Pollaczek contour integrals for the fixed-cycle traffic-light queue

The fixed-cycle traffic-light (FCTL) queue is the standard model for intersections with static signaling, where vehicles arrive, form a queue and depart during cycles controlled by a traffic light. Classical analysis of the FCTL queue based on transform methods requires a computationally challenging step of finding the complex-valued roots of some characteristic equation. Building on the recent work of Oblakova et al. (Exact expected delay and distribution for the fixed-cycle traffic-light model and similar systems in explicit form, 2016), we obtain a contour-integral expression, reminiscent of Pollaczek integrals for bulk-service queues, for the probability generating function of the steady-state FCTL queue. We also show that similar contour integrals arise for generalizations of the FCTL queue introduced in Oblakova et al. (2016) that relax some of the classical assumptions. Our results allow us to compute the queue-length distribution and all its moments using algorithms that rely on contour integrals and avoid root-finding procedures.

     

Monitoring selectivity in kinase-promoted phosphorylation of densely packed peptide monolayers using label-free electrochemical detection

This paper describes remarkably high sensitivities in the label-free detection of kinase-promoted phosphorylation for 14 different peptide substrates on electrode-immobilized monolayers (gold or nitride) using serine/threonine kinases PKA, PKC, and CaMK2. Peptide substrates were preselected using (33)P-labeling in a microarray of 1024 substrates. The three most active peptides (A1-A3, C1-C3, and M1-M3) were investigated using electrochemical impedance spectroscopy (EIS) and ion-sensitive field effect transistors (ISFETs). Some of the peptide substrates, for example, the PKC-specific substrate PPRRSSIRNAH (C1), showed a remarkably high sensitivity in the EIS-based sensor measurements. Our studies revealed that this high sensitivity is primarily due to the monolayer's packing density. Nanoscopic studies demonstrated a distinct disordering of the C1-monolayer upon phosphorylation, while phosphatase-promoted dephosphorylation regenerated the highly ordered peptide monolayer. As a matter of fact, the initial surface packing of the peptide monolayer mainly determined the level of sensitivity, whereas electrostatic repulsion of the redox-active species was found to be much less important.     

Nanostructures via noncovalent synthesis: 144 hydrogen bonds bring together 27 components.

This paper describes the spontaneous and reversible assembly of approximately 20 kDa synthetic hydrogen-bonded assemblies via the formation of 144 cooperative hydrogen bonds. These nanostructures ( approximately 3.0 x 5.5 nm), consisting of 27 different components, have been carefully characterized using a combination of (1)H NMR spectroscopy, MALDI-TOF MS using Ag(+)-labeling, gel permeation chromatography, and CD spectroscopy.     

General and Facile Route to Isomerically Pure Tricyclic Peptides Based on Templated Tandem CLIPS/CuAAC Cyclizations

We report a one‐pot ligation/cyclization technology for the rapid and clean conversion of linear peptides into tricyclic peptides that is based on using tetravalent scaffolds containing two benzyl bromide and two alkyne moieties. These react via CLIPS/CuAAC reactions with cysteines and azides in the peptide. Flexibility in the scaffolds is key to the formation of isomerically pure products as the flexible scaffolds T4 ₁ and T4 ₂ mostly promote the formation of single isomeric tricycles while the rigid scaffolds T4 ₃ and T4 ₄ do not yield clean products. There seems to be no limitation to the number and types of amino acids present as 18 canonical amino acids were successfully implemented. We also observed that azides at the peptide termini and cysteine residues in the center gave better results than compounds with the functional groups placed the other way round.     

Proximally functionalized cavitands and synthesis of a flexible hemicarcerand

A general study on the synthesis of partly bridged octols3a-d and4c-d is described. Tri-bridged diol3c can be prepared in 54% yield in DMSO at 70°C with excess CH₂BrCl or in 52% yield in DMF at 70°C with only 4 equiv. of CH₂BrCl. 1,3-Di-bridged tetrol4a, one of the two possible di-bridged isomers formed in preference to the other, was obtained in 30% yield. Tri-bridged diols3c andd can be selectively debrominated in one step by treatment with 5 equiv. ofn-BuLi in THF to afford the corresponding dibromo derivatives8a andb in 77% and 76% yields, respectively. After incorporation of the fourth bridge, the remaining two bromines can be replaced by C(O)OMe to give9c (60%), by OH to give9d (62%) or by CN to give9f (>95%). When the lithiated derivatives of3c andd are quenched with electrophiles other thanH ⁺, a selectively functionalized tri-bridged diol with hydroxyl (8c, 47%) and selectively functionalized cavitands with thiomethyl (9g, 25%) or iodo (9h, 20%) groups can be synthesized. Two molecules of9d were coupled with CH₂BrCl in DMSO/THF under high dilution conditions to give the flexible hemicarcerand10 in 71% yield. Supplementary Data. A list of observed and calculated structure factors have been deposited with the British Document Supply Centre as Supplementary Publication No. SUP 82170 (50 pages)This paper is dedicated to the commemorative issue on the 50th anniversary of calixarenes.     

Fullerene-Acetylene Molecular Scaffolding: Chemistry of 2-functionalized 1-ethynylated C60, oxidative homocoupling,hexakis-adduct formation,and attempted synthesis of C

On the way to the fullerene-acetylene hybrid carbon allotropes 2 and 6 , the oxidative homocoupling of the 2-functionalized 1-ethynylated C₆₀ derivatives 11, 12, 14 , and 15 was investigated. Under Glaser-Hay conditions, the two soluble dumbbell-shaped bisfullerenes 17 and 18 , with two C₆₀ moieties linked by a buta-1,3-diynediyl bridge, were formed in 52 and 82% yield, respectively (Scheme 2). Cyclic-voltammetric measurements revealed that there is no significant electronic communication between the two fullerene spheres via the buta-1,3-diynediyl linker. Removal of the 3,4,5,6-tetrahydro-2H-pyran-2-yl (Thp) protecting groups in 18 gave in 80% yield the highly insoluble dumbbell 19 with methanol groups in the 2,2′-positions of the buta-1,3-diynediyl-bridged carbon spheres. Attempted conversion of 19 to the all-carbon dianion 6 (C) via base-induced elimination of formaldehyde was not successful presumably due to exo-dig cyclization of the formed alkoxides. The occurrence of this cyclization under furan formation was proven for 2-[4-(trimethylsilyl)buta-1,3-diyn-1-yl][60]fullerene-1-methanol ( 21 ), a soluble model compound for 19 (Scheme 3). To compare the properties of ethynylated fullerene mono-adducts to those of corresponding higher adducts, hexakis-adducts 26 and 28 with an octahedral functionalization pattern resulting from all-e (equatorial) additions were prepared by the reversible-template method of Hirsch (Scheme 4). Reaction of the ethynylated mono-adducts 25 or 13 with diethyl 2-bromomalonate/1,8-diazabicyclo[5.4.0]undec-7-ene (DBU) in the presence of 1,9-dimethylanthracene (DMA) as reversible template led to 26 and 28 in 28 and 22% yield, respectively. Preliminary experiments indicated a significant change in reactivity and NMR spectral properties of the fullerene addends with increasing degree of functionalization.