Treatment of the Multiple Ionization State Problem

The electrostatic calculations result in elements of the interaction free energy matrix llG,yll. It is written in the following format by our program and contains all the energies required to solve for the pH-dependent properties of interest. The form and content of the data file is as follows  

The data from these electrostatics calculations may be used in the computation of the electrostatic free energy of the protein in any of its 2 ionization states, using Eq. [10]. Basically, evaluation of the average pH-dependent properties of a protein would require computation of energies of all ionization states 

Tanford and Roxby introduced the approximation that the average influence of site k on site i is proportional to the average charge of site k. The procedure of Tanford and Roxby iterates to a set of self-consistent partial charges on titrating sites at a given pH. The fractional protonation state, 0 is estimated from the Henderson-Hasselbalch equation 

Here 0, is the probability that site i is protonated, q° is the charge of site i in the unprotonated state, and is the interaction free energy between unit charges at sites i and k. 

It is first assumed that the equilibrium between acidic and basic forms of each titratable group is governed by its intrinsic pK. This leads at once to an initial value for 0, of each site based on Eq. [23]. These 0, values are used to calculate new pR, values using Eq. [24], and the new pK, values are put back into Eq. [23]. The process is iterated to convergence in the predicted pK, values. Tanford and Roxby s approximation can be derived from a mean-field approximation. The mean-field approximation often works well, but there are cases in which significant errors arise.  

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