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We prove continuity of certain cost functions arising from optimal control of affine control systems. We give sharp sufficient conditions for this continuity. As an application, we prove a version of weak KAM theorem and consider the Aubry–Mather problems corresponding to these systems.

Background: Metabolic flux profiling based on the analysis of distribution of stable isotope tracer in metabolites is an important method widely used in cancer research to understand the regulation of cell metabolism and elaborate new therapeutic strategies. Recently, we developed software Isodyn, which extends the methodology of kinetic modeling to the analysis of isotopic isomer distribution for the evaluation of cellular metabolic flux profile under relevant conditions. This tool can be applied to reveal the metabolic effect of proapoptotic drug edelfosine in leukemia Jurkat cell line, uncovering the mechanisms of induction of apoptosis in cancer cells. Results: The study of 13C distribution of Jukat cells exposed to low edelfosine concentration, which induces apoptosis in ≤5% of cells, revealed metabolic changes previous to the development of apoptotic program. Specifically, it was found that low dose of edelfosine stimulates the TCA cycle. These metabolic perturbations were coupled with an increase of nucleic acid synthesis de novo, which indicates acceleration of biosynthetic and reparative processes. The further increase of the TCA cycle fluxes, when higher doses of drug applied, eventually enhance reactive oxygen species (ROS) production and trigger apoptotic program. Conclusion: The application of Isodyn to the analysis of mechanism of edelfosine-induced apoptosis revealed primary drug-induced metabolic changes, which are important for the subsequent initiation of apoptotic program. Initiation of such metabolic changes could be exploited in anticancer therapy. [ABSTRACT FROM AUTHOR]

A current trend in neuroscience research is the use of stable isotope tracers in order to address metabolic processes in vivo. The tracers produce a huge number of metabolite forms that differ according to the number and position of labeled isotopes in the carbon skeleton (isotopomers) and such a large variety makes the analysis of isotopomer data highly complex. On the other hand, this multiplicity of forms does provide sufficient information to address cell operation in vivo. By the end of last millennium, a number of tools have been developed for estimation of metabolic flux profile from any possible isotopomer distribution data. However, although well elaborated, these tools were limited to steady state analysis, and the obtained set of fluxes remained disconnected from their biochemical context. In this review we focus on a new numerical analytical approach that integrates kinetic and metabolic flux analysis. The related computational algorithm estimates the dynamic flux based on the time-dependent distribution of all possible isotopomers of metabolic pathway intermediates that are generated from a labeled substrate. The new algorithm connects specific tracer data with enzyme kinetic characteristics, thereby extending the amount of data available for analysis: it uses enzyme kinetic data to estimate the flux profile, and vice versa, for the kinetic analysis it uses in vivo tracer data to reveal the biochemical basis of the estimated metabolic fluxes. [ABSTRACT FROM AUTHOR]

Stearoyl-CoA desaturase (SCD) is a key enzyme in the conversion of stearate to oleate (C18:0 to C18:1), and palmitate to palmitoleate (C16:0 to C16:1). There are two mouse SCD genes (SCD1 and SCD2). While SCD 1 is the isoform of SCD highly expressed in the liver and adipose tissue, and its expression is induced during adipocyte differentiation with dexamethasone and insulin, SCD2 is constitutively expressed in preadipocytes. The objective of the study is to evaluate the effect of SCD inhibition on fatty acid composition and turnover in NIH3T3 preadipocytes. NIH3T3 preadipocytes were grown in culture for 72 hours with [U-[sup 13]C] stearate and [1, 2 [sup 13]C]-acetate with 1) DMSO or 2) 0.8 µM of SCD inhibitor 06811M1005 (generously provided by CompleGen, Inc.). Analysis of fatty acid mass isotopomers was performed by gas chromatography/mass spectroscopy (GCMS). Fatty acid composition and the desaturation indices were calculated from the gas chromatogram. In cells cultured with SCD inhibitor 06811M1005 in [U-[sup 13]C]-stearate and [1,2 [sup 13]C]-acetate, the desaturation index for C18:1 n-9 was significantly reduced by ∼30% (p<0.03). There was a reduction in the conversion of U-stearate to U-oleate from 64% to 38% (p<0.04) when SCD was inhibited. While 13C isotopomer enrichment of palmitate and stearate reached the same plateau levels in treated and untreated cells, 13C isotopomer enrichment of oleate in the treated cells was significantly lower than control suggesting reduced oleate turnover during the study period. We conclude: NIH3T3 preadipocytes differentiate either in the presence of dexamethasone and insulin or PPAR υ agonist into adipocytes with phenotypes having different expression of SCD1. SCD inhibitor 06811M 1005 probably acts equally on SCD1 and SCD2 in the preadipocytes resulting in a change in desaturation index. Contrary to the expectation of reduced de novo lipogenesis, SCD inhibition primarily reduced on the conversion of stearate to oleate and the turnover of oleate without affecting the uptake and de novo synthesis of palmitate or stearate. [ABSTRACT FROM AUTHOR]

XXY men (Klinefelter syndrome) are testosterone deficient, socially isolated, exhibit impaired gender identity, and may experience more homosexual behaviors. Here, we characterize social behaviors in a validated XXY mouse model to understand mechanisms. Sociability and gender preference were assessed by three-chambered choice tasks before and after castration and after testosterone replacement. Metabolomic activities of brain and blood were quantified through fractional synthesis rates of palmitate and ribose (GC-MS). XXY mice exhibit greater sociability than XY littermates, particularly for male mice. The differences in sociability disappear after matching androgen exposure. Intact XXY, compared with XY, mice prefer male mice odors when the alternatives are ovariectomized female mice odors, but they prefer estrous over male mice odors, suggesting that preference for male mice may be due to social, not sexual, cues. Castration followed by testosterone treatment essentially remove these preferences. Fractional synthesis rates of palmitate are higher in the hypothalamus, amygdala, and hippocampus of XXY compared with XY mice but not with ribose in these brain regions or palmitate in blood. Androgen ablation in XY mice increases fractional synthesis rates of fatty acids in the brain to levels indistinguishable from those in XXY mice. We conclude that intact XXY mice exhibit increased sociability, differences in gender preference for mice and their odors are due to social rather than sexual cues and, these differences are mostly related to androgen deficiency rather than genetics. Specific metabolic changes in brain lipids, which are also regulated by androgens, are observed in brain regions that are involved in these behaviors.

Prenatal nutrient restriction with intrauterine growth restriction (IUGR) alters basal and glucose-stimulated insulin response and hepatic metabolic adaptation. The effect of early intervention with insulin-sensitizing peroxisome proliferator-activated receptor gamma agonists was examined in the metabolically maladapted F(1) pregestational IUGR offspring with a propensity toward pregnancy-induced gestational diabetes. The effect of rosiglitazone maleate [RG; 11 micromol/day from postnatal day (PN) 21 to PN60] vs. placebo (PL) on metabolic adaptations in 2-mo-old F(1) female rats subjected to prenatal (IUGR), postnatal (PNGR), or pre- and postnatal (IUGR + PNGR) nutrient restriction was investigated compared with control (CON). RG vs. PL had no effect on body weight or plasma glucose concentrations but increased subcutaneous white and brown adipose tissue and plasma cholesterol concentrations in all three experimental groups. Glucose tolerance tests with a 1:1 mixture of [2-(2)H(2)]- and [6,6-(2)H(2)]glucose in RG IUGR vs. PL IUGR revealed glucose tolerance with a lower glucose-stimulated insulin release (GSIR) and suppressed endogenous hepatic glucose production (HGP) with no difference in glucose clearance (GC) and recycling (GR). RG PNGR, although similar to PL CON, was hyperglycemic vs. PL PNGR with reduced GR but no difference in the existent low GSIR, HGP, and GC. RG IUGR + PNGR overall was no different from the PL counterpart. Insulin tolerance tests revealed perturbed recovery to baseline from the exaggerated hypoglycemia in RG vs. the PL groups with the only exception being RG PNGR where further worsening of hypoglycemia over PL PNGR was minimal with full recovery to baseline. These observations support that early intervention with RG suppressed HGP in IUGR vs. PL IUGR, without increasing GSIR similar to that seen in CON. Although RG reversed PNGR to the PL CON metabolic state, no such insulin-sensitizing effect was realized in IUGR + PNGR.

The metabolism of [1, 2 (13)C(2)] glucose via the tricarboxylic acid (TCA) cycle yields a number of key glutamate mass isotopomers whose formation is a function of pyruvate carboxylase (PC) and pyruvate dehydrogenase (PDH). Analysis of the isotopomer distribution patterns was used to determine the relative flux of glucose entry into the TCA cycle through anaplerotic and oxidative pathways in the cerebral cortex of both uninjured and traumatically injured adult male rats. In the cerebral cortex of uninjured animals the PC/PDH ratio showed greater metabolism of glucose via pyruvate carboxylase, which is consistent with the notion that the majority of glucose taken up at rest is used as a substrate for anaplerotic processes and not as an energy source. While traumatic brain injury did not change the overall (13)C enrichment of glutamate indicating a continued oxidation of glucose, the PC/PDH ratio was reduced in the injured cortex at 3.5 h after injury. This suggests that glucose metabolism is primarily directed through pathways associated with energy production in the early postinjury period. By 24 h, the anaplerotic flux decreased and the PC/PDH ratio increased in both the injured and non-injured cortex indicating a switch away from energy production to pathways associated with anabolic and/or regenerative processes.