Adsorption of charged macromolecules at a gold electrode

Using an optical reflectometer with impinging-jet system, the adsorption from aqueous solution onto gold of three charged macromolecules has been studied: the strong linear-chain polyelectrolyte polyvinyl pyridine (PVP(+)), the fifth-generation poly(propylene imine) dendrimer DAB-64, which has a pH-dependent charge and a relatively fixed shape, and the protein lysozyme, of which both the charge and the structure-stability are dependent on solution composition. Experimental conditions that have been varied include the adsorbate concentration, electrolyte concentration, pH, and externally applied potential across the gold/solution interface. Making use of the earlier established dependency of the double layer potential of the gold substrate on solution conditions and externally applied potential, the results of measurements as a function of pH and as a function of external potential control are compared. The total set of results enables us to draw conclusions with respect to the relative importance of electrostatic interactions for the adsorption process. PVP(+) adsorption follows the electric potential of the gold/solution interface and is further determined by a rather strong nonelectrostatic affinity between segments and surface. The adsorption behavior of DAB-64 is not quite understood, but electrostatic interactions with the gold surface seem to play a minor role. For lysozyme, surface-induced conformational changes dominate the adsorption process. The extent of spreading of the molecules decreases with increasing polarity of the surface, resulting in a minimum in adsorbed amount around the point of zero potential of the gold.     

Reactive dications: the superacid-catalyzed reactions of alkynes bearing adjacent N-heterocycles or amine groups

A variety of aminoalkynes and related heterocycles are reacted in the Bronsted superacid CF(3)SO(3)H (triflic acid), and products are obtained in generally good yields (69-99%) from Friedel-Crafts-type reactions. The reactions are consistent with the formation of novel dicationic intermediates having a vinyl cationic site and an adjacent protonated N-heterocycle or ammonium cation.     

Synthesis, characterization, and preliminary intramolecular energy transfer studies of rigid, emissive, rhenium-linked porphyrin dimers

The reaction of pyridyl functionalized porphyrins with Re(CO)(5)Cl in THF results in the formation of porphyrin dimers which, despite incorporation of rhenium into the assemblies, remain fluorescent. The rigid compounds provide an efficient geometry and/or orbital pathway for singlet energy transfer, rendering these compounds suitable, in principle, for the study of both through-bond and through-space energy transfer. Derivatives containing both metallated and freebase porphyrins connected via the metal corners display efficient porphyrin-porphyrin energy transfer. The photophysical properties of the assemblies have been studied by both steady-state and time-resolved fluorescence techniques, yielding approximate rates and efficiencies for porphyrin-porphyrin energy transfer.     

Dynamics of curved DNA molecules: prediction and experiment

We have developed a quantitative predictive model capable of describing the dynamics of migration of intrinsically curved DNA fragments on polyacrylamide gels. The model takes into account structural features of DNA, end-to-end distance, screening of hydrodynamic interactions, ionic strength of buffer, electrostatic persistence length, structural fluctuations of the macromolecule, counter condensation, and variation of dielectric constant and viscosity of water with MPD. In doing so, we have also addressed a decade old issue on the effect of the organic solvent 2-methyl-2,4-pentanediol on gel migration of phased A-tracts. We show here that A-tract-solvent interactions are less favored compared with A-tract-A-tract and solvent-solvent interactions.     

Generating M-Indeterminate Probability Densities by Way of Quantum Mechanics

Probability densities that are not uniquely determined by their moments are said to be “moment-indeterminate,” or “M-indeterminate.” Determining whether or not a density is M-indeterminate, or how to generate an M-indeterminate density, is a challenging problem with a long history. Quantum mechanics is inherently probabilistic, yet the way in which probability densities are obtained is dramatically different in comparison with standard probability theory, involving complex wave functions and operators, among other aspects. Nevertheless, the end results are standard probabilistic quantities, such as expectation values, moments and probability density functions. We show that the quantum mechanics procedure to obtain densities leads to a simple method to generate an infinite number of M-indeterminate densities. Different self-adjoint operators can lead to new classes of M-indeterminate densities. Depending on the operator, the method can produce densities that are of the Stieltjes class or new formulations that are not of the Stieltjes class. As such, the method complements and extends existing approaches and opens up new avenues for further development. The method applies to continuous and discrete probability densities. A number of examples are given.

     

Correction to: Preface

Foundations of Computational Mathematics -     

New results for diffusion in Lorentz lattice gas cellular automata

New calculations to over ten million time steps have revealed a more complex diffusive behavior than previously reported of a point particle on a square and triangular lattice randomly occupied by mirror or rotator scatterers. For the square lattice fully occupied by mirrors where extended closed particle orbits occur, anomalous diffusion was still found. However, for a not fully occupied lattice the superdiffusion, first noticed by Owczarek and Prellberg for a particular concentration, obtains for all concentrations. For the square lattice occupied by rotators and the triangular lattice occupied by mirrors or rotators, an absence of diffusion (trapping) was found for all concentrations, except on critical lines, where anomalous diffusion (extended closed orbits) occurs and hyperscaling holds for all closed orbits withuniversal exponentsd _f =7/4 and =15/7. Only one point on these critical lines can be related to a corresponding percolation problem. The questions arise therefore whether the other critical points can be mapped onto a new percolation-like problem and of the dynamical significance of hyperscaling.