Theory of three-dimensional alignment by intense laser pulses

We introduce a theoretical framework for study of three-dimensional alignment by moderately intense laser pulses and discuss it at an elementary level. Several features of formal interest are noted and clarified. Our approach is nonperturbative, treating the laser field within classical and the material system within quantum mechanics. The theory is implemented numerically using a basis set of rotational eigenstates, transforming the time-dependent Schrodinger equation to a set of coupled differential equations where all matrix elements are analytically soluble. The approach was applied over the past few years to explore different adiabatic and nonadiabatic three-dimensional alignment approaches in conjunction with experiments, but its formal details and numerical implementation were not reported in previous studies. Although we provide simple numerical examples to illustrate the content of the equations, our main goal is to complement previous reports through an introductory discussion of the underlying theory.     

Quantum mechanics/molecular mechanics investigation of the chemical reaction in Dpo4 reveals water-dependent pathways and requirements for active site reorganization

The nucleotidyl-transfer reaction coupled with the conformational transitions in DNA polymerases is critical for maintaining the fidelity and efficiency of DNA synthesis. We examine here the possible reaction pathways of a Y-family DNA polymerase, Sulfolobus solfataricus DNA polymerase IV (Dpo4), for the correct insertion of dCTP opposite 8-oxoguanine using the quantum mechanics/molecular mechanics (QM/MM) approach, both from a chemistry-competent state and a crystal closed state. The latter examination is important for understanding pre-chemistry barriers to interpret the entire enzyme mechanism, since the crystal closed state is not an ideal state for initiating the chemical reaction. The most favorable reaction path involves initial deprotonation of O3'H via two bridging water molecules to O1A, overcoming an overall potential energy barrier of approximately 20.0 kcal/mol. The proton on O1A-P(alpha) then migrates to the gamma-phosphate oxygen of the incoming nucleotide as O3' attacks P(alpha), and the P(alpha)-O3A bond breaks. The other possible pathway in which the O3'H proton is transferred directly to O1A on P(alpha) has an overall energy barrier of 25.0 kcal/mol. In both reaction paths, the rate-limiting step is the initial deprotonation, and the trigonal-bipyramidal configuration for P(alpha) occurs during the concerted bond formation (O3'-P(alpha)) and breaking (P(alpha)-O3A), indicating the associative nature of the chemical reaction. In contrast, the Dpo4/DNA complex with an imperfect active-site geometry corresponding to the crystal state must overcome a much higher activation energy barrier (29.0 kcal/mol) to achieve a tightly organized site due to hindered O3'H deprotonation stemming from larger distances and distorted conformation of the proton acceptors. This significant difference demonstrates that the pre-chemistry reorganization in Dpo4 costs approximately 4.0 to 9.0 kcal/mol depending on the primer terminus environment. Compared to the higher fidelity DNA polymerase beta from the X-family, Dpo4 has a higher chemical reaction barrier (20.0 vs 15.0 kcal/mol) due to the more solvent-exposed active site.     

Optimal design of nanoplasmonic materials using genetic algorithms as a multiparameter optimization tool

An optimal control approach based on multiple parameter genetic algorithms is applied to the design of plasmonic nanoconstructs with predetermined optical properties and functionalities. We first develop nanoscale metallic lenses that focus an incident plane wave onto a prespecified, spatially confined spot. Our results illustrate the mechanism of energy flow through wires and cavities. Next we design a periodic array of silver particles to modify the polarization of an incident, linearly polarized plane wave in a desired fashion while localizing the light in space. The results provide insight into the structural features that determine the birefringence properties of metal nanoparticles and their arrays. Of the variety of potential applications that may be envisioned, we note the design of nanoscale light sources with controllable coherence and polarization properties that could serve for coherent control of molecular, electronic, or electromechanical dynamics in the nanoscale.     

Octahydroxypyridine[4]arene self-assembles spontaneously to form hexameric capsules and dimeric aggregates

In recent years it has been observed that resorcin[4]arenes and pyrogallol[4]arenes form hydrogen-bonded hexameric capsules in nonpolar solvents. In the present study we have used NMR spectroscopy, with an emphasis on diffusion NMR, to investigate the self-assembly and the aggregation mode of solutions of octahydroxypyridine[4]arene (1 b) in chloroform. In spectroscopic studies, the hexameric capsule of C-undecylresorcin[4]arene (2 b) was used as a reference compound and in some cases also as an internal reference. The current diffusion NMR spectroscopy study shows, in contrast to a previous report, that compound 1 b self-assembles spontaneously into hexameric and dimeric aggregates in solutions in chloroform. The (1)H NMR and diffusion NMR spectroscopic studies on a solution of 1 b in CHCl(3) show the presence of new upfield-shifted peaks, which diffuse with the same diffusion coefficient as the hexameric peaks in the spectrum. Therefore, these new upfield-shifted peaks were attributed to encapsulated CHCl(3) molecules. Interestingly, diffusion NMR measurements showed that the addition of trifluoroacetic acid (6.7 equiv), which had no effect on the hexameric capsules of 2 b, led to the disassembly of the hexamer and the dimer of 1 b into its monomers. Therefore, we conclude that compound 1 b self-assembles spontaneously into hexameric capsules in nonpolar organic solvents, as do resorcin[4]arenes 2 b and 2 c and pyrogallol[4]arenes 3 a and 3 b.     

Self-assembled ionophores from isoguanosine: diffusion NMR spectroscopy clarifies cation's and anion's influence on supramolecular structure

Cation-templated self-assembly of the lipophilic isoguanosine (isoG 1) with different monovalent cations (M(+)=Li(+), Na(+), K(+), NH(4) (+), and Cs(+)) was studied in solvents of different polarity by using diffusion NMR spectroscopy. Previous studies that did not use diffusion NMR techniques concluded that isoG 1 forms both pentamers (isoG 1)(5)M(+) and decamers (isoG 1)(10)M(+) in the presence of alkali-metal cations. The present diffusion NMR studies demonstrate, however, that isoG 1 does not form (isoG 1)(5)M(+) pentamers. In fact, the diffusion NMR data indicates that both doubly charged decamers of formula (isoG 1)(10)2 M(+) and singly charged decamers, (isoG 1)(10)M(+), are formed with lithium, sodium, potassium, and ammonium tetraphenylborate salts (LiB(Ph)(4), KB(Ph)(4), NaB(Ph)(4) and NH(4)B(Ph)(4)), depending on the isoG 1:salt stoichiometry of the solution. In the presence of CsB(Ph)(4), isoG 1 affords only the singly charged decamers (isoG 1)(10)Cs(+). By monitoring the diffusion coefficient of the B(Ph)(4) (-) ion in the different mixtures of solvents, we also concluded that the anion is more strongly associated to the doubly charged decamers (isoG 1)(10)2 M(+) than to the singly charged decamers (isoG 1)(10)M(+). The (isoG 1)(10)2 M(+) species can, however, exist in solution without the mediation of the anion. This last conclusion was supported by the finding that the doubly charged decamers (isoG 1)(10)2 M(+) also prevail in 1:1 CD(3)CN:CDCl(3), a solvent mixture in which the B(Ph)(4) (-) ion does not interact significantly with the self-assembled complex. These diffusion measurements, which have provided new and improved structural information about these decameric isoG 1 assemblies, demonstrate the utility of combining diffusion NMR techniques with conventional NMR methods in seeking to characterize labile, multicomponent, supramolecular systems in solution, especially those with high symmetry.     

Universal characteristic factors and Furstenberg averages

Let be an ergodic probability measure-preserving system. For a natural number we consider the averages

where , and are integers. A factor of is characteristic for averaging schemes of length (or -characteristic) if for any nonzero distinct integers , the limiting behavior of the averages in (*) is unaltered if we first project the functions onto the factor. A factor of is a -universal characteristic factor (-u.c.f.) if it is a -characteristic factor, and a factor of any -characteristic factor. We show that there exists a unique -u.c.f., and it has the structure of a -step nilsystem, more specifically an inverse limit of -step nilflows. Using this we show that the averages in (*) converge in . This provides an alternative proof to the one given by Host and Kra.

     

Enzymatic condensation and polycondensation reactions in organic solvents

Lipases in organic solvents catalyse lactonisation or polymerisation of ω-hydroxyesters. Under these conditions the enzymes exhibit both enantioselectivity and prochiral selectivity. This approach was used to develop the synthesis of chiral γ-lactones and A-B type polyesters from racemic or prochiral hydroxyester substrate.     

Unfavorable electrostatic and steric interactions in DNA polymerase β E295K mutant interfere with the enzyme's pathway

Mutations in DNA polymerase β (pol β) have been associated with approximately 30% of human tumors. The E295K mutation of pol β has been linked to gastric carcinoma via interference with base excision repair. To interpret the different behavior of E295K as compared to wild-type pol β in atomic and energetic detail, we resolve a binary crystal complex of E295K at 2.5 ? and apply transition path sampling (TPS) to delineate the closing pathway of the E295K pol β mutant. Conformational changes are important components in the enzymatic pathway that lead to and ready the enzyme for the chemical reaction. Our analyses show that the closing pathway of E295K mutant differs from the wild-type pol β in terms of the individual transition states along the pathway, associated energies, and the active site conformation in the final closed form of the mutant. In particular, the closed state of E295K has a more distorted active site than the active site in the wild-type pol β. In addition, the total energy barrier in the conformational closing pathway is 65 ± 11 kJ/mol, much higher than that estimated for both correct (e.g., G:C) and incorrect (e.g., G:A) wild-type pol β systems (42 ± 8 and 45 ± 7 kJ/mol, respectively). In particular, the rotation of Arg258 is the rate-limiting step in the conformational pathway of E295K due to unfavorable electrostatic and steric interactions. The distorted active site in the closed relative to open state and the high energy barrier in the conformational pathway may explain in part why the E295K mutant is observed to be inactive. Interestingly, however, following the closing of the thumb but prior to the rotation of Arg258, the E295K mutant complex has a similar energy level as compared to the wild-type pol β. This suggests that the E295K mutant may associate with DNA with similar affinity, but it may be hampered in continuing the process of chemistry. Supporting experimental data come from the observation that the catalytic activity of wild-type pol β is hampered when E295K is present: this may arise from the competition between E295K and wild-type enzyme for the DNA. These combined results suggest that the low insertion efficiency of E295K mutant as compared to wild-type pol β may be related to a closed form distorted by unfavorable electrostatic and steric interactions between Arg258 and other key residues. The active site is thus less competent for proceeding to the chemical reaction, which may also involve a higher reaction barrier than the wild-type or may not be possible in this mutant. Our analysis also suggests further experiments for other mutants to test the above hypothesis and dissect the roles of steric and electrostatic factors on enzyme behavior.     

Hypokinetic stress and neuronal porosome complex in the rat brain: the electron microscopic study

Porosomes are the universal secretory machinery in cells, where membrane-bound secretory vesicles transiently dock and fuse to release intravesicular contents to the outside of the cell during cell secretion. Studies using atomic force microscopy, electron microscopy, electron density and 3D contour mapping, provided rich nanoscale information on the structure and assembly of proteins within the neuronal porosome complex in normal brain. However it remains uncertain whether pathological conditions that alter process of neurotransmission, provoke alterations in the porosome structure also. To determine if porosomes are altered in disease states, the current study was undertaken for first time using high resolution electron microscope. One of pathologies that produce subtle alteration at the presynaptic terminals has been demonstrated to be hypokinetic stress. The central nucleus of amygdale is the brain region, where such alterations are mostly expressed. We have examined the width and depth of the neuronal porosome complex and their alterations provoked by chronic hypokinetic stress in above mentioned limbic region. Specifically, we have demonstrated that despite alterations in the presynaptic terminals and synaptic transmission provoked by this pathological condition in this region, the final step/structure in neurosecretion--the porosome--remains unaffected: the morphometric analysis of the depth and diameter of this cup-shaped structure at the presynaptic membrane point out to the heterogeneity of porosome dimensions, but with unchanged fluctuation in norm and pathology.     

Relative Goursat categories

We define relative Goursat categories and prove relative versions of the equivalent conditions defining regular Goursat categories. These include 3-permutability of equivalence relations, preservation of equivalence relations under direct images, a condition on so-called Goursat pushouts, and the denormalised 3×3 Lemma. This extends recent work by Gran and Rodelo on a new characterisation of Goursat categories to a relative context.