Stochastic monotonicity and duality for continuous time Markov chains with general q-Matrix

The key problems in discussing stochastic monotonicity and duality for continuous time Markov chains are to give the criteria for existence and uniqueness and to construct the associated monotone processes in terms of their infinitesimal q -matrices. In their recent paper, Chen and Zhang [6] discussed these problems under the condition that the given q-matrix Q is conservative. The aim of this paper is to generalize their results to a more general case, i.e., the given q-matrix Q is not necessarily conservative. New problems arise 'in removing the conservative assumption. The existence and uniqueness criteria for this general case are given in this paper. Another important problem, the construction of all stochastically monotone Q-processes, is also considered.

Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

Salivary antimicrobial peptides (LL-37 and alpha-defensins HNP1-3), antimicrobial and IgA responses to prolonged exercise

There are many factors in mucosal secretions that contribute to innate immunity and the 'first line of defence' at mucosal surfaces. Few studies, however, have investigated the effects of exercise on many of these 'defence' factors. The aim of the present study was to determine the acute effects of prolonged exercise on salivary levels of selected antimicrobial peptides (AMP) that have not yet been studied in response to exercise (HNP1-3 and LL-37) in addition to immunoglobulin A (IgA). A secondary objective was to assess the effects of exercise on saliva antibacterial capacity. Twelve active men exercised on a cycle ergometer for 2.5 h at approximately 60% of maximal oxygen uptake. Unstimulated whole saliva samples were obtained before and after exercise. There was a significant decrease (P < 0.05) in salivary IgA:osmolality ratio, following exercise, but IgA concentration and secretion rate were unaltered. Salivary HNP1-3 and LL-37 concentrations (P < 0.01 and P < 0.05, respectively), concentration:osmolality ratios (P < 0.01) and secretion rates (P < 0.01) all increased following exercise. Salivary antibacterial capacity (against E. coli) did not change. The increased concentration of AMPs in saliva may confer some benefit to the 'first line of defence' and could result from synergistic compensation within the mucosal immune system and/or airway inflammation and epithelial damage. Further study is required to determine the significance of such changes on the overall 'defence' capacity of saliva and how this influences the overall risk for infection.

Effect of caffeine ingestion during prolonged exhaustive exercise on salivary immunoglobulin A, alpha-amylase and cortisol

Exercise can have deleterious effects on the secretion of salivary immunoglobulin A (s-IgA), which appears to be related to perturbations in sympatheticoadrenal activation (Teeuw et al., 2004). Caffeine, commonly used for its ergogenic properties is associated with increased sympathetic nervous system activity, and it has been previously shown that caffeine ingestion before intensive cycling enhances s-IgA responses during exercise (Bishop et al., 2006). Therefore, the aim of the present study was to examine the effect of a performance cereal bar, containing caffeine, before and during prolonged exhaustive cycling on exercise performance and the salivary secretion of IgA, alpha-amylase activity and cortisol. Using a randomised cross-over design and following a 10 – 12 hour overnight fast, 12 trained cyclists, mean (SEM) age: 21(1) yr; height: 179(2) cm; body mass: 73.6(2.5) kg; maximal oxygen uptake, VO2max: 57.9(1.2) completed 2.5 h of cycling at 60%VO2max (with regular water ingestion) on a stationary ergometer, which was followed by a ride to exhaustion at 75% VO2max. Immediately before exercise, and after 55 min and 115 min of exercise participants ingested a 0.9 MJ cereal bar containing 45 g carbohydrate, 5 g protein, 3 g fat and 100 mg of caffeine (CAF) or an isocaloric noncaffeine bar (PLA). Unstimulated timed saliva samples were collected immediately before exercise, after 70 min and 130 min of exercise, and immediately after the exhaustive exercise bout. Saliva was analysed for s-IgA, alpha-amylase activity and cortisol concentration. Saliva flow rates were determined to calculate the s-IgA secretion rate. Data were analysed using a 2-way repeated measures ANOVA and post-hoc t-tests with Holm Bonferroni adjustments applied where appropriate. Time to exhaustion was 35% longer in CAF compared with PLA ((2177 (0.2) vs 1615 (0.16) s; P < 0.05)). Saliva flow rate did not change significantly during the exercise protocol. Exercise was associated with elevations in s-IgA concentration (9% increase), s-IgA secretion rate (24% increase) and alpha-amylase activity (224% increase) post-exhaustion (P < 0.01), but there was no effect of CAF on these responses. Salivary cortisol concentration increased by 64% post-exhaustion in the CAF trial only (P < 0.05), indicating an increase in adrenal activity following caffeine ingestion. Values were 35.7 (5.5) and 19.6 (3.4) nmol/L post-exhaustion for CAF and PLA, respectively. These findings show that ingestion of a caffeine containing cereal bar during prolonged exhaustive cycling enhances endurance performance, increases salivary cortisol secretion post-exhaustion, but does not affect the exercise-induced increases in s-IgA or alpha-amylase activity.

Vibrational spectroscopic studies of the structure of di-amino acid peptides. Part II: cyclo(L-Asp-L-Asp) in the solid state and in aqueous solution

Solid-state protonated and N,O-deuterated Fourier transform infrared (IR) and Raman scattering spectra together with the protonated and deuterated Raman spectra in aqueous solution of the cyclic di-amino acid peptide cyclo(L-Asp-L-Asp) are reported. Vibrational band assignments have been made on the basis of comparisons with previously cited literature values for diketopiperazine (DKP) derivatives and normal coordinate analyses for both the protonated and deuterated species based upon DFT calculations at the B3-LYP/cc-pVDZ level of the isolated molecule in the gas phase. The calculated minimum energy structure for cyclo(L-Asp-L-Asp), assuming C-2 symmetry, predicts a boat conformation for the DKP ring with both the two L-aspartyl side chains being folded slightly above the ring. The C=O stretching vibrations have been assigned for the side-chain carboxylic acid group (e.g. at 1693 and 1670 cm(-1) in the Raman spectrum) and the cis amide I bands (e.g. at 1660 cm(-1) in the Raman spectrum). The presence of two bands for the carboxylic acid C=O stretching modes in the solid-state Raman spectrum can be accounted for by factor group splitting of the two nonequivalent molecules in a crystallographic unit cell. The cis amide II band is observed at 1489 cm(-1) in the solid-state Raman spectrum, which is in agreement with results for cyclic di-amino acid peptide molecules examined previously in the solid state, where the DKP ring adopts a boat conformation. Additionally, it also appears that as the molecular mass of the substituent on the C-alpha atom is increased, the amide II band wavenumber decreases to below 1500 cm(-1); this may be a consequence of increased strain on the DKP ring. The cis amide II Raman band is characterized by its relatively small deuterium shift (29 cm(-1)), which indicates that this band has a smaller N-H bending contribution than the trans amide II vibrational band observed for linear peptides.

IR/Raman spectroscopy and DFT calculations of cyclic di-amino acid peptides. Part III: comparison of solid state and solution structures of cyclo(L-Ser-L-Ser)

B3-LYP/cc-pVDZ calculations of the gas-phase structure and vibrational spectra of the isolated molecule cyclo(L-Ser-L-Ser), a cyclic di-amino acid peptide (CDAP), were carried out by assuming C-2 symmetry. It is predicted that the minimum-energy structure is a boat conformation for the diketopiperazine (DKP) ring with both L-Beryl side chains being folded slightly above the ring. An additional structure of higher energy (15.16 kJ mol(-1)) has been calculated for a DKP ring with a planar geometry, although in this case two fundamental vibrations have been calculated with imaginary wavenumbers. The reported X-ray crystallographic structure of cyclo(L-Ser-L-Ser), shows that the DKP ring displays a near-planar conformation, with both the two L-Beryl side chains being folded above the ring. It is hypothesized that the crystal packing forces constrain the DKP ring in a planar conformation and it is probable that the lower energy boat conformation may prevail in the aqueous environment. Raman scattering and Fourier-transform infrared (FT-IR) spectra of solid state and aqueous solution samples of cyclo(L-Ser-L-Ser) are reported and discussed. Vibrational band assignments have been made on the basis of comparisons with the calculated vibrational spectra and band wavenumber shifts upon deuteration of labile protons. The experimental Raman and IR results for solid-state samples show characteristic amide I vibrations which are split (Raman:1661 and 1687 cm(-1), IR:1666 and 1680 cm(-1)), possibly due to interactions between molecules in a crystallographic unit cell. The cis amide I band is differentiated by its deuterium shift of ~ 30 cm(-1), which is larger than that previously reported for trans amide I deuterium shifts. A cis amide II mode has been assigned to a Raman band located at 1520 cm(-1). The occurrence of this cis amide II mode at a wavenumber above 1500 cm(-1) concurs with results of previously examined CDAP molecules with low molecular weight substituents on the C-alpha atoms, and is also indicative of a relatively unstrained DKP ring.

The interaction of zinc oxide-based dental cements with aqueous solutions of potassium fluoride

The ability of zinc oxide-based dental cements (zinc phosphate and zinc polycarboxylate) to take up fluoride from aqueous solution has been studied. Only zinc phosphate cement was found to take up any measurable fluoride after 5 h exposure to the solutions. The zinc oxide filler of the zinc phosphate also failed to take up fluoride from solution. The key interaction for this uptake was thus shown to involve the phosphate groups of the set cement. However, whether this took the form of phosphate/fluoride exchange, or the formation of oxyfluoro-phosphate groups was not clear. Fluoride uptake followed radicaltime kinetics for about 2 h in some cases, but was generally better modelled by the Elovich equation, dq(t)/dt = alpha exp(-beta q(t)). Values for alpha varied from 3.80 to 2.48 x 10(4), and for beta from 7.19 x 10(-3) to 0.1946, though only beta showed any sort of trend, becoming smaller with increasing fluoride concentration. Fluoride was released from the zinc phosphate cements in processes that were diffusion based up to M(t)/M(infinity) of about 0.4. No further release occurred when specimens were placed in fresh volumes of deionised water. Only a fraction of the fluoride taken up was re-released, demonstrating that most of the fluoride taken up becomes irreversibly bound within the cement.