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We have developed a rigid-body Brownian dynamics algorithm that allows for simulations of a globular protein suspended in an ionic solution confined by a charged planar boundary, with an explicit treatment of pH-dependent protein protonation equilibria and their couplings to the electrostatic potential of the plane. Electrostatic interactions are described within a framework of the continuum Poisson-Boltzmann model, whereas protein-plane hydrodynamic interactions are evaluated based on analytical expressions for the position- and orientation-dependent near-wall friction tensor of a spheroid. The algorithm was applied to simulate near-surface diffusion of lysozyme in solutions having pH in the range 4-10 and ionic strengths of 10 and 150 mM. As a reference, we performed Brownian dynamics simulations in which the protein is assigned a fixed, most probable protonation state, appropriate for given solution conditions and unaffected by the presence of the charged plane, and Brownian dynamics simulations in which the protein probes possible protonation states with the pH-dependent probability, but these variations are not coupled to the electric field generated by the boundary. We show that electrostatic interactions with the negatively charged plane substantially modify probabilities of different protonation states of lysozyme and shift protonation equilibria of both acidic and basic amino acid side chains toward higher pH values. Consequently, equilibrium energy distributions, equilibrium position-orientation distributions, and functions that characterize rotational dynamics, which for a protein with multiple ionization sites, such as lysozyme, in the presence of a charged obstacle are pH-dependent, are significantly affected by the approach taken to incorporate the solution pH into simulations.

Constant-pH Brownian Dynamics Simulations of a Protein near a Charged Surface