Biochemical reactions species reactants, transformed properties

When the pH is specified, we enter into a whole new world of thermodynamics because there is a complete set of new thermodynamic properties, called transformed properties, new fundamental equations, new Maxwell equations, new Gibbs-Helmholtz equations, and a new Gibbs-Duhem equation. These new equations are similar to those in chemical thermodynamics, which were discussed in the preceding chapter, but they deal with properties of reactants (sums of species) rather than species. The fundamental equations for transformed thermodynamic potentials include additional terms for hydrogen ions, and perhaps metal ions. The transformed thermodynamic properties of reactants in biochemical reactions are connected with the thermodynamic properties of species in chemical reactions by equations given here. 

R. A. Alberty, Calculation of standard formation properties of species from standard transformed formation properties of reactants in biochemical reactions at specified pH, J. Phys. Chem.. 103, 261 265... 

Chapters 3-5 have described the calculation of various transformed thermodynamic properties of biochemical reactants and reactions from standard thermodynamic properties of species, but they have not discussed how these species properties were determined. Of course, some species properties came directly out of the National Bureau of Standard Tables (1) and CODATA Tables (2). One way to calculate standard thermodynamic properties of species not in the tables of chemical thermodynamic properties is to express the apparent equilibrium constant K in terms of the equilibrium constant K of a reference chemical reaction, that is a reference reaction written in terms of species, and binding polynomials of reactants, as described in Chapter 2. In order to do this the piiTs of the reactants in the pH range of interest must be known, and if metal ions are bound, the dissociation constants of the metal ion complexes must also be known. For the hydrolysis of adenosine triphosphate to adenosine diphosphate, the apparent equilibrium constant is given by... 

We have seen that calculating species properties from experimental values of K and A // ° is more complicated than calculating K and Ar ° from species values. Thermodynamic calculations can be made by alternate paths, and so there is more than one way to calculate species properties from experimental properties. This chapter emphasizes the concept of the inverse Legendre transform discussed by Callen (8). Biochemical reaction systems are described by transformed thermodynamic properties, and the inverse transform given in equation 6.2-1 provides the transformation from experimental reactant properties to calculated species properties. In this ehapter we first considered calculations of species properties at 298.15 K from measurements of K and Ar ° at 298.15 K. Then we considered the more difficult problem of calculating Af G°(298.15 K) and Af //°(298.15 K) from Ar G "(313.15 K) and Ar H (313.15 K). The programs developed here make it possible to go from Ar G and Ar H (F.pH,/) to Af G (298.15 K,/=0) and Af H (298.15 K,/=0) in one step. 

The calculation of Af G° and Af H° of species from experimental data on apparent equilibrium constants and transformed enthalpies of reaction is described in R. A. Alberty, Thermodynamics of Biochemical Reactions, Wiley, Hoboken, NJ (2003) and a number of places in the literature. That is not discussed here because this package is oriented toward the derivation of mathematical functions to calculate thermodynamic properties at specified T, pH, and ionic strength. There are two types of biochemical reactants in the database ... 

This chapter has emphasized again the advantage of having A, G ° for an enzyme-catalyzed reaction as a function of temperature, pH, and ionic strength. If magnesium ions or other ions are bound by reactants, the free concentrations of more ions can be included as independent variables. This chapter has also emphasized the value of calorimetric data. More standard transformed enthalpies of reaction need to be measured so that temperature effeets can be calculated for more reactions. The database can also be extended by use of reliable estimation methods based on species properties. This may be especially useful with larger biochemical reactants where reactive sites are nearly independent. 

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