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R A Alberty

Publications and source records attributed to R A Alberty.

At least 19 recordsLinked to original sources
PubMed2002

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.

Animals↗
PubMed2001

Systems of biochemical reactions from the point of view of a semigrand partition function.

Semigrand partition functions contain all the thermodynamic information on reaction systems. When they are written for systems at specified pH, they yield the transformed Gibbs energy G' of the system and the thermodynamic properties that can be calculated from G'. When they are written for systems at specified pH and specified concentrations of coenzymes, they yield the further transformed Gibbs energy G" and properties that can be calculated from G". This is illustrated by considering: (1) a reactant that is a weak monoprotic acid at a specified pH; (2) a reaction between two pseudoisomer groups at a specified pH; and (3) the first five reactions of glycolysis. Equilibrium compositions in glycolysis are calculated at pH 7 and different steady-state concentrations of ATP and ADP.

Adenosine Diphosphate↗
PubMed2001

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.

Acetone↗
PubMed1998

Calculation of standard transformed formation properties of biochemical reactants and standard apparent reduction potentials of half reactions.

The standard Gibbs energies of formation and standard enthalpies of formation of species involved in biochemical reactions are used to calculate standard transformed Gibbs energies of formation and standard transformed enthalpies of formation of 62 biochemical reactants (sums of species) at 298.15 K, pH 7, and ionic strengths of 0, 0.10, and 0.25 M. It has been possible to put the oxidized and reduced forms of some reactants in this table because their standard apparent reduction potentials are known at pH 7. This paper emphasizes redox reactions. Two applications have been made of these 62 new values of standard transformed Gibbs energies of formation at pH 7: (1) They have been used to calculate standard transformed Gibbs energies of formation of 16 more biochemical reactants from measurements of apparent equilibrium constants of redox reactions. (2) They have been used to calculate standard apparent reduction potentials at pH 7 for half reactions involving reactants discussed in this article and the previous one. This table of standard apparent reduction potentials can be extended considerably from known apparent equilibrium constants for enzyme-catalyzed redox reactions. This brings the total number of reactants for which the standard transformed Gibbs energy of formation at 298K, pH 7, and ionic strengths of 0, 0.10, and 0.25 M have been calculated to 142.

Energy Transfer↗
PubMed1998

Calculation of standard transformed Gibbs energies and standard transformed enthalpies of biochemical reactants.

The standard Gibbs energies of formation and standard enthalpies of formation of species involved in biochemical reactions are used to calculate standard transformed Gibbs energies of formation and standard transformed enthalpies of formation of 53 reactants (sums of species) at 298.15 K, pH 7, and ionic strengths of 0, 0.1, and 0. 25 M. The standard transformed Gibbs energies of formation are used to calculate apparent equilibrium constants K' for 22 biochemical reactions for which apparent equilibrium constants have been determined close to these conditions. This comparison is generally satisfactory given the differences in experimental conditions. The transformed formation properties for the 53 reactants make it possible to calculate transformed formation properties for other reactants involved in biochemical reactions with some of these reactants. This is illustrated by calculating standard transformed Gibbs energies of formation for 11 more reactants without information on the standard Gibbs energies of formation of the species. The list of 64 reactants for which standard transformed Gibbs energies of formation are presented can be considerably extended. The use of tables of standard transformed Gibbs energies of formation to store information on apparent equilibrium constants is more efficient than simply storing apparent equilibrium constants because a reactant can be looked up in a table and may be involved in hundreds of reactions. The effects of magnesium ions on several reactions involving ATP are calculated. The advantages of using enzyme-catalyzed reactions for determining thermodynamic properties of complicated molecules in aqueous solution are discussed.

Biochemistry↗
PubMed1998

Change in the binding of hydrogen ions and magnesium ions in the hydrolysis of ATP.

The binding of hydrogen ions and magnesium ions by a biochemical reactant, like ATP, can be calculated by writing the binding polynomial (partition function) Q and taking the partial derivatives of log Q with respect to pH and pMg by use of a mathematical program in a personal computer. The change in binding of hydrogen ions and magnesium ions in a biochemical reaction, like the hydrolysis of ATP, can be calculated by taking the partial derivatives of log (K'/K), where K' is the apparent equilibrium constant and K is the equilibrium constant for a reference chemical reaction. These calculations can be checked by using the computer to calculate the mixed partial derivatives, which must be equal. The effects of pH, pMg, and ionic strength on the changes in binding in the hydrolysis of ATP are calculated. At 298.15 K, pH7, pMg 3, and 0.25 M ionic strength, the hydrolysis of ATP to ADP and inorganic phosphate liberates 0.62 mol of hydrogen ions and 0.45 mol of magnesium ions into the medium.

Acid-Base Equilibrium↗
PubMed1997

Apparent equilibrium constants and standard transformed Gibbs energies of biochemical reactions involving carbon dioxide.

When carbon dioxide is produced in a biochemical reaction, the expression for the apparent equilibrium constant K' can be written in terms of the partial pressure of carbon dioxide in the gas phase or the total concentration of species containing CO2 in the aqueous phase, referred to here as [TotCO2]. The values of these two apparent equilibrium constants are different because they correspond to different ways of writing the biochemical equations. Their dependencies on pH and ionic strength are also different. The ratio of these two apparent equilibrium constants is equal to the apparent Henry's law constant K'H. This article provides derivations of equations for the calculation of the standard transformed Gibbs energies of formation of TotCO2 and values of the apparent Henry's law constant at various pH levels and ionic strengths. These equations involve the four equilibrium constants interconnecting the five species [CO2(g), CO2(aq), H2CO3, HCO3-, and CO3(2-)] of carbon dioxide. In the literature there are many errors in the treatment of equilibrium data on biochemical reactions involving carbon dioxide, and so several examples are discussed here, including calculation of standard transformed Gibbs energies of formation of reactants. This approach also applies to net reactions, and the net reaction for the oxidation of glucose to carbon dioxide and water is discussed.

Calorimetry↗
PubMed1997

Determination of the seven apparent equilibrium constants for the binding of oxygen by hemoglobin from measured fractional saturations.

Subunit dissociation has to be taken into account in the determination of the oxygen binding constants of hemoglobin, as described by Ackers and Halvorson in 1974. The seven apparent equilibrium constants for a particular set of conditions can be determined by using extrapolations to determine the fractional saturations YT of tetramer and YD of dimer from measured values of the fractional saturation Y of partially dissociated hemoglobin. Analytical methods are used to show that YT as a function of [O2] for tetramers can be calculated from Y of hemoglobin by linear extrapolation of measured Y values at high [heme] versus [heme]-1/2 to [heme]-1/2 = 0. YD for dimers can be calculated from measured Y values by linear extrapolation of Y versus [heme] to [heme] = 0 if sufficiently low [heme] can be used. These extrapolations have been tested with numerical calculations of Y for a particular hemoglobin as a function of [heme] and [O2] by using the seven apparent equilibrium constants determined by Mills, Johnson, and Ackers in 1976. The proposed procedure also yields the apparent association constant K" for 2TotD = TotT, where TotD is the sum of the dimers and TotT is the sum of the tetramers. This thermodynamic analysis of experimental data to determine the seven apparent equilibrium constants is independent of the model used to interpret the values of the thermodynamic parameters.

Chemical Phenomena↗
PubMed1997

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.

Models, Chemical↗
PubMed1996

Thermodynamics of the binding of ligands by macromolecules.

The thermodynamics of the binding of ligands by proteins and other biological macromolecules has been treated by Wyman and others on the basis of the binding polynomial and the binding potential. However, the thermodynamics of the binding of ligands by small molecules and the effects of ligands on the apparent equilibrium constants of biochemical reactions has been developed on the basis of Legendre transformed Gibbs energies of formation. This article brings these seemingly disparate approaches together by considering simple systems and the binding of oxygen by hemoglobin. When the ligand is H+, examples involving small molecules show that the standard transformed Gibbs energy of formation of a reactant at a specified pH is equal to the negative of the binding potential plus a term related to the standard thermodynamic properties of the elements. The standard transformed Gibbs energies of formation of eight forms of deoxygenated and oxygenated hemoglobin are calculated here for a specific set of conditions. This is the most efficient way to store the information from the seven independent apparent equilibrium constants involved. In a second step, a Legendre transform is used to introduce the concentration of molecular oxygen as a natural variable and calculate the apparent equilibrium constant K" for 2TotD = TotT at specified values of [O2], where TotD is the sum of the concentrations of the dimer and its oxygenated forms and TotT is the sum of the concentrations of the tetramer and its oxygenated forms.

Chemical Phenomena↗
PubMed1996

IUPAC-IUBMB Joint Commission on Biochemical Nomenclature (JCBN). Recommendations for nomenclature and tables in biochemical thermodynamics. Recommendations 1994.

Chemical equations are written in terms of specific ionic and elemental species and balance elements and charge, whereas biochemical equations are written in terms of reactants that often consist of species in equilibrium with each other and do not balance elements that are assumed fixed such as hydrogen at constant pH. Both kinds of reaction equations are needed in biochemistry. When the pH and the free concentrations of certain metal ions are specified, the apparent equilibrium constant K' for a biochemical reaction is written in terms of sums of species and can be used to calculate a standard transformed Gibbs energy of reaction deltarG'o. Transformed thermodynamic properties can be calculated directly from conventional thermodynamic properties of species. Calorimetry or the dependence of K' on temperature can be used to obtain the standard transformed enthalpy of reaction deltarH'o. Standard transformed Gibbs energies of formation deltafG'o(i) and standard transformed enthalpies of formation deltafH'o(i) for reactants (sums of species) can be calculated at various T, pH, pMg, and ionic strength (I) if sufficient information about the chemical reactions involved is available. These quantities can also be calculated from measurement if K' for a number of reactions under the desired conditions. Tables can be used to calculate deltafG'o and deltarH'o for many more reactions.

Biochemical Phenomena↗
PubMed1996

Calculation of biochemical net reactions and pathways by using matrix operations.

Pathways for net biochemical reactions can be calculated by using a computer program that solves systems of linear equations. The coefficients in the linear equations are the stoichiometric numbers in the biochemical equations for the system. The solution of the system of linear equations is a vector of the stoichiometric numbers of the reactions in the pathway for the net reaction; this is referred to as the pathway vector. The pathway vector gives the number of times the various reactions have to occur to produce the desired net reaction. Net reactions may involve unknown numbers of ATP, ADP, and Pi molecules. The numbers of ATP, ADP, and Pi in a desired net reaction can be calculated in a two-step process. In the first step, the pathway is calculated by solving the system of linear equations for an abbreviated stoichiometric number matrix without ATP, ADP, Pi, NADred, and NADox. In the second step, the stoichiometric numbers in the desired net reaction, which includes ATP, ADP, Pi, NADred, and NADox, are obtained by multiplying the full stoichiometric number matrix by the calculated pathway vector.

Adenosine Diphosphate↗
PubMed1994

Biochemical thermodynamics.

Biochemists need two types of reaction equations, chemical equations in terms of species and biochemical equations in terms of reactants at specified pH and concentrations of free metal ions that are bound by reactant species. Both types of reaction equations have corresponding equilibrium constants, K for chemical reactions and K' for biochemical reactions. When the pH is specified you enter a whole new world of thermodynamics. There are new thermodynamic properties, new names (transformed thermodynamic properties), and new values, which are quite different, especially for the standard transformed Gibbs energy. This raises nomenclature problems because it is important to be able to distinguish between chemical equations and biochemical equations at a glance. It is also important to distinguish between the standard thermodynamic properties calculated from K and its temperature coefficient and the standard transformed thermodynamic properties calculated from K' and its temperature coefficient.

Biochemistry↗
PubMed1994

Thermodynamics of the nitrogenase reactions.

The thermodynamics of the nitrogenase reactions are discussed in terms of chemical equations and biochemical equations. Chemical equations balance all elements and electric charge. Biochemical equations represent changes at specified pH and specified free concentrations of metal ions that are bound by reactants, but they do not balance hydrogen or metal ions that have specified free concentrations. At a specified pH, it takes three separate biochemical equations to represent the changes catalyzed by nitrogenase. [formula; see text] The first two equations are required because the nitrogenase and hydrogenase activities of the enzyme have not been separated. The hydrolysis of ATP is necessary, but it is not coupled stoichiometrically to the first two equations. The function of the hydrolysis of ATP by nitrogenase may be to provide the 10 H+ required per mol of N2 consumed. However, reactions cannot generally be coupled stoichiometrically through H+ because H+ is potentially available by dissociation of protein, buffer, and H2O. The standard Gibbs energies of formation of the reactant species are calculated for 25 degrees C, 1 bar, and ionic strengths of 0 and 0.25 M. The standard transformed Gibbs energies of formation of the reactants are calculated at 25 degrees C, 1 bar, pH 7, and ionic strengths of 0 and 0.25 M.

Hydrogen-Ion Concentration↗
PubMed1993

Thermodynamics of reactions of nicotinamide adenine dinucleotide and nicotinamide adenine dinucleotide phosphate.

The thermodynamics of six reactions of nicotinamide adenine dinucleotide and nicotinamide adenine dinucleotide phosphate is discussed both from the viewpoint of the chemical equations and the biochemical equations for these reactions. Tables of the standard enthalpies of formation and standard Gibbs energies of formation of species are presented and are used to calculate standard enthalpies of reaction, standard Gibbs energies of reaction, and equilibrium constants K of chemical reactions at 25 degrees C, 1 bar, and ionic strengths of 0, 0.1, and 0.25 M. These tables are used to calculate standard transformed enthalpies of formation and standard transformed Gibbs energies of formation of reactants, standard transformed enthalpies of reaction, standard transformed Gibbs energies of reaction, and apparent equilibrium constants K' of biochemical reactions at 25 degrees C, 1 bar, pH 7, and ionic strengths of 0, 0.1, and 0.25 M. Since these reactions do not involve pK's of acid groups in the vicinity of pH 7, these reactions produce exactly 0, 1, or 2 mol of H+ per mole of reaction. The calculations are compared with experimental values.

Alanine Dehydrogenase↗
PubMed1993

Calorimetric determination of the standard transformed enthalpy of a biochemical reaction at specified pH and pMg.

In a biochemical reaction there is generally a change in the binding of hydrogen ions and metal ions. Therefore, calorimetric measurements of enthalpies of reaction have to be adjusted for the enthalpies of reaction of the hydrogen ions and metal ions produced or consumed with the buffer. It can be shown that this yields the standard transformed enthalpy of reaction that determines the change in the apparent equilibrium constant K' (written in terms of sums of concentrations of species of a reactant) with temperature at the chosen pH and concentration of free metal ion. The derivations are based on the assumption that the changes in pH and free metal ion concentrations in the calorimetric experiment are small. This assumption is experimentally realized if a solution is well buffered for hydrogen and metal ions. The derived equations are discussed in terms of the implications they have for the performance and interpretation of calorimetric measurements.

Calorimetry↗
PubMed1993

The pH dependence of the apparent equilibrium constant, K', of a biochemical reaction.

Biochemical reactions can be discussed in terms of chemical equations or biochemical equations. Both are right and both are needed. Therefore, it is important to be able to distinguish between them at a glance. Sometimes the relations between the apparent equilibrium constant 'K" for a biochemical reaction and the equilibrium constant, K, for a reference reaction written as a chemical equation is simple, and sometimes it is complicated. This article will discuss several examples.

Hydrogen-Ion Concentration↗