Two different ways that hydrogen ions are involved in the thermodynamics and rapid-equilibrium kinetics of the enzymatic catalysis of S=P and S+H2O=P

Hydrogen ions are involved in two different ways in the thermodynamics and rapid-equilibrium kinetics of enzyme-catalyzed reactions. The two ways are through pKs and through the production or consumption of hydrogen ions in the mechanism. These ways are examined for the catalyzed reactions S=P and S+H2O=P. Since the apparent equilibrium constant K' can be calculated from the kinetic parameters by use of the Haldane equation, the treatment of the effects of pH must be consistent in thermodynamics and kinetics. This leads to a new kind of Haldane equation that involves 10(pH) or 10(-pH) in addition to the kinetic parameters when hydrogen ions are produced or consumed. These concepts are applicable to more complicated reactions and rate equations. Derivations of equations for calculating these two types of pH effects are discussed in thermodynamics and rapid-equilibrium kinetics. A computer program is used to make four plots of apparent equilibrium constants and changes in the binding of hydrogen ions in the catalyzed reaction.     

Three mechanisms and rapid-equilibrium rate equations for a type of reductase reaction

Rapid-equilibrium rate equations for enzyme-catalyzed reactions are especially useful when the mechanism involves a number of pKs, but they are also useful when some reactants have stoichiometric numbers greater than one or hydrogen ions are produced or consumed in the rate-determining step. The pH dependencies of limiting velocities, Michaelis constants, and reaction velocities for the forward reaction are discussed for two examples of reductase reactions of the type mR + O -> products, where R is the reductant and O is the oxidant. For the nitrate reductase reaction (EC 1.9.6.1), m = 2 and two hydrogen ions are consumed. For the nitrite-ferredoxin reductase reaction (EC 1.7.7.1), m = 6 and eight hydrogen ions are consumed. The expressions for the limiting velocities, Michaelis constants, and rate equations for the forward reaction are derived for two ordered mechanisms and the random mechanism. Three Mathematica programs are used to make plots of kinetic parameters as functions of pH and three-dimensional plots of rapid-equilibrium velocities as functions of [O] and [R] for arbitrary sets of input parameters.     

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.     

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.     

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.     

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.     

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.     

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.     

Immobilized enzyme catalysis with reaction-generated pH change

Many enzyme-catalyzed reactions involve the liberation or consumption of hydrogen ions. In this paper a mathematical model is employed to investigate how such reactions behave when the enzyme is immobilized. Shifted pH optima, disappearance of an optimum pH, insensitivity to bulk pH, and very large effectiveness factors are some of the phenomena which appear as a result of pH coupling between the reaction and the enzyme's activity. Several of the qualitative features revealed by the model are consistent with earlier experimental observations. In addition, preliminary guidelines for optimal choice of enzyme support are suggested.     

Thermodynamics of systems of biochemical reactions

When a reaction system described in terms of species is in a certain state, the Gibbs energy G provides the means for determining whether each reaction will go to the right or the left, and the equilibrium composition of the whole system can be calculated using G. When the pH is specified, a system of biochemical reactions is described in terms of reactants, like ATP (a sum of species), and the transformed Gibbs energy G' provides the means for determining whether each reaction will go to the right or the left. The equilibrium composition of the whole system can be calculated using G'. Since metabolism is complicated, the thermodynamics of systems of reactions like glycolysis and the citric acid cycle can also be considered at specified concentrations of coenzymes like ATP, ADP, NAD(ox), and NAD(red). This is of interest because coenzymes tend to be in steady states because they are involved in many reactions. When the concentrations of coenzymes are constant, the further transformed Gibbs energy G" provides the means for calculating whether each reaction will go to the right or the left, and the equilibrium composition of the whole system can be calculated using G". Under these conditions, a metabolic reaction system can be reconceptualized in terms of sums of reactants; for example, glycolysis can be represented by C(6)=2C(3), where C(6) is the sum of the reactants with six carbon atoms and C(3) is the sum of the reactants with three carbon atoms. These calculations can also be described by use of semigrand partition functions. Semigrand partition functions have the advantage of containing all the thermodynamic information on a series of reactions at specified pH or at specified pH and specified concentrations of coenzymes.     

Constraints and missing reactions in the urea cycle.

The stoichiometric relations in a series of biochemical reactions are summarized by a stoichiometric number matrix (with a column for each reaction) and a conservation matrix (with a row for each constraint). These two matrices for a series or cycle of biochemical reactions are related because the columns of the stoichiometric number matrix are in the null space of the conservation matrix, and the rows of the transpose of the conservation matrix are in the null space of the transpose of the stoichiometric number matrix. The conservation matrix for a system of biochemical reactions is of interest because it shows the nature of the constraints in addition to the conservation of atoms and groups. Constraints beyond those for the conservation of atoms and groups indicate "missing reactions" that do not occur because the enzymes involved couple reactions that could occur and still conserve atoms and groups. The interpretation of conservation matrices and stoichiometric matrices for a reaction system is complicated by the fact that they are not unique. However, their row-reduced forms are unique, as are their dimensions, which represent the number of reactants and number of independent reactions. Two matrices that look different contain the same information if they have the same row-reduced form. The urea cycle, which involves five enzyme-catalyzed reactions, and its net reaction are discussed in terms of the linear constraints produced by enzyme catalysis. A procedure to obtain a set of conservation equations that will yield the correct net reaction is described.     

Generation of a pH gradient in an immobilized enzyme system

Several examples of two-step sequential reactions exist where, because of the poor equilibrium conversion by the first reaction, it is desirable to conduct the two reactions simultaneously. In such a scheme, the product of the first reaction is continuously removed by the second reaction, thus not allowing the first reaction to approach chemical equilibrium. Therefore, the first reaction is allowed to proceed in the desired direction at an appreciable rate. However, in many biochemical applications where enzyme catalysts are involved, the enzyme's activities are strong functions of pH. Where the pH optima of the first and second reaction differ by three to four units, the above reaction scheme would be difficult to implement. In these cases, the two reactions can be separated by a thin permeable membrane across which the desired pH gradient is maintained. In this article, it was shown, both by theory and experiment, that a thin, flat membrane of immobilized urease can accomplish this goal when one face of the membrane is exposed to the acidic bulk solution (pH(b) = 4.5) containing a small quantity of urea (0.01 M). In this particular case, the ammonia that was produced in the membrane consumed the incoming hydrogen ions and thus maintained the desired pH gradient. Experimental results indicate that with sufficient urease loading, the face of the membrane opposite to the bulk solution could be maintained at a pH that would allow many enzymes to realize their maximum activities ( approximately 7.5). It was also found that this pH gradient could be maintained even in the presence of a buffer, which greatly enhances the transport of protons into the membrane. (c) 1993 John Wiley & Sons, Inc.     

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.     

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.     

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.     

Effects of domain connection and disconnection on the yields of in-plane bimolecular reactions in membranes.

It has recently been shown (Vaz, W.L.C., E.C.C. Melo, and T.E. Thompson. 1989. Biophys. J. 56:869-875; 1990. Biophys. J. 58:273-275) that in lipid bilayer membranes in which ordered and disordered phases coexist, the ordered phase can form a two-dimensional reticular structure that subdivides the coexisting disordered phase into a disconnected domain structure. Here we consider theoretically the yields of bimolecular reactions between membrane-localized reactants, when both the reactants and products are confined to the disordered phase. It is shown that compartmentalization of reactants in disconnected domains can lead to significant reductions in reaction yields. The reduction in yield was calculated for classical bimolecular processes and for enzyme-catalyzed reactions. These ideas can be used to explain certain experimental observations.     

Thermodynamic properties of oxidoreductase, transferase, hydrolase, and ligase reactions

Transferases formally couple together two oxidoreductase reactions or two hydrolase reactions. Therefore the thermodynamic properties of transferase reactions can be calculated from differences between thermodynamic properties of two oxidoreductase or two hydrolase reactions. Ligases couple together two hydrolase reactions, and so their thermodynamic properties can be calculated from differences between two hydrolase reactions. These relationships are demonstrated by calculating standard transformed Gibbs energies of reaction and the changes in binding of hydrogen ions at pHs 5-9 of a number of oxidoreductase, transferase, hydrolase, and ligase reactions by use of the data base BasicBiochemData2 and its recent extensions. Coupling is not restricted to two reactions, and an example is given of the coupling of three reactions.     

Demonstration of pH control in a commercial immobilized glucose isomerase

The synthesis of a variety of important biochemicals involves multistep enzyme-catalyzed reactions. In many cases, the optimal operating pH is much different for the individual enzymatic steps of such synthesis reactions. Yet, it may be beneficial if such reaction steps are combined or paired, allowing them to occur simultaneously, in proximity to one another, and at their respective optimal pH. This can be achieved by separating the micro-environments of the two steps of a reaction pathway using a thin urease layer that catalyzes an ammonia-forming reaction. In this article, the pH control system in a commercial immobilized glucose (xylose) isomerase pellet, which has an optimal pH of 7.5, is demonstrated. This system allows the glucose isomerase to have near its optimal pH activity when immersed in a bulk solution of pH 4.6. A theoretical analysis is also given for the effective fraction of the immobilized glucose isomerase, which remains active when the bulk pH is at 4.6 in the presence of 20 mM urea versus when the bulk pH is at its optimal pH of 7.5. Both theoretical and experimental results show that this pH control system works well in this case. (c) 1996 John Wiley & Sons, Inc.     

Isothermal titration calorimetry uncovers substrate promiscuity of bicupin oxalate oxidase from Ceriporiopsis subvermispora

Isothermal titration calorimetry (ITC) may be used to determine the kinetic parameters of enzyme-catalyzed reactions when neither products nor reactants are spectrophotometrically visible and when the reaction products are unknown. We report here the use of the multiple injection method of ITC to characterize the catalytic properties of oxalate oxidase (OxOx) from Ceriporiopsis subvermispora (CsOxOx), a manganese dependent enzyme that catalyzes the oxygen-dependent oxidation of oxalate to carbon dioxide in a reaction coupled with the formation of hydrogen peroxide. CsOxOx is the first bicupin enzyme identified that catalyzes this reaction. The multiple injection ITC method of measuring OxOx activity involves continuous, real-time detection of the amount of heat generated (dQ) during catalysis, which is equal to the number of moles of product produced times the enthalpy of the reaction (ΔH_app). Steady-state kinetic constants using oxalate as the substrate determined by multiple injection ITC are comparable to those obtained by a continuous spectrophotometric assay in which H₂O₂ production is coupled to the horseradish peroxidase-catalyzed oxidation of 2,2′-azinobis-(3-ethylbenzthiazoline-6-sulfonic acid) and by membrane inlet mass spectrometry. Additionally, we used multiple injection ITC to identify mesoxalate as a substrate for the CsOxOx-catalyzed reaction, with a kinetic parameters comparable to that of oxalate, and to identify a number of small molecule carboxylic acid compounds that also serve as substrates for the enzyme.     

Metal-catalyzed oxidation renders silver intensification selective. Applications for the histochemistry of diaminobenzidine and neurofibrillary changes

Physical developers can increase the visibility of end products of certain histochemical reactions, such as oxidative polymerization of diaminobenzidine and selective binding of complex silver iodide ions to Alzheimer's neurofibrillary changes. Unfortunately, this intensification by silver coating is generally superimposed on a nonspecific staining originating from the argyrophil III reaction, which also takes place when tissue sections are treated with physical developers. The present study reveals that the argyrophil III reaction can be suppressed when tissue sections are treated with certain metal ions and hydrogen peroxide before they are transferred to the physical developer. The selective intensification of Alzheimer's neurofibrillary changes requires a pre-treatment with lanthanum nitrate (10 mM/liter) and 3% hydrogen peroxide for 1 hr. The diaminobenzidine reaction can be selectively intensified when physical development is preceded by consecutive treatments with copper sulfate (10 mM/liter, pH 5, 10 min) and hydrogen peroxide (3%, pH 7, 10 min). In peroxidase histochemistry, this high-grade intensification may help to increase specificity and reduce the threshold of detectability in tracing neurons with horseradish peroxidase or in immunohistochemistry when the peroxidase-antiperoxidase method is used.