Iterative approach for network refinement and phenotype prediction.

<p>By using an iterative approach, we increased the comprehensiveness of the integrated network model by adding new interactions (Network III) and iteratively refining the model using GEMINI. This process enriched the fraction of validated interactions in the network (shown in red) and improved the predictive ability of the integrated network model.</p

Comparative Analysis of Yeast Metabolic Network Models Highlights Progress, Opportunities for Metabolic Reconstruction

<div><p>We have compared 12 genome-scale models of the <i>Saccharomyces cerevisiae</i> metabolic network published since 2003 to evaluate progress in reconstruction of the yeast metabolic network. We compared the genomic coverage, overlap of annotated metabolites, predictive ability for single gene essentiality with a selection of model parameters, and biomass production predictions in simulated nutrient-limited conditions. We have also compared pairwise gene knockout essentiality predictions for 10 of these models. We found that varying approaches to model scope and annotation reflected the involvement of multiple research groups in model development; that single-gene essentiality predictions were affected by simulated medium, objective function, and the reference list of essential genes; and that predictive ability for single-gene essentiality did not correlate well with predictive ability for our reference list of synthetic lethal gene interactions (R = 0.159). We conclude that the reconstruction of the yeast metabolic network is indeed gradually improving through the iterative process of model development, and there remains great opportunity for advancing our understanding of biology through continued efforts to reconstruct the full biochemical reaction network that constitutes yeast metabolism. Additionally, we suggest that there is opportunity for refining the process of deriving a metabolic model from a metabolic network reconstruction to facilitate mechanistic investigation and discovery. This comparative study lays the groundwork for developing improved tools and formalized methods to quantitatively assess metabolic network reconstructions independently of any particular model application, which will facilitate ongoing efforts to advance our understanding of the relationship between genotype and cellular phenotype.</p></div

Metabolic Constraint-Based Refinement of Transcriptional Regulatory Networks

<div><p>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 <i>Gene Expression and Metabolism Integrated for Network Inference</i> (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 <i>Saccharomyces cerevisiae</i> 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 <a href="https://sourceforge.net/projects/gemini-data/" target="_blank">https://sourceforge.net/projects/gemini-data/</a></p></div

Distribution of inconsistencies across the regulatory and metabolic network.

<p>The distribution of phenotype inconsistencies was exponential across the TRN, suggesting that a few TFs led to most of the inconsistencies. In contrast, the distribution of inconsistencies across the metabolic network was linear and did not reveal any strong trend towards specific metabolic genes.</p

Growth simulations demonstrate interplay between network reconstruction and constraints.

<p>A) Optimal biomass flux calculated by flux balance analysis increased linearly with glucose uptake flux for all models when the glucose exchange reaction is the only constrained media component. All model predictions had a 0.8158 correlation with previously reported measured growth rate. B) When glucose and oxygen exchange reactions were both constrained to experimental values, there are high-correlation (black) and low-correlation models (red). C) Restricting flux through a mitochondrial aspartate transport reaction did not affect the predictions for the high correlation models, and improved all remaining correlations to >0.9, with the exception of the Yeast 4 model, which still over-predicted the maximum biomass flux at high glucose:oxygen exchange constraint ratios.</p

Model prediction of single-gene essentiality is sensitive to biomass definition.

<p>Since objective function is a tunable model parameter, we calculated Matthews’ Correlation Coefficients for the sum of all true positive, true negative, false positive and false negative predictions across all conditions using two different objective functions for each model: the biomass definition provided by the model authors, and the biomass function used for the iFF708 model. We found that with the exception of the Yeast 4 model, all model predictions were improved by tuned objective function, independent of refinements to the biochemical network reconstruction. Models are arranged in chronological order across the horizontal axis.</p

Summary statistics of yeast metabolic network models.

<p>General parameters described or used for simulation in this study include: number of genes included as reaction modifiers; number of included genes that are currently annotated by the Saccharomyces Genome Database as “dubious”, or unlikely to encode an expressed protein; number of metabolites; number of dead end metabolites (those metabolites that are either produced by known metabolic reactions of an organism but not consumed, or vice versa); number of reactions; and number of reactions associated with genes. Simulations were conducted for each model using the as-distributed model default biomass objective function and with the biomass objective from the iFF708 model. Reported simulation results are divided into two subcolumns to reflect the use of two different objective functions for each model. Simulation results include the number of blocked reactions for each biomass definition (those reactions which cannot carry flux due to network structural constraints); the Matthews’ Correlation Coefficient (MCC) for model predictions of single gene essentiality across all conditions simulated; and the Matthews’ Correlation Coefficient for model prediction of double gene essentiality (i.e., pairwise synthetic lethal interactions) for simulations using each models’ default biomass definition. Some parameter values differ from previously published values due to differing software implementation and annotation conventions.</p

Network sizes and the number of interactions retained after running GEMINI for each network type.

<p>The hyper-geometric enrichment p-value compared to the original inferred network is shown. Note that for Network III with validated interactions, a single p-value was obtained because we were unable to differentiate between direct and indirect interactions in some of the new interactions that were added. So a single p-value for validated interactions was obtained.</p

Refining regulatory interaction data in yeast using GEMINI.

<p><b>A.</b> GEMINI was evaluated for its ability to preferentially retain the gold-standard interactions (blue edges) and the indirect interactions (green edges). The hyper-geometric p-values for enrichment with various data sets are shown. <b>B.</b> Running GEMINI on the network derived using Yeastract resulted in the elimination of ∼9,000 phenotype-inconsistent interactions and produced a refined integrated network model that was more highly enriched for known interactions than the original network (p-value<10⁻¹⁷², hyper-geometric test). Most of the interactions eliminated by GEMINI were found to have little supporting experimental evidence (interactions that did have strong supporting evidence were preferentially retained). <b>C.</b> The number of true interactions (direct and indirect) recalled was significantly higher than could be recalled using mutual information (MI) or correlation (Corr)-based approaches, which rely on gene expression alone (estimated from the same gene expression dataset and for networks of the same size). We also measured the best prediction obtained by MI and correlation over all possible cut offs and this was still significantly lower than the enrichment obtained by GEMINI. The supplementary <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003370#pcbi.1003370.s001" target="_blank">figures S1</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003370#pcbi.1003370.s002" target="_blank">S2</a> show the enrichment for direct interactions over the entire range of thresholds for both MI and correlation. The number of interactions recalled by random sampling from the Yeastract database (DB) is also shown, as a reference.</p

Change in gene essentiality predictions between model and its nearest ancestor.

<p>When comparing the Matthews Correlation Coefficient for model gene essentiality predictions to the models’ nearest progenitors, we observe that the models may be segregated between those focusing on expanding model scope, and those focused on iterative refining an existing model by plotting the change in MCC between models. Generally, when the stated focus of a model developer is to expand the scope of the yeast metabolic network reconstruction, predictive ability suffers relative to the progenitor model. When the stated focus is to refine and curate a model, predictive ability improves relative to the progenitor model. Thus, our analysis finds that model predictive ability reflects the iterative process of model development. The asterisk near the Yeast 4 comparison indicates that it is an integrative model that not have a single nearest progenitor (we compared it to iFF708 for this analysis).</p