Modeling the electrophoresis of lysozyme .2. Inclusion of ion relaxation

In this work, boundary element methods are used to model the electrophoretic mobility of lysozyme over the pH range 2-6. The model treats the protein as a rigid body of arbitrary shape and charge distribution derived from the crystal structure. Extending earlier studies, the present work treats the equilibrium electrostatic potential at the level of the full Poisson-Boltzmann (PB) equation and accounts for ion relaxation. This is achieved by solving simultaneously the Poisson, ion transport, and Navier-Stokes equations by an iterative boundary element procedure. Treating the equilibrium electrostatics at the level of the full rather than the linear PB equation, but leaving relaxation out, does improve agreement between experimental and simulated mobilities. Including ion relaxation improves it even more. The effects of nonlinear electrostatics and ion relaxation are greatest at low pH, where the net charge on lysozyme is greatest. In the absence of relaxation, a linear dependence of mobility and average polyion surface potential, [Lambda(0)](s), is observed, and the mobility is well described by the equation mu approximate to epsilon(0)[Lambda(0)]/6 pi eta where epsilon(0) is the dielectric constant of the solvent, and eta is the solvent viscosity. This breaks down, however, when ion relaxation is included and the mobility is less than predicted by the above equation, Whether or not ion relaxation is included, the mobility is found to be fairly insensitive to the charge distribution within the lysozyme model or the internal dielectric constant.