Opacity analysis of the H3 system: Modified rotating-rod versus Frozen-Orientation models

The Rotating-Rod Model is modified to make the adjustable α parameter which appears in the treatment energy dependent. Its predictions for opacity and excitation functions compare well with quasi-classical H₃ trajectory results, for translational and vibrationalenergy variations and isotopic mass effects. The Frozen-Orientation Model in its present form is incapable of such an agreement for mass combinations other than H + D₂. It is suggested that the decreaseof α with energy can be interpreted as a transition from adiabatic tosudden behavior, where alignment is only on the average, and much energy isdeposited in the bending modes. This is supported by a correlation between α and the average final rotation.     

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.     

Elementary steps in excited-state proton transfer

The absorption of a photon by a hydroxy-aromatic photoacid triggers a cascade of events contributing to the overall phenomenon of intermolecular excited-state proton transfer. The fundamental steps involved were studied over the last 20 years using a combination of theoretical and experimental techniques. They are surveyed in this sequel in sequential order, from fast to slow. The excitation triggers an intramolecular charge transfer to the ring system, which is more prominent for the anionic base than the acid. The charge redistribution, in turn, triggers changes in hydrogen-bond strengths that set the stage for the proton-transfer step itself. This step is strongly influenced by the solvent, resulting in unusual dependence of the dissociation rate coefficient on water content, temperature, and isotopic substitution. The photolyzed proton can diffuse in the aqueous solution in a mechanism that involves collective changes in hydrogen-bonding. On longer times, it may recombine adiabatically with the excited base or quench it. The theory for these diffusion-influenced geminate reactions has been developed, showing nice agreement with experiment. Finally, the effect of inert salts, bases, and acids on these reactions is analyzed.     

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.     

Diffusion-influenced excited-state reversible transfer reactions, A* + Bright harpoon over left harpoonC* + D, with two different lifetimes: theories and simulations

We report accurate Brownian simulation results for the kinetics of the pseudo-first-order diffusion-influenced excited-state reversible transfer reaction A(*) + Bright harpoon over left harpoonC(*) + D with two different lifetimes using two different propagation algorithms. The results are used to test approximate solutions for this many-particle problem. Available theories fail when one of the two reactions or (decay) rate constants is large. To remedy this situation, we develop two uniform approximations, which are based on introducing a generalized Smoluchowski term into the relaxation-time approximation. The best of these is the extended unified theory of reversible target reactions, which reduces correctly in all limits and exhibits superior agreement with simulations.     

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.     

Theory and simulation of diffusion-controlled Michaelis-Menten kinetics for a static enzyme in solution

We develop a uniform theory for the many-particle diffusion-control effects on the Michaelis-Menten scheme in solution, based on the Gopich-Szabo relaxation-time approximation (Gopich, I. V.; Szabo, A. J. Chem. Phys. 2002, 117, 507). We extend the many-particle simulation algorithm to the Michaelis-Menten case by utilizing the Green function previously derived for excited-state reversible geminate recombination with different lifetimes (Gopich, I. V.; Agmon, N. J. Chem. Phys. 2000, 110, 10433). Running the simulation for representative parameter sets in the time domain and under steady-state conditions, we find poor agreement with classical kinetics but excellent agreement with some of the modern theories for bimolecular diffusion-influenced reactions. Our simulation algorithm can be readily extended to the biologically interesting case of dense patches of membrane-bound enzymes.     

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.     

A Locust-Inspired Model of Collective Marching on Rings

We study the collective motion of autonomous mobile agents in a ringlike environment. The agents’ dynamics are inspired by known laboratory experiments on the dynamics of locust swarms. In these experiments, locusts placed at arbitrary locations and initial orientations on a ring-shaped arena are observed to eventually all march in the same direction. In this work we ask whether, and how fast, a similar phenomenon occurs in a stochastic swarm of simple locust-inspired agents. The agents are randomly initiated as marching either clockwise or counterclockwise on a discretized, wide ring-shaped region, which we subdivide into k concentric tracks of length n. Collisions cause agents to change their direction of motion. To avoid this, agents may decide to switch tracks to merge with platoons of agents marching in their direction. We prove that such agents must eventually converge to a local consensus about their direction of motion, meaning that all agents on each narrow track must eventually march in the same direction. We give asymptotic bounds for the expected time it takes for such convergence or “stabilization” to occur, which depends on the number of agents, the length of the tracks, and the number of tracks. We show that when agents also have a small probability of “erratic”, random track-jumping behavior, a global consensus on the direction of motion across all tracks will eventually be reached. Finally, we verify our theoretical findings in numerical simulations.