Dynamics of Bacteriorhodopsin in the Dark-Adapted State from Solution Nuclear Magnetic Resonance Spectroscopy

To achieve efficient proton pumping in the light-driven proton pump bacteriorhodopsin (bR), the protein must be tightly coupled to the retinal to rapidly convert retinal isomerization into protein structural rearrangements. Methyl group dynamics of bR embedded in lipid nanodiscs were determined in the dark-adapted state, and were found to be mostly well ordered at the cytosolic side. Methyl groups in the M145A mutant of bR, which displays only 10 % residual proton pumping activity, are less well ordered, suggesting a link between side-chain dynamics on the cytosolic side of the bR cavity and proton pumping activity. In addition, slow conformational exchange, attributed to low frequency motions of aromatic rings, was indirectly observed for residues on the extracellular side of the bR cavity. This may be related to reorganization of the water network. These observations provide a detailed picture of previously undescribed equilibrium dynamics on different time scales for ground-state bR.     

Synthesis and Photophysical Properties of a Sc3N@C80‐Corrole Electron Donor–Acceptor Conjugate

Embedding endohdedral metallofullerenes (EMFs) into electron donor–acceptor systems is still a challenging task owing to their limited quantities and their still largely unexplored chemical properties. In this study, we have performed a 1,3‐dipolar cycloaddition reaction of a corrole‐based precursor with Sc₃N@C₈₀ to regioselectively form a [5,6]‐adduct ( 1 ). The successful attachment of the corrole moiety was confirmed by mass spectrometry. In the electronic ground state, absorption spectra suggest sizeable electronic communications between the electron acceptor and the electron donor. Moreover, the addition pattern occurring at a [5,6]‐bond junction is firmly proven by NMR spectroscopy and electrochemical investigations performed with 1 . In the electronically excited state, which is probed in photophysical assays with 1 , a fast electron‐transfer yields the radical ion pair state consisting of the one‐electron‐reduced Sc₃N@C₈₀ and of the one‐electron‐oxidized corrole upon its exclusive photoexcitation. As such, our results shed new light on the practical work utilizing EMFs as building blocks in photovoltaics.     

PtII-Catalyzed Hydroxylation of Terminal Aliphatic C(sp3)−H Bonds with Molecular Oxygen

The practical application of Shilov-type Pt catalysis to the selective hydroxylation of terminal aliphatic C−H bonds remains a formidable challenge, due to difficulties in replacing Pt^IV with a more economically viable oxidant, particularly O₂. We report the potential of employing FeCl₂ as a suitable redox mediator to overcome the kinetic hurdles related to the direct use of O₂ in the Pt reoxidation. For the selective conversion of butyric acid to γ-hydroxybutyric acid (GHB), a significantly enhanced catalyst activity and stability (turnover numbers (TON)>30) were achieved under 20 bar O₂ in comparison to current state-of-the-art systems (TON<10). In this regard, essential reaction parameters affecting the overall activity were identified, along with specific additives to attain catalyst stability at longer reaction times. Notably, deactivation by reduction to Pt⁰ was prevented by the addition of monodentate pyridine derivatives, such as 2-fluoropyridine, but also by introducing varying partial pressures of N₂ in the gaseous atmosphere. Finally, stability tests revealed the involvement of Pt^II and FeCl₂ in catalyzing the non-selective overoxidation of GHB. Accordingly, in situ esterification with boric acid proved to be a suitable strategy to maintain enhanced selectivities at much higher conversions (TON>60). Altogether, a useful catalytic system for the selective hydroxylation of primary aliphatic C−H bonds with O₂ is presented.     

Anatomy of a gauge theory

We exhibit the role of Hochschild cohomology in quantum field theory with particular emphasis on gauge theory and Dyson–Schwinger equations, the quantum equations of motion. These equations emerge from Hopf- and Lie algebra theory and free quantum field theory only. In the course of our analysis, we exhibit an intimate relation between the Slavnov–Taylor identities for the couplings and the existence of Hopf sub-algebras defined on the sum of all graphs at a given loop order, surpassing the need to work on single diagrams.     

Virtual logarithms

The modification of the number field sieve which Joux and Lercier recently used to compute logarithms in a prime field of a record 120 decimal digits makes use of the notion of a virtual logarithm of a prime ideal in a number ring. We provide necessary and sufficient conditions for their method to succeed and give an explicit formula for the virtual logarithm of an ideal.     

The Hopf Algebra of Rooted Trees in Epstein-Glaser Renormalization

We show how the Hopf algebra of rooted trees encodes the combinatorics of Epstein-Glaser renormalization and coordinate space renormalization in general. In particular, we prove that the Epstein-Glaser time-ordered products can be obtained from the Hopf algebra by suitable Feynman rules, mapping trees to operator-valued distributions. Twisting the antipode with a renormalization map formally solves the Epstein-Glaser recursion and provides local counterterms due to the Hochschild 1-closedness of the grafting operator B₊.submitted 29/03/04, accepted 01/06/04