Hopf bifurcation and related stability problems for periodic differential systems

This paper deals with 2π-periodic one parameter differential systems in the plane. Those systems all admit the null solution which is asymptotically stable for a fixed value, say μ=0, and completely unstable for μ>0 small. We find that for the perturbed systems 2π-periodic solutions occur only if another parameter ε which regulates the angular velocity is involved. In any other case an annulus which is asimptotically stable replaces the 2π-periodic solutions

Energy dependence of infrared emission from azulene C–H stretching vibrations

New data are described on the energy dependence of infrared fluorescence (IRF) from the C–H stretch modes (∼3050 cm−1) of vibrationally excited azulene (C10H8). An optoacoustic method was used to measure the absorbed laser energy and determine the number of excited molecules, while time‐resolved infrared emission was recorded. The experimental uncertainties of ∼5% are much smaller than in previous work and the agreement between the experiments and the theory for the IRF intensity is excellent for total vibrational energies from 14 000 to 33 000 cm−1.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70442/2/JCPSA6-88-10-6211-1.pd

Phospholipase D-Dependent mTORC1 Activation by Glutamine

Glutamine, the conditionally essential amino acid and most abundant amino acid in human sera, is a key nutrient required for sustaining cell proliferation. Glutamine is essential for nucleotide, protein, and lipid synthesis, all of which are essential for cell proliferation. The mammalian target of rapamycin complex 1 (mTORC1) is a highly conserved protein complex that acts as a sensor of nutrients, relaying signals for the shift from catabolic to anabolic metabolism. While glutamine plays an important role in activating mTORC1, the mechanism is not completely clear. Here we describe a Rag-independent mechanism of mTORC1 activation by glutamine that is dependent on phospholipase D (PLD). PLD catalyzes the hydrolysis of phosphatidylcholine to generate phosphatidic acid (PA) – a metabolite required for the stability and activity of both mTORC1 and mTORC2. Suppressing the production of PA by PLD blocked mTORC1 activation by glutamine. It has been reported that glutamine stimulates mTORC1 through an amino acid transporter that exchanges glutamine for leucine. However, our data suggests that glutamine can stimulate PLD and mTORC1 independently of leucine, in an ADP-ribosylation factor 1 (Arf1), RalA, and Rheb-dependent manner. α-ketoglutarate, a downstream metabolite of glutamine, was able to rescue mTORC1 activation following glutamine deprivation and also required Arf1 and PLD, but not Rag GTPases. Collectively, our data describe a novel mechanism by which glutamine stimulates mTORC1 in a PLD-PA-dependent manner. This pathway runs parallel to the leucine-dependent, Rag-GTPase pathway for mTORC1 activation and likely represents a compensatory mechanism for glutamine to activate mTORC1 in the absence of leucine