On the arithmetic of Krull monoids with infinite cyclic class group

Let $H$ be a Krull monoid with infinite cyclic class group $G$ and let $G_P \subset G$ denote the set of classes containing prime divisors. We study under which conditions on $G_P$ some of the main finiteness properties of factorization theory--such as local tameness, the finiteness and rationality of the elasticity, the structure theorem for sets of lengths, the finiteness of the catenary degree, and the existence of monotone and of near monotone chains of factorizations--hold in $H$. In many cases, we derive explicit characterizations

Inverse Additive Problems for Minkowski Sumsets II

The Brunn-Minkowski Theorem asserts that $\mu_d(A+B)^{1/d}\geq \mu_d(A)^{1/d}+\mu_d(B)^{1/d}$ for convex bodies $A,\,B\subseteq \R^d$, where $\mu_d$ denotes the $d$-dimensional Lebesgue measure. It is well-known that equality holds if and only if $A$ and $B$ are homothetic, but few characterizations of equality in other related bounds are known. Let $H$ be a hyperplane. Bonnesen later strengthened this bound by showing $$\mu_d(A+B)\geq (M^{1/(d-1)}+N^{1/(d-1)})^{d-1}(\frac{\mu_d(A)}{M}+\frac{\mu_d(B)}{N}),$$ where $M=\sup\{\mu_{d-1}((\mathbf x+H)\cap A)\mid \mathbf x\in \R^d\}$ and $N=\sup\{\mu_{d-1}((\mathbf y+H)\cap B)\mid \mathbf y\in \R^d\}$. Standard compression arguments show that the above bound also holds when $M=\mu_{d-1}(\pi(A))$ and $N=\mu_{d-1}(\pi(B))$, where $\pi$ denotes a projection of $\mathbb R^d$ onto $H$, which gives an alternative generalization of the Brunn-Minkowski bound. In this paper, we characterize the cases of equality in this later bound, showing that equality holds if and only if $A$ and $B$ are obtained from a pair of homothetic convex bodies by `stretching' along the direction of the projection, which is made formal in the paper. When $d=2$, we characterize the case of equality in the former bound as well

MRI sensing based on the displacement of paramagnetic ions from chelated complexes

We introduce a mechanism for ion sensing by MRI in which analytes compete with paramagnetic ions for binding to polydentate chelating agents. Displacement of the paramagnetic ions results in alteration of solvent interaction parameters and consequent changes in relaxivity and MRI contrast. The MRI changes can be tuned by the choice of chelator. As an example, we show that calcium-dependent displacement of Mn[superscript 2+] ions bound to EGTA and BAPTA results in a T[subscript 1]-weighted MRI signal increase, whereas displacement from calmodulin results in a signal decrease. The changes are ion selective and can be explained using relaxivity theory. The ratio of T[subscript 2] to T[subscript 1] relaxivity is also calcium-dependent, indicating the feasibility of “ratiometric” analyte detection, independent of the probe concentration. Measurement of paramagnetic ion displacement effects could be used to determine analyte ion concentrations with spatial resolution in opaque specimens.National Institutes of Health (U.S.) (grant DP2-OD2441)National Institutes of Health (U.S.) (grant R01-GM65519)McGovern Institute for Brain Research at MIT. Neurotechnology (MINT) Progra

Imaging Mitochondrial Calcium Fluxes with Fluorescent Probes and Single- or Two-Photon Confocal Microscopy

The concentration of calcium ions in the mitochondria has been shown to affect its function, modulating respiratory activity at low levels and causing lethal damage at high concentrations. The rhodamine series of dyes can be used to measure mitochondrial calcium concentration, but the reliability of measurements depends upon correct partitioning of the dye within to the mitochondria. Methods are described to aid verification and quantification of the mitochondrial calcium concentration using single- or two-photon confocal microscopy. The method of linear unmixing to separate fluorescent signals based on either differing excitation or emission spectra is outlined and for the purposes of illustration is applied to the separation of rhod-2 signals originating from the dye within the mitochondria and nucleoli

Dose-linearity of the pharmacokinetics of an intravenous [C-14]midazolam microdose in children

Aims Drug disposition in children may vary from adults due to age-related variation in drug metabolism. Microdose studies present an innovation to study pharmacokinetics (PK) in paediatrics; however, they should be used only when the PK is dose linear. We aimed to assess dose linearity of a [C-14]midazolam microdose, by comparing the PK of an intravenous (IV) microtracer (a microdose given simultaneously with a therapeutic midazolam dose), with the PK of a single isolated microdose. Methods Preterm to 2-year-old infants admitted to the intensive care unit received [C-14]midazolam IV as a microtracer or microdose, followed by dense blood sampling up to 36 hours. Plasma concentrations of [C-14]midazolam and [C-14]1-hydroxy-midazolam were determined by accelerator mass spectrometry. Noncompartmental PK analysis was performed and a population PK model was developed. Results Of 15 infants (median gestational age 39.4 [range 23.9-41.4] weeks, postnatal age 11.4 [0.6-49.1] weeks), 6 received a microtracer and 9 a microdose of [C-14]midazolam (111 Bq kg(-1); 37.6 ng kg(-1)). In a 2-compartment PK model, bodyweight was the most significant covariate for volume of distribution. There was no statistically significant difference in any PK parameter between the microdose and microtracer, nor in the area under curve ratio [C-14]1-OH-midazolam/[C-14]midazolam, showing the PK of midazolam to be linear within the range of the therapeutic and microdoses. Conclusion Our data support the dose linearity of the PK of an IV [C-14]midazolam microdose in children. Hence, a [C-14]midazolam microdosing approach may be used as an alternative to a therapeutic dose of midazolam to study developmental changes in hepatic CYP3A activity in young children

Dose-linearity of the pharmacokinetics of an intravenous [C-14]midazolam microdose in children

Aims Drug disposition in children may vary from adults due to age-related variation in drug metabolism. Microdose studies present an innovation to study pharmacokinetics (PK) in paediatrics; however, they should be used only when the PK is dose linear. We aimed to assess dose linearity of a [C-14]midazolam microdose, by comparing the PK of an intravenous (IV) microtracer (a microdose given simultaneously with a therapeutic midazolam dose), with the PK of a single isolated microdose. Methods Preterm to 2-year-old infants admitted to the intensive care unit received [C-14]midazolam IV as a microtracer or microdose, followed by dense blood sampling up to 36 hours. Plasma concentrations of [C-14]midazolam and [C-14]1-hydroxy-midazolam were determined by accelerator mass spectrometry. Noncompartmental PK analysis was performed and a population PK model was developed. Results Of 15 infants (median gestational age 39.4 [range 23.9-41.4] weeks, postnatal age 11.4 [0.6-49.1] weeks), 6 received a microtracer and 9 a microdose of [C-14]midazolam (111 Bq kg(-1); 37.6 ng kg(-1)). In a 2-compartment PK model, bodyweight was the most significant covariate for volume of distribution. There was no statistically significant difference in any PK parameter between the microdose and microtracer, nor in the area under curve ratio [C-14]1-OH-midazolam/[C-14]midazolam, showing the PK of midazolam to be linear within the range of the therapeutic and microdoses. Conclusion Our data support the dose linearity of the PK of an IV [C-14]midazolam microdose in children. Hence, a [C-14]midazolam microdosing approach may be used as an alternative to a therapeutic dose of midazolam to study developmental changes in hepatic CYP3A activity in young children

Novel model of neuronal bioenergetics: postsynaptic utilization of glucose but not lactate correlates positively with Ca2+ signalling in cultured mouse glutamatergic neurons

We have previously investigated the relative roles of extracellular glucose and lactate as fuels for glutamatergic neurons during synaptic activity. The conclusion from these studies was that cultured glutamatergic neurons utilize glucose rather than lactate during NMDA (N-methyl-d-aspartate)-induced synaptic activity and that lactate alone is not able to support neurotransmitter glutamate homoeostasis. Subsequently, a model was proposed to explain these results at the cellular level. In brief, the intermittent rises in intracellular Ca2+ during activation cause influx of Ca2+ into the mitochondrial matrix thus activating the tricarboxylic acid cycle dehydrogenases. This will lead to a lower activity of the MASH (malate–aspartate shuttle), which in turn will result in anaerobic glycolysis and lactate production rather than lactate utilization. In the present work, we have investigated the effect of an ionomycin-induced increase in intracellular Ca2+ (i.e. independent of synaptic activity) on neuronal energy metabolism employing 13C-labelled glucose and lactate and subsequent mass spectrometric analysis of labelling in glutamate, alanine and lactate. The results demonstrate that glucose utilization is positively correlated with intracellular Ca2+ whereas lactate utilization is not. This result lends further support for a significant role of glucose in neuronal bioenergetics and that Ca2+ signalling may control the switch between glucose and lactate utilization during synaptic activity. Based on the results, we propose a compartmentalized CiMASH (Ca2+-induced limitation of the MASH) model that includes intracellular compartmentation of glucose and lactate metabolism. We define pre- and post-synaptic compartments metabolizing glucose and glucose plus lactate respectively in which the latter displays a positive correlation between oxidative metabolism of glucose and Ca2+ signalling

Functional maturation of isolated neural progenitor cells from the adult rat hippocampus

Although neural progenitor cells (NPCs) may provide a source of new neurons to alleviate neural trauma, little is known about their electrical properties as they differentiate. We have previously shown that single NPCs from the adult rat hippocampus can be cloned in the presence of heparan sulphate chains purified from the hippocampus, and that these cells can be pushed into a proliferative phenotype with the mitogen FGF2 [Chipperfield, H., Bedi, K.S., Cool, S.M. & Nurcombe, V. (2002) Int. J. Dev. Biol., 46, 661-670]. In this study, the active and passive electrical properties of both undifferentiated and differentiated adult hippocampal NPCs, from 0 to 12 days in vitro as single-cell preparations, were investigated. Sparsely plated, undifferentiated NPCs had a resting membrane potential of approximate to -90 mV and were electrically inexcitable. In > 70%, ATP and benzoylbenzoyl-ATP evoked an inward current and membrane depolarization, whereas acetylcholine, noradrenaline, glutamate and GABA had no detectable effect. In Fura-2-loaded undifferentiated NPCs, ATP and benzoylbenzoyl-ATP evoked a transient increase in the intracellular free Ca2+ concentration, which was dependent on extracellular Ca2+ and was inhibited reversibly by pyridoxalphosphate-6-azophenyl-2'-4'-disulphonic acid (PPADS), a P2 receptor antagonist. After differentiation, NPC-derived neurons became electrically excitable, expressing voltage-dependent TTX-sensitive Na+ channels, low- and high-voltage-activated Ca2+ channels and delayed-rectifier K+ channels. Differentiated cells also possessed functional glutamate, GABA, glycine and purinergic (P2X) receptors. Appearance of voltage-dependent and ligand-gated ion channels appears to be an important early step in the differentiation of NPCs