Rapid assays based on immobilized bioluminescent enzymes and photographic detection of light-emission

Sensitive assays have been developed for adenosine 5'-triphosphate, the reduced form of nicotinamide adenine dinucleotide, cholyl glycine and alcohol, with immobilized and co-immobilized preparations of bacterial and firefly luciferase as reagents. With high-speed (ASA 20000) instant photographic film as detector, picomole amounts of the various analytes can be detected rapidly. The simplicity and convenience of the analytical combination of co-immobilized bioluminescent enzymes and photographic film for the detection of light make this an ideal technique for rapid screening tests.     

Studies on azaspiracid biotoxins. I. Ultrafast high-resolution liquid chromatography/mass spectrometry separations using monolithic columns

In this study, the performance of monolithic columns was evaluated for ultrafast liquid chromatography/mass spectrometry (LC/MS) analyses and for high-resolution separations of several azaspiracid biotoxin analogs. Because of their high permeability, monolithic columns offer a number of advantages over conventional packed columns; viz., very low backpressures and relatively flat van Deemter curves at high flow rates. That is, very high flow rates can be used for ultrafast analyses or, by using longer than normal columns, high-resolution separations are possible. In a series of experiments, we varied the mobile phase flow rates between 1 and 8 mL/min, and studied their impact on chromatographic parameters such as retention time, resolution, number of plates and pressure. The chromatographic run times could be reduced to ca. 30 s without a significant change in the separation efficiency. A signal intensity comparison revealed interesting differences between atmospheric-pressure chemical ionization (APCI) and electrospray ionization (ESI) in their flow-rate dependency. An explanation with respect to the behavior as of a mass-flow or a concentration-dependent device is given in the paper. Additionally, the column length was varied between 10 and 70 cm. As a result, the number of theoretical plates increased substantially. In the example shown in the report, an increase from 13 000 plates for a 10-cm column to 80 000 for a 70-cm column is demonstrated. In addition, the potential of the monolithic columns for high-resolution LC/MS separations is shown for a complex biotoxin mixture, which was separated on a 40-cm-long column.     

Standard deviation in reduced errors (SDRE): A criterion to assess the relative overall quality of approximate wavefunctions

The standard deviation in reduced errors (SDRE) quantitatively measures the similarity between an approximate and exact wavefunction. It is the Euclidean distance between the vector of the one-electron property expectation values calculated using the approximate and exact expectation values.     

Estimating reaction parameters in mechanism-enabled population balance models of nanoparticle size distributions: A Bayesian inverse problem approach

In order to quantitatively predict nano- as well as other particle-size distributions, one needs to have both a mathematical model and estimates of the parameters that appear in these models. Here, we show how one can use Bayesian inversion to obtain statistical estimates for the parameters that appear in recently derived mechanism-enabled population balance models (ME-PBM) of nanoparticle growth. The Bayesian approach addresses the question of “how well do we know our parameters, along with their uncertainties?.” The results reveal that Bayesian inversion statistical analysis on an example, prototype nanoparticle formation system allows one to estimate not just the most likely rate constants and other parameter values, but also their SDs, confidence intervals, and other statistical information. Moreover, knowing the reliability of the mechanistic model's parameters in turn helps inform one about the reliability of the proposed mechanism, as well as the reliability of its predictions. The paper can also be seen as a tutorial with the additional goal of achieving a “Gold Standard” Bayesian inversion ME-PBM benchmark that others can use as a control to check their own use of this methodology for other systems of interest throughout nature. Overall, the results provide strong support for the hypothesis that there is substantial value in using a Bayesian inversion methodology for parameter estimation in particle formation systems.     

Single-Molecule Force Spectroscopy of DNA-Based Reversible Polymer Bridges: Surface Robustness and Homogeneity

Single-molecule force spectroscopy, as implemented in an atomic force microscope, provides a rarely used method by which to monitor dynamic processes that occur near surfaces. Here, a methodology is presented and characterized that facilitates the study of polymer bridging across nanometer-sized gaps. The model system employed is that of DNA-based reversible polymers, and an automated procedure is introduced that allows the AFM tip–surface contact point to be automatically determined, and the distance d between opposing surfaces to be actively controlled. Using this methodology, the importance of several experimental parameters was systematically studied, e.g. the frequency of repeated tip/surface contacts, the area of the substrate surface sampled by the AFM, and the use of multiple AFM tips and substrates. Experiments revealed the surfaces to be robust throughout pulling experiments, so that multiple touches and pulls could be carried out on a single spot with no measurable affect on the results. Differences in observed bridging probabilities were observed, both on different spots on the same surface and, more dramatically, from one day to another. Data normalization via a reference measurement allows data from multiple days to be directly compared.     

Efficient p-adic Cell Decompositions for Univariate Polynomials

Cell decompositions are constructed for polynomials f(x)Z_p[x] of degree n, such that n<p, using O(n²) cells. When f is square-free this yields a polynomial-time algorithm for counting and approximating roots in Z_p. These results extend to give a polynomial-time algorithm in the bit model for fZ[x].     

Non self-consistent field theory — A new approach in quantum mechanical calculations

An R ^o-independent electronic repulsion matrix is constructed, replacing the R ^o-dependent Hamiltonian matrix (R ^o is the density matrix). A non-SCF theory is developed to solve the eigenequation without using an iterative procedure. Three methods are proposed to solve for the eigenvectors and eigenvalues. Illustrative calculations are reported comparing the non-SCF and SCF theories. The calculated results are as expected: the ground state energies are nearly unchanged while the orbital energies are nearer to the experimental results. Other physical properties and spectral quantities are also compared. It is found that the ZDO assumption is applicable in the non-SCF theory if it is applicable in SCF theory.

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Zusammenfassung Eine R ^o-unabhängige Elektronenabstoßungsmatrix wird eingeführt, die die R ^o-abhängige Hamiltonmatrix ersetzt (R ^o ist die Dichtematrix). Zur Lösung der Eigenwertgleichung ohne iterative Prozeduren wird eine sog. Nicht-SCF-Theorie aufgestellt. An Beispielen werden die Ergebnisse von SCF- und Nicht-SCF-Rechnungen verglichen; dabei erweisen sich die Energien des Grundzustandes als nahezu unverändert, während die Energien der Orbitale näher bei den experimentellen Werten liegen. Die zero-differential-overlap-Näherung ist immer dann in der neuen Theorie anwendbar, wenn sie in der SCF-Theorie anwendbar ist.

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Résumé Une matrice de répulsion électronique indépendante de R ^o est construite, remplaçant la matrice hamiltonienne dépendant de R ^o (R ^o matrice de densité). Une théorie non SCF est développée afin de résoudre l'équation aux valeurs propres sans itérations. Trois méthodes de résolution du problème aux valeurs propres sont proposées. Des calculs illustrent la comparaison entre les théories SCF et non SCF. Les résultats des calculs sont comme prévus: l'énergie de l'état fondamental varie peu alors que les énergies orbitales sont plus proches des résultats expérimentaux. D'autres propriétés physiques ainsi que des grandeurs spectrales sont comparées. On trouve que l'approximation du recouvrement différentiel nul est applicable dans la théorie non SCF si elle est applicable dans la théorie SCF.

     

The effect of two distinct fast time scales in the rotating,stratified Boussinesq equations: variations from quasi-geostrophy

Inspired by the use of fast singular limits in time-parallel numerical methods for a single fast frequency, we consider the limiting, nonlinear dynamics for a system of partial differential equations when two fast, distinct time scales are present. First-order slow equations are derived via the method of multiple time scales when the two small parameters are related by a rational power. We find that the resultant system depends only on the relationship of the two fast time scales, i.e. which fast time is fastest? Using the theory of cancellation of fast oscillations, we show that with the appropriate assumptions on the nonlinear operator of the full system, this reduced slow system is exactly that which the solution will converge to if each asymptotic limit is considered sequentially. The same result is also obtained via the method of renormalization. The specific example of the rotating, stratified Boussinesq equations is explored in detail, indicating that the most common distinguished limit of this system—quasi-geostrophy, is not the only limiting asymptotic system.