Pathway Thermodynamics Highlights Kinetic Obstacles in Central Metabolism

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.

Global characterization of in vivo enzyme catalytic rates and their correspondence to in vitro k cat measurements

“…Indeed, it has been suggested that mdh evolved a high k cat value to compensate for a thermodynamically unfavorable reaction in the direction of the tricarboxylic acid cycle, which causes much backward flux in vivo. This may result in reduction in the k vivo max , which is not accounted for under in vitro conditions (21). Other outliers serve as good candidates for in-depth biochemical analysis.…”

Computational protein design enables a novel one-carbon assimilation pathway

“…All energy-conserving electron bifurcation reactions were neglected in this analysis. The max-min driving force (MDF) is the lowest value of −Δ r G′ in the pathway [i.e., the reaction(s) with the smallest chemical driving force], after optimizing reactant concentrations within a physiological range (1 μM to 10 mM for noncofactors) as described in the SI Appendix, SI Materials and Methods and Bar-Even et al (37). The cytoplasmic concentration of formate was assumed to be 10 mM.…”

Energy Conservation Associated with Ethanol Formation from H 2 and CO 2 in Clostridium autoethanogenum Involving Electron Bifurcation

“…This can be explained by the fact that during growth of C. autoethanogenum on H 2 /CO 2 or fructose, the function of the enzyme is to catalyze the endergonic reduction of CO 2 to CO (E 0 = ϭ Ϫ520 mV) with reduced ferredoxin (E 0 = ϭ Ϫ400 mV), a step in the total synthesis of acetate from 2 CO 2 , whereas during growth on CO the function of the enzyme is to catalyze the exergonic oxidation of CO to CO 2 with ferredoxin. The Haldane equation predicts that the catalytic efficiency (k cat /K m ) of the enzyme to oxidize CO divided by the catalytic efficiency of the enzyme to reduce CO 2 is equal to the equilibrium constant (57,58).…”