Excited-state intermolecular proton transfer of firefly luciferin V. Direct proton transfer to fluoride and other mild bases

We studied the direct proton transfer (PT) from electronically excited D-luciferin to several mild bases. The fluorescence up-conversion technique is used to measure the rise and decay of the fluorescence signals of the protonated and deprotonated species of D-luciferin. From a base concentration of 0.25 M or higher the proton transfer rates to the fluoride, dihdyrogen phosphate or acetate bases are fast and comparable. The fluorescence signals are nonexponential and complex. We suggest that the fastest decay component arises from a direct proton transfer process from the hydroxyl group of D-luciferin to the mild base. The proton donor and acceptor molecules form an ion pair prior to photoexcitation. Upon photoexcitation solvent rearrangement occurs on a 1 ps time-scale. The PT reaction time constant is ～2 ps for all three bases. A second decay component of about 10 ps is attributed to the proton transfer in a contact pair bridged by one water molecule. The longest decay component is due to both the excited-state proton transfer (ESPT) to the solvent and the diffusion-assisted PT process between a photoacid and a base pair positioned remotely from each other prior to photoexcitation.     

Excited-state intermolecular proton transfer of firefly luciferin IV. Temperature and pH dependence

Time-resolved emission as well as steady-state UV-vis techniques were employed to study the photoprotolytic processes that d-luciferin, the natural substrate of the firefly luciferase, undergoes in both acidic aqueous solutions and ice. The emission spectrum of D-luciferin in a 20 mM HCl aqueous solution or higher has an additional emission band at 590 nm red-shifted with respect to the strongest emission band positioned at 530 nm of the deprotonated NRO(-*) form in a pH-neutral aqueous solution. We attribute this emission band to the zwitterion form designated as (+)HNRO(-). The time-resolved emission signals show that the NRO(-*) emission band at 530 nm and the zwitterion emission band at 590 are strongly quenched by a recombination process with a proton in an acidic solution and in ice. In ice, the quenching rate is 10 times faster than in the liquid state. We attribute the fast quenching rate to the high value of the proton diffusion constant in ice.     

Dimensions of some fractals defined via the semigroup generated by 2 and 3

We compute the Hausdorff and Minkowski dimension of subsets of the symbolic space Σ _m ={0, ...,m?1}^? that are invariant under multiplication by integers. The results apply to the sets {x∈Σ _m :? k, x _k x _2k ... x _nk =0}, where n ≥ 3. We prove that for such sets, the Hausdorff and Minkowski dimensions typically differ.     

A stability result for balanced dictatorships in Sn

We prove that a balanced Boolean function on S_n whose Fourier transform is highly concentrated on the first two irreducible representations of S_n, is close in structure to a dictatorship, a function which is determined by the image or pre‐image of a single element. As a corollary, we obtain a stability result concerning extremal isoperimetric sets in the Cayley graph on S_n generated by the transpositions. Our proof works in the case where the expectation of the function is bounded away from 0 and 1. In contrast, [6] deals with Boolean functions of expectation O(1/ n) whose Fourier transform is highly concentrated on the first two irreducible representations of S_n. These need not be close to dictatorships; rather, they must be close to a union of a constant number of cosets of point‐stabilizers. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 494–530, 2015     

Toward extracting $$\gamma $$ from $$B\rightarrow DK$$ without binning

SABRE (Sodium iodide with Active Background REjection) is a direct detection dark matter experiment based on arrays of radio-pure NaI(Tl) crystals. The experiment aims at achieving an ultra-low background rate and its primary goal is to confirm or refute the results from the DAMA/LIBRA experiment. The SABRE Proof-of-Principle phase was carried out in 2020–2021 at the Gran Sasso National Laboratory (LNGS), in Italy. The next phase consists of two full-scale experiments: SABRE South at the Stawell Underground Physics Laboratory, in Australia, and SABRE North at LNGS. This paper focuses on SABRE South and presents a detailed simulation of the detector, which is used to characterise the background for dark matter searches including DAMA/LIBRA-like modulation. We estimate an overall background of 0.72 cpd/kg/\(\hbox {keV}_{\hbox {{ee}}}\) in the energy range 1–6 \(\hbox {keV}_{\hbox {{ee}}}\) primarily due to radioactive contamination in the crystals. Given this level of background and considering that the SABRE South has a target mass of 50 kg, we expect to exclude (confirm) DAMA/LIBRA modulation at \(4~(5)\sigma \) within 2.5 years of data taking.