VDAC Solvation Free Energy Calculation by a Nonuniform Size Modified Poisson-Boltzmann Ion Channel Model

Voltage-dependent anion channel (VDAC) is the primary conduit for regulated passage of ions and metabolites into and out of a mitochondrion. Calculating the solvation free energy for VDAC is crucial for understanding its stability, function, and interactions within the cellular environment. In this article, numerical schemes for computing the total solvation free energy for VDAC-comprising electrostatic, ideal gas, and excess free energies plus the nonpolar energy-are developed based on a nonuniform size modified Poisson-Boltzmann ion channel (nuSMPBIC) finite element solver along with tetrahedral meshes for VDAC proteins. The current mesh generation package is also updated to improve mesh quality and accelerate mesh generation. A VDAC Solvation Free Energy Calculation (VSFEC) package is then created by integrating these schemes with the updated mesh package, the nuSMPBIC finite element package, the PDB2PQR package, and the OPM database, as well as one uniform SMPBIC finite element package and one Poisson-Boltzmann ion channel (PBIC) finite element package. With the VSFEC package, many numerical experiments are made using six VDAC proteins, eight ionic solutions containing up to four ionic species, including ATP^4- and Ca²⁺, two reference states, different boundary values, and different permittivity constants. The test results underscore the importance of considering nonuniform ionic size effects to explore the varying patterns of the total solvation free energy, and demonstrate the high performance of the VSFEC package for VDAC solvation free energy calculation.