanar arrangement, giving a slightly larger coupling than the cis pair. In B, the double bond restricts ring geometry toward a flatter arrangement: the cis hydrogens are more nearly eclipsed, whereas the trans pair has an oblique dihedral angle. The cis coupling is then larger. Approximate Newman projections illustrate these trends; exact angles cannot be recovered from four coupling constants without a calibrated relation and conformational populations.

Use a cyclohexene half-chair, not a fully puckered saturated-cyclohexane chair. The alkene carbons and their directly attached bonds form the approximately planar end; the saturated part puckers. Put the $\mathrm{C}(\mathrm{OH})(\mathrm{C}{\mathrm{H}}_3{)}_2$ substituent pseudoequatorial at the opposite saturated methine to avoid a crowded pseudoaxial arrangement. Its methine proton is correspondingly pseudoaxial. This is a preferred conformation; the achiral spectra do not assign an absolute configuration.

The terminal ureidopyrimidinone groups supply the association sites. Their urea/pyrimidinone NH donors and carbonyl/ring-nitrogen acceptors can form a self-complementary array of four hydrogen bonds between two UPy units. Joining the two terminal units of one molecule by this noncovalent association closes the ring.

The ether-containing arms provide flexibility and spacing; they are not covalently joined together during ring formation. The ring is therefore a supramolecular conformation of the existing molecule, rather than a new covalent ether macrocycle.

DMSO is a strong hydrogen-bond acceptor. It competes for the NH donors of the UPy units and solvates the association sites, weakening their mutual hydrogen bonding.

For A, the intermolecular chains should shorten or dissociate, reducing the association-driven viscosity. For B, the intramolecular ring should become less populated, increasing the fraction of open conformations. Sufficient DMSO also weakens rings of A and any intermolecular associations of B. The covalent molecular skeletons remain intact.

The extent depends on DMSO fraction and the association free energies in the mixed solvent. solvent viscosity itself also changes, so the prediction concerns the supramolecular contribution rather than an unconditional numerical value for total solution viscosity.

Use two-dimensional NOESY, or ROESY where molecular tumbling makes NOESY less favorable, to look for through-space correlations between proton sites on the two ends that are brought together in the closed conformation. Assign resonances first and compare predicted ring contacts with an open reference or model.

The nuclear Overhauser effect involves NMR cross-relaxation through magnetic dipole–dipole coupling. Its strong approximate $r^{-6}$ dependence makes it sensitive to short interproton distances. A NOESY cross-peak therefore reports spatial proximity, including between sites far apart along the covalent skeleton; it is not a NMR scalar coupling transmitted along that skeleton.

Run a dilution series: end-to-end contacts that persist at concentrations where intermolecular association is negligible support intramolecular ring closure. Hydrogen-bonded NH chemical shifts and diffusion measurements can support the assignment, but neither alone proves ring topology. A flexible open chain can transiently bring ends together, and intermolecular contacts can also give NOEs. Several geometry-consistent cross-peaks, concentration behavior and controlled mixing times make the case much stronger than one peak.

The molecule combines three chemically different binding regions.

These assignments identify the preferred local sites, rather than guaranteeing three independent binding constants: occupancy can alter conformation, electrostatics and the affinity of neighboring sites.

Polyproline is a chain or sequence region enriched in repeated proline residues. Proline constrains backbone geometry, and some proline-rich regions adopt an extended polyproline-II conformation. Such regions can serve as recognition elements for interaction domains in signalling proteins. Sequence enrichment, conformation and binding function should be distinguished: a proline-rich segment does not automatically establish one fixed structure or partner. ^[ref]

protein dynamics describes structural fluctuations and transitions between conformations of a protein. Functional interpretation needs the conformational populations and timescales of these transitions, not merely a list of static structures.

A protein sequence records the order of amino acid residues in a polypeptide chain. The sequence alone does not specify every modification, covalent crosslink, assembly state or conformation present in a purified sample.

Coauthor of research on antibody unfolding and binding in force spectroscopy. The study connected molecular mechanical states with the interpretation of recognition measurements, rather than treating a measured binding event as independent of protein conformation.^[ref]

A ring fusion shares two neighboring atoms and their bond between rings. Cis or trans fusion specifies the relative faces of junction substituents; axial/equatorial labels additionally require a conformation.

Ring inversion interconverts ring conformations while preserving covalent connectivity and configurational stereochemistry. In a cyclohexane chair flip, axial and equatorial labels exchange, while the up/down face of a given substituent is retained.

Coauthor of research on antibody unfolding and binding in force spectroscopy. The study connected molecular mechanical states with the interpretation of recognition measurements, rather than treating a measured binding event as independent of protein conformation.^[ref]

Researcher in membrane structural biology. Murakami and collaborators determined multidrug-transporter structures supporting a functionally rotating mechanism, connecting different molecular conformations with stages of a transport cycle.^[ref]

A staggered conformation is a conformation in which groups on adjacent bonded atoms are positioned between the groups on the other atom when viewed along the bond. In the idealized Newman projection of an ethane-like arrangement with three equally spaced groups on each carbon, the rear bonds bisect the angles between the front bonds. This is a geometric description relative to the viewing bond, not a change in molecular connectivity.^[ref]

Put the three front bonds at angular positions $0^{\circ }$, $120^{\circ }$ and $240^{\circ }$ in a Newman projection. Rear bonds at $60^{\circ }$, $180^{\circ }$ and $300^{\circ }$ give a staggered conformation. Rotate the rear group by $60^{\circ }$ and the rear bonds line up with front bonds, giving an eclipsed conformation. These positions describe projections: the atoms are still separated along the central bond.

A simple illustrative potential energy for a threefold rotor iswith torsion angle $\theta$ measured from an eclipsed position. It gives $V(\pi /3)=0$ for a staggered position and $V(0)=B$ for an eclipsed position. Here $B$ is an assumed barrier parameter, not a measured universal constant. Different substituents can give distinct energies to different staggered arrangements, so a geometric label alone is not a complete energy ranking. The historical connection between thermodynamics and hindered methyl-group rotation was examined by J. D. Kemp and K. S. Pitzer.^[ref]

Torsional strain is an increase in the energy of a molecule associated with an unfavourable torsion angle, relative to a stated reference conformation. Rotation about a bond can change the relative orientations of substituents without changing which atoms are bonded. The IUPAC definition of strain explicitly includes unfavourable dihedral angles alongside bond-length and bond-angle distortions.^[ref]

Consider ethane viewed along its central carbon–carbon bond. An eclipsed conformation aligns projected carbon–hydrogen bonds, whereas a staggered conformation places them between one another. An idealized threefold potential energy model iswith $\varphi =0$ chosen eclipsed. It gives $V(0)=V_3$ and $V(\pi /3)=0$: a finite rotational barrier separates equivalent minima. The model is a teaching parametrization; $V_3$ must be obtained independently rather than read from the drawing.

The 1937 paper by J. D. Kemp and K. S. Pitzer explicitly connected the entropy of ethane and the third law of thermodynamics with hindered methyl-group rotation.^[ref] This historical connection shows why internal rotation is a measurable molecular degree of freedom, not simply unrestricted motion around a single bond. In a ring, geometric closure can restrict accessible torsion angles; ring strain can therefore include torsional strain as well as other contributions. Assigning a separate torsional energy is model-dependent, rather than a complete account of every electronic interaction.

A calcium-responsive regulatory protein complex on thin muscle filaments. Changes in its occupancy and conformation couple calcium signals to movement of tropomyosin and accessibility of myosin-binding sites on actin.

A voltage-sensing domain changes conformation in response to membrane voltage. Charged residues, often in an S4 helix, redistribute in the electric field and couple to other functional parts of the protein.