We present a collection of molecular dynamics computer simulation studies on a model protein-membrane system, namely a cytochrome c monolayer attached to an organic self-assembled monolayer (SAM). Modifications of the system are explored, including the polarity of the SAM endgroups, the amount of water present for hydration, and the coordination number of the heme iron atom. Various structural parameters are measured, e.g., the protein radius of gyration and eccentricity, the deviation of the protein backbone from the x-ray crystal structure, the orientation of the protein relative to the SAM surface, and the profile structures of the SAM, protein, and water. The polar SAM appears to interact more strongly with the protein than does the nonpolar SAM. Increased hydration of the system tends to reduce the effects of other parameters. The choice of iron coordination model has a significant effect on the protein structure and the heme orientation. The overall protein structure is largely conserved, except at each end of the sequence and in one loop region. The SAM structure is only perturbed in the region of its direct contact with the protein. Our calculations are in reasonably good agreement with experimental measurements (polarized optical absorption/emission spectroscopy, x-ray interferometry, and neutron interferometry).
We examine the ability of gravitational lens time delays to reveal complex structure in lens potentials. In a previous paper, we predicted how the time delay between the bright pair of images in a "fold" lens scales with the image separation, for smooth lens potentials. Here we show that the proportionality constant increases with the quadrupole moment of the lens potential, and depends only weakly on the position of the source along the caustic. We use Monte Carlo simulations to determine the range of time delays that can be produced by realistic smooth lens models consisting of isothermal ellipsoid galaxies with tidal shear. We can then identify outliers as "time delay anomalies." We find evidence for anomalies in close image pairs in the cusp lenses RX J1131−1231 and B1422+231. The anomalies in RX J1131−1231 provide strong evidence for substructure in the lens potential, while at this point the apparent anomalies in B1422+231 mainly indicate that the time delay measurements need to be improved. We also find evidence for time delay anomalies in larger-separation image pairs in the fold lenses, B1608+656 and WFI 2033−4723, and the cusp lens RX J0911+0551. We suggest that these anomalies are caused by some combination of substructure and a complex lens environment. Finally, to assist future monitoring campaigns we use our smooth models with shear to predict the time delays for all known four-image lenses.
Gravitational lensing provides a unique and powerful probe of the mass distributions of distant galaxies. Four‐image lens systems with fold and cusp configurations have two or three bright images near a critical point. Within the framework of singularity theory, we derive analytic relations that are satisfied for a light source that lies a small but finite distance from the astroid caustic of a four‐image lens. Using a perturbative expansion of the image positions, we show that the time delay between the close pair of images in a fold lens scales with the cube of the image separation, with a constant of proportionality that depends on a particular third derivative of the lens potential. We also apply our formalism to cusp lenses, where we develop perturbative expressions for the image positions, magnifications and time delays of the images in a cusp triplet. Some of these results were derived previously for a source asymptotically close to a cusp point, but using a simplified form of the lens equation whose validity may be in doubt for sources that lie at astrophysically relevant distances from the caustic. Along with the work of Keeton, Gaudi & Petters, this paper demonstrates that perturbation theory plays an important role in theoretical lensing studies.
Polarized x-ray absorption fine structure (XAFS) spectroscopy has been performed in fluorescence mode under total external reflection conditions on frozen hydrated single monolayers of yeast cytochrome c (YCC). The protein molecules were vectorially oriented within the monolayer by tethering their naturally occurring and unique surface cysteine residues to the sulfhydryl-endgroups at the surface of a mixed organic self-assembled monolayer, itself covalently attached to an ultrapure silicon wafer. The sulfhydryl-endgroups were isolated by dilution with either methyl- or hydroxyl-endgroups, producing macroscopically nonpolar or uncharged-polar soft surfaces, respectively. Independent information on the heme-plane orientation relative to the monolayer plane was obtained experimentally via optical linear dichroism. The polarized XAFS data have been analyzed both qualitatively and by a global mapping approach limited to systematically altering the various iron-ligand distances within a model for the local atomic environment of the heme prosthetic group, and comparing the theoretically generated XAFS spectra with those obtained experimentally. A similar analysis of unpolarized XAFS data from a frozen solution of YCC was performed using either the heme environment from the NMR solution or the x-ray crystallographic data for YCC as the model structure. All resulting iron-ligand distances were then used in molecular dynamics (MD) computer simulations of YCC in these three systems to investigate the possible effects of anisotropic ligand motions on the fits of the calculated to the experimental XAFS spectra.
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