Standardized Characterization of Electrocatalytic Electrodes

This paper investigates the utility of ‘cross–lab’ comparative analysis of electrocatalytic electrode performance using standardized modular stack cells and test protocols. Using poly(methylene green)‐modified glassy carbon electrodes as the model system, we characterized electrode fabrication and performance with respect to the catalytic oxidation of NADH at neutral pH and low overpotential. Three sets of experiments were duplicated across four independent laboratories and the experimental results from each set were analyzed and compared in terms of key electroanalytical parameters. Statistical analyses were performed at three distinct levels: 1) the standard deviation among repetitive cycles within an experiment; 2) the standard deviation among repetitive experiments in the same laboratory, and 3) the standard deviation among experiments performed across all four laboratories. Using predefined criteria of ‘reproducibility’ for each level, most parameters were found to be statistically reproducible at most levels. When a particular parameter was found to be irreproducible in a given level, commentary is given on how that information can be used diagnose what chemical/physical aspects of the process were uncontrolled or poorly understood and therefore candidates for future research. This exercise, which is presented as a ‘proof–of‐principle’ step towards the concept of standardizing electrocatalytic evaluation, illustrates the importance of executing electrochemical characterization protocols across several labs and using fixed geometry and dimensions, system configuration, and applied electrochemical conditions. Future work is under way to extend these principles to systems with fluid flow.     

Askey-Wilson type functions with bound states

The two linearly independent solutions of the three-term recurrence relation of the associated Askey-Wilson polynomials, found by Ismail and Rahman in [22], are slightly modified so as to make it transparent that these functions satisfy a beautiful symmetry property. It essentially means that the geometric and the spectral parameters are interchangeable in these functions. We call the resulting functions the Askey-Wilson functions. Then, we show that by adding bound states (with arbitrary weights) at specific points outside of the continuous spectrum of some instances of the Askey-Wilson difference operator, we can generate functions that satisfy a doubly infinite three-term recursion relation and are also eigenfunctions of q-difference operators of arbitrary orders. Our result provides a discrete analogue of the solutions of the purely differential version of the bispectral problem that were discovered in the pioneering work [8] of Duistermaat and Grünbaum. 2000 Mathematics Subject Classification Primary—33D45, 37K10, 14H70, 39A70, 39A13     

Heat Kernel Expansions on the Integers

In the case of the heat equation u _t =u _xx +Vu on the real line, there are some remarkable potentials V for which the asymptotic expansion of the fundamental solution becomes a finite sum and gives an exact formula.We show that a similar phenomenon holds when one replaces the real line by the integers. In this case the second derivative is replaced by the second difference operator L ₀. We show if L denotes the result of applying a finite number of Darboux transformations to L ₀ then the fundamental solution of u _t =Lu is given by a finite sum of terms involving the Bessel function I of imaginary argument.     

Multivariable Askey–Wilson function and bispectrality

For every positive integer d, we define a meromorphic function F _d (n;z), where n,z∈ℂ ^d , which is a natural extension of the multivariable Askey–Wilson polynomials of Gasper and Rahman (Theory and Applications of Special Functions, Dev. Math., vol. 13, pp. 209–219, Springer, New York, 2005). It is defined as a product of very-well-poised ₈ φ ₇ series and we show that it is a common eigenfunction of two commutative algebras A_z{\mathcal{A}}_{z} and A_n{\mathcal{A}}_{n} of difference operators acting on z and n, with eigenvalues depending on n and z, respectively. In particular, this leads to certain identities connecting products of very-well-poised ₈ φ ₇ series.     

Electrochemical DNA Hybridization Assay: Enzyme‐Labeled Detection of Mutation in p53 Gene

This paper discusses a new electrochemical DNA hybridization sensing approach based on the detection of a linked enzyme label. In this method we employ enzyme that is attached to a tethered ssDNA oligomer on the surface and the target analyte is a complementary ssDNA oligomer that does not require any pre‐treatment. The advantage of using of enzyme label is in its amplification of the registration of the hybridization event due to the catalytic reaction facilitated in the process. One particular novelty is associated with the use of enzymes that directly communicate with the electrode surface thus allowing for minimizing the need of additional reagents in the assay. The electrochemical assay was demonstrated when using mixed self‐assembled monolayers from thiolated oligonucleotide and 6‐mercapto 1‐hexanol on gold surfaces. Horseradish peroxidase (HRP) is attached to the surface tethered oligonucleotide using streptavidin‐biotin chemistry, and the enzyme successfully established direct electron transfer (DET) with the electrode or mediated electron transfer (MET) using a mediator. Hybridization results in increasing the angle of contact between electrode and DNA and also the stiffness of the ds DNA, which results in displacing the enzyme away from the electrode surface, and thereby reducing the occurrence of direct electron transfer between the enzyme and the electrode. The cyclic voltammetry showed a clear distinction in response between the complete complementary sequence and the two‐base mismatch sequence. Ellipsometric measurements show that the thickness of the thiol modified oligonucleotide on gold surfaces changes before and after hybridization for the complementary sequence, where as a minimal change in thickness was observed for the noncomplementary sequence. The model target analyte in this study was TP53 gene where a specific mutation is a marker for a list of cancers. Mutations of the TP53 gene have been demonstrated in tumors of the colon, breast, lung, ovary, bladder, and many other organs. Analysis of p53 mutations may provide useful information for the diagnosis, prognosis and therapy of cancer.     

Selective amidoalkylation of cyclic enamino ketones with N-acyliminium salts of 3,4-dihydroisoquinolines

A series of cyclic enaminoketones were selectively amidoalkylated at the α-carbon in reactions with acyliminium reagents derived from 3,4-dihydroisoquinolines.     

Heat kernel expansions on the integers and the Toda lattice hierarchy

We consider the heat equation u _t = Lu where L is a second-order difference operator in a discrete variable n. The fundamental solution has an expansion in terms of the Bessel functions of imaginary argument. The coefficients α _k (n, m) in this expansion are analogs of Hadamard’s coefficients for the (continuous) Schr?dinger operator. We derive an explicit formula for α _k in terms of the wave and the adjoint wave functions of the Toda lattice hierarchy. As a first application of this result, we prove that the values of these coefficients on the diagonals n = m and n = m + 1 define a hierarchy of differential-difference equations which is equivalent to the Toda lattice hierarchy. Using this fact and the correspondence between commutative rings of difference operators and algebraic curves we show that the fundamental solution can be summed up, giving a finite formula involving only two Bessel functions with polynomial coefficients in the time variable t, if and only if the operator L belongs to the family of bispectral operators constructed in [18].      

Isotope depletion of large biomolecules: Implications for molecular mass measurements

Isotope depletion (or enrichment) of large biomolecules is a procedure already used in high resolution Fourier transform ion cyclotron resonance mass spectrometry for improving the reliability and accuracy of biomolecular mass characterization. In this work, effects of isotope depletion on a number of mass spectrometric parameters are systematically studied. Implementation of the isotope depletion techniques in conjunction with lower resolution mass analyzers is discussed as well. We investigate theoretically the position of the centroid of the isotopic mass distributions (centroid mass) and the shift between the monoisotopic and the centroid masses of biopolymers as a function of the isotope abundance (e.g., ¹²C:¹³C ratio). The behaviour of other additive mass parameters, like the ratio between the monoisotopic and the first isotopic peak, is also discussed. We address by computer simulations the effects of different instrumental parameters like mass resolution and ion statistics as a function of isotope abundances and from there the achievable mass accuracy for high-mass biopolymers. We assess some of the practical issues of the isotope depletion technique, viz., to what degree and with what accuracy the depletion procedure should be performed for achieving the desired mass accuracy.