Hydrogen ions binding calculations

Since it is possible to calculate the mole fractions of the various species of ATP at a specified pH, the average binding of hydrogen ions NH can be calculated by use of... 

Since JVH and NMg can be calculated for these reactants, ArJVH and Ar/VMg can be calculated as a function of pH and pMg. However, when a computer is available there is an easier way to do this by using equation 1.3-13 for the binding of hydrogen ions and 1.3-14 for the binding of magnesium ions. For example, equation 1.5-1 can be written... 

Calculation of the Binding of Hydrogen Ions by Reactants and the Changes in Binding of Hydrogen Ions in Biochemical Reactions... 

CALCULATION OF THE BINDING OF HYDROGEN IONS BY REACTANTS AND THE CHANGES IN BINDING OF HYDROGEN IONS IN BIOCHEMICAL REACTIONS... 

The change in binding of hydrogen ions in the dissociation of the site-L-tartrate complex can be calculated by taking the derivative of log K with respect to pH (equation 4.7-5). The pH dependence of ArNH is shown in Fig. 7.6. 

The binding capacity for the unoccupied site, which is calculated using equation 7.6-11, is plotted versus pH in Fig. 7.8. The number of hydrogen ions bound by the catalytic site in the fumarase-L -tartrate complex is plotted in Fig. 7.9. This is steeper than the titration curve of a diprotic acid with identical and independent groups. The binding capacity for the site occupied by meso-tartrate is shown in Fig. 7.10. The slope of the binding curve is steeper than for the unoccupied site shown in Fig. 7.6, as expected since the binding is cooperative. 

The subscripts on the partial derivatives have been omitted because they are complicated, as indicated by the fundamental equation. The change in binding of coenzymes in a reaction can be studied at constant concentrations of coenzymes, just as the change in binding of hydrogen ions in a reaction can be studied at constant pH. The further transformed enthalpy H" of the system can be calculated by use of the Gibbs-Helmholtz equation or from G" = II" — TS". 

These tables can be used to calculate ArG ° and ATH ° at pH 7 and ionic strengths of 0, 0.10, and 0.25 M or at ionic strength 0.25 M and pHs of 5, 6, 7, 8, and 9 for any reaction for which all the reactants are in these tables. They can also be used to calculate standard apparent reduction potentials. The species data can be used to calculate average bindings of hydrogen ions by reactants. Mathematica programs for carrying out these calculations are provided. 

Calculations of changes in binding of hydrogen ions in biochemical reactions... 

The binding of hydrogen ions HMg when magnesium ions are present can be calculated using equation 2.1-6, where the derivative is now a partial derivative because the binding is affected by both pH and pMg. 

One of the Maxwell relations in equation 3.4-14 shows that the average binding of hydrogen ions by a reactant can be calculated by taking the partial derivative of the standard transformed Gibbs energy of formation of a reactant with respect to pH. 

This program can be used to calculate standard transformed Gibbs energies of reaction, standard transformed enthalpies of reaction, standard transformed entropies of reaction and the change in the binding of hydrogen ions in a reaction. 

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