pH-dependent association of proteins. The test case of monoclonal antibody HyHEL-5 and its antigen hen egg white lysozyme.

We describe a method for determining diffusion-controlled rate constants for protein-protein association that explicitly includes the solution pH. The method combines the transient-complex theory for computing electrostatically enhanced association rates with an approach based on a rigorous thermodynamic cycle and partition functions for energy levels characterizing protonation states of associating proteins and their complexes. To test our method, we determine the pH-dependent kinetics of association of the HyHEL-5 antibody with its antigen hen egg white lysozyme. It was shown experimentally that their association rate constant depends on pH, increasing linearly in the pH range 6-8 and saturating or even exhibiting a flat maximum in the pH range 8-10. The presented methodology leads to a qualitative agreement with the experimental data. Our approach allows one to study diffusion-controlled protein-protein association under different pH conditions by taking into account the ensembles of protonation states rather than just the most probable protonation state of each protein.