Page 94 - Thermodynamics of Biochemical Reactions

Thernwdyanamics of Biochemical Reactions. Robert A. Alberty
Copyright 0 2003 John Wiley & Sons, Inc.
ISBN 0-471-22851-6

F 5.1 Chemical Equations as Matrix Equations
S 5.2 Biochemical Equations as Matrix Equations
@ 5.3 Coupling of Biochemical Reactions
kg 5.4 Matrix Forms of the Fundamental Equations
for Chemical Reaction Systems
li 5.5 Matrix Forms of the Fundamental Equations
for Biochemical Reaction Systems
? 5.6 Operations of Linear Algebra

When a system involves more than one chemical reaction, it is convenient to
represent the conservation equations and reaction equations by matrices. Chemi-
cal reactions balance atoms of elements and electric charges, and that means that
there is a set of conservation equations. The coefficients in these conservation
equations are related to the stoichiometric numbers in the reaction equations
(Alberty, 1991b). For larger systems of reactions, it is very convenient to use
conservation matrices and stoichiometric number matrices because linear algebra
provides mathematical operations for changing and interconverting matrices.
Conservation matrices and stoichiometric number matrices are related mathemat-
ically and actually contain the same information. But for some purposes it is
better to use conservation matrices, and for other purposes it is better to use
stoichiometric number matrices. Conservation matrices are very helpful in ident-
ifying components and showing how noncomponents are made up of components.
Biochemical reactions balance the atoms of all elements except for hydrogen,
or of metals when they are bound reversibly and their ionic concentrations are
held constant. Thus a system of biochemical reactions can be represented by an
apparent conservation matrix or an apparent stoichiometric number matrix. The
adjective “apparent” is used because hydrogen ions are omitted in the apparent
conservation matrix since they are not conserved. Hydrogen ions are also omitted
in the apparent stoichiometric number matrix since they do not appear in
biochemical reactions. The conservation and stoichiometric number matrices for
a system of biochemical reactions can be derived from the conservation matrix