VDAC Solvation Free Energy Calculation by a Nonuniform Size Modified Poisson–Boltzmann Ion Channel Model
Liam Jemison
Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin, USA
Search for more papers by this authorMatthew Stahl
Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin, USA
Search for more papers by this authorRanjan K. Dash
Department of Biomedical Engineering, Medical College of Wisconsin, Milwaukee, Wisconsin, USA
Search for more papers by this authorCorresponding Author
Dexuan Xie
Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin, USA
Correspondence:
Dexuan Xie ([email protected])
Search for more papers by this authorLiam Jemison
Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin, USA
Search for more papers by this authorMatthew Stahl
Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin, USA
Search for more papers by this authorRanjan K. Dash
Department of Biomedical Engineering, Medical College of Wisconsin, Milwaukee, Wisconsin, USA
Search for more papers by this authorCorresponding Author
Dexuan Xie
Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin, USA
Correspondence:
Dexuan Xie ([email protected])
Search for more papers by this authorFunding: This study was supported by supported by the US National Science Foundation through the award number DMS-2153376.
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.
Open Research
Data Availability Statement
The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.
References
- 1M. Colombini, “The VDAC Channel: Molecular Basis for Selectivity,” Biochimica et Biophysica Acta (BBA)-Molecular Cell Research 1863, no. 10 (2016): 2498–2502.
- 2M. Colombini, “VDAC Structure, Selectivity, and Dynamics,” Biochimica et Biophysica Acta (BBA) - Biomembranes 1818, no. 6 (2012): 1457–1465.
- 3J. J. Lemasters and E. Holmuhamedov, “Voltage-Dependent Anion Channel (VDAC) as Mitochondrial Governator–Thinking Outside the Box,” Biochimica et Biophysica Acta (BBA) - Molecular Basis of Disease 1762, no. 2 (2006): 181–190.
- 4T. Hodge and M. Colombini, “Regulation of Metabolite Flux Through Voltage-Gating of VDAC Channels,” Journal of Membrane Biology 157, no. 3 (1997): 271–279.
- 5T. K. Rostovtseva and S. M. Bezrukov, “ATP Transport Through a Single Mitochondrial Channel, VDAC, Studied by Current Fluctuation Analysis,” Biophysical Journal 74, no. 5 (1998): 2365–2373.
- 6T. Rostovtseva and M. Colombini, “VDAC Channels Mediate and Gate the Flow of ATP: Implications for the Regulation of Mitochondrial Function,” Biophysical Journal 72, no. 5 (1997): 1954.
- 7C. P. Baines, R. A. Kaiser, T. Sheiko, W. J. Craigen, and J. D. Molkentin, “Voltage-Dependent Anion Channels are Dispensable for Mitochondrial-Dependent Cell Death,” Nature Cell Biology 9, no. 5 (2007): 550–555.
- 8A. K. Camara, Y. Zhou, E. Tajkhorshid, and W.-M. Kwok, “Mitochondrial VDAC1: A Key Gatekeeper as Potential Therapeutic Target,” Frontiers in Physiology 8, no. 460 (2017): 1–18.
- 9S. Das, C. Steenbergen, and E. Murphy, “Does the Voltage Dependent Anion Channel Modulate Cardiac Ischemia–Reperfusion Injury?,” Biochimica et Biophysica Acta (BBA) - Biomembranes 1818, no. 6 (2012): 1451–1456.
- 10K. S. McCommis and C. P. Baines, “The Role of VDAC in Cell Death: Friend or Foe?,” Biochimica et Biophysica Acta (BBA) - Biomembranes 1818, no. 6 (2012): 1444–1450.
- 11J. G. Pastorino and J. B. Hoek, “Regulation of Hexokinase Binding to VDAC,” Journal of Bioenergetics and Biomembranes 40, no. 3 (2008): 171–182.
- 12T. K. Rostovtseva and S. M. Bezrukov, “VDAC Inhibition by Tubulin and its Physiological Implications,” Biochimica et Biophysica Acta (BBA) - Biomembranes 1818, no. 6 (2012): 1526–1535.
- 13T. K. Rostovtseva, K. L. Sheldon, E. Hassanzadeh, et al., “Tubulin Binding Blocks Mitochondrial Voltage-Dependent Anion Channel and Regulates Respiration,” Proceedings of the National Academy of Sciences 105, no. 48 (2008): 18746–18751.
- 14V. Shoshan-Barmatz, S. De, and A. Meir, “The Mitochondrial Voltage-Dependent Anion Channel 1, Ca2+ Transport, Apoptosis, and Their Regulation,” Frontiers in Oncology 7 (2017): 12.
- 15V. Shoshan-Barmatz and D. Ben-Hail, “VDAC, a Multi-Functional Mitochondrial Protein as a Pharmacological Target,” Mitochondrion 12, no. 1 (2012): 24–34.
- 16V. Shoshan-Barmatz, V. De Pinto, M. Zweckstetter, Z. Raviv, N. Keinan, and N. Arbel, “Vdac, A Multi-Functional Mitochondrial Protein Regulating Cell Life and Death,” Molecular Aspects of Medicine 31, no. 3 (2010): 227–285.
- 17V. Shoshan-Barmatz, A. Israelson, D. Brdiczka, and S. Sheu, “The Voltage-Dependent Anion Channel (VDAC): Function in Intracellular Signalling, Cell Life and Cell Death,” Current Pharmaceutical Design 12, no. 18 (2006): 2249–2270.
- 18M. Bayrhuber, T. Meins, M. Habeck, et al., “Structure of the Human Voltage-Dependent Anion Channel,” Proceedings of the National Academy of Sciences 105, no. 40 (2008): 15370–15375.
- 19S. Hiller, R. G. Garces, T. J. Malia, V. Y. Orekhov, M. Colombini, and G. Wagner, “Solution Structure of the Integral Human Membrane Protein VDAC-1 in Detergent Micelles,” Science 321, no. 5893 (2008): 1206–1210.
- 20R. Ujwal, D. Cascio, J.-P. Colletier, et al., “The Crystal Structure of Mouse VDAC1 at 2.3 Å Resolution Reveals Mechanistic Insights into Metabolite Gating,” Proceedings of the National Academy of Sciences 105, no. 46 (2008): 17742–17747.
- 21K. Zeth and U. Zachariae, “Ten Years of High Resolution Structural Research on the Voltage Dependent Anion Channel (VDAC)—Recent Developments and Future Directions,” Frontiers in Physiology 9 (2018): 108.
- 22B. Honig and A. Nicholls, “Classical Electrostatics in Biology and Chemistry,” Science 268 (1995): 1144–1149.
- 23B. Roux and T. Simonson, “Implicit Solvent Models,” Biophysical Chemistry 78 (1999): 1–20.
- 24F. Fogolari, A. Brigo, and H. Molinari, “The Poisson-Boltzmann Equation for Biomolecular Electrostatics: A Tool for Structural Biology,” Journal of Molecular Recognition: JMR 15, no. 6 (2002): 377–392.
- 25D. Chen, Z. Chen, C. Chen, W. Geng, and G. Wei, “MIBPB: A Software Package for Electrostatic Analysis,” Journal of Computational Chemistry 32, no. 4 (2011): 756–770.
- 26R. Luo, L. David, and M. K. Gilson, “Accelerated Poisson–Boltzmann calculations for Static and Dynamic Systems,” Journal of Computational Chemistry 23, no. 13 (2002): 1244–1253.
- 27D. Xie, “New Solution Decomposition and Minimization Schemes for Poisson-Boltzmann Equation in Calculation of Biomolecular Electrostatics,” Journal of Computational Physics 275 (2014): 294–309.
- 28I. Borukhov, D. Andelman, and H. Orland, “Steric Effects in Electrolytes: A Modified Poisson-Boltzmann Equation,” Physical Review Letters 79, no. 3 (1997): 435–438.
- 29J. Li and D. Xie, “An Effective Minimization Protocol for Solving a Size Modified Poisson-Boltzmann Equation for Biomolecule in Ionic Solvent,” International Journal of Numerical Analysis and Modeling 12, no. 2 (2015): 286–301.
- 30J. Ying and D. Xie, “A Hybrid Solver of Size Modified Poisson-Boltzmann Equation by Domain Decomposition, Finite Element, and Finite Difference,” Applied Mathematical Modelling 58 (2018): 166–180.
- 31D. Xie, “New Finite Element Iterative Methods for Solving a Nonuniform Ionic Size Modified Poisson-Boltzmann Equation,” International Journal of Numerical Analysis and Modeling 14, no. 4-5 (2017): 688–711.
- 32D. Xie, S. H. Audi, and R. K. Dash, “A Size Modified Poisson-Boltzmann Ion Channel Model in a Solvent of Multiple Ionic Species: Application to VDAC,” Journal of Computational Chemistry 41, no. 3 (2020): 218–231.
- 33D. Xie, “An Efficient Finite Element Iterative Method for Solving a Nonuniform Size Modified Poisson-Boltzmann ion Channel Model,” Journal of Computational Physics 470 (2022): 111556.
- 34W. Rocchia, E. Alexov, and B. Honig, “Extending the Applicability of the Nonlinear Poisson-Boltzmann Equation: Multiple Dielectric Constants and Multivalent Ions,” Journal of Physical Chemistry B 105 (2001): 6507–6514.
- 35S. Jo, M. Vargyas, J. Vasko-Szedlar, B. Roux, and W. Im, “PBEQ-Solver for Online Visualization of Electrostatic Potential of Biomolecules,” Nucleic Acids Research 36, no. Suppl 2 (2008): W270–W275.
- 36N. Baker, D. Sept, M. Holst, and J. A. McCammon, “The Adaptive Multilevel Finite Element Solution of the Poisson-Boltzmann Equation on Massively Parallel Computers,” IBM Journal of Research and Development 45 (2001): 427–438.
- 37A. Logg, K.-A. Mardal, and G. N. Wells, Automated Solution of Differential Equations by the Finite Element Method, vol. 84 of Lecture Notes in Computational Science and Engineering, (Berlin, Germany: Springer Verlag, 2012).
10.1007/978-3-642-23099-8 Google Scholar
- 38Z. Chao, S. Gui, B. Lu, and D. Xie, “Efficient Generation of Membrane and Solvent Tetrahedral Meshes for Finite Element Ion Channel Calculation,” International Journal of Numerical Analysis and Modeling 19, no. 6 (2022): 887–906.
- 39T. Liu, S. Bai, B. Tu, M. Chen, and B. Lu, “Membrane-Channel Protein System Mesh Construction for Finite Element Simulations,” Computational and Mathematical Biophysics 1 (2015): 128–139.
- 40T. Liu, M. Chen, Y. Song, H. Li, and B. Lu, “Quality Improvement of Surface Triangular Mesh Using a Modified Laplacian Smoothing Approach Avoiding Intersection,” PLoS One 12, no. 9 (2017): e0184206.
- 41T. Dolinsky, J. Nielsen, J. McCammon, and N. Baker, “PDB2PQR: An Automated Pipeline for the Setup of Poisson–Boltzmann Electrostatics Calculations,” Nucleic Acids Research 32, no. Suppl 2 (2004): W665.
- 42T. Dolinsky, P. Czodrowski, H. Li, et al., “PDB2PQR: Expanding and Upgrading Automated Preparation of Biomolecular Structures for Molecular Simulations,” Nucleic Acids Research 35, no. suppl 2 (2007): W522.
- 43K. Sharp and B. Honig, “Calculating Total Electrostatic Energies with the Nonlinear Poisson-Boltzmann Equation,” Journal of Physical Chemistry 94, no. 19 (1990): 7684–7692.
- 44M. K. Gilson and B. Honig, “Calculation of the Total Electrostatic Energy of a Macromolecular System: Solvation Energies, Binding Energies, and Conformational Analysis,” Proteins: Structure, Function, and Bioinformatics 4, no. 1 (1988): 7–18.
- 45H. Si, “TetGen, A Delaunay-Based Quality Tetrahedral Mesh Generator,” ACM Transactions on Mathematical Software 41, no. 2 (2015): 11.
- 46B. R. Brooks, R. E. Bruccoleri, B. D. Olafson, D. J. States, S. Swaminathan, and M. Karplus, “CHARMM: A Program for Macromolecular Energy, Minimization, and Dynamics Calculations,” Journal of Computational Chemistry 4 (1983): 187–217.
- 47J. Schredelseker, A. Paz, C. J. López, et al., “High Resolution Structure and Double Electron-Electron Resonance of the Zebrafish Voltage-dependent Anion Channel 2 Reveal an Oligomeric Population*,” Journal of Biological Chemistry 289, no. 18 (2014): 12566–12577.
- 48T. Hosaka, M. Okazaki, T. Kimura-Someya, et al., “Crystal Structural Characterization Reveals Novel Oligomeric Interactions of Human Voltage-Dependent Anion Channel 1,” Protein Science 26, no. 9 (2017): 1749–1758.
- 49A. Razeto, P. Gribbon, and C. Loew, “The Dynamic Nature of the VDAC1 Channels in Bilayers as Revealed by Two Crystal Structures of the Human Isoform in Bicelles at 2.7 and 3.3 Angstrom Resolution: Implications for VDAC1 Voltage-Dependent Mechanism and for its Oligomerization,” 2018, https://www.rcsb.org/structure/6G73.
- 50A. Razeto, P. Gribbon, and C. Loew, “The Dynamic Nature of the VDAC1 Channels in Bilayers as Revealed by Two Crystal Structures of the Human Isoform in Bicelles at 2.7 and 3.3 Angstrom Resolution: Implications for VDAC1 Voltage-Dependent Mechanism and for its Oligomerization,” 2018, https://www.rcsb.org/structure/6g6u.
- 51M. Amin and J. Küpper, “Variations in Proteins Dielectric Constants,” ChemistryOpen 9, no. 6 (2020): 691–694.
- 52C. N. Schutz and A. Warshel, “What are the Dielectric “Constants” of Proteins and How to Validate Electrostatic Models?,” Proteins: Structure, Function, and Bioinformatics 44, no. 4 (2001): 400–417.
- 53S. Brenner and L. Scott, The Mathematical Theory of Finite Element Methods, 3rd ed. (New York: Springer-Verlag, 2008).
10.1007/978-0-387-75934-0 Google Scholar
