Factor analysis for gene regulatory networks and transcription factor activity profiles

BACKGROUND: Most existing algorithms for the inference of the structure of gene regulatory networks from gene expression data assume that the activity levels of transcription factors (TFs) are proportional to their mRNA levels. This assumption is invalid for most biological systems. However, one might be able to reconstruct unobserved activity profiles of TFs from the expression profiles of target genes. A simple model is a two-layer network with unobserved TF variables in the first layer and observed gene expression variables in the second layer. TFs are connected to regulated genes by weighted edges. The weights, known as factor loadings, indicate the strength and direction of regulation. Of particular interest are methods that produce sparse networks, networks with few edges, since it is known that most genes are regulated by only a small number of TFs, and most TFs regulate only a small number of genes. RESULTS: In this paper, we explore the performance of five factor analysis algorithms, Bayesian as well as classical, on problems with biological context using both simulated and real data. Factor analysis (FA) models are used in order to describe a larger number of observed variables by a smaller number of unobserved variables, the factors, whereby all correlation between observed variables is explained by common factors. Bayesian FA methods allow one to infer sparse networks by enforcing sparsity through priors. In contrast, in the classical FA, matrix rotation methods are used to enforce sparsity and thus to increase the interpretability of the inferred factor loadings matrix. However, we also show that Bayesian FA models that do not impose sparsity through the priors can still be used for the reconstruction of a gene regulatory network if applied in conjunction with matrix rotation methods. Finally, we show the added advantage of merging the information derived from all algorithms in order to obtain a combined result. CONCLUSION: Most of the algorithms tested are successful in reconstructing the connectivity structure as well as the TF profiles. Moreover, we demonstrate that if the underlying network is sparse it is still possible to reconstruct hidden activity profiles of TFs to some degree without prior connectivity information

The Infinite Hierarchical Factor Regression Model

We propose a nonparametric Bayesian factor regression model that accounts for uncertainty in the number of factors, and the relationship between factors. To accomplish this, we propose a sparse variant of the Indian Buffet Process and couple this with a hierarchical model over factors, based on Kingman's coalescent. We apply this model to two problems (factor analysis and factor regression) in gene-expression data analysis

Using temporal correlation in factor analysis for reconstructing transcription factor activities

Two-level gene regulatory networks consist of the transcription factors (TFs) in the top level and their regulated genes in the second level. The expression profiles of the regulated genes are the observed high-throughput data given by experiments such as microarrays. The activity profiles of the TFs are treated as hidden variables as well as the connectivity matrix that indicates the regulatory relationships of TFs with their regulated genes. Factor analysis (FA) as well as other methods, such as the network component algorithm, has been suggested for reconstructing gene regulatory networks and also for predicting TF activities. They have been applied to E. coli and yeast data with the assumption that these datasets consist of identical and independently distributed samples. Thus, the main drawback of these algorithms is that they ignore any time correlation existing within the TF profiles. In this paper, we extend previously studied FA algorithms to include time correlation within the transcription factors. At the same time, we consider connectivity matrices that are sparse in order to capture the existing sparsity present in gene regulatory networks. The TFs activity profiles obtained by this approach are significantly smoother than profiles from previous FA algorithms. The periodicities in profiles from yeast expression data become prominent in our reconstruction. Moreover, the strength of the correlation between time points is estimated and can be used to assess the suitability of the experimental time interval

Modelling transcriptional regulation with Gaussian processes

A challenging problem in systems biology is the quantitative modelling of transcriptional regulation. Transcription factors (TFs), which are the key proteins at the centre of the regulatory processes, may be subject to post-translational modification, rendering them unobservable at the mRNA level, or they may be controlled outside of the subsystem being modelled. In both cases, a mechanistic model description of the regula- tory system needs to be able to deal with latent activity profiles of the key regulators. A promising approach to deal with these difficulties is based on using Gaussian processes to define a prior distribution over the latent TF activity profiles. Inference is based on the principles of non-parametric Bayesian statistics, consistently inferring the posterior distribution of the unknown TF activities from the observed expression levels of potential target genes. The present work provides explicit solutions to the differ- ential equations needed to model the data in this manner, as well as the derivatives needed for effective optimisation. The work further explores identifiability issues not fully shown in previous work and looks at how this can cause difficulties with inference. We subsequently look at how the method works on two different TFs, including looking at how the model works with a more biologically realistic mechanistic model. Finally we analyse the effect of more biologically realistic non-Gaussian noise on the biologically realistic model showing how this can cause a reduction in the accuracy of the inference

Sparse regulatory networks

In many organisms the expression levels of each gene are controlled by the activation levels of known "Transcription Factors" (TF). A problem of considerable interest is that of estimating the "Transcription Regulation Networks" (TRN) relating the TFs and genes. While the expression levels of genes can be observed, the activation levels of the corresponding TFs are usually unknown, greatly increasing the difficulty of the problem. Based on previous experimental work, it is often the case that partial information about the TRN is available. For example, certain TFs may be known to regulate a given gene or in other cases a connection may be predicted with a certain probability. In general, the biology of the problem indicates there will be very few connections between TFs and genes. Several methods have been proposed for estimating TRNs. However, they all suffer from problems such as unrealistic assumptions about prior knowledge of the network structure or computational limitations. We propose a new approach that can directly utilize prior information about the network structure in conjunction with observed gene expression data to estimate the TRN. Our approach uses $L_1$ penalties on the network to ensure a sparse structure. This has the advantage of being computationally efficient as well as making many fewer assumptions about the network structure. We use our methodology to construct the TRN for E. coli and show that the estimate is biologically sensible and compares favorably with previous estimates.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS350 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Matrix--free Likelihood Method for Exploratory Factor Analysis of High-dimensional Gaussian Data

This paper proposes a novel profile likelihood method for estimating the covariance parameters in exploratory factor analysis of high-dimensional Gaussian datasets with fewer observations than number of variables. An implicitly restarted Lanczos algorithm and a limited-memory quasi-Newton method are implemented to develop a matrix-free framework for likelihood maximization. Simulation results show that our method is substantially faster than the expectation-maximization solution without sacrificing accuracy. Our method is applied to fit factor models on data from suicide attempters, suicide ideators and a control group.Comment: 10 pages, 5 figures, 4 table

An integrated machine learning approach for predicting DosR-regulated genes in Mycobacterium tuberculosis.

BACKGROUND: DosR is an important regulator of the response to stress such as limited oxygen availability in Mycobacterium tuberculosis. Time course gene expression data enable us to dissect this response on the gene regulatory level. The mRNA expression profile of a regulator, however, is not necessarily a direct reflection of its activity. Knowing the transcription factor activity (TFA) can be exploited to predict novel target genes regulated by the same transcription factor. Various approaches have been proposed to reconstruct TFAs from gene expression data. Most of them capture only a first-order approximation to the complex transcriptional processes by assuming linear gene responses and linear dynamics in TFA, or ignore the temporal information in data from such systems. RESULTS: In this paper, we approach the problem of inferring dynamic hidden TFAs using Gaussian processes (GP). We are able to model dynamic TFAs and to account for both linear and nonlinear gene responses. To test the validity of the proposed approach, we reconstruct the hidden TFA of p53, a tumour suppressor activated by DNA damage, using published time course gene expression data. Our reconstructed TFA is closer to the experimentally determined profile of p53 concentration than that from the original study. We then apply the model to time course gene expression data obtained from chemostat cultures of M. tuberculosis under reduced oxygen availability. After estimation of the TFA of DosR based on a number of known target genes using the GP model, we predict novel DosR-regulated genes: the parameters of the model are interpreted as relevance parameters indicating an existing functional relationship between TFA and gene expression. We further improve the prediction by integrating promoter sequence information in a logistic regression model. Apart from the documented DosR-regulated genes, our prediction yields ten novel genes under direct control of DosR. CONCLUSIONS: Chemostat cultures are an ideal experimental system for controlling noise and variability when monitoring the response of bacterial organisms such as M. tuberculosis to finely controlled changes in culture conditions and available metabolites. Nonlinear hidden TFA dynamics of regulators can be reconstructed remarkably well with Gaussian processes from such data. Moreover, estimated parameters of the GP can be used to assess whether a gene is controlled by the reconstructed TFA or not. It is straightforward to combine these parameters with further information, such as the presence of binding motifs, to increase prediction accuracy.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

Gene Expression Signatures of Radiation Response Are Specific, Durable and Accurate in Mice and Humans

Background: Previous work has demonstrated the potential for peripheral blood (PB) gene expression profiling for the detection of disease or environmental exposures. Methods and Findings: We have sought to determine the impact of several variables on the PB gene expression profile of an environmental exposure, ionizing radiation, and to determine the specificity of the PB signature of radiation versus other genotoxic stresses. Neither genotype differences nor the time of PB sampling caused any lessening of the accuracy of PB signatures to predict radiation exposure, but sex difference did influence the accuracy of the prediction of radiation exposure at the lowest level (50 cGy). A PB signature of sepsis was also generated and both the PB signature of radiation and the PB signature of sepsis were found to be 100 % specific at distinguishing irradiated from septic animals. We also identified human PB signatures of radiation exposure and chemotherapy treatment which distinguished irradiated patients and chemotherapy-treated individuals within a heterogeneous population with accuracies of 90 % and 81%, respectively. Conclusions: We conclude that PB gene expression profiles can be identified in mice and humans that are accurate i

Joint analysis of transcriptional and post- transcriptional brain tumor data: searching for emergent properties of cellular systems

<p>Abstract</p> <p>Background</p> <p>Advances in biotechnology offer a fast growing variety of high-throughput data for screening molecular activities of genomic, transcriptional, post-transcriptional and translational observations. However, to date, most computational and algorithmic efforts have been directed at mining data from each of these molecular <it>levels </it>(genomic, transcriptional, etc.) separately. In view of the rapid advances in technology (new generation sequencing, high-throughput proteomics) it is important to address the problem of analyzing these data as a whole, i.e. preserving the emergent properties that appear in the cellular system when all molecular levels are interacting. We analyzed one of the (currently) few datasets that provide both transcriptional and post-transcriptional data of the same samples to investigate the possibility to extract more information, using a joint analysis approach.</p> <p>Results</p> <p>We use Factor Analysis coupled with pre-established knowledge as a theoretical base to achieve this goal. Our intention is to identify structures that contain information from both mRNAs and miRNAs, and that can explain the complexity of the data. Despite the small sample available, we can show that this approach permits identification of meaningful structures, in particular two polycistronic miRNA genes related to transcriptional activity and likely to be relevant in the discrimination between gliosarcomas and other brain tumors.</p> <p>Conclusions</p> <p>This suggests the need to develop methodologies to simultaneously mine information from different levels of biological organization, rather than linking separate analyses performed in parallel.</p