Impaction of spray droplets on leaves: influence of formulation and leaf character on shatter,bounce and adhesion

This paper combines experimental data with simple mathematical models to investigate the influence of spray formulation type and leaf character (wettability) on shatter, bounce and adhesion of droplets impacting with cotton, rice and wheat leaves. Impaction criteria that allow for different angles of the leaf surface and the droplet impact trajectory are presented; their predictions are based on whether combinations of droplet size and velocity lie above or below bounce and shatter boundaries. In the experimental component, real leaves are used, with all their inherent natural variability. Further, commercial agricultural spray nozzles are employed, resulting in a range of droplet characteristics. Given this natural variability, there is broad agreement between the data and predictions. As predicted, the shatter of droplets was found to increase as droplet size and velocity increased, and the surface became harder to wet. Bouncing of droplets occurred most frequently on hard-to-wet surfaces with high-surface-tension mixtures. On the other hand, a number of small droplets with low impact velocity were observed to bounce when predicted to lie well within the adhering regime. We believe this discrepancy between the predictions and experimental data could be due to air layer effects that were not taken into account in the current bounce equations. Other discrepancies between experiment and theory are thought to be due to the current assumption of a dry impact surface, whereas, in practice, the leaf surfaces became increasingly covered with fluid throughout the spray test runs.     

Translation between external representation systems in mathematics: All-or-none or skill conglomerate?

The study described herein represents an initial, exploratory attempt to understand what it means to translate between external representation systems. Researchers have traditionally considered translation as an all-or-none activity. We hypothesize that translation is comprised of both knowledge and skill components, and accordingly construe translation as an activity that our framework allows us to define as partial or complete. We examined the effects of part-whole knowledge in change unknown subtraction situations and the structure of three different external representations on first grade students’ ability to translate in a partitioning task. Based on three interviews conducted with each student, results from our mixed methods analysis showed that translation skill was affected by what students knew about subtraction and the structure of the ER. Further, whereas high knowledge students demonstrated greater difficulty with translating to the ERs, low knowledge students had difficulty translating from the problem statement as well as translating to the ERs.     

The “Problem” of Experience in Mathematics Teaching

Prior research has established that teachers' use of curriculum materials is affected by a range of factors, such as teachers' conceptions of mathematics teaching, and the nature and extent of their teaching experience. What is less clear, and far less examined, in prior research is the role that the teacher guide (TG) may play in mediating the influence of these and other factors on teachers' decisions and actions. Accordingly, this study examines how two 6th grade teachers use the TG from Connected Mathematics Project as a resource in making planning and enactment decisions, and factors associated with patterns of TG use. Through cross‐case analysis, the author found that these teachers seemed to draw largely from their previous experiences and their own conceptions of mathematics teaching and learning when making planning and enactment decisions related to mathematical tasks, and not particularly from the TG. For example, when faced with certain planning and instructional challenges, such as students struggling with the content, teachers tended to rely on their particular conceptions of mathematics teaching to address these challenges. Despite the fact that the TG provided suggestions for teachers as to how address such challenges, it was not extensively used as a resource by the teachers in this study in their planning and enactment of lessons.     

Asymptotic bounds for permutations containing many different patterns

We say that a permutation σ∈Sn contains a permutation π∈Sk as a pattern if some subsequence of σ has the same order relations among its entries as π. We improve on results of Wilf, Coleman, and Eriksson et al. that bound the asymptotic behavior of pat(n), the maximum number of distinct patterns of any length contained in a single permutation of length n. We prove that by estimating the amount of redundancy due to patterns that are contained multiple times in a given permutation. We also consider the question of k-superpatterns, which are permutations that contain all patterns of a given length k. We give a simple construction that shows that Lk, the length of the shortest k-superpattern, is at most . This may lend evidence to a conjecture of Eriksson et al. that .     

Femtomolar Zn(II) affinity in a peptide-based ligand designed to model thiolate-rich metalloprotein active sites

Metal-ligand interactions are critical components of metalloprotein assembly, folding, stability, electrochemistry, and catalytic function. Research over the past 3 decades on the interaction of metals with peptide and protein ligands has progressed from the characterization of amino acid-metal and polypeptide-metal complexes to the design of folded protein scaffolds containing multiple metal cofactors. De novo metalloprotein design has emerged as a valuable tool both for the modular synthesis of these complex metalloproteins and for revealing the fundamental tenets of metalloprotein structure-function relationships. Our research has focused on using the coordination chemistry of de novo designed metalloproteins to probe the interactions of metal cofactors with protein ligands relevant to biological phenomena. Herein, we present a detailed thermodynamic analysis of Fe(II), Co(II), Zn(II), and[4Fe-4S]2(+/+) binding to IGA, a 16 amino acid peptide ligand containing four cysteine residues, H2N-KLCEGG-CIGCGAC-GGW-CONH2. These studies were conducted to delineate the inherent metal-ion preferences of this unfolded tetrathiolate peptide ligand as well as to evaluate the role of the solution pH on metal-peptide complex speciation. The [4Fe-4S]2(+/+)-IGA complex is both an excellent peptide-based synthetic analogue for natural ferredoxins and is flexible enough to accommodate mononuclear metal-ion binding. Incorporation of a single ferrous ion provides the FeII-IGA complex, a spectroscopic model of a reduced rubredoxin active site that possesses limited stability in aqueous buffers. As expected based on the Irving-Williams series and hard-soft acid-base theory, the Co(II) and Zn(II) complexes of IGA are significantly more stable than the Fe(II) complex. Direct proton competition experiments, coupled with determinations of the conditional dissociation constants over a range of pH values, fully define the thermodynamic stabilities and speciation of each MII-IGA complex. The data demonstrate that FeII-IGA and CoII-IGA have formation constant values of 5.0 x 10(8) and 4.2 x 10(11) M-1, which are highly attenuated at physiological pH values. The data also evince that the formation constant for ZnII-IGA is 8.0 x 10(15) M-1, a value that exceeds the tightest natural protein Zn(II)-binding affinities. The formation constant demonstrates that the metal-ligand binding energy of a ZnII(S-Cys)4 site can stabilize a metalloprotein by -21.6 kcal/mol. Rigorous thermodynamic analyses such as those demonstrated here are critical to current research efforts in metalloprotein design, metal-induced protein folding, and metal-ion trafficking.     

Determination of MK-0431 in human plasma using high turbulence liquid chromatography online extraction and tandem mass spectrometry

A robust and sensitive method using high turbulence liquid chromatography (HTLC) online extraction with tandem mass spectrometry (MS/MS) for the determination of MK-0431 in human plasma was developed and validated to support the clinical studies. This HTLC online extraction method eliminated the time-consuming offline sample extraction procedures and significantly increased productivity. A narrow bore large particle size reversed-phase column (Cyclone, 50 x 1.0 mm, 60 microm) and a BDS Hypersil C18 column (30 x 2.1 mm, 3 microm) were used as extraction and analytical columns, respectively. The linear dynamic range of the calibration curve was 0.5 to 1000 ng/mL. Intraday validation was conducted using five calibration curves prepared in five lots of human control plasma, and the intraday precision (RSD%) was from 2.4 to 9.0% and the accuracy was from 98.0 to 103% of the nominal value. The intraday precision (RSD%, n = 5) for plasma quality control (QC) samples varied from 2.0 to 5.3% and accuracy from 103 to 105% of the nominal value. The interday precision (RSD%) for 100 sets of plasma QC samples in 29 analytical runs varied from 6.3 to 9.0% and the accuracy from 98.8 to 104% of the nominal value. No significant difference was observed between the interday and intraday precision and accuracy of the QC samples.     

Investigating the structural properties of amyloid-like fibrils formed in vitro from beta2-microglobulin using limited proteolysis and electrospray ionisation mass spectrometry

The protein beta(2)-microglobulin (beta(2)m) aggregates to form classical amyloid fibrils in patients undergoing long-term haemodialysis. Amyloid-like fibrils with a cross-beta fold can also be formed from wild-type beta(2)m under acidic conditions in vitro. The morphology of such fibrils depends critically on the conditions used: incubation of beta(2)m in low ionic strength buffers at pH 2.5 results in the formation of long (microm), straight fibrils while, at pH 3.6, short (<500 nm) fibrils form. At higher ionic strengths (0.2-0.4 M) at pH 1.5-3.6, the fibrils have a distinct curved and nodular morphology. To determine the conformational properties of beta(2)m within in vitro fibrils of different morphologies, limited proteolysis of each fibril type using pepsin was performed and the resulting peptide fragments identified by tandem mass spectrometry. For comparison, the proteolytic degradation patterns of monomeric beta(2)m and seven synthetic peptides spanning the entire sequence of the intact protein were similarly analysed. The results show that fibrils with different morphologies result in distinct digestion patterns. While the curved, worm-like fibrils are relatively weakly protected from proteolysis, the long, straight fibrils formed at pH 2.5 at low ionic strength show only a single cut-site at Val9, demonstrating that substantial refolding of the initially acid-denatured and unprotected state of beta(2)m occurs during assembly. The data demonstrate that the organisation of the polypeptide chain in fibrils with different morphological features differs considerably, despite the fact that the fibrils possess a common cross-beta architecture.     

Tandem Nazarov cyclization-michael addition sequence catalyzed by an Ir(III) complex

The first examples of a tandem Nazarov cyclization/Michael addition process are described. The sequence is efficiently catalyzed by Ir[Me(CO)(dppe)(DIB)]2+ and occurs with high diastereoselectivity, creating three contiguous stereocenters. The mechanistic factors controlling the reactivity and diastereoselectivity are discussed.     

Microscale patterning of organic films on carbon surfaces using electrochemistry and soft lithography

We have demonstrated three simple strategies employing poly(dimethylsiloxane) (PDMS) molds for patterning carbon surfaces with two different modifiers in an 18 microm line pattern. The PDMS molds are patterned with microfluidic channels (approximately 22 microm wide and 49 microm deep) and form a reversible, conformal seal to the pyrolyzed photoresist film (PPF) and modified PPF surfaces. Modifiers are electrochemically grafted to the PPF surface by the reduction of aryl diazonium salts and the oxidation of primary amines. For the fill-in patterning approach, the first modifier is electrografted to the PPF surface exposed within the microchannels, and in a second grafting step after removal of the PDMS mold, the second modifier fills in the remaining surface. The selective conversion strategy involves electrografting a continuous film of the modifier to the PPF surface, sealing the PDMS mold to the modified surface and carrying out an irreversible electrochemical reaction of the modifier exposed within the microchannels. In the build-up patterning approach, the PDMS mold is sealed to the modified PPF surface, and a chemical coupling reaction is effected in the microchannels to build up the pattern. The patterns are characterized using SEM, optical microscopy, the formation of condensation figures, and SEM imaging after the assembly of Au nanoparticles.     

15N NMR chemical shifts for the identification of dipyrrolic structures

A variety of dipyrromethanes and dipyrromethenes have been prepared, and their 15N NMR chemical shifts have been measured by two-dimensional correlation to 1H NMR signals. The nitrogen atoms in five examples of dipyrromethanes consistently exhibit chemical shifts around -231 ppm, relative to nitromethane. Seven examples of hydrobromide salts of meso-unsubstituted dipyrromethenes consistently display 15N chemical shifts around -210 ppm, while their corresponding zinc(II) complexes exhibit chemical shifts around -170 ppm. The presence of electron-withdrawing substituents on one of the pyrrolic rings of dipyrromethenes affects the chemical shifts of both of the nitrogen nuclei in the molecule. Boron difluoride complexes of meso-unsubstituted dipyrromethenes display 15N chemical shifts around -190 ppm. Two examples of free-base dipyrromethenes bearing substituents at the meso-position exhibit 15N chemical shifts at approximately -156 ppm, and for the zinc complexes of these compounds at -162 ppm. One-bond nitrogen-hydrogen coupling constants, when measurable, were consistently in the range of -96 Hz. Since the measured 15N chemical shifts have such a high regularity correlated to structure, they can be used as diagnostic indications for identifying the structure of dipyrrolic compounds.