Lie powers and Witt vectors

In the study of Lie powers of a module V in prime characteristic p, a basic role is played by certain modules B _n introduced by Bryant and Schocker. The isomorphism types of the B _n are not fully understood, but these modules fall into infinite families , one family B(k) for each positive integer k not divisible by p, and there is a recursive formula for the modules within B(k). Here we use combinatorial methods and Witt vectors to show that each module in B(k) is isomorphic to a direct sum of tensor products of direct summands of the kth tensor power V ^{⊗ k} . To the memory of Manfred Schocker.     

Photosystem I/molecular wire/metal nanoparticle bioconjugates for the photocatalytic production of H2

Photosystem I (PS I) is a robust photosynthetic complex that adeptly captures photons to create a charge-separated state with a quantum efficiency that approaches 1.0. This charge-separated state is stable for approximately 100 ms, and the low-potential reductant that is produced is poised at a redox potential favorable for H2 evolution. PS I has been covalently linked to Pt and Au nanoparticle surfaces by 1,6-hexanedithiol which serves as a molecular wire to both connect PS I to the particles and transfer electrons from the terminal electron transfer cofactor of PS I, FB, to the nanoparticle. Illumination of these Photosystem I/molecular wire/nanoparticle bioconjugates is able to catalyze the reaction: 2H+ + 2e(-)--> H2. Transfer of the electrons from PS I to the nanoparticle through the molecular wire is not rate-limiting for H2 evolution. Supplying the system with more efficient donor-side electron donating species results in a 5-fold increase in the rate of H2 evolution.     

Linkage isomerism in the binding of pentapeptide Ac-His(Ala)3His-NH2 to (ethylenediamine)palladium(II): effect of the binding mode on peptide conformation

The reaction of the pentapeptide Ac-His1-Ala2-Ala3-Ala4-His5-NH2 (AcHAAAHNH2) (1) with [Pd(en)(ONO2)2] (en = NH2CH2CH2NH2) in either DMF-d(7) or H2O:D2O (90%:10%) gave three linkage isomers of [Pd(en)(AcHAAAHNH2)](2+) (2), 2a, 2b, and 2c, which differ only in which pair of imidazole nitrogen atoms bind to Pd. In the most abundant isomer, 2a, Pd is bound by N1 from each of the two imidazole rings. In the minor isomers 2b and 2c, Pd is bound by N1(His1) and N3(His5) and by N3(His1) and N1(His5), respectively. The reactions of [Pd(en)(ONO2)2] with the N-methylated peptides Ac-(N3-MeHis)-Ala-Ala-Ala-(N3-MeHis)-NH2 (AcH*AAAH*NH2) (3), Ac-(N3-MeHis)-Ala-Ala-Ala-(N1-MeHis)-NH2 (AcH(*)AAAH(#)NH2) (4), and Ac-(N1-MeHis)-Ala-Ala-Ala-(N3-Me-His)-NH2 (AcH(#)AAAH(*)NH2) (5) each gave a single species [Pd(en)(peptide)](2+) in N,N-dimethylformamide (DMF) or aqueous solution, 7, 8, and 9, respectively, with Pd bound by the two nonmethylated imidazole nitrogen atoms in each case. These complexes were analogous to 2a, 2b, and 2c, respectively. Ac-(N1-MeHis)-Ala-Ala-Ala-(N1-MeHis)-NH2 (AcH(#)AAAH(#)NH2) (6) with [Pd(en)(ONO2)2] in DMF slowly gave a single product, [Pd(en)(AcH(#)AAAH(#)NH2)](2+) (10), in which Pd was bound by the N3 of each imidazole ring. The corresponding linkage isomer of 2 was not observed. Complex 10 was also the major product in aqueous solution, but other species were also present. All compounds were exhaustively characterized in solution by multinuclear 1D ((1)H , (13)C, and, with (15)N-labeled ethylenediamine, (15)N) and 2D (correlation spectroscopy, total correlation spectroscopy, transverse rotating-frame Overhauser effect spectroscopy (T-ROESY), heteronuclear multiple-bond correlation, and heteronuclear single quantum coherence) NMR spectra, circular dichroism (CD) spectra, electrospray mass spectroscopy, and reversed-phase high-performance liquid chromatography. ROESY spectra were used to calculate the structure of 2a, which contained a single turn of a peptide alpha helix in both DMF and water, the helix being better defined in DMF. The Pd(en)(2+) moiety was not used in structure calculations, but its location and coordination by one imidazole N1 from each histidine to form a 22-membered metallocycle were unambiguously established. Convergence of the structures was greatest when calculated with two hydrogen-bond constraints (Ala4 peptide NH...OC acetyl and His5 peptide NH...OC-His1) that were indicated by the low temperature dependence of these NH chemical shifts. Vicinal HN-CHalpha coupling constants and chemical shifts of alpha-H atoms were also consistent with a helical conformation. Similar long-range ROE correlations were observed for [Pd(en)(AcH(*)AAAH(*)NH2)](2+) (7), which displayed a CD spectrum in aqueous solution that suggested the presence of some helicity. Long-range ROE correlations were not observed for 8, 9, or 10, but a combination of NMR data and CD spectroscopy was interpreted in terms of the conformational behavior of the coordinated pentapeptide. Only for the linkage isomer [Pd(en)(AcH(*)AAAH(#)NH2)](2+) (8) was there evidence of a contribution from a helical conformation. The data for 8 were interpreted as interconversion between the helix and random coil conformations. Zn(2+) with peptides gave broad NMR peaks attributed to lability of this metal ion, while reactions of cis-[Pt(NH3)2(ONO2)2] were slow, giving a complex mixture of products rather than the macrochelate ring observed with Pd(en)(2+). In summary, these studies indicate that Pd(en)(2+) coordinates to histidine with similar preference for each of the two imidazole nitrogens, enabling the formation of up to four linkage isomers in its complexes with pentapeptides His-xxx-His. Only the N1-N1 linkage isomer that forms a 22-membered macrochelate ring is able to induce an alpha-helical peptide conformation, whereas the 20- and 21-membered rings of linkage isomers do not. This suggests that linkage isomeric mixtures may compromise histidine coordination to metal ions and reduce alpha-helicity.     

Structural insights of a PI3K/mTOR dual inhibitor with the morpholino-triazine scaffold

Stimulation of the PI3K/Akt/mTOR pathway, which controls cell proliferation and growth, is often observed in cancer cell. Inhibiting both PI3K and mTOR in this pathway can switch off Akt activation and hence, plays a powerful role for modulating this pathway. PKI-587, a drug containing the structure of morpholino-triazines, shows a dual and nano-molar inhibition activity and is currently in clinical trial. To provide an insight into the mechanism of this dual inhibition, pharmacophore and QSAR models were developed in this work using compounds based on the morpholino-triazines scaffold, followed by a docking study. Pharmacophore model suggested the mechanism of the inhibition of PI3Kα and mTOR by the compounds were mostly the same, which was supported by the docking study showing similar docking modes. The analysis also suggested the importance of the flat plane shape of the ligands, the space surrounding the ligands in the binding pocket, and the slight difference in the shape of the binding sites between PI3Kα and mTOR.     

Improved prediction of drug-target interactions using regularized least squares integrating with kernel fusion technique

Identification of drug-target interactions (DTI) is a central task in drug discovery processes. In this work, a simple but effective regularized least squares integrating with nonlinear kernel fusion (RLS-KF) algorithm is proposed to perform DTI predictions. Using benchmark DTI datasets, our proposed algorithm achieves the state-of-the-art results with area under precision–recall curve (AUPR) of 0.915, 0.925, 0.853 and 0.909 for enzymes, ion channels (IC), G protein-coupled receptors (GPCR) and nuclear receptors (NR) based on 10 fold cross-validation. The performance can further be improved by using a recalculated kernel matrix, especially for the small set of nuclear receptors with AUPR of 0.945. Importantly, most of the top ranked interaction predictions can be validated by experimental data reported in the literature, bioassay results in the PubChem BioAssay database, as well as other previous studies. Our analysis suggests that the proposed RLS-KF is helpful for studying DTI, drug repositioning as well as polypharmacology, and may help to accelerate drug discovery by identifying novel drug targets.     

OPTIMAL FISH HARVESTING FOR A POPULATION MODELED BY A NONLINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATION

As the human population continues to grow, there is a need for better management of our natural resources in order for our planet to be able to produce enough to sustain us. One important resource we must consider is marine fish populations. We use the tool of optimal control to investigate harvesting strategies for maximizing yield of a fish population in a heterogeneous, finite domain. We determine whether these solutions include no‐take marine reserves as part of the optimal solution. The fishery stock is modeled using a nonlinear, parabolic partial differential equation with logistic growth, movement by diffusion and advection, and with Robin boundary conditions. The objective for the problem is to find the harvest rate that maximizes the discounted yield. Optimal harvesting strategies are found numerically.     

Preparation and characterization of particles with small differences in polydispersity

Colloidal particles are widely used both in fundamental research and in materials science. One important parameter influencing the physical properties of colloidal materials is the particle size distribution (polydispersity) of the colloidal particles. Recent work on colloidal crystallization has demonstrated that even subtle changes in polydispersity can have significant effects. In this study we present centrifugation techniques for subtly manipulating the width and the shape of the particle size distribution, for polydispersities less than 10%. We use scanning electron microscopy as well as dynamic and static light scattering to characterize the particle size distributions. We compare the results and highlight the difficulties associated with the determination of accurate particle size distributions.     

High-field DNP and ENDOR with a novel multiple-frequency resonance structure.

We describe a new triply tuned (e(-), (1)H, and (13)C) resonance structure operating at an electron Larmor frequency of 139.5 GHz for dynamic nuclear polarization (DNP) and electron nuclear double-resonance (ENDOR) experiments. In contrast to conventional double-resonance structures, the body of the microwave cavity simultaneously acts as a NMR coil, allowing for increased efficiency of radiofrequency irradiation while maintaining a high quality factor for microwave irradiation. The resonator design is ideal for low-gamma-nuclei ENDOR, where sensitivity is limited by the fact that electron spin relaxation times are on the order of the RF pulse lengths. The performance is demonstrated with (2)H ENDOR on a standard perdeuterated bis-diphenylene-phenyl-allyl stable radical. In DNP experiments, we show that the use of this resonator, combined with a low microwave power setup (17 mW), leads to significantly higher (1)H signal enhancement (epsilon approximately 400 +/- 50) than previously achieved at 5-T fields. The results emphasize the importance of optimizing the microwave B(1) field by improving either the quality factor of the microwave resonator or the microwave power level.     

D-branes and Spin structures

It was recently pointed out by E. Witten that for a D-brane to consistently wrap a submanifold of some manifold, the normal bundle must admit a Spin^c structure. We examine this constraint in the case of type II string compactifications with vanishing cosmological constant, and argue that in all such cases, the normal bundle to a supersymmetric cycle is automatically Spin^c.     

Star factorizations of graph products

A k‐star is the graph K_1,k. We prove a general theorem about k‐star factorizations of Cayley graphs. This is used to give necessary and sufficient conditions for the existence of k‐star factorizations of any power (K_q)^s of a complete graph with prime power order q, products C × C ×··· × C of k cycles of arbitrary lengths, and any power (C_r)^s of a cycle of arbitrary length. © 2001 John Wiley & Sons, Inc. J Graph Theory 36: 59–66, 2001