A Finite Element Solution of Lateral Periodic Poisson–Boltzmann Model for Membrane Channel Proteins
Abstract
:1. Introduction
2. Results and Discussion
2.1. Validation for the Treatments of Fixed Singular Charge
2.2. Application of Lateral Periodic Boundary Condition
2.2.1. Validation of Lateral Periodic Boundary Conditions
2.2.2. Application to the Channel Protein
2.2.3. Non-Polar Contribution to Solvation Energy
3. Materials and Methods
3.1. Finite Element Method of Poisson–Boltzmann Equation
3.2. Mesh Construction for Membrane Protein System
3.3. Treatments of Fixed Singular Charges
4. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Abbreviations
PB | Poisson–Boltzmann |
FEM | Finite element method |
FDM | Finite difference method |
BEM | Boundary element method |
FEPB | FEM for PB electrostatics calculations of the membrane channel systems with periodical boundary conditions |
TPM | The thickness of the filled membrane in the pore region |
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Singular Charges Treatments | Elements | DOFs | (kcal/mol) | |
---|---|---|---|---|
Average assignment method | 22614 | 3745 | −77.01 | %4.9 |
92595 | 17037 | −80.11 | %1.03 | |
Weighted assignment method | 22614 | 3745 | −77.79 | %3.9 |
92595 | 17037 | −80.21 | %0.90 | |
Direct integral method | 22614 | 3745 | −77.98 | %3.6 |
92595 | 17037 | −80.23 | %0.87 |
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Ji, N.; Liu, T.; Xu, J.; Shen, L.Q.; Lu, B. A Finite Element Solution of Lateral Periodic Poisson–Boltzmann Model for Membrane Channel Proteins. Int. J. Mol. Sci. 2018, 19, 695. https://doi.org/10.3390/ijms19030695
Ji N, Liu T, Xu J, Shen LQ, Lu B. A Finite Element Solution of Lateral Periodic Poisson–Boltzmann Model for Membrane Channel Proteins. International Journal of Molecular Sciences. 2018; 19(3):695. https://doi.org/10.3390/ijms19030695
Chicago/Turabian StyleJi, Nan, Tiantian Liu, Jingjie Xu, Longzhu Q. Shen, and Benzhuo Lu. 2018. "A Finite Element Solution of Lateral Periodic Poisson–Boltzmann Model for Membrane Channel Proteins" International Journal of Molecular Sciences 19, no. 3: 695. https://doi.org/10.3390/ijms19030695