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Robert A Alberty

Publications and source records attributed to Robert A Alberty.

At least 19 recordsLinked to original sources
PubMed2006

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. Calculations presented here show that the calculation of further transformed Gibbs energies of formation of reactants other than coenzymes can be avoided by using equcalcrx to calculate equilibrium concentrations.

Catalysis↗
PubMed2006

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.

Acetyl Coenzyme A↗
PubMed2006

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. There are two ways to calculate the change in binding of hydrogen ions for an enzyme-catalyzed reaction. The first, which has been used for a long time, involves calculating the partial derivative of the standard transformed Gibbs energy of reaction with respect to pH. The second involves calculating the average numbers of hydrogen ions in each reactant and adding and subtracting these average numbers. The changes in binding of hydrogen ions calculated by the second method at pHs 5, 6, 7, 8, and 9 are given for 23 enzyme-catalyzed reactions. Values are given for 206 more reactions on the web. This database can be extended to include more reactions for which pKs of reactants are known or can be estimated.

Catalysis↗
PubMed2006

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. the equation with parameters for the reverse reaction as well as the forward reaction) is determined, there are one or more Haldane relations between some of the kinetic parameters and the apparent equilibrium constant for the reaction that is catalyzed. When the apparent equilibrium constant can be calculated from the kinetic parameters, the equilibrium composition can be calculated. This is remarkable because the kinetic parameters all depend on the properties of the enzymatic site, but the apparent equilibrium constant and the equilibrium composition do not. The effects of ionic strength and pH on the unoccupied enzymatic site and the occupied enzymatic site have to cancel in the Haldane relation or in the calculation of the apparent equilibrium constant using the rate constants for the steps in the mechanism. Several simple enzymatic mechanisms and their complete rate equations are discussed.

Biochemical Phenomena↗
PubMed2006

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.

Ammonia↗
PubMed2006

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.

Adenosine Monophosphate↗
PubMed2006

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 298.15 K. Standard enthalpies of formation of all the species are known for 27 of these reactants, and so their pKs can be calculated as functions of temperature and ionic strength. This article also presents calculations of delta(r)G degrees, delta(r)H degrees, and delta(r)S degrees at 298.15 K and three ionic strengths for the 42 pKs of these 27 reactants.

Acids↗
PubMed2006

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.

Catalysis↗
PubMed2006

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. The most important of these transformed thermodynamic properties is the standard transformed Gibbs energy of formation of a reactant (sum of species). It is the most important because when this function of temperature, pH, and ionic strength is known, all the other standard transformed properties can be calculated by taking partial derivatives. The species database in this package contains data matrices for 199 reactants. For 94 of these reactants, standard enthalpies of formation of species are known, and so standard transformed Gibbs energies, standard transformed enthalpies, standard transformed entropies, and average numbers of hydrogen atoms can be calculated as functions of temperature, pH, and ionic strength. For reactions between these 94 reactants, the changes in these properties can be calculated over a range of temperatures, pHs, and ionic strengths, and so can apparent equilibrium constants. For the other 105 reactants, only standard transformed Gibbs energies of formation and average numbers of hydrogen atoms at 298.15 K can be calculated. The loading of this package provides functions of pH and ionic strength at 298.15 K for standard transformed Gibbs energies of formation and average numbers of hydrogen atoms for 199 reactants. It also provides functions of temperature, pH, and ionic strength for the standard transformed Gibbs energies of formation, standard transformed enthalpies of formation, standard transformed entropies of formation, and average numbers of hydrogen atoms for 94 reactants. Thus loading this package makes available 774 mathematical functions for these properties. These functions can be added and subtracted to obtain changes in these properties in biochemical reactions and apparent equilibrium constants.

Biochemistry↗
PubMed2005

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. The Delta(f)H degrees of species of a reactant can be calculated from the heat of reaction if the Delta(f)H degrees values are known for all species of the other reactants and Delta(f)G degrees values are known for all species in the reaction. The standard enthalpies of acid dissociation of the reactant of interest are also needed. The inverse Legendre transformation is accomplished by using computer programs to set up the simultaneous equations that involve the Delta(f)H degrees of the species and solving them. Thirty two new species matrixes providing Delta(f)G degrees values and eight new species matrixes providing Delta(f)H degrees values are calculated. It is the specificity and speed of enzyme-catalyzed reactions that make it possible to determine standard thermodynamic properties of complicated species in aqueous solution that could never have been obtained classically.

Biochemical Phenomena↗
PubMed2005

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.

Hydrogen-Ion Concentration↗
PubMed2005

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. The investigation of these additional conservation equations by use of linear algebra is complicated by the fact that in dilute aqueous solutions, the activity of water is taken to be unity. This causes an incompatibility of conservation matrices and stoichiometric number matrices that can be avoided by use of the further transformed Gibbs energy G' ' that provides the criterion for spontaneous change and equilibrium when the standard transformed Gibbs energy of water is constant. In the most striking example discussed, the enzyme mechanism of a ligase reaction introduces three constraints in addition to conservation of atoms of elements. This is completely unheard of in chemical reaction thermodynamics.

Biochemistry↗
PubMed2004

Thermodynamics of the mechanism of the nitrogenase reaction.

The fixation of molecular nitrogen by nitrogenase requires a lot of energy because 16 mol of ATP are hydrolyzed per mole of nitrogen converted to ammonia. Kim and Dees determined the crystallograpic structure of nitrogenase and this has led to a three-step mechanism that involves Feprotein and MoFeprotein in addition to ferredoxin. Each of these steps can be interpreted in terms of two half reactions that are connected through their transfer of electrons. Estimates can be made of the standard apparent reduction potentials of these three steps and their dependencies on pH and ionic strength. This mechanism is compared with the same type of analysis of an alternative three-step mechanism in which the hydrolysis of ATP is coupled with the reduction of molecular nitrogen, rather than the reduction of Feprotein. The problem with the first mechanism is that the second step produces 12 mol of hydrogen ions per mole of nitrogen fixed and the third step consumes 10 mol of hydrogen ions per mole of nitrogen fixed. The alternative mechanism does not have this problem.

Models, Chemical↗
PubMed2004

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.

Energy Transfer↗
PubMed2004

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.

Adenosine Diphosphate↗
PubMed2004

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.

Citric Acid Cycle↗
PubMed2003

Calculation of thermodynamic properties of species from binding of a ligand by a macromolecule.

In the absence of experimental methods for determining concentrations of species in protein-ligand binding, it is not possible to determine the thermodynamic properties of species directly. However, this article on a simple reaction system shows that measurements of the average number of oxygen molecules bound at various T, pH and concentrations of molecular oxygen can be used to calculate thermodynamic properties of species. The simple system considered has some of the characteristics of the binding of oxygen by hemoglobin, but it has been simplified so that the method for obtaining thermodynamic information can be clarified. A table of standard thermodynamic properties of species is the most efficient way to store thermodynamic information on a reaction system. All the standard further transformed thermodynamic properties at specified T, pH and concentrations of molecular oxygen, all the standard transformed thermodynamic properties at specified T and pH, and all the standard thermodynamic properties of species at a specified temperature can be calculated. These calculations are based on the fact that the mathematical function for the standard further transformed Gibbs energy of the system contains all the thermodynamic information on the system. These properties are all interrelated by Maxwell equations.

Hemoglobins↗