Multiplets of linearized SO(2) supergravity

A set of fields for SO(2) supergravity theories is presented on which the gauge algebra closes at the linearized level. The Poincaré Lagrangian and three higher-order invariants are constructed. One of them, an extension of the Weyl Lagrangian, is manifestly invariant under chiral U(2) transformations. Several aspects of our results are discussed, like the particle content of the various Lagrangians and the ghost interactions that occur in the quantised Poincaré action.     

Synthesis and physicochemical properties of metallobacteriochlorins

Access to metallobacteriochlorins is essential for investigation of a wide variety of fundamental photochemical processes, yet relatively few synthetic metallobacteriochlorins have been prepared. Members of a set of synthetic bacteriochlorins bearing 0-4 carbonyl groups (1, 2, or 4 carboethoxy substituents, or an annulated imide moiety) were examined under two conditions: (i) standard conditions for zincation of porphyrins [Zn(OAc)(2)·2H(2)O in N,N-dimethylformamide (DMF) at 60-80 °C], and (ii) treatment in tetrahydrofuran (THF) with a strong base [e.g., NaH or lithium diisopropylamide (LDA)] followed by a metal reagent MX(n). Zincation of bacteriochlorins that bear 2-4 carbonyl groups proceeded under the former method whereas those with 0-2 carbonyl groups proceeded with NaH or LDA/THF followed by Zn(OTf)(2). The scope of metalation (via NaH or LDA in THF) is as follows: (a) for bacteriochlorins that bear two electron-releasing aryl groups, M = Cu, Zn, Pd, and InCl (but not Mg, Al, Ni, Sn, or Au); (b) for bacteriochlorins that bear two carboethoxy groups, M = Ni, Cu, Zn, Pd, Cd, InCl, and Sn (but not Mg, Al, or Au); and (c) a bacteriochlorin with four carboethoxy groups was metalated with Mg (other metals were not examined). Altogether, 15 metallobacteriochlorins were isolated and characterized. Single-crystal X-ray analysis of 8,8,18,18-tetramethylbacteriochlorin reveals the core geometry provided by the four nitrogen atoms is rectangular; the difference in length of the two sides is ～0.08 ?. Electronic characteristics of (metal-free) bacteriochlorins were probed through electrochemical measurements along with density functional theory calculation of the energies of the frontier molecular orbitals. The photophysical properties (fluorescence yields, triplet yields, singlet and triplet excited-state lifetimes) of the zinc bacteriochlorins are generally similar to those of the metal-free analogues, and to those of the native chromophores bacteriochlorophyll a and bacteriopheophytin a. The availability of diverse metallobacteriochlorins should prove useful in a variety of fundamental photochemical studies and applications.     

Molecular Electronic Tuning of Photosensitizers to Enhance Photodynamic Therapy: Synthetic Dicyanobacteriochlorins as a Case Study

Photophysical, photostability, electrochemical and molecular‐orbital characteristics are analyzed for a set of stable dicyanobacteriochlorins that are promising photosensitizers for photodynamic therapy (PDT). The bacteriochlorins are the parent compound (BC), dicyano derivative (NC)₂BC and corresponding zinc (NC)₂BC‐Zn and palladium chelate (NC)₂BC‐Pd. The order of PDT activity against HeLa human cancer cells in vitro is (NC)₂BC‐Pd > (NC)₂BC > (NC)₂BC‐Zn ≈ BC. The near‐infrared absorption feature of each dicyanobacteriochlorin is bathochromically shifted 35–50 nm (748–763 nm) from that for BC (713 nm). Intersystem crossing to the PDT‐active triplet excited state is essentially quantitative for (NC)₂BC‐Pd. Phosphorescence from (NC)₂BC‐Pd occurs at 1122 nm (1.1 eV). This value and the measured ground‐state redox potentials fix the triplet excited‐state redox properties, which underpin PDT activity via Type‐1 (electron transfer) pathways. A perhaps counterintuitive (but readily explicable) result is that of the three dicyanobacteriochlorins, the photosensitizer with the shortest triplet lifetime (7 μs), (NC)₂BC‐Pd has the highest activity. Photostabilities of the dicyanobacteriochlorins and other bacteriochlorins studied recently are investigated and discussed in terms of four phenomena: aggregation, reduction, oxidation and chemical reaction. Collectively, the results and analysis provide fundamental insights concerning the molecular design of PDT agents.     

Switchable Organocatalysis from N-heterocyclic Carbene-Carbodiimide Adducts with Tunable Release Temperature**

N-Heterocyclic carbenes (NHCs) are powerful organocatalysts, but practical applications often require in situ generation from stable precursors that “mask” the NHC reactivity via reversible binding. Previously established “masks” are often simple small molecules, such that the NHC structure is used to control both catalytic activity and activation temperature, leading to undesirable tradeoffs. Herein, we show that NHC-carbodiimide (CDI) adducts can be masked precursors for switchable organocatalysis and that the CDI substituents can control the reaction profile without changing the NHC structure. Large electronic variations on the CDI (e.g., alkyl versus aryl) drastically change the catalytically active temperature, whereas smaller perturbations (e.g., different para-substituted phenyls) tune the catalyst release within a narrower window. This control was demonstrated for three classic NHC-catalyzed reactions, each influencing the NHC-CDI equilibrium in different ways. Our results introduce a new paradigm for controlling NHC organocatalysis as well as present practical considerations for designing appropriate masks for various reactions.     

Gravitational Waves and Black Holes

In these lectures general relativity is outlined as the classical field theory of gravity, emphasizing physical phenomena rather than formalism. Dynamical solutions representing traveling waves as well as stationary fields like those of black holes are discussed. Their properties are investigated by studying the geodesic structure of the corresponding space-times, as representing the motion of point-like test particles. The interaction between gravitational, electro-magnetic and scalar fields is also considered.     

Forces associated with non-linear non-holonomic constraint equations

A concise method has been formulated for identifying a set of forces needed to constrain the behavior of a mechanical system, modeled as a set of particles and rigid bodies, when it is subject to motion constraints described by non-holonomic equations that are inherently non-linear in velocity. An expression in vector form is obtained for each force; a direction is determined, together with the point of application. This result is a consequence of expressing constraint equations in terms of dot products of vectors rather than in the usual way, which is entirely in terms of scalars and matrices. The constraint forces in vector form are used together with two new analytical approaches for deriving equations governing motion of a system subject to such constraints. If constraint forces are of interest they can be brought into evidence in explicit dynamical equations by employing the well-known non-holonomic partial velocities associated with Kane's method; if they are not of interest, equations can be formed instead with the aid of vectors introduced here as non-holonomic partial accelerations. When the analyst requires only the latter, smaller set of equations, they can be formed directly; it is not necessary to expend the labor first to form the former, larger set and subsequently perform matrix multiplications.     

An experimental investigation of the sonic criterion for transition from regular to Mach reflection of weak shock waves

The signal speed, namely the local sound speed plus the flow velocity, behind the reflected shocks produced by the interaction of weak shock waves (M _i < 1.4) with rigid inclined surfaces has been measured for several shock strengths close to the point of transition from regular to Mach reflection. The signal speed was measured using piezo-electric transducers, and with a multiple schlieren system to photograph acoustic signals created by a spark discharge behind a small aperture in the reflecting surfaces. Both methods yielded results with equal values within experimental error. The theoretical signal speeds behind regularly reflected shocks were calculated using a non-stationary model, and these agreed with the measured results at large angles of incidence. As the angle of incidence was reduced, for the same incident shock Mach number, so as to approach the point of transition from regular to Mach reflection, the measured values of the signal speed deviated significantly from the theoretical predictions. It was found, within experimental uncertainty, that transition from regular to Mach reflection occurred at the experimentally observed sonic point, namely, when the signal speed was equal to the speed of the reflection point along the reflecting surface. This sonic condition did not coincide with the theoretical value.     

Sortase‐Catalyzed Initiator Attachment Enables High Yield Growth of a Stealth Polymer from the C Terminus of a Protein

Conventional methods for synthesizing protein/peptide–polymer conjugates, as a means to improve the pharmacological properties of therapeutic biomolecules, typically have drawbacks including low yield, non‐trivial separation of conjugates from reactants, and lack of site‐ specificity, which results in heterogeneous products with significantly compromised bioactivity. To address these limitations, the use of sortase A from Staphylococcus aureus is demonstrated to site‐specifically attach an initiator solely at the C‐terminus of green fluorescent protein (GFP), followed by in situ growth of a stealth polymer, poly(oligo(ethylene glycol) methyl ether methacrylate) by atom transfer radical polymerization (ATRP). Sortase‐catalyzed initiator attachment proceeds with high specificity and near‐complete (≈95%) product conversion. Subsequent in situ ATRP in aqueous buffer produces 1:1 stoichiometric conjugates with >90% yield, low dispersity, and no denaturation of the protein. This approach introduces a simple and useful method for high yield synthesis of protein/peptide–polymer conjugates.