MULTIPLE-SITE TITRATION CURVES OF PROTEINS - AN ANALYSIS OF EXACT AND APPROXIMATE METHODS FOR THEIR CALCULATION

The exact calculation of a multisite titration curve, given the intrinsic pK(a)s of the sites and the site-site interaction constants, grows exponentially in the number of sites and becomes prohibitive for molecules having more than 15 or 20 sites. A commonly used approximation method, introduced by Tanford and Roxby (Biochemistry 1972, 11, 2192) gives large computational savings and is routinely employed for proteins. This method is shown to be a mean field approximation to the multiple-site problem. It gives significant errors when strongly interacting sites titrate at similar pH values. An alternative method, the reduced-site approximation, is introduced. Both approximations are tested against the exact method on a set of randomly generated hypothetical molecules. The reduced-site approximation is found to have much greater accuracy throughout most of the titration curve. It is recommended that the reduced site approximation be used when computationally feasible.