Matula numbers, Gödel numbering and Fock space

By making use of Matula numbers, which give a 1-1 correspondence between rooted trees and natural numbers, and a Gödel type relabelling of quantum states, we construct a bijection between rooted trees and vectors in the Fock space. As a by product of the aforementioned correspondence (rooted trees $\leftrightarrow $ ? Fock space) we show that the fundamental theorem of arithmetic is related to the grafting operator, a basic construction in many Hopf algebras. Also, we introduce the Heisenberg–Weyl algebra built in the vector space of rooted trees rather than the usual Fock space. This work is a cross-fertilization of concepts from combinatorics (Matula numbers), number theory (Gödel numbering) and quantum mechanics (Fock space).     

Rayleigh scattering of a new lyotropic nematic liquid crystal system: crossover of propagative and diffusive behaviour

In this paper we present to our knowledge the first light-scattering measurements on a rather new lyotropic system potassium laurate, decylammonium chloride, H₂O. Relative concentrations were chosen in order to obtain the discotic N_D phase over a large temperature range. Measurements involve digital recording of the autocorrelation function resulting from selfbeating of the depolarized scattered light. They were carried out at a fixed temperature in the N_D phase range, by varying the scattering angle. A strong tendency to oscillations, superimposed on the usual relaxation signal, was found. This behaviour is quite surprising, as special precautions had been taken to minimize any eventual propagative signal. Such precautions have been tested previously, while investigating the older system potassium laurate, decanol, D₂O. Nevertheless, we have found that in the new lyotropic system, a propagative component may occur in a significant way, or even become dominant for some particular situations. Actually, the characterization of such situations is the main purpose of the present paper. Based upon a detailed analysis of photocorrelation data, it will be shown that the observed behaviour is consistent with the expected wave vector dependences of propagative and diffusive modes. Finally, a discussion is given on possible causes for the tendency to instability of lyotropic nematic liquid crystals.     

Small-angle X-ray scattering and structural modeling of full-length: cellobiohydrolase I from Trichoderma harzianum

Cellobiohydrolases hydrolyze cellulose releasing cellobiose units. They are very important for a number of biotechnological applications, such as, for example, production of cellulosic ethanol and cotton fiber processing. The Trichoderma cellobiohydrolase I (CBH1 or Cel7A) is an industrially important exocellulase. It exhibits a typical two domain architecture, with a small C-terminal cellulose-binding domain and a large N-terminal catalytic core domain, connected by an O-glycosylated linker peptide. The mechanism by which the linker mediates the concerted action of the two domains remains a conundrum. Here, we probe the protein shape and domain organization of the CBH1 of Trichoderma harzianum (ThCel7A) by small angle X-ray scattering (SAXS) and structural modeling. Our SAXS data shows that ThCel7A linker is partially-extended in solution. Structural modeling suggests that this linker conformation is stabilized by inter- and intra-molecular interactions involving the linker peptide and its O-glycosylations.     

A combined experimental and theoretical approach for radical-scavenging activity of edaravone and its related derivatives

The experimental and theoretical study for evaluation of scavenging activity of edaravone (S1) and related derivatives, such as antipyrine (S2), dipyrone (S3), and phenylbutazone (S4), was carried out against DPPH and ABTS radicals. Structure–activity relationship study was performed using quantum chemical calculations at the DFT/B3LYP level of theory along with the 6-31G* basis sets. S1 and S4 are more effective scavengers against DPPH and ABTS. We observed little effects of S2 and S3 at several concentrations against these two free radicals. The calculations of HOMO, ionization potential, and bond dissociation energy confirmed that a hydrogen transfer is more preferential than an electron transfer. The radical stability of these compounds is related with spin densities. In accordance with experimental and theoretical results, edaravone is more active than phenylbutazone as scavenging drug.     

Evaluation of thermal stability and parameters of dissolution of nifedipine crystals

Nifedipine is a calcium channel blocker as well as a powerful vasodilator used to treat ischemic heart disease and hypertension. Its photosensitivity and very low solubility in water have been widely acknowledged as important properties deserving improvements. The main thrust of this study is to characterize the nature and the solid-state of nifedipine crystals obtained using different solvents as well as assess the stability by thermal methods (TG and DSC) and crystals structure by means of spectroscopic techniques (MID FTIR and XRD) and assess the dissolution parameters for such crystals. The calculated kinetic parameters activation energy (E _a = 123.3 kJ mol^?1 ± 0.1), the factor frequency (A = 25.93 ± 0.9 min^?1), and the reaction order (n = 0.2) of the main stage of thermal decomposition of nifedipine raw material were performed according to the Ozawa model. The data showed a zero-order kinetic behavior for all crystals despite the different values of E _a and A. The dissolution profiles were obtained for such crystals in three dissolution media with different pH values. After 1 h of dissolution, the higher amount of nifedipine dissolved was observed for crystals obtained in isopropyl alcohol (52.5 %, pH 4.5), followed by those in chloroform (48.1 %, pH 1.2) and subsequently in acetone (32.5 %, pH 6.8). Results showed different thermal stabilities and significant variations in the solubility of the crystals.     

New insight into the mechanism of action of wasp mastoparan peptides: lytic activity and clustering observed with giant vesicles

Antimicrobial peptides of the mastoparans family exert their bactericidal activity by binding to lipid membranes, inducing pores or defects and leaking the internal contents of vesicles and cells. However, this does not seem to be the only mechanism at play, and they might be important in the search for improved peptides with lower undesirable side effects. This work deals with three mastoparans peptides, Polybia-MP-1(MP-1), N2-Polybia-MP-1 (N-MP-1), and Mastoparan X (MPX), which exhibit high sequence homology. They all have three lysine residues and amidated C termini, but because of the presence of two, one, and no aspartic acid residues, respectively, they have +2, +3, and +4 net charges at physiological pH. Here we focus on the effects of these mastoparans peptides on anionic model membranes made of palmitoleyoilphosphatidylcholine (POPC) and palmitoleyoilphosphatidylglycerol (POPG) at 1:1 and 3:1 molar ratios in the presence and in the absence of saline buffer. Zeta potential experiments were carried out to measure the extent of the peptides' binding and accumulation at the vesicle surface, and CD spectra were acquired to quantify the helical structuring of the peptides upon binding. Giant unilamellar vesicles were observed under phase contrast and fluorescence microscopy. We found that the three peptides induced the leakage of GUVs at a gradual rate with many characteristics of the graded mode. This process was faster in the absence of saline buffer. Additionally, we observed that the peptides induced the formation of dense regions of phospholipids and peptides on the GUV surface. This phenomenon was easily observable for the more charged peptides (MPX > N-MP-1 > MP-1) and in the absence of added salt. Our data suggest that these mastoparans accumulate on the bilayer surface and induce a transient interruption to its barrier properties, leaking the vesicle contents. Next, the bilayer recovers its continuity, but this happens in an inhomogeneous way, forming a kind of ply with peptides sandwiched between two juxtaposed membranes. Eventually, a peptide-lipid aggregate forming a lump is formed at high peptide-to-lipid ratios.     

Electroanalytical Performance of (SiPy+Cl−/CuTsPc)5 LbL Film for Detecting Promethazine Hydrochloride

A (SiPy⁺Cl^?/CuTsPc)₅ layer‐by‐layer film was employed for the electroanalytical determination of promethazine hydrochloride in BR buffer pH 5.0 with peaks at 0.48 and 0.79 V. After optimisation of the square‐wave parameters (f=100 s^?1, a=40 mV and ΔE_s=2 mV), the peak at 0.79 V was used for quantification and a detection limit of 8.71×10^?9 mol L^?1 and a quantification limit of 9.31×10^?8 were calculated. The applicability of this procedure was tested on commercial formulations of promethazine hydrochloride by observing the stability, specificity, recovery and precision of the procedure in complex samples, without any preliminary treatment.     

Coercive field behavior of permalloy antidot arrays based on self-assembled template fabrication

High-density magnetic antidot arrays have been fabricated by deposition of Fe₂₀Ni₈₀ thin films on self-assembled nanoporous alumina membranes (NAM) with high-order hexagonal symmetry. The magnetic properties induced by the size and the geometry configuration of the holes introduced in a Fe₂₀Ni₈₀ thin film are discussed based on hysteresis loops measured as a function of temperature. The precursor NAMs have pore diameters ranging between 35 and 95 nm (55 and 75 nm after the film deposition) and a lattice parameter of 105 nm. An enormous increase of coercitivity, as compared with the corresponding continuous films, was observed for temperatures between 2 and 300 K. This effect depends on the size and surface density of holes in the Fe₂₀Ni₈₀ antidot arrays. Rutherford backscattering spectrometry (RBS) measurements were performed in order to better clarify the magnetic material that was eventually deposited within the NAM pores.     

Multi-magnetic phases in Fe1−xNixTa2O6

X-ray, neutron diffraction and magnetic susceptibility are reported for Fe_xNi_1−xTa₂O₆ mixed oxides. X-ray refinement indicates homogeneous samples for all the reported concentrations. The neutron-diffraction measurements reveal magnetic structures with double propagation vectors. This system exhibits at least two bicritical points at about x=0.15 and 0.60. For these concentrations, at low temperatures, the system shows the coexistence of two magnetic structures. This bicritical behaviour is interpreted as induced by competition between the different magnetic structures.