Contents

1. Introduction

2. Sources of Experimental Data

3. Calculation of Standard Thermodynamic Properties of Species from Apparent Equilibrium Constants and Heats of Biochemical Reactions

4. Calculation of Standard Transformed Thermodynamic Properties of Reactants and Reactions at Specified pH

5. Further Transformed Thermodynamic Properties

6. Maxwell Relations

7. Use of Mathematica^®

8. Statistical Mechanics of Systems of Biochemical Reactions

9. Names of Enzymes

10. Acknowledgement

1. Introduction

The objective of this site is to provide information on recent developments in the thermodynamics of biochemical reactions and to provide references to journals, books, and the web. The following four articles in 1992 introduced a new way of treating the thermodynamics of biochemical reactions:

R.A. Alberty, Equilibrium Calculations on Systems of Biochemical Reactions, Biophys. Chem., 42, 117-131 (1992).

R.A. Alberty, Calculation of Transformed Thermodynamic Properties of Biochemical Reactants at Specified pH and pMg, Biophys. Chem., 43, 239-254 (1992).

R.A. Alberty, Degrees of Freedom in Biochemical Reaction Systems at Specified pH and pMg, J. Phys. Chem., 96, 9614-9621 (1992).

R.A. Alberty and R.N. Goldberg, Calculation of Thermodynamic Formation Properties for the ATP Series at Specified pH and pMg, Biochemistry, 31, 10610-10615 (1992).

These articles made the point that when the equilibrium of a biochemical reaction is affected by the pH, the Gibbs energy G does not provide the criterion for spontaneous change and equilibrium. The Gibbs energy does provide the criterion when a reaction is described in terms of species at a specified temperature and pressure, but this is not convenient in studying biochemical reactions. Biochemical reactants like ATP consist of species that are in equilibrium with each other at a specified temperature, pressure and pH. In thermodynamics the pH has to be treated as an independent variable in the same way as T and P. In 1873 Gibbs showed how to treat T and P as independent variables by defining the thermodynamic potential that we now refer to as the Gibbs energy by G = U + PV – TS, where U is the internal energy defined by the first law of thermodynamics and S is the entropy introduced by the second law. This type of definition is referred to as a Legendre transform. The transformed Gibbs energy G’ that does provide the criterion for spontaneous change and equilibrium at constant T, P, and pH is defined by the Legendre transform G’ = G – n_c(H)µ(H⁺), where n_c(H) is the amount of the hydrogen component in the system and µ(H⁺) is the chemical potential of hydrogen ions at the specified pH, temperature, and ionic strength. The components of a reaction system are the things that are conserved; in chemical thermodynamics the components are usually taken to be the atoms of elements, but in biochemical thermodynamics it is often convenient to use groups of atoms. The definition of the transformed Gibbs energy automatically leads to a transformed entropy S’ and transformed enthalpy H’. These properties, which are functions of the pH as well as the temperature and ionic strength, can be obtained by experimentally determining the apparent equilibrium constant K’ of a biochemical reaction at a series of temperatures or by measuring K’ at a single temperature and measuring the heat of reaction calorimetrically. Recommendations for using transformed thermodynamic properties were approved by both the International Union of Pure and Applied Chemistry and by the International Union of Biochemistry and Molecular Biology.

R.A. Alberty, A. Cornish-Bowden, Q.H. Gibson, R.N. Goldberg, G.G. Hammes, W. Jencks, K.F. Tipton, R. Veech, H.V. Westerhoff, and E. C. Webb, Recomendations for Nomenclature and Tables in Biochemical Thermodynamics, Pure Appl. Chem., 66, 1641-1666 (1994). Reprinted in Europ. J. Biochem., 240, 1-14 (1996).

These recommendations are available on the web.
http://www.chem.qmul.as.uk/iubmb/thermod/

An early review of these concepts is available in:

R.A. Alberty, Biochemical Thermodynamics (a review), Biochem. Biophys. Acta, 1207, 1-11 (1994).

An introduction to thermodynamics for undergraduates, including the thermodynamics of biochemical reactions, is available in

R.J. Silbey and R.A. Alberty, Physical Chemistry, Wiley, New York, 2001.

The status of the use of transformed thermodynamic properties in treating biochemical reactions up to 2002 is described in

R.A. Alberty, Thermodynamics of Biochemical Reactions, Wiley, Hoboken, NJ, 2003.

Before going into more detail, it is important to understand what thermodynamics can tell us about a system of biochemical reactions. With the capability to calculate the standard transformed Gibbs energies of formation of all the reactants in a system of biochemical reactions, thermodynamics can tell us the direction in which each reaction will go at specified pH, temperature, ionic strength and concentrations of reactants. Furthermore, it can tell us the equilibrium composition that will be reached by this system of reactions. If steady state concentrations of coenzymes are known, a more global view of a system of reactions can be obtained. For example, glycolysis can be represented with C₆ = 2C₃, where C₆ represents the sum of the species with six carbon atoms and C₃ represents the sum of species with three carbon atoms. The equilibrium concentrations of the C₆ and C₃ pseudoisomer groups can be calculated. These equilibrium concentrations can be used to calculate the concentrations of all the reactants, and even the equilibrium concentrations of all the species, because no information is lost when a Legendre transform is made.

Since enzymes are catalysts, they do not determine whether a given biochemical reaction will go to the right or the left at specified conditions. For a series or cycle of enzyme-catalyzed reactions, the net reaction cannot occur unless this reaction goes to the right at specified conditions. Living things are dependent on the thermodynamics of the reactions that are catalyzed by the enzymes that are present because thermodynamics determines whether the reactions go to the right or the left.

Thermodynamic provides multiple ways to look at a reaction system involving many enzyme-catalyzed reactions. First of all, the system can be considered to be a system of chemical reactions that is described in terms of species; in this case, the Gibbs energy G provides the criterion for spontaneous change and equilibrium. When an initial composition is specified in terms of species, the equilibrium composition can be calculated in terms of species. When this is done, the hydrogen ion concentration is a dependent variable, and its concentration has to be calculated.

Alternatively the pH can be specified and the system can be described in terms of reactants, like ATP, which represents a sum of species. In this case, the transformed Gibbs energy G’ provides the criterion for spontaneous change and equilibrium. When the initial composition is specified in terms of reactants, the equilibrium composition can be calculated in terms of reactants. Some reaction systems produce hydrogen ions and some consume hydrogen ions, but the pH at equilibrium is measured and is associated with the equilibrium composition. A still more global view can be obtained by specifying the steady state concentrations of coenzymes. In this case the further transformed Gibbs energy G’’ provides the criterion for spontaneous change and equilibrium.

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