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

The Voltage-Dependent Anion Channel (VDAC) protein is the primary conduit for the regulated passage of ions and metabolites into and out of mitochondria. Calculating its solvation free energy is crucial for understanding its stability, function, and interactions within the cellular environment. In this paper, we introduce a total solvation free energy, $E$, which is the sum of electrostatic, ideal gas, and excess free energies, along with a non-polar energy to yield a zero of $E$ in the absence of charges. We develop numerical schemes for computing $E$ and update the current mesh generation package to accelerate the generation of tetrahedral meshes and improve the quality of meshes for computing $E$. By integrating these schemes and the updated mesh package with our non-uniform size modified Poisson-Boltzmann ion channel (nuSMPBIC), SMPBIC, and PBIC finite element packages, the PDB2PQR package, and the OPM database, we create the VDAC Solvation Free Energy Calculation (VSFEC) package. Using the VSFEC package, we perform comparison tests on the nuSMPBIC, SMPBIC, and PBIC models by using six VDAC proteins and various ionic solutions containing up to four ionic species, including ATP$^{4-}$ and Ca$^{2+}$. We also conduct tests with different neutral voltages and permittivity constants to explore the varying patterns of $E$. Our test results underscore the importance of considering non-uniform ionic size effects and demonstrate the high performance of the VSFEC package in calculating the solvation free energy of VDAC proteins.