A highly selective detection method of native protein tyrosine phosphatase 1B (PTP1B) is described using a target specific probe equipped with 1‐naphthylamine (λex=330 nm, λem=445 nm). Irradiation of a mixture of PTP1B and Probe 1 with ultraviolet light of 280 nm (corresponding to PTP1B excitation maximum) resulted in significant fluorescence increase at 445 nm, following FRET characteristics. This phenomenon does not occur with other closely related phosphatases or cellular abundant alkaline phosphatase (APP). Probe 1, the most potent and selective probe, was found to competitively inhibit PTP1B (Ki≈42 nm), whereas APP inhibition was found to be in the low micromolar range. Furthermore, Probe 1 discriminates between PTP1B and several other phosphatases. Here, we report real‐time label‐free FRET detection of pure PTP1B as well as induced human PTP1B in Escherichia coli cell lysate. In contrast to 6,8‐difluoro‐4‐methylumbelliferyl phosphate (DiFMUP), a representative fluorescence turn‐on PTP substrate, our FRET probe successfully differentiated human cervical carcinoma cell lysate, SiHa, which has a high expression level of PTP1B, from PTP1B‐knockdown SiHa cell lysate (that is, siRNA was used for PTP1B knockdown).

Burban-Drozd showed that the degenerate cusp singularities have tame Cohen-Macaulay representation type, and classified all indecomposable Cohen-Macaulay modules over them. One of their main example is the non-isolated singularity W = x y z. On the other hand, Abouzaid-Auroux-Efimov-Katzarkov-Orlov showed that W = x y z is mirror to a pair of pants. In this paper, we investigate homological mirror symmetry of these indecomposable Cohen-Macaulay modules for x y z.Namely, we show that closed geodesics (with a flat C-bundle) of a hyperbolic pair of pants have a one-toone correspondence with indecomposable Cohen-Macaulay modules for x y z with multiplicity one that are locally free on the punctured spectrum. In particular, this correspondence is established first by a geometric A ∞ -functor from the Fukaya category of the pair of pants to the matrix factorization category of x y z, and next by the correspondence between Cohen-Macaulay modules and matrix factorizations due to Eisenbud. For the latter, we compute explicit Macaulayfications of modules from Burban-Drozd's classification and find a canonical form of the corresponding matrix factorizations. In the sequel, we will show that indecomposable modules with higher multiplicity correspond to twisted complexes of closed geodesics.We also find mirror images of rank 1 indecomposable Cohen-Macaulay modules (of band type) over the singularity W = x 3 + y 2 − x y z as closed loops in the orbifold sphere P 1 3,2,∞ .

No abstract

We propose a new method of compressing laser pulses to ultra-high powers based on spatially varying dispersion of a plasma plume that has a density gradient. Here, compression is achieved when a long, negatively frequency-chirped laser pulse reflects off the density ramp of an over-dense plasma slab. As the density increases longitudinally, high frequency photons at the leading part of the laser pulse penetrate more deeply into the plasma region than lower frequency photons, leading to pulse compression in a similar way to that off a chirped mirror. Proof-of-principle simulations carried out using a one-dimensional (1-D) particle-in-cell (PIC) simulation code demonstrate compression of 2.35 ps laser pulse to 10.3 fs, with a compression ratio of 225. As plasma is robust and resistant to damage at high intensities, unlike solid-state gratings commonly used in chirped-pulse amplification (CPA), the method could be used as a compressor to reach exawatt or zettawatt peak powers.

No abstract