Quantitative prediction of cellular metabolism with constraint-based models: the COBRA Toolbox

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Abstract

The manner in which microorganisms utilize their metabolic processes can be predicted using constraint-based analysis of genome-scale metabolic networks. Herein, we present the constraint-based reconstruction and analysis toolbox, a software package running in the Matlab environment, which allows for quantitative prediction of cellular behavior using a constraint-based approach. Specifically, this software allows predictive computations of both steady-state and dynamic optimal growth behavior, the effects of gene deletions, comprehensive robustness analyses, sampling the range of possible cellular metabolic states and the determination of network modules. Functions enabling these calculations are included in the toolbox, allowing a user to input a genome-scale metabolic model distributed in Systems Biology Markup Language format and perform these calculations with just a few lines of code. The results are predictions of cellular behavior that have been verified as accurate in a growing body of research. After software installation, calculation time is minimal, allowing the user to focus on the interpretation of the computational results.

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The effects of alternate optimal solutions in constraint-based genome-scale metabolic models.

R. Mahadevan, C.H. Schilling (2003)

Genome-scale constraint-based models of several organisms have now been constructed and are being used for model driven research. A key issue that may arise in the use of such models is the existence of alternate optimal solutions wherein the same maximal objective (e.g., growth rate) can be achieved through different flux distributions. Herein, we investigate the effects that alternate optimal solutions may have on the predicted range of flux values calculated using currently practiced linear (LP) and quadratic programming (QP) methods. An efficient LP-based strategy is described to calculate the range of flux variability that can be present in order to achieve optimal as well as suboptimal objective states. Sample results are provided for growth predictions of E. coli using glucose, acetate, and lactate as carbon substrates. These results demonstrate the extent of flux variability to be highly dependent on environmental conditions and network composition. In addition we examined the impact of alternate optima for growth under gene knockout conditions as calculated using QP-based methods. It was observed that calculations using QP-based methods can show significant variation in growth rate if the flux variability among alternate optima is high. The underlying biological significance and general source of such flux variability is further investigated through the identification of redundancies in the network (equivalent reaction sets) that lead to alternate solutions. Collectively, these results illustrate the variability inherent in metabolic flux distributions and the possible implications of this heterogeneity for constraint-based modeling approaches. These methods also provide an efficient and robust method to calculate the range of flux distributions that can be derived from quantitative fermentation data.

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Analysis of optimality in natural and perturbed metabolic networks.

Daniel Segrè, Dennis Vitkup, George Church (2002)

An important goal of whole-cell computational modeling is to integrate detailed biochemical information with biological intuition to produce testable predictions. Based on the premise that prokaryotes such as Escherichia coli have maximized their growth performance along evolution, flux balance analysis (FBA) predicts metabolic flux distributions at steady state by using linear programming. Corroborating earlier results, we show that recent intracellular flux data for wild-type E. coli JM101 display excellent agreement with FBA predictions. Although the assumption of optimality for a wild-type bacterium is justifiable, the same argument may not be valid for genetically engineered knockouts or other bacterial strains that were not exposed to long-term evolutionary pressure. We address this point by introducing the method of minimization of metabolic adjustment (MOMA), whereby we test the hypothesis that knockout metabolic fluxes undergo a minimal redistribution with respect to the flux configuration of the wild type. MOMA employs quadratic programming to identify a point in flux space, which is closest to the wild-type point, compatibly with the gene deletion constraint. Comparing MOMA and FBA predictions to experimental flux data for E. coli pyruvate kinase mutant PB25, we find that MOMA displays a significantly higher correlation than FBA. Our method is further supported by experimental data for E. coli knockout growth rates. It can therefore be used for predicting the behavior of perturbed metabolic networks, whose growth performance is in general suboptimal. MOMA and its possible future extensions may be useful in understanding the evolutionary optimization of metabolism.

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Integrating high-throughput and computational data elucidates bacterial networks.

Markus Covert, Eric M. Knight, Jennifer Reed … (2004)

The flood of high-throughput biological data has led to the expectation that computational (or in silico) models can be used to direct biological discovery, enabling biologists to reconcile heterogeneous data types, find inconsistencies and systematically generate hypotheses. Such a process is fundamentally iterative, where each iteration involves making model predictions, obtaining experimental data, reconciling the predicted outcomes with experimental ones, and using discrepancies to update the in silico model. Here we have reconstructed, on the basis of information derived from literature and databases, the first integrated genome-scale computational model of a transcriptional regulatory and metabolic network. The model accounts for 1,010 genes in Escherichia coli, including 104 regulatory genes whose products together with other stimuli regulate the expression of 479 of the 906 genes in the reconstructed metabolic network. This model is able not only to predict the outcomes of high-throughput growth phenotyping and gene expression experiments, but also to indicate knowledge gaps and identify previously unknown components and interactions in the regulatory and metabolic networks. We find that a systems biology approach that combines genome-scale experimentation and computation can systematically generate hypotheses on the basis of disparate data sources.