Gene expression analysis on biochemical networks using the Potts spin model

MOTIVATION: Microarray technology allows us to profile the expression of a large subset or all genes of a cell. Biochemical research over the last three decades has elucidated an increasingly complete image of the metabolic architecture. For less complex organisms, such as Escherichia coli, the biochemical network has been described in much detail. Here, we investigate the clustering of such networks by applying gene expression data that define edge lengths in the network. RESULTS: The Potts spin model is used as a nearest neighbour based clustering algorithm to discover fragmentation of the network in mutants or in biological samples when treated with drugs. As an example, we tested our method with gene expression data from E.coli treated with tryptophan excess, starvation and trpyptophan repressor mutants. We observed fragmentation of the tryptophan biosynthesis pathway, which corresponds well to the commonly known regulatory response of the cells.     

Using effective subnetworks to predict selected properties of gene networks

Background

Difficulties associated with implementing gene therapy are caused by the complexity of the underlying regulatory networks. The forms of interactions between the hundreds of genes, proteins, and metabolites in these networks are not known very accurately. An alternative approach is to limit consideration to genes on the network. Steady state measurements of these influence networks can be obtained from DNA microarray experiments. However, since they contain a large number of nodes, the computation of influence networks requires a prohibitively large set of microarray experiments. Furthermore, error estimates of the network make verifiable predictions impossible.

Methodology/Principal Findings

Here, we propose an alternative approach. Rather than attempting to derive an accurate model of the network, we ask what questions can be addressed using lower dimensional, highly simplified models. More importantly, is it possible to use such robust features in applications? We first identify a small group of genes that can be used to affect changes in other nodes of the network. The reduced effective empirical subnetwork (EES) can be computed using steady state measurements on a small number of genetically perturbed systems. We show that the EES can be used to make predictions on expression profiles of other mutants, and to compute how to implement pre-specified changes in the steady state of the underlying biological process. These assertions are verified in a synthetic influence network. We also use previously published experimental data to compute the EES associated with an oxygen deprivation network of E.coli, and use it to predict gene expression levels on a double mutant. The predictions are significantly different from the experimental results for less than of genes.

Conclusions/Significance

The constraints imposed by gene expression levels of mutants can be used to address a selected set of questions about a gene network.     

Temporal Controls of the Asymmetric Cell Division Cycle in Caulobacter crescentus

The asymmetric cell division cycle of Caulobacter crescentus is orchestrated by an elaborate gene-protein regulatory network, centered on three major control proteins, DnaA, GcrA and CtrA. The regulatory network is cast into a quantitative computational model to investigate in a systematic fashion how these three proteins control the relevant genetic, biochemical and physiological properties of proliferating bacteria. Different controls for both swarmer and stalked cell cycles are represented in the mathematical scheme. The model is validated against observed phenotypes of wild-type cells and relevant mutants, and it predicts the phenotypes of novel mutants and of known mutants under novel experimental conditions. Because the cell cycle control proteins of Caulobacter are conserved across many species of alpha-proteobacteria, the model we are proposing here may be applicable to other genera of importance to agriculture and medicine (e.g., Rhizobium, Brucella).     

Regulation of hSos1 activity is a system-level property generated by its multi-domain structure

The multi-domain protein hSos1 plays a major role in cell growth and differentiation through its Ras-specific guanine nucleotide exchange domain whose complex regulation involves intra-molecular, inter-domain rearrangements. We present a stochastic mathematical model describing intra-molecular regulation of hSos1 activity. The population macroscopic effect is reproduced through a Monte-Carlo approach. Key model parameters have been experimentally determined by BIAcore analysis. Complementation experiments of a Saccharomyces cerevisiae cdc25(ts) strain with Sos deletion mutants provided a comprehensive data set for estimation of unknown parameters and model validation. The model is robust against parameter alteration and describes both the behavior of Sos deletion mutants and modulation of activity of the full length molecule under physiological conditions. By incorporating the calculated effect of amino acid changes at an inter-domain interface, the behavior of a mutant correlating with a developmental syndrome could be simulated, further validating the model. The activation state of Ras-specific guanine nucleotide exchange domain of hSos1 arises as an "emergent property" of its multi-domain structure that allows multi-level integration of a complex network of intra- and inter-molecular signals.     

Characterization of null mutants of the glyoxylate cycle and gluconeogenic enzymes in S. cerevisiae through metabolic network modeling verified by chemostat cultivation.

Biomass yields for several null mutants in Saccharomyces cerevisiae were successfully predicted with a metabolic network model. Energetic parameters of the model were obtained from growth data in C-limited aerobic chemostat cultures of the corresponding wild-type strain, which exhibited a P/O ratio of 1.46, a non-growth-related maintenance of 56 mmol ATP/C-mol biomass/h, and a growth-related requirement of 655 mmol ATP/C-mol biomass. Biomass yields and carbon uptake rates were modeled for different mutants incapacitated in their glyoxylate cycle and their gluconeogenesis. Biomass yields were calculated for different feed ratios of glucose to ethanol, and decreases for higher ethanol fractions were correctly predicted for mutants with deletions of the malate synthase, the isocitrate lyase, or the phosphoenolpyruvate carboxykinase. The growth of the fructose- 1,6-bisphosphatase deletion mutant was anticipated less accurate, but the tendency was modeled correctly.     

The role of MEN (mitosis exit network) proteins in the cytokinesis of Saccharomyces cerevisiae.

At the latest stages of their cell cycle, cells carry out crucial processes for the correct segregation of their genetic and cytoplasmic material. In this work, we provide evidence demonstrating that the cell cycle arrest of some MEN (mitosis exit network) mutants in the anaphase-telophase transition is bypassed. In addition, the ability of cdc15 diploid mutant strains to develop non-septated chains of cells, supported by nuclear division, is shown. This phenotype is also displayed by haploid cdc15 mutant strains when cell lysis is prevented by osmotic protection, and shared by other MEN mutants. By contrast, anaphase-telophase arrest is strictly observed in double MEN-FEAR (fourteen early anaphase release) mutants. In this context, the overexpression of a FEAR component, SPO12, in a MEN mutant background enhances the ability of MEN mutants to bypass cell cycle arrest. Taken together, these data suggest a critical role of Cdc15 and other MEN proteins in cytokinesis, allowing a new model for their cellular function to be proposed.     

GrowMatch: An Automated Method for Reconciling In Silico/In Vivo Growth Predictions

Genome-scale metabolic reconstructions are typically validated by comparing in silico growth predictions across different mutants utilizing different carbon sources with in vivo growth data. This comparison results in two types of model-prediction inconsistencies; either the model predicts growth when no growth is observed in the experiment (GNG inconsistencies) or the model predicts no growth when the experiment reveals growth (NGG inconsistencies). Here we propose an optimization-based framework, GrowMatch, to automatically reconcile GNG predictions (by suppressing functionalities in the model) and NGG predictions (by adding functionalities to the model). We use GrowMatch to resolve inconsistencies between the predictions of the latest in silico Escherichia coli (iAF1260) model and the in vivo data available in the Keio collection and improved the consistency of in silico with in vivo predictions from 90.6% to 96.7%. Specifically, we were able to suggest consistency-restoring hypotheses for 56/72 GNG mutants and 13/38 NGG mutants. GrowMatch resolved 18 GNG inconsistencies by suggesting suppressions in the mutant metabolic networks. Fifteen inconsistencies were resolved by suppressing isozymes in the metabolic network, and the remaining 23 GNG mutants corresponding to blocked genes were resolved by suitably modifying the biomass equation of iAF1260. GrowMatch suggested consistency-restoring hypotheses for five NGG mutants by adding functionalities to the model whereas the remaining eight inconsistencies were resolved by pinpointing possible alternate genes that carry out the function of the deleted gene. For many cases, GrowMatch identified fairly nonintuitive model modification hypotheses that would have been difficult to pinpoint through inspection alone. In addition, GrowMatch can be used during the construction phase of new, as opposed to existing, genome-scale metabolic models, leading to more expedient and accurate reconstructions.     

Ionic network at the C-terminus of the beta-glycosidase from the hyperthermophilic archaeon Sulfolobus solfataricus: Functional role in the quaternary structure thermal stabilization

Biochemical, crystallographic, and computational data support the hypothesis that electrostatic interactions are among the dominant forces in stabilizing hyperthermophilic proteins. The thermostable beta-glycosidase from the hyperthermophile Sulfolobus solfataricus (Ssbeta-gly) is an interesting model system for the study of protein adaptation to high temperatures. The largest ion-pair network of Ssbeta-gly is located at the tetrameric interface of the molecule; in this paper, key residues in this region were modified by site-directed mutagenesis and the stability of the mutants was analyzed by kinetics of thermal denaturation. All mutations produced faster enzyme inactivation, suggesting that the C-terminal ionic network prevents the dissociation into monomers, which is the limiting step in the mechanism of Ssbeta-gly inactivation. Moreover, the calculated reaction order showed that the mechanism of inactivation depends on the mutation introduced, suggesting that intermediates maintaining enzymatic activity are produced during the inactivation transition of some, but not all, mutants. Molecular models of each mutant allow us to rationalize the experimental evidence and give support to the current theories on the mechanism of ion pair stabilization in proteins from hyperthermophiles.     

The HCL gene of Medicago truncatula controls Rhizobium-induced root hair curling

The symbiotic infection of the model legume Medicago truncatula by Sinorhizobium meliloti involves marked root hair curling, a stage where entrapment of the microsymbiont occurs in a chamber from which infection thread formation is initiated within the root hair. We have genetically dissected these early symbiotic interactions using both plant and rhizobial mutants and have identified a M. truncatula gene, HCL, which controls root hair curling. S. meliloti Nod factors, which are required for the infection process, induced wild-type epidermal nodulin gene expression and root hair deformation in hcl mutants, while Nod factor induction of cortical cell division foci was reduced compared to wild-type plants. Studies of the position of nuclei and of the microtubule cytoskeleton network of hcl mutants revealed that root hair, as well as cortical cells, were activated in response to S. meliloti. However, the asymmetric microtubule network that is typical of curled root hairs, did not form in the mutants, and activated cortical cells did not become polarised and did not exhibit the microtubular cytoplasmic bridges characteristic of the pre-infection threads induced by rhizobia in M. truncatula. These data suggest that hcl mutations alter the formation of signalling centres that normally provide positional information for the reorganisation of the microtubular cytoskeleton in epidermal and cortical cells.     

Gene Circuit Analysis of the Terminal Gap Gene huckebein

The early embryo of Drosophila melanogaster provides a powerful model system to study the role of genes in pattern formation. The gap gene network constitutes the first zygotic regulatory tier in the hierarchy of the segmentation genes involved in specifying the position of body segments. Here, we use an integrative, systems-level approach to investigate the regulatory effect of the terminal gap gene huckebein (hkb) on gap gene expression. We present quantitative expression data for the Hkb protein, which enable us to include hkb in gap gene circuit models. Gap gene circuits are mathematical models of gene networks used as computational tools to extract regulatory information from spatial expression data. This is achieved by fitting the model to gap gene expression patterns, in order to obtain estimates for regulatory parameters which predict a specific network topology. We show how considering variability in the data combined with analysis of parameter determinability significantly improves the biological relevance and consistency of the approach. Our models are in agreement with earlier results, which they extend in two important respects: First, we show that Hkb is involved in the regulation of the posterior hunchback (hb) domain, but does not have any other essential function. Specifically, Hkb is required for the anterior shift in the posterior border of this domain, which is now reproduced correctly in our models. Second, gap gene circuits presented here are able to reproduce mutants of terminal gap genes, while previously published models were unable to reproduce any null mutants correctly. As a consequence, our models now capture the expression dynamics of all posterior gap genes and some variational properties of the system correctly. This is an important step towards a better, quantitative understanding of the developmental and evolutionary dynamics of the gap gene network.     

The Drosophila gap gene network is composed of two parallel toggle switches

Drosophila "gap" genes provide the first response to maternal gradients in the early fly embryo. Gap genes are expressed in a series of broad bands across the embryo during first hours of development. The gene network controlling the gap gene expression patterns includes inputs from maternal gradients and mutual repression between the gap genes themselves. In this study we propose a modular design for the gap gene network, involving two relatively independent network domains. The core of each network domain includes a toggle switch corresponding to a pair of mutually repressive gap genes, operated in space by maternal inputs. The toggle switches present in the gap network are evocative of the phage lambda switch, but they are operated positionally (in space) by the maternal gradients, so the synthesis rates for the competing components change along the embryo anterior-posterior axis. Dynamic model, constructed based on the proposed principle, with elements of fractional site occupancy, required 5-7 parameters to fit quantitative spatial expression data for gap gradients. The identified model solutions (parameter combinations) reproduced major dynamic features of the gap gradient system and explained gap expression in a variety of segmentation mutants.     

Expression of mutant keratin cDNAs in epithelial cells reveals possible mechanisms for initiation and assembly of intermediate filaments

We have deleted cDNA sequences encoding portions of the amino- and carboxy-terminal end of a human type I epidermal keratin K14, and examined the molecular consequences of forcing the expression of these mutants in simple epithelial and squamous cell carcinoma lines. To follow the expression of our mutant products in transfected cells, we have tagged the 3' end of the K14 coding sequence with a sequence encoding an antigenic domain of the neuropeptide substance P. Using DNA transfection and immunohistochemistry (with an antibody against substance P), we have defined the limits of K14 sequence necessary to incorporate into a keratin filament network in vivo without disrupting its architecture. We have also uncovered major differences in the behavior of carboxy- and amino-terminal alpha-helical mutants which do perturb the cytoskeletal network of IFs: whereas carboxy terminal mutants give rise to aggregates of keratin in the cytoplasm, amino-terminal mutants tend to produce aggregates of keratins which seem to localize at the nuclear surface. An examination of the phenotypes generated by the carboxy and amino-terminal mutants and the behavior of cells at late times after transfection suggests a model whereby initiation of filament assembly occurs at discrete sites on the nuclear envelope and filaments grow from the nucleus toward the cytoplasm.     

A guide to choosing and implementing reference models for social network analysis

Analysing social networks is challenging. Key features of relational data require the use of non-standard statistical methods such as developing system-specific null, or reference, models that randomize one or more components of the observed data. Here we review a variety of randomization procedures that generate reference models for social network analysis. Reference models provide an expectation for hypothesis testing when analysing network data. We outline the key stages in producing an effective reference model and detail four approaches for generating reference distributions: permutation, resampling, sampling from a distribution, and generative models. We highlight when each type of approach would be appropriate and note potential pitfalls for researchers to avoid. Throughout, we illustrate our points with examples from a simulated social system. Our aim is to provide social network researchers with a deeper understanding of analytical approaches to enhance their confidence when tailoring reference models to specific research questions.     

Diversity as a product of inter-specific interactions

We demonstrate diversification rather than optimization for highly interacting organisms in a well-mixed biological system by means of a simple model of coevolution. We find the cause to be the complex network of interactions formed, allowing species that are less well adapted to an environment to succeed, instead of the 'best' species. This diversification can be considered as the construction of many coevolutionary niches by the network of interactions between species. The model predictions are discussed in relation to experimental work on dense communities of the bacteria Escherichia coli, which may coexist with their own mutants under certain conditions. We find that diversification only occurs above a certain threshold interaction strength, below which competitive exclusion occurs.     

Potential Benefits of Sequential Inhibitor-Mutagen Treatments of RNA Virus Infections

Lethal mutagenesis is an antiviral strategy consisting of virus extinction associated with enhanced mutagenesis. The use of non-mutagenic antiviral inhibitors has faced the problem of selection of inhibitor-resistant virus mutants. Quasispecies dynamics predicts, and clinical results have confirmed, that combination therapy has an advantage over monotherapy to delay or prevent selection of inhibitor-escape mutants. Using ribavirin-mediated mutagenesis of foot-and-mouth disease virus (FMDV), here we show that, contrary to expectations, sequential administration of the antiviral inhibitor guanidine (GU) first, followed by ribavirin, is more effective than combination therapy with the two drugs, or than either drug used individually. Coelectroporation experiments suggest that limited inhibition of replication of interfering mutants by GU may contribute to the benefits of the sequential treatment. In lethal mutagenesis, a sequential inhibitor-mutagen treatment can be more effective than the corresponding combination treatment to drive a virus towards extinction. Such an advantage is also supported by a theoretical model for the evolution of a viral population under the action of increased mutagenesis in the presence of an inhibitor of viral replication. The model suggests that benefits of the sequential treatment are due to the involvement of a mutagenic agent, and to competition for susceptible cells exerted by the mutant spectrum. The results may impact lethal mutagenesis-based protocols, as well as current antiviral therapies involving ribavirin.     

PLENA and FARINELLI: redundancy and regulatory interactions between two Antirrhinum MADS-box factors controlling flower development.

We report the discovery of an Antirrhinum MADS-box gene, FARINELLI (FAR), and the isolation of far mutants by a reverse genetic screen. Despite striking similarities between FAR and the class C MADS-box gene PLENA (PLE), the phenotypes of their respective mutants are dramatically different. Unlike ple mutants, which show homeotic conversion of reproductive organs to perianth organs and a loss of floral determinacy, far mutants have normal flowers which are partially male-sterile. Expression studies of PLE and FAR, in wild-type and mutant backgrounds, show complex interactions between the two genes. Double mutant analysis reveals an unexpected, redundant negative control over the B-function MADS-box genes. This feature of the two Antirrhinum C-function-like genes is markedly different from the control of the inner boundary of the B-function expression domain in Arabidopsis, and we propose and discuss a model to account for these differences. The difference in phenotypes of mutants in two highly related genes illustrates the importance of the position within the regulatory network in determining gene function.