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.     

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.     

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 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.     

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.     

Standard thermodynamic formation properties for the adenosine 5'-triphosphate series.

The criterion for chemical equilibrium at specified temperature, pressure, pH, concentration of free magnesium ion, and ionic strength is the transformed Gibbs energy, which can be calculated from the Gibbs energy. The apparent equilibrium constant (written in terms of the total concentrations of reactants like adenosine 5'-triphosphate, rather than in terms of species) yields the standard transformed Gibbs energy of reaction, and the effect of temperature on the apparent equilibrium constant at specified pressure, pH, concentration of free magnesium ion, and ionic strength yields the standard transformed enthalpy of reaction. From the apparent equilibrium constants and standard transformed enthalpies of reaction that have been measured in the adenosine 5'-triphosphate series and the dissociation constants of the weak acids and magnesium complexes involved, it is possible to calculate standard Gibbs energies of formation and standard enthalpies of formation of the species involved at zero ionic strength. This requires the convention that the standard Gibbs energy of formation and standard enthalpy of formation for adenosine in dilute aqueous solutions be set equal to zero. On the basis of this convention, standard transformed Gibbs energies of formation and standard transformed enthalpies of formation of adenosine 5'-trisphosphate, adenosine 5'-diphosphate, adenosine 5'-monophosphate, and adenosine at 298.15 K, 1 bar, pH = 7, a concentration of free magnesium ions of 10(-3) M, and an ionic strength of 0.25 M have been calculated.     

Thermodynamics of reactions catalyzed by PABA synthase

Microcalorimetry and high-performance liquid chromatography (HPLC) have been used to conduct a thermodynamic investigation of reactions catalyzed by PABA synthase, the enzyme located at the first step in the shikimic acid metabolic pathway leading from chorismate to 4-aminobenzoate (PABA). The overall biochemical reaction catalyzed by the PabB and PabC components of PABA synthase is: chorismate(aq)+ammonia(aq)=4-aminobenzoate(aq)+pyruvate(aq)+H(2)O(l). This reaction can be divided into two partial reactions involving the intermediate 4-amino-4-deoxychorismate (ADC): chorismate(aq)+ammonia(aq)=ADC(aq)+H(2)O(l) and ADC(aq)=4-aminobenzoate(aq)+pyruvate(aq). Microcalorimetric measurements were performed on all three of these reactions at a temperature of 298.15 K and pH values in the range 8.72-8.77. Equilibrium measurements were performed on the first partial (ADC synthase) reaction at T=298.15 K and at pH=8.78. The saturation molality of 4-aminobenzoate(cr) in water is (0.00382+/-0.0004) mol kg(-1) at T=298.15 K. The results of the equilibrium and calorimetric measurements were analyzed in terms of a chemical equilibrium model that accounts for the multiplicity of ionic states of the reactants and products. These calculations gave thermodynamic quantities at the temperature 298.15 K and an ionic strength of zero for chemical reference reactions involving specific ionic forms. For the reaction: chorismate(2-)(aq)+NH(4)(+)(aq)=ADC(-)(aq)+H(2)O(l), K=(10.8+/-4.2) and Delta(r)H(m)(o)=-(35+/-15) kJ mol(-1). For the reaction: ADC(-)(aq)=4-aminobenzoate(-)(aq)+pyruvate(-)(aq)+H(+)(aq), Delta(r)H(m)(o)=-(139+/-23) kJ mol(-1). For the reaction: chorismate(2-)(aq)+NH(4)(+)(aq)=4-aminobenzoate(-)(aq)+pyruvate(-)(aq)+H(2)O(l)+H(+)(aq), Delta(r)H(m)(o)=-(174+/-6) kJ mol(-1). Thermodynamic cycle calculations were used to calculate thermodynamic quantities for three additional reactions that utilize L-glutamine rather than ammonia and that are pertinent to this branch point of the shikimic acid pathway. The quantities obtained in this study permit the calculation of the position of equilibrium of these reactions as a function of temperature, pH, and ionic strength. Values of the apparent equilibrium constants and the standard transformed Gibbs energy changes Delta(r)G'(m)(o) under approximately physiological conditions are given.     

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.     

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.     

An investigation of the equilibria between aqueous ribose, ribulose, and arabinose

The thermodynamics of the equilibria between aqueous ribose, ribulose, and arabinose were investigated using high-pressure liquid chromatography and microcalorimetry. The reactions were carried out in aqueous phosphate buffer over the pH range 6.8-7.4 and over the temperature range 313.15-343.75 K using solubilized glucose isomerase with either Mg(NO3)2 or MgSO4 as cofactors. The equilibrium constants (K) and the standard state Gibbs energy (delta G degrees) and enthalpy (delta H degrees) changes at 298.15 K for the three equilibria investigated were found to be: ribose(aq) = ribulose(aq) K = 0.317, delta G degrees = 2.85 +/- 0.14 kJ mol-1, delta H degrees = 11.0 +/- 1.5 kJ mol-1; ribose(aq) = arabinose(aq) K = 4.00, delta G degrees = -3.44 +/- 0.30 kJ mol-1, delta H degrees = -9.8 +/- 3.0 kJ mol-1; ribulose(aq) = arabinose(aq) K = 12.6, delta G degrees = -6.29 +/- 0.34 kJ mol-1, delta H degrees = -20.75 +/- 3.4 kJ mol-1. Information on rates of the above reactions was also obtained. The temperature dependencies of the equilibrium constants are conveniently expressed as R in K = -delta G degrees 298.15/298.15 + delta H degrees 298.15[(1/298.15)-(1/T)] where R is the gas constant (8.31441 J mol-1 K-1) and T the thermodynamic temperature.     

Thermodynamics and kinetics of the glyoxylate cycle

Because the standard Gibbs energies of formation of all the species of reactants in the glyoxylate cycle are known at 298.15 K, it is possible to calculate the apparent equilibrium constants of the five reactions in the cycle in the pH range 5-9 and ionic strengths from 0 to approximately 0.35 M. In making calculations on such a system, it is convenient to specify concentrations of coenzymes like NADox and NADred because they are involved in many reactions and may be in steady states. Calculations are given for [NADox] = 1000[NADred] and [NADox] = 10[NADred]. Equilibrium compositions are calculated using computer programs when all the reactants are present initially and when only glyoxylate and CoA are present initially. The kinetics of the reactions in the glyoxylate cycle at specified concentrations of NADox and NADred are calculated by numerical solution of the steady-state rate equations for the case where the reactant concentrations are below their Michaelis constants and only glyoxylate and CoA are present initially.     

Thermodynamics of the reduction of NADP with 2-propanol catalyzed by an NADP-dependent alcohol dehydrogenase

The apparent equilibrium constant of the biochemical reaction, 2-propanol+NADP(ox) = acetone+NADP(red), was determined at I = 0.25 M over a wide range of pH (5.63 to 8.02) and temperature (5 to 40 degrees C). The reaction was catalyzed by an NADP-dependent alcohol dehydrogenase. The results were used to calculate thermodynamic quantities for the chemical (ionic) reference reaction: 2-propanol+NADP(ox)(3-) = acetone+NADP(red)(4-)+H(+). The thermodynamic quantities for this reference reaction are as follows: equilibrium constant K = (5.98+/-0.46) x 10(-10); standard molar Gibbs energy change Delta(r)G(0) = (52.65+/-0.19) kJmol(-1); standard molar enthalpy change Delta(r)H(0) = (38.9+/-0.6) kJmol(-1); and standard molar entropy change Delta(r)S(0) = -(46.1+/-2.2)J K(-1)mol(-1). All of these results pertain to 25 degrees C (298.15 K) and I = 0. The results also lead, in conjunction with tabulated thermodynamic quantities, to the standard electromotive force E(0) = -0.140 V for the reduction of NADP(ox)(3-) to NADP(red)(4-).     

Thermodynamics of reactions catalyzed by anthranilate synthase

Microcalorimetry and high performance liquid chromatography have been used to conduct a thermodynamic investigation of reactions catalyzed by anthranilate synthase, the enzyme located at the first step in the biosynthetic pathway leading from chorismate to tryptophan. One of the overall biochemical reactions catalyzed by anthranilate synthase is: chorismate(aq) + ammonia(aq) = anthranilate(aq) + pyruvate(aq) + H2O(l). This reaction can be divided into two partial reactions involving the intermediate 2-amino-4-deoxyisochorismate (ADIC): chorismate(aq) + ammonia(aq) = ADIC(aq) + H2O(l) and ADIC(aq) = anthranilate(aq) + pyruvate(aq). The native anthranilate synthase and a mutant form of it that is deficient in ADIC lyase activity but has ADIC synthase activity were used to study the overall ammonia-dependent reaction and the first of the above two partial reactions, respectively. Microcalorimetric measurements were performed on the overall reaction at a temperature of 298.15 K and pH 7.79. Equilibrium measurements were performed on the first partial (ADIC synthase) reaction at temperatures ranging from 288.15 to 302.65 K, and at pH values from 7.76 to 8.08. The results of the equilibrium and calorimetric measurements were analyzed in terms of a chemical equilibrium model that accounts for the multiplicity of ionic states of the reactants and products. These calculations gave thermodynamic quantities at the temperature 298.15 K and an ionic strength of zero for chemical reference reactions involving specific ionic forms. For the reaction: chorismate2-(aq) + NH4+(aq) = anthranilate-(aq) + pyruvate-(aq) + H+(aq) + H2O(l), delta rHmo = -(116.3 +/- 5.4) kJ mol-1. For the reaction: chorismate2-(aq) + NH4+(aq) = ADIC-(aq) + H2O(l), K = (20.3 +/- 4.5) and delta rHmo = (7.5 +/- 0.6) kJ mol-1. Thermodynamic cycle calculations were used to calculate thermodynamic quantities for three additional reactions that are pertinent to this branch point of the chorismate pathway. The quantities obtained in this study permit the calculation of the position of equilibrium of these reactions as a function of temperature, pH, and ionic strength. Values of the apparent equilibrium constants and the standard transformed Gibbs energy changes delta rG'mo under approximately physiological conditions are given.     

Estimation of Gibbs energy changes of central metabolism reactions

Changes in Gibbs energies of metabolic reactions of glycolysis and Krebs cycle have been calculated from literature data including G, pK values, and complex formation constants values. Neutral, charged species and Mg-complexes are included in the data base. Results show that most of the reactions investigated proceed near thermodynamic equilibrium conditions whereas the reactions out of equilibrium are related to the metabolic regulation and seem associated with cyclic sequences or with parallel pathways. Examples of fructose 6-phosphate/fructose 1,6-diphosphate cycle and phosphotranferase system and hexokinase are presented.     

Fundamental equation of thermodynamics for protein-ligand binding

For the internal energy and every thermodynamic potential that can be defined by a Legendre transform, there is a fundamental equation that contains all the thermodynamic information about a system. For a system involving the binding of molecular oxygen and hydrogen ions by a protein, fundamental equations are given for the Gibbs energy G, the transformed Gibbs energy G' at specified pH, and the further transformed Gibbs energy G" at specified pH and specified concentration of molecular oxygen. The Maxwell equations for these various Gibbs energies are important because they provide the connection with experimentally determined properties and increase our understanding of these properties. Measurements of the average number of oxygen molecules bound as a function of T, pH and concentration of molecular oxygen make it possible to calculate Delta(f)G"(o) of the reactant. Maxwell equations make it possible to calculate the average number of hydrogen ions bound, Delta(f)S"(o), Delta(f)H"(o) and their partial derivatives. These relations are illustrated with numerical calculations on a simple reaction system.     

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.     

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.     

Golgi β-glucuronidase of androgen-stimulated mouse kidney

The equilibrium constant of the phosphoglyceromutase reaction was determined over a range of pH (5.4-7.9), in solutions of different ionic strength (0.06-0.3) and in the presence of Mg(2+), at 30 degrees C and at 20 degrees C. The values obtained (8.65-11.65) differ substantially from previously published values. The third acid dissociation constants were redetermined for 2- and 3-phosphoglycerate, and in contrast with previous reports the pK values (7.03 and 6.97 respectively at zero ionic strength) were closely similar. The Mg(2+)-binding constants were measured spectrophotometrically and the values, 286mm(-1) and 255mm(-1) for 2- and 3-phosphoglycerate at pH7 and ionic strength 0.02, were also very similar. From the relative lack of effect of temperature, pH and ionic strength it is concluded that the equilibrium constant differs from unity largely because of entropic factors. At low ionic strength, in the neutral region, the pH-dependence can be attributed to the small difference in the acid dissociation constants, but the difference in dissociation constants does not explain the pH-dependence in the acid region or at high ionic strength. Within physiological ranges of pH, Mg(2+) concentration and ionic strength there will be little variation in equilibrium constant.     

Thermodynamics of the conversion of fumarate to L-(-)-malate

The thermodynamics of the conversion of aqueous fumarate to L-(-)-malate has been investigated using both heat conduction microcalorimetry and a gas chromatographic method for determining equilibrium constants. The reaction was carried out in aqueous Tris-HCl buffer over the pH range 6.3-8.0, the temperature range 25-47 degrees C, and at ionic strengths varying from 0.0005 to 0.62 mol kg-1. Measured enthalpies and equilibrium ratios have been adjusted to zero ionic strength and corrected for ionization effects to obtain the following standard state values for the conversion of aqueous fumarate 2- to malate 2- at 25 degrees C: K = 4.20 +/- 0.05, delta G degrees = -3557 +/- 30 J mol-1, delta H degrees = -15670 +/- 150 J mol-1, and delta C degrees p = -36 +/- J mol-1 K-1. Equations are given which allow one to calculate the combined effects of pH and temperature on equilibrium constants and enthalpies of this reaction.