Page 6 - Thermodynamics of Biochemical Reactions

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V~U Preface

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