Global stability and a non-standard finite difference scheme for a diffusion driven HBV model with capsids

A diffusion driven model for hepatitis B virus (HBV) infection, taking into account the spatial mobility of both the HBV and the HBV DNA-containing capsids is presented. The global stability for the continuous model is discussed in terms of the basic reproduction number. The analysis is further carried out on a discretized version of the model. Since the standard finite difference (SFD) approximation could potentially lead to numerical instability, it has to be restricted or eliminated through dynamic consistency. The latter is accomplished by using a non-standard finite difference (NSFD) scheme and the global stability properties of the discretized model are studied. The results are numerically illustrated for the dynamics and stability of the various populations in addition to demonstrating the advantages of the usage of NSFD method over the SFD scheme.     

Structural and Functional Consequences of the Weak Binding of Chlorin e6 to Bovine Rhodopsin

The chlorophyll‐derivative chlorin e6 (Ce6) identified in the retinas of deep‐sea ocean fish is proposed to play a functional role in red bioluminescence detection. Fluorescence and ¹H NMR spectroscopy studies with the bovine dim‐light photoreceptor, rhodopsin, indicate that Ce6 weakly binds to it with μm affinity. Absorbance spectra prove that red light sensitivity enhancement is not brought about by a shift in the absorbance maximum of rhodopsin. ¹⁹F NMR experiments with samples where ¹⁹F labels are either placed at the cytoplasmic binding site or incorporated as fluorinated retinal indicate that the cytoplasmic domain is highly perturbed by binding, while little to no changes are detected near the retinal. Binding of Ce6 also inhibits G‐protein activation. Chemical shift changes in ¹H‐¹⁵N NMR spectroscopy of ¹⁵N‐Trp labeled bovine rhodopsin reveal that Ce6 binding perturbs the entire structure. These results provide experimental evidence that Ce6 is an allosteric modulator of rhodopsin.     

On a family of elliptic curves of rank at least 2

Let C_m:y² = x³ ? m²x + p²q² be a family of elliptic curves over ?, where m is a positive integer and p, q are distinct odd primes. We study the torsion part and the rank of C_m(?). More specifically, we prove that the torsion subgroup of C_m(?) is trivial and the ?-rank of this family is at least 2, whenever m ? 0 (mod 3), m ? 0 (mod 4) and m ≡ 2 (mod 64) with neither p nor q dividing m.

     

Control over Kinetic and Thermodynamically Driven Pathways of Crystallization to Yield Cofacial and Slipped-Stack Dimers in Single Crystals

Control over the molecular packing in the solid state is of utmost importance in regulating the bulk optical properties of organic semiconductors. The electronic coupling between the molecules makes it possible to improve the properties of the bulk materials. This work reports an example of control over the selective formation of polymorphic single crystals of donor–acceptor-type small-molecule compound 25TR by 1) kinetic or 2) thermodynamic course of crystallisation to yield slipped stack (S) and cofacial (C) dimers in the single crystals. The distinct optical characteristics of the C-dimer and S-dimer are summarised. Both forms show significant excitonic interactions in the solid state, and the S-dimeric form has strong yellowish orange fluorescence, whereas the C-dimeric form is non-fluorescent in the crystalline state. DFT calculations and differential scanning calorimetric experiments revealed that the C-dimer polymorph is the thermodynamically stable form with a free energy offset of 0.43 eV in comparison with the S-dimer. Interestingly, the thermodynamically driven non-fluorescent single crystal was found to be convertible to its fluorescent form irreversibly by thermal trigger. The charge-carrier-transport characteristics of these two polymorphs were computed by using the Marcus–Hush formalism. The computations of the charge-carrier-transport behaviour revealed that the S-dimer ( 25TR_(R) ) is ambipolar, whereas the C-dimer ( 25TR_(Y) ) is predominantly n-type.     

Total chemical and semisynthetic approaches for the preparation of ubiquitinated proteins and their applications

Protein ubiquitination is an important post-translational modification (PTM) in eukaryotic organisms that regulates a variety of cellular processes, such as protein degradation, signal transduction, apoptosis, and DNA damage tolerance. To decipher mechanistically the diverse biological functions of ubiquitination, homogeneous ubiquitinated proteins are greatly needed. Although direct isolation from cell source and in vitro enzymatic methods can be used to produce such proteins, these methods often suffer from problems of low yield or heterogeneous products. Comparably, total chemical and semisynthetic approaches offer good alternatives to produce the ubiquitinated proteins with high purity and selectivity. This review summarizes the recent developments of protein ubiquitination strategies and the use of the synthesized proteins to help garner structural and functional insight into the inner workings of the ubiquitin system.     

Modified o-methyl-substituted IBX: room temperature oxidation of alcohols and sulfides in common organic solvents

o-Methyl-substituted Me-IBX is the first modified analog of IBX that oxidizes alcohols in common organic solvents at room temperature, due to a composite of two factors, that is, low solubility and hypervalent twisting-promoted rate enhancement. Furthermore, the reagent is efficient for selective oxidation of sulfides to sulfoxides, a transformation that otherwise occurs only sluggishly with standard IBX. The facile synthetic accessibility and its mild as well as non-hazardous nature render Me-IBX a stable equivalent of Dess-Martin periodinane reagent in organic oxidations.     

Simple Chemical Route Synthesis of Fe2O3 Nanoparticles and its Application for Adsorptive Removal of Congo Red from Aqueous Media: Artificial Neural Network Modeling

Nanocrystalline Fe₂O₃ powder was synthesized by a simple chemical route involving FeCl₃ and NaOH. The Fe₂O₃ powder thus prepared was characterized using x-ray diffraction study, scanning electron microscopy, and Fourier transform infrared spectroscopy. The adsorption properties of crystalline Fe₂O₃ powder have been investigated with an aim to explore a possible low cost and efficient way to remove Congo red (CR) from waste water. Fe₂O₃ powder was found as an excellent adsorbent for CR from aqueous medium. Adsorption capacity as much as 203.66 mg g^?1 is reported at room temperature. Effect of different experimental parameters such as reaction pH, initial CR dye concentration, adsorbent dose, and reaction temperature were studied on adsorption capacity of Fe₂O₃ powder and modeled by artificial neural network (ANN). Optimal ANN structure (4–5–1) shows minimum mean squared error (MSE) of 0.00235 and determination coefficient (R²) of 0.991 with Levenberg–Marquardt algorithm. Isotherm analysis of experimental data exhibited better fit to the Langmuir isotherm. The adsorption process was found to follow second-order kinetics as depicted by the analysis of experimental results. Thermodynamic study shows that the adsorption process is endothermic, spontaneous, and thermodynamically favorable in the temperature range of 27°C to 60°C.     

Synthesis of 3‐aminomethylidenechroman‐2‐carboxamides by a Sequential One‐pot Three Component Reaction and by Post‐Passerini Condensation Modification

3‐Arylaminomethylidenechroman‐2‐carboxamide has been synthesized by a one‐pot three component reaction among 3‐formylchromone, aromatic amine, and cyclohexyl isocyanide. 3‐(N‐alkylsubstitued/unsubstituted)aminomethylidenechroman‐2‐carboxamides were synthesized by heating Passerini products derived from chromone‐3‐carbaldehyde with different aliphatic primary amines. The products obtained from the reactions of aliphatic primary amines readily form chromeno[2,3‐c]pyrrole when heated in acetic acid. Bischromanones have also been synthesized using this methodology.     

High-throughput miniaturized microfluidic microscopy with radially parallelized channel geometry

In this article, we present a novel approach to throughput enhancement in miniaturized microfluidic microscopy systems. Using the presented approach, we demonstrate an inexpensive yet high-throughput analytical instrument. Using the high-throughput analytical instrument, we have been able to achieve about 125,880 cells per minute (more than one hundred and twenty five thousand cells per minute), even while employing cost-effective low frame rate cameras (120 fps). The throughput achieved here is a notable progression in the field of diagnostics as it enables rapid quantitative testing and analysis. We demonstrate the applicability of the instrument to point-of-care diagnostics, by performing blood cell counting. We report a comparative analysis between the counts (in cells per μl) obtained from our instrument, with that of a commercially available hematology analyzer.     

Inclusion properties of 3-fluoromesotetraphenylporphyrin with C60 and C70

To improve the selectivity ratio of C70 over C60, a new designer molecule, viz., 3-fluoromesotetraphenylporphyrin (1) has been reported in the present investigations. Fluorescence studies reveal that the Q-absorption band of 1 gets sufficient quenching effect upon addition of both C60 and C70. Binding constants (K) of the C60/1 and C70/1 complexes are estimated to be 580 and 10,800 dm3 mol(-1), respectively. Thus, K(C70)/K(C60) is approximately 19 which is very large and even comparable with other macrocyclic host molecules like calix[5]arene, azacalix[m]arene[n]pyridine, cyclotriveratrylenophane and calixarene bisporphyrin. 1H NMR chemical shift measurements show that the -NH- proton of 1 suffers more shifts in presence of C70 compared to C60. This finding also offers a good support in favor of high K value for C70/1 complex as well as large selectivity ratio of C70 over C60.