Bayesian model-based inference of transcription factor activity

<b>Background:</b> In many approaches to the inference and modeling of regulatory interactions using microarray data, the expression of the gene coding for the transcription factor is considered to be an accurate surrogate for the true activity of the protein it produces. There are many instances where this is inaccurate due to post-translational modifications of the transcription factor protein. Inference of the activity of the transcription factor from the expression of its targets has predominantly involved linear models that do not reflect the nonlinear nature of transcription. We extend a recent approach to inferring the transcription factor activity based on nonlinear Michaelis-Menten kinetics of transcription from maximum likelihood to fully Bayesian inference and give an example of how the model can be further developed.<p></p> <b>Results:</b> We present results on synthetic and real microarray data. Additionally, we illustrate how gene and replicate specific delays can be incorporated into the model.<p></p> <b>Conclusion:</b> We demonstrate that full Bayesian inference is appropriate in this application and has several benefits over the maximum likelihood approach, especially when the volume of data is limited. We also show the benefits of using a non-linear model over a linear model, particularly in the case of repression.<p></p&gt

Probabilistic modeling and machine learning in structural and systems biology

This supplement contains extended versions of a selected subset of papers presented at the workshop PMSB 2007, Probabilistic Modeling and Machine Learning in Structural and Systems Biology, Tuusula, Finland, from June 17 to 18, 2006

GNU MCSim : bayesian statistical inference for SBML-coded systems biology models

International audienceStatistical inference about the parameter values of complex models, such as the ones routinely developed in systems biology, is efficiently performed through Bayesian numerical techniques. In that framework, prior information and multiple levels of uncertainty can be seamlessly integrated. GNU MCSim was precisely developed to achieve those aims, in a general non-linear differential context. Starting with version 5.3.0, GNU MCSim reads in and simulates Systems Biology Markup Language models. Markov chain Monte Carlo simulations can be used to generate samples from the joint posterior distribution of the model parameters, given a dataset and prior distributions. Hierarchical statistical models can be used. Optimal design of experiments can also be investigated

Mathematical and computational modelling of post-transcriptional gene relation by micro-RNA

Mathematical models and computational simulations have proved valuable in many areas of cell biology, including gene regulatory networks. When properly calibrated against experimental data, kinetic models can be used to describe how the concentrations of key species evolve over time. A reliable model allows ‘what if’ scenarios to be investigated quantitatively in silico, and also provides a means to compare competing hypotheses about the underlying biological mechanisms at work. Moreover, models at different scales of resolution can be merged into a bigger picture ‘systems’ level description. In the case where gene regulation is post-transcriptionally affected by microRNAs, biological understanding and experimental techniques have only recently matured to the extent that we can postulate and test kinetic models. In this chapter, we summarize some recent work that takes the first steps towards realistic modelling, focusing on the contributions of the authors. Using a deterministic ordinary differential equation framework, we derive models from first principles and test them for consistency with recent experimental data, including microarray and mass spectrometry measurements. We first consider typical mis-expression experiments, where the microRNA level is instantaneously boosted or depleted and thereafter remains at a fixed level. We then move on to a more general setting where the microRNA is simply treated as another species in the reaction network, with microRNA-mRNA binding forming the basis for the post-transcriptional repression. We include some speculative comments about the potential for kinetic modelling to contribute to the more widespread sequence and network based approaches in the qualitative investigation of microRNA based gene regulation. We also consider what new combinations of experimental data will be needed in order to make sense of the increased systems-level complexity introduced by microRNAs

Quantitative model for inferring dynamic regulation of the tumour suppressor gene p53

Background: The availability of various "omics" datasets creates a prospect of performing the study of genome-wide genetic regulatory networks. However, one of the major challenges of using mathematical models to infer genetic regulation from microarray datasets is the lack of information for protein concentrations and activities. Most of the previous researches were based on an assumption that the mRNA levels of a gene are consistent with its protein activities, though it is not always the case. Therefore, a more sophisticated modelling framework together with the corresponding inference methods is needed to accurately estimate genetic regulation from "omics" datasets. Results: This work developed a novel approach, which is based on a nonlinear mathematical model, to infer genetic regulation from microarray gene expression data. By using the p53 network as a test system, we used the nonlinear model to estimate the activities of transcription factor (TF) p53 from the expression levels of its target genes, and to identify the activation/inhibition status of p53 to its target genes. The predicted top 317 putative p53 target genes were supported by DNA sequence analysis. A comparison between our prediction and the other published predictions of p53 targets suggests that most of putative p53 targets may share a common depleted or enriched sequence signal on their upstream non-coding region. Conclusions: The proposed quantitative model can not only be used to infer the regulatory relationship between TF and its down-stream genes, but also be applied to estimate the protein activities of TF from the expression levels of its target genes

STARNET 2: a web-based tool for accelerating discovery of gene regulatory networks using microarray co-expression data

<p>Abstract</p> <p>Background</p> <p>Although expression microarrays have become a standard tool used by biologists, analysis of data produced by microarray experiments may still present challenges. Comparison of data from different platforms, organisms, and labs may involve complicated data processing, and inferring relationships between genes remains difficult.</p> <p>Results</p> <p><b>S<smcaps>TAR</smcaps>N<smcaps>ET</smcaps> 2 </b>is a new web-based tool that allows post hoc visual analysis of correlations that are derived from expression microarray data. <b>S<smcaps>TAR</smcaps>N<smcaps>ET</smcaps> 2 </b>facilitates user discovery of putative gene regulatory networks in a variety of species (human, rat, mouse, chicken, zebrafish, <it>Drosophila</it>, <it>C. elegans</it>, <it>S. cerevisiae</it>, <it>Arabidopsis </it>and rice) by graphing networks of genes that are closely co-expressed across a large heterogeneous set of preselected microarray experiments. For each of the represented organisms, raw microarray data were retrieved from NCBI's Gene Expression Omnibus for a selected Affymetrix platform. All pairwise Pearson correlation coefficients were computed for expression profiles measured on each platform, respectively. These precompiled results were stored in a MySQL database, and supplemented by additional data retrieved from NCBI. A web-based tool allows user-specified queries of the database, centered at a gene of interest. The result of a query includes graphs of correlation networks, graphs of known interactions involving genes and gene products that are present in the correlation networks, and initial statistical analyses. Two analyses may be performed in parallel to compare networks, which is facilitated by the new <b>H<smcaps>EAT</smcaps>S<smcaps>EEKER </smcaps></b>module.</p> <p>Conclusion</p> <p><b>S<smcaps>TAR</smcaps>N<smcaps>ET</smcaps> 2 </b>is a useful tool for developing new hypotheses about regulatory relationships between genes and gene products, and has coverage for 10 species. Interpretation of the correlation networks is supported with a database of previously documented interactions, a test for enrichment of Gene Ontology terms, and heat maps of correlation distances that may be used to compare two networks. The list of genes in a <b>S<smcaps>TAR</smcaps>N<smcaps>ET </smcaps></b>network may be useful in developing a list of candidate genes to use for the inference of causal networks. The tool is freely available at <url>http://vanburenlab.medicine.tamhsc.edu/starnet2.html</url>, and does not require user registration.</p

A Visual Data Mining Tool that Facilitates Reconstruction of Transcription Regulatory Networks

Background: Although the use of microarray technology has seen exponential growth, analysis of microarray data remains a challenge to many investigators. One difficulty lies in the interpretation of a list of differentially expressed genes, or in how to plan new experiments given that knowledge. Clustering methods can be used to identify groups of genes with similar expression patterns, and genes with unknown function can be provisionally annotated based on the concept of ‘‘guilt by association’’, where function is tentatively inferred from the known functions of genes with similar expression patterns. These methods frequently suffer from two limitations: (1) visualization usually only gives access to group membership, rather than specific information about nearest neighbors, and (2) the resolution or quality of the relationships are not easily inferred. Methodology/Principal Findings: We have addressed these issues by improving the precision of similarity detection over that of a single experiment and by creating a tool to visualize tractable association networks: we (1) performed metaanalysis computation of correlation coefficients for all gene pairs in a heterogeneous data set collected from 2,145 publicly available micorarray samples in mouse, (2) filtered the resulting distribution of over 130 million correlation coefficients to build new, more tractable distributions from the strongest correlations, and (3) designed and implemented a new Web based tool (StarNet

Bifurcation analysis informs Bayesian inference in the Hes1 feedback loop

&lt;p&gt;Background Ordinary differential equations (ODEs) are an important tool for describing the dynamics of biological systems. However, for ODE models to be useful, their parameters must first be calibrated. Parameter estimation, that is, finding parameter values given experimental data, is an inference problem that can be treated systematically through a Bayesian framework.&lt;/p&gt; &lt;p&gt;A Markov chain Monte Carlo approach can then be used to sample from the appropriate posterior probability distributions, provided that suitable prior distributions can be found for the unknown parameter values. Choosing these priors is therefore a vital first step in the inference process. We study here a negative feedback loop in gene regulation where an ODE incorporating a time delay has been proposed as a realistic model and where experimental data is available. Our aim is to show that a priori mathematical analysis can be exploited in the choice of priors.&lt;/p&gt; &lt;p&gt;Results By focussing on the onset of oscillatory behaviour through a Hopf Bifurcation, we derive a range of analytical expressions and constraints that link the model parameters to the observed dynamics of the system. Computational tests on both simulated and experimental data emphasise the usefulness of this analysis.&lt;/p&gt; &lt;p&gt;Conclusion Mathematical analysis not only gives insights into the possible dynamical behaviour of gene expression models, but can also be used to inform the choice of priors when parameters are inferred from experimental data in a Bayesian setting.&lt;/p&gt