Modulational instability of co-propagating internal wavetrains under rotation.

Weakly-nonlinear unidirectional long internal waves in a non-rotating frame are well described by the Korteweg-de Vries equation (KdV). Within the KdV framework, all isolated monochromatic wavetrains are stable to modulational instability. However, analysis of a coupled nonlinear Schrödinger equation system (CNLS) has shown that all systems of two co-propagating monochromatic wavetrains in the KdV are modulationally unstable. To take into account the effect of the background rotation of the Earth on long internal waves, this analysis is extended here to derive the CNLS for the rotation-modified KdV, or Ostrovsky, equation. Rotation stabilises wavetrain pairs when the wavelengths of both waves comprising the wavetrains are longer than the linear wave with maximum group velocity. The particular case when the wavetrains have different wavenumbers but the same linear group speed is emphasised.

Whitham modulation theory for the Ostrovsky equation.

This paper derives the Whitham modulation equations for the Ostrovsky equation. The equations are then used to analyse localized cnoidal wavepacket solutions of the Ostrovsky equation in the weak rotation limit. The analysis is split into two main parameter regimes: the Ostrovsky equation with normal dispersion relevant to typical oceanic parameters and the Ostrovsky equation with anomalous dispersion relevant to strongly sheared oceanic flows and other physical systems. For anomalous dispersion a new steady, symmetric cnoidal wavepacket solution is presented. The new wavepacket can be represented as a solution of the modulation equations and an analytical solution for the outer solution of the wavepacket is given. For normal dispersion the modulation equations are used to describe the unsteady finite-amplitude wavepacket solutions produced from the rotation-induced decay of a Korteweg-de Vries solitary wave. Again, an analytical solution for the outer solution can be given. The centre of the wavepacket closely approximates a train of solitary waves with the results suggesting that the unsteady wavepacket is a localized, modulated cnoidal wavetrain. The formation of wavepackets from solitary wave initial conditions is considered, contrasting the rapid formation of the packets in anomalous dispersion with the slower formation of unsteady packets under normal dispersion.

ATP-binding cassette transporter G8 gene as a determinant of apolipoprotein B-100 kinetics in overweight men.

OBJECTIVE: We examined the influence of genetic variation of the ATP-binding cassette (ABC) transporter G8 on apolipoprotein B (apoB) kinetics in overweight/obese men. METHODS AND RESULTS: Very low-density lipoprotein (VLDL) and low-density lipoprotein (LDL) apoB kinetics were determined in 47 men (body mass index 32+/-3 kg/m2) using stable isotope and multicompartmental modeling to estimate production rate (PR), fractional catabolic rate (FCR), and VLDL to LDL-apoB conversion. Relative to the wild-type (400TT), subjects carrying the ABCG8 400K allele had significantly decreased plasma concentrations of triglycerides, sitosterol, and campesterol, lower PR of VLDL-apoB, and higher VLDL to LDL-apoB conversion (P<0.05). The PR and FCR of LDL-apoB were also significantly higher with 400K allele (P<0.05). No association was found with ABCG8 D19H. Compared with APOE2 or APOE3, APOE4 carriers had significantly higher plasma LDL-cholesterol concentrations and lower LDL-apoB FCR. During multiple regression analysis including age, homeostasis model assessment score, plasma concentrations of sitosterol, and lathosterol, ABCG8 and apoE genotypes were independent determinants of VLDL-apoB PR and LDL-apoB FCR, respectively (P<0.05). CONCLUSIONS: Variation in the ABC transporter G8 appears to independently influence the metabolism of apoB-containing lipoproteins in overweight/obese subjects. This may have therapeutic implications for the management of dyslipidemia in these subjects.

Wave-packet formation at the zero-dispersion point in the Gardner-Ostrovsky equation.

The long-time effect of weak rotation on an internal solitary wave is the decay into inertia-gravity waves and the eventual emergence of a coherent, steadily propagating, nonlinear wave packet. There is currently no entirely satisfactory explanation as to why these wave packets form. Here the initial value problem is considered within the context of the Gardner-Ostrovsky, or rotation-modified extended Korteweg-de Vries, equation. The linear Gardner-Ostrovsky equation has maximum group velocity at a critical wave number, often called the zero-dispersion point. It is found here that a nonlinear splitting of the wave-number spectrum at the zero-dispersion point, where energy is shifted into the modulationally unstable regime of the Gardner-Ostrovsky equation, is responsible for the wave-packet formation. Numerical comparisons of the decay of a solitary wave in the Gardner-Ostrovsky equation and a derived nonlinear Schrödinger equation at the zero-dispersion point are used to confirm the spectral splitting.

Four novel mutations in APOB causing heterozygous and homozygous familial hypobetalipoproteinemia.

Familial hypobetalipoproteinemia (FHBL) is a rare codominant disorder of lipoprotein metabolism characterized by low levels of low-density lipoprotein (LDL) cholesterol and apolipoprotein (apo) B. Heterozygotes for FHBL have less-than-half normal LDL-cholesterol and apoB concentrations, whereas homozygotes have extremely low or undetectable LDL-cholesterol and apoB levels. These reductions in LDL-cholesterol and apoB have been suggested to provide FHBL subjects with resistance to atherosclerosis. FHBL can be caused by mutations in the APOB gene on chromosome 2. We present four novel mutations and one previously described mutation in APOB causing FHBL in five families. Immunoblotting and DNA sequencing were used to characterize the novel mutation apoB-40.3 (c.5564_5565insC) and the previously reported mutation apoB-80.5 (c.11040T>G). The apoB-6.9 (c.1018_1025del) and apoB-25.8 (c.3600T>A) mutations were identified by DNA sequence analysis, as variants shorter than apoB-31 are not detectable in plasma. A fifth mutation, the splice variant c.82+1G>A, was identified by sequencing and was found in a homozygous subject. In approximately 50% of the FHBL subjects, plasma alanine aminotransferase concentrations were mildly increased, suggestive of fatty liver. All affected FHBL subjects had low to low-normal serum vitamin E concentrations, highlighting the important and recognized relationship between lipid and vitamin E concentrations.