Interassociates of the Free Commutative Semigroup on n Generators

The interassociates of the free commutative semigroup on n generators, for n > 1, are identified. For fixed n, let (S, ·) denote this semigroup. We show that every interassociate can be written in the form , depending only on a n-tuple . Next, if and are isomorphic interassociates of (S, ·) such that , for x_ii and x_j in the generating set of S, then . Moreover, if and only if is a permutation of .     

Improved treatment of cyclic β‐amino acids and successful prediction of β‐peptide secondary structure using a modified force field: AMBER*C

We added parameters to the AMBER* force field to model cyclic β‐amino acid derivatives more accurately within the commonly used MacroModel program. In an effort to generate an improved treatment of cyclohexane and cyclopentane conformational preferences, carbon–carbon torsional parameters were modified and incorporated into a force field we call AMBER*C. Simulation of trans‐2‐aminocyclohexanecarboxylic acid (trans‐ACHC) and trans‐2‐aminocyclopentanecarboxylic acid (trans‐ACPC) derivatives using AMBER*C produces more realistic energy differences between (pseudo)diaxial and (pseudo)diequatorial conformations than does simulation using AMBER*. AMBER*C molecular dynamics simulations more accurately reproduce the experimental hydrogen‐bonding tendencies of simple diamide derivatives of trans‐ACHC and trans‐ACPC than do simulations using the AMBER* force field. More importantly, this modified force field allows accurate qualitative prediction of the helical secondary structures adopted by β‐amino acid homo‐oligomers. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 763–773, 2000     

Stimuli-responsive polymers. III. Poly(aryl ether ketone amide)s with reversible trans- ↔ cis-4,4′-azobenzene and fixed 2,2′-binaphthyl kinking elements in the main chain

The low-temperature polycondensation of trans-azobenzene-4,4′-dicarbonyl chloride with (S)-(−)-1,1′-binaphthyl-2,2′-diamine and/or 1,4-bis(3-aminophenoxy-4′-benzoyl)benzene afforded a new series of poly(aryl ether ketone amide)s with both fixed and photoinducible kinking elements positioned randomly along the main chain. In their lower energy, trans-azobenzene configurations, the orange, film-forming materials were amorphous, highly tractable, and thermally stable under air or nitrogen up to about 420°C. Variants endowed with higher loadings of the bent binaphthyl monomer were soluble in a variety of organic solvent media including THF and acetone. The introduction of cis-azobenzene backbone kinks into these materials was carried out by irradiating the polymer solutions with near-UV light. Up to 70% of the azobenzene moieties in these polymers were capable of assuming the higher energy cis-configuration, thus greatly increasing the number of bent or kinked sites positioned along each polymer backbone. In solution, reverse cis → trans isomerization reactions were triggered thermally and were quantitatively tracked by both optical absorbance and ¹H NMR spectroscopies. Activation parameters calculated for cis → trans reorganization of the polymer backbone were not dependent upon the chemical composition or molecular weight of the polymers but did exhibit a small dependence upon the nature of the solvent medium used to conduct the isomerization experiment. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 2827–2837, 1998     

Facilitating the culture of mammalian nerve cells with polyelectrolyte multilayers

When neuron-like cells (NLCs) derived from pluripotent embryonal carcinoma cells (P19) are cultured on bare tissue culture substrates, they require a monolayer of fibroblast cells to exhibit normal neurite outgrowth, behavior typical of neuronal cultures. However, substrate treatment with polyelectrolyte multilayers (PEMs) composed of poly(allylamine hydrochloride) (PAH) and poly(styrenesulfonic acid) (PSS) significantly improved these cultures. Cell morphology was more spread, indicative of healthy cells, and direct attachment of neuronal cell bodies to the treated surface was observed. Neuronal outgrowth across the surface was not dependent on an underlying fibroblast monolayer with the PEMs surface treatment. Additionally, the PEMs surface treatment can be used to condition various surfaces, facilitating neuronal cultures on surfaces which are natively hydrophilic (tissue culture polystyrene) or hydrophobic (poly(dimethylsiloxane), PDMS). Microfluidic networks were used to micropattern the PEMs onto PDMS, resulting in confined regions of cellular attachment and directed neuronal outgrowth. The ability of PEMs to encourage NLC attachment without supporting cells to a variety of surfaces and surface geometries greatly simplifies neuronal culture methodology and enables neuronal investigations in new environments.     

A Collaboration-based Approach to CFD Model Validation and Uncertainty Quantification (VUQ) Using Data from a Laminar Helium Plume

An effective approach to the model VUQ process by means of direct collaboration between computationalist and experimental data analyst is proposed. An analysis of data from a laminar helium plume experiment provides a demonstration of the proposed collaboration process. Consistency analysis serves a central role in the collaboration. It takes the data and uncertainties from both analyst and computationalist and provides an objective and quantifiable measure of agreement between the two. Despite the simplicity of the laminar helium system and the computational model, certain phenomena brought to light in the collaboration process make it difficult to find quantitative agreement in the data. These phenomena include the unsteady behavior of air flow in an open room, and the presence of helium permeation to the region near the plume. Important sources of error in the simulation include uncertainty in the room temperature (295.15 to 305.15 K), uncertainty in the helium inlet velocity (0.1215 \(\frac {m}{s}\) to 0.1415 \(\frac {m}{s}\)), and uncertainty in local helium permeation (0 % to 3 % by mass.) The collaboration process allows for a better understanding of the phenomena affecting the plume and the relative sensitivies of the system to these phenomena.     

Langevin Dynamics,Large Deviations and Instantons for the Quasi-Geostrophic Model and Two-Dimensional Euler Equations

We investigate a class of simple models for Langevin dynamics of turbulent flows, including the one-layer quasi-geostrophic equation and the two-dimensional Euler equations. Starting from a path integral representation of the transition probability, we compute the most probable fluctuation paths from one attractor to any state within its basin of attraction. We prove that such fluctuation paths are the time reversed trajectories of the relaxation paths for a corresponding dual dynamics, which are also within the framework of quasi-geostrophic Langevin dynamics. Cases with or without detailed balance are studied. We discuss a specific example for which the stationary measure displays either a second order (continuous) or a first order (discontinuous) phase transition and a tricritical point. In situations where a first order phase transition is observed, the dynamics are bistable. Then, the transition paths between two coexisting attractors are instantons (fluctuation paths from an attractor to a saddle), which are related to the relaxation paths of the corresponding dual dynamics. For this example, we show how one can analytically determine the instantons and compute the transition probabilities for rare transitions between two attractors.     

DNA molecules descending a nanofluidic staircase by entropophoresis

A complex entropy gradient for confined DNA molecules was engineered for the first time. Following the second law of thermodynamics, this enabled the directed self-transport and self-concentration of DNA molecules. This new nanofluidic method is termed entropophoresis. As implemented in experiments, long DNA molecules were dyed with cyanine dimers, dispersed in a high ionic strength buffer, and confined by a nanofluidic channel with a depth profile approximated by a staircase function. The staircase step depths spanned the transition from strong to moderate confinement. The diffusion of DNA molecules across slitlike steps was ratcheted by entropic forces applied at step edges, so that DNA molecules descended and collected at the bottom of the staircase, as observed by fluorescence microscopy. Different DNA morphologies, lengths, and stoichiometric base pair to dye molecule ratios were tested and determined to influence the rate of transport by entropophoresis. A model of ratcheted diffusion was used to interpret a shifting balance of forces applied to linear DNA molecules of standard length in a complex free energy landscape. Related metrics for the overall and optimum performance of entropophoresis were developed. The device and method reported here transcend current limitations in nanofluidics and present new possibilities in polymer physics, biophysics, separation science, and lab-on-a-chip technology.     

Studies of iron(II) and iron(III) complexes with fac-N2O, cis-N2O2 and N2O3 donor ligands: models for the 2-His 1-carboxylate motif of non-heme iron monooxygenases

Enzymes in the oxygen-activating class of mononuclear non-heme iron oxygenases (MNOs) contain a highly conserved iron center facially ligated by two histidine nitrogen atoms and one carboxylate oxygen atom that leave one face of the metal center (three binding sites) open for coordination to cofactor, substrate, and/or dioxygen. A comparative family of [Fe(II/III)(N(2)O(n))(L)(4-n))](±x), n = 1-3, L = solvent or Cl(-), model complexes, based on a ligand series that supports a facially ligated N,N,O core that is then modified to contain either one or two additional carboxylate chelate arms, has been structurally and spectroscopically characterized. EPR studies demonstrate that the high-spin d(5) Fe(III)g = 4.3 signal becomes more symmetrical as the number of carboxylate ligands decreases across the series Fe(N(2)O(3)), Fe(N(2)O(2)), and Fe(N(2)O(1)), reflecting an increase in the E/D strain of these complexes as the number of exchangeable/solvent coordination sites increases, paralleling the enhanced distribution of electronic structures that contribute to the spectral line shape. The observed systematic variations in the Fe(II)-Fe(III) oxidation-reduction potentials illustrate the fundamental influence of differential carboxylate ligation. The trend towards lower reduction potential for the iron center across the [Fe(III)(N(2)O(1))Cl(3)](-), [Fe(III)(N(2)O(2))Cl(2)](-) and [Fe(III)(N(2)O(3))Cl](-) series is consistent with replacement of the chloride anions with the more strongly donating anionic O-donor carboxylate ligands that are expected to stabilize the oxidized ferric state. This electrochemical trend parallels the observed dioxygen sensitivity of the three ferrous complexes (Fe(II)(N(2)O(1)) < Fe(II)(N(2)O(2)) < Fe(II)(N(2)O(3))), which form μ-oxo bridged ferric species upon exposure to air or oxygen atom donor (OAD) molecules. The observed oxygen sensitivity is particularly interesting and discussed in the context of α-ketoglutarate-dependent MNO enzyme mechanisms.     

Synthesis of 4-substituted chlorophthalazines, dihydrobenzoazepinediones, 2-pyrazolylbenzoic acid, and 2-pyrazolylbenzohydrazide via 3-substituted 3-hydroxyisoindolin-1-ones

Herein we describe a general three-step synthesis of 4-substituted chlorophthalazines in good overall yields. In the key step, N,N-dimethylaminophthalimide (8a) directs the selective monoaddition of alkyl, aryl, and heteroaryl organometallic reagents to afford 3-substituted 3-hydroxyisoindolinones 9b, 9i-9am. Many of these hydroxyisoindolinones are converted to chlorophthalazines 1b-1v via reaction with hydrazine, followed by chlorination with POCl(3). We have also discovered two novel transformations of 3-vinyl- and 3-alkynyl-3-hydroxyisoindolinones. Addition of vinyl organometallic reagents to N,N-dimethylaminophthalimide (8a) provided dihydrobenzoazepinediones 15a-15c via the proposed ring expansion of 3-vinyl-3-hydroxyisoindolinone intermediates. 3-Alkynyl-3-hydroxyisoindolinones react with hydrazine and substituted hydrazines to afford 2-pyrazolyl benzoic acids 16a-16d and 2-pyrazolyl benzohydrazides 17a-17g rather than the expected alkynyl phthalazinones.     

Auditory perception of material is fragile while action is strikingly robust

While many psychoacoustic studies have found that listeners can recover some causal properties of sound-generating objects (such as the material), comparatively little is known about the causal properties of the sound-generating actions and how they are perceived. This article reports on a study comparing the performance of listeners required to identify either the actions or the materials used to generate sound stimuli. Stimuli were recordings of a set of cylinders of two sizes and four materials (wood, plastic, glass, metal) undergoing four different actions (scraping, rolling, hitting, bouncing). Experiment 1 tested how well each sound conveyed that it was generated with a different action or material. Experiment 2 measured both accuracy and reaction times for the identification of actions and materials. Listeners were faster and more accurate at identifying the action than the material. Even for the subset of sounds for which actions and materials were equivalently well identified, listeners were faster at identifying the action than the material. These results suggest that the auditory system is well-suited to extract information about sound-generating actions.