Tidal torques. A critical review of some techniques

We point out that the MacDonald formula for body-tide torques is valid only in the zeroth order of e/Q, while its time-average is valid in the first order. So the formula cannot be used for analysis in higher orders of e/Q. This necessitates corrections in the theory of tidal despinning and libration damping. We prove that when the inclination is low and phase lags are linear in frequency, the Kaula series is equivalent to a corrected version of the MacDonald method. The correction to MacDonald's approach would be to set the phase lag of the integral bulge proportional to the instantaneous frequency. The equivalence of descriptions gets violated by a nonlinear frequency-dependence of the lag. We explain that both the MacDonald- and Darwin-torque-based derivations of the popular formula for the tidal despinning rate are limited to low inclinations and to the phase lags being linear in frequency. The Darwin-torque-based derivation, though, is general enough to accommodate both a finite inclination and the actual rheology. Although rheologies with Q scaling as the frequency to a positive power make the torque diverge at a zero frequency, this reveals not the impossible nature of the rheology, but a flaw in mathematics, i.e., a common misassumption that damping merely provides lags to the terms of the Fourier series for the tidal potential. A hydrodynamical treatment (Darwin 1879) had demonstrated that the magnitudes of the terms, too, get changed. Reinstating of this detail tames the infinities and rehabilitates the "impossible" scaling law (which happens to be the actual law the terrestrial planets obey at low frequencies).Comment: arXiv admin note: sections 4 and 9 of this paper contain substantial text overlap with arXiv:0712.105

Crystal Structure of an Integron Gene Cassette-Associated Protein from Vibrio cholerae Identifies a Cationic Drug-Binding Module

Background The direct isolation of integron gene cassettes from cultivated and environmental microbial sources allows an assessment of the impact of the integron/gene cassette system on the emergence of new phenotypes, such as drug resistance or virulence. A structural approach is being exploited to investigate the modularity and function of novel integron gene cassettes. Methodology/Principal Findings We report the 1.8 A crystal structure of Cass2, an integron-associated protein derived from an environmental V. cholerae. The structure defines a monomeric beta-barrel protein with a fold related to the effector-binding portion of AraC/XylS transcription activators. The closest homologs of Cass2 are multi-drug binding proteins, such as BmrR. Consistent with this, a binding pocket made up of hydrophobic residues and a single glutamate side chain is evident in Cass2, occupied in the crystal form by polyethylene glycol. Fluorescence assays demonstrate that Cass2 is capable of binding cationic drug compounds with submicromolar affinity. The Cass2 module possesses a protein interaction surface proximal to its drug-binding cavity with features homologous to those seen in multi-domain transcriptional regulators. Conclusions/Significance Genetic analysis identifies Cass2 to be representative of a larger family of independent effector-binding proteins associated with lateral gene transfer within Vibrio and closely-related species. We propose that the Cass2 family not only has capacity to form functional transcription regulator complexes, but represents possible evolutionary precursors to multi-domain regulators associated with cationic drug compounds.National Health and Medical Research Council (Australia) (NHMRC grant 488502)National Institutes of Health (U.S.) (Grant GM62414-0 )Ontario. Ministry of Revenue (Challenge Fund

A seven-planet resonant chain in TRAPPIST-1

The TRAPPIST-1 system is the first transiting planet system found orbiting an ultra-cool dwarf star1. At least seven planets similar to Earth in radius were previously found to transit this host star2. Subsequently, TRAPPIST-1 was observed as part of the K2 mission and, with these new data, we report the measurement of an 18.77 d orbital period for the outermost transiting planet, TRAPPIST-1h, which was unconstrained until now. This value matches our theoretical expectations based on Laplace relations3 and places TRAPPIST-1h as the seventh member of a complex chain, with three-body resonances linking every member. We find that TRAPPIST-1h has a radius of 0.727 R⊕ and an equilibrium temperature of 169 K. We have also measured the rotational period of the star at 3.3 d and detected a number of flares consistent with a low-activity, middle-aged, late M dwarf