Abstract:
Calculations of electrostatic potential and solvation energy of macromolecules are essential for understanding the mechanism of many biological processes. In the classical implicit solvent Poisson-Boltzmann (PB) model, the macromolecule and water are modeled as two-dielectric media with a sharp border. However, the dielectric property of interior cavities and ion-channels is difficult to model in a two-dielectric setting. In fact, whether there are water molecules or cavity-fluid inside a protein cavity remains to be an experimental challenge. Physically, this uncertainty affects the subsequent solvation free energy calculation. In order to compensate this uncertainty, a novel super-Gaussian dielectric PB model is introduced in this work, which devices an inhomogeneous dielectric distribution to represent the compactness of atoms and characterize empty cavities via a gap dielectric value. Moreover, the minimal molecular surface level set function is adopted so that the dielectric profile remains to be smooth when the protein is transfer from water phase to vacuum. A nice feature of this new model is that as the order of super-Gaussian function approaches the infinity, the dielectric distribution reduces a piecewise constant of the two-dielectric model. Mathematically, a simple effective dielectric constant analysis is introduced in this work to benchmark the dielectric model and select optimal parameter values. Computationally, a pseudo-time alternative direction implicit (ADI) algorithm is utilized for solving the super-Gaussian PB equation, which is found to be unconditionally stable in a smooth dielectric setting. Solvation free energy calculation of a Kirkwood sphere and various proteins is carried out to validate the super-Gaussian model and ADI algorithm. One macromolecule with both cavity-fluids and empty cavities is employed to demonstrate how the cavity uncertainty in protein structure can be bypassed through dielectric modeling in the biomolecular electrostatic analysis.
