Virtual cell model for osmotic pressure calculation of charged biomolecules

The osmotic pressure of dilute electrolyte solutions containing charged macro-ions as well as counterions can be computed directly from the particle distribution via the well-known cell model. Originally derived within the Poisson-Boltzmann mean-field approximation, the cell model considers a single macro-ion centered into a cell, together with counterions needed to neutralize the total cell charge, while it neglects the phenomena due to macro-ion correlations. While extensively applied in coarse-grained Monte Carlo (MC) simulations of continuum solvent systems, the cell model, in its original formulation, neglects the macro-ion shape anisotropy and details of the surface charge distribution. In this paper, by comparing one-body and two-body coarse-grained MC simulations, we first establish an upper limit for the assumption of neglecting correlations between macro-ions, and second, we validate the approximation of 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 counterions 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.