Spectral properties of the tandem Jackson network, seen as a quasi-birth-and-death process

Quasi-birth-and-death (QBD) processes with infinite “phase spaces” can exhibit unusual and interesting behavior. One of the simplest examples of such a process is the two-node tandem Jackson network, with the “phase” giving the state of the first queue and the “level” giving the state of the second queue. In this paper, we undertake an extensive analysis of the properties of this QBD. In particular, we investigate the spectral properties of Neuts’s R-matrix and show that the decay rate of the stationary distribution of the “level” process is not always equal to the convergence norm of R. In fact, we show that we can obtain any decay rate from a certain range by controlling only the transition structure at level zero, which is independent of R. We also consider the sequence of tandem queues that is constructed by restricting the waiting room of the first queue to some finite capacity, and then allowing this capacity to increase to infinity. We show that the decay rates for the finite truncations converge to a value, which is not necessarily the decay rate in the infinite waiting room case. Finally, we show that the probability that the process hits level n before level 0 given that it starts in level 1 decays at a rate which is not necessarily the same as the decay rate for the stationary distribution.

The novel mitochondrial gene arrangement of the cattle tick, Boophilus microplus: Fivefold tandem repetition of a coding region

We sequenced across all of the gene boundaries in the mitochondrial genome of the cattle tick, Boophilus microplus, to determine the arrangement of its genes. The mtDNA of B. microplus has a coding region, composed of tRNA(Glu) and 60 bp of the 3' end of ND1, that is repeated five times. Boophilus microplus is the first coelomate animal known to have more than two copies of a coding sequence. The mitochondrial genome of B, microplus has other unusual features, including (1) reduced T arms in tRNAs, (2) an AT bias in codon use, (3) two control regions that have evolved in concert, (4) three gene rearrangements, and (5) a stem-loop between tRNA(Gln) and tRNA(Phe). The short T arms and small control regions (CRs) of B. microplus and other ticks suggest strong selection for small genomes. Imprecise termination of replication beyond its origin, which can account for the evolution of tandem repeats of coding regions in other mitochondrial genomes, cannot explain the evolution of the fivefold repeated sequence in the mitochondrial genome of B. microplus. Instead, slipped-strand mispairing or recombination are the most plausible explanations for the evolution of these tandem repeats.

Quantification of free mycophenolic acid by high-performance liquid chromatography-atmospheric pressure chemical ionisation tandem mass spectrometry

To facilitate the investigation of free mycophenolic acid concentrations we developed a high-performance liquid chromatography tandem mass spectrometry method using indomethacin as an internal standard. Free drug was isolated from plasma samples (500 mul) using ultrafiltration, The analytes were extracted from the ultrafiltrate (200 mul) using C-18 solid-phase extraction. Detection was by selected reactant monitoring of mycophenolic acid (m/z 318.9-->190.9) and the internal standard (m/z 356.0-->297.1) with an atmospheric pressure chemical ionisation interface. The total chromatographic analysis time was 12 min. The method was found to be linear over the range investigated, 2.5-200 mug/l (r>0.990, n=6). The relative recovery of the method for the control samples studied (7.5, 40.0 and 150 mug/l) ranged from 95 to 104%. The imprecision of the method, expressed in terms of intra- and inter-day coefficients of variation, was

A sensitive and specific assay for glutathione with potential application to glutathione disulphide, using high-performance liquid chromatography-tandem mass spectrometry

We have utilised the combination of sensitivity and specificity afforded by coupling high-performance liquid chromatography (HPLC) to a tandem mass spectrometer (MS-MS) to produce an assay which is suitable for assaying glutathione (GSH) concentrations in liver tissue. The sensitivity suggests it may also be suitable for extrahepatic tissues, The method has been validated for GSH using mouse liver samples and also allows the assay of GSSG. The stability of GSH under conditions relevant to the assay has been determined. A 20-mul amount of a diluted methanol extract of tissue is injected with detection limits of 0.2 pmol for GSH and 2 pmol for GSSG. The HPLC uses an Altima C-18 (150X4.6 mm, 5 mum) column at 35 degreesC. Chromatography utilises a linear gradient from 0 to 10% methanol in 0.1% formic acid over 5 min, with a final isocratic stage holding at 10% methanol for 5 min. Total flow rate is 0.8 ml/min. The transition from the M+H ion (308.1 m/z for GSH, and 613.3 m/z for GSSG) to the 162.0 m/z (GSH) and 355.3 m/z (GSSG) fragments are monitored. (C) 2001 Elsevier Science B.V. All rights reserved.

Efficient simulation of a Tandem Jackson Network

The two-node tandem Jackson network serves as a convenient reference model for the analysis and testing of different methodologies and techniques in rare event simulation. In this paper we consider a new approach to efficiently estimate the probability that the content of the second buffer exceeds some high level L before it becomes empty, starting from a given state. The approach is based on a Markov additive process representation of the buffer processes, leading to an exponential change of measure to be used in an importance sampling procedure. Unlike changes of measures proposed and studied in recent literature, the one derived here is a function of the content of the first buffer. We prove that when the first buffer is finite, this method yields asymptotically efficient simulation for any set of arrival and service rates. In fact, the relative error is bounded independent of the level L; a new result which is not established for any other known method. When the first buffer is infinite, we propose a natural extension of the exponential change of measure for the finite buffer case. In this case, the relative error is shown to be bounded (independent of L) only when the second server is the bottleneck; a result which is known to hold for some other methods derived through large deviations analysis. When the first server is the bottleneck, experimental results using our method seem to suggest that the relative error is bounded linearly in L.

Quantification and stability of everolimus (SDZ RAD) in human blood by high-performance liquid chromatography-electrospray tandem mass spectrometry

We report here a validated method for the quantification of a new immunosuppressant drug, everolimus (SDZ RAD), using HPLC-tandem mass spectrometry. Whole blood samples (500 mul) were prepared by protein precipitation, followed by C-18 solid-phase extraction. Mass spectrometric detection was by selected reaction monitoring with an electrospray interface operating in positive ionization mode. The assay was linear from 0.5 to 100 mug/l (r(2) > 0.996, n = 9). The analytical recovery and inter-day imprecision, determined using whole blood quality control samples (n = 5) at 0.5, 1.2, 20.0, and 75.0 mug/l, was 100.3-105.4% and less than or equal to7.6%, respectively. The assay had a mean relative recovery of 94.8 +/- 3.8%. Extracted samples were stable for up to 24 h. Fortified everolimus blood samples were stable at -80 degreesC for at least 8 months and everolimus was found to be stable in blood when taken through at least three freeze-thaw cycles. The reported method provides accurate, precise and specific measurement of everolimus in blood over a wide analytical range and is currently supporting phase 11 and III clinical trials. (C) 2002 Elsevier Science B.V. All rights reserved.

The measurement of nicotine in human plasma by high-performance liquid chromatography-electrospray-tandem mass spectrometry

The authors describe a reverse-phase high-performance liquid chromatography-electrospray-tandem mass spectrometry method for the measurement of nicotine in human plasma. Samples (500 muL) with added deuterium-labeled d(3)-nicotine as an internal standard (IS) were treated with a 2-step process of ether extraction (6 mL) followed by back-extraction into 0.1% formic acid (50 muL). Chromatography was performed on a phenyl Novapak column with a mobile phase consisting of 50% 10 mM ammonium fortriate (pH 3.3) and acetonitrile (50:50, vol/vol). A flow rate of 0.2 mL/min resulted in a total analysis time of 5 minutes per sample. Mass spectrometric detection was by selected reactant monitoring (nicotine m/z 163.2 --> 130.2; IS m/z 166.2 --> 87.2). The assay was linear from 0.5 to 100 mug/L (r > 0.993, n = 9). The accuracy and imprecision of the method for quality control sampleswere 87.5% to 113% and < 10.2%, respectively. Interday accuracy and imprecision at the limit of quantification (0.5 mug/L) was 113% and 7.2% (n = 4). The process efficiency for nicotine in plasma was > 75%. The method described has good process efficiency, stabilized nicotine, avoided concentration steps, and most importantly minimized potential contamination. Further, we have established that water-based standards and controls are interchangeable with plasma-based samples. This method was used successfully to measure the pharmacokinetic profiles of subjects involved in the development of an aerosol inhalation drug delivery system.

Simultaneous determination of morphine, oxycodone, morphine-3-glucuronide, and noroxycodone concentrations in rat serum by high performance liquid chromatography-electrospray ionization-tandem mass spectrometry

An assay using high performance liquid chromatography (HPLC)-electrospray ionization-tandem mass spectrometry (ESI-MS-MS) was developed for simultaneously determining concentrations of morphine, oxycodone, morphine-3-glucuronide, and noroxycodone, in 50 mul samples of rat serum. Deuterated (d(3)) analogues of each compound were used as internal standards. Samples were treated with acetonitrile to precipitate plasma proteins: acetonitrile was removed from the supernatant by centrifugal evaporation before analysis. Limits of quantitation (ng/ml) and their between-day accuracy and precision (%deviation and %CV) were-morphine, 3.8 (4.3% and 7.6%); morphine-3-glucuronide, 5.0 (4.5% and 2.9%); oxycodone, 4.5 (0.4% and 9.3%); noroxycodone, 5.0 (8.5% and 4.6%). (C) 2004 Elsevier B.V. All rights reserved.

Matrix effects: The Achilles heel of quantitative high-performance liquid chromatography-electrospray-tandem mass spectrometry

High-performance liquid chromatography coupled by an electrospray ion source to a tandem mass spectrometer (HPLC-EST-MS/ MS) is the current analytical method of choice for quantitation of analytes in biological matrices. With HPLC-ESI-MS/MS having the characteristics of high selectivity, sensitivity, and throughput, this technology is being increasingly used in the clinical laboratory. An important issue to be addressed in method development, validation, and routine use of HPLC-ESI-MS/MS is matrix effects. Matrix effects are the alteration of ionization efficiency by the presence of coeluting substances. These effects are unseen in the chromatograrn but have deleterious impact on methods accuracy and sensitivity. The two common ways to assess matrix effects are either by the postextraction addition method or the postcolumn infusion method. To remove or minimize matrix effects, modification to the sample extraction methodology and improved chromatographic separation must be performed. These two parameters are linked together and form the basis of developing a successful and robust quantitative HPLC-EST-MS/MS method. Due to the heterogenous nature of the population being studied, the variability of a method must be assessed in samples taken from a variety of subjects. In this paper, the major aspects of matrix effects are discussed with an approach to address matrix effects during method validation proposed. (c) 2004 The Canadian Society of Clinical Chemists. All rights reserved.

Measurement and stability of FTY720 in human whole blood by high-performance liquid chromatography-atmospheric pressure chemical ionization-tandem mass spectrometry

We report here a validated method for the quantification of a new immunosuppressant drug FTY720, using HPLC-tandem mass spectrometry. Whole blood samples (500 mu l) were subjected to liquid-liquid extraction, in the presence of an internal standard (Y-32919). Mass spectrometric detection was by selected reaction monitoring with an atmospheric pressure chemical ionization source in positive ionization mode (FTY720: m/z 308.3 -> 255.3). The assay was linear from 0.2 to 25 mu g/l (r(2) > 0.997, n = 5). The inter- and intra-day analytical recovery and imprecision for quality control samples (0.5, 7 and 15 mu g/l) were 95.8-103.2 and < 5.5%, respectively. At the lower limit of quantification (0.2 mu g/l) the interand intra-day analytical recovery was 99.0-102.8% with imprecision of < 7.6% (n = 5). The assay had a mean relative recovery of 100.5 +/- 5.8% (n = 15). Extracted samples were stable for 16 h. IFTY720 quality control samples were stable at room temperature for 16 h at 4 degrees C for at least 8 days and when taken through at least three freeze-thaw cycles. In conclusion, the method described displays analytical performance characteristics that are suitable for pharmacokinetic studies in humans. (c) 2006 Elsevier B.V. All rights reserved.