Mapping the hydration dynamics of ubiquitin

The nature of water's interaction with biomolecules such as proteins has been difficult to examine in detail at atomic resolution. Solution NMR spectroscopy is potentially a powerful method for characterizing both the structural and temporal aspects of protein hydration but has been plagued by artifacts. Encapsulation of the protein of interest within the aqueous core of a reverse micelle particle results in a general slowing of water dynamics, significant reduction in hydrogen exchange chemistry and elimination of contributions from bulk water thereby enabling the use of nuclear Overhauser effects to quantify interactions between the protein surface and hydration water. Here we extend this approach to allow use of dipolar interactions between hydration water and hydrogens bonded to protein carbon atoms. By manipulating the molecular reorientation time of the reverse micelle particle through use of low viscosity liquid propane, the T(1ρ) relaxation time constants of (1)H bonded to (13)C were sufficiently lengthened to allow high quality rotating frame nuclear Overhauser effects to be obtained. These data supplement previous results obtained from dipolar interactions between the protein and hydrogens bonded to nitrogen and in aggregate cover the majority of the molecular surface of the protein. A wide range of hydration dynamics is observed. Clustering of hydration dynamics on the molecular surface is also seen. Regions of long-lived hydration water correspond with regions of the protein that participate in molecular recognition of binding partners suggesting that the contribution of the solvent entropy to the entropy of binding has been maximized through evolution.     

Trigonometric–fitted hybrid four–step methods of sixth order for solving

A two–stage, explicit, hybrid four–step method of sixth order for the solution of the special second order initial value problem is presented here. The new method is trigonometric fitted, thus it uses variable coefficients. Numerical tests illustrate the superiority of our proposal over similar methods found in the relevant literature on a set of standard problems.     

Hybrid,phase–fitted,four–step methods of seventh order for solving x″(t) = f(t,x)

A four‐step method of seventh algebraic order is presented. It is tuned for addressing the special second order initial value problem. The new method is hybrid, explicit, and uses three stages per step. In addition is phase fitted. In consequence it uses variable coefficients that depend on the magnitude of the step‐size. We also present numerical tests on a set of standard problems that illustrate the efficiency of the derived method over older ones given in the relevant literature.     

Surface modification of microchip input reservoirs for pressure-induced sample injection into microreactors.

Optimization of geometry and surface modification of microchip input reservoirs were performed to achieve uninterferenced pressure-induced sample injection of multiple samples into microreactors using a single syringe pump. Nine samples of 3.5 microL were pipetted onto input reservoirs and loading of PCR mixture into 260 nL microreactors was achieved followed by successful PCR amplification, confirming that no cross-contamination occurs during injection.     

A Borg-Type Theorem Associated with Orthogonal Polynomials on the Unit Circle

We prove a general Borg-type result for reflectionless unitaryCMV operators U associated with orthogonal polynomials on theunit circle. The spectrum of U is assumed to be a connectedarc on the unit circle. This extends a recent result of Simonin connection with a periodic CMV operator with spectrum thewhole unit circle. In the course of deriving the Borg-type result we also use exponentialHerglotz representations of Caratheodory functions to provean infinite sequence of trace formulas connected with the CMVoperator U.