Order parameters and orientation distributions of solution adsorbed and microcontact printed cytochrome c protein films on glass and ITO

The structure of solution adsorbed and microcontact printed (muCP) cytochrome c (cyt c) films on glass and indium tin oxide (ITO) was investigated using attenuated total reflectance (ATR) and total internal reflectance fluorescence (TIRF) spectroscopies to determine the orientation of the heme groups in the films. The second and fourth order parameters of the heme as well as information on the angle between the absorption and emission dipoles of the heme, gamma, were experimentally determined. The order parameters of the heme are related to the order parameters of the protein molecule using the known angle between the heme plane and the electrostatic dipole moment of the cyt c protein. The effect of the surface roughness of the substrates (glass and ITO) was also taken into account quantitatively using AFM data. Physically possible order parameters were obtained for the heme group in both solution adsorbed and muCP films, but not for the electrostatic dipole moment of the protein. In addition, the experimental values of {cos2 gamma} for immobilized zinc-substituted cyt c are greater than the values of {cos2 gamma} determined in viscous solutions, which could be an indication that the environment of the heme groups changes upon adsorption. The electron transfer behavior of solution adsorbed and muCP films on ITO, determined using electrochemical methods, is compared to their orientation distribution and surface coverage as determined by spectroscopic methods.     

Combination of polarized TIRF and ATR spectroscopies for determination of the second and fourth order parameters of molecular orientation in thin films and construction of an orientation distribution based on the maximum entropy method

This article describes two mathematical formalisms for the determination of the second and fourth order parameters of molecular films using optical spectroscopy. Method A uses polarized total internal reflection fluorescence (TIRF) to calculate the second and fourth order parameters, {P2(cos theta)} and {P4(cos theta)}, using an independently determined value for the angle between the absorption and emission dipoles, gamma. Method B uses {P2(cos theta)} obtained from attenuated total reflectance (ATR) data, along with polarized TIRF measurements to calculate {P4(cos theta)} and {cos2 gamma}. The choice of a specific method should rely on experimental considerations. We also present a method to separate the contributions of substrate surface roughness and dipole orientation with respect to the molecular axis from the spectroscopically determined second and fourth order parameters. Finally, a maximum entropy approach for construction of an orientation distribution from order parameters is compared with the commonly used delta and Gaussian distributions.     

Characterization of proton transport across a waveguide-supported lipid bilayer

Cellular energy transduction processes are often driven by transmembrane ion gradients, and numerous artificial biomembrane systems have been developed that allow for chemically or light-induced charge transport into/out of liposomes. Liposomal architectures, however, are not readily interfaced to a solid-state transducer. Formation of an ion gradient across a planar-supported membrane, "wired" to a substrate electrode, may ultimately allow utilization of the potential energy to drive other electrochemical processes. Described here is a novel conductive polymer/planar waveguide assembly that provides for highly sensitive transduction of proton transport across a planar-supported lipid bilayer (PSLB). A quinone proton shuttle is embedded in the PSLB, which is coupled to the planar optical waveguide electrode through a pH-sensitive, self-assembled conductive polymer film. Interfacial potential and absorbance changes in the conductive polymer film provide for sensitive characterization of transmembrane proton transport. The general and flexible nature of this architecture makes it adaptable to many different types of transmembrane transport chemistries, particularly light-activated systems.     

Effect of high-frequency modes and hot transitions on free energy gap dependence of charge recombination rate

The charge recombination (CR) dynamics of geminate ion pairs formed by excitation of the ground-state donor-acceptor complexes in polar solvent have been investigated within the framework of stochastic approach. It is shown that for low exergonic reactions these dynamics critically depend on the reorganization energy of intramolecular high-frequency mode. Even moderate reorganization energies (0.1-0.2 eV) significantly accelerate the excited-state population decay making it nearly exponential. In the solvent-controlled regime, the majority of the excited donor-acceptor complexes recombine at nonthermal (hot) stage when the nonequilibrium initial wave packet passes through a number of term crossings corresponding to the transitions with creation of several vibrational quanta. Analysis of this mechanism allows to conclude (i) the CR in viscous solvents proceeds much faster than the diffusive relaxation of solvent, (ii) under certain conditions, the CR rate becomes practically independent of the diffusive component of solvent relaxation which is determined by solvent viscosity, (iii) in contrast to predictions of Marcus theory, the CR rate decreases monotonically with the rise of reaction exergonicity even at small free energy gaps, in accordance with experimental results. Two semiquantitative approaches providing rather simple analytical expressions for the hot charge recombination dynamics are suggested. These approximations give a good reproduction of the excited-state decay in the wide area of model parameters.     

The Inverse Resonance Problem for Hermite Operators

In this paper the inverse resonance problem for the Hermite operator is investigated. The Hermite operator with the creation operator , the annihilation operator , and a finitely supported multiplication operator b, is an unbounded operator on ℓ ²(ℕ₀) having finitely many eigenvalues and infinitely many resonances (except for b=0, when there are no eigenvalues or resonances). It is shown that knowing the location of eigenvalues and resonances determines the potential b uniquely.      

Drawing 4-Pfaffian graphs on the torus

We say that a graph G is k-Pfaffian if the generating function of its perfect matchings can be expressed as a linear combination of Pfaffians of k matrices corresponding to orientations of G. We prove that 3-Pfaffian graphs are 1-Pfaffian, 5-Pfaffian graphs are 4-Pfaffian and that a graph is 4-Pfaffian if and only if it can be drawn on the torus (possibly with crossings) so that every perfect matching intersects itself an even number of times. We state conjectures and prove partial results for k>5. The author was supported in part by NSF under Grant No. DMS-0200595 and DMS-0701033.