Needle & knot : binder boilerplate tied up

To lighten the burden of programming language mechanization, many approaches have been developed that tackle the substantial boilerplate which arises from variable binders. Unfortunately, the existing approaches are limited in scope. They typically do not support complex binding forms (such as multi-binders) that arise in more advanced languages, or they do not tackle the boilerplate due to mentioning variables and binders in relations. As a consequence, the human mechanizer is still unnecessarily burdened with binder boilerplate and discouraged from taking on richer languages. This paper presents Knot, a new approach that substantially extends the support for binder boilerplate. Knot is a highly expressive language for natural and concise specification of syntax with binders. Its meta-theory constructively guarantees the coverage of a considerable amount of binder boilerplate for well-formed specifications, including that for well-scoping of terms and context lookups. Knot also comes with a code generator, Needle, that specializes the generic boilerplate for convenient embedding in COQ and provides a tactic library for automatically discharging proof obligations that frequently come up in proofs of weakening and substitution lemmas of type-systems. Our evaluation shows, that Needle & Knot significantly reduce the size of language mechanizations (by 40% in our case study). Moreover, as far as we know, Knot enables the most concise mechanization of the POPLmark Challenge (1a + 2a) and is two-thirds the size of the next smallest. Finally, Knot allows us to mechanize for instance dependentlytyped languages, which is notoriously challenging because of dependent contexts and mutually-recursive sorts with variables

Two-Photon Spectra of Chlorophylls and Carotenoid–Tetrapyrrole Dyads

We present a direct comparison of two-photon spectra of various carotenoid–tetrapyrrole dyads and phthalocyanines (Pc) as well as chlorophylls (Chl) in the spectral range between 950 and 1360 nm, corresponding to one-photon spectra between 475 and 680 nm. For carotenoids (Car) with 8, 9, or 10 conjugated double bonds, the two-photon absorption cross section of states below the optical allowed carotenoid S₂ is at least about 3–10 times higher than that of Pc or chlorophyll <i>a</i> and <i>b</i> at 550/1100 nm. A quantitative comparison of spectra from Pc with and without carotenoids of eight and nine conjugated double bonds confirms energy transfer from optically forbidden carotenoid states to Pc in these dyads. When considering that less than 100% efficient energy transfer reduces the two-photon contribution of the carotenoids in the spectra, the actual Car two-photon cross sections relative to Chl/Pc are even higher than a factor of 3–10. In addition, strong spectroscopic two-photon signatures at energies below the optical allowed carotenoid S₂ state support the presence of additional optical forbidden carotenoid states such as S*, S_<i>x</i>, or, alternatively, contributions from higher vibronic or hot S₁ states dominating two-photon spectra or energy transfer from the carotenoids. The onset of these states is shifted about 1500–3500 cm^–1 to lower energies in comparison to the S₂ states. Our data provides evidence that two-photon excitation of the carotenoid S*, S_<i>x</i>, or hot S₁ states results in energy transfer to tetrapyrroles or chlorophylls similar to that observed with the Car S₁ two-photon excitation

Carotenoid dark state to chlorophyll energy transfer in isolated light-harvesting complexes CP24 and CP29

We present a comparison of the energy transfer between carotenoid dark states and chlorophylls for the minor complexes CP24 and CP29. To elucidate the potential involvement of certain carotenoid–chlorophyll coupling sites in fluorescence quenching of distinct complexes, varying carotenoid compositions and mutants lacking chlorophylls at specific binding sites were examined. Energy transfers between carotenoid dark states and chlorophylls were compared using the coupling parameter, ΦCouplingCar S1-Chl, which is calculated from the chlorophyll fluorescence observed after preferential carotenoid two-photon excitation. In CP24, artificial reconstitution with zeaxanthin leads to a significant reduction in the chlorophyll fluorescence quantum yield, Φ F1, and a considerable increase in ΦCouplingCar S1-Chl. Similar effects of zeaxanthin were also observed in certain samples of CP29. In CP29, also the replacement of violaxanthin by the sole presence of lutein results in a significant quenching and increased ΦCouplingCar S1-Chl. In contrast, the replacement of violaxanthin by lutein in CP24 is not significantly increasing ΦCouplingCar S1-Chl. In general, these findings provide evidence that modification of the electronic coupling between carotenoid dark states and chlorophylls by changing carotenoids at distinct sites can significantly influence the quenching of these minor proteins, particularly when zeaxanthin or lutein is used. The absence of Chl612 in CP24 and of Chl612 or Chl603 in CP29 has a considerably smaller effect on Φ F 1 and ΦCouplingCar S1-Chl than the influence of some carotenoids reported above. However, in CP29 our results indicate slightly dequenching and decreased ΦCouplingCar S1-Chl when these chlorophylls are absent. This might indicate that both, Chl612 and Chl603 are involved in carotenoid-dependent quenching in isolated CP29

A red-shifted two-photon-only caging group for three-dimensional photorelease

Based on nitrodibenzofuran (NDBF) a new photocage with higher two-photon action cross section and red-shifted absorption was developed. Due to calculations, a dimethylamino functionality (DMA) was added at ring position 7. The uncaging of nucleobases after two-photon excitation (2PE) could be visualized via double-strand displacement in a hydrogel. With this assay we achieved three-dimensional photorelease of DMA-NDBF-protected DNA orthogonal to NDBF-protected strands. While being an excellent 2P-cage, DMA-NDBF is surprisingly stable under visible-light one-photon excitation (1PE). This case of excitation-specific photochemistry enhances the scope of orthogonal photoregulation

Selective modification for red-shifted excitability: a small change in structure, a huge change in photochemistry

We developed three bathochromic, green-light activatable, photolabile protecting groups based on a nitrodibenzofuran (NDBF) core with D-π-A push–pull structures. Variation of donor substituents (D) at the favored ring position enabled us to observe their impact on the photolysis quantum yields. Comparing our new azetidinyl-NDBF (Az-NDBF) photolabile protecting group with our earlier published DMA-NDBF, we obtained insight into its excitation-specific photochemistry. While the “two-photon-only” cage DMA-NDBF was inert against one-photon excitation (1PE) in the visible spectral range, we were able to efficiently release glutamic acid from azetidinyl-NDBF with irradiation at 420 and 530 nm. Thus, a minimal change (a cyclization adding only one carbon atom) resulted in a drastically changed photochemical behavior, which enables photolysis in the green part of the spectrum

Microscopic Rates of Peptide–Phospholipid Bilayer Interactions from Single-Molecule Residence Times

The binding of glucagon-like peptide-1 (GLP-1) to a planar phospholipid bilayer is measured using single-molecule total internal reflection fluorescence microscopy. From several reports in the literature, GLP-1 has been shown to be a random coil in free solution, adopting a folded, α-helix conformation when intercalated into membrane environments. Single-molecule fluorescence measurements of GLP-1 binding to supported lipid bilayers show evidence of two populations of membrane-associated molecules having different residence times, suggesting weakly adsorbed peptides and strongly bound peptides in the lipid bilayer. The path to and from a strongly bound (folded, intercalated) state would likely include an adsorbed state as an intermediate, so that the resulting kinetics would correspond to a consecutive first-order reversible three-state model. In this work, the relationships between measured single-molecule residence times and the microscopic rates in a three-state kinetic model are derived and used to interpret the binding of GLP-1 to a supported lipid bilayer. The system of differential equations associated with the proposed consecutive-three state kinetics scheme is solved, and the solution is applied to interpret histograms of single-molecule, GLP-1 residence times in terms of the microscopic rates in the sequential two-step model. These microscopic rates are used to estimate the free energy barrier to adsorption, the fraction of peptides adsorbing to the membrane surface that successfully intercalate in the bilayer, the lifetime of inserted peptides in the membrane, and the free energy change of insertion into the lipid bilayer from the adsorbed state. The transition from a random coil in solution to a folded state in a membrane has been recognized as a common motif for insertion of membrane active peptides. Therefore, the relationships developed here could have wide application to the kinetic analysis of peptide–membrane interactions