Thermodynamics and Kinetics of Glycolytic Reactions. Part I: Kinetic Modeling Based on Irreversible Thermodynamics and Validation by Calorimetry

In systems biology, material balances, kinetic models, and thermodynamic boundary conditions are increasingly used for metabolic network analysis. It is remarkable that the reversibility of enzyme-catalyzed reactions and the influence of cytosolic conditions are often neglected in kinetic models. In fact, enzyme-catalyzed reactions in numerous metabolic pathways such as in glycolysis are often reversible, i.e., they only proceed until an equilibrium state is reached and not until the substrate is completely consumed. Here, we propose the use of irreversible thermodynamics to describe the kinetic approximation to the equilibrium state in a consistent way with very few adjustable parameters. Using a flux-force approach allowed describing the influence of cytosolic conditions on the kinetics by only one single parameter. The approach was applied to reaction steps 2 and 9 of glycolysis (i.e., the phosphoglucose isomerase reaction from glucose 6-phosphate to fructose 6-phosphate and the enolase-catalyzed reaction from 2-phosphoglycerate to phosphoenolpyruvate and water). The temperature dependence of the kinetic parameter fulfills the Arrhenius relation and the derived activation energies are plausible. All the data obtained in this work were measured efficiently and accurately by means of isothermal titration calorimetry (ITC). The combination of calorimetric monitoring with simple flux-force relations has the potential for adequate consideration of cytosolic conditions in a simple manner.

Thermodynamics and Kinetics of Glycolytic Reactions. Part II: Influence of Cytosolic Conditions on Thermodynamic State Variables and Kinetic Parameters

For systems biology, it is important to describe the kinetic and thermodynamic properties of enzyme-catalyzed reactions and reaction cascades quantitatively under conditions prevailing in the cytoplasm. While in part I kinetic models based on irreversible thermodynamics were tested, here in part II, the influence of the presumably most important cytosolic factors was investigated using two glycolytic reactions (i.e., the phosphoglucose isomerase reaction (PGI) with a uni-uni-mechanism and the enolase reaction with an uni-bi-mechanism) as examples. Crowding by macromolecules was simulated using polyethylene glycol (PEG) and bovine serum albumin (BSA). The reactions were monitored calorimetrically and the equilibrium concentrations were evaluated using the equation of state ePC-SAFT. The pH and the crowding agents had the greatest influence on the reaction enthalpy change. Two kinetic models based on irreversible thermodynamics (i.e., single parameter flux-force and two-parameter Noor model) were applied to investigate the influence of cytosolic conditions. The flux-force model describes the influence of cytosolic conditions on reaction kinetics best. Concentrations of magnesium ions and crowding agents had the greatest influence, while temperature and pH-value had a medium influence on the kinetic parameters. With this contribution, we show that the interplay of thermodynamic modeling and calorimetric process monitoring allows a fast and reliable quantification of the influence of cytosolic conditions on kinetic and thermodynamic parameters.

Standard Gibbs energy of metabolic reactions: IV. Triosephosphate isomerase reaction

The glycolytic pathway is present in most organisms and represents a central part of the energy production mechanism in a cell. For a general understanding of glycolysis, the investigation from a thermodynamic point of view is essential and allows realising thermodynamic feasibility analyses under in vivo conditions. However, available literature standard Gibbs energies of reaction, Δ^Rg'⁰, are calculated using equilibrium-molality ratios K_m', which might lead to a misinterpretation of the glycolytic pathway. It was the aim of this work to thermodynamically investigate the triosephosphate isomerase (TPI) reaction to provide new activity-based reaction data. In vitro equilibrium experiments were performed, and activity coefficients were predicted with the equation of state electrolyte PC-SAFT (ePC-SAFT). The combination of experimental concentrations and predicted activity coefficients yielded the thermodynamic equilibrium constant K_a and a new value for Δ^Rg'⁰(298.15 K, pH 7) = 7.1 ± 0.3 kJ mol^‑1. The availability of the new Δ^Rg'⁰ value allowed predicting influences of the reaction medium on the reaction equilibrium of the TPI reaction. In this work, influences of the initial substrate concentration, pH and Mg²⁺ concentration on the reaction equilibrium were investigated and a method is presented to predict these influences. The higher the substrate concentration and the higher the temperature, the stronger the reaction equilibrium is shifted on the product side. While the pH did not have a significant influence on the reaction equilibrium, Mg²⁺ yielded a shift of the reaction equilibrium to the substrate side. All these effects were predicted correctly with ePC-SAFT. Based on the ePC-SAFT predictions we concluded that a charge-reduction of the product by complexation of the product with Mg²⁺ was responsible for the strong influence of Mg²⁺ on the reaction equilibrium. Finally, the standard enthalpy of reaction of Δ^Rh^'0(pH 7) = 18 ± 7 kJ mol^‑1 was determined with the equilibrium constants K_a at 298.15 K, 304.15 K and 310.15 K using the van 't Hoff equation.