The genome encodes thousands of genes whose pro ducts enable cell survival and numerous cellular func tions. The amounts and the temporal pattern in which these products appear in the cell are crucial to the pro cesses of life. Gene regulatory networks govern the levels of these gene products. A gene regulatory net work is the collection of molecular species and their inter actions, which together control geneproduct abundance. Numerous cellular processes are affected by regulatory networks. Innovations in experimental methods have ena bled largescale studies of gene regulatory networks and can reveal the mechanisms that underlie them. Consequently, biologists must come to grips with extremely complex networks and must analyse and integrate great quantities of experimental data. Essential to this challenge are computational tools, which can answer various questions: what is the full range of behaviours that this system exhibits under different conditions? What changes are expected in the dynamics of the system if certain parts stop functioning? How robust is the system under extreme conditions? Various computational models have been developed for regulatory network analysis. These models can be roughly divided into three classes. The first class, logi cal models, describes regulatory networks qualitatively. They allow users to obtain a basic understanding of the different functionalities of a given network under dif ferent conditions. Their qualitative nature makes them flexible and easy to fit to biological phenomena, although they can only answer qualitative questions. To under stand and manipulate behaviours that depend on finer timing and exact molecular concentrations, a second class of models was developed -continuous models. For example, to simulate the effects of dietary restriction on yeast cells under different nutrient concentrations 1 , users must resort to the finer resolution of continuous models. A third class of models was introduced follow ing the observation that the functionality of regulatory networks is often affected by noise. As the majority of these models account for interactions between individual molecules, they are referred to here as singlemolecule level models. Singlemolecule level models explain the relationship between stochasticity and gene regulation. Predictive computational models of regulatory net works are expected to benefit several fields. In medi cine, mechanisms of diseases that are characterized by dysfunction of regulatory processes can be elucidated. Biotechnological projects can benefit from predictive models that will replace some tedious and costly lab experiments. And, computational analysis may con tribute to basic biological research, for example, by explaining developmental mechanisms or new aspects of the evolutionary process. Here we review the available methodologies for mod elling and analysing regulatory networks. These meth odologies have already proved to be a valuable research tool, both for the development of network models and for the analysis of their functionality. We discuss their relative advantages and limitations, and outline some open questions regarding regulatory networks, includ ing how structure, dynamics and functionality relate to each other, how organisms use regulatory networks to adapt to their environments, and the interplay between regulatory networks and other cellular processes, such as metabolism. Stochasticity The property of a system whose behaviour depends on probabilities. In a model with stochasticity, a single initial state can evolve into several different trajectories, each with an associated probability. Modelling and analysis of gene regulatory networks Guy Karlebach and Ron Shamir Abstract | Gene regulatory networks have an important role in every process of life, including cell differentiation, metabolism, the cell cycle and signal transduction. By understanding the dynamics of these networks we can shed light on the mechanisms of diseases that occur when these cellular processes are dysregulated. Accurate prediction of the behaviour of regulatory networks will also speed up biotechnological projects, as such predictions are quicker and cheaper than lab experiments. Computational methods, both for supporting the development of network models and for the analysis of their functionality, have already proved to be a valuable research tool.

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technique for accurately and reliably profiling and quantifying gene expression. Typically, samples ob-tained from the organism of study have to be processed via several preparative steps before qPCR. METHOD: We estimated the errors of sample with-drawal and extraction, reverse transcription (RT), and qPCR that are introduced into measurements of mRNA concentrations. We performed hierarchically arranged experiments with 3 animals, 3 samples, 3 RT reactions, and 3 qPCRs and quantified the expression of several genes in solid tissue, blood, cell culture, and single cells. RESULTS: A nested ANOVA design was used to model the experiments, and relative and absolute errors were calculated with this model for each processing level in the hierarchical design.We found that intersubject dif-ferences became easily confounded by sample hetero-geneity for single cells and solid tissue. In cell cultures and blood, the noise from the RT and qPCR steps con-tributed substantially to the overall error because the sampling noise was less pronounced. CONCLUSIONS: We recommend the use of sample repli-cates preferentially to any other replicates when work-ing with solid tissue, cell cultures, and single cells, and we recommend the use of RT replicates when working with blood. We show how an optimal sampling plan can be calculated for a limited budget.

Transcriptional regulation in the nucleus is the culmination of the actions of a diverse range of factors, such as transcription factors, chromatin remodellers, polymerases, helicases, topoisomerases, kinases, chaperones, proteasomes, acetyltransferases, deacetylases and methyltransferases. Determining how these molecules work in concert in the eukaryotic nucleus to regulate genes remains a central challenge in molecular biology. Dynamics lie at the heart of this mystery. Megadalton complexes assemble and disassemble on genes within seconds 1,2 ; nucleosome turnover ranges from minutes to hours 3 ; and gene activity demonstrates complex temporal patterns such as oscillation and transcriptional bursting Chromatin immunoprecipitation (ChIP) provides genome-wide occupancy profiles for chromatininteracting factors at near base-pair resolution in populations of cells

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ABSTRACT Transcription is a vital stage in the process of gene expression and a major contributor to fluctuations in gene expression levels for which it is typically modeled as a single-step process with Poisson statistics. However, recent single molecule experiments raise questions about the validity of such a simple single-step picture. We present a molecular multistep model of transcription elongation that demonstrates that transcription times are in general non-Poisson-distributed. In particular, we model transcriptional pauses due to backtracking of the RNA polymerase as a first passage process. By including such pauses, we obtain a broad, heavy-tailed distribution of transcription elongation times, which can be significantly longer than would be otherwise. When transcriptional pauses result in long transcription times, we demonstrate that this naturally leads to bursts of mRNA production and non-Poisson statistics of mRNA levels. These results suggest that transcriptional pauses may be a significant contributor to the variability in transcription rates with direct implications for noise in cellular processes as well as variability between cells.

We know a great deal about the relative population-averaged rates of transcriptional initiation at many promoters, but little about absolute rates, and even less about the temporal distributions of initiations at single loci. Such data has now begun to accumulate; recently developed techniques such as RNA fluorescence in situ hybridization (FISH) and the MS2-GFP transcript-tagging system now allow single transcripts to be counted in single cells and in real time. Recent efforts have combined these methods with mathematical modeling to provide evidence that the transcriptional activity of a given gene can vary widely from cell to cell and from minute to minute; many so-called "active" genes seem to spend much of their time inactive, before switching to produce a brief "burst" of transcripts. We briefly review the basic mechanisms of transcription, before focusing on initiation rates. We discuss recent studies of initiation and relate findings to known mechanisms of regulation (concentrating on results obtained in mammalian systems). General Introduction The existence of RNA polymerases (RNAPs) in mammals was first demonstrated in 1959, when it was shown that isolated rat liver nuclei could incorporate [ 32 P] CTP into RNA in the presence of ATP, UTP, and GTP [1]. Shortly thereafter, three types of DNA-dependant RNA polymerizing enzymes (named I, II, III) were isolated from soluble cell lysates on the basis of differential binding to DEAEcellulose columns, differential sensitivity to a-amanitin, and different structural properties

Background: Upon antigen encounter, naïve B lymphocytes differentiate into antibody-secreting plasma cells. This humoral immune response is suppressed by the environmental contaminant 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) and other dioxin-like compounds, which belong to the family of aryl hydrocarbon receptor (AhR) agonists. Results: To achieve a better understanding of the immunotoxicity of AhR agonists and their associated health risks, we have used computer simulations to study the behavior of the gene regulatory network underlying B cell terminal differentiation. The core of this network consists of two coupled double-negative feedback loops involving transcriptional repressors Bcl-6, Blimp-1, and Pax5. Bifurcation analysis indicates that the feedback network can constitute a bistable system with two mutually exclusive transcriptional profiles corresponding to naïve B cells and plasma cells. Although individual B cells switch to the plasma cell state in an all-or-none fashion when stimulated by the polyclonal activator lipopolysaccharide (LPS), stochastic fluctuations in gene expression make the switching event probabilistic, leading to heterogeneous differentiation response among individual B cells. Moreover, stochastic gene expression renders the dose-response behavior of a population of B cells substantially graded, a result that is consistent with experimental observations. The steepness of the dose response curve for the number of plasma cells formed vs. LPS dose, as evaluated by the apparent Hill coefficient, is found to be inversely

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