Doob-Martin compactification of a Markov chain for growing random words sequentially

We consider a Markov chain that iteratively generates a sequence of random finite words in such a way that the $n^{\mathrm{th}}$ word is uniformly distributed over the set of words of length $2n$ in which $n$ letters are $a$ and $n$ letters are $b$: at each step an $a$ and a $b$ are shuffled in uniformly at random among the letters of the current word. We obtain a concrete characterization of the Doob-Martin boundary of this Markov chain. Writing $N(u)$ for the number of letters $a$ (equivalently, $b$) in the finite word $u$, we show that a sequence $(u_n)_{n \in \mathbb{N}}$ of finite words converges to a point in the boundary if, for an arbitrary word $v$, there is convergence as $n$ tends to infinity of the probability that the selection of $N(v)$ letters $a$ and $N(v)$ letters $b$ uniformly at random from $u_n$ and maintaining their relative order results in $v$. We exhibit a bijective correspondence between the points in the boundary and ergodic random total orders on the set $\{a_1, b_1, a_2, b_2, \ldots \}$ that have distributions which are separately invariant under finite permutations of the indices of the $a'$s and those of the $b'$s. We establish a further bijective correspondence between the set of such random total orders and the set of pairs $(\mu,\nu)$ of diffuse probability measures on $[0,1]$ such that $\frac{1}{2}(\mu+\nu)$ is Lebesgue measure: the restriction of the random total order to $\{a_1, b_1, \ldots, a_n, b_n\}$ is obtained by taking $X_1, \ldots, X_n$ (resp. $Y_1, \ldots, Y_n$) i.i.d. with common distribution $\mu$ (resp. $\nu$), letting $(Z_1, \ldots, Z_{2n})$ be $\{X_1, Y_1, \ldots, X_n, Y_n\}$ in increasing order, and declaring that the $k^{\mathrm{th}}$ smallest element in the restricted total order is $a_i$ (resp. $b_j$) if $Z_k = X_i$ (resp. $Z_k = Y_j$).Comment: 24 pages, revised to deal with reviewer's comment

Overexpression of phospholipase D enhances Bcl-2 expression by activating STAT3 through independent activation of ERK and p38MAPK in HeLa cells

AbstractThe purpose of this study was to identify the role of phospholipase D (PLD) isozymes in Bcl-2 expression. Overexpression of PLD1 or PLD2 increased Bcl-2 expression and phosphatidic acid (PA), the product of PLDs, also upregulated Bcl-2 expression. Treatment with PA activated the phospholipase A2 (PLA2)/Gi/ERK1/2, RhoA/Rho-associated kinase (ROCK)/p38 MAPK, and Rac1/p38 MAPK pathways. PA-induced phosphorylation of ERK1/2 was attenuated by a PLA2 inhibitor (mepacrine) and, a Gi protein inhibitor (pertussis toxin, PTX). On the other hand, p38 MAPK phosphorylation was attenuated by a dominant negative Rac1 and a specific Rho-kinase inhibitor (Y-27632). These results suggest that PLA2/Gi acts at the upstream of ERK1/2, while Rac1 and RhoA/ROCK act upstream of p38 MAPK. We next, tried to determine which transcription factor is involved in PLD-related Bcl-2 expression. When signal transducer and activator of transcription 3 (STAT3) activity was blocked by a STAT3 specific siRNA, PA-induced Bcl-2 expression was remarkably decreased, suggesting that STAT3 is an essential transcription factor linking PLD to Bcl-2 upregulation. Taken together, these findings indicate that PLD acts as an important regulator in Bcl-2 expression by activating STAT3 involving the phosphorylation of Ser727 through the PLA2/Gi/ERK1/2, RhoA/ROCK/p38 MAPK, and Rac1/p38 MAPK pathways

Matrix Metalloproteinase-3 Causes Dopaminergic Neuronal Death through Nox1-Regenerated Oxidative Stress

In the present study we investigated the interplay between matrix metalloproteinase 3 (MMP3) and NADPH oxidase 1 (Nox1) in the process of dopamine (DA) neuronal death. We found that MMP3 activation causes the induction of Nox1 via mitochondrial reactive oxygen species (ROS) production and subsequently Rac1 activation, eventually leading to Nox1-derived superoxide generation in a rat DA neuronal N27 cells exposed to 6-OHDA. While a MMP3 inhibitor, NNGH, largely attenuated mitochondrial ROS and subsequent Nox1 induction, both apocynin, a putative Nox inhibitor and GKT137831, a Nox1 selective inhibitor failed to reduce 6-OHDA-induced mitochondrial ROS. However, both inhibitors for MMP3 and Nox1 similarly attenuated 6-OHDA-induced N27 cell death. RNAi-mediated selective inhibition of MMP3 or Nox1 showed that knockdown of either MMP3 or Nox1 significantly reduced 6-OHDA-induced ROS generation in N27 cells. While 6-OHDA-induced Nox1 was abolished by MMP3 knockdown, Nox1 knockdown did not alter MMP3 expression. Direct overexpression of autoactivated MMP3 (actMMP3) in N27 cells or in rat substantia nigra (SN) increased expression of Nox1. Selective knockdown of Nox1 in the SN achieved by adeno-associated virus-mediated overexpression of Nox1-specific shRNA largely attenuated the actMMP3-mediated dopaminergic neuronal loss. Furthermore, Nox1 expression was significantly attenuated in Mmp3 null mice treated with N-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP). Together we established novel molecular mechanisms underlying oxidative stress-mediated dopaminergic neuronal death in which MMP3 activation is a key upstream event that leads to mitochondrial ROS, Nox1 induction and eventual dopaminergic neuronal death. Our findings may lead to the development of novel therapeutic approach

Matrix Metalloproteinase-3 Causes Dopaminergic Neuronal Death through Nox1-Regenerated Oxidative Stress

In the present study we investigated the interplay between matrix metalloproteinase 3 (MMP3) and NADPH oxidase 1 (Nox1) in the process of dopamine (DA) neuronal death. We found that MMP3 activation causes the induction of Nox1 via mitochondrial reactive oxygen species (ROS) production and subsequently Rac1 activation, eventually leading to Nox1-derived superoxide generation in a rat DA neuronal N27 cells exposed to 6-OHDA. While a MMP3 inhibitor, NNGH, largely attenuated mitochondrial ROS and subsequent Nox1 induction, both apocynin, a putative Nox inhibitor and GKT137831, a Nox1 selective inhibitor failed to reduce 6-OHDA-induced mitochondrial ROS. However, both inhibitors for MMP3 and Nox1 similarly attenuated 6-OHDA-induced N27 cell death. RNAi-mediated selective inhibition of MMP3 or Nox1 showed that knockdown of either MMP3 or Nox1 significantly reduced 6-OHDA-induced ROS generation in N27 cells. While 6-OHDA-induced Nox1 was abolished by MMP3 knockdown, Nox1 knockdown did not alter MMP3 expression. Direct overexpression of autoactivated MMP3 (actMMP3) in N27 cells or in rat substantia nigra (SN) increased expression of Nox1. Selective knockdown of Nox1 in the SN achieved by adeno-associated virus-mediated overexpression of Nox1-specific shRNA largely attenuated the actMMP3-mediated dopaminergic neuronal loss. Furthermore, Nox1 expression was significantly attenuated in Mmp3 null mice treated with N-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP). Together we established novel molecular mechanisms underlying oxidative stress-mediated dopaminergic neuronal death in which MMP3 activation is a key upstream event that leads to mitochondrial ROS, Nox1 induction and eventual dopaminergic neuronal death. Our findings may lead to the development of novel therapeutic approach

Prediction of the Chemical Composition and Fermentation Parameters of Fresh Coarse Italian Ryegrass Haylage Using Near Infrared Spectroscopy

Italian ryegrass (Lolium multiflorum) is an annual forage grass species which is widely cultivated in South Korea. It grows extensively in the southern part of the country and is an important component of winter forage for livestock. Each year, in Korea, over one million hectares of Italian ryegrass is converted to round bale haylage. Quality control is an important field in forage utilization research and marketing, and involves the estimation of forage nutrient content. Wet chemistry is the traditional method used to analyze the nutrient content of forage. However, this technique is often destructive, expensive, and time consuming, and it is not suitable for real-time feedstuff analysis. Near infrared spectroscopy (NIRS), on the other hand, is an alternative technique that has several major advantages over traditional methods. The analysis of silage nutrient content, using NIR, conventionally includes the drying and milling of samples. However, these processes can lead to reduction of volatile acids, which are important components of silage. NIRS can be affected by spectral regions, drying and grinding methods, particle size, packing density and the temperature of samples (Reeves and Blosser, 1991). In order to obtain accurate NIRS results, sample preparation, and the measurement conditions of the calibration set and predicted samples, need to match. The objectives of this study were to (1) assess the usefulness of NIRS in determining the nutritional composition and fermentative parameters of fresh coarse samples of Italian ryegrass haylage, (2) assess the predictive value of various NIRS calibration models, and (3) explore cost-effective and time saving methods for forage quality estimation, in field populations

Cell type–dependent variation in paracrine potency determines therapeutic efficacy against neonatal hyperoxic lung injury

AbstractBackground aimsThe aim of this study was to determine the optimal cell type for transplantation to protect against neonatal hyperoxic lung injury. To this end, the in vitro and in vivo therapeutic efficacies and paracrine potencies of human umbilical cord blood–derived mesenchymal stromal cells (HUMs), human adipose tissue–derived mesenchymal stromal cells (HAMs) and human umbilical cord blood mononuclear cells (HMNs) were compared.MethodsHyperoxic injury was induced in vitro in A549 cells by challenge with H2O2. Alternatively, hyperoxic injury was induced in newborn Sprague-Dawley rats in vivo by exposure to hyperoxia (90% oxygen) for 14 days. HUMs, HAMs or HMNs (5 × 105 cells) were given intratracheally at postnatal day 5.ResultsHyperoxia-induced increases in in vitro cell death and in vivo impaired alveolarization were significantly attenuated in both the HUM and HAM groups but not in the HMN group. Hyperoxia impaired angiogenesis, increased the cell death and pulmonary macrophages and elevated inflammatory cytokine levels. These effects were significantly decreased in the HUM group but not in the HAM or HMN groups. The levels of human vascular endothelial growth factor and hepatocyte growth factor produced by donor cells were highest in HUM group, followed by HAM group and then HMN group.ConclusionsHUMs exhibited the best therapeutic efficacy and paracrine potency than HAMs or HMNs in protecting against neonatal hyperoxic lung injury. These cell type-dependent variations in therapeutic efficacy might be associated or mediated with the paracrine potency of the transplanted donor cells

Role of Neuronal NADPH Oxidase 1 in the Peri-Infarct Regions after Stroke

The molecular mechanism underlying the selective vulnerability of neurons to oxidative damage caused by ischemia-reperfusion (I/R) injury remains unknown. We sought to determine the role of NADPH oxidase 1 (Nox1) in cerebral I/R-induced brain injury and survival of newborn cells in the ischemic injured region. Male Wistar rats were subjected to 90 min middle cerebral artery occlusion (MCAO) followed by reperfusion. After reperfusion, infarction size, level of superoxide and 8-hydroxy-20-deoxyguanosine (8-oxo-2dG), and Nox1 immunoreactivity were determined. RNAi-mediated knockdown of Nox1 was used to investigate the role of Nox1 in I/R-induced oxidative damage, neuronal death, motor function recovery, and ischemic neurogenesis. After I/R, Nox1 expression and 8-oxo-2dG immunoreactivity was increased in cortical neurons of the peri-infarct regions. Both infarction size and neuronal death in I/R injury were significantly reduced by adeno-associated virus (AAV)-mediated transduction of Nox1 short hairpin RNA (shRNA). AAV-mediated Nox1 knockdown enhanced functional recovery after MCAO. The level of survival and differentiation of newborn cells in the peri-infarct regions were increased by Nox1 inhibition. Our data suggest that Nox-1 may be responsible for oxidative damage to DNA, subsequent cortical neuronal degeneration, functional recovery, and regulation of ischemic neurogenesis in the peri-infarct regions after stroke