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ionic strength by use of the replacement operator (/.), as illustrated by typing atp/.pH->7/.is->. 1 or atp/.pH->{ 6,7,8}/.is-
>(0..1,.25). In addition the average number of hydrogen atoms in a reactant at specified pH and ionic strength can be
calculated by taking the derivative of AfC'" with respect to pH. For example, the number of hydrogen atoms bound by ATP
at pH 7 and 0.10 M ionic strength is given by
(l/RTLog[ lO])*D[atp,pH]/.pH->7/.is->.l.
In writing chemical equations and biochemical equations it is important to be careful with names of reactants. Chemi-
cal reactions are written in terms of species. In chemical reaction equations, atoms of all elements and electric charges must
balance. Biochemical reaction equations are written in terms of reactants, that is in terms of sums of species, H+ is not
included as a reactant and electric charges are not shown or balanced. In biochemical reaction equations, atoms of all
elements other than hydrogen must balance. The names of the reactants that must be used in making calculations with this
data base are given later.
The program calctrGerx can be used to calculate the standard transformed Gibbs energy of reaction Ar G'" for a
biochemical reaction in the form atp+h2o+de=adp+pi, where de is required for the Mathematica operation Solve. The
desired pHs and ionic strengths can be specified. The program calckprime can be used to calculate the apparent equilibrium
constant K for a reaction at desired pHs and ionic strengths. The program calctrGerx can also be used to calculate Af H'" by
typing in a biochemical reaction in the form atph+h2oh+de=adph+pih.
When oxidation and reduction are involved in an enzyme-catalyzed reaction, the standard apparent reduction poten-
tial for a half reaction can be calculated by typing the half reaction in calcappredpot and specifying the pHs and ionic
strengths.
The mathematical functions for the standard transformed Gibbs energies of formation of biochemical reactants
contain information about the average number of hydrogen atoms bound, as mentioned above. The change in binding of
hydrogen atoms in a biochemical reaction can be calculated by taking the difference between products and reactants, but in
using Mathernatica there is an easier way and that is to take the derivative of Ar G'" with respect to pH:
A, NH = (1/R7ln( lO))(dA, C'" /dpH) (3)
The equilibrium composition for an enzyme-catalyzed reaction or a series of enzyme-catalyzed reactions can be
calculated by using equcalcc or equcalccrx. The first of these programs requires a conservation matrix. The second requires
a stoichiometric matrix. The second program is recommended, especially when water is involved as a reactant, because the
convention that when dilute aqueous solutions are considered, the activity of water is taken to be unity, means that a second
Legendre transform is necessary.
This version of the package provides eleven additional programs. One of the prgrams calcdGHT makes it possible to
take the effect of temperature into account if enthalpy data are available (ref. 6). The uses of these programs are illustrated in
the notebook.
Since the standard thermodynamic properties of adenosine have been determined (ref. 7), new values are given for
the ATP series. These changes do not change the values of apparent equilibrium constants that are calculated between
reactants in this series, but will be useful in investigating the production of adenosine..
The current table can be considerably extended by use of the compilations of Goldberg and Tewari of evaluated
equilibrium data on biochemical reactions (ref. 8). Akers and Goldberg have published "BioEqCalc; A Package for Perform-
ing Equilibrium Calculations in Biohemical Reactions" (ref. 9).
I am indebted to NIH 5-RO1-GM48358 for support of the research that produced these tables and to Robert A.
Goldberg and Ian Brooks for many helpful discussions.
References:
1. Alberty, R. A. Biophys. Chem. 1992 42, 117; 1992 43,239.
2. Alberty, R. A.; Goldberg, R. N. Biochemistry 1992 31, 10610.
3. Alberty, R. A. J. Phys. Chem. 1992 96, 9614.
4. Alberty, R. A. Arch. Biochem. Biophys. 1998 353, 116; 1998 358, 25.
5. Alberty, R. A. J. Phys. Chem. B 2001 105, 7865.
6. Boerio-Goates, J.; Francis, M. R.; Goldberg, R. N.; Ribeiro da Silva, M. A. V.; Ribeiro da Silva, M. D. M. C.; Tewari, Y.
J. Chem. Thermo. 2001 33,929.
7. Goldberg, R. N. J. Phys. Chem. Ref. Data 1999 28, 931 and earlier articles in this series.
8. Akers, D. L.; Goldberg, R. N. Mathematicu J. 2001 8, 1. (URL: http://www.mathematica-journal.com/issue/v8il/)