Thermodynamic properties of enzyme-catalyzed reactions involving guanine, xanthine, and their nucleosides and nucleotides

The standard Gibbs energies of formation of species in the guanosine triphosphate and the xanthosine triphosphate series have been calculated on the basis of the convention that the standard Gibbs energy of formation for the neutral form of guanosine is equal to zero in aqueous solution at 298.15 K and zero ionic strength. This makes it possible to calculate apparent equilibrium constants for a number of enzyme-catalyzed reactions for which apparent equilibrium constants have not been measured or cannot be measured directly because they are too large. The eventual elimination of this convention is discussed. This adds ten reactants to the database BasicBiochemData3 that has 199 reactants. The standard transformed Gibbs energies of formation of these ten reactants are used to calculate apparent equilibrium constants at 298.15 K, 0.25 M ionic strength, and pHs 5, 6, 7, 8, and 9. The pKs, standard Gibbs energies of hydrolysis, and standard Gibbs energies of deamination are given for the reactants in the ATP, IMP, GTP, and XTP series.     

Thermodynamics of the purine nucleotide cycle

Since the standard Gibbs energies of formation are known for all the species in the purine nucleotide cycle at 298.15 K, the functions of pH and ionic strength that yield the standard transformed Gibbs energies of formation of the ten reactants can be calculated. This makes it possible to calculate the standard transformed Gibbs energies of reaction, apparent equilibrium constants, and changes in the binding of hydrogen ions for the three reactions at desired pHs and ionic strengths. These calculations are also made for the net reaction and a reaction that is related to it. The equilibrium concentrations for the cycle are calculated when all the reactants are initially present or only some are present initially. Since the concentrations of GTP, GDP, and P(i) may be in steady states, the equilibrium concentrations are also calculated for the system at specified steady-state concentrations.     

Thermodynamic properties of enzyme-catalyzed reactions involving cytosine, uracil, thymine, and their nucleosides and nucleotides

The standard Gibbs energies of formation of species in the cytidine triphosphate series, uridine triphosphate series, and thymidine triphosphate series have been calculated on the basis of the convention that Delta(f)G=0 for the neutral form of cytidine in aqueous solution at 298.15 K at zero ionic strength. This makes it possible to calculate apparent equilibrium constants for a number of reactions for which apparent equilibrium constants have not been measured or cannot be measured because they are too large. This paper adds fifteen reactants to the database BasicBiochemData3 at MathSource that includes 199 reactants. The standard transformed Gibbs energies of formation of these fifteen reactants are used to calculate apparent equilibrium constants at 298.15 K, ionic strength 0.25 M, and pHs 5, 6, 7, 8, and 9 for thirty two reactions. The pKs, standard Gibbs energies of hydrolysis, and standard Gibbs energies of deamination are given for these fifteen reactants.     

Standard transformed Gibbs energies of coenzyme A derivatives as functions of pH and ionic strength

The best way to store data on apparent equilibrium constants for enzyme-catalyzed reactions is to calculate the standard Gibbs energies of formation of the species involved at 298.15 K and zero ionic strength so that equilibrium constants can be calculated at the desired pH and ionic strength. These calculations are described for CoA, acetyl-CoA, oxalyl-CoA, succinyl-CoA, methylmalonyl-CoA, malyl-CoA and CoA-glutathione. The species properties are then used to calculate standard transformed Gibbs energies of formation for these reactants as functions of pH at ionic strength 0.25 M. The species data also make it possible to calculate apparent equilibrium constants of 23 enzyme-catalyzed reactions as a function of pH, including some that cannot be determined directly because they are so large.     

Thermodynamics of the arginine kinase reaction.

The effect of temperature, pH, free [Mg(2+)], and ionic strength on the apparent equilibrium constant of arginine kinase (EC 2.7.3.3) was determined. At equilibrium, the apparent K' was defined as [see text] where each reactant represents the sum of all the ionic and metal complex species. The K' at pH 7.0, 1.0 mM free [Mg(2+)], and 0. 25 M ionic strength was 29.91 +/- 0.59, 33.44 +/- 0.46, 35.44 +/- 0. 71, 39.64 +/- 0.74, and 45.19 +/- 0.65 (n = 8) at 40, 33, 25, 15, and 5 degrees C, respectively. The standard apparent enthalpy (DeltaH degrees') is -8.19 kJ mol(-1), and the corresponding standard apparent entropy of the reaction (DeltaS degrees') is + 2. 2 J K(-1)mol(-1) in the direction of ATP formation at pH 7.0, free [Mg(2+)] =1.0 mM, ionic strength (I) =0.25 M at 25 degrees C. We further show that the magnitude of transformed Gibbs energy (DeltaG degrees ') of -8.89 kJ mol(-1) is mostly comprised of the enthalpy of the reaction, with 7.4% coming from the entropy TDeltaS degrees' term (+0.66 kJ mol(-1)). Our results are discussed in relation to the thermodynamic properties of its evolutionary successor, creatine kinase.     

Equilibrium calculations on systems of biochemical reactions at specified pH and pMg.

The use of G' in discussing the thermodynamics of biochemical reactions at a specified pH and pMg is justified by use of a Legendre transform of the Gibbs energy G. When several enzymatic reactions occur simultaneously in a system, the standard transformed Gibbs energies of reaction delta rG'0 can be used in a computer program to calculate the equilibrium composition that minimizes the transformed Gibbs energy at the specified pH and pMg. The calculation of standard transformed Gibbs energies of formation of reactants at pH 7 and pMg 3 is described. In addition a method for calculating the equilibrium concentrations of reactants is illustrated for a system with steady state concentrations of some reactants like ATP and NAD.     

Levels of thermodynamic treatment of biochemical reaction systems.

Equilibrium calculations on biochemical reaction systems can be made at three levels. Level 1 is the usual chemical calculation with species at specified temperature and pressure using standard Gibbs energies of formation of species or equilibrium constants K. Level 2 utilizes reactants such as ATP (a sum of species) at specified T, P, pH, and pMg with standard transformed Gibbs energies of formation of reactants or apparent equilibrium constants K'. Calculations at this level can also be made on the enzymatic mechanism for a biochemical reaction. Level 3 utilizes reactants at specified T, P, pH, and pMg, but the equilibrium concentrations of certain reactants are also specified. The fundamental equation of thermodynamics is derived here for Level 3. Equilibrium calculations at this level use standard transformed Gibbs energies of formation of reactants at specified concentrations of certain reactants or apparent equilibrium constants K". Level 3 is useful in calculating equilibrium concentrations of reactants that can be reached in a living cell when some of the reactants are available at steady-state concentrations. Calculations at all three levels are facilitated by the use of conservation matrices and stoichiometric number matrices for systems. Three cases involving glucokinase, glucose-6-phosphatase, and ATPase are discussed.     

Equilibrium concentrations for pyruvate dehydrogenase and the citric acid cycle at specified concentrations of certain coenzymes

It is of interest to calculate equilibrium compositions of systems of biochemical reactions at specified concentrations of coenzymes because these reactants tend to be in steady states. Thermodynamic calculations under these conditions require the definition of a further transformed Gibbs energy G" by use of a Legendre transform. These calculations are applied to the pyruvate dehydrogenase reaction plus the citric acid cycle, but steady-state concentrations of CoA, acetyl-CoA and succinyl-CoA cannot be specified because they are involved in the conservation of carbon atoms. These calculations require the use of linear algebra to obtain further transformed Gibbs energies of formation of reactants and computer programs to calculate equilibrium compositions. At specified temperature, pH, ionic strength and specified concentrations of several coenzymes, the equilibrium composition depends on the specified concentrations of the coenzymes and the initial amounts of reactants.     

Recommendations for terminology and databases for biochemical thermodynamics

Chemical equations are normally written in terms of specific ionic and elemental species and balance atoms of elements and electric charge. However, in a biochemical context it is usually better to write them with ionic reactants expressed as totals of species in equilibrium with each other. This implies that atoms of elements assumed to be at fixed concentrations, such as hydrogen at a specified pH, should not be balanced in a biochemical equation used for thermodynamic analysis. However, both kinds of equations are needed in biochemistry. The apparent equilibrium constant K' for a biochemical reaction is written in terms of such sums of species and can be used to calculate standard transformed Gibbs energies of reaction Δ(r)G'°. This property for a biochemical reaction can be calculated from the standard transformed Gibbs energies of formation Δ(f)G(i)'° of reactants, which can be calculated from the standard Gibbs energies of formation of species Δ(f)G(j)° and measured apparent equilibrium constants of enzyme-catalyzed reactions. Tables of Δ(r)G'° of reactions and Δ(f)G(i)'° of reactants as functions of pH and temperature are available on the web, as are functions for calculating these properties. Biochemical thermodynamics is also important in enzyme kinetics because apparent equilibrium constant K' can be calculated from experimentally determined kinetic parameters when initial velocities have been determined for both forward and reverse reactions. Specific recommendations are made for reporting experimental results in the literature.     

Thermodynamic properties of nucleotide reductase reactions

Recent thermodynamic measurements have made it possible to calculate the apparent equilibrium constants of the ribonucleoside diphosphate reductase reaction and the ribonucleoside triphosphate reductase reaction with various reducing agents. Third law heat capacity measurements on crystals of d-ribose and other calorimetric measurements make it possible to calculate Delta(f)G degrees for D-ribose and two species of D-ribose 5-phosphate. The experimental value of the apparent equilibrium constant K' for the deoxyribose-phosphate aldolase reaction makes it possible to calculate the standard Gibbs energies of formation Delta(f)G degrees for two protonation states of 2'-deoxy-D-ribose 5-phosphate. This shows that Delta(f)G degrees (2'-deoxy-D-ribose 5-phosphate(2)(-)) - Delta(f)G degrees (D-ribose 5-phosphate(2)(-)) = 147.86 kJ mol(-1) at 298.15 K and zero ionic strength in dilute aqueous solutions. This difference between reduced and oxidized forms is expected to apply to D-ribose, D-ribose 1-phosphate, ribonucleosides, and ribonucleotides in general. This expectation is supported by two other enzyme-catalyzed reactions for which apparent equilibrium constants have been determined. The availability of Delta(f)G degrees values for the species of 2'-deoxy-D-ribose and its derivatives makes it possible to calculate standard transformed Gibbs energies of formation of these reactants, apparent equilibrium constants for their reactions, changes in the binding of hydrogen ions in these reactions, and standard apparent reduction potentials of the half reactions involved as a function of pH and ionic strength at 298.15 K. The apparent equilibrium constant for ADP + thioredoxin(red) = 2'-deoxyADP + H(2)O + thioredoxin(ox) is 1.4 x 10(11) at 298.15 K, pH 7, and 0.25 M ionic strength.     

Thermodynamics of the reactions of carbamoyl phosphate

Two measurements of equilibrium constants by Marshall and Cohen make it possible to calculate standard Gibbs energies of formation of the species of carbamate and carbamoyl phosphate. Carbamate formation from carbon dioxide and ammonia does not require an enzyme, and the equilibrium concentrations of carbamate in ammonium bicarbonate are calculated. Knowing the values of standard Gibbs energies of formation of species of carbamate and carbamoyl phosphate make it possible to calculate the dependencies of the standard transformed Gibbs energies of formation of these reactants on pH and ionic strength and to calculate apparent equilibrium constants for several enzyme-catalyzed reactions and several chemical reactions. These calculations are sufficiently complicated that computer programs in Mathematica are used to make tables and plots. The dependences of apparent equilibrium constants on pH are consequences of the production or consumption of hydrogen ions, which are shown in plots. As usual the increase in the number of enzyme-catalyzed reactions for which apparent equilibrium constants can be calculated is larger than the number of reactions required to obtain the thermodynamic properties of the species involved.     

Standard apparent reduction potentials of biochemical half reactions and thermodynamic data on the species involved

Standard apparent reduction potentials E' degrees of half reactions of enzyme-catalyzed reactions are useful because they provide a global view of the apparent equilibrium constants of redox reactions. A table of E' degrees at a specified pH shows at a glance whether a given half reaction will drive another half reaction or be driven by it. This table can be used to calculate apparent equilibrium constants. Standard Gibbs energies of formation of species in a half reaction can be used to calculate E' degrees values at pHs in the range 5-9 and ionic strengths in the range of 0-0.35 M. My previously published values of E' degrees values for 42 half reactions has been extended by 22 new E' degrees values in this paper. When DeltafG degrees and DeltafH degrees are both known for all the species in an enzyme-catalyzed reaction at 298.15 K, it is possible to calculate all the standard transformed thermodynamic properties of the reaction over a range of pHs, ionic strengths, and temperatures.     

Thermodynamics of hexokinase catalyzed reactions. II. Measurement and calculation of enthalpies of reaction as a function of magnesium ion concentration.

Enthalpies of phosphorylation of glucose by adenosine 5'-triphosphate have been measured as a function of concentrations of magnesium chloride in TRIS/TRIS-HCl buffer in the pH range 8.64 to 8.98. These measurements are compared with the results of calculations of these enthalpies that use a coupled equilibrium formalism with equilibrium data and enthalpy values selected from the literature. The experimental results span the range of magnesium ion concentrations 1 X 10(-6) to 0.3 mol alpha-1 and show a total variation in the enthalpy of reaction of almost 10 kJ mol-1, with the most exothermic reaction occurring at a magnesium ion concentration of 6.0 X 10(-4) mol alpha-1. The calculated enthalpies of reaction, except for the magnesium ion concentration range 4 X 10(-6) to 5 X 10(-4) mol alpha-1, are, within estimated uncertainty intervals (0.8 to 10.2 kJ mol-1), in agreement with the measured values.     

Standard apparent reduction potentials for biochemical half reactions as a function of pH and ionic strength

Standard apparent reduction potentials are important because they give a more global view of the driving forces for redox reactions than do the standard transformed Gibbs energies of formation of the reactants. This paper emphasizes the effects of pH on biochemical half reactions in the range pH 5 to 9, but it also shows the effect of ionic strength. These effects can be calculated if the pKs of acid groups in the reactants are known in the range pH 4 to 10. Raising the pH decreases the standard apparent reduction potentials of half reactions when it has an effect, and the slope is proportional to minus one times the ratio of the change in binding of hydrogen ions in the half reaction to the number of electrons transferred. These effects are discussed for 19 biochemical reactions. This effect is most striking for the nitrogenase reaction, where the apparent equilibrium constant is proportional to 10(-10 pH) and is unfavorable for nitrogen fixation above pH 8.     

Thermodynamics of the disproportionation of adenosine 5'-diphosphate to adenosine 5'-triphosphate and adenosine 5'-monophosphate. I. Equilibrium model

The thermodynamic treatment of the disproportionation reaction of adenosine 5′-diphosphate to adenosine 5′-triphosphate and adenosine 5′-monophosphate is discussed in terms of an equilibrium model which includes the effects of the multiplicity of ionic and metal bound species and the presence of long range electrostatic and short range repulsive interactions. Calculated quantities include equilibrium constants, enthalpies, heat capacities, entropies, and the stoichiometry of the overall reaction. The matter of how these calculations can be made self-consistent with respect to both calculated values of the ionic strength and the molality of the free magnesium ion is discussed. The thermodynamic data involving proton and magnesium-ion binding data for the nucleotides involved in this reaction have been evaluated.     

Calculating apparent equilibrium constants of enzyme-catalyzed reactions at pH 7

Apparent equilibrium constants K' of biochemical reactions at pH 7 and standard apparent reduction potentials of half reactions at pH 7 can be calculated using a table of standard transformed Gibbs energies of formation Delta(f)G'(0) at pH 7. A table is provided for 136 reactants at 25 degrees C, pH 7, and ionic strengths of 0, 0.10, and 0.25 M. Examples are given to illustrate the use of the table.     

The role of water in the thermodynamics of dilute aqueous solutions

Water plays a role in the thermodynamics of dilute aqueous solutions that is unusual in two ways. First, knowledge of hydration equilibrium constants of species is not required in calculations of thermodynamic properties of biochemical reactants and reactions at specified pH. Second, since solvent provides an essentially infinite source of oxygen atoms in a reaction system where water is a reactant, oxygen atoms are not conserved in the reaction system in dilute aqueous solutions. This is related to the fact that H₂O is omitted in equilibrium expressions for dilute aqueous solutions. Calculations of the standard transformed Gibbs energies of formation of total carbon dioxide and total ammonia at specified pH are discussed, and the average bindings of hydrogen ions by these reactants are calculated by differentiation. Since both of these reactants are involved in the urease reaction, the apparent equilibrium constants and changes in the numbers of hydrogen ions bound are calculated for this reaction as functions of pH.     

Effect of temperature on the creatine kinase equilibrium.

The effect of temperature on the apparent equilibrium constant of creatine kinase (ATP:creatine N-phosphotransferase (EC 2.7.3.2)) was determined. At equilibrium the apparent K' for the biochemical reaction was defined as [formula: see text] The symbol sigma denotes the sum of all the ionic and metal complex species of the reactant components in M. The K' at pH 7.0, 1.0 mM free Mg2+, and ionic strength of 0.25 M at experimental conditions was 177 +/- 7.0, 217 +/- 11, 255 +/- 10, and 307 +/- 13 (n = 8) at 38, 25, 15, and 5 degrees C, respectively. The standard apparent enthalpy or heat of the reaction at the specified conditions (delta H' degree) was calculated from a van't Hoff plot of log10K' versus 1/T, and found to be -11.93 kJ mol-1 (-2852 cal mol-1) in the direction of ATP formation. The corresponding standard apparent entropy of the reaction (delta S' degree) was +4.70 J K-1 mol-1. The linear function (r2 = 0.99) between log10 K' and 1/K demonstrates that both delta H' degree and delta S' degree are independent of temperature for the creatine kinase reaction, and that delta Cp' degree, the standard apparent heat capacity of products minus reactants in their standard states, is negligible between 5 and 38 degrees C. We further show from our data that the sign and magnitude of the standard apparent Gibbs energy (delta G' degree) of the creatine kinase reaction was comprised mostly of the enthalpy of the reaction, with 11% coming from the entropy T delta S' degree term. The thermodynamic quantities for the following two reference reactions of creatine kinase were also determined. [formula: see text] The delta H degree for Reaction 2 was -16.73 kJ mol-1 (-3998 cal mol-1) and for Reaction 3 was -23.23 kJ mol-1 (-5552 cal mol-1) over the temperature range 5-38 degrees C. The corresponding delta S degree values for the reactions were +110.43 and +83.49 J K-1 mol-1, respectively. Using the delta H' degree of -11.93 kJ mol-1, and one K' value at one temperature, a second K' at a second temperature can be calculated, thus permitting bioenergetic investigations of organs and tissues using the creatine kinase equilibria over the entire physiological temperature range.     

Thermodynamic studies of binary and ternary complexes of pig heart lactate dehydrogenase.

The thermodynamics of the reaction catalyzed by pig heart muscle lactate dehydrogenase (LDH; EC1.1.1,27) have been studied in 0,2 M potassium phosphate buffer, pH 7, over the temperature range of 10 to 35 degrees C by using oxamate and oxalate to simulate the corresponding reactions of the substrates pyruvate and lactate, respectively. The various complexes formed are characterized by Gibbs free energies, enthalpies, and entropies. The Gibbs free energies were determined by equilibrium dialysis investigations, fluorescence titrations, and ultraviolet difference spectroscopy, while the reaction enthalpies stem from direct calorimetric measurements, Formulas are given for both the temperature dependence of the equilibrium constants and the variation with temperature of the enthalpies involved in the four reactions between LDH and NADH or NAD, LDH-NADH and oxamate, and LDH-NAD and oxalate. All reactions show a marked negative temperature coefficient, deltacp, of the binding enthalpies indicating partial refolding to be associated with binary and ternary complex formation. This interpretation appears very probable in view of recent x-ray crystallographic studies on lactate dehydrogenase from dogfish, which demonstrate a volume decrease to occur on binding of oxamate to the LDH-NADH complex. The validity of the thermodynamic parameters, as derived with substrate analogues, for the actual catalytic reaction, gains strong support from the agreement between the sum of the heats involved in the four intermediary reactions reported in this study and direct determinations of the overall enthalpy associated with the catalytic process published in the literature.     

Thermodynamics of the hydrolysis of adenosine 5'-triphosphate to adenosine 5'-diphosphate

The enthalpy of hydrolysis of the enzyme-catalyzed (heavy meromyosin) conversion of adenosine 5'-triphosphate (ATP) to adenosine 5'-diphosphate (ADP) and inorganic phosphate has been investigated using heat-conduction microcalorimetry. Enthalpies of reaction were measured as a function of ionic strength (0.05-0.66 mol kg-1), pH (6.4-8.8), and temperature (25-37 degrees C) in Tris/HCl buffer. The measured enthalpies were adjusted for the effects of proton ionization and metal ion binding, protonation and interaction with the Tris buffer, and ionic strength effects to obtain a value of delta H0 = -20.5 +/- 0.4 kJ mol-1 at 25 degrees C for the process, ATP4-(aq) + H2O(l) = ADP3-(aq) + HPO2-4(aq) + H+(aq) where aq is aqueous and l is liquid. Heat measurements carried out at different temperatures lead to a value of delta C0p = -237 +/- 30 J mol-1 K-1 for the above process.