In-situ investigation of the adsorption of globular model proteins on stimuli-responsive binary polyelectrolyte brushes

Binary brushes constituted from two incompatible polymers can be used in the form of ultrathin polymeric layers as a versatile tool for surface engineering to tune physicochemical surface characteristics such as wettability, surface charge, chemical composition, and morphology and furthermore to create responsive surface properties. Mixed brushes of oppositely charged weak polyelectrolytes represent a special case of responding surfaces that are sensitive to changes in the pH value of the aqueous environment and therefore represent interesting tools for biosurface engineering. The polyelectrolyte brushes used for this study were composed of two oppositely charged polyelelctrolytes poly(2-vinylpyridine) (P2VP) and poly(acrylic acid) (PAA). The in-situ properties and surface characteristics such as as surface charge, surface tension, and extent of swelling of these brush layers are functions of the pH value of the surrounding aqueous solution. To test the behavior of the mixed polylelctrolyte brushes in contact with biosystems, protein adsorption experiments with globular model proteins were performed at different pH values and salt concentrations (confinement of counterions) of the buffer solutions. The influence of the pH value, buffer salt concentration, and isoelectric points (IEP) of the brush and protein on the adsorbed amount and the interfacial tension during protein adsorption as well as the protein adsorption mechanism postulated in reference to recently developed theories of protein adsorption on polyelectrolyte brushes is discussed. In the salted regime, protein adsorption was found to be similar to the often-described adsorption at hydrophobic surfaces. However, in the osmotic regime the balance of electrostatic repulsion and a strong entropic driving force, "counterion release", was found to be the main influence on protein adsorption.     

Temperature-sensitive swelling of poly(N-isopropylacrylamide) brushes with low molecular weight and grafting density

Temperature-sensitive poly(N-isopropylacrylamide) (PNIPAAm) brushes with different molecular weights M(n) and grafting densities σ were prepared by the "grafting-to" method. Changes in their physicochemical properties according to temperature were investigated with the help of in situ spectroscopic ellipsometry and in situ attenuated total reflection Fourier-transform infrared (ATR-FTIR) spectroscopy. Brush criteria indicate a transition between a brush conformation below the lower critical solution temperature (LCST) and an intermediate to mushroom conformation above the LCST. By in situ ellipsometry distinct changes in the brush layer parameters (wet thickness, refractive index, buffer content) were observed. A broadening of the temperature region with maximum deswelling occurred with decreasing grafting density. The brush layer properties were independent of the grafting density below the LCST, but showed a virtually monotonic behavior above the LCST. The midtemperature ?(half) of the deswelling process increased with increasing grafting density. Thus grafting density-dependent design parameters for such functional films were presented. For the first time, ATR-FTIR spectroscopy was used to monitor segment density and hydrogen bonding changes of these very thin PNIPAAm brushes as a function of temperature based on significant variations of the methyl stretching, Amide I, as well as Amide II bands with respect to intensity and wavenumber position. No dependence on M(n) and σ in the wavenumber shift of these bands above the LCST was found. The temperature profile of these band intensities and thus segment density was found to be rather step-like, exceeding temperatures around the LCST, while the respective profile of their wavenumber positions suggested continuous structural and hydration processes. Remaining buffer amounts and residual intermolecular segment/water interaction in the collapsed brushes above the LCST could be confirmed by both in situ methods.     

The attenuated ray transform for connections and Higgs fields

We show that for a simple surface with boundary the attenuated ray transform in the presence of a unitary connection and a skew-Hermitian Higgs field is injective modulo the natural obstruction for functions and vector fields. We also show that the connection and the Higgs field are uniquely determined by the scattering relation modulo a gauge transformation. The proofs involve a Pestov type energy identity for connections together with holomorphic gauge transformations which arrange the curvature of the connection to have definite sign.     

A uniqueness theorem for an inverse boundary value problem in electrical prospection

We show that a near constant conductivity of a two-dimensional body can be uniquely determined by steady state direct current measurements at the boundary. Mathematically, we show that the coefficient γ in the operator ?.γ? is uniquely determined by its Dirichlet integrals.     

Concurrence and Foliations Induced by Some 1-Qubit Channels

We start with a short introduction to the roof concept. An elementary discussion of phase-damping channels shows the role of antilinear operators in representing their concurrences. A general expression for some concurrences is derived. We apply it to 1-qubit channels of length 2, getting the induced foliations of the state space, the optimal decompositions, and the entropy of a state with respect to these channels. For amplitude-damping channels one obtains an expression for the Holevo capacity allowing for easy numerical calculations.     

Characterization and `Source-Receiver' Continuation of Seismic Reflection Data

In reflection seismology one places sources and receivers on the Earth's surface. The source generates elastic waves in the subsurface, that are reflected where the medium properties, stiffness and density, vary discontinuously. In the field, often, there are obstructions to collect seismic data for all source-receiver pairs desirable or needed for data processing and application of inverse scattering methods. Typically, data are measured on the Earth's surface. We employ the term data continuation to describe the act of computing data that have not been collected in the field. Seismic data are commonly modeled by a scattering operator developed in a high-frequency, single scattering approximation. We initially focus on the determination of the range of the forward scattering operator that models the singular part of the data in the mentioned approximation. This encompasses the analysis of the properties of, and the construction of, a minimal elliptic projector that projects a space of distributions on the data acquisition manifold to the range of the mentioned scattering operator. This projector can be directly used for the purpose of seismic data continuation, and is derived from the global parametrix of a homogeneous pseudodifferential equation the solution of which coincides with the range of the scattering operator. We illustrate the data continuation by a numerical example. This research was supported in part under NSF CMG grant EAR-0417891. Partly supported by a John Simon Guggenheim fellowship.     

Global identifiability for an inverse problem for the Schrödinger equation in a magnetic field

Partially supported by NSF Grant DMS-9123742