Thermodynamics of biochemical reactions

Abstract

This book is about the thermodynamics of enzyme-catalyzed reactions that make up the metabolism of living organisms. It is not an introductory text, but the fundamental principles of thermodynamics are reviewed. The reader does need some background in thermodynamics, such as that provided by a first course in physical chemistry. The book uses a generalized approach to thermodynamics that makes it possible to calculate the effects of changing pH, free concenrations of metal ions that are bound by reactants, and steady-state concentrations of coenzymes. This approach can be extended to other types of work that may be involved in a living organism. The concepts involved in this approach are simple, but the equations become rather complicated. Biochemical reactions are written in terms of reactants like ATP that are made up of sums of species, and they are referred to as biochemical reactions to differentiate them from the underlying chemical reactions that are written in terms of species. The thermodynamics of biochemical reactions is independent of the properties of the enzymes that catalyze them. However, the fact that enzymes may couple reactions that might otherwise occur separately increases the number of constraints that have to be considered in thermodynamics. Biochemical thermodynamics is complicated for several reasons: (1) Bio- chemical reactants consist of sums of species whenever a reactant has a pK within about two units of the pH of interest or binds metal ions reversibly. (2) Species of a biochemical reactant are often ions, and the activity coefficients of ions are functions of ionic strength. (3) Enzyme catalysis may introduce constraints in biochemical reactions in addition to balances of atoms of elements. (4) Metab- olism is sufficiently complicated that it is important to find ways to obtain a more global view. (5) In biochemistry other kinds of work, such as electric work, elongation work, and surface work may be involved. It is remarkable that the same basic reactions are found in all living systems. The most important thing about these reactions is that they provide the means to carry out the oxidation of organic matter in a sequence of steps that store energy that is needed for the synthesis of organic molecules, mechanical work, and other functions required for life. The theme of this book is that Legendre transforms make the application of thermodynamics more convenient for the users. The logic used here is a continu- ation of the process described by Gibbs that introduced the enthalpy H, Helmholtz energy A, and the Gibbs energy G by use of Legendre transforms of the internal energy U.In Chapter 4 a Legendre transform is used to introduce pH and pMg as independent intensive variables. In Chapter 6 the steady-state concentrations of various coenzymes are introduced as independent intensive variables in discussing systems of enzyme-catalyzed reactions. In Chapter 8 a Legendre transform is used to introduce the electric potential of a phase as an independent intensive variable. These uses of Legendre transforms illustrate the comment by Callen (1985)that "The choice of variables in terms of which a given problem is formulated, while a seemingly innocuous step, is often the most crucial step in the solution." Choices of dependent and independent variables are not unique, and so choices can be made to suit the convenience of the experimenter. Gibbs has provided a mathematical structure for thermodynamics that is expand- able in many directions and is rich in interrelationships between measurable properties because thermodynamic properties obey all the rules of calculus. This book on thermodynamics differs from others in its emphasis on the fundamental equations of thermodynamics and the application of these equations to systems of biochemical reactions. The emphasis on fundamental equations leads to new thermodynamic potentials that provide criteria for spontaneous change and equilibrium under the conditions in a living cell. The equilibrium composition of a reaction system involving one or more enzyme-catalyzed reactions usually depends on the pH, and so the Gibbs energy G does not provide the criterion for spontaneous change and equilibrium. It is necessary to use a Legendre transform to define a transformed Gibbs energy G' that provides the criterion for spontaneous change and equilibrium at the specified pH. This process brings in a transformed entropy S' and a transformed enthalpy H', but this new world of thermodynamics is similar to the familiar world of G, S, and H, in spite of the fact that there are significant differences. Since coenzymes, and perhaps other reactants, are in steady states in living cells, it is of interest to use a Legendre transform to define a further transformed Gibbs energy G" that provides the criterion for spontaneous change and equilib- rium at a specified pH and specified concentrations of coenzymes. This process brings in a further transformed entropy S" and a further transformed enthalpy H", but the relations between these properties have the familiar form. Quantitative calculations on systems of biochemical reactions are sufficiently complicated that it is necessary to use a personal computer with a mathematical application. Mathematica'~'"(Wolfram Research, Inc. 100 World Trade Center, Champaign, IL, 61820-7237)is well suited for these purposes and is used in this book to make calculations, construct tables and figures, and solve problems. The last third of the book provides a computer-readable database, programs, and worked-out solutions to computer problems. The database BasicBiochemData2 is available on the Web at http:,'/www.mathsource.com/cgi-bin/msitem?O211-662. Systems of biochemical reactions can be represented by stoichiometric num- ber matrices and conservation matrices, which contain the same information and can be interconverted by use of linear algebra. Both are needed. The advantage of writing computer programs in terms of matrices is that they can then be used with larger systems without change. This field owes a tremendous debt to the experimentalists who have measured apparent equilibrium constants and heats of enzyme-catalyzed reactions and to those who have made previous thermodynamic tables that contain information needed in biochemical thermodynamics. Although I have been involved with the thermodynamics of biochemical reactions since 1950,I did not understand the usefulness of Legendre transforms until 1 had spent the decade of the 1980s working on the thermodynamics of petroleum processing. During this period I learned from Irwin Oppenheim (MIT) and Fred Krambeck (Mobil Research and Development) about Legendre trans- forms, calculations using matrices, and semigrand partition functions. In the 1990s 1 returned to biochemical thermodynamics and profited from many helpful