Quantitative measurement of collagen methylation by capillary electrophoresis

Collagen methylation has been exploited in various applications involving living cells. We have observed correlation between the collagen methylation with the rate of cell proliferation in three-dimensional (3-D) microenvironment. To quantify the degree of collagen methylation, we have developed a capillary zone electrophoresis method. Using a polyvinyl alcohol-coated fused-silica capillary and UV detection at 200 nm, we have optimized pH and separated the native collagen into three major bands in phosphate buffer (50 mM, pH 2.5) with 0.05% hydroxypropylmethylcellulose. Under these conditions, the methylated collagens were separated into four major bands, which changed with different methylation reaction conditions. We propose an index to quantify the degree of collagen methylation that also correlates with their effects on cell proliferation.     

Fourier multipliers of Lipschitz spaces

Let G denote an infinite, compact, metrizable, 0-dimensional, Abelian group. The following are characterized: (i) the multipliers from one Lipschitz space Lip(α, p; G) to another Lipschitz space Lip(β, q; G) for 0 < α < β < ∞ and 1 ? p, q ? ∞; and (ii) the multipliers from Lip(α, p; G) to Lip(β, q; G) for 0 < β ? α < ∞ and 1 < q ? 2 ? p < ∞. Two special cases of (i), namely the case q = ∞ and the case p = 1, were obtained by the authors in an earlier publication (1981). A. Zygmund (J. Math. Mech.8 (1959), 889–895) and T. Mizuhara (Tôhoku Math. J.24 (1972), 263–268) have characterized the multipliers of certain Lipschitz spaces defined on the circle group.     

Factorization of Lipschitz functions and absolute convergence of Vilenkin-Fourier series

LetG be a Vilenkin group (i.e., an infinite, compact, metrizable, zero-dimensional Abelian group). Our main result is a factorization theorem for functions in the Lipschitz spaces \(\mathfrak{L}\mathfrak{i}\mathfrak{p}\) (α,p; G). As colloraries of this theorem, we obtain (i) an extension of a factorization theorem ofY. Uno; (ii) a convolution formula which says that \(\mathfrak{L}\mathfrak{i}\mathfrak{p} (\alpha , r; G) = \mathfrak{L}\mathfrak{i}\mathfrak{p} (\beta , l; G)*\mathfrak{L}\mathfrak{i}\mathfrak{p} (\alpha - \beta , r; G)\) for 0<β<α<∞ and 1≤r≤∞; and (iii) an analogue, valid for allG, of a classical theorem ofHardy andLittlewood. We also present several results on absolute convergence of Fourier series defined onG, extending a theorem ofC. W. Onneweer and four results ofN. Ja. Vilenkin andA. I. Rubinshtein. The fourVilenkin-Rubinshtein results are analogues of classical theorems due, respectively, toO. Szász, S. B. Bernshtein, A. Zygmund, andG. G. Lorentz.     

Improved RP‐HPLC method for determination of bovine lactoferrin and its proteolytic degradation in simulated gastrointestinal fluids

The objective of this study was to qualitatively and quantitatively evaluate bovine lactoferrin (bLf) and its stability using a rapid RP‐HPLC method. bLf could be rapidly detected within 20 min and quantitated at levels down to 5 µg/mL, and the equation of linearity was y = 86.10x + 178.31 with the correlation coefficient (r²) 0.9997. Quantitative data obtained in the present study proved the improved RP‐HPLC method to be a sensitive and accurate analytical tool for bLf determination. The proteolytic cleavage of bLf in simulated human gastrointestinal fluids was further analyzed by RP‐HPLC, and found to follow pseudo‐first‐order kinetics. The typical equation obtained by pepsin was log₁₀ [A_t]/[A₀] = ?0.03x (r² = 0.85), and log₁₀ [A_t]/[A₀] = ?0.01x (r² = 0.81) for trypsin and chymotrypsin combination. Pepsinolysis of bLf in simulated gastric fluid was relatively fast with the half‐life t_1/2 23.1 min. The digestion of bLf in simulated intestinal fluid was slower with about a 3‐fold increase in half‐life (69.3 min). After the complete proteolysis of bLf, small cleaved peptide fragments were fully separated and identified by RP‐HPLC. The proteolytic study indicated that this validated RP‐HPLC was able to evaluate bLf stability though monitoring the derivatization products. Copyright © 2012 John Wiley & Sons, Ltd.     

RAFT synthesis of thioether-based,AB diblock copolymer nanocarriers for reactive oxygen species–triggered release

A well-defined AB diblock copolymer of 2-vinyl-4,4-dimethylazlactone (VDA) and N,N-dimethylacrylamide (DMA) was generated by reversible addition-fragmentation chain transfer (RAFT) radical polymerization. The VDA-DMA diblock copolymer was reacted with 2-(methylthio)ethylamine (MTEA) and 3-(methylthio)propylamine (MTPA) to yield two novel thioether functional diblock copolymers whose structure was confirmed using ¹H NMR and FTIR spectroscopy. Both diblock copolymers formed micelles (20–30 nm) in aqueous media as confirmed by dynamic light scattering (DLS) and transmission electron microscopy. The self-assembled micelles were loaded with Nile Red, a model hydrophobic drug to study their ROS-triggered release mechanism. On addition of hydrogen peroxide (H₂O₂), the most common ROS species, the hydrophobic thioether core of these micelles oxidized, and both diblock copolymers became more hydrophilic. This triggered their disassembly and subsequent cargo release as characterized by UV–visible spectroscopy. The Nile Red loaded micelles demonstrated similar in-vitro ROS-mediated release when exposed to endogenous oxidants in a model inflammation environment simulated by the presence of activated macrophages. The responsive nanomaterials developed in this article have promising potential as drug carriers in applications where ROS-triggered delivery of cargo is required such as in inflammatory conditions.     

Teacher preparation for a problem-solving curriculum in Singapore

Problem solving is at the heart of the Singapore Mathematics curriculum. However, it remains a challenge for teachers to realise this curricular goal in practice. Here, we review the efforts of Singapore mathematics teacher educators in incorporating problem-solving (teaching) competency in teacher education and PD programmes. We discuss conceptual and practical issues, actions taken and changes made in building teachers?? capacity to enact a problem-solving curriculum in a school-based design experiment project. In the project, teachers learnt problem solving, observed and then carried out lessons, using the ??Mathematics Practical????akin to the science practical??as key to instruction and assessment.     

Reviving Pólya's “Look Back” in a Singapore school

This study is based on the stance that Pólya's “Look Back,” though understudied, remains relevant to Mathematics curricula that place emphasis on problem solving. Although the Singapore Mathematics curriculum adopts the goal of teaching Look Back, research about how it is carried out in actual classroom practice is rare. In our project, we focus on a redesign of a teacher development programme that is targeted to help teachers realize Pólya's original vision of Look Back in the classroom. We report the cases of two teachers who have participated in the teacher development programme: their thinking about Look Back (through interview records) and their interpretation of Look Back in their classroom practice (through video records). By bringing these two spheres of data together, we discuss their degree of ‘buy-in’ to Look Back in the overall problem solving enterprise.     

Littlewood–Paley and Multiplier Theorems on Weighted Spaces over Locally Compact Vilenkin Groups

We extend the Littlewood–Paley theorem toL^p_w(G), whereGis a locally compact Vilenkin group andware weights satisfying the MuckenhouptA_pcondition. As an application we obtain a mixed-norm type multiplier result onL^p_w(G) and prove the sharpness of our result. We also obtain a sufficient condition for φ L^∞(Γ) to be a multiplier on the power weightedL^p_α(G) in terms of its smoothness condition.     

Removal of copper by oxygenated pyrolytic tire char: kinetics and mechanistic insights

The kinetics of copper ion (Cu(II)) removal from aqueous solution by pyrolytic tire char was modeled using five different conventional models. A modification to these models was also developed through a modified equation that accounts for precipitation. Conventional first- and second-order reaction models did not fit the copper sorption kinetics well, indicating a lack of simple rate-order dependency on solute concentration. Instead, a reversible first-order rate reaction showed the best fit to the data, indicating a dependence on surface functional groups. Due to the varying solution pH during the sorption process, modified external and internal mass transfer models were employed. Results showed that the sorption of copper onto oxygenated chars was limited by external mass transfer and internal resistance with and without the modification. However, the modification of the sorption process produced very different results for unoxygenated chars, which showed neither internal nor external limitation to sorption. Instead, its slow sorption rate indicates a lack of surface functional groups. The sorption of Cu(II) by oxygenated and unoxygenated chars was also found to occur via three and two distinct stages, respectively.     

Active role of buried ultrathin oxide layers in adsorption of O2 on Au films

Ultrathin oxide layers can exhibit special behavior by enabling the coupling of structural distortions and charge transfer beyond that allowed in the bulk. In this work, we show from first-principles calculations that ultrathin layers of titania, a prototypical oxide, are active in stabilizing adsorption of O₂ on Au overlayers. The adsorbed O₂ molecules induce charge redistribution in Au that penetrates to the Au-titania interface, which responds through structural distortions that lower the total energy of the system. We suggest that this effect may be of more general nature and useful in catalysis.