Stochastic processes induced by dichotomous markov noise: Some exact dynamical results

Stochastic processes defined by a general Langevin equation of motion where the noise is the non-Gaussian dichotomous Markov noise are studied. A non-FokkerPlanck master differential equation is deduced for the probability density of these processes. Two different models are exactly solved. In the second one, a nonequilibrium bimodal distribution induced by the noise is observed for a critical value of its correlation time. Critical slowing down does not appear in this point but in another one.

Approximation and support theorem for a wave equation in two space dimensions

We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space. The result is a consequence of an approximation theorem, in the convergence of probability, for equations obtained by smoothing the random noise. For some particular classes of coefficients, approximation in the Lp-norm for p¿1 is also proved.

Cognate microRNA-Gene Regulatory Networks Mediating Glioblastoma Oncogenic Properties

Malignant gliomas, including the most common and fatal form glioblastoma (GBM, WHO grade IV astrocytoma), remain a challenge to treat. In the United States and Europe, more than 30,000 patients per year are newly diagnosed with GBM. Despite ongoing trials, the best currently available multimodal treatment approaches include surgical resection followed by concomitant and adjuvant radiation (RT) and temozolomide (TMZ) therapy, resulting in a low median overall survival (OS) rate ranging from 12.2 - 15.9 months. The important role of genetic and epigenetic changes in DNA, RNA, and protein alteration as well as epigenetic changes secondary to the tumor microenvironment and outside selection pressure (therapeutic interventions), are increasingly being recognized. In GBM treatment, the focus is shifting toward a more patient-centered (personalized) therapy. In this regard, in particular, microRNAs are being increasingly studied. MicroRNAs are non¬protein coding small RNAs that serve as negative gene regulators by binding to a specific sequence in the promoter region of a target gene, thus regulating gene expression. A single microRNA potentially targets hundreds of genes; thus, microRNAs and their cognate target genes have important roles as tumor suppressors and oncogenes as well as regulators of various cancer- specific cellular features, such as proliferation, apoptosis, invasion, and metastasis. The identification of distinct microRNA-gene regulatory networks in GBM patients can be expected to provide novel therapeutic insights by identifying candidate patients for targeted therapies. To this end, in this work we identified and validated clinically relevant and meaningful novel gene- microRNA regulatory networks that correlated with MR tumor phenotypes, histopathology, and patient survival and response rates to therapy. - Le traitement des gliomes malins, y compris sous leur forme la plus commune et meurtrière, le glioblastome (GBM, ou astrocytome de grade IV selon l'OMS), demeure à ce jour un défi. Aux États-Unis et en Europe, un nouveau diagnostic de GBM est prononcé dans plus de 30Ό00 cas par an. En dépit de tests en cours, les meilleures approches thérapeutiques combinées actuellement disponibles comprennent la résection chirurgicale de la tumeur, suivie d'une radiothérapie adjuvante ainsi que d'un traitement au temozolomide (RT/TMZ), thérapies dont résulte une médiane de survie globale basse (overall survival, OS), comprise entre 12.2 et 15.9 mois. On reconnaît de plus en plus le rôle majeur de l'ADN, de l'ARN et de l'altération des protéines ainsi que des modifications épigénétiques, secondaires par rapport au microenvironnement de la tumeur et à la pression de sélection extérieure (les interventions thérapeutiques). Dans le traitement du GBM, le centre d'intérêt se déplace vers une thérapie centrée sur le cas individuel du patient. Dans ce but, en particulier les microARN sont de plus en plus analysés. Les microARN sont de petits ARN non-codants (les protéines) qui servent de régulateurs négatifs de gènes en s'attachant à une séquence spécifique dans la région promotrice d'un gène-cible, régulant ainsi l'expression du gène. Un seul microARN cible potentiellement des centaines de gènes; on a ainsi découvert que les microARN et leurs gènes-cibles apparentés ont une fonction importante en tant que suppresseurs de tumeurs et d'oncogènes, ainsi que comme régulateurs de diverses caractéristiques cellulaires spécifiques du cancer, comme la prolifération, l'apoptose, l'invasion et la métastase. On peut s'attendre à ce que l'identification de réseaux microARN régulateurs de gènes, distincts selon les patients de GBM, fournisse une approche thérapeutique inédite par la détermination des patients susceptibles de réagir favorablement à des thérapies ciblées.

Research resource: the dynamic transcriptional profile of sertoli cells during the progression of spermatogenesis.

Sertoli cells (SCs), the only somatic cells within seminiferous tubules, associate intimately with developing germ cells. They not only provide physical and nutritional support but also secrete factors essential to the complex developmental processes of germ cell proliferation and differentiation. The SC transcriptome must therefore adapt rapidly during the different stages of spermatogenesis. We report comprehensive genome-wide expression profiles of pure populations of SCs isolated at 5 distinct stages of the first wave of mouse spermatogenesis, using RNA sequencing technology. We were able to reconstruct about 13 901 high-confidence, nonredundant coding and noncoding transcripts, characterized by complex alternative splicing patterns with more than 45% comprising novel isoforms of known genes. Interestingly, roughly one-fifth (2939) of these genes exhibited a dynamic expression profile reflecting the evolving role of SCs during the progression of spermatogenesis, with stage-specific expression of genes involved in biological processes such as cell cycle regulation, metabolism and energy production, retinoic acid synthesis, and blood-testis barrier biogenesis. Finally, regulatory network analysis identified the transcription factors endothelial PAS domain-containing protein 1 (EPAS1/Hif2α), aryl hydrocarbon receptor nuclear translocator (ARNT/Hif1β), and signal transducer and activator of transcription 1 (STAT1) as potential master regulators driving the SC transcriptional program. Our results highlight the plastic transcriptional landscape of SCs during the progression of spermatogenesis and provide valuable resources to better understand SC function and spermatogenesis and its related disorders, such as male infertility.

Stochastic approximation methods in stochastic optimization

Stochastic approximation methods for stochastic optimization are considered. Reviewed the main methods of stochastic approximation: stochastic quasi-gradient algorithm, Kiefer-Wolfowitz algorithm and adaptive rules for them, simultaneous perturbation stochastic approximation (SPSA) algorithm. Suggested the model and the solution of the retailer's profit optimization problem and considered an application of the SQG-algorithm for the optimization problems with objective functions given in the form of ordinary differential equation.

Une nouvelle approche computationnelle pour la découverte des sites de fixation de facteurs de transcription à l’ADN, adaptée aux données de ChIP-chip et de ChIP-séquençage

Les facteurs de transcription sont des protéines spécialisées qui jouent un rôle important dans différents processus biologiques tel que la différenciation, le cycle cellulaire et la tumorigenèse. Ils régulent la transcription des gènes en se fixant sur des séquences d’ADN spécifiques (éléments cis-régulateurs). L’identification de ces éléments est une étape cruciale dans la compréhension des réseaux de régulation des gènes. Avec l’avènement des technologies de séquençage à haut débit, l’identification de tout les éléments fonctionnels dans les génomes, incluant gènes et éléments cis-régulateurs a connu une avancée considérable. Alors qu’on est arrivé à estimer le nombre de gènes chez différentes espèces, l’information sur les éléments qui contrôlent et orchestrent la régulation de ces gènes est encore mal définie. Grace aux techniques de ChIP-chip et de ChIP-séquençage il est possible d’identifier toutes les régions du génome qui sont liées par un facteur de transcription d’intérêt. Plusieurs approches computationnelles ont été développées pour prédire les sites fixés par les facteurs de transcription. Ces approches sont classées en deux catégories principales: les algorithmes énumératifs et probabilistes. Toutefois, plusieurs études ont montré que ces approches génèrent des taux élevés de faux négatifs et de faux positifs ce qui rend difficile l’interprétation des résultats et par conséquent leur validation expérimentale. Dans cette thèse, nous avons ciblé deux objectifs. Le premier objectif a été de développer une nouvelle approche pour la découverte des sites de fixation des facteurs de transcription à l’ADN (SAMD-ChIP) adaptée aux données de ChIP-chip et de ChIP-séquençage. Notre approche implémente un algorithme hybride qui combine les deux stratégies énumérative et probabiliste, afin d’exploiter les performances de chacune d’entre elles. Notre approche a montré ses performances, comparée aux outils de découvertes de motifs existants sur des jeux de données simulées et des jeux de données de ChIP-chip et de ChIP-séquençage. SAMD-ChIP présente aussi l’avantage d’exploiter les propriétés de distributions des sites liés par les facteurs de transcription autour du centre des régions liées afin de limiter la prédiction aux motifs qui sont enrichis dans une fenêtre de longueur fixe autour du centre de ces régions. Les facteurs de transcription agissent rarement seuls. Ils forment souvent des complexes pour interagir avec l’ADN pour réguler leurs gènes cibles. Ces interactions impliquent des facteurs de transcription dont les sites de fixation à l’ADN sont localisés proches les uns des autres ou bien médier par des boucles de chromatine. Notre deuxième objectif a été d’exploiter la proximité spatiale des sites liés par les facteurs de transcription dans les régions de ChIP-chip et de ChIP-séquençage pour développer une approche pour la prédiction des motifs composites (motifs composés par deux sites et séparés par un espacement de taille fixe). Nous avons testé ce module pour prédire la co-localisation entre les deux demi-sites ERE qui forment le site ERE, lié par le récepteur des œstrogènes ERα. Ce module a été incorporé à notre outil de découverte de motifs SAMD-ChIP.

A mathematical model of the sterol regulatory element binding protein 2 cholesterol biosynthesis pathway

Cholesterol is one of the key constituents for maintaining the cellular membrane and thus the integrity of the cell itself. In contrast high levels of cholesterol in the blood are known to be a major risk factor in the development of cardiovascular disease. We formulate a deterministic nonlinear ordinary differential equation model of the sterol regulatory element binding protein 2 (SREBP-2) cholesterol genetic regulatory pathway in an hepatocyte. The mathematical model includes a description of genetic transcription by SREBP-2 which is subsequently translated to mRNA leading to the formation of 3-hydroxy-3-methylglutaryl coenzyme A reductase (HMGCR), a main precursor of cholesterol synthesis. Cholesterol synthesis subsequently leads to the regulation of SREBP-2 via a negative feedback formulation. Parameterised with data from the literature, the model is used to understand how SREBP-2 transcription and regulation affects cellular cholesterol concentration. Model stability analysis shows that the only positive steady-state of the system exhibits purely oscillatory, damped oscillatory or monotic behaviour under certain parameter conditions. In light of our findings we postulate how cholesterol homestasis is maintained within the cell and the advantages of our model formulation are discussed with respect to other models of genetic regulation within the literature.

Inferring Contagion in Regulatory Networks

Several gene regulatory network models containing concepts of directionality at the edges have been proposed. However, only a few reports have an interpretable definition of directionality. Here, differently from the standard causality concept defined by Pearl, we introduce the concept of contagion in order to infer directionality at the edges, i.e., asymmetries in gene expression dependences of regulatory networks. Moreover, we present a bootstrap algorithm in order to test the contagion concept. This technique was applied in simulated data and, also, in an actual large sample of biological data. Literature review has confirmed some genes identified by contagion as actually belonging to the TP53 pathway.

Density-Profile Processes Describing Biological Signaling Networks: Almost Sure Convergence to Deterministic Trajectories

We introduce jump processes in R(k), called density-profile processes, to model biological signaling networks. Our modeling setup describes the macroscopic evolution of a finite-size spin-flip model with k types of spins with arbitrary number of internal states interacting through a non-reversible stochastic dynamics. We are mostly interested on the multi-dimensional empirical-magnetization vector in the thermodynamic limit, and prove that, within arbitrary finite time-intervals, its path converges almost surely to a deterministic trajectory determined by a first-order (non-linear) differential equation with explicit bounds on the distance between the stochastic and deterministic trajectories. As parameters of the spin-flip dynamics change, the associated dynamical system may go through bifurcations, associated to phase transitions in the statistical mechanical setting. We present a simple example of spin-flip stochastic model, associated to a synthetic biology model known as repressilator, which leads to a dynamical system with Hopf and pitchfork bifurcations. Depending on the parameter values, the magnetization random path can either converge to a unique stable fixed point, converge to one of a pair of stable fixed points, or asymptotically evolve close to a deterministic orbit in Rk. We also discuss a simple signaling pathway related to cancer research, called p53 module.

Dynamic hedging with stocastic differential utility

In this paper we study the dynamic hedging problem using three different utility specifications: stochastic differential utility, terminal wealth utility, and we propose a particular utility transformation connecting both previous approaches. In all cases, we assume Markovian prices. Stochastic differential utility, SDU, impacts the pure hedging demand ambiguously, but decreases the pure speculative demand, because risk aversion increases. We also show that consumption decision is, in some sense, independent of hedging decision. With terminal wealth utility, we derive a general and compact hedging formula, which nests as special all cases studied in Duffie and Jackson (1990). We then show how to obtain their formulas. With the third approach we find a compact formula for hedging, which makes the second-type utility framework a particular case, and show that the pure hedging demand is not impacted by this specification. In addition, with CRRA- and CARA-type utilities, the risk aversion increases and, consequently the pure speculative demand decreases. If futures price are martingales, then the transformation plays no role in determining the hedging allocation. We also derive the relevant Bellman equation for each case, using semigroup techniques.

A Higher order and stable method for the numerical integration of Random Differential Equations

Trabalho apresentado no Congresso Nacional de Matemática Aplicada à Indústria, 18 a 21 de novembro de 2014, Caldas Novas - Goiás

HTRIdb: an open-access database for experimentally verified human transcriptional regulation interactions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

MKK3/6-p38 MAPK negatively regulates murine MMP-13 gene expression induced by IL-1 beta and TNF-alpha in immortalized periodontal ligament fibroblasts

Matrix metalloprotease-13 (MMP-13) or collagenase-3 is involved in a number of pathologic processes such as tumor metastasis and angiogenesis, osteoarthritis, rheumatoid arthritis and periodontal diseases. These conditions are associated with extensive degradation of both connective tissue and bone. This report examines gene regulation mechanisms and signal transduction pathways involved in Mmp-13 expression induced by proinflammatory cytokines in periodontal ligament (PDL) fibroblasts. Mmp-13 mRNA expression was increased 10.7 and 9.5 fold after stimulation with IL-1 beta (5 ng/mL) and TNF-alpha (10 ng/mL), respectively. However, inhibition of p38 MAPKinase with SB203580 resulted in significant (p < 0.001) induction (23.2 and 18.1 fold, respectively) of Mmp-13 mRNA as assessed by real time PCR. Negative regulation of IL-1 induced Mmp-13 expression was confirmed by inhibiting p38 MAPK gene expression with siRNA. Transient transfection of dominant negative forms of MKK3 and MKK6 also resulted in increased levels of Mmp-13 mRNA after IL-1 beta stimulation. Mmp-13 mRNA expression induced by TNF-alpha was decreased by JNK and ERK inhibition. Western blot and zymogram analysis indicated that Mmp-13 protein expression induced by the proinflammatory cytokines were also upregulated by inhibition of p38 MAPK. Reporter gene experiments using stable cell lines harboring 660-bp sequence of the murine Mmp-13 proximal promoter indicated that transcriptional mechanisms were at least partially involved in this negative regulation of Mmp-13 expression by p38 MAPK and upstream MKK3/6. These results suggest a negative transcriptional regulatory mechanism mediated by p38 MAPK and upstream MKK3/6 on Mmp-13 expression induced by proinflammatory cytokines in PDL fibroblasts. (c) 2005 Elsevier B.V./International Society of Matrix Biology. All rights reserved.

Comparative analysis of noncoding sequences of orthologous bovine and human gene pairs

Genomic sequence comparison across species has enabled the elucidation of important coding and regulatory sequences encoded within DNA. Of particular interest are the noncoding regulatory sequences, which influence gene transcriptional and posttranscriptional processes. A phylogenetic footprinting strategy was employed to identify noncoding conservation patterns of 39 human and bovine orthologous genes. Seventy-three conserved noncoding sequences were identified that shared greater than 70% identity over at least 100 bp. Thirteen of these conserved sequences were also identified in the mouse genome. Evolutionary conservation of noncoding sequences across diverse species may have functional significance, and these conserved sequences may be good candidates for regulatory elements.

O gene PHF21B como candidato a predisposição familia em familial em cânceres de cabeça e pescoço

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)