Research Article: Pathway Thermodynamics Highlights Kinetic Obstacles in Central Metabolism

Date Published: February 20, 2014

Publisher: Public Library of Science

Author(s): Elad Noor, Arren Bar-Even, Avi Flamholz, Ed Reznik, Wolfram Liebermeister, Ron Milo, Daniel A. Beard

Abstract: In metabolism research, thermodynamics is usually used to determine the directionality of a reaction or the feasibility of a pathway. However, the relationship between thermodynamic potentials and fluxes is not limited to questions of directionality: thermodynamics also affects the kinetics of reactions through the flux-force relationship, which states that the logarithm of the ratio between the forward and reverse fluxes is directly proportional to the change in Gibbs energy due to a reaction (ΔrG′). Accordingly, if an enzyme catalyzes a reaction with a ΔrG′ of -5.7 kJ/mol then the forward flux will be roughly ten times the reverse flux. As ΔrG′ approaches equilibrium (ΔrG′ = 0 kJ/mol), exponentially more enzyme counterproductively catalyzes the reverse reaction, reducing the net rate at which the reaction proceeds. Thus, the enzyme level required to achieve a given flux increases dramatically near equilibrium. Here, we develop a framework for quantifying the degree to which pathways suffer these thermodynamic limitations on flux. For each pathway, we calculate a single thermodynamically-derived metric (the Max-min Driving Force, MDF), which enables objective ranking of pathways by the degree to which their flux is constrained by low thermodynamic driving force. Our framework accounts for the effect of pH, ionic strength and metabolite concentration ranges and allows us to quantify how alterations to the pathway structure affect the pathway’s thermodynamics. Applying this methodology to pathways of central metabolism sheds light on some of their features, including metabolic bypasses (e.g., fermentation pathways bypassing substrate-level phosphorylation), substrate channeling (e.g., of oxaloacetate from malate dehydrogenase to citrate synthase), and use of alternative cofactors (e.g., quinone as an electron acceptor instead of NAD). The methods presented here place another arrow in metabolic engineers’ quiver, providing a simple means of evaluating the thermodynamic and kinetic quality of different pathway chemistries that produce the same molecules.

Partial Text: A primary scientific goal of metabolic research is to develop an understanding of the evolutionary, chemical and physical forces that shape the structure of cellular metabolism. Specifically, to what extent are present-day metabolic pathways the result of evolutionary optimization rather than fossilized accidents? In recent years various aspects of central metabolism have been explained on the basis of specific selection pressures and constraints imposed during evolution [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13]. Among the various constraints that shape the structure of metabolic pathways, thermodynamics features prominently, linking fundamental physical properties to pathway architecture [1], [9], [10], [11], [14], [15], [16]. Thermodynamic profiling also plays a central role in synthetic pathway design by identifying the most promising candidate pathways and discarding infeasible ones [14], [17], [18], [19], [20], [21].

We introduce a quantitative framework for analyzing the thermodynamic profile of metabolic pathways and identifying reactions that limit metabolic flux within feasible pathways (i.e., require high enzyme levels to sustain a specific rate). While near-equilibrium reactions can significantly increase the protein burden of a pathway, they may have certain advantages. For example, if the direction of a reaction must change quickly in response to some stimulus, operating near equilibrium (and at high enzyme level) is a good strategy: a small change in reactant concentrations can reverse the reaction direction while maintaining a similar absolute flux. This may be particularly important for glycolysis, where some carbon sources require glycolytic flux (e.g., glucose and fructose) and others require flux in the direction of gluconeogenesis (e.g., acetate and succinate). Therefore, fast environmental fluctuations in the availability of carbon sources may require speedy reversal of most glycolytic reactions, which is consistent with recent measurements indicating that reactions in glycolysis mostly operate with low driving-force in E. coli[45], [96]. Other functional advantages of working near equilibrium were recently suggested [97], [98].