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In this paper, a nonuniform size modified Poisson-Boltzmann ion channel (nuSMPBIC) model is presented as a nonlinear system of an electrostatic potential and multiple ionic concentrations. It mixes nonlinear algebraic equations with a Poisson boundary value problem involving Dirichlet-Neumann mixed boundary value conditions and a membrane surface charge density to reflect the effects of ion sizes and membrane charges on electrostatics and ionic concentrations. To overcome the difficulties of strong singularities and exponential nonlinearities, it is split into three submodels with a solution of Model 1 collecting all the singular points and Models 2 and 3 much easier to solve numerically than the original nuSMPBIC model. A damped two-block iterative method is then presented to solve Model 3, along with a novel modified Newton iterative scheme for solving each related nonlinear algebraic system. To this end, an effective nuSMPBIC finite element solver is derived and then implemented as a program package that works for an ion channel protein with a three-dimensional molecular structure and a mixture of multiple ionic species. Numerical results for a voltage-dependent anion channel (VDAC) in a mixture of four ionic species demonstrate a fast convergence rate of the damped two-block iterative method, the high performance of the software package, and the importance of considering nonuniform ion sizes. Moreover, the nuSMPBIC model is validated by the anion selectivity property of VDAC.
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This content will become publicly available on December 26, 2025
VDAC Solvation Free Energy Calculation by a Nonuniform Size Modified Poisson–Boltzmann Ion Channel Model
ABSTRACT 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 ATP4−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.
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- PAR ID:
- 10562164
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Journal of Computational Chemistry
- Volume:
- 46
- Issue:
- 1
- ISSN:
- 0192-8651
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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