SDPBS web server for calculation of electrostatics of ionic solvated biomolecules. (English) Zbl 1347.92025

Summary: The Poisson-Boltzmann equation (PBE) is one important implicit solvent continuum model for calculating electrostatics of protein in ionic solvent. We recently developed a PBE solver library, called SDPBS, that incorporates the finite element, finite difference, solution decomposition, domain decomposition, and multigrid methods. To make SDPBS more accessible to the scientific community, we present an SDPBS web server in this paper that allows clients to visualize and manipulate the molecular structure of a biomolecule, and to calculate PBE solutions in a remote and user friendly fashion. The web server is available on the website https://lsextrnprod.uwm.edu/electrostatics/.


92C40 Biochemistry, molecular biology
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
68N30 Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)
Full Text: DOI


[1] [1] J. Ahrens, B. Geveci, and C. Law. ParaView: An end user tool for large data visualization. In C. Hansen and C. Johnson, editors, The Visualization Handbook, pages 717-731. Academic Press, 2005.
[2] N. Baker, M. Holst, and F. Wang. Adaptive multilevel finite element solution of the Poisson-Boltzmann equation II. Refinement at solvent-accessible surfaces in biomolecular systems. Journal of Computational Chemistry, 21(15):1343-1352, 2000.
[3] N. A. Baker, D. Sept, S. Joseph, M. Holst, and J. A. McCammon. Electrostatics of nanosystems: Application to microtubules and the ribosome. Proc. Natl. Acad. Sci. USA, 98(18):10037-10041, 2001.
[4] N.A. Baker, D. Sept, M.J. Holst, and J.A.McCammon. The adaptivemultilevel finite element solution of the Poisson-Boltzmann equation on massively parallel computers. IBM Journal of Research and Development, 45(3.4):427-438, 2001.
[5] S. Balay, J. Brown, K. Buschelman, V. Eijkhout,W.D. Gropp, D. Kaushik, M.G. Knepley, L.C. McInnes, B.F. Smith, and H. Zhang. PETSc users manual. Technical Report ANL-95/11 - Revision 3.1, Argonne National Laboratory, 2010.
[6] S. Balay, J. Brown, K. Buschelman, W.D. Gropp, D. Kaushik, M.G. Knepley, L.C. McInnes, B.F. Smith, and H. Zhang. PETSc Web page, 2012. http://www.mcs.anl.gov/petsc.
[7] Donald Bashford and Martin Karplus. pKa’s of ionizable groups in proteins: atomic detail from a continuum electrostatic model. Biochemistry, 29(44):10219-10225, 1990.
[8] C. Bertonati, B. Honig, and E. Alexov. Poisson-Boltzmann calculations of nonspecific salt effects on protein-protein binding free energies. Biophysical Journal, 92(6):1891-1899, 2007.
[9] Kenneth J Breslauer, David P Remeta, Wan-Yin Chou, Robert Ferrante, James Curry, Denise Zaunczkowski, James G Snyder, and Luis A Marky. Enthalpy-entropy compensations in drug-DNA binding studies. Proceedings of the National Academy of Sciences, 84(24):8922-8926, 1987.
[10] D. Chen, Z. Chen, C. Chen, W. Geng, and G. Wei. MIBPB: A software package for electrostatic analysis. Journal of Computational Chemistry, 32(4):756-770, 2011.
[11] L. Chen, M. J. Holst, and J. Xu. The finite element approximation of the nonlinear Poisson-Boltzmann equation. SIAM Journal on Numerical Analysis, 45(6):2298-2320, 2007. · Zbl 1152.65478
[12] I.L. Chern, J.G. Liu, and W.C. Wang. Accurate evaluation of electrostatics for macromolecules in solution. Methods and Applications of Analysis, 10(2):309-328, 2003. · Zbl 1099.92500
[13] M. E. Davis, J. D. Madura, B. A. Luty, and J. A. McCammon. Electrostatics and diffusion of molecules in solution: Simulations with the University of Houston Browian dynamics program. Comp. Phys. Comm., 62:187-197, 1991.
[14] M. E. Davis and J. A. McCammon. Solving the finite difference linearized Poisson-Boltzmann equation: A comparison of relaxation and conjugate gradient methods. J. Comp. Chem., 10:386-391, 1989.
[15] J. E. Dennis, Jr. and R. B. Schnabel. Numerical Methods for Unconstrained Optimization and Nonlinear Equations, volume 16 of Classics in Applied Mathematics. SIAM, Philadelphia, PA, 1996.
[16] T.J. Dolinsky, J.E. Nielsen, J.A. McCammon, and N.A. Baker. PDB2PQR: An automated pipeline for the setup of Poisson- Boltzmann electrostatics calculations. Nucleic Acids Research, 32(suppl 2):W665, 2004.
[17] David Eisenberg and Andrew D McLachlan. Solvation energy in protein folding and binding. Nature, 319:199 - 203, 1986.
[18] Marcia O Fenley, Robert C Harris, B Jayaram, and Alexander H Boschitsch. Revisiting the association of cationic groovebinding drugs to DNA using a Poisson-Boltzmann approach. Biophysical Journal, 99(3):879-886, 2010.
[19] F. Fogolari, A. Brigo, and H. Molinari. The Poisson-Boltzmann equation for biomolecular electrostatics: A tool for structural biology. J. Mol. Recognit., 15(6):377-392, 2002.
[20] C. García-García and D.E. Draper. Electrostatic interactions in a peptide-RNA complex. J. Mol. Biol., 331(1):75-88, 2003.
[21] Weihua Geng and Robert Krasny. A treecode-accelerated boundary integral Poisson-Boltzmann solver for electrostatics of solvated biomolecules. J. Comput. Phys., 247:62-78, 2013. · Zbl 1349.78084
[22] Weihua Geng, Sining Yu, and Guowei Wei. Treatment of charge singularities in implicit solvent models. The Journal of Chemical Physics, 127(11):114106, 2007.
[23] M.K. Gilson, A. Rashin, R. Fine, and B. Honig. On the calculation of electrostatic interactions in proteins. Journal ofMolecular Biology, 184(3):503-516, 1985.
[24] M. Holst, N. Baker, and F.Wang. Adaptive multilevel finite element solution of the Poisson-Boltzmann equation I: Algorithms and examples. J. Comput. Chem., 21:1319-1342, 2000.
[25] M. Holst, J. A. McCammon, Z. Yu, Y. Zhou, and Y. Zhu. Adaptive finite element modeling techniques for the Poisson-Boltzmann equation. Communications in Computational Physics, 11(1):179-214, 2012. · Zbl 1373.82077
[26] B. Honig and A. Nicholls. Classical electrostatics in biology and chemistry. Science, 268:1144-1149, May 1995.
[27] W. Humphrey, A. Dalke, and K. Schulten. VMD: Visual molecular dynamics. Journal of Molecular Graphics, 14(1):33-38, 1996.
[28] R.M. Jackson and M.J.E. Sternberg. A continuummodel for protein-protein interactions: Application to the docking problem. Journal of Molecular Biology, 250(2):258-275, 1995.
[29] Y. Jiang, J. Ying, and D. Xie. A Poisson-Boltzmann equation test model for protein in spherical solute region and its applications. Molecular Based Mathematical Biology, 2:86-97, 2014. Open Access. · Zbl 1347.92006
[30] Sunhwan Jo, Miklos Vargyas, Judit Vasko-Szedlar, Benoît Roux, and Wonpil Im. PBEQ-solver for online visualization of electrostatic potential of biomolecules. Nucleic Acids Research, 36(suppl 2):W270-W275, 2008.
[31] John G Kirkwood and Jacques C Poirier. The statistical mechanical basis of the Debye-hüekel theory of strong electrolytes. The Journal of Physical Chemistry, 58(8):591-596, 1954.
[32] Isaac Klapper, Ray Hagstrom, Richard Fine, Kim Sharp, and Barry Honig. Focusing of electric fields in the active site of cu-zn superoxide dismutase: Effects of ionic strength and amino-acid modification. Proteins: Structure, Function, and Bioinformatics, 1(1):47-59, 1986.
[33] Lev Davidovich Landau and EM Lifshitz. Statistical physics, part I. Course of Theoretical Physics, 5:468, 1980.
[34] J. 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(2):286-301, 2015. · Zbl 1343.92161
[35] J. Li and D. Xie. A new linear Poisson-Boltzmann equation and finite element solver by solution decomposition approach. Communications in Mathematical Sciences, 13(2):315-325, 2015. International Press. · Zbl 1327.65124
[36] Tiantian Liu, Minxin Chen, and Benzhuo Lu. Parameterization for molecular gaussian surface and a comparison study of surface mesh generation. Journal of molecular modeling, 21(5):1-14, 2015. · Zbl 1393.65027
[37] A. Logg, K.-A. Mardal, and G. N. Wells, editors. Automated Solution of Differential Equations by the Finite Element Method, volume 84 of Lecture Notes in Computational Science and Engineering. Springer Verlag, 2012. · Zbl 1247.65105
[38] B. Lu, Y. Zhou, M.J. Holst, and J.A. McCammon. Recent progress in numerical methods for the Poisson-Boltzmann equation in biophysical applications. Commun. Comput. Phys., 3(5):973-1009, 2008. · Zbl 1186.92005
[39] Benzhuo Lu, Xiaolin Cheng, and J Andrew McCammon. “New-version-fast-multipole-method” accelerated electrostatic calculations in biomolecular systems. Journal of Computational Physics, 226(2):1348-1366, 2007. · Zbl 1121.92007
[40] Ray Luo, Laurent David, and Michael K Gilson. Accelerated Poisson-Boltzmann calculations for static and dynamic systems. Journal of Computational Chemistry, 23(13):1244-1253, 2002.
[41] Gerald S Manning. The molecular theory of polyelectrolyte solutions with applications to the electrostatic properties of polynucleotides. Quarterly Reviews of Biophysics, 11(02):179-246, 1978.
[42] Vinod K Misra, Kim A Sharp, Richard A Friedman, and Barry Honig. Salt effects on ligand-DNA binding: Minor groove binding antibiotics. Journal of Molecular Biology, 238(2):245-263, 1994.
[43] Jens Erik Nielsen and J Andrew McCammon. Calculating pKa values in enzymeactive sites. Protein Science, 12(9):1894-1901, 2003.
[44] J. Nocedal and S. Wright. Numerical Optimization. Springer Series in Operations Research and Financial Engineering. Springer, New York, second edition, 2006.
[45] Michael J Potter, Michael K Gilson, and J Andrew McCammon. Small molecule pKa prediction with continuum electrostatics calculations. Journal of the American Chemical Society, 116(22):10298-10299, 1994.
[46] Pengyu Ren, Jaehun Chun, Dennis G Thomas, Michael J Schnieders, Marcelo Marucho, Jiajing Zhang, and Nathan A Baker. Biomolecular electrostatics and solvation: A computational perspective. Quarterly Reviews of Biophysics, 45(04):427-491, 2012.
[47] W. Rocchia, E. Alexov, and B. Honig. Extending the applicability of the nonlinear Poisson-Boltzmann equation: Multiple dielectric constants and multivalent ions. J. Phys. Chem. B, 105:6507-6514, 2001.
[48] B. Roux and T. Simonson. Implicit solvent models. Biophys. Chem., 78:1-20, 1999.
[49] W. Rudin. Functional Analysis. McGraw-Hill, New York, 2nd edition, 1991. · Zbl 0867.46001
[50] Subhra Sarkar, ShawnWitham, Jie Zhang,Maxim Zhenirovskyy,Walter Rocchia, and Emil Alexov. Delphi web server: A comprehensive online suite for electrostatic calculations of biological macromolecules and their complexes. Communications in Computational Physics, 13(1):269, 2013. · Zbl 1373.92003
[51] Schrödinger, LLC. The PyMOL molecular graphics system, version 1.3r1. August 2010.
[52] D. Sitkoff, K. A Sharp, and B. Honig. Accurate calculation of hydration free energies using macroscopic solvent models. J. Phys. Chem., 98(7):1978-1988, 1994.
[53] N. Smith, S. Witham, S. Sarkar, J. Zhang, L. Li, C. Li, and E. Alexov. DelPhi web server v2: Incorporating atomic-style geometrical figures into the computational protocol. Bioinformatics, 28(12):1655-1657, 2012.
[54] C. Tanford. Physical Chemistry of Macromolecules. John Wiley & Sons, New York, NY, 1961.
[55] Samir Unni, Yong Huang, Robert M Hanson, Malcolm Tobias, Sriram Krishnan, Wilfred W Li, Jens E Nielsen, and Nathan A Baker. Web servers and services for electrostatics calculations with APBS and PDB2PQR. J. Comput. Chem., 32(7):1488- 1491, 2011.
[56] J.A. Wagoner and N.A. Baker. Assessing implicit models for nonpolar mean solvation forces: the importance of dispersion and volume terms. Proceedings of the National Academy of Sciences, 103(22):8331, 2006.
[57] ChanghaoWang, JunWang, Qin Cai, Zhilin Li, Hong-Kai Zhao, and Ray Luo. Exploring accurate Poisson-Boltzmann methods for biomolecular simulations. Computational and Theoretical Chemistry, 1024:34-44, 2013.
[58] Philip Weetman, Saul Goldman, and CG Gray. Use of the Poisson-Boltzmann equation to estimate the electrostatic free energy barrier for dielectric models of biological ion channels. The Journal of Physical Chemistry B, 101(31):6073-6078, 1997.
[59] D. Xie. New solution decomposition and minimization schemes for Poisson-Boltzmann equation in calculation of biomolecular electrostatics. J. Comput. Phys., 275:294-309, 2014. · Zbl 1349.78077
[60] D. Xie, Y. Jiang, P. Brune, and L.R. Scott. A fast solver for a nonlocal dielectric continuum model. SIAM J. Sci. Comput., 34(2):B107-B126, 2012. · Zbl 1260.78016
[61] D. Xie, Y. Jiang, and L.R. Scott. Eflcient algorithms for a nonlocal dielectric model for protein in ionic solvent. SIAM J. Sci. Comput., 38:B1267-1284, 2013.
[62] D. Xie and S. Zhou. A new minimization protocol for solving nonlinear Poisson-Boltzmann mortar finite element equation. BIT Num. Math., 47:853-871, 2007. · Zbl 1147.65096
[63] Dexuan Xie and Jiao Li. A new analysis of electrostatic free energy minimization and Poisson-Boltzmann equation for protein in ionic solvent. Nonlinear Analysis: Real World Applications, 21:185-196, 2015. · Zbl 1298.78036
[64] Dong Xu and Yang Zhang. Generating triangulated macromolecular surfaces by Euclidean distance transform. PloS ONE, 4(12):e8140, 2009.
[65] J. Ying and D. Xie. A new finite element and finite difference hybrid method for computing electrostatics of ionic solvated biomolecule. Journal of Computational Physics, 298:636-651, 2015. · Zbl 1349.78103
[66] Z. Yu, M.J. Holst, Y. Cheng, and J.A. McCammon. Feature-preserving adaptive mesh generation for molecular shape modeling and simulation. Journal of Molecular Graphics and Modelling, 26(8):1370-1380, 2008.
[67] Y. C. Zhou, M. Holst, and J. A. McCammon. A nonlinear elasticity model of macromolecular conformational change induced by electrostatic forces. Journal of Mathematical Analysis and Applications, 340(1):135-164, 2008. · Zbl 1128.74013
[68] Z. Zhou, P. Payne, M. Vasquez, N. Kuhn, and M. Levitt. Finite-difference solution of the Poisson-Boltzmann equation: Complete elimination of self-energy. Journal of Computational Chemistry, 17(11):1344-1351, 1996.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.