Virtual Cell Model for Osmotic Pressure Calculation of Charged Biomolecules

The osmotic pressure of dilute poly-electrolyte solutions containing charged macro-ions as well as counter-ions can be computed directly from the particle distribution via the well-known cell model. While extensively applied in coarse-grained Monte Carlo (MC) simulations of continuum solvent systems, the cell model neglects the macro-ion shape anisotropy and details of the surface charge distribution. By comparing one-body and two-body coarse-grained Monte Carlo simulations we validate this approximation using a non-spherical macro-ion. Next, we extend the cell model to all-atom molecular dynamics simulations and show that protein concentration-dependent osmotic pressures can be obtained by confining counter-ions in a virtual, spherical subspace defining the protein number density. Finally, we show the possibility of using specific interaction parameters for the protein-ion and ion-ion interactions, enabling studies of protein concentration-dependent ion-specific effects using merely a single protein molecule.