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.

Biochemical thermodynamics and rapid-equilibrium enzyme kinetics.

Biochemical thermodynamics is based on the chemical thermodynamics of aqueous solutions, but it is quite different because pH is used as an independent variable. A transformed Gibbs energy G' is used, and that leads to transformed enthalpies H' and transformed entropies S'. Equilibrium constants for enzyme-catalyzed reactions are referred to as apparent equilibrium constants K' to indicate that they are functions of pH in addition to temperature and ionic strength.

Consumption of hydrogen ions in rapid-equilibrium enzyme kinetics.

Enzyme-catalyzed reductase reactions in particular are characterized by large changes in the binding of hydrogen ions Δ(r)N(H). This is a thermodynamic property of the reaction that is catalyzed. For example, in the ferredoxin-nitrite reductase reaction, there is an increase of eight in the binding of hydrogen ions for every molecule of nitrite reduced to ammonia H(2)O.

Estimation of kinetic parameters when modifiers are bound in enzyme-catalyzed reactions.

Modifiers of enzyme-catalyzed reactions can have various types of effects on the velocity, but the most important effect is that they provide multiple pathways to products. The rapid-equilibrium kinetic effects of modifiers are explored for the enzyme-catalyzed reaction A --> products. When a single molecule of modifier X is bound, the mechanism involves three independent equilibrium expressions and two rate constants.

Determination of rapid-equilibrium kinetic parameters of ordered and random enzyme-catalyzed reaction A+B=P+Q.

This article deals with the rapid-equilibrium kinetics of the forward and reverse reactions together for the ordered and random enzyme-catalyzed A+B=P+Q and emphasizes the importance of reporting the values of the full set of equilibrium constants. Equilibrium constants that are not in the rate equation can be calculated for random mechanisms using thermodynamic cycles. This treatment is based on the use of a computer to derive rate equations for three mechanisms and to estimate the kinetic parameters with the minimum number of velocity measurements.

Determination of kinetic parameters of enzyme-catalyzed reaction a + B + C --> products with the minimum number of velocity measurements.

Rapid-equilibrium rate equations are derived for the five different mechanisms for the enzymatic catalysis of A + B + C --> products using a computer. These rate equations are used to determine the minimum number of velocities required to estimate the values of the kinetic parameters. The rate equation for the completely ordered mechanism involves four kinetic parameters, and the rate equation for the completely random mechanism involves eight kinetic parameters.

Determination of kinetic parameters of enzyme-catalyzed reactions with a minimum number of velocity measurements.

Duggleby [Duggleby, R.G., 1979.

Rapid-equilibrium rate equations for the enzymatic catalysis of A+B=P+Q over a range of pH.

This article shows how pKs for the enzymatic site and enzyme-substrate complexes can be obtained from kinetic experiments on the reaction A+B=P+Q, with and without the consumption of hydrogen ions. The rapid-equilibrium rate equation makes it possible to obtain the pKs and chemical equilibrium constants involved in the mechanism, the apparent equilibrium constant K' for the catalyzed reaction, and the number of hydrogen ions consumed in the rate-determining reaction. Experimentally-determined Michaelis constants can be adjusted for the pKs of the substrates A, B, P, and Q so that it is easier to obtain the pKs of E, EA, EB, EAB, EQ, and EPQ, and the chemical equilibrium constants.

Effects of pH in rapid-equilibrium enzyme kinetics.

The effects of pH on the rates of enzyme-catalyzed reactions are very important because they yield information on the pKs of acidic groups in the enzymatic site and the various enzyme-substrate complexes. But many enzyme-catalyzed reactions produce or consume hydrogen ions in a way that cannot be explained with pKs. These pH effects extend over the whole pH range of interest.

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.

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.

Changes in the standard transformed thermodynamic properties of enzyme-catalyzed reactions with ionic strength.

The ionic strength has significant effects on the thermodynamic properties of ionic species and on the transformed thermodynamic properties of biochemical reactants at specified pH values. These effects are discussed for species, reactants, and enzyme-catalyzed reactions. This has led to three new thermodynamic properties: (z(j)(2) - NH(j)), (z(2) - N(H))(i), and Delta(r)(z((2)-N(H)), which are referred to as ionic strength coefficients.

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.

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.

Calculation of equilibrium compositions of systems of enzyme-catalyzed reactions.

When a system of enzyme-catalyzed reactions does not involve H(2)O as a reactant, the equilibrium composition at specified temperature, pH, and ionic strength can be calculated using the Mathematica programs equcalcc, which uses the conservation matrix, or equcalcrx, which uses the stoichiometric number matrix. When H(2)O is involved as a reactant, equcalcrx must be used because H(2)O is not in the stoichiometric number matrix. It is shown here that the use of equcalcrx is equivalent to using the further transformed Gibbs energy G" that eliminates oxygen from the conservation matrix.

Changes in binding of hydrogen ions in enzyme-catalyzed reactions.

Most enzyme-catalyzed reactions produce or consume hydrogen ions, and this is expressed by the change in the binding of hydrogen ions in the biochemical reaction, as written in terms of reactants (sums of species). This property of a biochemical reaction is important because it determines the change in the apparent equilibrium constant K' with pH. This property is also important because it is the number of moles of hydrogen ions that can be produced by a biochemical reaction for passage through a membrane, or can be accepted from a transfer through a membrane.

Biochemical thermodynamics: applications of Mathematica.

The most efficient way to store thermodynamic data on enzyme-catalyzed reactions is to use matrices of species properties. Since equilibrium in enzyme-catalyzed reactions is reached at specified pH values, the thermodynamics of the reactions is discussed in terms of transformed thermodynamic properties. These transformed thermodynamic properties are complicated functions of temperature, pH, and ionic strength that can be calculated from the matrices of species values.

Calculation of thermodynamic properties of species of biochemical reactants using the inverse Legendre transform.

The determination of apparent equilibrium constants and heats of enzyme-catalyzed reactions provides a way to determine Delta(f)G degrees and Delta(f)H degrees of species of biochemical reactants. These calculations are more difficult than the calculation of transformed thermodynamic properties from species properties, and they are an application of the inverse Legendre transform. The Delta(f)G degrees values of species of a reactant can be calculated from an apparent equilibrium constant if the Delta(f)G degrees values are known for all the species of all the other reactants and the pKs of the reactant of interest are known.

Components and coupling in enzyme-catalyzed reactions.

Many enzyme-catalyzed reactions involve coupling of two or more reactions that could otherwise be catalyzed separately. When biochemical reactions are coupled, the equilibrium composition is very different from that when the reactions are not coupled. The number of components in a chemical reaction is equal to the number of independent conservation equations for atoms of elements, but the number of components in an enzyme-catalyzed reaction that is coupled is larger than the number of independent conservation equations for atoms of elements.

Relations between biochemical thermodynamics and biochemical kinetics.

The parameters in steady-state or rapid-equilibrium rate equations for enzyme-catalyzed reactions depend on the temperature, pH, and ionic strength, and may depend on the concentrations of specific species in the buffer. When the complete rate equation (i.e.

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.

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.

Thermodynamic properties of weak acids involved in enzyme-catalyzed reactions.

Measurements of apparent equilibrium constants and transformed enthalpies of enzyme-catalyzed reactions are making it possible to obtain delta(f)G degrees and delta(f)H degrees of species of biochemical reactants in dilute aqueous solution that could never have been determined classically. This article is concerned with the pKs that determine the pH dependencies of the standard transformed thermodynamic properties of biochemical reactants. The database BasicBiochemData3 makes it possible to calculate 82 pKs of 60 reactants as functions of ionic strength at 298.