Stability in a metabolic system may not be obtained if incorrect amounts of enzymes are used. Without stability, some metabolites may accumulate or deplete leading to the irreversible loss of the desired operating point. Even if initial enzyme amounts achieve a stable steady state, changes in enzyme amount due to stochastic variations or environmental changes may move the system to the unstable region and lose the steady-state or quasi-steady-state flux. This situation is distinct from the phenomenon characterized by typical sensitivity analysis, which focuses on the smooth change before loss of stability. Here we show that metabolic networks differ significantly in their intrinsic ability to attain stability due to the network structure and kinetic forms, and that after achieving stability, some enzymes are prone to cause instability upon changes in enzyme amounts. We use Ensemble Modelling for Robustness Analysis (EMRA) to analyze stability in four cell-free enzymatic systems when enzyme amounts are changed. Loss of stability in continuous systems can lead to lower production even when the system is tested experimentally in batch experiments. The predictions of instability by EMRA are supported by the lower productivity in batch experimental tests. The EMRA method incorporates properties of network structure, including stoichiometry and kinetic form, but does not require specific parameter values of the enzymes.

BACKGROUND: Network Component Analysis (NCA) has been used to deduce the activities of transcription factors (TFs) from gene expression data and the TF-gene binding relationship. However, the TF-gene interaction varies in different environmental conditions and tissues, but such information is rarely available and cannot be predicted simply by motif analysis. Thus, it is beneficial to identify key TF-gene interactions under the experimental condition based on transcriptome data. Such information would be useful in identifying key regulatory pathways and gene markers of TFs in further studies. RESULTS: We developed an algorithm to trim network connectivity such that the important regulatory interactions between the TFs and the genes were retained and the regulatory signals were deduced. Theoretical studies demonstrated that the regulatory signals were accurately reconstructed even in the case where only three independent transcriptome datasets were available. At least 80% of the main target genes were correctly predicted in the extreme condition of high noise level and small number of datasets. Our algorithm was tested with transcriptome data taken from mice under rapamycin treatment. The initial network topology from the literature contains 70 TFs, 778 genes, and 1423 edges between the TFs and genes. Our method retained 1074 edges (i.e. 75% of the original edge number) and identified 17 TFs as being significantly perturbed under the experimental condition. Twelve of these TFs are involved in MAPK signaling or myeloid leukemia pathways defined in the KEGG database, or are known to physically interact with each other. Additionally, four of these TFs, which are Hif1a, Cebpb, Nfkb1, and Atf1, are known targets of rapamycin. Furthermore, the trimmed network was able to predict Eno1 as an important target of Hif1a; this key interaction could not be detected without trimming the regulatory network. CONCLUSIONS: The advantage of our new algorithm, relative to the original NCA, is that our algorithm can identify the important TF-gene interactions. Identifying the important TF-gene interactions is crucial for understanding the roles of pleiotropic global regulators, such as p53. Also, our algorithm has been developed to overcome NCA's inability to analyze large networks where multiple TFs regulate a single gene. Thus, our algorithm extends the applicability of NCA to the realm of mammalian regulatory network analysis.

Understanding the relationship between genetic variation and gene expression is a central question in genetics. With the availability of data from high-throughput technologies such as ChIP-Chip, expression, and genotyping arrays, we can begin to not only identify associations but to understand how genetic variations perturb the underlying transcription regulatory networks to induce differential gene expression. In this study, we describe a simple model of transcription regulation where the expression of a gene is completely characterized by two properties: the concentrations and promoter affinities of active transcription factors. We devise a method that extends Network Component Analysis (NCA) to determine how genetic variations in the form of single nucleotide polymorphisms (SNPs) perturb these two properties. Applying our method to a segregating population of Saccharomyces cerevisiae, we found statistically significant examples of trans-acting SNPs located in regulatory hotspots that perturb transcription factor concentrations and affinities for target promoters to cause global differential expression and cis-acting genetic variations that perturb the promoter affinities of transcription factors on a single gene to cause local differential expression. Although many genetic variations linked to gene expressions have been identified, it is not clear how they perturb the underlying regulatory networks that govern gene expression. Our work begins to fill this void by showing that many genetic variations affect the concentrations of active transcription factors in a cell and their affinities for target promoters. Understanding the effects of these perturbations can help us to paint a more complete picture of the complex landscape of transcription regulation. The software package implementing the algorithms discussed in this work is available as a MATLAB package upon request.

In this article, we introduce an exploratory framework for learning patterns of conditional co-expression in gene expression data. The main idea behind the proposed approach consists of estimating how the information content shared by a set of M nodes in a network (where each node is associated to an expression profile) varies upon conditioning on a set of L conditioning variables (in the simplest case represented by a separate set of expression profiles). The method is non-parametric and it is based on the concept of statistical co-information, which, unlike conventional correlation based techniques, is not restricted in scope to linear conditional dependency patterns. Moreover, such conditional co-expression relationships can potentially indicate regulatory interactions that do not manifest themselves when only pair-wise relationships are considered. A moment based approximation of the co-information measure is derived that efficiently gets around the problem of estimating high-dimensional multi-variate probability density functions from the data, a task usually not viable due to the intrinsic sample size limitations that characterize expression level measurements. By applying the proposed exploratory method, we analyzed a whole genome microarray assay of the eukaryote Saccharomices cerevisiae and were able to learn statistically significant patterns of conditional co-expression. A selection of such interactions that carry a meaningful biological interpretation are discussed.

MOTIVATION: Many biological networks, including transcriptional regulation, metabolism, and the absorbance spectra of metabolite mixtures, can be represented in a bipartite fashion. Key to understanding these bipartite networks are the network architecture and governing source signals. Such information is often implicitly imbedded in the data. Here we develop a technique, network component mapping (NCM), to deduce bipartite network connectivity and regulatory signals from data without any need for prior information. RESULTS: We demonstrate the utility of our approach by analyzing UV-vis spectra from mixtures of metabolites and gene expression data from Saccharomyces cerevisiae. From UV-vis spectra, hidden mixing networks and pure component spectra (sources) were deduced to a higher degree of resolution with our method than other current bipartite techniques. Analysis of S. cerevisiae gene expression from two separate environmental conditions (zinc and DTT treatment) yielded transcription networks consistent with ChIP-chip derived network connectivity. Due to the high degree of noise in gene expression data, the transcription network for many genes could not be inferred. However, with relatively clean expression data, our technique was able to deduce hidden transcription networks and instances of combinatorial regulation. These results suggest that NCM can deduce correct network connectivity from relatively accurate data. For noisy data, NCM yields the sparsest network capable of explaining the data. In addition, partial knowledge of the network topology can be incorporated into NCM as constraints. AVAILABILITY: Algorithm available on request from the authors. Soon to be posted on the web, http://www.seas.ucla.edu/~liaoj/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Data from DNA microarrays and ChIP-chip binding assays often form the basis of transcriptional regulatory analyses. However, experimental noise in both data types combined with environmental dependence and uncorrelation between binding and regulation in ChIP-chip binding data complicate analyses that utilize these complimentary data sources. Therefore, to minimize the impact of these inaccuracies on transcription analyses it is desirable to identify instances of gene expression-ChIP-chip agreement, under the premise that inaccuracies are less likely to be present when separate data sources corroborate each other. Current methods for such identification either make key assumptions that limit their applicability and/or yield high false positive and false negative rates. The goal of this work was to develop a method with a minimal amount of assumptions, and thus widely applicable, that can identify agreement between gene expression and ChIP-chip data at a higher confidence level than current methods. RESULTS: We demonstrate in Saccharomyces cerevisiae that currently available ChIP-chip binding data explain microarray data from a variety of environments only as well as randomized networks with the same connectivity density. This suggests a high degree of inconsistency between the two data types and illustrates the need for a method that can identify consistency between the two data sources. Here we have developed a Gibbs sampling technique to identify genes whose expression and ChIP-chip binding data are mutually consistent. Compared to current methods that could perform the same task, the Gibbs sampling method developed here exceeds their ability at high levels (>50%) of transcription network and gene expression error, while performing similarly at lower levels. Using this technique, we show that on average 73% more gene expression features can be captured per gene as compared to the unfiltered use of gene expression and ChIP-chip-derived network connectivity data. It is important to note that the method described here can be generalized to other transcription connectivity data (e.g. sequence analysis, etc.). AVAILABILITY: Our algorithm is available on request from the authors and soon to be posted on the web. See author's homepage for details, http://www.seas.ucla.edu/~liaoj/

UNLABELLED: Network component analysis (NCA) is a method to deduce transcription factor (TF) activities and TF-gene regulation control strengths from gene expression data and a TF-gene binding connectivity network. Previously, this method could analyze a maximum number of regulators equal to the total sample size because of the identifiability limit in data decomposition. As such, the total number of source signal components was limited to the total number of experiments rather than the total number of biological regulators. However, networks that have less transcriptome data points than the number of regulators are of interest. Thus it is imperative to develop a theoretical basis that allows realistic source signal extraction based on relatively few data points. On the other hand, such methods would inherently increase numerical challenges leading to multiple solutions. Therefore, solutions to both the problems are needed. RESULTS: We have improved NCA for transcription factor activity (TFA) estimation, based on the observation that most genes are regulated by only a few TFs. This observation leads to the derivation of a new identifiability criterion which is tested during numerical iteration that allows us to decompose data when the number of TFs is greater than the number of experiments. To show that our method works with real microarray data and has biological utility, we analyze Saccharomyces cerevisiae cell cycle microarray data (73 experiments) using a TF-gene connectivity network (96 TFs) derived from ChIP-chip binding data. We compare the results of NCA analysis with the results obtained from ChIP-chip regression methods, and we show that NCA and regression produce TFAs that are qualitatively similar, but the NCA TFAs outperform regression in statistical tests. We also show that NCA can extract subtle TFA signals that correlate with known cell cycle TF function and cell cycle phase. Overall we determined that 31 TFs have statistically periodic TFAs in one or more experiments, 75% of which are known cell cycle regulators. In addition, we find that the 12 TFAs that are periodic in two or more experiments correspond to well-known cell cycle regulators. We also investigated TFA sensitivity to the choice of connectivity network we constructed two networks using different ChIP-chip p-value cut-offs. AVAILABILITY: The NCA Toolbox for MATLAB is available at http://www.seas.ucla.edu/~liaoj/download.htm.

MOTIVATION: Gene expression arrays enable measurements of transcription values for a large number or all genes in the genome. In order to better interpret these results and to use them to reconstruct transcription networks, information on location of binding sites for regulatory proteins in the entire genome is needed. In particular, this represents an open problem in Escherichia coli. RESULTS: We describe the first implementation of dictionary-style models to the study of transcription factors binding sites in an entire genome. Vocabulon's unique feature is that it can both reconstruct binding sites characterized by unknown motifs and impute locations of known binding sites in long sequences by simultaneous search. On one hand, the dictionary model specifies a probability for the entire sequence taking simultaneously into account all the possible binding sites. This greatly reduces the number of false positives. On the other hand, the possibility of refining motif description, as an increasing number of binding sites are identified, augments the sensitivity of the method. We illustrate these properties with examples in E.coli. The results of gene expression arrays are used both to guide the search and corroborate it.

The authors recently introduced a framework, named Network Component Analysis (NCA), for the reconstruction of the dynamics of transcriptional regulators' activities from gene expression assays. The original formulation had certain shortcomings that limited NCA's application to a wide class of network dynamics reconstruction problems, either because of limitations in the sample size or because of the stringent requirements imposed by the set of identifiability conditions. In addition, the performance characteristics of the method for various levels of data noise or in the presence of model inaccuracies were never investigated. In this article, the following aspects of NCA have been addressed, resulting in a set of extensions to the original framework: 1) The sufficient conditions on the a priori connectivity information (required for successful reconstructions via NCA) are made less stringent, allowing easier verification of whether a network topology is identifiable, as well as extending the class of identifiable systems. Such a result is accomplished by introducing a set of identifiability requirements that can be directly tested on the regulatory architecture, rather than on specific instances of the system matrix. 2) The two-stage least square iterative procedure used in NCA is proven to identify stationary points of the likelihood function, under Gaussian noise assumption, thus reinforcing the statistical foundations of the method. 3) A framework for the simultaneous reconstruction of multiple regulatory subnetworks is introduced, thus overcoming one of the critical limitations of the original formulation of the decomposition, for example, occurring for poorly sampled data (typical of microarray experiments). A set of monte carlo simulations we conducted with synthetic data suggests that the approach is indeed capable of accurately reconstructing regulatory signals when these are the input of large-scale networks that satisfy the suggested identifiability criteria, even under fairly noisy conditions. The sensitivity of the reconstructed signals to inaccuracies in the hypothesized network topology is also investigated. We demonstrate the feasibility of our approach for the simultaneous reconstruction of multiple regulatory subnetworks from the same data set with a successful application of the technique to gene expression measurements of the bacterium Escherichia coli.

One of the main obstacles in applying genetic algorithms (GA's) to complex problems has been the high computational cost due to their slow convergence rate. We encountered such a difficulty in our attempt to use the classical GA for estimating parameters of a metabolic model. To alleviate this difficulty, we developed a hybrid approach that combines a GA with a stochastic variant of the simplex method in function optimization. Our motivation for developing the stochastic simplex method is to introduce a cost-effective exploration component into the conventional simplex method. In an attempt to make effective use of the simplex operation in a hybrid GA framework, we used an elite-based hybrid architecture that applies one simplex step to a top portion of the ranked population. We compared our approach with five alternative optimization techniques including a simplex-GA hybrid independently developed by Renders-Bersini (R-B) and adaptive simulated annealing (ASA). Our empirical evaluations showed that our hybrid approach for the metabolic modeling problem outperformed all other techniques in terms of accuracy and convergence rate. We used two additional function optimization problems to compare our approach with the five alternative methods.

Genetic algorithms (GA) have been demonstrated to be a promising search and optimization technique that is more likely to converge to a global optimum than most alternative techniques. In an attempt to apply GA to estimate parameters of a metabolic model, however, we found that the slow convergence rate of GA becomes a major problem for its applications to model identification of dynamic systems due to the high computational costs associated with the evaluation of models. To alleviate this difficulty, we developed a hybrid approach that combines Nelder and Mead's (1965) simplex method with the genetic algorithm. The hybrid approach not only speeds up GA's rate of convergence, but also improves the quality of the solution found by pure GA.