Some Remarks on the Approximation of Transitional Density in Stochastic Differential Equations

Aijt-Sahalia (2002) introduced a method to estimate transitional probability densities of di®usion processes by means of Hermite expansions with coe±cients determined by means of Taylor series. This note describes a numerical procedure to ¯nd these coe±cients based on the calculation of moments. One advantage of this procedure is that it can be used e®ectively when the mathematical operations required to ¯nd closed-form expressions for these coe±cients are otherwise infeasible.

Numerical methods for second-order stochastic differential equations

We seek numerical methods for second‐order stochastic differential equations that reproduce the stationary density accurately for all values of damping. A complete analysis is possible for scalar linear second‐order equations (damped harmonic oscillators with additive noise), where the statistics are Gaussian and can be calculated exactly in the continuous‐time and discrete‐time cases. A matrix equation is given for the stationary variances and correlation for methods using one Gaussian random variable per timestep. The only Runge–Kutta method with a nonsingular tableau matrix that gives the exact steady state density for all values of damping is the implicit midpoint rule. Numerical experiments, comparing the implicit midpoint rule with Heun and leapfrog methods on nonlinear equations with additive or multiplicative noise, produce behavior similar to the linear case.

High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations

The pioneering work of Runge and Kutta a hundred years ago has ultimately led to suites of sophisticated numerical methods suitable for solving complex systems of deterministic ordinary differential equations. However, in many modelling situations, the appropriate representation is a stochastic differential equation and here numerical methods are much less sophisticated. In this paper a very general class of stochastic Runge-Kutta methods is presented and much more efficient classes of explicit methods than previous extant methods are constructed. In particular, a method of strong order 2 with a deterministic component based on the classical Runge-Kutta method is constructed and some numerical results are presented to demonstrate the efficacy of this approach.

Computational interrogation of cis-regulatory elements of genes that are common targets of luteotropin and luteolysin in the primate corpus luteum

The rapid recent increase in microarray-based gene expression studies in the corpus luteum (CL) utilizing macaque models gathered increasing volume of data in publically accessible microarray expression databases. Examining gene pathways in different functional states of CL may help to understand the factors that control luteal function and hence human fertility. Co-regulation of genes in microarray experiments may imply common transcriptional regulation by sequence-specific DNA-binding transcriptional factors. We have computationally analyzed the transcription factor binding sites (TFBS) in a previously reported macaque luteal microarray gene set (n = 15) that are common targets of luteotropin (luteinizing hormone (LH) and human chorionic gonadotropin (hCG)) and luteolysin (prostaglandin (PG) F-2 alpha). This in silico approach can reveal transcriptional networks that control these important genes which are representative of the interplay between luteotropic and luteolytic factors in the control of luteal function. Our computational analyses revealed 6 matrix families whose binding sites are significantly over-represented in promoters of these genes. The roles of these factors are discussed, which might help to understand the transcriptional regulatory network in the control of luteal function. These factors might be promising experimental targets for investigation of human luteal insufficiency. (C) 2012 Elsevier B.V. All rights reserved.

Differential and numerical models of hysteretic systems with stochastic and deterministic inputs

Many deterministic models with hysteresis have been developed in the areas of economics, finance, terrestrial hydrology and biology. These models lack any stochastic element which can often have a strong effect in these areas. In this work stochastically driven closed loop systems with hysteresis type memory are studied. This type of system is presented as a possible stochastic counterpart to deterministic models in the areas of economics, finance, terrestrial hydrology and biology. Some price dynamics models are presented as a motivation for the development of this type of model. Numerical schemes for solving this class of stochastic differential equation are developed in order to examine the prototype models presented. As a means of further testing the developed numerical schemes, numerical examination is made of the behaviour near equilibrium of coupled ordinary differential equations where the time derivative of the Preisach operator is included in one of the equations. A model of two phenotype bacteria is also presented. This model is examined to explore memory effects and related hysteresis effects in the area of biology. The memory effects found in this model are similar to that found in the non-ideal relay. This non-ideal relay type behaviour is used to model a colony of bacteria with multiple switching thresholds. This model contains a Preisach type memory with a variable Preisach weight function. Shown numerically for this multi-threshold model is a pattern formation for the distribution of the phenotypes among the available thresholds.

Predicting Cell Cycle Regulated Genes by Causal Interactions

The fundamental difference between classic and modern biology is that technological innovations allow to generate high-throughput data to get insights into molecular interactions on a genomic scale. These high-throughput data can be used to infer gene networks, e. g., the transcriptional regulatory or signaling network, representing a blue print of the current dynamical state of the cellular system. However, gene networks do not provide direct answers to biological questions, instead, they need to be analyzed to reveal functional information of molecular working mechanisms. In this paper we propose a new approach to analyze the transcriptional regulatory network of yeast to predict cell cycle regulated genes. The novelty of our approach is that, in contrast to all other approaches aiming to predict cell cycle regulated genes, we do not use time series data but base our analysis on the prior information of causal interactions among genes. The major purpose of the present paper is to predict cell cycle regulated genes in S. cerevisiae. Our analysis is based on the transcriptional regulatory network, representing causal interactions between genes, and a list of known periodic genes. No further data are used. Our approach utilizes the causal membership of genes and the hierarchical organization of the transcriptional regulatory network leading to two groups of periodic genes with a well defined direction of information flow. We predict genes as periodic if they appear on unique shortest paths connecting two periodic genes from different hierarchy levels. Our results demonstrate that a classical problem as the prediction of cell cycle regulated genes can be seen in a new light if the concept of a causal membership of a gene is applied consequently. This also shows that there is a wealth of information buried in the transcriptional regulatory network whose unraveling may require more elaborate concepts than it might seem at first.

Computer simulation of the stochastic transport equation

Trabalho apresentado no 37th Conference on Stochastic Processes and their Applications - July 28 - August 01, 2014 -Universidad de Buenos Aires

Balancing immunity and tolerance: genetic footprint of natural selection in the transcriptional regulatory region of HLA-G

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

The SUCEST-FUN regulatory network database: Designing an energy grass

Modern sugarcane cultivars are complex hybrids resulting from crosses among several Saccharum species. Traditional breeding methods have been employed extensively in different countries over the past decades to develop varieties with increased sucrose yield and resistance to pests and diseases. Conventional variety improvement, however, may be limited by the narrow pool of suitable genes. Thus, molecular genetics is seen as a promising tool to assist in the process of developing improved varieties. The SUCEST-FUN Project (http://sucest-fun.org) aims to associate function with sugarcane genes using a variety of tools, in particular those that enable the study of the sugarcane transcriptome. An extensive analysis has been conducted to characterise, phenotypically, sugarcane genotypes with regard to their sucrose content, biomass and drought responses. Through the analysis of different cultivars, genes associated with sucrose content, yield, lignin and drought have been identified. Currently, tools are being developed to determine signalling and regulatory networks in grasses, and to sequence the sugarcane genome, as well as to identify sugarcane promoters. This is being implemented through the SUCEST-FUN (http://sucest-fun.org) and GRASSIUS databases (http://grassius.org), the cloning of sugarcane promoters, the identification of cis-regulatory elements (CRE) using Chromatin Immunoprecipitation-sequencing (ChIP-Seq) and the generation of a comprehensive Signal Transduction and Transcription gene catalogue (SUCAST Catalogue).

Modeling gene expression regulatory networks with the sparse vector autoregressive model

Abstract Background To understand the molecular mechanisms underlying important biological processes, a detailed description of the gene products networks involved is required. In order to define and understand such molecular networks, some statistical methods are proposed in the literature to estimate gene regulatory networks from time-series microarray data. However, several problems still need to be overcome. Firstly, information flow need to be inferred, in addition to the correlation between genes. Secondly, we usually try to identify large networks from a large number of genes (parameters) originating from a smaller number of microarray experiments (samples). Due to this situation, which is rather frequent in Bioinformatics, it is difficult to perform statistical tests using methods that model large gene-gene networks. In addition, most of the models are based on dimension reduction using clustering techniques, therefore, the resulting network is not a gene-gene network but a module-module network. Here, we present the Sparse Vector Autoregressive model as a solution to these problems. Results We have applied the Sparse Vector Autoregressive model to estimate gene regulatory networks based on gene expression profiles obtained from time-series microarray experiments. Through extensive simulations, by applying the SVAR method to artificial regulatory networks, we show that SVAR can infer true positive edges even under conditions in which the number of samples is smaller than the number of genes. Moreover, it is possible to control for false positives, a significant advantage when compared to other methods described in the literature, which are based on ranks or score functions. By applying SVAR to actual HeLa cell cycle gene expression data, we were able to identify well known transcription factor targets. Conclusion The proposed SVAR method is able to model gene regulatory networks in frequent situations in which the number of samples is lower than the number of genes, making it possible to naturally infer partial Granger causalities without any a priori information. In addition, we present a statistical test to control the false discovery rate, which was not previously possible using other gene regulatory network models.

Systems Biology Approaches to Probe Gene Regulation in Bacteria

Mechanisms that allow pathogens to colonize the host are not the product of isolated genes, but instead emerge from the concerted operation of regulatory networks. Therefore, identifying components and the systemic behavior of networks is necessary to a better understanding of gene regulation and pathogenesis. To this end, I have developed systems biology approaches to study transcriptional and post-transcriptional gene regulation in bacteria, with an emphasis in the human pathogen Mycobacterium tuberculosis (Mtb). First, I developed a network response method to identify parts of the Mtb global transcriptional regulatory network utilized by the pathogen to counteract phagosomal stresses and survive within resting macrophages. As a result, the method unveiled transcriptional regulators and associated regulons utilized by Mtb to establish a successful infection of macrophages throughout the first 14 days of infection. Additionally, this network-based analysis identified the production of Fe-S proteins coupled to lipid metabolism through the alkane hydroxylase complex as a possible strategy employed by Mtb to survive in the host. Second, I developed a network inference method to infer the small non-coding RNA (sRNA) regulatory network in Mtb. The method identifies sRNA-mRNA interactions by integrating a priori knowledge of possible binding sites with structure-driven identification of binding sites. The reconstructed network was useful to predict functional roles for the multitude of sRNAs recently discovered in the pathogen, being that several sRNAs were postulated to be involved in virulence-related processes. Finally, I applied a combined experimental and computational approach to study post-transcriptional repression mediated by small non-coding RNAs in bacteria. Specifically, a probabilistic ranking methodology termed rank-conciliation was developed to infer sRNA-mRNA interactions based on multiple types of data. The method was shown to improve target prediction in Escherichia coli, and therefore is useful to prioritize candidate targets for experimental validation.

A potential role for the nuclear factor of activated T cells family of transcriptional regulatory proteins in adipogenesis

NFAT (nuclear factor of activated T cells) is a family of transcription factors implicated in the control of cytokine and early immune response gene expression. Recent studies have pointed to a role for NFAT proteins in gene regulation outside of the immune system. Herein we demonstrate that NFAT proteins are present in 3T3-L1 adipocytes and, upon fat cell differentiation, bind to and transactivate the promoter of the adipocyte-specific gene aP2. Further, fat cell differentiation is inhibited by cyclosporin A, a drug shown to prevent NFAT nuclear localization and hence function. Thus, these data suggest a role for NFAT transcription factors in the regulation of the aP2 gene and in the process of adipocyte differentiation.

Smad proteins function as co-modulators for MEF2 transcriptional regulatory proteins

An emerging theme in transforming growth factor-β (TGF-β) signalling is the association of the Smad proteins with diverse groups of transcriptional regulatory proteins. Several Smad cofactors have been identified to date but the diversity of TGF-β effects on gene transcription suggests that interactions with other co-regulators must occur. In these studies we addressed the possible interaction of Smad proteins with the myocyte enhancer-binding factor 2 (MEF2) transcriptional regulators. Our studies indicate that Smad2 and 4 (Smad2/4) complexes cooperate with MEF2 regulatory proteins in a GAL4-based one-hybrid reporter gene assay. We have also observed in vivo interactions between Smad2 and MEF2A using co-immunoprecipitation assays. This interaction is confirmed by glutathione S-transferase pull-down analysis. Immunofluorescence studies in C2C12 myotubes show that Smad2 and MEF2A co-localise in the nucleus of multinuclear myotubes during differentiation. Interestingly, phospho-acceptor site mutations of MEF2 that render it unresponsive to p38 MAP kinase signalling abrogate the cooperativity with the Smads suggesting that p38 MAP Kinase-catalysed phosphorylation of MEF2 is a prerequisite for the Smad–MEF2 interaction. Thus, the association between Smad2 and MEF2A may subserve a physical link between TGF-β signalling and a diverse array of genes controlled by the MEF2 cis element.

Domains with transcriptional regulatory activity within the ALL1 and AF4 proteins involved in acute leukemia.

The ALLI gene, located at chromosome band 11q23, is involved in acute leukemia through a series of chromosome translocations and fusion to a variety of genes, most frequently to A4 and AF9. The fused genes encode chimeric proteins proteins. Because the Drosophila homologue of ALL1, trithorax, is a positive regulator of homeotic genes and acts at the level of transcription, it is conceivable that alterations in ALL1 transcriptional activity may underlie its action in malignant transformation. To begin studying this, we examined the All1, AF4, AF9, and AF17 proteins for the presence of potential transcriptional regulatory domains. This was done by fusing regions of the proteins to the yeast GAL4 DNA binding domain and assaying their effect on transcription of a reporter gene. A domain of 55 residues positioned at amino acids 2829-2883 of ALL1 was identified as a very strong activator. Further analysis of this domain by in vitro mutagenesis pointed to a core of hydrophobic and acidic residues as critical for the activity. An ALL1 domain that repressed transcription of the reporter gene coincided with the sequence homologous to a segment of DNA methyltransferase. An AF4 polypeptide containing residues 480-560 showed strong activation potential. The C-terminal segment of AF9 spanning amino acids 478-568 transactivated transcription of the reporter gene in HeLa but not in NIH 3T3 cells. These results suggest that ALL1, AF4, and probably AF9 interact with the transcriptional machinery of the cell.

Conservation and function of the transcriptional regulatory protein Runt.

A phylogenetic approach was used to identify conserved regions of the transcriptional regulator Runt. Alignment of the deduced protein sequences from Drosophila melanogaster, Drosophila pseudoobscura, and Drosophila virilis revealed eight blocks of high sequence homology separated by regions with little or no homology. The largest conserved block contains the Runt domain, a DNA and protein binding domain conserved in a small family of mammalian transcription factors. The functional properties of the Runt domain from the D. melanogaster gene and the human AML1 (acute myeloid leukemia 1) gene were compared in vitro and in vivo. Electrophoretic mobility-shift assays with Runt/AML1 chimeras demonstrated that the different DNA binding properties of Runt and AML1 are due to differences within their respective Runt domains. Ectopic expression experiments indicated that proteins containing the AML1 Runt domain function in Drosophila embryos and that sequences outside of this domain are important in vivo.