New thermodynamic activity-based approach allows predicting the feasibility of glycolysis.

Thermodynamic feasibility analyses help evaluating the feasibility of metabolic pathways. This is an important information used to develop new biotechnological processes and to understand metabolic processes in cells. However, literature standard data are uncertain for most biochemical reactions yielding wrong statements concerning their feasibility. In this article we present activity-based equilibrium constants for all the ten glycolytic reactions, accompanied by the standard reaction data (standard Gibbs energy of reaction and standard enthalpy of reaction). We further developed a thermodynamic activity-based approach that allows to correctly determine the feasibility of glycolysis under different chosen conditions. The results show for the first time that the feasibility of glycolysis can be explained by thermodynamics only if (1) correct standard data are used and if (2) the conditions in the cell at non-equilibrium states are accounted for in the analyses. The results here will help to determine the feasibility of other metabolisms and to understand metabolic processes in cells in the future.

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.

Influence of cytosolic conditions on the reaction equilibrium and the reaction enthalpy of the enolase reaction accessed by calorimetry and van 't HOFF.

BACKGROUND: Thermodynamic methods are finding more and more applications in systems biology, which attempts to understand cell functions mechanistically. Unfortunately, the state variables used (reaction enthalpy and Gibbs energy) do not take sufficient account of the conditions inside of cells, especially the crowding with macromolecules. METHODS: For this reason, the influence of crowding agents and various other parameters such as salt concentrations, pH and temperature on equilibrium position and reaction enthalpy of the glycolytic example reaction 9 (2-Phospoglycerate - > Phosphoenolpyruvate + H2O) was investigated. The conditions were chosen to be as close as possible to the cytosolic conditions. Poly(ethylene glycol) MW = 20,000 g mol-1 (PEG 20,000) was used to analyze the influence of crowding with macromolecules. The equation of state electrolyte Perturbed-Chain Statistical Associating Fluid Theory (ePC-SAFT) was applied to consider the influence of crowding agents on the reaction equilibria. RESULTS AND CONCLUSIONS: For the reaction enthalpies and for the equilibria, it was found that the influence of salts and temperature is not pronounced while that of pH and PEG 20,000 concentration is considerable. Furthermore, it could be shown that under identical measurement conditions there are no differences between the van 't Hoff and the calorimetrically determined reaction enthalpy. GENERAL SIGNIFICANCE: The results show how important it is to consider the special cytosolic conditions when applying thermodynamic data in systems biology.

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, ΔRg'0, are calculated using equilibrium-molality ratios Km', 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 Ka and a new value for ΔRg'0(298.15 K, pH 7) = 7.1 ± 0.3 kJ mol­1. The availability of the new ΔRg'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 ΔRh'0(pH 7) = 18 ± 7 kJ mol­1 was determined with the equilibrium constants Ka at 298.15 K, 304.15 K and 310.15 K using the van 't Hoff equation.

Standard Gibbs energy of metabolic reactions: V. Enolase reaction.

The glycolytic pathway is one of the most important pathways for living organisms, due to its role in energy production and as supplier of precursors for biosynthesis in living cells. This work focuses on determination of the standard Gibbs energy of reaction ΔRg'0 of the enolase reaction, the ninth reaction in the glycolysis pathway. Exact ΔRg'0 values are required to predict the thermodynamic feasibility of single metabolic reactions or even of metabolic reaction sequences under cytosolic conditions. So-called "apparent" standard data from literature are only valid at specific conditions. Nevertheless, such data are often used in pathway analyses, which might lead to misinterpretation of the results. In this work, equilibrium measurements were combined with activity coefficients in order to obtain new standard values ΔRg'0 for the enolase reaction that are independent of the cytosolic conditions. Reaction equilibria were measured at different initial substrate concentrations and temperatures of 298.15 K, 305.15 K and 310.15 K at pH 7. The activity coefficients were predicted using the equation of state electrolyte Perturbed-Chain Statistical Associating Fluid Theory (ePC-SAFT). The ePC-SAFT parameters were taken from literature or fitted to new experimentally determined osmotic coefficients and densities. At 298.15 K and pH 7, a ΔRg'0(298.15 K, pH 7) value of -2.8 ± 0.2 kJ mol-1 was obtained. This value differs by up to 5 kJ mol-1 from literature data. Reasons are the poorly defined "standard" conditions and partly undefined reaction conditions of literature works. Finally, using temperature-dependent equilibrium constants and the van 't Hoff equation, the standard enthalpy of reaction of ΔRh'0(298.15 K, pH 7) = 27 ± 10 kJ mol-1 was determined, and a similar value was found by quantum-chemistry calculations.

Thermodynamics of enzyme-catalyzed esterifications: I. Succinic acid esterification with ethanol.

Succinic acid (SA) was esterified with ethanol using Candida antarctica lipase B immobilized on acrylic resin at 40 and 50 °C. Enzyme activity in the reaction medium was assured prior to reaction experiments. Reaction-equilibrium experiments were performed for varying initial molalities of SA and water in the reaction mixtures. This allowed calculating the molality-based apparent equilibrium constant K m as function of concentration and temperature. K m was shown to depend strongly on the molality of water and SA as well as on temperature. It could be concluded that increasing the molality of SA shifted the reaction equilibrium towards the products. Water had a strong effect on the activity of the enzyme and on K m . The concentration dependence of K m values was explained by the activity coefficients of the reacting agents. These were predicted with the thermodynamic models Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT), NRTL, and Universal Quasichemical Functional Group Activity Coefficients (UNIFAC), yielding the ratio of activity coefficients of products and reactants K γ . All model parameters were taken from literature. The models yielded K γ values between 25 and 115. Thus, activity coefficients have a huge impact on the consistent determination of the thermodynamic equilibrium constants K th. Combining K m and PC-SAFT-predicted K γ allowed determining K th and the standard Gibbs energy of reaction as function of temperature. This value was shown to be in very good agreement with results obtained from group contribution methods for Gibbs energy of formation. In contrast, inconsistencies were observed for K th using K γ values from the classical gE-models UNIFAC and NRTL. The importance of activity coefficients opens the door for an optimized reaction setup for enzymatic esterifications.