Temperature and length scale dependence of hydrophobic effects and their possible implications for protein folding

The Lum–Chandler–Weeks theory of hydrophobicity [Lum, K., Chandler, D. & Weeks, J. D. (1999) J. Phys. Chem. 103, 4570–4577] is applied to treat the temperature dependence of hydrophobic solvation in water. The application illustrates how the temperature dependence for hydrophobic surfaces extending less than 1 nm differs significantly from that for surfaces extending more than 1 nm. The latter is the result of water depletion, a collective effect, that appears at length scales of 1 nm and larger. Because of the contrasting behaviors at small and large length scales, hydrophobicity by itself can explain the variable behavior of entropies of protein folding.

Five-fold symmetry in crystalline quasicrystal lattices

To demonstrate that crystallographic methods can be applied to index and interpret diffraction patterns from well-ordered quasicrystals that display non-crystallographic 5-fold symmetry, we have characterized the properties of a series of periodic two-dimensional lattices built from pentagons, called Fibonacci pentilings, which resemble aperiodic Penrose tilings. The computed diffraction patterns from periodic pentilings with moderate size unit cells show decagonal symmetry and are virtually indistinguishable from that of the infinite aperiodic pentiling. We identify the vertices and centers of the pentagons forming the pentiling with the positions of transition metal atoms projected on the plane perpendicular to the decagonal axis of quasicrystals whose structure is related to crystalline η phase alloys. The characteristic length scale of the pentiling lattices, evident from the Patterson (autocorrelation) function, is ∼τ2 times the pentagon edge length, where τ is the golden ratio. Within this distance there are a finite number of local atomic motifs whose structure can be crystallographically refined against the experimentally measured diffraction data.

Polarity and permeation profiles in lipid membranes

The isotropic 14N-hyperfine coupling constant, a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{o}^{N}}}\end{equation*}\end{document}, of nitroxide spin labels is dependent on the local environmental polarity. The dependence of a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{o}^{N}}}\end{equation*}\end{document} in fluid phospholipid bilayer membranes on the C-atom position, n, of the nitroxide in the sn-2 chain of a spin-labeled diacyl glycerophospholipid therefore determines the transmembrane polarity profile. The polarity variation in phospholipid membranes, with and without equimolar cholesterol, is characterized by a sigmoidal, trough-like profile of the form {1 + exp [(n − no)/λ]}−1, where n = no is the point of maximum gradient, or polarity midpoint, beyond which the free energy of permeation decreases linearly with n, on a characteristic length-scale, λ. Integration over this profile yields a corresponding expression for the permeability barrier to polar solutes. For fluid membranes without cholesterol, no ≈ 8 and λ ≈ 0.5–1 CH2 units, and the permeability barrier introduces an additional diffusive resistance that is equivalent to increasing the effective membrane thickness by 35–80%, depending on the lipid. For membranes containing equimolar cholesterol, no ≈ 9–10, and the total change in polarity is greater than for membranes without cholesterol, increasing the permeability barrier by a factor of 2, whereas the decay length remains similar. The permeation of oxygen into fluid lipid membranes (determined by spin-label relaxation enhancements) displays a profile similar to that of the transmembrane polarity but of opposite sense. For fluid membranes without cholesterol no ≈ 8 and λ ≈ 1 CH2 units, also for oxygen. The permeation profile for polar paramagnetic ion complexes is closer to a single exponential decay, i.e., no lies outside the acyl-chain region of the membrane. These results are relevant not only to the permeation of water and polar solutes into membranes and their permeabilities, but also to depth determinations of site-specifically spin-labeled protein residues by using paramagnetic relaxation agents.

Slip complexity in earthquake fault models.

We summarize studies of earthquake fault models that give rise to slip complexities like those in natural earthquakes. For models of smooth faults between elastically deformable continua, it is critical that the friction laws involve a characteristic distance for slip weakening or evolution of surface state. That results in a finite nucleation size, or coherent slip patch size, h*. Models of smooth faults, using numerical cell size properly small compared to h*, show periodic response or complex and apparently chaotic histories of large events but have not been found to show small event complexity like the self-similar (power law) Gutenberg-Richter frequency-size statistics. This conclusion is supported in the present paper by fully inertial elastodynamic modeling of earthquake sequences. In contrast, some models of locally heterogeneous faults with quasi-independent fault segments, represented approximately by simulations with cell size larger than h* so that the model becomes "inherently discrete," do show small event complexity of the Gutenberg-Richter type. Models based on classical friction laws without a weakening length scale or for which the numerical procedure imposes an abrupt strength drop at the onset of slip have h* = 0 and hence always fall into the inherently discrete class. We suggest that the small-event complexity that some such models show will not survive regularization of the constitutive description, by inclusion of an appropriate length scale leading to a finite h*, and a corresponding reduction of numerical grid size.

The nuclear region of the spiral galaxy M81.

Very-long-baseline radio interferometry images of the nuclear region of the nearby spiral galaxy M81 reveal the most compact galactic core outside the Galaxy of which the size has been determined: 700 x 300 astronomical units (AU). The observations exclude a starburst or supernova interpretation for the core. Instead they favor an active galactic nucleus. There is evidence for a northeastern jet bent by approximately 35 degrees over a length scale from 700 to 4000 AU. The jet is, on average, directed toward an extended emission region, probably a radio lobe, about 1 kiloparsec (kpc) away from the core. A corresponding emission region was found in the southwest at a distance of only 30 pc from the core. The observed jet is extremely stable and likely to be associated with a steady-state channel. There is no detectable motion along the jet beyond the nominal value of -60 +/- 60 km.s-1. The level of activities in the core region of M81 is intermediate between that of SgrA* and that of powerful radio galaxies and quasars.

Scale dependence in earthquake phenomena and its relevance to earthquake prediction.

The recent discovery of a low-velocity, low-Q zone with a width of 50-200 m reaching to the top of the ductile part of the crust, by observations on seismic guided waves trapped in the fault zone of the Landers earthquake of 1992, and its identification with the shear zone inferred from the distribution of tension cracks observed on the surface support the existence of a characteristic scale length of the order of 100 m affecting various earthquake phenomena in southern California, as evidenced earlier by the kink in the magnitude-frequency relation at about M3, the constant corner frequency for earthquakes with M below about 3, and the sourcecontrolled fmax of 5-10 Hz for major earthquakes. The temporal correlation between coda Q-1 and the fractional rate of occurrence of earthquakes in the magnitude range 3-3.5, the geographical similarity of coda Q-1 and seismic velocity at a depth of 20 km, and the simultaneous change of coda Q-1 and conductivity at the lower crust support the hypotheses that coda Q-1 may represent the activity of creep fracture in the ductile part of the lithosphere occurring over cracks with a characteristic size of the order of 100 m. The existence of such a characteristic scale length cannot be consistent with the overall self-similarity of earthquakes unless we postulate a discrete hierarchy of such characteristic scale lengths. The discrete hierarchy of characteristic scale lengths is consistent with recently observed logarithmic periodicity in precursory seismicity.

Subparsec-scale structure and evolution of Centaurus A (NGC5128).

We present a series of 8.4-GHz very-long-baseline radio interferometry images of the nucleus of Centaurus A (NGC5128) made with a Southern Hemisphere array, representing a 3.3-year monitoring effort. The nuclear radio jet is approximately 50 milliarcseconds in extent, or at the 3.5-megaparsec distance of NGC5128, approximately 1 parsec in length. Subluminal motion is seen and structural changes are observed on time scales shorter than 4 months. High-resolution observations at 4.8 and 8.4 GHz made in November 1992 reveal a complex morphology and allow us to unambiguously identify the self-absorbed core located at the southwestern end of the jet.