Journal of Physical Chemistry B, Vol.107, No.19, 4653-4666, 2003
Effects of cooperativity in proton binding on the net charge of proteins in charge ladders
This paper addresses the effects of cooperativity of proton binding on values of net charge and the change in net charge of a protein DeltaZ due to the modification of charged groups. Capillary electrophoresis (CE) and charge ladders-collections of protein derivatives that differ in charge-are used to measure the net charge of lysozyme and values of pK(a), of the N-terminal alpha-amino group of this protein with different numbers of Lys epsilon-amino groups acetylated. Values of pK(a), serve as local thermodynamic reporters of electrostatic potentials and therefore provide a direct measure of cooperativity in proton binding. Measured values are compared with values calculated using a model which combines the Poisson-Boltzmann (PB) equation and atomically detailed models of the distribution of charges on lysozyme with Monte Carlo (MC) sampling of different protonation states of the protein to determine the average extent of protonation of each titratable residue as a function of pH. Calculations with the PB-MC model together with experimental results demonstrate significant cooperativity in proton binding between acetylated. Lys epsilon-amino groups and other titratable groups on lysozyme. Two types of interactions are identified: (i) nonspecific interactions between acetylated Lys epsilon-amino group and many other titratable groups on the protein result in the collective reduction in the magnitude of DeltaZ of up to 0.1 charge units and (ii) specific interactions between a particular acetylated Lys epsilon-amino group and another titratable group on the protein results in the reduction in magnitude of DeltaZ of up to -0.3 charge units. These specific interactions occur between groups separated by less than similar to15 Angstrom. Specific interactions are demonstrated for lysozyme at pH 8.4 by the cooperativity in proton binding between the epsilon-amino and N-terminal alpha-amino groups of Lys(1). The PB-MC model effectively identifies both specific and nonspecific cooperative interactions between titratable groups that can affect values of DeltaZ. The results of the detailed PB-MC model can be expressed by a simple empirical relationship that describes the cooperativity in proton binding between titratable groups using a screened Coulombic potential. This relationship is useful for the quick and efficient identification of specific cooperative interactions between titratable groups. Finally, an analysis of the effects of uncertainty in DeltaZ on the values of net charge and hydrodynamic radius of proteins measured using CE and charge ladders is presented. The percent uncertainty in these parameters are shown to be less than or equal to the percent uncertainty in DeltaZ.