Optimal strategies in political elections

In the Majoritarian Parliamentary System, the government has a constitutional right to call an early election. This right provides the government a control to achieve its objective to remain in power for as long as possible. We model the early election problem mathematically using opinion polls data as a stochastic process to proxy the government's probability of re-election. These data measure the difference in popularity between the government and the opposition. We fit a mean reverting Stochastic Differential Equation to describe the behaviour of the process and consider the possibility for the government to use other control tools, which are termed 'boosts' to induce shocks to the opinion polls by making timely policy announcements or economic actions. These actions improve the government's popularity and have some impact upon the early-election exercise boundary. © Austral. Mathematical Soc. 2005.

Stochastic delay differential equations for genetic regulatory networks

Time delay is an important aspect in the modelling of genetic regulation due to slow biochemical reactions such as gene transcription and translation, and protein diffusion between the cytosol and nucleus. In this paper we introduce a general mathematical formalism via stochastic delay differential equations for describing time delays in genetic regulatory networks. Based on recent developments with the delay stochastic simulation algorithm, the delay chemical masterequation and the delay reaction rate equation are developed for describing biological reactions with time delay, which leads to stochastic delay differential equations derived from the Langevin approach. Two simple genetic regulatory networks are used to study the impact of' intrinsic noise on the system dynamics where there are delays. (c) 2006 Elsevier B.V. All rights reserved.

Identification of two evolutionarily conserved and functional regulatory elements in intron 2 of the human BRCA1 gene

Cross-species comparative genomics is a powerful strategy for identifying functional regulatory elements within noncoding DNA. In this paper, comparative analysis of human and mouse intronic sequences in the breast cancer susceptibility gene (BRCA1) revealed two evolutionarily conserved noncoding sequences (CNS) in intron 2, 5 kb downstream of the core BRCA1 promoter. The functionality of these elements was examined using homologous-recombination-based mutagenesis of reporter gene-tagged cosmids incorporating these regions and flanking sequences from the BRCA1 locus. This showed that CNS-1 and CNS-2 have differential transcriptional regulatory activity in epithelial cell lines. Mutation of CNS-1 significantly reduced reporter gene expression to 30% of control levels. Conversely mutation of CNS-2 increased expression to 200% of control levels. Regulation is at the level of transcription and shows promoter specificity. Both elements also specifically bind nuclear proteins in vitro. These studies demonstrate that the combination of comparative genomics and functional analysis is a successful strategy to identify novel regulatory elements and provide the first direct evidence that conserved noncoding sequences in BRCA1 regulate gene expression. (c) 2005 Elsevier Inc. All rights reserved.

Transcriptional network dynamics in macrophage activation

Transcriptional regulatory networks govern cell differentiation and the cellular response to external stimuli. However, mammalian model systems have not yet been accessible for network analysis. Here, we present a genome-wide network analysis of the transcriptional regulation underlying the mouse macrophage response to bacterial lipopolysaccharide (LPS). Key to uncovering the network structure is our combination of time-series cap analysis of gene expression with in silico prediction of transcription factor binding sites. By integrating microarray and qPCR time-series expression data with a promoter analysis, we find dynamic subnetworks that describe how signaling pathways change dynamically during the progress of the macrophage LPS response, thus defining regulatory modules characteristic of the inflammatory response. In particular, our integrative analysis enabled us to suggest novel roles for the transcription factors ATF-3 and NRF-2 during the inflammatory response. We believe that our system approach presented here is applicable to understanding cellular differentiation in higher eukaryotes. (c) 2006 Elsevier Inc. All rights reserved.

Inherent size constraints on prokaryote gene networks due to "accelerating" growth

Networks exhibiting accelerating growth have total link numbers growing faster than linearly with network size and either reach a limit or exhibit graduated transitions from nonstationary-to-stationary statistics and from random to scale-free to regular statistics as the network size grows. However, if for any reason the network cannot tolerate such gross structural changes then accelerating networks are constrained to have sizes below some critical value. This is of interest as the regulatory gene networks of single-celled prokaryotes are characterized by an accelerating quadratic growth and are size constrained to be less than about 10,000 genes encoded in DNA sequence of less than about 10 megabases. This paper presents a probabilistic accelerating network model for prokaryotic gene regulation which closely matches observed statistics by employing two classes of network nodes (regulatory and non-regulatory) and directed links whose inbound heads are exponentially distributed over all nodes and whose outbound tails are preferentially attached to regulatory nodes and described by a scale-free distribution. This model explains the observed quadratic growth in regulator number with gene number and predicts an upper prokaryote size limit closely approximating the observed value. (c) 2005 Elsevier GmbH. All rights reserved.

Small regulatory RNAs in mammals

Mammalian cells harbor numerous small non-protein-coding RNAs, including small nucleolar RNAs (snoRNAs), microRNAs (miRNAs), short interfering RNAs (siRNAs) and small double-stranded RNAs, which regulate gene expression at many levels including chromatin architecture, RNA editing, RNA stability, translation, and quite possibly transcription and splicing. These RNAs are processed by multistep pathways from the introns and exons of longer primary transcripts, including protein-coding transcripts. Most show distinctive temporal- and tissue-specific expression patterns in different tissues, including embryonal stem cells and the brain, and some are imprinted. Small RNAs control a wide range of developmental and physiological pathways in animals, including hematopoietic differentiation, adipocyte differentiation and insulin secretion in mammals, and have been shown to be perturbed in cancer and other diseases. The extent of transcription of non-coding sequences and the abundance of small RNAs suggests the existence of an extensive regulatory network on the basis of RNA signaling which may underpin the development and much of the phenotypic variation in mammals and other complex organisms and which may have different genetic signatures from sequences encoding proteins.

LPS regulates proinflammatory gene expression in macrophages by altering histone deacetylase expression

Bacterial LPS triggers dramatic changes in gene expression in macrophages. We show here that LPS regulated several members of the histone deacetylase (HDAC) family at the mRNA level in murine bone marrow-derived macrophages (BMM). LPS transiently repressed, then induced a number of HDACs (Hdac-4, 5, 7) in BMM, whereas Hdac-1 mRNA was induced more rapidly. Treatment of BMM with trichostatin A (TSA), an inhibitor of HDACs, enhanced LPS-induced expression of the Cox-2, Cxcl2, and Ifit2 genes. In the case of Cox-2, this effect was also apparent at the promoter level. Overexpression of Hdac-8 in RAW264 murine macrophages blocked the ability of LPS to induce Cox-2 mRNA. Another class of LPS-inducible genes, which included Ccl2, Ccl7, and Edn1, was suppressed by TSA, an effect most likely mediated by PU.1 degradation. Hence, HDACs act as potent and selective negative regulators of proinflammatory gene expression and act to prevent excessive inflammatory responses in macrophages.

Stochastic modelling and simulations for solute transport in porous media

A stochastic model for solute transport in aquifers is studied based on the concepts of stochastic velocity and stochastic diffusivity. By applying finite difference techniques to the spatial variables of the stochastic governing equation, a system of stiff stochastic ordinary differential equations is obtained. Both the semi-implicit Euler method and the balanced implicit method are used for solving this stochastic system. Based on the Karhunen-Loeve expansion, stochastic processes in time and space are calculated by means of a spatial correlation matrix. Four types of spatial correlation matrices are presented based on the hydraulic properties of physical parameters. Simulations with two types of correlation matrices are presented.

Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.

The EBNA- 3 gene family proteins disrupt the G2/M checkpoint

The Epstein - Barr nuclear antigens (EBNA), EBNA-3, -4 and - 6, have previously been shown to act as transcriptional regulators, however, this study identifies another function for these proteins, disruption of the G2/M checkpoint. Lymphoblastoid cell lines (LCLs) treated with a G2/M initiating drug azelaic bishydroxamine ( ABHA) did not show a G2/M checkpoint response, but rather they display an increase in cell death, a characteristic of sensitivity to the cytotoxic effects of the drug. Cell cycle analysis demonstrated that the individual expression of EBNA-3, - 4 or - 6 are capable of disrupting the G2/M checkpoint response induced by ABHA resulting in increased toxicity, whereas EBNA-2, and - 5 were not. EBNA-3 gene family protein expression also disrupted the G2/M checkpoint initiated in response to the genotoxin etoposide and the S phase inhibitor hydroxyurea. The G2 arrest in response to these drugs were sensitive to caffeine, suggesting that ATM/ATR signalling in these checkpoint responses may be blocked by the EBNA-3 family proteins. The function of EBNA-3, - 4 and - 6 proteins appears to be more complex than anticipated and these data suggest a role for these proteins in disrupting the host cell cycle machinery.

Quantum nondemolition measurement of Fock states of mesoscopic mechanical oscillators

We investigate a scheme that makes a quantum nondemolition (QND) measurement of the excitation level of a mesoscopic mechanical oscillator by utilizing the anharmonic coupling between two beam bending modes. The nonlinear coupling between the two modes shifts the resonant frequency of the readout oscillator in proportion to the excitation level of the system oscillator. This frequency shift may be detected as a phase shift of the readout oscillation when driven on resonance. We derive an equation for the reduced density matrix of the system oscillator, and use this to study the conditions under which discrete jumps in the excitation level occur. The appearance of jumps in the actual quantity measured is also studied using the method of quantum trajectories. We consider the feasibility of the scheme for experimentally accessible parameters.

Cardiac expression of the cystic fibrosis transmembrane conductance regulator involves novel Exon 1 usage to produce a unique amino-terminal protein

Cystic fibrosis is caused by mutations in the cystic fibrosis transmembrane conductance regulator (CFTR) gene, which encodes a chloride channel present in many cells. In cardiomyocytes, we report that multiple exon 1 usage and alternative splicing produces four CFTR transcripts, with different 5'-untranslated regions, CFTRTRAD-139, CFTR-1C/-1A, CFTR-1C, and CFTR-1B. CFTR transcripts containing the novel upstream exons (exons -1C, -1B, and -1A) represent more than 90% of cardiac expressed CFTR mRNA. Regulation of cardiac CFTR expression, in response to developmental and pathological stimuli, is exclusively due to the modulation of CFTR-1C and CFTR-1C/-1A expression. Upstream open reading frames have been identified in the 5'-untranslated regions of all CFTR transcripts that, in conjunction with adjacent stem-loop structures, modulate the efficiency of translation initiation at the AUG codon of the main CFTR coding region in CFTRTRAD-139 and CFTR-1C/-1A transcripts. Exon(-1A), only present in CFTR-1C/-1A transcripts, encodes an AUG codon that is in-frame with the main CFTR open reading frame, the efficient translation of which produces a novel CFTR protein isoform with a curtailed amino terminus. As the expression of this CFTR transcript parallels the spatial and temporal distribution of the cAMP-activated whole-cell current density in normal and diseased hearts, we suggest that CFTR-1C/-1A provides the molecular basis for the cardiac cAMP-activated chloride channel. Our findings provide further insight into the complex nature of in vivo CFTR expression, to which multiple mRNA transcripts, protein isoforms, and post-transcriptional regulatory mechanisms are now added.

Gauge Poisson representations for birth/death master equations

Poisson representation techniques provide a powerful method for mapping master equations for birth/death processes -- found in many fields of physics, chemistry and biology -- into more tractable stochastic differential equations. However, the usual expansion is not exact in the presence of boundary terms, which commonly occur when the differential equations are nonlinear. In this paper, a gauge Poisson technique is introduced that eliminates boundary terms, to give an exact representation as a weighted rate equation with stochastic terms. These methods provide novel techniques for calculating and understanding the effects of number correlations in systems that have a master equation description. As examples, correlations induced by strong mutations in genetics, and the astrophysical problem of molecule formation on microscopic grain surfaces are analyzed. Exact analytic results are obtained that can be compared with numerical simulations, demonstrating that stochastic gauge techniques can give exact results where standard Poisson expansions are not able to.