Vibrational dynamics of pyrrole via frequency-domain spectroscopy

The N-H stretch overtones of pyrrole, a key constituent of biologic building blocks, were studied by room temperature photoacoustic and jet-cooled action spectroscopies to unravel their intramolecular dynamics. Contrary to "isolated" states excited with two and three N-H stretch quanta, the one with four quanta shows strong accidental resonances with two other states involving three quanta of N-H stretch and one quantum of C-H stretch. The inhomogeneously reduced features in the action spectra provide the means for getting insight into the intramolecular interactions and the factors controlling energy flow within pyrrole. The time dependence of the survival probability of the 4ν(1) N-H stretch, deduced from the vibrational Hamiltonian, shows an initial decay in ~0.3 ps with ensuing quantum beats from the N-H-C-H resonance and their decay with a time constant of about 5 ps as a result of weaker coupling to bath states.     

A case study of dynamic visualization and problem solving

This paper reports an example of a situation in which university students had to solve geometrical problems presented to them dynamically using the interactive computerized environment of the ‘MicroWorlds Project Builder’. In the process of the problem solving, the students used ten different solution strategies. The unsuccessful strategies were then classified into three main categories: distracting, reducing and confusing. One student group had to solve the same problem in its non-dynamic version. The results received from both groups were compared and analysed. Analysis of the solution strategies and the process of the categorization revealed that the percentage of success in both groups was similar and in the case of the given problem, the dynamic visual mode of the problem distracted the students’ attention away from proper handling of the solution of the problem.     

The Emergence of Mathematical Collaboration in an Interactive Computer Environment

We present a case study of two students engaged in an investigation of number theory concepts in the computer environment, Geoboard. The two students struggle with significant problems to communicate mathematics, and the computer plays a vital role in helping them overcome these difficulties. In fact, the students constantly use the screen images to help them make sense of each other's vague ideas and incomplete utterances. Using the qualitative research methods of discourse analysis, we construct the learning profiles of the two students and show how the characteristics of each contributed to the shared process, and how they used the computer presence to enable this process. We trace this process through the students' construction of two mathematical concepts that arose in their activities, the n-star and common denominators.This revised version was published online in September 2005 with corrections to the Cover Date.     

Total Chemical Synthesis of SUMO and SUMO‐Based Probes for Profiling the Activity of SUMO‐Specific Proteases

SUMO is a post‐translational modifier critical for cell cycle progression and genome stability that plays a role in tumorigenesis, thus rendering SUMO‐specific enzymes potential pharmacological targets. However, the systematic generation of tools for the activity profiling of SUMO‐specific enzymes has proven challenging. We developed a diversifiable synthetic platform for SUMO‐based probes by using a direct linear synthesis method, which permits N‐ and C‐terminal labelling to incorporate dyes and reactive warheads, respectively. In this manner, activity‐based probes (ABPs) for SUMO‐1, SUMO‐2, and SUMO‐3‐specific proteases were generated and validated in cells using gel‐based assays and confocal microscopy. We further expanded our toolbox with the synthesis of a K11‐linked diSUMO‐2 probe to study the proteolytic cleavage of SUMO chains. Together, these ABPs demonstrate the versatility and specificity of our synthetic SUMO platform for in vitro and in vivo characterization of the SUMO protease family.     

H and D release in approximately 243.1 nm photolysis of vibrationally excited 3nu1, 4nu1, and 4nuCD overtones of propyne-d3

The photofragmentation of propyne-d(3), D(3)C-C[Triple Bond]C-H, following approximately 243.1 nm photodissociation of rovibrationally excited molecules promoted to the second (3nu(1)) and third (4nu(1)) acetylenic C-H overtone and to the third (4nu(CD)) methyl overtone has been investigated. The resulting H and D photoproducts were detected via (2+1) resonantly enhanced multiphoton ionization. The measured room-temperature photoacoustic and jet-cooled action spectra allowed derivation of the molecular parameters of the C-H overtones and the Doppler profiles revealed the translational energies associated with the H(D) photofragments and the H to D branching ratios. Propensities toward the latter were encountered, while the translational energy disposal in both photofragments was essentially identical for a given preexcitation. This behavior agrees with that found for the almost isoenergetic 193.3 nm photolysis of propyne [Qadiri et al., J. Chem. Phys. 119, 12842 (2003)], but contradicts previous findings. The bond fission of C-H and C-D is preceded by internal conversion to, and isomerization on, the ground-state potential energy surface (PES), followed by extensive intramolecular vibrational redistribution. For molecules preexcited to 3nu(1) and 4nu(1) an additional minor channel opens, where elimination of H occurs directly on the accessed excited PES, while that of D on the ground state.     

Vibrational overtone spectra of N-H stretches and intramolecular dynamics on the ground and electronically excited states of methylamine

The vibrational pattern and energy flow in the N-H stretch manifolds and the dissociation dynamics of methylamine (CH(3)NH(2)) were investigated via vibrationally mediated photodissociation. Action spectra and Doppler profiles, reflecting the yield of the ensuing H photofragments, versus near infrared/visible vibrational excitation and UV excitation, respectively, were measured. The jet-cooled action spectra and the simultaneously measured room temperature photoacoustic spectra of the first to third N-H stretching overtones exhibit broad features, somewhat narrower in the former, consisting of barely recognized multiple bands. Two phases of fitting of the spectroscopic data were performed. In the first phase, the raw data were analyzed to obtain band positions, types, intensities, and transition linewidths. In the second, the information derived from the first phase was then used as data in a fit to joint local mode/normal mode (LM/NM) and NM Hamiltonian parameters. The derived parameters predicted well band positions and allowed band assignment. The LM/NM Hamiltonian and the extracted Lorentzian linewidths enabled the determination of the initial pathways for energy redistribution and the overall temporal behavior of the N-H stretch and doorway states, as a result of Fermi couplings and interactions with bath states. The results indicate a nonstatistical energy flow in the V=2 manifold region, pointing to the dependence of the coupling on specific low order resonances rather than on the total density of bath states. The Doppler profiles suggest lower average translational energies for the released H photofragments, in particular, for V=3 and 4 as compared to V=1 and 2, implying a change in the mechanism for bond cleavage.     

Assessment of extravascular extracellular space fraction in human melanoma xenografts by DCE-MRI and kinetic modeling

Tumor aggressiveness and response to therapy are influenced by the extravascular extracellular space fraction (EESF) of the malignant tissue. The EESF may, therefore, be an important prognostic parameter for cancer patients. The aim of this study was to investigate whether gadopentetate dimeglumine (Gd-DTPA)-based dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) can be used to assess the EESF of tumors. Amelanotic human melanoma xenografts (A-07, R-18) were used as preclinical models of human cancer. Images of E.F (E is the initial extraction fraction of Gd-DTPA and F is perfusion) and lambda (the partition coefficient of Gd-DTPA) were obtained by Kety analysis of DCE-MRI data. Our study was based on the hypothesis that lambda is governed by the EESF and is not influenced significantly by microvascular density (MVD) or blood perfusion. To test this hypothesis, we searched for correlations between lambda and E.F, MVD or EESF by comparing lambda images with E.F images, histological preparations from the imaged tissue and the radial heterogeneity in EESF obtained by invasive imaging. Positive correlations were found between lambda and EESF. Thus, median lambda was larger in A-07 tumors than in R-18 tumors by a factor of 4.2 (P<.00001), consistent with the histological observation that EESF is approximately fourfold larger in A-07 tumors than in R-18 tumors. The radial heterogeneity in lambda in A-07 and R-18 tumors was almost identical to the radial heterogeneity in EESF. Moreover, lambda was larger in tissue regions with high EESF than in tissue regions with low EESF in A-07 tumors (P=.048). On the other hand, significant correlations between lambda and MVD or E.F could not be detected. Consequently, Kety analysis of Gd-DTPA-based DCE-MRI series of xenografted tumors provides lambda images that primarily reflect the EESF of the tissue.     

Where do Fractions Encounter their Equivalents? – Can this Encounter Take Place in Elementary-School?

The concept of equivalence class plays a significant role in the structure of Rational Numbers. Piaget taught that in order to help elementary school children develop mathematical concepts, concrete objects and concrete reflection-enhancing-activities are needed. The “Shemesh” software was specially designed for learning equivalence-classes of fractions. The software offers concrete representations of such classes, as well as activities which cannot be constructed without a computer. In a discrete Cartesian system students construct points on the grid and learn to identify each such point as a fraction-numeral (a denominator-numerator pair). The children then learn to construct sets of such points, all of which are located on a line through the origin point. They learn to identify the line with the set of its constituent equivalent fractions. Subsequently, they investigate other phenomena and constructions in such systems, developing these constructions into additional fraction concepts. These concrete constructions can be used in solving traditional fraction problems as well as in broadening the scope of fraction meaning. Fifth-graders who used “Shemesh” in their learning activities were clinically interviewed several months after the learning sessions ended. These interviews revealed evidence indicating initial actual development of the desired mathematical concepts. This revised version was published online in July 2006 with corrections to the Cover Date.