Some limit results for longest common subsequences

The length l_n of a longest common subsequence before time n sequences (B₁₁, B₁₂, …) (B₂₁, B₂₂, …) is the cardinality of the largest increasing set of pairs of integers {(j_1α, j_2α)}

$\text{l?}\text{j}{}_{11}\text{<}\text{j}{}_{12}\text{<·<}\text{j}{}_{11}{}_{\mathrm{n}}\text{?}\text{n}\text{l?}\text{j}{}_{21}\text{<}\text{j}{}_{22}\text{<·<}\text{j}{}_{21}{}_{\mathrm{n}}\text{?}\text{n}$

such that ?1?α?l_n, (B_1j1α=B_2j2α). If B₁ and B₂ are independent random sequences with co-ordinates i.i.d. uniform on {1, 2, …, k}, it follows from Kingman's subadditive ergodic theorem that the ratio l_n/n converges to a constant c_k a.s. A method of deriving lower bounds for the constants c_k is given, the bounds obtained improving known lower bounds, for k>2. The rate of decrease of c_k with k is shown to be no faster than 1/√k, contrasting with P{B_1i?B_2i}=1/k. Finally, an alternative method of deriving lower bounds is given and used to improve the lower bound for c₂.     

Screening an In-House Isoquinoline Alkaloids Library for New Blockers of Voltage-Gated Na+ Channels Using Voltage Sensor Fluorescent Probes: Hits and Biases

Voltage-gated Na⁺ (Na_V) channels are significant therapeutic targets for the treatment of cardiac and neurological disorders, thus promoting the search for novel Na_V channel ligands. With the objective of discovering new blockers of Na_V channel ligands, we screened an In-House vegetal alkaloid library using fluorescence cell-based assays. We screened 62 isoquinoline alkaloids (IA) for their ability to decrease the FRET signal of voltage sensor probes (VSP), which were induced by the activation of Na_V channels with batrachotoxin (BTX) in GH3b6 cells. This led to the selection of five IA: liriodenine, oxostephanine, thalmiculine, protopine, and bebeerine, inhibiting the BTX-induced VSP signal with micromolar IC₅₀. These five alkaloids were then assayed using the Na⁺ fluorescent probe ANG-2 and the patch-clamp technique. Only oxostephanine and liriodenine were able to inhibit the BTX-induced ANG-2 signal in HEK293-hNa_V1.3 cells. Indeed, liriodenine and oxostephanine decreased the effects of BTX on Na⁺ currents elicited by the hNa_V1.3 channel, suggesting that conformation change induced by BTX binding could induce a bias in fluorescent assays. However, among the five IA selected in the VSP assay, only bebeerine exhibited strong inhibitory effects against Na⁺ currents elicited by the hNav1.2 and hNav1.6 channels, with IC₅₀ values below 10 µM. So far, bebeerine is the first BBIQ to have been reported to block Na_V channels, with promising therapeutical applications.     

Application of Cleavable Linkers to Improve Therapeutic Index of Radioligand Therapies

Radioligand therapy (RLT) is an emergent drug class for cancer treatment. The dose administered to cancer patients is constrained by the radiation exposure to normal tissues to maintain an appropriate therapeutic index. When a radiopharmaceutical or its radiometabolite is retained in the kidneys, radiation dose deposition in the kidneys can become a dose-limiting factor. A good exemplar is [¹⁷⁷Lu]Lu-DOTATATE, where patients receive a co-infusion of basic amino acids for nephroprotection. Besides peptides, there are other classes of targeting vectors like antibody fragments, antibody mimetics, peptidomimetics, and small molecules that clear through the renal pathway. In this review, we will review established and emerging strategies that can be used to mitigate radiation-induced nephrotoxicity, with a focus on the development and incorporation of cleavable linkers for radiopharmaceutical designs. Finally, we offer our perspectives on cleavable linkers for RLT, highlighting future areas of research that will help advance the technology.     

Reduced Endocannabinoid Tone in Saliva of Chronic Orofacial Pain Patients

Background: the endocannabinoid system (ECS) participates in many physiological and pathological processes including pain generation, modulation, and sensation. Its involvement in chronic orofacial pain (OFP) in general, and the reflection of its involvement in OFP in salivary endocannabinoid (eCBs) levels in particular, has not been examined. Objectives: to evaluate the association between salivary (eCBs) levels and chronic OFP. Methods: salivary levels of 2 eCBs, anandamide (AEA), 2-arachidonoylglycerol (2-AG), 2 endocannabinoid-like compoundsN-palmitoylethanolamine (PEA), N-oleoylethanolamine (OEA), and their endogenous precursor and breakdown product, arachidonic acid (AA), were analyzed using liquid chromatography/tandem mass spectrometry in 83 chronic OFP patients and 43 pain-free controls. The chronic OFP patients were divided according to diagnosis into musculoskeletal, neurovascular/migraine, and neuropathic pain types. Results: chronic OFP patients had lower levels of OEA (p = 0.02) and 2-AG (p = 0.01). Analyzing specific pain types revealed lower levels of AEA and OEA in the neurovascular group (p = 0.04, 0.02, respectively), and 2-AG in the neuropathic group compared to controls (p = 0.05). No significant differences were found between the musculoskeletal pain group and controls. Higher pain intensity was accompanied by lower levels of AA (p = 0.028), in neuropathic group. Conclusions: lower levels of eCBs were found in the saliva of chronic OFP patients compared to controls, specifically those with neurovascular/migraine, and neuropathic pain. The detection of changes in salivary endocannabinoids levels related to OFP adds a new dimension to our understanding of OFP mechanisms, and may have diagnostic as well as therapeutic implications for pain.     

Oxygen-sensitive 19F NMR imaging of the vascular system in vivo

The fluorine nuclear magnetic resonance spin-lattice relaxation rate (1/T1) of the perfluorochemical blood substitute perfluorotripropylamine (FTPA) is very sensitive to oxygen tension. This presents the possibility of measuring blood oxygen tension by 19F MR imaging. We obtained oxygen-sensitive 19F NMR images of the circulatory system of rats infused with emulsified FTPA. Blood oxygenation was assessed under conditions of both air- and 100% O2-breathing. T1 relaxation times were derived from MR images using a partial saturation pulse sequence. The T1 times were compared with a phantom calibration curve to calculate average blood pO2 values in the lung, liver, and spleen. The results showed marked, organ-specific increases in blood oxygen tension when the rat breathed 100% O2 instead of air.     

A comparison of quantitative nuclear magnetic resonance methods: internal,external, and electronic referencing

The performance of three quantitative NMR methods was compared in terms of short‐term and long‐term precision and accuracy, robustness, linear range, and general applicability. The Internal Reference method employs a reference material co‐dissolved with sample; the External Reference method employs a reference material contained in a separate solution; and the third method, known as Electronic REference To access In vivo Concentrations (ERETIC), employs an externally calibrated digital reference peak. The Internal Reference method results were the most precise and remained stable within 0.1% for at least 4 weeks. The results from the External Reference and ERETIC methods were practically equivalent to each other during this time. These methods exhibited small differences relative to the standard set by the Internal Reference method and slightly lower precision, establishing them as practical alternatives to the Internal Reference method. In contrast to the Internal Reference method, the External Reference and ERETIC methods possess several advantages that address peak overlap, flexibility of calibration, and duration of applicability. The study was designed such that each spectrum contained the information needed to compare the three methods while all other variables were kept constant. Applicability of pulse width compensation is addressed. ERETIC software compensation and minor adjustments to 90° pulse width were concluded to be unnecessary for this system. Although each of the methods was applied here to specifically calculate and compare chemical purity values, this evaluation applies generally to absolute quantitation by NMR. Copyright © 2013 John Wiley & Sons, Ltd.     

Synthesis of two dihydropyrroloindoledione‐based copolymers for organic electronics

Two novel dihydropyrroloindoledione (DPID)‐based copolymers have been synthesized in a two directional approach and characterized (gel permeation chromatography (GPC), ultraviolet‐visible (UV–vis), cyclic voltammetry, and computational models). These planar, broad absorption copolymers show promise for use in organic electronics, with deep energy levels and low bandgaps. The two‐directional Knoevenagel condensation used demonstrates the versatility of DPID as a useful yet underexploited conjugated unit. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013