Global existence for the Cauchy problem of the parabolic–parabolic Keller–Segel system on the plane

This paper is concerned with the Cauchy problem for the Keller–Segel system $$\left\{\begin{array}{l@{\quad}l}u_t = \nabla \cdot (\nabla u - u \nabla v) & \hbox{in } {\bf R}^{2} \times(0,\infty),\\v_t = \Delta v - \lambda v + u & \hbox{ in } {\bf R}^2 \times(0,\infty),\\u(x,0) = u_0 (x) \geq 0, \; v(x,0) = v_0 (x) \geq 0 & \hbox{ in} {\bf R}^2\end{array}\right.$$ with a constant λ ≥ 0, where ${(u_0, v_0) \in (L^1 ({\bf R}^2) \cap L^\infty ({\bf R}^2) ) \times (L^1 ({\bf R}^2) \cap H^1 ({\bf R}^2))}$ . Let $$m (u_0;{\bf R}^2) = \int\limits_{{\bf R}^2} u_0 (x) dx$$ . The same method as in [9] yields the existence of a blowup solution with m (u ₀; R ²) > 8π. On the other hand, it was recently shown in [7] that under additional hypotheses ${u_0 \log (1 + |x|^2) \in L^1 ({\bf R}^2)}$ and ${u_0 \log u_0 \in L^1 ({\bf R}^2)}$ , any solution with m(u ₀; R ²) < 8π exists globally in time. In[18], the extra assumptions were taken off, but the condition on mass was restricted to m (u ₀; R ²) < 4π. In this paper, we prove that any solution with m (u ₀; R ²) < 8π exists globally in time under no extra conditions. Furthermore the global existence of solutions is obtained under some condition on u ₀ also in the critical case m (u ₀; R ²) = 8π.     

Thermal step bunching on the restricted solid-on-solid model with point contact inter-step attractions

We present the restricted solid-on-solid (RSOS) model with the inter-ledge interaction of the point contact type (p-RSOS model). We have made detailed calculation of the Andreev free energy , which is similar to the equilibrium crystal shape (ECS) z=z(x,y), and the surface gradient as the function of the Andreev field . From the calculated and , we have obtained the vicinal surface free energy . The inter-ledge attraction between adjacent steps affects the surface free energies in the equilibrium, and causes the first-order transition on the profile of ECS at low temperature. The inter-ledge attraction also destabilizes the regular train of steps. We also have obtained the thermal step bunching.     

Amelioration of Airway Stenosis in Rabbit Models by Photodynamic Therapy with Talaporfin Sodium (NPe6)

It is difficult to treat patients with acquired airway stenosis, and the quality of life of such patients is therefore lowered. We have suggested the application of photodynamic therapy (PDT) as a new treatment for airway stenosis and have determined the efficacy of PDT in animal disease models using a second-generation photosensitizer with reduced photosensitivity. An airway stenosis rabbit model induced by scraping of the tracheal mucosa was administered NPe6 (5 mg kg⁻¹), and the stenotic lesion was irradiated with 670 nm light emitted from a cylindrical diffuser tip at 60 J cm⁻² under bronchoscopic monitoring. PDT using NPe6 improved airway stenosis ( P  = 0.043) and respiratory stridor. A significant prolongation of survival time was seen in the PDT-treated animals compared to that in the untreated animals ( P  = 0.025) and 44% of the treated animals achieved long-term survival (>60 days). In conclusion, PDT using NPe6 is effective for improvement in airway stenosis.     

Re-Evaluations of Zr-DFO Complex Coordination Chemistry for the Estimation of Radiochemical Yields and Chelator-to-Antibody Ratios of 89Zr Immune-PET Tracers

(1) Background: Deferoxamine B (DFO) is the most widely used chelator for labeling of zirconium-89 (⁸⁹Zr) to monoclonal antibody (mAb). Despite the remarkable developments of the clinical ⁸⁹Zr-immuno-PET, chemical species and stability constants of the Zr-DFO complexes remain controversial. The aim of this study was to re-evaluate their stability constants by identifying species of Zr-DFO complexes and demonstrate that the stability constants can estimate radiochemical yield (RCY) and chelator-to-antibody ratio (CAR). (2) Methods: Zr-DFO species were determined by UV and ESI-MS spectroscopy. Stability constants and speciation of the Zr-DFO complex were redetermined by potentiometric titration. Complexation inhibition of Zr-DFO by residual impurities was investigated by competition titration. (3) Results: Unknown species, ZrH_qDFO₂, were successfully detected by nano-ESI-Q-MS analysis. We revealed that a dominant specie under radiolabeling condition (pH 7) was ZrHDFO, and its stability constant (logβ₁₁₁) was 49.1 ± 0.3. Competition titration revealed that residual oxalate inhibits Zr-DFO complex formation. RCYs in different oxalate concentration (0.1 and 0.04 mol/L) were estimated to be 86% and >99%, which was in good agreement with reported results (87%, 97%). (4) Conclusion: This study succeeded in obtaining accurate stability constants of Zr-DFO complexes and estimating RCY and CAR from accurate stability constants established in this study.     

Deuterium Isotope Effect on the Phase Separation of Zipper‐Type Hydrogen‐Bonding Inter‐Polymer Complexes in Solution

We have investigated the deuterium isotope effect on phase separation in aqueous zipper‐type hydrogen‐bonding polymer solutions. The phase separation temperature of poly(acrylic acid)‐poly(acrylamide) in heavy water is about 16°C higher than that in water. This large isotope effect in the aqueous zipper‐type macromolecular system arises from the polymer‐polymer interaction due to cooperative hydrogen bonds in the polymer‐polymer complex.     

SPECTROSCOPIC STUDIES ON THE STRUCTURES OF RETINOCHROME and METARETINOCHROME*

Abstract– Spectroscopic measurements of retinochrome and the related photoproduct, metaretino-chrome, were carried out to determine the conformation of the retinal and the protein. Absorption spectra with fourth derivatives indicate that the tryptophan residues are located in a hydrophobic core and that the environment around these residues does not change after light irradiation. Circular dichroism measurements indicate that retinochrome has a high helical content which is not altered by the conversion of retinochrome to metaretinochrome. Fourier transform infrared difference spectra demonstrate that retinochrome has the all-trans retinal and metaretinochrome has the 11-CM retinal. Retinochrome has an absorption due to amino acid residue(s) which changes in metaretinochrome. This work demonstrates that conformational changes are not induced during the conversion but the electrical charge(s) of the protein are changed by irradiation.     

On the configuration of 4,4′,6,6′-tetraphenyl-2,2′-dithiopyrylene

The title compound showed in its UV-VIS absorption spectra large red shifts of bands from solution to crystal indicating a pronounced intermolecular interaction between the dithiopyrylene π-electron systems. Dipole moment measurement in benzene solution gave a dipole moment value of 1.90 D which offers a direct evidence for the molecule in cis-configuration.     

Guanidine is a Zn(2+)-binding ligand at neutral pH in aqueous solution

We have found the first well-characterized coordination of guanidine with Zn(2+) in a 1:1 complex (ZnL(1)) with cyclen (= 1,4,7,10-tetraazacyclododecane) functionalized with guanidinylethyl group (L(1) = (2-guanidinyl)ethyl-cyclen). The X-ray structure analysis of the 1:1 complex crystallized at pH 7.5 revealed an apical coordination of the pendant guanidinyl group to Zn(2+) ion in ZnL(1). By potentiometrtic pH titration, initial formation of a 1:1 Zn(L(1).H(+)) complex was indicated, where only the cyclen N's bind to Zn(2+) with the complexation constant, log K(s) (K(s) = [Zn(L(1).H(+))]/[Zn(2+)][L(1).H(+)] (M(-1))), being 12.4 +/- 0.1. Facile deprotonation of the guanidinium pendant in the Zn(L(1).H(+)) occurred with a pK(a) value of 5.9 +/- 0.1 at 25 degrees C with I = 0.1 (NaNO(3)) to yield the guanidine-coordinating complex ZnL(1). 4-Nitrophenyl phosphate dianion (NPP(2-)) interacted with ZnL(1) through a new Zn(2+)-phosphate coordination, as indicated by (31)P NMR titration and potentiometric pH titration. An apparent complexation constant for this new species, log K(app)(Zn(L(1).H(+))-NPP), was 4.0 +/- 0.1, which is larger than the log K(app)(ZnL(2)-NPP) value of 3.1 for the 1:1 complex of Zn(2+)-cyclen (ZnL(2)) with NPP at the common pH 5.6. The interaction of ZnL(1) with a phosphate dianion was proven by the X-ray crystal structure analysis of the 1:1 ZnL(1)-PP(2-) complex (PP(2-) is a dianion of phenyl phosphate) obtained from an aqueous solution at pH 6.5. At higher pH, the pendant guanidinium cation is deprotonated to displace the phosphate to yield the Zn(2+)-guanidine bond.