The coordinated expression of the different genes in an organism is essential to sustain functionality under the random external perturbations to which the organism might be subjected. To cope with such external variability, the global dynamics of the genetic network must possess two central properties. (a) It must be robust enough as to guarantee stability under a broad range of external conditions, and (b) it must be flexible enough to recognize and integrate specific external signals that may help the organism to change and adapt to different environments. This compromise between robustness and adaptability has been observed in dynamical systems operating at the brink of a phase transition between order and chaos. Such systems are termed critical. Thus, criticality, a precise, measurable, and well characterized property of dynamical systems, makes it possible for robustness and adaptability to coexist in living organisms. In this work we investigate the dynamical properties of the gene transcription networks reported for S. cerevisiae, E. coli, and B. subtilis, as well as the network of segment polarity genes of D. melanogaster, and the network of flower development of A. thaliana. We use hundreds of microarray experiments to infer the nature of the regulatory interactions among genes, and implement these data into the Boolean models of the genetic networks. Our results show that, to the best of the current experimental data available, the five networks under study indeed operate close to criticality. The generality of this result suggests that criticality at the genetic level might constitute a fundamental evolutionary mechanism that generates the great diversity of dynamically robust living forms that we observe around us.
The inference of genetic regulatory networks from global measurements of gene expressions is an important problem in computational biology. Recent studies suggest that such dynamical molecular systems are poised at a critical phase transition between an ordered and a disordered phase, affording the ability to balance stability and adaptability while coordinating complex macroscopic behavior. We investigate whether incorporating this dynamical system-wide property as an assumption in the inference process is beneficial in terms of reducing the inference error of the designed network. Using Boolean networks, for which there are well-defined notions of ordered, critical, and chaotic dynamical regimes as well as well-studied inference procedures, we analyze the expected inference error relative to deviations in the networks' dynamical regimes from the assumption of criticality. We demonstrate that taking criticality into account via a penalty term in the inference procedure improves the accuracy of prediction both in terms of state transitions and network wiring, particularly for small sample sizes.
An important problem in molecular biology is to build a complete understanding of transcriptional regulatory processes in the cell. We have developed a flexible, probabilistic framework to predict TF binding from multiple data sources that differs from the standard hypothesis testing (scanning) methods in several ways. Our probabilistic modeling framework estimates the probability of binding and, thus, naturally reflects our degree of belief in binding. Probabilistic modeling also allows for easy and systematic integration of our binding predictions into other probabilistic modeling methods, such as expression-based gene network inference. The method answers the question of whether the whole analyzed promoter has a binding site, but can also be extended to estimate the binding probability at each nucleotide position. Further, we introduce an extension to model combinatorial regulation by several TFs. Most importantly, the proposed methods can make principled probabilistic inference from multiple evidence sources, such as, multiple statistical models (motifs) of the TFs, evolutionary conservation, regulatory potential, CpG islands, nucleosome positioning, DNase hypersensitive sites, ChIP-chip binding segments and other (prior) sequence-based biological knowledge. We developed both a likelihood and a Bayesian method, where the latter is implemented with a Markov chain Monte Carlo algorithm. Results on a carefully constructed test set from the mouse genome demonstrate that principled data fusion can significantly improve the performance of TF binding prediction methods. We also applied the probabilistic modeling framework to all promoters in the mouse genome and the results indicate a sparse connectivity between transcriptional regulators and their target promoters. To facilitate analysis of other sequences and additional data, we have developed an on-line web tool, ProbTF, which implements our probabilistic TF binding prediction method using multiple data sources. Test data set, a web tool, source codes and supplementary data are available at: http://www.probtf.org.
Macrophages are versatile immune cells that can detect a variety of pathogen-associated molecular patterns through their Toll-like receptors (TLRs). In response to microbial challenge, the TLR-stimulated macrophage undergoes an activation program controlled by a dynamically inducible transcriptional regulatory network. Mapping a complex mammalian transcriptional network poses significant challenges and requires the integration of multiple experimental data types. In this work, we inferred a transcriptional network underlying TLR-stimulated murine macrophage activation. Microarray-based expression profiling and transcription factor binding site motif scanning were used to infer a network of associations between transcription factor genes and clusters of co-expressed target genes. The time-lagged correlation was used to analyze temporal expression data in order to identify potential causal influences in the network. A novel statistical test was developed to assess the significance of the time-lagged correlation. Several associations in the resulting inferred network were validated using targeted ChIP-on-chip experiments. The network incorporates known regulators and gives insight into the transcriptional control of macrophage activation. Our analysis identified a novel regulator (TGIF1) that may have a role in macrophage activation.
Macrophages play a vital role in host defense against infection by recognizing pathogens through pattern recognition receptors, such as the Toll-like receptors (TLRs), and mounting an immune response. Stimulation of TLRs initiates a complex transcriptional program in which induced transcription factor genes dynamically regulate downstream genes. Microarray-based transcriptional profiling has proved useful for mapping such transcriptional programs in simpler model organisms; however, mammalian systems present difficulties such as post-translational regulation of transcription factors, combinatorial gene regulation, and a paucity of available gene-knockout expression data. Additional evidence sources, such as DNA sequence-based identification of transcription factor binding sites, are needed. In this work, we computationally inferred a transcriptional network for TLR-stimulated murine macrophages. Our approach combined sequence scanning with time-course expression data in a probabilistic framework. Expression data were analyzed using the time-lagged correlation. A novel, unbiased method was developed to assess the significance of the time-lagged correlation. The inferred network of associations between transcription factor genes and co-expressed gene clusters was validated with targeted ChIP-on-chip experiments, and yielded insights into the macrophage activation program, including a potential novel regulator. Our general approach could be used to analyze other complex mammalian systems for which time-course expression data are available.
As part of a National Institute of Allergy and Infectious Diseases funded collaborative project, we have performed over 150 microarray experiments measuring the response of C57/BL6 mouse bone marrow macrophages to toll-like receptor stimuli. These microarray expression profiles are available freely from our project web site . Here, we report the development of a database of computationally predicted transcription factor binding sites and related genomic features for a set of over 2000 murine immune genes of interest. Our database, which includes microarray co-expression clusters and a host of web-based query, analysis and visualization facilities, is available freely via the internet. It provides a broad resource to the research community, and a stepping stone towards the delineation of the network of transcriptional regulatory interactions underlying the integrated response of macrophages to pathogens.
We constructed a database indexed on genes and annotations of the immediate surrounding genomic regions. To facilitate both gene-specific and systems biology oriented research, our database provides the means to analyze individual genes or an entire genomic locus. Although our focus to-date has been on mammalian toll-like receptor signaling pathways, our database structure is not limited to this subject, and is intended to be broadly applicable to immunology. By focusing on selected immune-active genes, we were able to perform computationally intensive expression and sequence analyses that would currently be prohibitive if applied to the entire genome. Using six complementary computational algorithms and methodologies, we identified transcription factor binding sites based on the Position Weight Matrices available in TRANSFAC. For one example transcription factor (ATF3) for which experimental data is available, over 50% of our predicted binding sites coincide with genome-wide chromatin immnuopreciptation (ChIP-chip) results. Our database can be interrogated via a web interface. Genomic annotations and binding site predictions can be automatically viewed with a customized version of the Argo genome browser.
We present the Innate Immune Database (IIDB) as a community resource for immunologists interested in gene regulatory systems underlying innate responses to pathogens. The database website can be freely accessed at .
A significant amount of attention has recently been focused on modeling of gene regulatory networks. Two frequently used large-scale modeling frameworks are Bayesian networks (BNs) and Boolean networks, the latter one being a special case of its recent stochastic extension, probabilistic Boolean networks (PBNs). PBN is a promising model class that generalizes the standard rule-based interactions of Boolean networks into the stochastic setting. Dynamic Bayesian networks (DBNs) is a general and versatile model class that is able to represent complex temporal stochastic processes and has also been proposed as a model for gene regulatory systems. In this paper, we concentrate on these two model classes and demonstrate that PBNs and a certain subclass of DBNs can represent the same joint probability distribution over their common variables. The major benefit of introducing the relationships between the models is that it opens up the possibility of applying the standard tools of DBNs to PBNs and vice versa. Hence, the standard learning tools of DBNs can be applied in the context of PBNs, and the inference methods give a natural way of handling the missing values in PBNs which are often present in gene expression measurements. Conversely, the tools for controlling the stationary behavior of the networks, tools for projecting networks onto sub-networks, and efficient learning schemes can be used for DBNs. In other words, the introduced relationships between the models extend the collection of analysis tools for both model classes.
Gene regulatory networks; Probabilistic Boolean networks; Dynamic Bayesian networks
We study how the notions of importance of variables in Boolean functions as well as the sensitivities of the functions to changes in these variables impact the dynamical behavior of Boolean networks. The activity of a variable captures its influence on the output of the function and is a measure of that variable's importance. The average sensitivity of a Boolean function captures the smoothness of the function and is related to its internal homogeneity. In a random Boolean network, we show that the expected average sensitivity determines the well-known critical transition curve. We also discuss canalizing functions and the fact that the canalizing variables enjoy higher importance, as measured by their activities, than the noncanalizing variables. Finally, we demonstrate the important role of the average sensitivity in determining the dynamical behavior of a Boolean network.
Based on the consideration of Boolean dynamics, it has been hypothesized that cell types may correspond to alternative attractors of a gene regulatory network. Recent stochastic Boolean network analysis, however, raised the important question concerning the stability of such attractors. In this paper a detailed numerical analysis is performed within the framework of Langevin dynamics. While the present results confirm that the noise is indeed an important dynamical element, the cell type as represented by attractors can still be a viable hypothesis. It is found that the stability of an attractor depends on the strength of noise related to the distance of the system to the bifurcation point and it can be exponentially stable depending on biological parameters.
cell types; attractors; genetic networks; stability; robustness; stochastic processes; Langevin dynamics
As in many other areas of science, systems biology makes extensive use of statistical association and significance estimates in contingency tables, a type of categorical data analysis known in this field as enrichment (also over-representation or enhancement) analysis. In spite of efforts to create probabilistic annotations, especially in the Gene Ontology context, or to deal with uncertainty in high throughput-based datasets, current enrichment methods largely ignore this probabilistic information since they are mainly based on variants of the Fisher Exact Test.
We developed an open-source R-based software to deal with probabilistic categorical data analysis, ProbCD, that does not require a static contingency table. The contingency table for the enrichment problem is built using the expectation of a Bernoulli Scheme stochastic process given the categorization probabilities. An on-line interface was created to allow usage by non-programmers and is available at: .
We present an analysis framework and software tools to address the issue of uncertainty in categorical data analysis. In particular, concerning the enrichment analysis, ProbCD can accommodate: (i) the stochastic nature of the high-throughput experimental techniques and (ii) probabilistic gene annotation.
Transcript enumeration methods such as SAGE, MPSS, and sequencing-by-synthesis EST "digital northern", are important high-throughput techniques for digital gene expression measurement. As other counting or voting processes, these measurements constitute compositional data exhibiting properties particular to the simplex space where the summation of the components is constrained. These properties are not present on regular Euclidean spaces, on which hybridization-based microarray data is often modeled. Therefore, pattern recognition methods commonly used for microarray data analysis may be non-informative for the data generated by transcript enumeration techniques since they ignore certain fundamental properties of this space.
Here we present a software tool, Simcluster, designed to perform clustering analysis for data on the simplex space. We present Simcluster as a stand-alone command-line C package and as a user-friendly on-line tool. Both versions are available at: http://xerad.systemsbiology.net/simcluster.
Simcluster is designed in accordance with a well-established mathematical framework for compositional data analysis, which provides principled procedures for dealing with the simplex space, and is thus applicable in a number of contexts, including enumeration-based gene expression data.
Insulin-like growth factor binding protein 2 (IGFBP2) is overexpressed in ovarian malignant tissues and in the serum and cystic fluid of ovarian cancer patients, suggesting an important role of IGFBP2 in the biology of ovarian cancer. The purpose of this study was to assess the role of increased IGFBP2 in ovarian cancer cells.
Using western blotting and tissue microarray analyses, we showed that IGFBP2 was frequently overexpressed in ovarian carcinomas compared with normal ovarian tissues. Furthermore, IGFBP2 was significantly overexpressed in invasive serous ovarian carcinomas compared with borderline serous ovarian tumors. To test whether increased IGFBP2 contributes to the highly invasive nature of ovarian cancer cells, we generated IGFBP2-overexpressing cells from an SKOV3 ovarian cancer cell line, which has a very low level of endogenous IGFBP2. A Matrigel invasion assay showed that these IGFBP2-overexpressing cells were more invasive than the control cells. We then designed small interference RNA (siRNA) molecules that attenuated IGFBP2 expression in PA-1 ovarian cancer cells, which have a high level of endogenous IGFBP2. The Matrigel invasion assay showed that the attenuation of IGFBP2 expression indeed decreased the invasiveness of PA-1 cells.
We therefore showed that IGFBP2 enhances the invasion capacity of ovarian cancer cells. Blockage of IGFBP2 may thus constitute a viable strategy for targeted cancer therapy.
Probabilistic Boolean networks (PBNs) have recently been introduced as a promising class of models of genetic regulatory networks. The dynamic behaviour of PBNs can
be analysed in the context of Markov chains. A key goal is the determination of the
steady-state (long-run) behaviour of a PBN by analysing the corresponding Markov
chain. This allows one to compute the long-term influence of a gene on another
gene or determine the long-term joint probabilistic behaviour of a few selected genes.
Because matrix-based methods quickly become prohibitive for large sizes of networks,
we propose the use of Monte Carlo methods. However, the rate of convergence to
the stationary distribution becomes a central issue. We discuss several approaches
for determining the number of iterations necessary to achieve convergence of the
Markov chain corresponding to a PBN. Using a recently introduced method based on
the theory of two-state Markov chains, we illustrate the approach on a sub-network
designed from human glioma gene expression data and determine the joint steadystate
probabilities for several groups of genes.
Microarray or DNA chip technology is revolutionizing biology by empowering researchers in the collection of broad-scope gene information. It is well known that microarray-based measurements exhibit a substantial amount of variability due to a number of possible sources, ranging from hybridization conditions to image capture and analysis. In order to make reliable inferences and carry out quantitative analysis with microarray data, it is generally advisable to have more than one measurement of each gene. The availability of both between-array and within-array replicate measurements is essential for this purpose. Although statistical considerations call for increasing the number of replicates of both types, the latter is particularly challenging in practice due to a number of limiting factors, especially for in-house spotting facilities. We propose a novel approach to design so-called composite microarrays, which allow more replicates to be obtained without increasing the number of printed spots.