Title: pH dependence of charge multipole moments in proteins,
Abstract: Electrostatic interactions play a fundamental role in the structure and
function of proteins. Due to ionizable amino acid residues present on the
solvent-exposed surfaces of proteins, the protein charge is not constant but
varies with the changes in the environment -- most notably, the pH of the
surrounding solution. We study the effects of pH on the charge of four globular
proteins by expanding their surface charge distributions in terms of
multipoles. The detailed representation of the charges on the proteins is in
this way replaced by the magnitudes and orientations of the multipole moments
of varying order. Focusing on the three lowest-order multipoles -- the total
charge, dipole, and quadrupole moment -- we show that the value of pH
influences not only their magnitudes, but more notably and importantly also the
spatial orientation of their principal axes. Our findings imply important
consequences for the study of protein-protein interactions and the assembly of
both proteinaceous shells and patchy colloids with dissociable charge groups.