Quantitative assignment of reaction directionality in constraint-based models of metabolism: Application to Escherichia coli

Abstract

Constraint-based modeling is an approach for quantitative prediction of net reaction flux in genome-scale biochemical networks. In vivo, the second law of thermodynamics requires that net macroscopic flux be forward, when the transformed reaction Gibbs energy is negative. We calculate the latter by using (i) group contribution estimates of metabolite species Gibbs energy, combined with (ii) experimentally measured equilibrium constants. In an application to a genome-scale stoichiometric model of Escherichia coli metabolism, iAF1260, we demonstrate that quantitative prediction of reaction directionality is increased in scope and accuracy by integration of both data sources, transformed appropriately to in vivo pH, temperature and ionic strength. Comparison of quantitative versus qualitative assignment of reaction directionality in iAF1260, assuming an accommodating reactant concentration range of 0.02–20 mM, revealed that quantitative assignment leads to a low false positive, but high false negative, prediction of effectively irreversible reactions. The latter is partly due to the uncertainty associated with group contribution estimates. We also uncovered evidence that the high intracellular concentration of glutamate in E. coli may be essential to direct otherwise thermodynamically unfavorable essential reactions, such as the leucine transaminase reaction, in an anabolic direction.

Introduction

Biological systems can be modeled at a large scale by taking an approach which balances computationally tractability with physically and biochemical realistic representation. Constraint-based modeling is a flexible and scalable approach for in silico phenotype prediction [1]. It relies on an accurate biochemical network reconstruction which is a biochemically, genetically and genomically structured representation of experimental biochemical and molecular biological literature [2]. In the case of metabolic networks, biochemical characterization of an enzyme establishes the substrate(s) and product(s) and genetic studies establish the gene–protein-reaction associations which tie a particular metabolic function in a model to a particular genomic location. A biochemical network reconstruction is then converted into a prototype computational model such that predictions may be compared with experimental data. In many cases, initial in silico tests suggest further refinements to the reconstruction underlying the prototype computational model. Iterative refinement of a constraint-based model, by comparison of prediction with experiment, supports its use for a priori in silico prediction of phenotypic capabilities for a posteriori in vivo experimental validation.

There have been many practical biological uses of constraint-based models, including study of bacterial evolution [3], analysis of network properties [4], [5], [6], [7], study of phenotypic behavior [8], [9], biological discovery [10], [11], [12], and metabolic engineering [13], [14], [15]. The growing scope of applications of genome-scale metabolic reconstructions in metabolic engineering and other fields has recently been reviewed [16]. The predictive fidelity of a constraint-based model is dependent on the accuracy of the constraints used to eliminate physicochemically and biochemically infeasible network states. Generally, the resulting constraint equations define an under-determined feasible set of network states. Therefore, in unicellular organisms, a biological objective, such as maximization of growth rate, can be used to predict a single network state within this feasible set depending on the objective. The sensitivity of in silico predictions to the choice of objective function was treated in detail by Savinell and Palsson [17], and more recently by comparison of predictions with fluxomics data [18].

In this work, we focus on the assignment of reaction directionality in stoichiometric, metabolic models since it has a significant effect on the feasible set of functional states [19], [20], [21], [22]. There are two forms of thermodynamic constraints on reaction directionality. Local thermodynamic constraints apply on a reaction, by reaction basis. Essentially, a negative reaction Gibbs energy dictates a net forward reaction flux. This application of thermodynamics to the direction of biochemical reactions has a long history [23], with the first comprehensive treatment by Burton et al. [24]. Non-local thermodynamic constraints apply to sets of reactions [25] and arise due to the necessity to satisfy energy conservation, in addition to the second law of thermodynamics. Non-local thermodynamic constraints have been applied to small systems of biochemical reactions [26], but that approach “cannot be efficiently applied directly to genome-scale problems” [27] due to limitations imposed by computational complexity. Here, our focus is on local thermodynamic constraints for a system of reactions at genome scale. We summarize the theory underlying quantitative assignment of local reaction directionality at physiologically relevant conditions. Then, we apply this theory to a stoichiometric model of Escherichia coli metabolism [28]. Our study relies on the extensive body of work on the thermodynamics of biochemical reactions by Alberty [29], [30] which we apply to a genome-scale model for the first time. We complemented Alberty's approach with ongoing efforts by Henry et al. [19], [20] and Jankowski et al. [31] which seek to estimate the standard Gibbs energy of metabolite species based on a group contribution methodology.