Exciton delocalization and energy transport mechanisms in R-phycoerythrin

Energy transport mechanisms in R-Phycoerythrin (RPE), a light harvesting protein located at the top of the phycobilisome antenna in red algae, are investigated using nonlinear optical spectroscopies and theoretical models. The RPE hexamer possesses a total of 30 bilin pigments, which can be subdivided into three classes based on their molecular structures and electronic resonance frequencies. Of particular interest to this study is the influence of exciton delocalization on the real-space paths traversed by photoexcitations as they concentrate on the lowest energy pigment sites. Transient grating measurements show that significant nuclear relaxation occurs at delay times less than 100 fs, whereas energy transport spans a wide range of time scales depending on the proximity of the initial and final states involved in the process. The fastest energy transport dynamics within the RPE complex are close to 1 ps; however, evidence for sub-100 fs exciton self-trapping is also obtained. In addition, photon echo experiments reveal vibronic interactions with overdamped and underdamped nuclear modes. To establish signatures of exciton delocalization, energy transport is simulated using both modified Redfield and Fo?rster theories, which respectively employ delocalized and localized basis states. We conclude that exciton delocalization occurs between six pairs of phycoerythrobilin pigments (i.e., dimers) within the protein hexamer. It is interesting that these dimers are bound in locations analogous to the well-studied phycocyanobilin dimers of cyanobacterial allophycocyanin and c-phycocyanin in which wave function delocalization is also known to take hold. Strong conclusions regarding the electronic structures of the remaining pigments cannot be drawn based on the present experiments and simulations due to overlapping resonances and broad spectroscopic line widths, which prevent the resolution of dynamics at particular pigment sites.     

Ferromagnetic spin-delocalized electron donors for multifunctional materials: π-conjugated benzotriazinyl radicals

We have developed new synthetic methodology for benzotriazinyl radicals that exhibit spin delocalization, low oxidation potentials, and ferromagnetic interactions in the solid state via π-π interactions, making them promising candidates for multifunctional magnetic materials.     

The orientation-preserving diffeomorphism group of {\mathbb{S}^{2}} deforms to SO(3) smoothly

Smale proved that the orientation-preserving diffeomorphism group of \mathbbS²{\mathbb{S}^{2}} has a continuous strong deformation retraction to SO(3). In this paper, we construct such a strong deformation retraction which is diffeologically smooth.     

Interaction between a Novel Oligopeptide Fragment of the Human Neurotrophin Receptor TrkB Ectodomain D5 and the C-Terminal Fragment of Tetanus Neurotoxin

This article presents experimental evidence and computed molecular models of a potential interaction between receptor domain D5 of TrkB with the carboxyl-terminal domain of tetanus neurotoxin (Hc-TeNT). Computational simulations of a novel small cyclic oligopeptide are designed, synthesized, and tested for possible tetanus neurotoxin-D5 interaction. A hot spot of this protein-protein interaction is identified in analogy to the hitherto known crystal structures of the complex between neurotrophin and D5. Hc-TeNT activates the neurotrophin receptors, as well as its downstream signaling pathways, inducing neuroprotection in different stress cellular models. Based on these premises, we propose the Trk receptor family as potential proteic affinity receptors for TeNT. In vitro, Hc-TeNT binds to a synthetic TrkB-derived peptide and acts similar to an agonist ligand for TrkB, resulting in phosphorylation of the receptor. These properties are weakened by the mutagenesis of three residues of the predicted interaction region in Hc-TeNT. It also competes with Brain-derived neurotrophic factor, a native binder to human TrkB, for the binding to neural membranes, and for uptake in TrkB-positive vesicles. In addition, both molecules are located together in vivo at neuromuscular junctions and in motor neurons.     

Multi-level lotsizing and scheduling by batch sequencing

We consider a single-machine scheduling problem with a multi-level product structure. Setups are required if the machine changes production from one product type to another, and the scheduling decision must satisfy dynamic demand. We propose a lotsizing as well as a scheduling model, and we compare solution procedures for both models on a very restricted set of instances. As a result the multi-level structure complicates the inventory balance constraints in the lotsizing model. In the scheduling model, however, the multi-level structure translates into precedence constraints between jobs (leading to a smaller search space) which allows it to solve the scheduling model to optimality.     

Characteristic time scales of velocity and pressure events

Numerical and wind tunnel simulations of full-scale wind loads on structures are usually performed at a lower Reynolds number and different turbulence parameters. One way to assess the validity of such simulations is through matching magnitudes, duration and/or spectral characteristics of simulated pressure peaks with full-scale data. Because wavelet analysis provides a time/frequency decomposition, it has been proposed as an analysis tool for the intermittent and transient pressure peaks. This work aims at answering the question as to whether different wavelets yield the same-scale decomposition of pressure peaks and velocity events and could, thus, be used as a tool for the analysis of extreme loads on structures. The results show that, by isolating the peaks or events with a modified Gaussian window prior to applying the wavelet transform, the dependence of the measured time scale on different wavelet functions is reduced. The time scales of the pressure peak and the velocity event are estimated to be about the same indicating that one contributing factor, at the peak scale, to the pressure peak lies in the variation of the incoming flow at the same scale.     

Asymptotic behavior of unbounded solutions of linear Volterra integral equations

The asymptotic behavior as t → ∞ of solutions of ∝₀^tu(t ? s) dA(s) = f(t) is studied when f(t) satisfies a “o” estimate as $\text{t ” ∞}$, and A belongs to a weighted space and its Laplace-Stieltjes transform has finitely many zeros in its closed half-plane of convergence. Results for systems of integral equations as well as for integrodifferential systems are also given.