Covariant Bethe-Salpeter approximation in models of strongly correlated electron systems.

Strongly correlated electron systems are generally described by tight-binding lattice Hamiltonians with strong local (onsite) interactions, the most popular being the Hubbard model. Although the half-filled Hubbard model can be simulated by Monte Carlo (MC), physically more interesting cases beyond half-filling are plagued by the sign problem. One therefore should resort to other methods. It was demonstrated recently that a systematic truncation of the set of Dyson-Schwinger equations for correlators of the Hubbard, supplemented by a "covariant" calculation of correlators leads to a convergent series of approximants. The covariance preserves all the Ward identities among correlators describing various condensed matter probes. While first-order (classical), second-order (Hartree-Fock or Gaussian), and third-order (Cubic) covariant approximation were worked out, the fourth-order (quartic) seems too complicated to be effectively calculable in fermionic systems. It turns out that the complexity of the quartic calculation in local interaction models,is manageable computationally. The quartic (Bethe-Salpeter-type) approximation is especially important in 1D and 2D models in which the symmetry-broken state does not exists (the Mermin-Wagner theorem), although strong fluctuations dominate the physics at strong coupling. Unlike the lower-order approximations, it respects the Mermin-Wagner theorem. The scheme is tested and exemplified on the single-band 1D and 2D Hubbard model.

Photoactive chlorin e6 is a multifunctional modulator of amyloid-ß aggregation and toxicity via specific interactions with its histidine residues.

The self-assembly of Aß to ß-sheet-rich neurotoxic oligomers is a main pathological event leading to Alzheimer's disease (AD). Selective targeting of Aß oligomers without affecting other functional proteins is therefore an attractive approach to prevent the disease and its progression. In this study, we report that photodynamic treatment of Aß in the presence of catalytic amounts of chlorin e6 can selectively damage Aß and inhibit its aggregation and toxicity. Chlorin e6 also reversed the amyloid aggregation process in the dark by binding its soluble and low molecular weight oligomers, as shown by thioflavin T (ThT) fluorescence and photoinduced cross-linking of unmodified protein (PICUP) methods. Using HSQC NMR spectroscopy, ThT assays, amino acid analysis, SDS/PAGE, and EPR spectroscopy, we show that catalytic amounts of photoexcited chlorin e6 selectively damage the Aß histidine residues H6, H13, and H14, and induce Aß cross-linking by generating singlet oxygen. In contrast, photoexcited chlorin e6 was unable to cross-link ubiquitin and α-synuclein, demonstrating its high selectivity for Aß. By binding to the Aß histidine residues, catalytic amounts of chlorin e6 can also inhibit the Cu2+-induced aggregation and toxicity in darkness, while at stoichiometric amounts it acts as a chelator to reduce the amount of free Cu2+. This study demonstrates the great potential of chlorin e6 as a multifunctional agent for treatment of AD, and shows that the three N-terminal Aß histidine residues are a suitable target for Aß-specific drugs.