A size‐modified poisson–boltzmann ion channel model in a solvent of multiple ionic species: Application to voltage‐dependent anion channel

• Published in: Journal of computational chemistry Vol. 41; no. 3; pp. 218 - 230
• Main Authors: Xie, Dexuan, Audi, Said H., Dash, Ranjan K.
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 30.01.2020; Wiley Subscription Services, Inc
• Subjects: Anions; Boundary conditions; Charge density; Electric potential; Electrostatics; finite element method; Free energy; Humans; ion channel modeling; Ion channels; Ions; Ions - chemistry; Mathematical models; Membranes; Models, Molecular; Saline solutions; Selectivity; size‐modified Poisson–Boltzmann equation; Solvation; solvation free energy; Solvents - chemistry; Static Electricity; Surface charge; Thermodynamics; VDAC electrostatics; Voltage; Voltage-Dependent Anion Channels - chemistry; solvation free energy; finite element method; size-modified Poisson-Boltzmann equation; VDAC electrostatics; ion channel modeling
• ISSN: 0192-8651; 1096-987X; 1096-987X
• DOI: 10.1002/jcc.26091

We present a new size‐modified Poisson–Boltzmann ion channel (SMPBIC) model and use it to calculate the electrostatic potential, ionic concentrations, and electrostatic solvation free energy for a voltage‐dependent anion channel (VDAC) on a biological membrane in a solution mixture of multiple ionic species. In particular, the new SMPBIC model adopts a membrane surface charge density and a natural Neumann boundary condition to reflect the charge effect of the membrane on the electrostatics of VDAC. To avoid the singularity difficulties caused by the atomic charges of VDAC, the new SMPBIC model is split into three submodels such that the solution of one of the submodels is obtained analytically and contains all the singularity points of the SMPBIC model. The other two submodels are then solved numerically much more efficiently than the original SMPBIC model. As an application of this SMPBIC submodel partitioning scheme, we derive a new formula for computing the electrostatic solvation free energy. Numerical results for a human VDAC isoform 1 (hVDAC1) in three different salt solutions, each with up to five different ionic species, confirm the significant effects of membrane surface charges on both the electrostatics and ionic concentrations. The results also show that the new SMPBIC model can describe well the anion selectivity property of hVDAC1, and that the new electrostatic solvation free energy formula can significantly improve the accuracy of the currently used formula. © 2019 Wiley Periodicals, Inc. This work presents a new ion channel dielectric continuum model and its application in the calculation of the electrostatics, ionic concentrations, and electrostatic solvation free energy for a voltage‐dependent anion channel (VDAC) on the outer mitochondrial membrane in a solution of multiple ionic species with distinct ion sizes. The images from the article compare the electrostatics using membrane surface charges (B1 and B2) with that not using any membrane surface charge (A1 and A2) to demonstrate the influence of membrane surface charges on the electrostatics of VDAC.