A transcriptional regulatory network (TRN) constitutes the collection of regulatory rules that link environmental cues to the transcription state of a cell's genome. We recently proposed a matrix formalism that quantitatively represents a system of such rules (a transcriptional regulatory system [TRS]) and allows systemic characterization of TRS properties. The matrix formalism not only allows the computation of the transcription state of the genome but also the fundamental characterization of the input-output mapping that it represents. Furthermore, a key advantage of this "pseudo-stoichiometric" matrix formalism is its ability to easily integrate with existing stoichiometric matrix representations of signaling and metabolic networks. Here we demonstrate for the first time how this matrix formalism is extendable to large-scale systems by applying it to the genome-scale Escherichia coli TRS. We analyze the fundamental subspaces of the regulatory network matrix (R) to describe intrinsic properties of the TRS. We further use Monte Carlo sampling to evaluate the E. coli transcription state across a subset of all possible environments, comparing our results to published gene expression data as validation. Finally, we present novel in silico findings for the E. coli TRS, including (1) a gene expression correlation matrix delineating functional motifs; (2) sets of gene ontologies for which regulatory rules governing gene transcription are poorly understood and which may direct further experimental characterization; and (3) the appearance of a distributed TRN structure, which is in stark contrast to the more hierarchical organization of metabolic networks.

Abstract Motivation: Computational techniques have been applied to experimental datasets to identify drug mode-of-action. A shortcoming of existing approaches is the requirement of large reference databases of compound expression profiles. Here, we developed a new pathway-based compendium analysis that couples multi-timepoint, controlled microarray data for a single compound with systems-based network analysis to elucidate drug mechanism more efficiently. Results: We applied this approach to a transcriptional regulatory footprint of phthalimide neovascular factor 1 (PNF1)—a novel synthetic small molecule that exhibits significant in vitro endothelial potency—spanning 1–48 h post-supplementation in human micro-vascular endothelial cells (HMVEC) to comprehensively interrogate PNF1 effects. We concluded that PNF1 first induces tumor necrosis factor-alpha (TNF-α) signaling pathway function which in turn affects transforming growth factor-beta (TGF-β) signaling. These results are consistent with our previous observations of PNF1-directed TGF-β signaling at 24 h, including differential regulation of TGF-β-induced matrix metalloproteinase 14 (MMP14/MT1-MMP) which is implicated in angiogenesis. Ultimately, we illustrate how our pathway-based compendium analysis more efficiently generates hypotheses for compound mechanism than existing techniques. Availability: The microarray data generated as part of this study are available in the Gene Expression Omnibus (http://www.ncbi.nlm.nih.gov/geo/). Contact: [email protected]; [email protected] Supplementary information: Supplementary data are available at Bioinformatics online.

BACKGROUND: Optimization theory has been applied to complex biological systems to interrogate network properties and develop and refine metabolic engineering strategies. For example, methods are emerging to engineer cells to optimally produce byproducts of commercial value, such as bioethanol, as well as molecular compounds for disease therapy. Flux balance analysis (FBA) is an optimization framework that aids in this interrogation by generating predictions of optimal flux distributions in cellular networks. Critical features of FBA are the definition of a biologically relevant objective function (e.g., maximizing the rate of synthesis of biomass, a unit of measurement of cellular growth) and the subsequent application of linear programming (LP) to identify fluxes through a reaction network. Despite the success of FBA, a central remaining challenge is the definition of a network objective with biological meaning. RESULTS: We present a novel method called Biological Objective Solution Search (BOSS) for the inference of an objective function of a biological system from its underlying network stoichiometry as well as experimentally-measured state variables. Specifically, BOSS identifies a system objective by defining a putative stoichiometric "objective reaction," adding this reaction to the existing set of stoichiometric constraints arising from known interactions within a network, and maximizing the putative objective reaction via LP, all the while minimizing the difference between the resultant in silico flux distribution and available experimental (e.g., isotopomer) flux data. This new approach allows for discovery of objectives with previously unknown stoichiometry, thus extending the biological relevance from earlier methods. We verify our approach on the well-characterized central metabolic network of Saccharomyces cerevisiae. CONCLUSION: We illustrate how BOSS offers insight into the functional organization of biochemical networks, facilitating the interrogation of cellular design principles and development of cellular engineering applications. Furthermore, we describe how growth is the best-fit objective function for the yeast metabolic network given experimentally-measured fluxes.

Extracellular cues affect signaling, metabolic, and regulatory processes to elicit cellular responses. Although intracellular signaling, metabolic, and regulatory networks are highly integrated, previous analyses have largely focused on independent processes (e.g., metabolism) without considering the interplay that exists among them. However, there is evidence that many diseases arise from multifunctional components with roles throughout signaling, metabolic, and regulatory networks. Therefore, in this study, we propose a flux balance analysis (FBA)-based strategy, referred to as integrated dynamic FBA (idFBA), that dynamically simulates cellular phenotypes arising from integrated networks. The idFBA framework requires an integrated stoichiometric reconstruction of signaling, metabolic, and regulatory processes. It assumes quasi-steady-state conditions for "fast" reactions and incorporates "slow" reactions into the stoichiometric formalism in a time-delayed manner. To assess the efficacy of idFBA, we developed a prototypic integrated system comprising signaling, metabolic, and regulatory processes with network features characteristic of actual systems and incorporated kinetic parameters based on typical time scales observed in literature. idFBA was applied to the prototypic system, which was evaluated for different environments and gene regulatory rules. In addition, we applied the idFBA framework in a similar manner to a representative module of the single-cell eukaryotic organism Saccharomyces cerevisiae. Ultimately, idFBA facilitated quantitative, dynamic analysis of systemic effects of extracellular cues on cellular phenotypes and generated comparable time-course predictions when contrasted with an equivalent kinetic model. Since idFBA solves a linear programming problem and does not require an exhaustive list of detailed kinetic parameters, it may be efficiently scaled to integrated intracellular systems that incorporate signaling, metabolic, and regulatory processes at the genome scale, such as the S. cerevisiae system presented here.

Flux balance analysis (FBA) has emerged as an effective means to analyse biological networks in a quantitative manner. Much progress has been made on the extension of FBA to incorporate a priori biological knowledge, provide more practical descriptions of observed cell behaviours, and predict the outcome of network perturbations. Metabolomics is independently advancing as a set of high-throughput data acquisition tools providing dynamic profiles of metabolites in an unbiased manner. These data sets are neither yet sufficiently comprehensive nor accurate enough for generating large-scale kinetic models. Thus, there is a pressing need to develop quantitative techniques that can make use of the emerging data and embrace the associated uncertainties. This article reviews recent advances in FBA to meet this need and discusses the utility of FBA as a complement to metabolomics and the expected synergy as a result of combining these two techniques.

Complex regulatory networks control the transcription state of a genome. These transcriptional regulatory networks (TRNs) have been mathematically described using a Boolean formalism, in which the state of a gene is represented as either transcribed or not transcribed in response to regulatory signals. The Boolean formalism results in a series of regulatory rules for the individual genes of a TRN that in turn can be used to link environmental cues to the transcription state of a genome, thereby forming a complete transcriptional regulatory system (TRS). Herein, we develop a formalism that represents such a set of regulatory rules in a matrix form. Matrix formalism allows for the systemic characterization of the properties of a TRS and facilitates the computation of the transcriptional state of the genome under any given set of environmental conditions. Additionally, it provides a means to incorporate mechanistic detail of a TRS as it becomes available. In this study, the regulatory network matrix, R, for a prototypic TRS is characterized and the fundamental subspaces of this matrix are described. We illustrate how the matrix representation of a TRS coupled with its environment (R*) allows for a sampling of all possible expression states of a given network, and furthermore, how the fundamental subspaces of the matrix provide a way to study key TRS features and may assist in experimental design.