Extending partial isomorphisms of graphs

Theorem Let X be a finite graph. Then there exists a finite graph Z containing X as an induced subgraphs, such that every isomorphism between induced subgraphs of X extends to an automorphism of Z.The graphZ may be required to be edge-transitive. The result implies that for anyn, there exists a notion of a genericn-tuple of automorphism of the Rado graphR (the random countable graph): for almost all automorphism ₁,..., _n and ₁ ofR (in the sense of Baire category), (R,₁,..., _n ), (R,₁,..., _n ). The problem arose in a recent paper of Hodges, Hodgkinson, Lascar and Shelah, where the theorem is used to prove the small index property forR.Work supported by a Sloan Fellowship and by NSF grant DMS-8903378.     

Templating S100A9 amyloids on Aβ fibrillar surfaces revealed by charge detection mass spectrometry,microscopy, kinetic and microfluidic analyses

The mechanism of amyloid co-aggregation and its nucleation process are not fully understood in spite of extensive studies. Deciphering the interactions between proinflammatory S100A9 protein and Aβ₄₂ peptide in Alzheimer''s disease is fundamental since inflammation plays a central role in the disease onset. Here we use innovative charge detection mass spectrometry (CDMS) together with biophysical techniques to provide mechanistic insight into the co-aggregation process and differentiate amyloid complexes at a single particle level. Combination of mass and charge distributions of amyloids together with reconstruction of the differences between them and detailed microscopy reveals that co-aggregation involves templating of S100A9 fibrils on the surface of Aβ₄₂ amyloids. Kinetic analysis further corroborates that the surfaces available for the Aβ₄₂ secondary nucleation are diminished due to the coating by S100A9 amyloids, while the binding of S100A9 to Aβ₄₂ fibrils is validated by a microfluidic assay. We demonstrate that synergy between CDMS, microscopy, kinetic and microfluidic analyses opens new directions in interdisciplinary research.

Templating mechanism of S100A9 amyloids on Aβ fibrillar surfaces during amyloid co-aggregation process was revealed by synergy of biophysical methods including charge detection mass spectrometry, microscopy, kinetic and microfluidic analyses.     

Biologically Relevant Molecular Transducer with Increased Computing Power and Iterative Abilities

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Infrared and NMR Spectroscopic Fingerprints of the Asymmetric H7+O3 Complex in Solution

Infrared (IR) absorption in the 1000–3700 cm⁻¹ range and ¹H NMR spectroscopy reveal the existence of an asymmetric protonated water trimer, H₇⁺O_3, in acetonitrile. The core H₇⁺O₃ motif persists in larger protonated water clusters in acetonitrile up to at least 8 water molecules. Quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations reveal irreversible proton transport promoted by propagating the asymmetric H₇⁺O₃ structure in solution. The QM/MM calculations allow for the successful simulation of the measured IR absorption spectra of H₇⁺O₃ in the OH stretch region, which reaffirms the assignment of the H₇⁺O₃ spectra to a hybrid-complex structure: a protonated water dimer strongly hydrogen-bonded to a third water molecule with the proton exchanging between the two possible shared-proton Zundel-like centers. The H₇⁺O₃ structure lends itself to promoting irreversible proton transport in presence of even one additional water molecule. We demonstrate how continuously evolving H₇⁺O₃ structures may support proton transport within larger water solvates.     

Quench dynamics and nonequilibrium phase diagram of the bose-hubbard model

We investigate the time evolution of correlations in the Bose-Hubbard model following a quench from the superfluid to the Mott insulator. For large values of the final interaction strength the system approaches a distinctly nonequilibrium steady state that bears strong memory of the initial conditions. In contrast, when the final interaction strength is comparable to the hopping, the correlations are rather well approximated by those at thermal equilibrium. The existence of two distinct nonequilibrium regimes is surprising given the nonintegrability of the Bose-Hubbard model. We relate this phenomenon to the role of quasiparticle interactions in the Mott insulator.     

Decomposition of triacetone triperoxide is an entropic explosion

Both X-ray crystallography and electronic structure calculations using the cc-pVDZ basis set at the DFT B3LYP level were employed to study the explosive properties of triacetone triperoxide (TATP) and diacetone diperoxide (DADP). The thermal decomposition pathway of TATP was investigated by a series of calculations that identified transition states, intermediates, and the final products. Counterintuitively, these calculations predict that the explosion of TATP is not a thermochemically highly favored event. It rather involves entropy burst, which is the result of formation of one ozone and three acetone molecules from every molecule of TATP in the solid state.     

Enolstannanes as electrofugal groups in allylic alkylation

Enolstannanes serve as nucleophiles towards allylic acetates under the influence of palladium(O) catalyst.