The range order of a product of i transformations from a finite full transformation semigroup

Communicated by N. R. Reilly     

Gaining insight into the nanoscale properties of sol-gel-derived silicate thin films by single-molecule spectroscopy

The application of single-molecule spectroscopic methods in studies of individual nanoscale environments within sol-gel-derived silicate thin films is reviewed. Representative examples of the experiments performed and results obtained in several studies from the authors' laboratories are given. Included are investigations of the static and dynamic polarity properties of organically modified silicate (ORMOSIL) films. The results of these studies point to nonrandom variations in the film properties, providing strong evidence for the formation of phase-separated organic- and inorganic-rich domains. Studies of single-molecule diffusion through the same films yield important evidence for the formation of liquidlike silicate oligomers that facilitate probe molecule diffusion. Finally, single-molecule studies of the local pH within individual film environments are discussed. Valuable information on the contributions of local materials' acidity variations to overall sample heterogeneity is obtained. The results of immersion studies indicate that certain molecular environments are inaccessible to external solutions over periods as long as a few hours. The article concludes with a discussion of possible future challenges in this research that may be addressed by new and existing single-molecule methods.     

<Emphasis Type="Italic">N</Emphasis>-arachidonoyl glycine,an abundant endogenous lipid,potently drives directed cellular migration through GPR18, the putative abnormal cannabidiol receptor

Background  

Microglia provide continuous immune surveillance of the CNS and upon activation rapidly change phenotype to express receptors that respond to chemoattractants during CNS damage or infection. These activated microglia undergo directed migration towards affected tissue. Importantly, the molecular species of chemoattractant encountered determines if microglia respond with pro- or anti-inflammatory behaviour, yet the signaling molecules that trigger migration remain poorly understood. The endogenous cannabinoid system regulates microglial migration via CB₂ receptors and an as yet unidentified GPCR termed the 'abnormal cannabidiol' (Abn-CBD) receptor. Abn-CBD is a synthetic isomer of the phytocannabinoid cannabidiol (CBD) and is inactive at CB₁ or CB₂ receptors, but functions as a selective agonist at this G_i/o-coupled GPCR. N-arachidonoyl glycine (NAGly) is an endogenous metabolite of the endocannabinoid anandamide and acts as an efficacious agonist at GPR18. Here, we investigate the relationship between NAGly, Abn-CBD, the unidentified 'Abn-CBD' receptor, GPR18, and BV-2 microglial migration.     

Single molecule spectroscopy studies of diffusion in mesoporous silica thin films

Single molecule spectroscopy is applied in studies of diffusion and surface adsorption in sol-gel-derived mesoporous silica thin films. Mesoporous films are obtained by spin casting surfactant-templated sols onto glass substrates. Small-angle X-ray diffraction results are consistent with hexagonally ordered mesophases in as-synthesized (i.e., surfactant-containing) films. Upon calcination, a 30% contraction and disordering of these structures occurs. Nile Red is used as a fluorescent probe of both the as-synthesized and calcined films. It is loaded into the samples at subnanomolar levels either prior to spin casting or after calcination. Fluorescence imaging and single-point fluorescence time transients show the dye molecules to be relatively mobile in the as-synthesized samples. In contrast, the molecules appear entrapped at fixed locations in dry calcined films. In calcined films rehydrated under high humidity conditions, the Nile Red molecules again become mobile. Time transients obtained from the as-synthesized and rehydrated samples provide clear evidence for frequent reversible adsorption of the dye to the silica surfaces. Autocorrelations of the time transients provide quantitative data on the mean diffusion coefficients (D = 2.4 x 10(-10) and 2.6 x 10(-10) cm2/s) and mean desorption times (1/k = 25 and 40 s) for the as-synthesized and rehydrated films, respectively. The results prove both water and surfactant play important roles in governing matrix interactions and mass transport.     

Distribution-free tests for no effect of treatment in heteroscedastic functional data under both weak and long range dependence

In this paper, we present distribution-free tests to evaluate the effect of multiple treatments when there are a large number of repeated measurements from each subject nested in a treatment. We formulate new test statistics to account for heteroscedasticity and unbalanced designs. The asymptotic distributions for the test statistics are obtained when the repeated measurements from the same subject have long range dependence and weak dependence, respectively. The asymptotic results hold under the nonclassical setting in which the number of repeated measurements is large while the number of subjects per treatment may be small. A real application to compare cattle ear temperature profiles under different antibiotic treatments is given for illustration. Simulation studies are undertaken to compare the empirical performance of the proposed tests to commonly used methods.     

A Chemically Soldered Polyoxometalate Single-Molecule Transistor

Polyoxometalates have been proposed in the literature as nanoelectronic components, where they could offer key advantages with their structural versatility and rich electrochemistry. Apart from a few studies on their ensemble behaviour (as monolayers or thin films), this potential remains largely unexplored. We synthesised a pyridyl-capped Anderson–Evans polyoxometalate and used it to fabricate single-molecule junctions, using the organic termini to chemically “solder” a single cluster to two nanoelectrodes. Operating the device in an electrochemical environment allowed us to probe charge transport through different oxidation states of the polyoxometalate, and we report here an efficient three-state transistor behaviour. Conductance data fits a quantum tunnelling mechanism with different charge-transport probabilities through different charge states. Our results show the promise of polyoxometalates in nanoelectronics and give an insight on their single-entity electrochemical behaviour.     

Dimensional scaling of flame propagation in discrete particulate clouds

The critical dimension necessary for a flame to propagate in suspensions of fuel particles in oxidiser is studied analytically and numerically. Two types of models are considered: First, a continuum model, wherein the individual particulate sources are not resolved and the heat release is assumed spatially uniform, is solved via conventional finite difference techniques. Second, a discrete source model, wherein the heat diffusion from individual sources is modelled via superposition of the Green's function of each source, is employed to examine the influence of the random, discrete nature of the media. Heat transfer to cold, isothermal walls and to a layer of inert gas surrounding the reactive medium are considered as the loss mechanisms. Both cylindrical and rectangular (slab) geometries of the reactive medium are considered, and the flame speed is measured as a function of the diameter and thickness of the domains, respectively. In the continuum model with inert gas confinement, a universal scaling of critical diameter to critical thickness near 2:1 is found. In the discrete source model, as the time scale of heat release of the sources is made small compared to the interparticle diffusion time, the geometric scaling between cylinders and slabs exhibits values greater than 2:1. The ability of the flame in the discrete regime to propagate in thinner slabs than predicted by continuum scaling is attributed to the flame being able to exploit local fluctuations in concentration across the slab to sustain propagation. As the heat release time of the sources is increased, the discrete source model reverts back to results consistent with the continuum model. Implications of these results for experiments are discussed.     

Investigation of Molecular Diffusion at Block Copolymer Thin Films Using Maximum Entropy Method-Based Fluorescence Correlation Spectroscopy and Single Molecule Tracking

Fluorescence correlation spectroscopy (FCS) has been widely used to investigate molecular diffusion behavior in various samples. The use of the maximum entropy method (MEM) for FCS data analysis provides a unique means to determine multiple distinct diffusion coefficients without a priori assumption of their number. Comparison of the MEM-based FCS method (MEM-FCS) with another method will reveal its utility and advantage as an analytical tool to investigate diffusion dynamics. Herein, we measured diffusion of fluorescent probes doped into nanostructured thin films using MEM-FCS, and validated the results with single molecule tracking (SMT) data. The efficacy of the MEM code employed was first demonstrated by analyzing simulated FCS data for systems incorporating one and two diffusion modes with broadly distributed diffusion coefficients. The MEM analysis accurately afforded the number of distinct diffusion modes and their mean diffusion coefficients. These results contrasted with those obtained by fitting the simulated data to conventional two-component and anomalous diffusion models, which yielded inaccurate estimates of the diffusion coefficients. Subsequently, the MEM analysis was applied to FCS data acquired from hydrophilic dye molecules incorporated into microphase-separated polystyrene-block-poly(ethylene oxide) (PS-b-PEO) thin films characterized under a water-saturated N₂ atmosphere. The MEM analysis revealed distinct fast and slow diffusion components attributable to molecules diffusing on the film surface and inside the film, respectively. SMT studies of the same materials yielded trajectories for mobile molecules that appear to follow the curved PEO microdomains. Diffusion coefficients obtained from the SMT data were consistent with those obtained for the slow diffusion component detected by MEM-FCS. These results highlight the utility of MEM-FCS and SMT for gaining complementary information on molecular diffusion processes in heterogeneous material systems.

Graphical Abstract

     

Engineered Biocatalytic Synthesis of β-N-Substituted-α-Amino Acids

Non-canonical amino acids (ncAAs) are useful synthons for the development of new medicines, materials, and probes for bioactivity. Recently, enzyme engineering has been leveraged to produce a suite of highly active enzymes for the synthesis of β-substituted amino acids. However, there are few examples of biocatalytic N-substitution reactions to make α,β-diamino acids. In this study, we used directed evolution to engineer the β-subunit of tryptophan synthase, TrpB, for improved activity with diverse amine nucleophiles. Mechanistic analysis shows that high yields are hindered by product re-entry into the catalytic cycle and subsequent decomposition. Additional equivalents of l -serine can inhibit product reentry through kinetic competition, facilitating preparative scale synthesis. We show β-substitution with a dozen aryl amine nucleophiles, including demonstration on a gram scale. These transformations yield an underexplored class of amino acids that can serve as unique building blocks for chemical biology and medicinal chemistry.     

Grayscale patterning of polymer thin films with nanometer precision by direct-write multiphoton photolithography

The fabrication of arbitrary grayscale patterns in poly(ethylene dioxythiophene):poly(styrene sulfonate) (PEDOT:PSS) thin films is demonstrated. Patterns are formed by ablative direct-write multiphoton lithography using a sample scanning microscope and 870-nm light from a mode-locked Ti:sapphire laser. The surface profiles of all etched samples are characterized by atomic force microscopy. Grayscale patterns are produced by modulating the laser focus during etching. Quantitative models describing the etch depth as a function of laser power and focus are presented and employed to reproducibly control film patterning. PEDOT:PSS is found to be etched by a combination of linear and nonlinear optical processes. Sensitization by PEDOT in the composite is concluded to facilitiate removal of PSS. An ultimate etch depth precision of 1 nm is achieved.