Students' Concepts‐ and Theorems‐in‐Action on a Novel Task About Similarity

Similarity is a fundamental concept in the middle grades. In this study, we applied Vergnaud's theory of conceptual fields to answer the following questions: What concepts‐in‐action and theorems‐in‐action about similarity surfaced when students worked in a novel task that required them to enlarge a puzzle piece? How did students use geometric and multiplicative reasoning at the same time in order to construct similar figures? We found that students used concepts of scaling and proportional reasoning, as well as the concept of circle and theorems about similar triangles, in their work on the problem. Students relied not only on visual perception, but also on numeric reasoning. Moreover, students' use of multiplicative and proportional concepts supported their geometric constructions. Knowledge of the concepts and ideas that students have available when working on a task about similarity can inform instruction by helping to ground formal introduction of new concepts in students' informal prior experiences and knowledge.     

From molecules to visuals: Empowering drug discovery and development with mass spectrometry imaging

Over the past three decades, mass spectrometry imaging (MSI) has emerged as a valuable tool for the spatial localization of drugs and metabolites directly from tissue surfaces without the need for labels. MSI offers molecular specificity, making it increasingly popular in the pharmaceutical industry compared to conventional imaging techniques like quantitative whole-body autoradiography (QWBA) and immunohistochemistry, which are unable to distinguish parent drugs from metabolites. Across the industry, there has been a consistent uptake in the utilization of MSI to investigate drug and metabolite distribution patterns, and the integration of MSI with omics technologies in preclinical investigations. To continue the further adoption of MSI in drug discovery and development, we believe there are two key areas that need to be addressed. First, there is a need for accurate quantification of analytes from MSI distribution studies. Second, there is a need for increased interactions with regulatory agencies for guidance on the utility and incorporation of MSI techniques in regulatory filings. Ongoing efforts are being made to address these areas, and it is hoped that MSI will gain broader utilization within the industry, thereby becoming a critical ingredient in driving drug discovery and development.     

Correction of spatially dependent phase shifts for partial Fourier imaging

Partial Fourier MR images (PFI) are constructed from data that have fewer phase encoding views than are conventionally acquired using direct Fourier transform spin echo acquisition. The PFI data acquisition is structured to obtain the same spatial resolution as conventional acquisition, trading off signal-to-noise reduction for acquisition time improvement. The "missing" views can be zero filled or, if the data are Hermitian, supplied by symmetry (basic algorithm). The effect of spatially dependent phase shifts (SDPS) on PFI constructed with zero-fill or the basic algorithm is illustrated. The causes and typical magnitudes of such SDPS are discussed. In spin echo data only the low order, slowly varying SDPS, is shown to be significant. Through use of simulated and actual data sets these typical SDPS are shown to produce significant artifacts in PFI, when the amount of missing data is close to one-half. The artifacts are reduced when less data are missing. Good images can be generated with the zero-fill algorithm if less than 25% of the data is missing. Several methods of correcting phase shifts in PFI are developed: the basic Hermitian algorithm with frequency (x) direction correction (BAX), basic Fourier correction algorithm (BFC) and an improved iterative Fourier correction algorithm (IFC). The BFC and IFC can produce good images when as much as 46% of the data is missing. Data with rapidly varying SDPS, for example, gradient refocused data, make the phase correction task more difficult. With less than 25% of the data missing, however, acceptable gradient refocused PFI images can be created.     

Origins of enhanced proton transport in the Y7F mutant of human carbonic anhydrase II

Human carbonic anhydrase II (HCA II), among the fastest enzymes known, catalyzes the reversible hydration of CO 2 to HCO 3 (-). The rate-limiting step of this reaction is believed to be the formation of an intramolecular water wire and transfer of a proton across the active site cavity from a zinc-bound solvent to a proton shuttling residue (His64). X-ray crystallographic studies have shown this intramolecular water wire to be directly stabilized through hydrogen bonds via a small well-defined set of amino acids, namely, Tyr7, Asn62, Asn67, Thr199, and Thr200. Furthermore, X-ray crystallographic and kinetic studies have shown that the mutation of tyrosine 7 to phenylalanine, Y7F HCA II, has the effect of increasing the proton transfer rate by 7-fold in the dehydration direction of the enzyme reaction compared to wild-type (WT). This increase in the proton transfer rate is postulated to be linked to the formation of a more directional, less branched, water wire. To evaluate this proposal, molecular dynamics simulations have been employed to study water wire formation in both the WT and Y7F HCA II mutant. These studies reveal that the Y7F mutant enhances the probability of forming small water wires and significantly extends the water wire lifetime, which may account for the elevated proton transfer seen in the Y7F mutant. Correlation analysis of the enzyme and intramolecular water wire indicates that the Y7F mutant significantly alters the interaction of the active site waters with the enzyme while occupancy data of the water oxygens reveals that the Y7F mutant stabilizes the intramolecular water wire in a manner that maximizes smaller water wire formation. This increase in the number of smaller water wires is likely to elevate the catalytic turnover of an already very efficient enzyme.     

Miscible macromolecular antioxidants for polyethers

Oxidation reactions are one of the main reasons for the failure of polymeric materials. Antioxidants, compounds designed to protect against oxidation, must meet three main requirements for success: (1) an efficient antioxidative mechanism, (2) compatibility with the oxidizing polymer, and (3) permanence Within the oxidizing polymer. Common antioxidants are low molecular weight materials that can easily diffuse, leach, or evaporate from the polymer they are designed to protect. An increase in the molecular weight of the antioxidant not only decreases diffusion and volatility, but also decreases compatibility since most high molecular weight polymers will not mix. Selective sterically hindered phenolics, however, are concurrently antioxidants and “compatibilizers” through hydrogen bond formation. Carefully designed copolymers containing a small percentage of 2,6-diisopropyl-4-vinylphenol were found to mix intimately with two readily oxidizing polyethers and to protect them against oxidation.     

3d-Metal derivatives of the [Cu(I)(SO3)4]7- ion: structure and magnetism

The Cu(SO(3))(4)(7-) anion, which consists of a tetrahedrally coordinated Cu(I) centre coordinated to four sulfur atoms, is able to act as a multidentate ligand in discrete and infinite supramolecular species. The slow oxidation of an aqueous solution of Na(7)Cu(SO(3))(4) yields a mixed oxidation state, 2D network of composition Na(5){[Cu(II)(H(2)O)][Cu(I)(SO(3))(4)]}·6H(2)O. The addition of Cu(II) and 2,2'-bipyridine to an aqueous Na(7)Cu(SO(3))(4) solution leads to the formation of a pentanuclear complex of composition {[Cu(II)(H(2)O)(bipy)](4)[Cu(I)(SO(3))(4)]}(+); a combination of hydrogen bonding and π-π stacking interactions leads to the generation of infinite parallel channels that are occupied by disordered nitrate anions and water molecules. A pair of Cu(SO(3))(4)(7-) anions each act as a tridentate ligand towards a single Mn(II) centre when Mn(II) ions are combined with an excess of Cu(SO(3))(4)(7-). An anionic pentanuclear complex of composition {[Cu(I)(SO(3))(4)](2)[Fe(III)(H(2)O)](3)(O)} is formed when Fe(II) is added to a Cu(+)/SO(3)(2-) solution. Hydrated ferrous [Fe(H(2)O)(6)(2+)] and sodium ions act as counterions for the complexes and are responsible for the formation of an extensive hydrogen bond network within the crystal. Magnetic susceptibility studies over the temperature range 2-300 K show that weak ferromagnetic coupling occurs within the Cu(II) containing chains of Na(5){[Cu(II)(H(2)O)][Cu(I)(SO(3))(4)]}·6H(2)O, while zero coupling exists in the pentanuclear cluster {[Cu(II)(H(2)O)(bipy)](4)[Cu(I)(SO(3))(4)]}(NO(3))·H(2)O. Weak Mn(II)-O-S-O-Mn(II) antiferromagnetic coupling occurs in Na(H(2)O)(6){[Cu(I)(SO(3))(4)][Mn(II)(H(2)O)(2)](3)}, the latter formed when Mn was in excess during synthesis. The compound, Na(3)(H(2)O)(6)[Fe(II)(H(2)O)(6)](2){[Cu(I)(SO(3))(4)](2)[Fe(III)(H(2)O)](3)(O)}·H(2)O, contained trace magnetic impurities that affected the expected magnetic behaviour.     

Thermally stimulated contact potential difference as a possibility to determine the energy position of semiconductor surface levels

A possibility of determining certain parameters of a semiconductor surface by thermally stimulated change in the contact potential difference (TSCPD) is shown. On the basis of a simple model steplike changes in TSCPD are predicted. Suitable analytical expressions for the case of slight preliminary filling of surface traps with nonequilibrium charge carriers are deduced from the basic equations for a semiconductor surface and thermally stimulated phenomena. An initial experiment with high-resistance polycrystal CdS films is carried out. The character of the experimental TSCPD curves is in good agreement with the model.