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Amyloid-β (Aβ) is the core constituent protein of senile plaques, which is one of the key pathological hallmarks of Alzheimer’s disease (AD). Here we describe the design, synthesis, and evaluation of coumarin-derived small molecule fluorophores for Aβ imaging. By embedding the aromatic coumarin framework into π bridge of a push–pull chromophore, a novel fluorescence probe XCYC-3 applicable to efficient Aβ recognition was discovered. XCYC-3 displays higher fluorescent enhancement for aggregated Aβ than monomeric Aβ, and possesses good blood-brain barrier permeability. In vitro staining and in vivo imaging studies demonstrated that XCYC-3 could efficiently recognize Aβ plaques in the brain of AD transgenic mice. These results suggest that XCYC-3 is a promising fluorescence imaging agent for Aβ, which might provide important clues for the future development of potent NIR fluorescent probes for Aβ diagnosis.

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We study the initial value problem for a kind of Euler equation with a source term. Our main result is the existence of a globally-in-time weak solution whose total variation is bounded on the domain of definition, allowing the existence of shock waves. Our proof relies on a well-balanced random choice method called Glimm method which preserves the fluid equilibria and we construct a sequence of approximate weak solutions which converges to the exact weak solution of the initial value problem, based on the construction of exact solutions of the generalized Riemann problem associated with initially piecewise steady state solutions.