Rota–Baxter Algebras and New Combinatorial Identities

The word problem for an arbitrary associative Rota–Baxter algebra is solved. This leads to a noncommutative generalization of the classical Spitzer identities. Links to other combinatorial aspects are indicated.      

The Sixth Painlevé Equation as Similarity Reduction of $${\widehat{\mathfrak{gl}}_3}$$ Generalized Drinfel’d–Sokolov Hierarchy

Scaling symmetry of -type Drinfel’d–Sokolov hierarchy is investigated. Applying similarity reduction to the hierarchy, one can obtain the Schlesinger equation with (n + 1) regular singularities. Especially in the case of n = 3, the hierarchy contains the three-wave resonant system and the similarity reduction gives the generic case of the Painlevé VI equation. We also discuss Weyl group symmetry of the hierarchy.      

Solvent and pH Effects on the Fluorescence of 7-(Dimethylamino)-2-Fluorenesulfonate

A novel water-soluble solvatochromic molecule, 7-(dimethylamino)-2-fluorenesulfonate (2,7-DAFS), was prepared by a three-step reaction from 2-nitrofluorene in good overall yield. The pH and solvent effects on the UV-VIS absorption and fluorescence spectra of 2,7-DAFS have been studied. Protonation of the dimethylamino group switches the absorption from intramolecular charge-transfer (ICT) to π → π* transition. The ground state pKa value of 2,7-DAFS was determined as 4.51. The fluorescence spectrum of the excited basic form, *(DAFS), shows a structureless single band with a large Stokes shift, whereas that of the acidic form, *(⁺HDAFS), exhibits a structured band with a small Stokes shift. The emission intensities of the basic and acidic forms versus pH/Ho plots show stretched sigmoidal curves and indicate that (1) the rate of deprotonation of *(⁺HDAFS) is comparable to the fluorescence decay of the species, and (2) the efficient proton-induced quenching of *(DAFS) fluorescence occurs. The pKa* was estimated as −1.7 from the fluorescence titration curve. The fluorescence maximum of *(DAFS) is blue-shifted as the polarity of solvent decreases. However, no clear dependency of the emission intensity and spectral half width, and thus fluorescence quantum yield, on the solvent polarity was revealed. It appears that the fluorescence sensitivity of 2,7-DAFS is 15 ∼ 25 times greater than the sensitivity of a widely utilized fluorescent probe, 5-(dimethylamino)-1-naphthalenesulfonate. This higher sensitivity, together with the ease of derivatization, would provide the fluorene-based fluorescent molecules significant advantages for a variety of applications.     

Fluorescent Probe ABM for Screening Gastrointestinal Patient’s Immune State

The fluorescent probe-aminoderivative of benzanthrone, ABM (developed at Riga Technical University, Riga, Latvia) was used to characterize the membranes of lymphocytes of cancer patients: 46 patients with gastrointestinal diseases, 13 patients having different primary localizations with massive metastases and intoxication. Patients were divided into three groups: (1) with decreased fluorescence intensity, (2) normal fluorescence intensity, (3) increased fluorescence intensity. The lymphocytes distribution among subsets differed between groups, in correspondence to the level of florescence intensity. Surgical treatment affected the main immunological parameters and elevated the functional activity of lymphocytes. In the advanced tumors group, fluorescence intensity correlates with the survival rate. Results suggest that determination of lymphocytes functional activity by ABM can aid evaluation of the immune status in cancer patients.     

Stress-Induced Alteration of Chlorophyll Fluorescence Polarization and Spectrum in Leaves of <Emphasis Type="Italic">Alocasia macrorrhiza</Emphasis> L. Schott

The value of intrinsic chlorophyll fluorescence polarization, and the intensity in emission spectrum were investigated in leaf segments of Alocasia macrorrhiza under several stress conditions including different temperatures (25–50°C), various concentrations of NaCl (0–250 mM), methyl viologen (MV, 0–25 μM), SDS (0–1.0%) and NaHSO₃ (0–80 μM). Fluorescence emission spectrum of leaves at wavelength regions of 500–800 nm was monitored by excitation at 436 nm. The value of fluorescence polarization (P value), as result of energy transfer and mutual orientation between chlorophyll molecules, was determined by excitation at 436 nm and emission at 685 nm. The results showed that elevated temperature and concentrations of salt (NaCl), photooxidant (MV), surfactant (SDS) and simulated SO₂ (NaHSO₃) treatments all induced a reduction of fluorescence polarization to various degrees. However, alteration of the fluorescence spectrum and emission intensity of F₆₈₅ and F₇₃₁ depended on the individual treatment. Increase in temperature and concentration of NaHSO₃ enhanced fluorescence intensity mainly at F₆₈₅, while an increase in MV concentration led to a decrease at both F₆₈₅ and F₇₃₁. On the contrary, NaCl and SDS did not cause remarkable change in fluorescence spectrum. Among different treatments, the negative correlation between polarization and fluorescence intensity was found with NaHSO₃ treatments only. We concluded that P value being measured with intrinsic chlorophyll fluorescence as probe in leaves is a susceptible indicator responding to changes in environmental conditions. The alteration of P value and fluorescence intensity might not always be shown a functional relation pattern. The possible reasons of differed response to various treatments were discussed.     

Quantitative Time-Resolved Fluorescence Spectrum of the Cortical Sarcoma and the Adjacent Normal Tissue

The difference in time-resolved fluorescence spectrum between the cortical sarcoma and the adjacent normal tissue was studied in both experimental and theoretical ways. The Clinical data were obtained in vivo using a time-resolved fluorescence spectrometer employing a single fiber-optic probe for excitation and detection. Tissue was modeled as s-180 sarcoma tumor surrounded with normal muscle and was mediated by the Palladium-porphyrin photosensitizer (Pd-TCPP). The emitted fluorescence was considered as arising from the tumor tissue or the normal muscle, due to the presence of the photosensitizer. A computational code which could simulating time-resolved fluorescence emission was presented and applied to comparing fluorescence decay of photosensitizer in different stages of tumor growth. In this code the different stages of the tumor was modeled through changing the time τ, the delay of the fluorescence photon emission and z _max, the thickness of the tumor. It was found in the in vivo experiment that the fluorescence from tumor tissue decayed more quickly than from the adjacent normal muscle. For the ten rats in the first experiment day, the mean decay constant of tumor T _s and normal tissue T _n were 554 and 526 μs, respectively. And T _s increased with the tumor growth, from 554 μs in the first day to 634 μs in the eighth day while T _s kept steady. It was believed that the more adequate oxygen supplied by the normal tissue can more effectively quench the fluorescence and in the normal tissue the photosensitizer lifetime is smaller. As a result the simulated time-resolved fluorescence spectrum of normal tissue showed more quickly decay. And the thickness of the tumor can also delay the fluorescence decay. Both the experimental and simulated results indicated that the germination of the tumor would increase the decay constant of the time-resolved fluorescence spectrum. So decay constant of the tumor tissue spectrum should be larger than that of adjacent normal tissue for the reason of hypoxia and overgrouth. This fact could be of use in the tumor diagnoses.     

Microporated PEG Spheres for Fluorescent Analyte Detection

Poly(ethylene glycol) (PEG) hydrogels have been used to encapsulate fluorescently labeled molecules in order to detect a variety of analytes. The hydrogels are designed with a mesh size that will retain the sensing elements while allowing for efficient diffusion of small analytes. Some sensing assays, however, require a conformational change or binding of large macromolecules, which may be sterically prohibited in a dense polymer matrix. A process of hydrogel microporation has been developed to create cavities within PEG microspheres to contain the assay components in solution. This arrangement provides improved motility for large sensing elements, while limiting leaching and increasing sensor lifetime. Three hydrogel compositions, 100% PEG, 50% PEG, and microporated 100% PEG, were used to create pH-sensitive microspheres that were tested for response time and stability. In order to assess motility, a second, more complex sensor, namely a FITC-dextran/TRITC-Con A glucose-specific assay was encapsulated within the microspheres.     

Calcium Ion-Induced Stabilization and Refolding of Agkisacutacin from <Emphasis Type="Italic">Agkistrodon Acutus</Emphasis> Venom Studied by Fluorescent Spectroscopy

Agkisacutacin isolated from the venom of Agkistrodon acutus is a coagulation factor IX / coagulation factor X-binding protein with marked anticoagulant- and platelet-modulating activities. Ca²⁺ ion-induced stabilization and refolding of Agkisacutacin have been studied by following fluorescent measurements. Ca²⁺ ions not only increase the structural stability of agkisacutacin against GdnHCl denaturation, but also induce its refolding. The GdnHCl-induced unfolding of the apo-agkisacutacin and the purified agkisacutacin is a single-step process with no detectable intermediate state. Ca²⁺ ions play an important role in the stabilization of the structure of agkisacutacin. Ca²⁺-stabilized agkisacutacin exhibits higher resistance to GdnHCl denaturation than the apo-agkisacutacin. It is possible to induce refolding of the unfolded apo-agkisacutacin merely by adding 1 mM Ca²⁺ ions without changing the concentration of the denaturant. The kinetic result of Ca²⁺-induced refolding provides evidences for that agkisacutacin consists of at least two refolding phases and the first phase of Ca²⁺-induced refolding should involve the formation of the compact Ca²⁺-binding site regions, and subsequently, the protein undergoes further conformational rearrangements to form the native structure.     

A Feasible and Quantitative Encoding Method for Microbeads with Multicolor Quantum Dots

Multicolor encoded beads were achieved by incorporating two color core-shell quantum dots (QDs) (CdSe/ZnS) to commercial polystyrene (PS) beads. By controlling the concentration ratios of the two quantum dots (QDs) in doping solutions, a series of codes with different intensity ratios were obtained. Based on the multiple encoded carboxylic modified polystyrene beads, fluorescent dyes labeled antibodies were distinguished successfully on the beads’ surface. It suggests that the encoded beads from this method have the practicability in biological applications and chemical analysis. Hai-Qiao Wang and Zhen-Li Huang authors contribute equally to this work     

A Fe<Superscript>3+</Superscript>/Hg<Superscript>2+</Superscript>-Selective Anthracene-Based Fluorescent PET Sensor with Tridentate Ionophore of Amide/β-Amino Alcohol

A new anthracene-based fluorescent PET sensor 1 with a tridentate ionophore of amide/β-amino alcohol displays very good selectivity and sensitivity for Fe³⁺ (K _a = 1.6 × 10³ M⁻¹) and Hg²⁺ (K _a = 2.1 × 10³ M⁻¹) in CH₃CN–H₂O (3:7, v/v) with detection limit of 1 μM. More fluorescence enhancement was observed when 1 selectively detected Fe³⁺ or Hg²⁺ in CH₃CN and its detection limit was up to 0.03 μM.