Reply to the paper “comments on the theory of phase-conjugated waves”, by E. Wolf and W.H. Carter

The NH₄Br crystal is irradiated simultaneously with a modulated red light and a steady UV light in the region of the fundamental absorption band. The resulting recombination luminescence of electrons with V_K centers is phase-sensitively detected, and compared with the emission which is directly excited by UV light. From measurements of the excitation spectra for recombination luminescence, it is pointed out that the dissociation of free excitons occurs efficiently in NH₄Br.     

Four wave nonlinear optical mixing as real time holography

The phenomenon of four-wave optical mixing is an exact analog of the sequential operations of holographic recording and reconstruction. It should thus be possible to realize, in real time, holographic experiments and devices using such mixing.     

On residue complexes,dualizing sheaves and local cohomology modules

According to Grothendieck Duality Theory [RD], on each varietyV over a fieldk, there is a canonical complex of -modules, theresidue complex . These complexes satisfy (and are characterized by) functorial properties in the categoryV ofk-varieties. In [Ye] a complex is constructed explicitly (when the fieldk is perfect). The main result of this paper is that the two families of complexes, and , which carry certain additional data (such as trace maps…), are uniquely isomorphic. As a corollary we recover Lipman’s canonical dualizing sheaf of [Li], and we obtain formulas for residues of local cohomology classes of differential forms.     

Percolation,fractals, and anomalous diffusion

Both the infinite cluster and its backbone are self-similar at the percolation threshold,p _c . This self-similarity also holds at concentrationsp nearp _c , for length scalesL which are smaller than the percolation connectedness length,. ForL<, the number of bonds on the infinite cluster scales asL ^D , where the fractal dimensionalityD is equal to(d-/v). Geometrical fractal models, which imitate the backbone and on which physical models are exactly solvable, are presented. Above six dimensions, one has D=4 and an additional scaling length must be included. The effects of the geometrical structure of the backbone on magnetic spin correlations and on diffusion at percolation are also discussed.     

Elucidating dissociation activation energies in host–guest assemblies featuring fast exchange dynamics

The ability to mediate the kinetic properties and dissociation activation energies (E_a) of bound guests by controlling the characteristics of “supramolecular lids” in host–guest molecular systems is essential for both their design and performance. While the synthesis of such systems is well advanced, the experimental quantification of their kinetic parameters, particularly in systems experiencing fast association and dissociation dynamics, has been very difficult or impossible with the established methods at hand. Here, we demonstrate the utility of the NMR-based guest exchange saturation transfer (GEST) approach for quantifying the dissociation exchange rates (k_out) and activation energy (E_a,out) in host–guest systems featuring fast dissociation dynamics. Our assessment of the effect of different monovalent cations on the extracted E_a,out in cucurbit[7]uril:guest systems with very fast k_out highlights their role as “supramolecular lids” in mediating a guest''s dissociation E_a. We envision that GEST could be further extended to study kinetic parameters in other supramolecular systems characterized by fast kinetic properties and to design novel switchable host–guest assemblies.

GEST-NMR is utilized for quantifying the dissociation activation energy (E_a,out) in host-guest systems featuring fast dissociation dynamics.     

Nonperfect synchronization of reaction center rehybridization in the transition state of the hydride transfer catalyzed by dihydrofolate reductase

It has been suggested that the magnitudes of secondary kinetic isotope effects (2 degrees KIEs) of enzyme-catalyzed reactions are an indicator of the extent of reaction-center rehybridization at the transition state. A 2 degrees KIE value close to the corresponding secondary equilibrium isotope effects (2 degrees EIE) is conventionally interpreted as indicating a late transition state that resembles the final product. The reliability of using this criterion to infer the structure of the transition state is examined by carrying out a theoretical investigation of the hybridization states of the hydride donor and acceptor in the Escherichia coli dihydrofolate reductase (ecDHFR)-catalyzed reaction for which a 2 degrees KIE close to the 2 degrees EIE was reported. Our results show that the donor carbon at the hydride transfer transition state resembles the reactant state more than the product state, whereas the acceptor carbon is more productlike, which is a symptom of transition state imbalance. The conclusion that the isotopically substituted carbon is reactant-like disagrees with the conclusion that would have been derived from the criterion of 2 degrees KIEs and 2 degrees EIEs, but the breakdown of the correlation with the equilibrium isotope effect can be explained by considering the effect of tunneling.     

Retro [2 + 2 + 2] ring opening in tricyclobutabenzene derivatives. Thermochemistry and reaction barriers. A theoretical hybrid density functional study

The starting materials, transition states, and products of the concerted retro [2 + 2 + 2] ring-opening reactions of several tricyclobutabenzene derivatives substituted by double-bonded substituents were calculated at the B3LYP/6-31G theoretical level. It was found that the geometries of the products (cyclododecatriyne derivatives) are governed by the electronegativity of the substituents and hyperconjugation effects. The transition-state geometries of all the derivatives are similar. It was found that the retro [2 + 2 + 2] ring-opening reactions are endothermic (ca. 30-85 kcal mol(-1), depending on the substituents) with high barriers, ranging between ca. 95 and 115 kcal mol(-1). It is predicted that the tricyclobutabenzene derivatives under study will be stable when prepared and that they can be made by [2 + 2 + 2] intramolecular ring closure of the respective cyclododecatriyne derivative, especially with the use of transition metals as mediators or catalysts.     

Light-dependent Oxygen Consumption in Bacteriochlorophyll-Serine-treated Melanoma Tumors: On-line Determination Using a Tissue-inserted Oxygen Microsensor

Successful application of anticancer therapy, and especially photodynamic therapy (PDT) mediated by type II (PDTII) processes, depends on the oxygen content within the tumor before, during and after treatment. The high consumption of oxygen during type II PDT imposes constraints on therapy strategies. Although rates of oxygen consumption and repletion during PDTII were suggested by theoretical studies, direct measurements have not been reported. Application of a novel oxygen sensor allowed continuous and direct in situ measurements (up to a depth of 8–9 mm from the tumor surface and for several hours) of temporal variations in the oxygen partial pressure (pO₂) during PDT. Highly pigmented M2R mouse melanoma tumors implanted in CD1 nude mice were treated with bacteriochlorophyll-serine (Bchl-Ser; a new photodynamic reagent) and were subjected to fractionated illumination (700 < λ. < 900 nm) at a fluence rate of 12 mW cm^-2. This illumination led to total oxygen depletion with an average consumption rate of 7.2 uAf(O₂) s^-1. Spontaneous reoxygenation (at an average rate of 2.5 µM(O₂)/s) was observed during the following dark period. These rates are in good agreement with theoretical considerations (Foster et al., Radiat. Res. 126, 296,1991 and Henning et al, Radiat. Res. 142, 221, 1995). The observed patterns of oxygen consumption and recovery during prolonged periods of light/dark cycles were interpreted in terms of vasculature damage and sensitizer clearance. The presented data support the previously suggested advantages of fractionated illumination for type II photodynamic processes.     

Stepwise Versus Concerted Mechanisms in General‐Base Catalysis by Serine Proteases

General‐base catalysis in serine proteases still poses mechanistic challenges despite decades of research. Whether proton transfer from the catalytic Ser to His and nucleophilic attack on the substrate are concerted or stepwise is still under debate, even for the classical Asp‐His‐Ser catalytic triad. To address these key catalytic steps, the transformation of the Michaelis complex to tetrahedral complex in the covalent inhibition of two prototype serine proteases was studied: chymotrypsin (with the catalytic triad) inhibition by a peptidyl trifluoromethane and GlpG rhomboid (with Ser‐His dyad) inhibition by an isocoumarin derivative. The sampled MD trajectories of averaged pK_a values of catalytic residues were QM calculated by the MD‐QM/SCRF(VS) method on molecular clusters simulating the active site. Differences between concerted and stepwise mechanisms are controlled by the dynamically changing pK_a values of the catalytic residues as a function of their progressively reduced water exposure, caused by the incoming ligand.