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1.  Dynamic interaction networks in a hierarchically organized tissue 
We have integrated gene expression profiling with database and literature mining, mechanistic modeling, and cell culture experiments to identify intercellular and intracellular networks regulating blood stem cell self-renewal.Blood stem cell fate in vitro is regulated non-autonomously by a coupled positive–negative intercellular feedback circuit, composed of megakaryocyte-derived stimulatory growth factors (VEGF, PDGF, EGF, and serotonin) versus monocyte-derived inhibitory factors (CCL3, CCL4, CXCL10, TGFB2, and TNFSF9).The antagonistic signals converge in a core intracellular network focused around PI3K, Raf, PLC, and Akt.Model simulations enable functional classification of the novel endogenous ligands and signaling molecules.
Intercellular (between cell) communication networks are required to maintain homeostasis and coordinate regenerative and developmental cues in multicellular organisms. Despite the recognized importance of intercellular networks in regulating adult stem and progenitor cell fate, the specific cell populations involved, and the underlying molecular mechanisms are largely undefined. Although a limited number of studies have applied novel bioinformatic approaches to unravel intercellular signaling in other cell systems (Frankenstein et al, 2006), a comprehensive analysis of intercellular communication in a stem cell-derived, hierarchical tissue network has yet to be reported.
As a model system to explore intercellular communication networks in a hierarchically organized tissue, we cultured human umbilical cord blood (UCB)-derived stem and progenitor cells in defined, minimal cytokine-supplemented liquid culture (Madlambayan et al, 2006). To systematically explore the molecular and cellular dynamics underlying primitive progenitor growth and differentiation, gene expression profiles of primitive (lineage negative; Lin−) and mature (lineage positive; Lin+) populations were generated during phases of stem cell expansion versus depletion. Parallel phenotypic and subproteomic experiments validated that mRNA expression correlated with complex measures of proteome activity (protein secretion and cell surface expression). Using a curated list of secreted ligand–receptor interactions and published expression profiles of purified mature blood populations, we implemented a novel algorithm to reconstruct the intercellular signaling networks established between stem cells and multi-lineage progeny in vitro. By correlating differential expression patterns with stem cell growth, we predict cell populations, pathways, and secreted ligands associated with stem cell self-renewal and differentiation (Figure 3A).
We then tested the correlative predictions in a series of cell culture experiments. UCB progenitor cell cultures were supplemented with saturating amounts of 18 putative regulatory ligands, or cocultured with purified mature blood lineages (megakaryocytes, monocytes, and erythrocytes), and analyzed for effects on total cell, progenitor, and primitive progenitor growth. At the primitive progenitor level, 3/5 novel predicted stimulatory ligands (EGF, PDGFB, and VEGF) displayed significant positive effects, 5/7 predicted inhibitory factors (CCL3, CCL4, CXCL10, TNFSF9, and TGFB2) displayed negative effects, whereas only 1/5 non-correlated ligand (CXCL7) displayed an effect. Also consistent with predictions from gene expression data, megakaryocytes and monocytes were found to stimulate and inhibit primitive progenitor growth, respectively, and these effects were attributable to differential secretome profiles of stimulatory versus inhibitory ligands.
Cellular responses to external stimuli, particularly in heterogeneous and dynamic cell populations, represent complex functions of multiple cell fate decisions acting both directly and indirectly on the target (stem cell) populations. Experimentally distinguishing the mode of action of cytokines is thus a difficult task. To address this we used our previously published interactive model of hematopoiesis (Kirouac et al, 2009) to classify experimentally identified regulatory ligands into one of four distinct functional categories based on their differential effects on cell population growth. TGFB2 was classified as a proliferation inhibitor, CCL4, CXCL10, SPARC, and TNFSF9 as self-renewal inhibitors, CCL3 a proliferation stimulator, and EGF, VEGF, and PDGFB as self-renewal stimulators.
Stem and progenitor cells exposed to combinatorial extracellular signals must propagate this information through intracellular molecular networks, and respond appropriately by modifying cell fate decisions. To explore how our experimentally identified positive and negative regulatory signals are integrated at the intracellular level, we constructed a blood stem cell self-renewal signaling network through extensive literature curation and protein–protein interaction (PPI) network mapping. We find that signal transduction pathways activated by the various stimulatory and inhibitory ligands converge on a limited set of molecular control nodes, forming a core subnetwork enriched for known regulators of self-renewal (Figure 6A). To experimentally test the intracellular signaling molecules computationally predicted as regulators of stem cell self-renewal, we obtained five small molecule antagonists against the kinases Phosphatidylinositol 3-kinase (PI3K), Raf, Akt, Phospholipase C (PLC), and MEK1. Liquid cultures were supplemented with the five molecules individually, and resultant cell population outputs compared against model simulations to deconvolute the functional effects on proliferation (and survival) versus self-renewal. This analysis classifies inhibition of PI3K and Raf activity as selectively targeting self-renewal, PLC as selectively targeting survival, and Akt as selectively targeting proliferation; MEK inhibition appears non-specific for these processes.
This represents the first systematic characterization of how cell fate decisions are regulated non-autonomously through lineage-specific interactions with differentiated progeny. The complex intercellular communication networks can be approximated as an antagonistic positive–negative feedback circuit, wherein progenitor expansion is modulated by a balance of megakaryocyte-derived stimulatory factors (EGF, PDGF, VEGF, and possibly serotonin) versus monocyte-derived inhibitory factors (CCL3, CCL4, CXCL10, TGFB2, and TNFSF9). This complex milieu of endogenous regulatory signals is integrated and processed within a core intracellular signaling network, resulting in modulation of cell-level kinetic parameters (proliferation, survival, and self-renewal). We reconstruct a stem cell associated intracellular network, and identify PI3K, Raf, Akt, and PLC as functionally distinct signal integration nodes, linking extracellular and intracellular signaling. These findings lay the groundwork for novel strategies to control blood stem cell self-renewal in vitro and in vivo.
Intercellular (between cell) communication networks maintain homeostasis and coordinate regenerative and developmental cues in multicellular organisms. Despite the importance of intercellular networks in stem cell biology, their rules, structure and molecular components are poorly understood. Herein, we describe the structure and dynamics of intercellular and intracellular networks in a stem cell derived, hierarchically organized tissue using experimental and theoretical analyses of cultured human umbilical cord blood progenitors. By integrating high-throughput molecular profiling, database and literature mining, mechanistic modeling, and cell culture experiments, we show that secreted factor-mediated intercellular communication networks regulate blood stem cell fate decisions. In particular, self-renewal is modulated by a coupled positive–negative intercellular feedback circuit composed of megakaryocyte-derived stimulatory growth factors (VEGF, PDGF, EGF, and serotonin) versus monocyte-derived inhibitory factors (CCL3, CCL4, CXCL10, TGFB2, and TNFSF9). We reconstruct a stem cell intracellular network, and identify PI3K, Raf, Akt, and PLC as functionally distinct signal integration nodes, linking extracellular, and intracellular signaling. This represents the first systematic characterization of how stem cell fate decisions are regulated non-autonomously through lineage-specific interactions with differentiated progeny.
doi:10.1038/msb.2010.71
PMCID: PMC2990637  PMID: 20924352
cellular networks; hematopoiesis; intercellular signaling; self-renewal; stem cells
2.  An integer optimization algorithm for robust identification of non-linear gene regulatory networks 
BMC Systems Biology  2012;6:119.
Background
Reverse engineering gene networks and identifying regulatory interactions are integral to understanding cellular decision making processes. Advancement in high throughput experimental techniques has initiated innovative data driven analysis of gene regulatory networks. However, inherent noise associated with biological systems requires numerous experimental replicates for reliable conclusions. Furthermore, evidence of robust algorithms directly exploiting basic biological traits are few. Such algorithms are expected to be efficient in their performance and robust in their prediction.
Results
We have developed a network identification algorithm to accurately infer both the topology and strength of regulatory interactions from time series gene expression data in the presence of significant experimental noise and non-linear behavior. In this novel formulism, we have addressed data variability in biological systems by integrating network identification with the bootstrap resampling technique, hence predicting robust interactions from limited experimental replicates subjected to noise. Furthermore, we have incorporated non-linearity in gene dynamics using the S-system formulation. The basic network identification formulation exploits the trait of sparsity of biological interactions. Towards that, the identification algorithm is formulated as an integer-programming problem by introducing binary variables for each network component. The objective function is targeted to minimize the network connections subjected to the constraint of maximal agreement between the experimental and predicted gene dynamics. The developed algorithm is validated using both in silico and experimental data-sets. These studies show that the algorithm can accurately predict the topology and connection strength of the in silico networks, as quantified by high precision and recall, and small discrepancy between the actual and predicted kinetic parameters. Furthermore, in both the in silico and experimental case studies, the predicted gene expression profiles are in very close agreement with the dynamics of the input data.
Conclusions
Our integer programming algorithm effectively utilizes bootstrapping to identify robust gene regulatory networks from noisy, non-linear time-series gene expression data. With significant noise and non-linearities being inherent to biological systems, the present formulism, with the incorporation of network sparsity, is extremely relevant to gene regulatory networks, and while the formulation has been validated against in silico and E. Coli data, it can be applied to any biological system.
doi:10.1186/1752-0509-6-119
PMCID: PMC3444924  PMID: 22937832
Gene regulatory networks; Non-linear dynamics; S-system; Robust network identification; Bootstrapping; Integer programming; Optimization algorithm
3.  Optimization of minimum set of protein–DNA interactions: a quasi exact solution with minimum over-fitting 
Bioinformatics  2009;26(3):319-325.
Motivation: A major limitation in modeling protein interactions is the difficulty of assessing the over-fitting of the training set. Recently, an experimentally based approach that integrates crystallographic information of C2H2 zinc finger–DNA complexes with binding data from 11 mutants, 7 from EGR finger I, was used to define an improved interaction code (no optimization). Here, we present a novel mixed integer programming (MIP)-based method that transforms this type of data into an optimized code, demonstrating both the advantages of the mathematical formulation to minimize over- and under-fitting and the robustness of the underlying physical parameters mapped by the code.
Results: Based on the structural models of feasible interaction networks for 35 mutants of EGR–DNA complexes, the MIP method minimizes the cumulative binding energy over all complexes for a general set of fundamental protein–DNA interactions. To guard against over-fitting, we use the scalability of the method to probe against the elimination of related interactions. From an initial set of 12 parameters (six hydrogen bonds, five desolvation penalties and a water factor), we proceed to eliminate five of them with only a marginal reduction of the correlation coefficient to 0.9983. Further reduction of parameters negatively impacts the performance of the code (under-fitting). Besides accurately predicting the change in binding affinity of validation sets, the code identifies possible context-dependent effects in the definition of the interaction networks. Yet, the approach of constraining predictions to within a pre-selected set of interactions limits the impact of these potential errors to related low-affinity complexes.
Contact: ccamacho@pitt.edu; droleg@pitt.edu
Supplementary information: Supplementary data are available at Bioinformatics online.
doi:10.1093/bioinformatics/btp664
PMCID: PMC2815656  PMID: 19965883
4.  Integrated Module and Gene-Specific Regulatory Inference Implicates Upstream Signaling Networks 
PLoS Computational Biology  2013;9(10):e1003252.
Regulatory networks that control gene expression are important in diverse biological contexts including stress response and development. Each gene's regulatory program is determined by module-level regulation (e.g. co-regulation via the same signaling system), as well as gene-specific determinants that can fine-tune expression. We present a novel approach, Modular regulatory network learning with per gene information (MERLIN), that infers regulatory programs for individual genes while probabilistically constraining these programs to reveal module-level organization of regulatory networks. Using edge-, regulator- and module-based comparisons of simulated networks of known ground truth, we find MERLIN reconstructs regulatory programs of individual genes as well or better than existing approaches of network reconstruction, while additionally identifying modular organization of the regulatory networks. We use MERLIN to dissect global transcriptional behavior in two biological contexts: yeast stress response and human embryonic stem cell differentiation. Regulatory modules inferred by MERLIN capture co-regulatory relationships between signaling proteins and downstream transcription factors thereby revealing the upstream signaling systems controlling transcriptional responses. The inferred networks are enriched for regulators with genetic or physical interactions, supporting the inference, and identify modules of functionally related genes bound by the same transcriptional regulators. Our method combines the strengths of per-gene and per-module methods to reveal new insights into transcriptional regulation in stress and development.
Author Summary
The state of a cell is largely determined by the genes the cell expresses. Transcriptional control of gene expression is exerted by transcription factor proteins that bind to regulatory regions of genes and affect their expression. Transcriptional programs have a modular organization enabling multiple genes to be coordinately regulated, and at the same time are fine-tuned for each gene through interactions of transcription factors with a gene's regulatory region. Transcription factors are themselves controlled by upstream signaling proteins, that in turn can be transcriptionally controlled. This complex process of gene expression control is described by a regulatory network that captures who regulates whom. A key challenge in systems biology is to reconstruct regulatory networks that capture precise gene-specific regulatory information, as well as the modular organization of transcriptional programs. We developed a novel regulatory network inference approach, MERLIN, Modular regulatory network learning with per gene information. When applied to examine transcriptional responses in two distinct processes, stress response and cellular differentiation, MERLIN accurately reconstructed regulatory programs of individual genes while revealing regulatory module organization and predicted upstream signaling proteins for regulatory modules. MERLIN is applicable to different environmental, developmental and disease contexts to dissect regulatory programs and ultimately build network-based predictive models of cellular states.
doi:10.1371/journal.pcbi.1003252
PMCID: PMC3798279  PMID: 24146602
5.  Detecting and Removing Inconsistencies between Experimental Data and Signaling Network Topologies Using Integer Linear Programming on Interaction Graphs 
PLoS Computational Biology  2013;9(9):e1003204.
Cross-referencing experimental data with our current knowledge of signaling network topologies is one central goal of mathematical modeling of cellular signal transduction networks. We present a new methodology for data-driven interrogation and training of signaling networks. While most published methods for signaling network inference operate on Bayesian, Boolean, or ODE models, our approach uses integer linear programming (ILP) on interaction graphs to encode constraints on the qualitative behavior of the nodes. These constraints are posed by the network topology and their formulation as ILP allows us to predict the possible qualitative changes (up, down, no effect) of the activation levels of the nodes for a given stimulus. We provide four basic operations to detect and remove inconsistencies between measurements and predicted behavior: (i) find a topology-consistent explanation for responses of signaling nodes measured in a stimulus-response experiment (if none exists, find the closest explanation); (ii) determine a minimal set of nodes that need to be corrected to make an inconsistent scenario consistent; (iii) determine the optimal subgraph of the given network topology which can best reflect measurements from a set of experimental scenarios; (iv) find possibly missing edges that would improve the consistency of the graph with respect to a set of experimental scenarios the most. We demonstrate the applicability of the proposed approach by interrogating a manually curated interaction graph model of EGFR/ErbB signaling against a library of high-throughput phosphoproteomic data measured in primary hepatocytes. Our methods detect interactions that are likely to be inactive in hepatocytes and provide suggestions for new interactions that, if included, would significantly improve the goodness of fit. Our framework is highly flexible and the underlying model requires only easily accessible biological knowledge. All related algorithms were implemented in a freely available toolbox SigNetTrainer making it an appealing approach for various applications.
Author Summary
Cellular signal transduction is orchestrated by communication networks of signaling proteins commonly depicted on signaling pathway maps. However, each cell type may have distinct variants of signaling pathways, and wiring diagrams are often altered in disease states. The identification of truly active signaling topologies based on experimental data is therefore one key challenge in systems biology of cellular signaling. We present a new framework for training signaling networks based on interaction graphs (IG). In contrast to complex modeling formalisms, IG capture merely the known positive and negative edges between the components. This basic information, however, already sets hard constraints on the possible qualitative behaviors of the nodes when perturbing the network. Our approach uses Integer Linear Programming to encode these constraints and to predict the possible changes (down, neutral, up) of the activation levels of the involved players for a given experiment. Based on this formulation we developed several algorithms for detecting and removing inconsistencies between measurements and network topology. Demonstrated by EGFR/ErbB signaling in hepatocytes, our approach delivers direct conclusions on edges that are likely inactive or missing relative to canonical pathway maps. Such information drives the further elucidation of signaling network topologies under normal and pathological phenotypes.
doi:10.1371/journal.pcbi.1003204
PMCID: PMC3764019  PMID: 24039561
6.  Metabolic Constraint-Based Refinement of Transcriptional Regulatory Networks 
PLoS Computational Biology  2013;9(12):e1003370.
There is a strong need for computational frameworks that integrate different biological processes and data-types to unravel cellular regulation. Current efforts to reconstruct transcriptional regulatory networks (TRNs) focus primarily on proximal data such as gene co-expression and transcription factor (TF) binding. While such approaches enable rapid reconstruction of TRNs, the overwhelming combinatorics of possible networks limits identification of mechanistic regulatory interactions. Utilizing growth phenotypes and systems-level constraints to inform regulatory network reconstruction is an unmet challenge. We present our approach Gene Expression and Metabolism Integrated for Network Inference (GEMINI) that links a compendium of candidate regulatory interactions with the metabolic network to predict their systems-level effect on growth phenotypes. We then compare predictions with experimental phenotype data to select phenotype-consistent regulatory interactions. GEMINI makes use of the observation that only a small fraction of regulatory network states are compatible with a viable metabolic network, and outputs a regulatory network that is simultaneously consistent with the input genome-scale metabolic network model, gene expression data, and TF knockout phenotypes. GEMINI preferentially recalls gold-standard interactions (p-value = 10−172), significantly better than using gene expression alone. We applied GEMINI to create an integrated metabolic-regulatory network model for Saccharomyces cerevisiae involving 25,000 regulatory interactions controlling 1597 metabolic reactions. The model quantitatively predicts TF knockout phenotypes in new conditions (p-value = 10−14) and revealed potential condition-specific regulatory mechanisms. Our results suggest that a metabolic constraint-based approach can be successfully used to help reconstruct TRNs from high-throughput data, and highlights the potential of using a biochemically-detailed mechanistic framework to integrate and reconcile inconsistencies across different data-types. The algorithm and associated data are available at https://sourceforge.net/projects/gemini-data/
Author Summary
Cellular networks, such as metabolic and transcriptional regulatory networks (TRNs), do not operate independently but work together in unison to determine cellular phenotypes. Further, the phenotype and architecture of one network constrains the topology of other networks. Hence, it is critical to study network components and interactions in the context of the entire cell. Typically, efforts to reconstruct TRNs focus only on immediately proximal data such as gene co-expression and transcription factor (TF)-binding. Herein, we take a different strategy by linking candidate TRNs with the metabolic network to predict systems-level responses such as growth phenotypes of TF knockout strains, and compare predictions with experimental phenotype data to select amongst the candidate TRNs. Our approach goes beyond traditional data integration approaches for network inference and refinement by using a predictive network model (metabolism) to refine another network model (regulation) – thus providing an alternative avenue to this area of research. Understanding how the networks function together in a cell will pave the way for synthetic biology and has a wide-range of applications in biotechnology, drug discovery and diagnostics. Further we demonstrate how metabolic models can integrate and reconcile inconsistencies across different data-types.
doi:10.1371/journal.pcbi.1003370
PMCID: PMC3857774  PMID: 24348226
7.  Transcriptional Dynamics of the Embryonic Stem Cell Switch 
PLoS Computational Biology  2006;2(9):e123.
Recent ChIP experiments of human and mouse embryonic stem cells have elucidated the architecture of the transcriptional regulatory circuitry responsible for cell determination, which involves the transcription factors OCT4, SOX2, and NANOG. In addition to regulating each other through feedback loops, these genes also regulate downstream target genes involved in the maintenance and differentiation of embryonic stem cells. A search for the OCT4–SOX2–NANOG network motif in other species reveals that it is unique to mammals. With a kinetic modeling approach, we ascribe function to the observed OCT4–SOX2–NANOG network by making plausible assumptions about the interactions between the transcription factors at the gene promoter binding sites and RNA polymerase (RNAP), at each of the three genes as well as at the target genes. We identify a bistable switch in the network, which arises due to several positive feedback loops, and is switched on/off by input environmental signals. The switch stabilizes the expression levels of the three genes, and through their regulatory roles on the downstream target genes, leads to a binary decision: when OCT4, SOX2, and NANOG are expressed and the switch is on, the self-renewal genes are on and the differentiation genes are off. The opposite holds when the switch is off. The model is extremely robust to parameter changes. In addition to providing a self-consistent picture of the transcriptional circuit, the model generates several predictions. Increasing the binding strength of NANOG to OCT4 and SOX2, or increasing its basal transcriptional rate, leads to an irreversible bistable switch: the switch remains on even when the activating signal is removed. Hence, the stem cell can be manipulated to be self-renewing without the requirement of input signals. We also suggest tests that could discriminate between a variety of feedforward regulation architectures of the target genes by OCT4, SOX2, and NANOG.
Synopsis
One key issue in developmental biology is how embryonic stem cells are regulated at the genetic level. Recent high throughput experiments have elucidated the architecture of the gene regulatory network responsible for embryonic stem cell fate decisions in human and mouse. In this work the authors develop a computational model to describe the mutual regulation of the genes involved in these networks and their subsequent effects on downstream target genes. They find that the core genetic network incorporates the functionality of a bistable switch, which arises due to positive feedback loops in the system. Also, this switch behaviour is very robust with respect to model parameters. The switch and architecture by which the genetic network regulates the downstream genes, is responsible for either maintaining the genes responsible for self-renewal on, and genes involved with differentiation off, or the opposite outcome, depending on whether the switch is on/off, respectively. The model also provides several predictions which can lead to further understanding of the network. The methods employed are fairly standard and transparent which facilitates further uncovering in future experimental investigations of genetic networks.
doi:10.1371/journal.pcbi.0020123
PMCID: PMC1570179  PMID: 16978048
8.  A model of yeast cell-cycle regulation based on multisite phosphorylation 
Multisite phosphorylation of CDK target proteins provides the requisite nonlinearity for cell cycle modeling using elementary reaction mechanisms.Stochastic simulations, based on Gillespie's algorithm and using realistic numbers of protein and mRNA molecules, compare favorably with single-cell measurements in budding yeast.The role of transcription–translation coupling is critical in the robust operation of protein regulatory networks in yeast cells.
Progression through the eukaryotic cell cycle is governed by the activation and inactivation of a family of cyclin-dependent kinases (CDKs) and auxiliary proteins that regulate CDK activities (Morgan, 2007). The many components of this protein regulatory network are interconnected by positive and negative feedback loops that create bistable switches and transient pulses (Tyson and Novak, 2008). The network must ensure that cell-cycle events proceed in the correct order, that cell division is balanced with respect to cell growth, and that any problems encountered (in replicating the genome or partitioning chromosomes to daughter cells) are corrected before the cell proceeds to the next phase of the cycle. The network must operate robustly in the context of unavoidable molecular fluctuations in a yeast-sized cell. With a volume of only 5×10−14 l, a yeast cell contains one copy of the gene for each component of the network, a handful of mRNA transcripts of each gene, and a few hundreds to thousands of protein molecules carrying out each gene's function. How large are the molecular fluctuations implied by these numbers, and what effects do they have on the functioning of the cell-cycle control system?
To answer these questions, we have built a new model (Figure 1) of the CDK regulatory network in budding yeast, based on the fact that the targets of CDK activity are typically phosphorylated on multiple sites. The activity of each target protein depends on how many sites are phosphorylated. The target proteins feedback on CDK activity by controlling cyclin synthesis (SBF's role) and degradation (Cdh1's role) and by releasing a CDK-counteracting phosphatase (Cdc14). Every reaction in Figure 1 can be described by a mass-action rate law, with an accompanying rate constant that must be estimated from experimental data. As the transcription and translation of mRNA molecules have major effects on fluctuating numbers of protein molecules (Pedraza and Paulsson, 2008), we have included mRNA transcripts for each protein in the model.
To create a deterministic model, the rate laws are combined, according to standard principles of chemical kinetics, into a set of 60 differential equations that govern the temporal dynamics of the control system. In the stochastic version of the model, the rate law for each reaction determines the probability per unit time that a particular reaction occurs, and we use Gillespie's stochastic simulation algorithm (Gillespie, 1976) to compute possible temporal sequences of reaction events. Accurate stochastic simulations require knowledge of the expected numbers of mRNA and protein molecules in a single yeast cell. Fortunately, these numbers are available from several sources (Ghaemmaghami et al, 2003; Zenklusen et al, 2008). Although the experimental estimates are not always in good agreement with each other, they are sufficiently reliable to populate a stochastic model with realistic numbers of molecules.
By simulating thousands of cells (as in Figure 5), we can build up representative samples for computing the mean and s.d. of any measurable cell-cycle property (e.g. interdivision time, size at division, duration of G1 phase). The excellent fit of simulated statistics to observations of cell-cycle variability is documented in the main text and Supplementary Information.
Of particular interest to us are observations of Di Talia et al (2007) of the timing of a crucial G1 event (export of Whi5 protein from the nucleus) in a population of budding yeast cells growing at a specific growth rate α=ln2/(mass-doubling time). Whi5 export is a consequence of Whi5 phosphorylation, and it occurs simultaneously with the release (activation) of SBF (see Figure 1). Using fluorescently labeled Whi5, Di Talia et al could easily measure (in individual yeast cells) the time, T1, from cell birth to the abrupt loss of Whi5 from the nucleus. Correlating T1 to the size of the cell at birth, Vbirth, they found that, for a sample of daughter cells, αT1 versus ln(Vbirth) could be fit with two straight lines of slope −0.7 and −0.3. Our simulation of this experiment (Figure 7 of the main text) compares favorably with Figure 3d and e in Di Talia et al (2007).
The major sources of noise in our model (and in protein regulatory networks in yeast cells, in general) are related to gene transcription and the small number of unique mRNA transcripts. As each mRNA molecule may instruct the synthesis of dozens of protein molecules, the coefficient of variation of molecular fluctuations at the protein level (CVP) may be dominated by fluctuations at the mRNA level, as expressed in the formula (Pedraza and Paulsson, 2008) where NM, NP denote the number of mRNA and protein molecules, respectively, and ρ=τM/τP is the ratio of half-lives of mRNA and protein molecules. For a yeast cell, typical values of NM and NP are 8 and 800, respectively (Ghaemmaghami et al, 2003; Zenklusen et al, 2008). If ρ=1, then CVP≈25%. Such large fluctuations in protein levels are inconsistent with the observed variability of size and age at division in yeast cells, as shown in the simplified cell-cycle model of Kar et al (2009) and as we have confirmed with our more realistic model. The size of these fluctuations can be reduced to a more acceptable level by assuming a shorter half-life for mRNA (say, ρ=0.1).
There must be some mechanisms whereby yeast cells lessen the protein fluctuations implied by transcription–translation coupling. Following Pedraza and Paulsson (2008), we suggest that mRNA gestation and senescence may resolve this problem. Equation (3) is based on a simple, one-stage, birth–death model of mRNA turnover. In Supplementary Appendix 1, we show that a model of mRNA processing, with 10 stages each of mRNA gestation and senescence, gives reasonable fluctuations at the protein level (CVP≈5%), even if the effective half-life of mRNA is 10 min. A one-stage model with τM=1 min gives comparable fluctuations (CVP≈5%). In the main text, we use a simple birth–death model of mRNA turnover with an ‘effective' half-life of 1 min, in order to limit the computational complexity of the full cell-cycle model.
In order for the cell's genome to be passed intact from one generation to the next, the events of the cell cycle (DNA replication, mitosis, cell division) must be executed in the correct order, despite the considerable molecular noise inherent in any protein-based regulatory system residing in the small confines of a eukaryotic cell. To assess the effects of molecular fluctuations on cell-cycle progression in budding yeast cells, we have constructed a new model of the regulation of Cln- and Clb-dependent kinases, based on multisite phosphorylation of their target proteins and on positive and negative feedback loops involving the kinases themselves. To account for the significant role of noise in the transcription and translation steps of gene expression, the model includes mRNAs as well as proteins. The model equations are simulated deterministically and stochastically to reveal the bistable switching behavior on which proper cell-cycle progression depends and to show that this behavior is robust to the level of molecular noise expected in yeast-sized cells (∼50 fL volume). The model gives a quantitatively accurate account of the variability observed in the G1-S transition in budding yeast, which is governed by an underlying sizer+timer control system.
doi:10.1038/msb.2010.55
PMCID: PMC2947364  PMID: 20739927
bistability; cell-cycle variability; size control; stochastic model; transcription–translation coupling
9.  Insight into human alveolar macrophage and M. tuberculosis interactions via metabolic reconstructions 
A human alveolar macrophage genome-scale metabolic reconstruction was reconstructed from tailoring a global human metabolic network, Recon 1, by using computational algorithms and manual curation.A genome-scale host–pathogen network of the human alveolar macrophage and Mycobacterium tuberculosis is presented. This involved integrating two genome-scale network reconstructions.The reaction activity and gene essentiality predictions of the host–pathogen model represent a more accurate depiction of infection.Integration of high-throughput data into a host-pathogen model followed by systems analysis was performed in order to elucidate major metabolic differences under different types of M. tuberculosis infection.
Mycobacterium tuberculosis (M. tb) is an insidious and highly persistent pathogen that affects one-third of the world's population (WHO, 2009). Metabolism is foundational to M. tb's infection ability and the ensuing host–pathogen interactions. In addition, M. tb has a heterogeneous clinical presentation and can infect virtually every tissue. Depending on the location of the infection, different metabolic pathways are active and inactive in both the host and pathogen cells. In this study, we sought to model the host–pathogen interactions of the human alveolar macrophage and M. tb as well as detail the metabolic differences in specific infection types using genome-scale metabolic reconstructions (Figure 4A).
Genome-scale metabolic reconstructions are knowledge bases of all known metabolic reactions of a given organism. Reconstructions have been shown to elucidate the mechanistic genotype-to-phenotype relationship through the integration of high-throughput and physiological data (Oberhardt et al, 2009). Genome-scale reconstructions are converted into mathematical models under the constraints-based reconstruction and analysis (COBRA) platform (Becker et al, 2007). COBRA models use network stoichiometry and steady-state mass balances to define a solution space of potential flux states that a network can take. Thus, the COBRA approach does not require kinetic parameters.
Recently, the global human metabolic network, Recon 1, has been reconstructed (Duarte et al, 2007). To understand the metabolic host–pathogen integrations of M. tb with its human host, we first tailored the global human metabolic network into a cell-specific metabolic reconstruction of the human alveolar macrophage. This was carried out using established computational algorithms (Becker and Palsson, 2008; Shlomi et al, 2008) and manual curation to confirm the included and excluded reactions. The human alveolar macrophage reconstruction, iAB-AMØ-1410, accounts for 1410 genes, 3012 intracellular reactions, and 2572 metabolites (Figure 4C). iAB-AMØ-1410 was able to accurately predict maximum ATP and NO production rates obtained from experimental data (Griscavage et al, 1993; Newsholme et al, 1999).
The second step to studying host–pathogen interactions was integration of the human alveolar macrophage reconstruction with an existing genome-scale metabolic model of M. tb, iNJ661 (Jamshidi and Palsson, 2007). Interfacial constraints were set to create a phagosomal environment that was hypoxic, nitrosative, rich in fatty acids, and poor in carbohydrates. From the onset, it was apparent that some oxygen (<15% of in vitro uptake) was required for proper simulations. In addition, algorithmic tailoring of the M. tb biomass objective function was performed to better represent an infectious state. The integrated host–pathogen metabolic reconstruction was dubbed iAB-AMØ-1410-Mt-661.
Analysis of the integrated host–pathogen metabolic reconstruction resulted in three main findings. First, by setting interfacial constraints and tailoring the biomass objective function, the solution space better represents an infectious state. Without adding artificial constraints to the host portion of the integrated model, the iAB-AMØ-1410 solution space is greatly reduced (Figure 4B). Macrophage glycolysis and nitric oxide production are up-regulated and macrophage ATP production, nucleotide synthesis, and amino-acid metabolism are suppressed. In addition, M. tb glycolysis is suppressed and isocitrate lyase is up-regulated for generation of acetyl-CoA. Fatty acid oxidation pathways and production of mycolic acids are increased, while production of nucleotides, peptidoglycans, and phenolic glycolipids are reduced. The modified solution space of the alveolar macrophage and M. tb better represents the infectious state.
Second, the host-pathogen model more accurately predicts M. tb gene deletion tests than the current in vitro model, iNJ661. The host-pathogen model predicted 11 essential genes and 37 unessential genes differently than iNJ661. A total of 22 of the differentially predicted genes have been experimentally characterized (Sassetti and Rubin, 2003; Sohaskey, 2008). The host-pathogen model correctly predicted 18 of the 22 genes. Thus, iAB-AMØ-1410-Mt-661 is a more accurate platform for studying infectious states of M. tb.
Finally, we sought to determine metabolic differences in both the macrophage and M. tb between three different types of infection: latent, pulmonary, and meningeal. Transcription profiling data of the macrophage for the three infections (Thuong et al, 2008) were integrated in the context of the host–pathogen network to elucidate the reaction activity of the three infections. There was wide heterogeneity in the three infection states; some of these differences are highlighted. Macrophage hyaluronan synthase and export were only active in the pulmonary infection. This is potentially interesting from a pharmaceutical viewpoint as hyaluronan has been implicated as a potential carbon source for extracellular M. tb (Hirayama et al, 2009). In addition, we detected metabolic activity differences in M. tb pathways that have been previously discussed as potential drug targets (Eoh et al, 2007; Boshoff et al, 2008). Polyprenyl metabolic reactions were only active in the latent state infection, while de novo synthesis of nicotinamide cofactors was only active in latent and meningeal M. tb infections.
Host-pathogen modeling represents a novel approach for studying metabolic interactions during infection. iAB-AMØ-1410-Mt-661 is a more accurate platform for understanding the biology and pathophysiology of M. tb infection. Most importantly, genome-scale metabolic reconstructions can act as scaffolds for integrating high-throughput data. Particularly, in this study we were able to discern reaction activity differences between different infection types.
Metabolic coupling of Mycobacterium tuberculosis to its host is foundational to its pathogenesis. Computational genome-scale metabolic models have shown utility in integrating -omic as well as physiologic data for systemic, mechanistic analysis of metabolism. To date, integrative analysis of host–pathogen interactions using in silico mass-balanced, genome-scale models has not been performed. We, therefore, constructed a cell-specific alveolar macrophage model, iAB-AMØ-1410, from the global human metabolic reconstruction, Recon 1. The model successfully predicted experimentally verified ATP and nitric oxide production rates in macrophages. This model was then integrated with an M. tuberculosis H37Rv model, iNJ661, to build an integrated host–pathogen genome-scale reconstruction, iAB-AMØ-1410-Mt-661. The integrated host–pathogen network enables simulation of the metabolic changes during infection. The resulting reaction activity and gene essentiality targets of the integrated model represent an altered infectious state. High-throughput data from infected macrophages were mapped onto the host–pathogen network and were able to describe three distinct pathological states. Integrated host–pathogen reconstructions thus form a foundation upon which understanding the biology and pathophysiology of infections can be developed.
doi:10.1038/msb.2010.68
PMCID: PMC2990636  PMID: 20959820
computational biology; host–pathogen; Mycobacterium tuberculosis; systems biology; macrophage
10.  The auxin signalling network translates dynamic input into robust patterning at the shoot apex 
We provide a comprehensive expression map of the different genes (TIR1/AFBs, ARFs and Aux/IAAs) involved in the signalling pathway regulating gene transcription in response to auxin in the shoot apical meristem (SAM).We demonstrate a relatively simple structure of this pathway using a high-throughput yeast two-hybrid approach to obtain the Aux/IAA-ARF full interactome.The topology of the signalling network was used to construct a model for auxin signalling and to predict a role for the spatial regulation of auxin signalling in patterning of the SAM.We used a new sensor to monitor the input in the auxin signalling pathway and to confirm the model prediction, thus demonstrating that auxin signalling is essential to create robust patterns at the SAM.
The plant hormone auxin is a key morphogenetic signal involved in the control of cell identity throughout development. A striking example of auxin action is at the shoot apical meristem (SAM), a population of stem cells generating the aerial parts of the plant. Organ positioning and patterning depends on local accumulations of auxin in the SAM, generated by polar transport of auxin (Vernoux et al, 2010). However, it is still unclear how auxin is distributed at cell resolution in tissues and how the hormone is sensed in space and time during development. A complex ensemble of 29 Aux/IAAs and 23 ARFs is central to the regulation of gene transcription in response to auxin (for review, see Leyser, 2006; Guilfoyle and Hagen, 2007; Chapman and Estelle, 2009). Protein–protein interactions govern the properties of this transduction pathway (Del Bianco and Kepinski, 2011). Limited interaction studies suggest that, in the absence of auxin, the Aux/IAA repressors form heterodimers with the ARF transcription factors, preventing them from regulating target genes. In the presence of auxin, the Aux/IAA proteins are targeted to the proteasome by an SCF E3 ubiquitin ligase complex (Chapman and Estelle, 2009; Leyser, 2006). In this process, auxin promotes the interaction between Aux/IAA proteins and the TIR1 F-box of the SCF complex (or its AFB homologues) that acts as an auxin co-receptor (Dharmasiri et al, 2005a, 2005b; Kepinski and Leyser, 2005; Tan et al, 2007). The auxin-induced degradation of Aux/IAAs would then release ARFs to regulate transcription of their target genes. This includes activation of most of the Aux/IAA genes themselves, thus establishing a negative feedback loop (Guilfoyle and Hagen, 2007). Although this general scenario provides a framework for understanding gene regulation by auxin, the underlying protein–protein network remains to be fully characterized.
In this paper, we combined experimental and theoretical analyses to understand how this pathway contributes to sensing auxin in space and time (Figure 1). We first analysed the expression patterns of the ARFs, Aux/IAAs and TIR1/AFBs genes in the SAM. Our results demonstrate a general tendency for most of the 25 ARFs and Aux/IAAs detected in the SAM: a differential expression with low levels at the centre of the meristem (where the stem cells are located) and high levels at the periphery of the meristem (where organ initiation takes place). We also observed a similar differential expression for TIR1/AFB co-receptors. To understand the functional significance of the distribution of ARFs and Aux/IAAs in the SAM, we next investigated the global structure of the Aux/IAA-ARF network using a high-throughput yeast two-hybrid approach and uncover a rather simple topology that relies on three basic generic features: (i) Aux/IAA proteins interact with themselves, (ii) Aux/IAA proteins interact with ARF activators and (iii) ARF repressors have no or very limited interactions with other proteins in the network.
The results of our interaction analysis suggest a model for the Aux/IAA-ARF signalling pathway in the SAM, where transcriptional activation by ARF activators would be negatively regulated by two independent systems, one involving the ARF repressors, the other the Aux/IAAs. The presence of auxin would remove the inhibitory action of Aux/IAAs, but leave the ARF repressors to compete with ARF activators for promoter-binding sites. To explore the regulatory properties of this signalling network, we developed a mathematical model to describe the transcriptional output as a function of the signalling input that is the combinatorial effect of auxin concentration and of its perception. We then used the model and a simplified view of the meristem (where the same population of Aux/IAAs and ARFs exhibit a low expression at the centre and a high expression in the peripheral zone) for investigating the role of auxin signalling in SAM function. We show that in the model, for a given ARF activator-to-repressor ratio, the gene induction capacity increases with the absolute levels of ARF proteins. We thus predict that the differential expression of the ARFs generates differences in auxin sensitivities between the centre (low sensitivity) and the periphery (high sensitivity), and that the expression of TIR1/AFB participates to this regulation (prediction 1). We also use the model to analyse the transcriptional response to rapidly changing auxin concentrations. By simulating situations equivalent either to the centre or the periphery of our simplified representation of the SAM, we predict that the signalling pathway buffers its response to the auxin input via the balance between ARF activators and repressors, in turn generated by their differential spatial distributions (prediction 2).
To test the predictions from the model experimentally, we needed to assess both the input (auxin level and/or perception) and the output (target gene induction) of the signalling cascade. For measuring the transcriptional output, the widely used DR5 reporter is perfectly adapted (Figure 5) (Ulmasov et al, 1997; Sabatini et al, 1999; Benkova et al, 2003; Heisler et al, 2005). For assaying pathway input, we designed DII-VENUS, a novel auxin signalling sensor that comprises a constitutively expressed fusion of the auxin-binding domain (termed domain II or DII) (Dreher et al, 2006; Tan et al, 2007) of an IAA to a fast-maturating variant of YFP, VENUS (Figure 5). The degradation patterns from DII-VENUS indicate a high auxin signalling input both in flower primordia and at the centre of the SAM. This is in contrast to the organ-specific expression pattern of DR5::VENUS (Figure 5). These results indicate that the signalling pathway limits gene activation in response to auxin at the meristem centre and confirm the differential sensitivity to auxin between the centre and the periphery (prediction 1). We further confirmed the buffering capacities of the signalling pathway (prediction 2) by carrying out live imaging experiments to monitor DII-VENUS and DR5::VENUS expression in real time (Figure 5). This analysis reveals the presence of important temporal variations of DII-VENUS fluorescence, while DR5::VENUS does not show such global variations. Our approach thus provides evidence that the Aux/IAA-ARF pathway has a key role in patterning in the SAM, alongside the auxin transport system. Our results illustrate how the tight spatio-temporal regulation of both the distribution of a morphogenetic signal and the activity of the downstream signalling pathway provides robustness to a dynamic developmental process.
A comprehensive expression and interaction map of auxin signalling factors in the Arabidopsis shoot apical meristem is constructed and used to derive a mathematical model of auxin signalling, from which key predictions are experimentally confirmed.
The plant hormone auxin is thought to provide positional information for patterning during development. It is still unclear, however, precisely how auxin is distributed across tissues and how the hormone is sensed in space and time. The control of gene expression in response to auxin involves a complex network of over 50 potentially interacting transcriptional activators and repressors, the auxin response factors (ARFs) and Aux/IAAs. Here, we perform a large-scale analysis of the Aux/IAA-ARF pathway in the shoot apex of Arabidopsis, where dynamic auxin-based patterning controls organogenesis. A comprehensive expression map and full interactome uncovered an unexpectedly simple distribution and structure of this pathway in the shoot apex. A mathematical model of the Aux/IAA-ARF network predicted a strong buffering capacity along with spatial differences in auxin sensitivity. We then tested and confirmed these predictions using a novel auxin signalling sensor that reports input into the signalling pathway, in conjunction with the published DR5 transcriptional output reporter. Our results provide evidence that the auxin signalling network is essential to create robust patterns at the shoot apex.
doi:10.1038/msb.2011.39
PMCID: PMC3167386  PMID: 21734647
auxin; biosensor; live imaging; ODE; signalling
11.  Metabolic network reconstruction of Chlamydomonas offers insight into light-driven algal metabolism 
A comprehensive genome-scale metabolic network of Chlamydomonas reinhardtii, including a detailed account of light-driven metabolism, is reconstructed and validated. The model provides a new resource for research of C. reinhardtii metabolism and in algal biotechnology.
The genome-scale metabolic network of Chlamydomonas reinhardtii (iRC1080) was reconstructed, accounting for >32% of the estimated metabolic genes encoded in the genome, and including extensive details of lipid metabolic pathways.This is the first metabolic network to explicitly account for stoichiometry and wavelengths of metabolic photon usage, providing a new resource for research of C. reinhardtii metabolism and developments in algal biotechnology.Metabolic functional annotation and the largest transcript verification of a metabolic network to date was performed, at least partially verifying >90% of the transcripts accounted for in iRC1080. Analysis of the network supports hypotheses concerning the evolution of latent lipid pathways in C. reinhardtii, including very long-chain polyunsaturated fatty acid and ceramide synthesis pathways.A novel approach for modeling light-driven metabolism was developed that accounts for both light source intensity and spectral quality of emitted light. The constructs resulting from this approach, termed prism reactions, were shown to significantly improve the accuracy of model predictions, and their use was demonstrated for evaluation of light source efficiency and design.
Algae have garnered significant interest in recent years, especially for their potential application in biofuel production. The hallmark, model eukaryotic microalgae Chlamydomonas reinhardtii has been widely used to study photosynthesis, cell motility and phototaxis, cell wall biogenesis, and other fundamental cellular processes (Harris, 2001). Characterizing algal metabolism is key to engineering production strains and understanding photobiological phenomena. Based on extensive literature on C. reinhardtii metabolism, its genome sequence (Merchant et al, 2007), and gene functional annotation, we have reconstructed and experimentally validated the genome-scale metabolic network for this alga, iRC1080, the first network to account for detailed photon absorption permitting growth simulations under different light sources. iRC1080 accounts for 1080 genes, associated with 2190 reactions and 1068 unique metabolites and encompasses 83 subsystems distributed across 10 cellular compartments (Figure 1A). Its >32% coverage of estimated metabolic genes is a tremendous expansion over previous algal reconstructions (Boyle and Morgan, 2009; Manichaikul et al, 2009). The lipid metabolic pathways of iRC1080 are considerably expanded relative to existing networks, and chemical properties of all metabolites in these pathways are accounted for explicitly, providing sufficient detail to completely specify all individual molecular species: backbone molecule and stereochemical numbering of acyl-chain positions; acyl-chain length; and number, position, and cis–trans stereoisomerism of carbon–carbon double bonds. Such detail in lipid metabolism will be critical for model-driven metabolic engineering efforts.
We experimentally verified transcripts accounted for in the network under permissive growth conditions, detecting >90% of tested transcript models (Figure 1B) and providing validating evidence for the contents of iRC1080. We also analyzed the extent of transcript verification by specific metabolic subsystems. Some subsystems stood out as more poorly verified, including chloroplast and mitochondrial transport systems and sphingolipid metabolism, all of which exhibited <80% of transcripts detected, reflecting incomplete characterization of compartmental transporters and supporting a hypothesis of latent pathway evolution for ceramide synthesis in C. reinhardtii. Additional lines of evidence from the reconstruction effort similarly support this hypothesis including lack of ceramide synthetase and other annotation gaps downstream in sphingolipid metabolism. A similar hypothesis of latent pathway evolution was established for very long-chain fatty acids (VLCFAs) and their polyunsaturated analogs (VLCPUFAs) (Figure 1C), owing to the absence of this class of lipids in previous experimental measurements, lack of a candidate VLCFA elongase in the functional annotation, and additional downstream annotation gaps in arachidonic acid metabolism.
The network provides a detailed account of metabolic photon absorption by light-driven reactions, including photosystems I and II, light-dependent protochlorophyllide oxidoreductase, provitamin D3 photoconversion to vitamin D3, and rhodopsin photoisomerase; this network accounting permits the precise modeling of light-dependent metabolism. iRC1080 accounts for effective light spectral ranges through analysis of biochemical activity spectra (Figure 3A), either reaction activity or absorbance at varying light wavelengths. Defining effective spectral ranges associated with each photon-utilizing reaction enabled our network to model growth under different light sources via stoichiometric representation of the spectral composition of emitted light, termed prism reactions. Coefficients for different photon wavelengths in a prism reaction correspond to the ratios of photon flux in the defined effective spectral ranges to the total emitted photon flux from a given light source (Figure 3B). This approach distinguishes the amount of emitted photons that drive different metabolic reactions. We created prism reactions for most light sources that have been used in published studies for algal and plant growth including solar light, various light bulbs, and LEDs. We also included regulatory effects, resulting from lighting conditions insofar as published studies enabled. Light and dark conditions have been shown to affect metabolic enzyme activity in C. reinhardtii on multiple levels: transcriptional regulation, chloroplast RNA degradation, translational regulation, and thioredoxin-mediated enzyme regulation. Through application of our light model and prism reactions, we were able to closely recapitulate experimental growth measurements under solar, incandescent, and red LED lights. Through unbiased sampling, we were able to establish the tremendous statistical significance of the accuracy of growth predictions achievable through implementation of prism reactions. Finally, application of the photosynthetic model was demonstrated prospectively to evaluate light utilization efficiency under different light sources. The results suggest that, of the existing light sources, red LEDs provide the greatest efficiency, about three times as efficient as sunlight. Extending this analysis, the model was applied to design a maximally efficient LED spectrum for algal growth. The result was a 677-nm peak LED spectrum with a total incident photon flux of 360 μE/m2/s, suggesting that for the simple objective of maximizing growth efficiency, LED technology has already reached an effective theoretical optimum.
In summary, the C. reinhardtii metabolic network iRC1080 that we have reconstructed offers insight into the basic biology of this species and may be employed prospectively for genetic engineering design and light source design relevant to algal biotechnology. iRC1080 was used to analyze lipid metabolism and generate novel hypotheses about the evolution of latent pathways. The predictive capacity of metabolic models developed from iRC1080 was demonstrated in simulating mutant phenotypes and in evaluation of light source efficiency. Our network provides a broad knowledgebase of the biochemistry and genomics underlying global metabolism of a photoautotroph, and our modeling approach for light-driven metabolism exemplifies how integration of largely unvisited data types, such as physicochemical environmental parameters, can expand the diversity of applications of metabolic networks.
Metabolic network reconstruction encompasses existing knowledge about an organism's metabolism and genome annotation, providing a platform for omics data analysis and phenotype prediction. The model alga Chlamydomonas reinhardtii is employed to study diverse biological processes from photosynthesis to phototaxis. Recent heightened interest in this species results from an international movement to develop algal biofuels. Integrating biological and optical data, we reconstructed a genome-scale metabolic network for this alga and devised a novel light-modeling approach that enables quantitative growth prediction for a given light source, resolving wavelength and photon flux. We experimentally verified transcripts accounted for in the network and physiologically validated model function through simulation and generation of new experimental growth data, providing high confidence in network contents and predictive applications. The network offers insight into algal metabolism and potential for genetic engineering and efficient light source design, a pioneering resource for studying light-driven metabolism and quantitative systems biology.
doi:10.1038/msb.2011.52
PMCID: PMC3202792  PMID: 21811229
Chlamydomonas reinhardtii; lipid metabolism; metabolic engineering; photobioreactor
12.  Coordination of frontline defense mechanisms under severe oxidative stress 
Inference of an environmental and gene regulatory influence network (EGRINOS) by integrating transcriptional responses to H2O2 and paraquat (PQ) has revealed a multi-tiered oxidative stress (OS)-management program to transcriptionally coordinate three peroxidase/catalase enzymes, two superoxide dismutases, production of rhodopsins, carotenoids and gas vesicles, metal trafficking, and various other aspects of metabolism.ChIP-chip, microarray, and survival assays have validated important architectural aspects of this network, identified novel defense mechanisms (including two evolutionarily distant peroxidase enxymes), and showed that general transcription factors of the transcription factor B family have an important function in coordinating the OS response (OSR) despite their inability to directly sense ROS.A comparison of transcriptional responses to sub-lethal doses of H2O2 and PQ with predictions of these responses made by an EGRIN model generated earlier from responses to other environmental factors has confirmed that a significant fraction of the OSR is made up of a generalized component that is also observed in response to other stressors.Analysis of active regulons within environment and gene regulatory influence network for OS (EGRINOS) across diverse environmental conditions has identified the specialized component of oxidative stress response (OSR) that is triggered by sub-lethal OS, but not by other stressors, including sub-inhibitory levels of redox-active metals, extreme changes in oxygen tension, and a sub-lethal dose of γ rays.
Reactive oxygen species (ROS), such as hydrogen peroxide (H2O2), superoxide (O2−), and hydroxyl (OH−) radicals, are normal by-products of aerobic metabolism. Evolutionarily conserved mechanisms including detoxification enzymes (peroxidase/catalase and superoxide dismutase (SOD)) and free radical scavengers manage this endogenous production of ROS. OS is a condition reached when certain environmental stresses or genetic defects cause the production of ROS to exceed the management capacity. The damage to diverse cellular components including DNA, proteins, lipids, and carbohydrates resulting from OS (Imlay, 2003; Apel and Hirt, 2004; Perrone et al, 2008) is recognized as an important player in many diseases and in the aging process (Finkel, 2005).
We have applied a systems approach to characterize the OSR of an archaeal model organism, Halobacterium salinarum NRC-1. This haloarchaeon grows aerobically at 4.3 M salt concentration in which it routinely faces cycles of desiccation and rehydration, and increased ultraviolet radiation—both of which can increase the production of ROS (Farr and Kogoma, 1991; Oliver et al, 2001). We have reconstructed the physiological adjustments associated with management of excessive OS through the analysis of global transcriptional changes elicited by step exposure to growth sub-inhibitory and sub-lethal levels of H2O2 and PQ (a redox-cycling drug that produces O2−; Hassan and Fridovich, 1979) as well as during subsequent recovery from these stresses. We have integrated all of these data into a unified model for OSR to discover conditional functional links between protective mechanisms and normal aspects of metabolism. Subsequent phenotypic analysis of gene deletion strains has verified the conditional detoxification functions of three putative peroxidase/catalase enzymes, two SODs, and the protective function of rhodopsins under increased levels of H2O2 and PQ. Similarly, we have also validated ROS scavenging by carotenoids and flotation by gas vesicles as secondary mechanisms that may minimize OS.
Given the ubiquitous nature of OS, it is not entirely surprising that most organisms have evolved similar multiple lines of defense—both passive and active. Although such mechanisms have been extensively characterized using other model organisms, our integrated systems approach has uncovered additional protective mechanisms in H. salinarum (e.g. two evolutionarily distant peroxidase/catalase enzymes) and revealed a structure and hierarchy to the OSR through conditional regulatory associations among various components of the response. We have validated some aspects of the architecture of the regulatory network for managing OS by confirming physical protein–DNA interactions of six transcription factors (TFs) with promoters of genes they were predicted to influence in EGRINOS. Furthermore, we have also shown the consequence of deleting two of these TFs on transcript levels of genes they control and survival rate under OS. It is notable that these TFs are not directly associated with sensing ROS, but, rather, they have a general function in coordinating the overall response. This insight would not have been possible without constructing EGRINOS through systems integration of diverse datasets.
Although it has been known that OS is a component of diverse environmental stress conditions, we quantitatively show for the first time that much of the transcriptional responses induced by the two treatments could indeed have been predicted using a model constructed from the analysis of transcriptional responses to changes in other environmental factors (UV and γ-radiation, light, oxygen, and six metals). However, using specific examples we also reveal the specific components of the OSR that are triggered only under severe OS. Notably, this model of OSR gives a unified perspective of the interconnections among all of these generalized and OS-specific regulatory mechanisms.
Complexity of cellular response to oxidative stress (OS) stems from its wide-ranging damage to nucleic acids, proteins, carbohydrates, and lipids. We have constructed a systems model of OS response (OSR) for Halobacterium salinarum NRC-1 in an attempt to understand the architecture of its regulatory network that coordinates this complex response. This has revealed a multi-tiered OS-management program to transcriptionally coordinate three peroxidase/catalase enzymes, two superoxide dismutases, production of rhodopsins, carotenoids and gas vesicles, metal trafficking, and various other aspects of metabolism. Through experimental validation of interactions within the OSR regulatory network, we show that despite their inability to directly sense reactive oxygen species, general transcription factors have an important function in coordinating this response. Remarkably, a significant fraction of this OSR was accurately recapitulated by a model that was earlier constructed from cellular responses to diverse environmental perturbations—this constitutes the general stress response component. Notwithstanding this observation, comparison of the two models has identified the coordination of frontline defense and repair systems by regulatory mechanisms that are triggered uniquely by severe OS and not by other environmental stressors, including sub-inhibitory levels of redox-active metals, extreme changes in oxygen tension, and a sub-lethal dose of γ rays.
doi:10.1038/msb.2010.50
PMCID: PMC2925529  PMID: 20664639
gene regulatory network; microbiology; oxidative stress
13.  Efficient, sparse biological network determination 
BMC Systems Biology  2009;3:25.
Background
Determining the interaction topology of biological systems is a topic that currently attracts significant research interest. Typical models for such systems take the form of differential equations that involve polynomial and rational functions. Such nonlinear models make the problem of determining the connectivity of biochemical networks from time-series experimental data much harder. The use of linear dynamics and linearization techniques that have been proposed in the past can circumvent this, but the general problem of developing efficient algorithms for models that provide more accurate system descriptions remains open.
Results
We present a network determination algorithm that can treat model descriptions with polynomial and rational functions and which does not make use of linearization. For this purpose, we make use of the observation that biochemical networks are in general 'sparse' and minimize the 1-norm of the decision variables (sum of weighted network connections) while constraints keep the error between data and the network dynamics small. The emphasis of our methodology is on determining the interconnection topology rather than the specific reaction constants and it takes into account the necessary properties that a chemical reaction network should have – something that techniques based on linearization can not. The problem can be formulated as a Linear Program, a convex optimization problem, for which efficient algorithms are available that can treat large data sets efficiently and uncertainties in data or model parameters.
Conclusion
The presented methodology is able to predict with accuracy and efficiency the connectivity structure of a chemical reaction network with mass action kinetics and of a gene regulatory network from simulation data even if the dynamics of these systems are non-polynomial (rational) and uncertainties in the data are taken into account. It also produces a network structure that can explain the real experimental data of L. lactis and is similar to the one found in the literature. Numerical methods based on Linear Programming can therefore help determine efficiently the network structure of biological systems from large data sets. The overall objective of this work is to provide methods to increase our understanding of complex biochemical systems, particularly through their interconnection and their non-equilibrium behavior.
doi:10.1186/1752-0509-3-25
PMCID: PMC2671484  PMID: 19236711
14.  A linear programming approach for estimating the structure of a sparse linear genetic network from transcript profiling data 
Background
A genetic network can be represented as a directed graph in which a node corresponds to a gene and a directed edge specifies the direction of influence of one gene on another. The reconstruction of such networks from transcript profiling data remains an important yet challenging endeavor. A transcript profile specifies the abundances of many genes in a biological sample of interest. Prevailing strategies for learning the structure of a genetic network from high-dimensional transcript profiling data assume sparsity and linearity. Many methods consider relatively small directed graphs, inferring graphs with up to a few hundred nodes. This work examines large undirected graphs representations of genetic networks, graphs with many thousands of nodes where an undirected edge between two nodes does not indicate the direction of influence, and the problem of estimating the structure of such a sparse linear genetic network (SLGN) from transcript profiling data.
Results
The structure learning task is cast as a sparse linear regression problem which is then posed as a LASSO (l1-constrained fitting) problem and solved finally by formulating a Linear Program (LP). A bound on the Generalization Error of this approach is given in terms of the Leave-One-Out Error. The accuracy and utility of LP-SLGNs is assessed quantitatively and qualitatively using simulated and real data. The Dialogue for Reverse Engineering Assessments and Methods (DREAM) initiative provides gold standard data sets and evaluation metrics that enable and facilitate the comparison of algorithms for deducing the structure of networks. The structures of LP-SLGNs estimated from the INSILICO1, INSILICO2 and INSILICO3 simulated DREAM2 data sets are comparable to those proposed by the first and/or second ranked teams in the DREAM2 competition. The structures of LP-SLGNs estimated from two published Saccharomyces cerevisae cell cycle transcript profiling data sets capture known regulatory associations. In each S. cerevisiae LP-SLGN, the number of nodes with a particular degree follows an approximate power law suggesting that its degree distributions is similar to that observed in real-world networks. Inspection of these LP-SLGNs suggests biological hypotheses amenable to experimental verification.
Conclusion
A statistically robust and computationally efficient LP-based method for estimating the topology of a large sparse undirected graph from high-dimensional data yields representations of genetic networks that are biologically plausible and useful abstractions of the structures of real genetic networks. Analysis of the statistical and topological properties of learned LP-SLGNs may have practical value; for example, genes with high random walk betweenness, a measure of the centrality of a node in a graph, are good candidates for intervention studies and hence integrated computational – experimental investigations designed to infer more realistic and sophisticated probabilistic directed graphical model representations of genetic networks. The LP-based solutions of the sparse linear regression problem described here may provide a method for learning the structure of transcription factor networks from transcript profiling and transcription factor binding motif data.
doi:10.1186/1748-7188-4-5
PMCID: PMC2654898  PMID: 19239685
15.  Dynamics and Design Principles of a Basic Regulatory Architecture Controlling Metabolic Pathways 
PLoS Biology  2008;6(6):e146.
The dynamic features of a genetic network's response to environmental fluctuations represent essential functional specifications and thus may constrain the possible choices of network architecture and kinetic parameters. To explore the connection between dynamics and network design, we have analyzed a general regulatory architecture that is commonly found in many metabolic pathways. Such architecture is characterized by a dual control mechanism, with end product feedback inhibition and transcriptional regulation mediated by an intermediate metabolite. As a case study, we measured with high temporal resolution the induction profiles of the enzymes in the leucine biosynthetic pathway in response to leucine depletion, using an automated system for monitoring protein expression levels in single cells. All the genes in the pathway are known to be coregulated by the same transcription factors, but we observed drastically different dynamic responses for enzymes upstream and immediately downstream of the key control point—the intermediate metabolite α-isopropylmalate (αIPM), which couples metabolic activity to transcriptional regulation. Analysis based on genetic perturbations suggests that the observed dynamics are due to differential regulation by the leucine branch-specific transcription factor Leu3, and that the downstream enzymes are strictly controlled and highly expressed only when αIPM is available. These observations allow us to build a simplified mathematical model that accounts for the observed dynamics and can correctly predict the pathway's response to new perturbations. Our model also suggests that transient dynamics and steady state can be separately tuned and that the high induction levels of the downstream enzymes are necessary for fast leucine recovery. It is likely that principles emerging from this work can reveal how gene regulation has evolved to optimize performance in other metabolic pathways with similar architecture.
Author Summary
Single-cell organisms must constantly adjust their gene expression programs to survive in a changing environment. Interactions between different molecules form a regulatory network to mediate these changes. While the network connections are often known, figuring out how the network responds dynamically by looking at a static picture of its structure presents a significant challenge. Measuring the response at a finer time scales could reveal the link between the network's function and its structure. The architecture of the system we studied in this work—the leucine biosynthesis pathway in yeast—is shared by other metabolic pathways: a metabolic intermediate binds to a transcription factor to activate the pathway genes, creating an intricate feedback structure that links metabolism with gene expression. We measured protein abundance at high temporal resolution for genes in this pathway in response to leucine depletion and studied the effects of various genetic perturbations on gene expression dynamics. Our measurements and theoretical modeling show that only the genes immediately downstream from the intermediate are highly regulated by the metabolite, a feature that is essential to fast recovery from leucine depletion. Since the architecture we studied is common, we believe that our work may lead to general principles governing the dynamics of gene expression in other metabolic pathways.
A quantitative, high-temporal resolution study of gene induction in a metabolic pathway reveals an intricate connection between the regulatory architecture and the dynamic response of the system, pointing to possible principles underlying the design of these pathways.
doi:10.1371/journal.pbio.0060146
PMCID: PMC2429954  PMID: 18563967
16.  Systematic evaluation of objective functions for predicting intracellular fluxes in Escherichia coli 
The in vivo distribution of metabolic fluxes in Escherichia coli can be predicted from optimality principles At least two different sets of optimality principles govern the operation of the metabolic network under different environmental conditionsMetabolism during unlimited growth on glucose in batch culture is best described by the nonlinear maximization of ATP yield per unit of flux
Based on a long history of biochemical and lately genomic research, metabolic networks, in particular microbial ones, are among the best characterized cellular networks. Most components (genes, proteins and metabolites) and their interactions are known. This topological knowledge of the reaction stoichiometry allows to construct metabolic models up to the level of genome scale (Price et al, 2004). Experimentally, sophisticated 13C-tracer-based methodologies were developed that enable tracking of the intracellular flux traffic through the reaction network (Sauer, 2006). With the accumulation of such experimental flux data, the question arises why a particular distribution of flux within the network is realized and not one of many alternatives?
Here, we address the question whether the intracellular flux state can be predicted from optimality principles, with the underlying rational that evolution might have optimized metabolic operation toward particular objectives or combinations of multiple objectives. For this purpose, we performed a systematic and rigorous comparison between computational flux predictions and available experimental flux data (Emmerling et al, 2002; Perrenoud and Sauer, 2005; Nanchen et al, 2006) under six different environmental conditions for the model bacterium E. coli. For computational flux predictions, we used a constraint-based modeling approach that requires a stoichiometric model of metabolism (Stelling, 2004). More specifically, we employed flux balance analysis (FBA) where objective functions are defined that represent optimality principles of network operation (Price et al, 2004). This approach has been applied successfully to predict gene deletion lethality (Edwards and Palsson, 2000a, bEdwards and Palsson, 2000a, b; Forster et al, 2003; Kuepfer et al, 2005), network capacities and feasible network states (Edwards 2001, Ibarra 2002), but in only few cases to predict the intracellular flux state (Beard et al, 2002; Holzhütter, 2004).
While different objective functions were proposed for different biological systems (Holzhütter, 2004; Price et al, 2004; Knorr et al, 2006), by far the most common assumption is that microbial cells maximize their growth. To address this issue more generally, we evaluated the accuracy of FBA-based flux predictions for 11 linear and nonlinear objective functions that were combined with eight adjustable constraints. For this purpose, we constructed a highly interconnected stoichiometric network model with 98 reactions and 60 metabolites of E. coli central carbon metabolism. Based on mathematical analyses, the overall model could be reduced to a set of 10 reactions that summarize the actual systemic degree of freedom.
As a quantitative measure of how accurate the experimental data are predicted, we defined predictive fidelity as a single value to quantify the overall deviation between in silico and in vivo fluxes. By comparing all in silico predictions to 13C-based in vivo fluxes, we show that prediction of intracellular steady-state fluxes from network stoichiometry alone is, within limits, possible. An unexpected key result is that no further assumptions on network operation in the form of additional and potentially artificial constraints are necessary, provided the appropriate objective function is chosen for a given condition.
While no single objective was able to describe the flux states under all six conditions, we identified two sets of objectives for biologically meaningful predictions without the need for further constraints. For unlimited growth on glucose in aerobic or nitrate-respiring batch cultures, we find that the most accurate and robust results are obtained with the nonlinear maximization of ATP yield per flux unit (Figure 1). Under nutrient scarcity in glucose- or ammonium-limited continuous cultures, in contrast, linear maximization of the overall ATP or biomass yields achieved the highest predictive accuracy.
Since these identified optimality principles describe the system behavior without preconditioning of the network through further constraints, they reflect, to some extent, the evolutionary selection of metabolic network regulation that realizes the various flux states. For conditions of nutrient scarcity, the maximization of energy or biomass yield objective is consistent with the generally observed physiology (Russell and Cook, 1995). The meaning of the maximization of ATP yield per flux unit objective for unlimited growth, however, is less obvious. Generally, it selects for small networks with yet high, albeit suboptimal ATP formation, which has three biological consequences. Firstly, resources are economically allocated since expenditures for enzyme synthesis are, on average, greater for longer pathways. Secondly, suboptimal ATP yields dissipate more energy and thus enable higher catabolic rates. Thirdly, at a constant catabolic rate, a small network results in shorter residence times of substrate molecules until they generate ATP. The relative contribution of these consequences to the evolution of network regulation is unclear, but simultaneous optimization for ATP yield and catabolic rate under this optimality principle identifies a trade-off between the contradicting objectives of maximum overall ATP yield and maximum rate of ATP formation (Pfeiffer et al, 2001).
To which extent can optimality principles describe the operation of metabolic networks? By explicitly considering experimental errors and in silico alternate optima in flux balance analysis, we systematically evaluate the capacity of 11 objective functions combined with eight adjustable constraints to predict 13C-determined in vivo fluxes in Escherichia coli under six environmental conditions. While no single objective describes the flux states under all conditions, we identified two sets of objectives for biologically meaningful predictions without the need for further, potentially artificial constraints. Unlimited growth on glucose in oxygen or nitrate respiring batch cultures is best described by nonlinear maximization of the ATP yield per flux unit. Under nutrient scarcity in continuous cultures, in contrast, linear maximization of the overall ATP or biomass yields achieved the highest predictive accuracy. Since these particular objectives predict the system behavior without preconditioning of the network structure, the identified optimality principles reflect, to some extent, the evolutionary selection of metabolic network regulation that realizes the various flux states.
doi:10.1038/msb4100162
PMCID: PMC1949037  PMID: 17625511
13C-flux; evolution; flux balance analysis; metabolic network; network optimality
17.  An incoherent regulatory network architecture that orchestrates B cell diversification in response to antigen signaling 
B cell receptor signaling controls the expression of IRF-4, a transcription factor required for B cell differentiation. This study shows that IRF-4 regulates divergent B cell fates via a ‘kinetic-control' mechanism that determines the duration of a transient developmental state.
The intensity of signaling through the B cell receptor controls the level of expression of IRF-4, a transcription factor required for B cell differentiation. The rate of IRF-4 production dictates the extent of antibody gene diversification that B cells undergo upon antigen encounter before differentiating into antibody-secreting plasma cells.Computational modeling and experimental analyses substantiate a model, whereby IRF-4 regulates B cell fate trajectories via a ‘kinetic-control' mechanism.Kinetic control is a process by which B cells pass through an obligate state of variable duration that sets the degree of cellular diversification prior to their terminal differentiation.An incoherent regulatory network architecture, within which IRF-4 is embedded, is the basis for realization of kinetic control.
The generation of a diverse set of pathogen-specific antibodies, with differing affinities and effector functions, by B lymphocytes is essential for efficient protection from many microorganisms. Antibody gene diversification in B cells is mediated by two molecular processes termed class-switch recombination and somatic hypermutation (CSR/SHM) (F1A). The former enables the generation of antibodies with the same antigen-binding specificity, but different effector domains, whereas the latter results in a repertoire of antibodies with a range of affinities for a given antigen containing the same effector domain. CSR/SHM occurs in antigen-activated B cells before their terminal differentiation into plasma cells. The transcription factor IRF-4 is required for CSR/SHM as well as plasma-cell differentiation, with its highest levels of expression being necessary for the latter. IRF-4 acts in the context of a network of regulators that include Blimp-1, Pax5, Bach2 and Bcl-6 (F1B). Despite extensive characterization of these individual factors, how the network responds to sensing of antigen by the B cell antigen receptor (BCR, antibody molecule expressed on cell surface) to regulate the extent of antibody gene diversification and plasma-cell differentiation remains to be addressed.
To address this issue, we assemble a computational model. The model reveals two contrasting scenarios that can underlie B cell fate dynamics. In one case, the initial rate of IRF-4 production controls a binary cell fate choice that involves either going to the CSR/SHM state or to the plasma-cell state; the time spent in the CSR state is relatively insensitive to the initial rate of IRF-4 production (herein called ‘basic bistability'). In the other case, IRF-4 drives all cells through a transient CSR/SHM state, but the initial rate of IRF-4 production sets its duration (‘kinetic control'). Both scenarios predict that increasing the initial rate of IRF-4 production favors the generation of plasma cells at the expense of CSR/SHM, but they differ fundamentally with respect to the underlying gene expression patterns.
To distinguish between these two scenarios experimentally, we utilize two different genetic models. The first involves the B1-8i transgenic mouse whose B cells express a rearranged V187.2 VDJ Ig heavy chain gene segment that is specific for the hapten nitrophenol (NP). The second is a newly developed mouse model that allows exogenous control of IRF-4 expression in naive primary B cells using a tet-inducible allele. Using these models, we show that (i) BCR signal strength sets the initial rate of IRF-4 accumulation and (ii) the concentration of IRF-4 is sensed by an incoherent gene regulatory network architecture to regulate the extent of CSR/SHM prior to plasma-cell differentiation. Our results are consistent with the ‘kinetic-control model' in which the levels of BCR-induced IRF-4 expression control the duration of an obligate CSR/SHM state that enables B cell diversification before terminal differentiation into plasma cells. Evidence for the transient CSR/SHM state is corroborated by both patterns of gene expression and the presence of AID-dependent mutations in individual non-switched plasmablasts.
Our results provide a molecular framework for understanding how B cells balance the competing demands for Ig CSR and SHM with the secretion of antibodies during humoral immune responses. The key feature of the network architecture that allows IRF-4 to coordinate the two competing states of gene expression in a temporal manner is that it simultaneously but asymmetrically activates both sides of a bistable mutual repression circuit. Because the two effects of the primary regulator antagonize each other, we describe the circuit as being based on an ‘incoherent' regulatory motif. Other incoherent regulatory motifs in varied biological systems are also associated with the acquisition of transient cell states, and we consider how the kinetic-control mechanism proposed by us could more generally serve to translate developmental cues into elaborate morphogenetic patterns.
The B-lymphocyte lineage is a leading system for analyzing gene regulatory networks (GRNs) that orchestrate distinct cell fate transitions. Upon antigen recognition, B cells can diversify their immunoglobulin (Ig) repertoire via somatic hypermutation (SHM) and/or class switch DNA recombination (CSR) before differentiating into antibody-secreting plasma cells. We construct a mathematical model for a GRN underlying this developmental dynamic. The intensity of signaling through the Ig receptor is shown to control the bimodal expression of a pivotal transcription factor, IRF-4, which dictates B cell fate outcomes. Computational modeling coupled with experimental analysis supports a model of ‘kinetic control', in which B cell developmental trajectories pass through an obligate transient state of variable duration that promotes diversification of the antibody repertoire by SHM/CSR in direct response to antigens. More generally, this network motif could be used to translate a morphogen gradient into developmental inductive events of varying time, thereby enabling the specification of distinct cell fates.
doi:10.1038/msb.2011.25
PMCID: PMC3130558  PMID: 21613984
BCR signal strength; bistability; gene regulatory network; ghost of a fixed point; Irf4
18.  Construction and Validation of a Regulatory Network for Pluripotency and Self-Renewal of Mouse Embryonic Stem Cells 
PLoS Computational Biology  2014;10(8):e1003777.
A 30-node signed and directed network responsible for self-renewal and pluripotency of mouse embryonic stem cells (mESCs) was extracted from several ChIP-Seq and knockdown followed by expression prior studies. The underlying regulatory logic among network components was then learned using the initial network topology and single cell gene expression measurements from mESCs cultured in serum/LIF or serum-free 2i/LIF conditions. Comparing the learned network regulatory logic derived from cells cultured in serum/LIF vs. 2i/LIF revealed differential roles for Nanog, Oct4/Pou5f1, Sox2, Esrrb and Tcf3. Overall, gene expression in the serum/LIF condition was more variable than in the 2i/LIF but mostly consistent across the two conditions. Expression levels for most genes in single cells were bimodal across the entire population and this motivated a Boolean modeling approach. In silico predictions derived from removal of nodes from the Boolean dynamical model were validated with experimental single and combinatorial RNA interference (RNAi) knockdowns of selected network components. Quantitative post-RNAi expression level measurements of remaining network components showed good agreement with the in silico predictions. Computational removal of nodes from the Boolean network model was also used to predict lineage specification outcomes. In summary, data integration, modeling, and targeted experiments were used to improve our understanding of the regulatory topology that controls mESC fate decisions as well as to develop robust directed lineage specification protocols.
Author Summary
For this study we first constructed a directed and signed network consisting of 15 pluripotency regulators and 15 lineage commitment markers that extensively interact to regulate mouse embryonic stem cells fate decisions from data available in the public domain. Given the connectivity structure of this network, the underlying regulatory logic was learned using single cell gene expression measurements of mESCs cultured in two different conditions. With connectivity and logic learned, the network was then simulated using a dynamic Boolean logic framework. Such simulations enabled prediction of knockdown effects on the overall activity of the network. Such predictions were validated by single and combinatorial RNA interference experiments followed by expression measurements. Finally, lineage specification outcomes upon single and combinatorial gene knockdowns were predicted for all possible knockdown combinations.
doi:10.1371/journal.pcbi.1003777
PMCID: PMC4133156  PMID: 25122140
19.  MicrobesFlux: a web platform for drafting metabolic models from the KEGG database 
BMC Systems Biology  2012;6:94.
Background
Concurrent with the efforts currently underway in mapping microbial genomes using high-throughput sequencing methods, systems biologists are building metabolic models to characterize and predict cell metabolisms. One of the key steps in building a metabolic model is using multiple databases to collect and assemble essential information about genome-annotations and the architecture of the metabolic network for a specific organism. To speed up metabolic model development for a large number of microorganisms, we need a user-friendly platform to construct metabolic networks and to perform constraint-based flux balance analysis based on genome databases and experimental results.
Results
We have developed a semi-automatic, web-based platform (MicrobesFlux) for generating and reconstructing metabolic models for annotated microorganisms. MicrobesFlux is able to automatically download the metabolic network (including enzymatic reactions and metabolites) of ~1,200 species from the KEGG database (Kyoto Encyclopedia of Genes and Genomes) and then convert it to a metabolic model draft. The platform also provides diverse customized tools, such as gene knockouts and the introduction of heterologous pathways, for users to reconstruct the model network. The reconstructed metabolic network can be formulated to a constraint-based flux model to predict and analyze the carbon fluxes in microbial metabolisms. The simulation results can be exported in the SBML format (The Systems Biology Markup Language). Furthermore, we also demonstrated the platform functionalities by developing an FBA model (including 229 reactions) for a recent annotated bioethanol producer, Thermoanaerobacter sp. strain X514, to predict its biomass growth and ethanol production.
Conclusion
MicrobesFlux is an installation-free and open-source platform that enables biologists without prior programming knowledge to develop metabolic models for annotated microorganisms in the KEGG database. Our system facilitates users to reconstruct metabolic networks of organisms based on experimental information. Through human-computer interaction, MicrobesFlux provides users with reasonable predictions of microbial metabolism via flux balance analysis. This prototype platform can be a springboard for advanced and broad-scope modeling of complex biological systems by integrating other “omics” data or 13 C- metabolic flux analysis results. MicrobesFlux is available at http://tanglab.engineering.wustl.edu/static/MicrobesFlux.html and will be continuously improved based on feedback from users.
doi:10.1186/1752-0509-6-94
PMCID: PMC3447728  PMID: 22857267
20.  REST Regulates Distinct Transcriptional Networks in Embryonic and Neural Stem Cells 
PLoS Biology  2008;6(10):e256.
The maintenance of pluripotency and specification of cellular lineages during embryonic development are controlled by transcriptional regulatory networks, which coordinate specific sets of genes through both activation and repression. The transcriptional repressor RE1-silencing transcription factor (REST) plays important but distinct regulatory roles in embryonic (ESC) and neural (NSC) stem cells. We investigated how these distinct biological roles are effected at a genomic level. We present integrated, comparative genome- and transcriptome-wide analyses of transcriptional networks governed by REST in mouse ESC and NSC. The REST recruitment profile has dual components: a developmentally independent core that is common to ESC, NSC, and differentiated cells; and a large, ESC-specific set of target genes. In ESC, the REST regulatory network is highly integrated into that of pluripotency factors Oct4-Sox2-Nanog. We propose that an extensive, pluripotency-specific recruitment profile lends REST a key role in the maintenance of the ESC phenotype.
Author Summary
Embryonic stem cells have the unique and defining property of pluripotency: the ability to differentiate into all cell types. Key transcription factors form interconnected gene regulatory networks that control pluripotency and differentiation. Recently, the transcriptional repressor RE1-silencing transcription factor (REST) was implicated in the maintenance of pluripotency. This was surprising, given that REST has long been known as an essential regulator of neurodevelopment. How does REST regulate pluripotency? Does REST have distinct cohorts of binding sites and target genes in different developmental contexts? To address these questions, we made whole-genome maps of REST binding sites in two mouse stem cell types: embryonic (ESC) and neural (NSC) stem cells. These data were compared with each other and with gene expression data from cells in which REST activity was inhibited. The target genes were almost completely distinct in the two cell types. Surprisingly, we found that REST recruitment has two approximately equal components: common sites across all cells and an ESC-specific component. These pluripotency-associated sites are enriched for particular classes of genes, including those mediating the Wnt signaling pathway, which is an essential regulator of pluripotency.
Whole-genome mapping of the essential transcriptional repressor REST reveals distinct binding profiles and diverse roles in embryonic and neural stem cells.
doi:10.1371/journal.pbio.0060256
PMCID: PMC2573930  PMID: 18959480
21.  Identifying Tmem59 related gene regulatory network of mouse neural stem cell from a compendium of expression profiles 
BMC Systems Biology  2011;5:152.
Background
Neural stem cells offer potential treatment for neurodegenerative disorders, such like Alzheimer's disease (AD). While much progress has been made in understanding neural stem cell function, a precise description of the molecular mechanisms regulating neural stem cells is not yet established. This lack of knowledge is a major barrier holding back the discovery of therapeutic uses of neural stem cells. In this paper, the regulatory mechanism of mouse neural stem cell (NSC) differentiation by tmem59 is explored on the genome-level.
Results
We identified regulators of tmem59 during the differentiation of mouse NSCs from a compendium of expression profiles. Based on the microarray experiment, we developed the parallelized SWNI algorithm to reconstruct gene regulatory networks of mouse neural stem cells. From the inferred tmem59 related gene network including 36 genes, pou6f1 was identified to regulate tmem59 significantly and might play an important role in the differentiation of NSCs in mouse brain. There are four pathways shown in the gene network, indicating that tmem59 locates in the downstream of the signalling pathway. The real-time RT-PCR results shown that the over-expression of pou6f1 could significantly up-regulate tmem59 expression in C17.2 NSC line. 16 out of 36 predicted genes in our constructed network have been reported to be AD-related, including Ace, aqp1, arrdc3, cd14, cd59a, cds1, cldn1, cox8b, defb11, folr1, gdi2, mmp3, mgp, myrip, Ripk4, rnd3, and sncg. The localization of tmem59 related genes and functional-related gene groups based on the Gene Ontology (GO) annotation was also identified.
Conclusions
Our findings suggest that the expression of tmem59 is an important factor contributing to AD. The parallelized SWNI algorithm increased the efficiency of network reconstruction significantly. This study enables us to highlight novel genes that may be involved in NSC differentiation and provides a shortcut to identifying genes for AD.
doi:10.1186/1752-0509-5-152
PMCID: PMC3191490  PMID: 21955788
22.  Analysis of Regulatory Network Involved in Mechanical Induction of Embryonic Stem Cell Differentiation 
PLoS ONE  2012;7(4):e35700.
Embryonic stem cells are conventionally differentiated by modulating specific growth factors in the cell culture media. Recently the effect of cellular mechanical microenvironment in inducing phenotype specific differentiation has attracted considerable attention. We have shown the possibility of inducing endoderm differentiation by culturing the stem cells on fibrin substrates of specific stiffness [1]. Here, we analyze the regulatory network involved in such mechanically induced endoderm differentiation under two different experimental configurations of 2-dimensional and 3-dimensional culture, respectively. Mouse embryonic stem cells are differentiated on an array of substrates of varying mechanical properties and analyzed for relevant endoderm markers. The experimental data set is further analyzed for identification of co-regulated transcription factors across different substrate conditions using the technique of bi-clustering. Overlapped bi-clusters are identified following an optimization formulation, which is solved using an evolutionary algorithm. While typically such analysis is performed at the mean value of expression data across experimental repeats, the variability of stem cell systems reduces the confidence on such analysis of mean data. Bootstrapping technique is thus integrated with the bi-clustering algorithm to determine sets of robust bi-clusters, which is found to differ significantly from corresponding bi-clusters at the mean data value. Analysis of robust bi-clusters reveals an overall similar network interaction as has been reported for chemically induced endoderm or endodermal organs but with differences in patterning between 2-dimensional and 3-dimensional culture. Such analysis sheds light on the pathway of stem cell differentiation indicating the prospect of the two culture configurations for further maturation.
doi:10.1371/journal.pone.0035700
PMCID: PMC3338716  PMID: 22558203
23.  Zebrafish Pou5f1-dependent transcriptional networks in temporal control of early development 
Time-resolved transcriptome analysis of early pou5f1 mutant zebrafish embryos identified groups of developmental regulators, including SoxB1 genes, that depend on Pou5f1 activity, and a large cluster of differentiation genes which are prematurely expressed.Pou5f1 represses differentiation genes indirectly via activation of germlayer-specific transcriptional repressor genes, including her3, which may mediate in part Pou5f1-dependent repression of neural genes.A dynamic mathematical model is established for Pou5f1 and SoxB1 activity-dependent temporal behaviour of downstream transcriptional regulatory networks. The model predicts that Pou5f1-dependent increase in SoxB1 activity significantly contributes to developmental timing in the early gastrula.Comparison to mouse Pou5f1/Oct4 reveals evolutionary conserved targets. We show that Pou5f1 developmental function is also conserved by demonstrating rescue of Pou5f1 mutant zebrafish embryos by mouse POU5F1/OCT4.
The transcription factor Pou5f1/Oct4 controls pluripotency of mouse embryonic inner cell mass cells (Nichols et al, 1998), and of mouse and human ES cell lines (Boiani and Scholer, 2005). Although Pou5f1/Oct4-dependent pluripotency transcriptional circuits and many transcriptional targets have been characterized, little is known about the mechanisms by which Pou5f1/Oct4 controls early developmental events. A detailed understanding of Pou5f1/Oct4 functions during mammalian blastocyst and gastrula development as well as studies of the temporal changes in the Pou5f1/Oct4-regulated networks are precluded by the early lineage defects in pou5f1/oct4 mutant mice. To investigate Pou5f1-dependent transcriptional circuits in developmental control, we used the zebrafish (Danio rerio) as a genetic and experimental model representing an earlier state of vertebrate evolution. Zebrafish have one pou5f1/pou2 gene (Takeda et al, 1994) orthologous to the mammalian gene (Niwa et al, 2008; Frankenberg et al, 2009). Both fish and mammalian orthologs are expressed broadly in tissues giving rise to the embryo proper during blastula and early gastrula stages, as well as in the neural plate (Belting et al, 2001; Reim and Brand, 2002; Downs, 2008).
Zebrafish pou5f1 loss-of-function mutant embryos, MZspg (abbreviated ‘MZ'), are completely devoid of maternal and zygotic Pou5f1 activity (Lunde et al, 2004; Reim et al, 2004). MZ embryos have gastrulation abnormalities (Lachnit et al, 2008), dorsoventral patterning defects (Reim and Brand, 2006), and do not develop endoderm (Lunde et al, 2004; Reim et al, 2004). In contrast to Pou5f1/Oct4 mutant mice, which are blocked in development due to loss of inner cell mass, MZ mutant embryos are neither blocked in development nor display a general delay. Therefore, zebrafish present a good model system to identify specific transcriptional targets of Pou5f1 during development.
Our study aims to understand the structure, regulatory logic, and developmental temporal changes in the Pou5f1-dependent transcriptional network in the context of an intact embryo. Therefore, we investigated transcriptome changes in MZ compared with WT zebrafish by microarray analysis at 10 distinct time-points during development, from ovaries to late gastrulation. We identified changes in Pou5f1 target gene expression both with respect to their expression level and temporal behavior. We used correlation analysis to identify clusters of target genes enriched for genes with developmentally regulated expression profiles. This correlation analysis revealed a cluster of genes, which were not activated or were significantly delayed in MZ. Interestingly, there was also a large gene cluster with premature onset of expression in MZ.
Several targets activated by Pou5f1 encode known repressors of differentiation (RODs), of which we analyzed her3 in detail. Pou5f1 also activates several SoxB1 group transcription factors, which are known to act together with Pou5f1 in mammalian systems. Among the large group of genes prematurely activated in MZ, many genes encode developmental regulators of differentiation normally acting during organogenesis (promoters of differentiation—PODs). Our analysis of potential direct transcriptional interactions by suppression of translation of intermediate zygotic Pou5f1 or SoxB1 targets, enabled us to distinguish Sox-dependent and independent subgroups of the Pou5f1 transcriptional network. Interestingly, tissue-specific expression of Pou5f1 targets correlated with their regulation by Sox2, with Sox-dependent targets being mostly localized to ectoderm and neuroectoderm, whereas Sox-independent targets localized to mesendoderm of the developing zebrafish embryo. Further, SoxB1 independent Pou5f1 targets (for example foxD3) differ from SoxB1-dependent targets (e.g her3) in temporal dynamics of expression. Most Sox-independent direct Pou5f1 targets in WT reach maximal expression levels soon after midblastula transition (MBT) at 3–4 h postfertilization (hpf). In contrast, genes depending both on Sox2 and Pou5f1 tend to have a biphasic temporal expression curve or are activated with >2 h delay after MBT to reach maximum levels at 6–7 hpf only.
To better understand the impact of our findings on Pou5f1/SoxB1-dependent versus Pou5f1-only regulation on developmental mechanisms, we built a small dynamic network model that links the temporal control of target genes to regulatory principles exerted by Pou5f1 and SoxB1 proteins (Figure 6A). The model is based on ordinary differential equations, and parameters were determined by a fit to the WT and MZ gene expression data. The optimized model highlights two qualitatively different temporal expression modes of Pou5f1 downstream targets: monophasic for targets depending only on Pou5f1 (foxd3), and biphasic for Pou5f1- and SoxB1-dependent targets (sox2 and her3; Figure 6B). To test whether the model is also able to correctly predict a different genetic condition, we simulated the M mutant, which is lacking maternal Pou5f1, but gradually rescued by the paternal pou5f1 contribution after MBT (Figure 6B, blue, dashed curve). The model predicts an overall shift in the developmental program. Most importantly, the sox2 and her3 expression is rescued with a delay of about 2 h. The model predictions were checked experimentally by quantitative RT–PCR (Figure 6B, blue dots). Most predictions are in good agreement with the experimental data, for example the delayed rescue of the sox2 and her3 temporal expression profile. With respect to the ‘POD' nr2f1, the model correctly predicts the efficient downregulation by zygotic targets of Pou5f1 (Figure 6B).
We identified an evolutionary conserved core set of Pou5f1 targets, by comparing our gene list with the lists of mouse Pou5f1/Oct4 targets (Loh et al, 2006; Sharov et al, 2008). The evolutionary conservation suggests equivalent Pou5f1 functions during the pregastrulation and gastrulation period of vertebrate embryogenesis. Therefore, we tested whether mouse Pou5f1/Oct4 was able to rescue MZ embryos. Injection of mRNA encoding mouse Pou5f1/Oct4 into MZ embryos (Figure 8A) was able to restore normal zebrafish development to an extent comparable with zebrafish pou5f1/pou2 mRNA (Figure 8B and C). The significant overlap between zebrafish and mammalian Pou5f1 targets together with the ability of mouse Pou5f1/Oct4 to functionally replace the zebrafish Pou5f1/Pou2 (Figure 8A–C), suggests that the mammalian network may have evolved from a basal situation similar to what is observed in teleosts. We propose models that emphasize the evolution of Pou5f1-dependent transcriptional networks during development of the zebrafish (Figure 8D) and mammals (Figure 8E). Our representation highlights the evolutionary ancient germlayer-specific subnetworks downstream of Pou5f1, which are presumably used for controlling the timing of differentiation during gastrulation in all vertebrates (Figure 8D and E, black arrows). As the Pou5f1 downstream regulatory nodes revealed in our zebrafish model are likely conserved across vertebrates, we envision that their knowledge will contribute to the effort of directing differentiation of pluripotent stem cells to defined cell fates.
The transcription factor POU5f1/OCT4 controls pluripotency in mammalian ES cells, but little is known about its functions in the early embryo. We used time-resolved transcriptome analysis of zebrafish pou5f1 MZspg mutant embryos to identify genes regulated by Pou5f1. Comparison to mammalian systems defines evolutionary conserved Pou5f1 targets. Time-series data reveal many Pou5f1 targets with delayed or advanced onset of expression. We identify two Pou5f1-dependent mechanisms controlling developmental timing. First, several Pou5f1 targets are transcriptional repressors, mediating repression of differentiation genes in distinct embryonic compartments. We analyze her3 gene regulation as example for a repressor in the neural anlagen. Second, the dynamics of SoxB1 group gene expression and Pou5f1-dependent regulation of her3 and foxD3 uncovers differential requirements for SoxB1 activity to control temporal dynamics of activation, and spatial distribution of targets in the embryo. We establish a mathematical model of the early Pou5f1 and SoxB1 gene network to demonstrate regulatory characteristics important for developmental timing. The temporospatial structure of the zebrafish Pou5f1 target networks may explain aspects of the evolution of the mammalian stem cell networks.
doi:10.1038/msb.2010.9
PMCID: PMC2858445  PMID: 20212526
developmental timing; mathematical modeling; Oct4; transcriptional networks
24.  Modeling and analysis of retinoic acid induced differentiation of uncommitted precursor cells† 
Manipulation of differentiation programs has therapeutic potential in a spectrum of human cancers and neurodegenerative disorders. In this study, we integrated computational and experimental methods to unravel the response of a lineage uncommitted precursor cell-line, HL-60, to Retinoic Acid (RA). HL-60 is a human myeloblastic leukemia cell-line used extensively to study human differentiation programs. Initially, we focused on the role of the BLR1 receptor in RA-induced differentiation and G1/0-arrest in HL-60. BLR1, a putative G protein-coupled receptor expressed following RA exposure, is required for RA-induced cell-cycle arrest and differentiation and causes persistent MAPK signaling. A mathematical model of RA-induced cell-cycle arrest and differentiation was formulated and tested against BLR1 wild-type (wt) knock-out and knock-in HL-60 cell-lines with and without RA. The current model described the dynamics of 729 proteins and protein complexes interconnected by 1356 interactions. An ensemble strategy was used to compensate for uncertain model parameters. The ensemble of HL-60 models recapitulated the positive feedback between BLR1 and MAPK signaling. The ensemble of models also correctly predicted Rb and p47phox regulation and the correlation between p21-CDK4-cyclin D formation and G1/0-arrest following exposure to RA. Finally, we investigated the robustness of the HL-60 network architecture to structural perturbations and generated experimentally testable hypotheses for future study. Taken together, the model presented here was a first step toward a systematic framework for analysis of programmed differentiation. These studies also demonstrated that mechanistic network modeling can help prioritize experimental directions by generating falsifiable hypotheses despite uncertainty.
doi:10.1039/c0ib00141d
PMCID: PMC3685823  PMID: 21437295
25.  Modeling Reveals Bistability and Low-Pass Filtering in the Network Module Determining Blood Stem Cell Fate 
PLoS Computational Biology  2010;6(5):e1000771.
Combinatorial regulation of gene expression is ubiquitous in eukaryotes with multiple inputs converging on regulatory control elements. The dynamic properties of these elements determine the functionality of genetic networks regulating differentiation and development. Here we propose a method to quantitatively characterize the regulatory output of distant enhancers with a biophysical approach that recursively determines free energies of protein-protein and protein-DNA interactions from experimental analysis of transcriptional reporter libraries. We apply this method to model the Scl-Gata2-Fli1 triad—a network module important for cell fate specification of hematopoietic stem cells. We show that this triad module is inherently bistable with irreversible transitions in response to physiologically relevant signals such as Notch, Bmp4 and Gata1 and we use the model to predict the sensitivity of the network to mutations. We also show that the triad acts as a low-pass filter by switching between steady states only in response to signals that persist for longer than a minimum duration threshold. We have found that the auto-regulation loops connecting the slow-degrading Scl to Gata2 and Fli1 are crucial for this low-pass filtering property. Taken together our analysis not only reveals new insights into hematopoietic stem cell regulatory network functionality but also provides a novel and widely applicable strategy to incorporate experimental measurements into dynamical network models.
Author Summary
Hematopoiesis—blood cell development—has long served as a model for study of cellular differentiation and its control by underlying gene regulatory networks. The Scl-Gata2-Fli1 triad is a network module essential for the development of hematopoietic stem cells but its mechanistic role is not well understood. The transcription factors Scl, Gata2 and Fli1 act in combination to upregulate transcription of each other via distal enhancer site binding. Similar network architectures are essential in other multipotent cell lines. We propose a method that uses experimental results to circumvent the difficulties of mathematically modeling the combinatorial regulation of this triad module. Using this dynamical model we show that the triad exhibits robust bistable behavior. Environmental signals can irreversibly switch the triad between stable states in a manner that reflects the unidirectional switching in the formation and subsequent differentiation of hematopoietic stem cells. We also show that the triad makes reliable decisions in noisy environments by only switching in response to transient signals that persist longer than the threshold duration. These results suggest that the Scl-Gata2-Fli1 module possibly functions as a control switch for hematopoietic stem cell development. The proposed method can be extended for quantitative characterization of other combinatorial gene regulatory modules.
doi:10.1371/journal.pcbi.1000771
PMCID: PMC2865510  PMID: 20463872

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