A Newton-like iterative method implemented in the DelPhi for solving the nonlinear Poisson-Boltzmann equation

Chuan Li; Mark McGowan; Emil Alexov; Shan Zhao; Chuan Li; Mark McGowan; Emil Alexov; Shan Zhao

doi:10.3934/mbe.2020331

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 6: 6259-6277. doi: 10.3934/mbe.2020331

Previous Article Next Article

Research article Special Issues

A Newton-like iterative method implemented in the DelPhi for solving the nonlinear Poisson-Boltzmann equation

1.
Department of Mathematics, West Chester University of Pennsylvania, West Chester, Pennsylvania 19383, USA
2.
Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487, USA
3.
Department of Physics and Astronomy, Clemson University, Clemson, South Carolina 29634, USA

Received: 29 June 2020 Accepted: 06 September 2020 Published: 21 September 2020

DelPhi is a popular scientific program which numerically solves the Poisson-Boltzmann equation (PBE) for electrostatic potentials and energies of biomolecules immersed in water via finite difference method. It is well known for its accuracy, reliability, flexibility, and efficiency. In this work, a new edition of DelPhi that uses a novel Newton-like method to solve the nonlinear PBE, in addition to the already implemented Successive Over Relaxation (SOR) algorithm, is introduced. Our tests on various examples have shown that this new method is superior to the SOR method in terms of stability when solving the nonlinear PBE, being able to converge even for problems involving very strong nonlinearity.
- DelPhi,
- Poisson-Boltzmann equation,
- electrostatics,
- Newton method,
- finite difference technique
Citation: Chuan Li, Mark McGowan, Emil Alexov, Shan Zhao. A Newton-like iterative method implemented in the DelPhi for solving the nonlinear Poisson-Boltzmann equation[J]. Mathematical Biosciences and Engineering, 2020, 17(6): 6259-6277. doi: 10.3934/mbe.2020331

Related Papers:

Abstract

DelPhi is a popular scientific program which numerically solves the Poisson-Boltzmann equation (PBE) for electrostatic potentials and energies of biomolecules immersed in water via finite difference method. It is well known for its accuracy, reliability, flexibility, and efficiency. In this work, a new edition of DelPhi that uses a novel Newton-like method to solve the nonlinear PBE, in addition to the already implemented Successive Over Relaxation (SOR) algorithm, is introduced. Our tests on various examples have shown that this new method is superior to the SOR method in terms of stability when solving the nonlinear PBE, being able to converge even for problems involving very strong nonlinearity.

References

[1]	G. A. Cisneros, M. Karttunen, P. Ren, C. Sagui, Classical electrostatics for biomolecular simulations, Chem. Rev., 114 (2014), 779-814. doi: 10.1021/cr300461d
[2]	B. Honig, A. Nicholls, Classical electrostatics in biology and chemistry, Science, 268 (1995), 1144-1149. doi: 10.1126/science.7761829
[3]	Z. Zhang, S. Witham, E. Alexov, On the role of electrostatics in protein-protein interactions, Phys. Biol., 8 (2011), 035001. doi: 10.1088/1478-3975/8/3/035001
[4]	J. Batra, A. Szabó, T. R. Caulfield, A. S. Soares, M. Sahin-Tóth, E. S. Radisky, Long-range electrostatic complementarity governs substrate recognition by human chymotrypsin C, a key regulator of digestive enzyme activation, J. Biol. Chem. 288 (2013), 9848-9859. doi: 10.1074/jbc.M113.457382
[5]	H. Ikeuchi, Y. M. Ahn, T. Otokawa, B. Watanabe, L. Hegazy, J. Hiratake, et al., A sulfoximine-based inhibitor of human asparagine synthetase kills L-asparaginase-resistant leukemia cells, Bioorg. Med. Chem., 20 (2012), 5915-5927. doi: 10.1016/j.bmc.2012.07.047
[6]	X. Huang, F. Dong, H. X. Zhou, Electrostatic recognition and induced fit in the κ-PVIIA toxin binding to Shaker potassium channel, J. Am. Chem. Soc., 127 (2005), 6836-6849. doi: 10.1021/ja042641q
[7]	E. Alexov, Numerical calculations of the pH of maximal protein stability: The effect of the sequence composition and three-dimensional structure, Eur. J. Biochemi., 271 (2004), 173-185.
[8]	A. Isvoran, C. Craescu, E. Alexov, Electrostatic control of the overall shape of calmodulin: numerical calculations, Eur. Biophy. J., 36 (2007), 225-237. doi: 10.1007/s00249-006-0123-1
[9]	R. C. Mitra, Z. Zhang, E. Alexov, In silico modeling of pH-optimum of protein-protein binding, Proteins: Struct., Funct., Bioinf., 79 (2011), 925-936. doi: 10.1002/prot.22931
[10]	A. V. Onufriev, E. Alexov, Protonation and pK changes in protein-ligand binding, Q. Rev. Biophys., 46 (2013), 181-209. doi: 10.1017/S0033583513000024
[11]	K. Talley, E. Alexov, On the pH-optimum of activity and stability of proteins, Proteins: Struct., Funct., Bioinf., 78 (2010), 2699-2706.
[12]	M. Petukh, T. Kimmet, E. Alexov, BION web server: predicting non-specifically bound surface ions, Bioinformatics, 29 (2013), 805-806. doi: 10.1093/bioinformatics/btt032
[13]	M. Petukh, M. Zhang, E. Alexov, Statistical investigation of surface bound ions and further development of BION server to include p H and salt dependence, J. Comput. Chem., 36 (2015), 2381-2393. doi: 10.1002/jcc.24218
[14]	M. Petukh, M. Zhenirovskyy, C. Li, L. Li, L. Wang, E. Alexov, Predicting nonspecific ion binding using DelPhi, Biophys. J., 102 (2012), 2885-2893. doi: 10.1016/j.bpj.2012.05.013
[15]	E. Alexov, E. L. Mehler, N. Baker, A. M. Baptista, Y. Huang, F. Milletti, et al., Progress in the prediction of pKa values in proteins, Proteins: Struct., Funct., Bioinf., 79 (2011), 3260-3275. doi: 10.1002/prot.23189
[16]	R. E. Georgescu, E. G. Alexov, M. R. Gunner, Combining conformational flexibility and continuum electrostatics for calculating pKas in proteins, Biophys. J., 83 (2002), 1731-1748. doi: 10.1016/S0006-3495(02)73940-4
[17]	M. R. Gunner, N. A. Baker, Continuum electrostatics approaches to calculating pKas and Ems in proteins, Methods Enzymol., 578 (2016), 1-20. doi: 10.1016/bs.mie.2016.05.052
[18]	C. Bertonati, B. Honig, E. Alexov, Poisson-Boltzmann calculations of nonspecific salt effects on protein-protein binding free energies, Biophys. J., 92 (2007), 1891-1899. doi: 10.1529/biophysj.106.092122
[19]	J. H. Bredenberg, C. Russo, M. O. Fenley, Salt-mediated electrostatics in the association of TATA binding proteins to DNA: a combined molecular mechanics/Poisson-Boltzmann study, Biophys. J., 94 (2008), 4634-4645. doi: 10.1529/biophysj.107.125609
[20]	A. Ghosh, C. S. Rapp, R. A. Friesner, Generalized Born model based on a surface integral formulation, J. Phys. Chem. B, 102 (1998), 10983-10990. doi: 10.1021/jp982533o
[21]	P. Grochowski, J. Trylska, Continuum molecular electrostatics, salt effects, and counterion binding-a review of the Poisson-Boltzmann theory and its modifications, Biopolym.: Orig. Res. Biomol., 89 (2008), 93-113.
[22]	N. A. Baker, Poisson-Boltzmann methods for biomolecular electrostatics, Methods Enzymol., 383 (2004), 94-118. doi: 10.1016/S0076-6879(04)83005-2
[23]	L. Xiao, J. Diao, D. A. Greene, J. Wang, R. Luo, A continuum Poisson-Boltzmann model for membrane channel proteins, J. Chem. Theory Comput., 13 (2017), 3398-3412. doi: 10.1021/acs.jctc.7b00382
[24]	C. Li, L. Li, M. Petukh, E Alexov, Progress in developing Poisson-Boltzmann equation solvers, Comput. Math. Biophys., 1 (2013), 42-62. doi: 10.2478/mlbmb-2013-0002
[25]	J. Mongan, C. Simmerling, J. A. McCammon, D. A. Case, A. Onufriev, Generalized Born model with a simple, robust molecular volume correction, J. Chem. Theory Comput., 3 (2007), 156-169. doi: 10.1021/ct600085e
[26]	M. Feig, A. Onufriev, M. S. Lee, W. Im, D. A. Case, C. L. Brooks III, Performance comparison of generalized born and Poisson methods in the calculation of electrostatic solvation energies for protein structures, J. Comput. Chem., 25 (2004), 265-284. doi: 10.1002/jcc.10378
[27]	L. Li, C. Li, S. Sarkar, J. Zhang, S. Witham, Z. Zhang, et al., DelPhi: A comprehensive suite for DelPhi software and associated resources, BMC Biophys., 5 (2012), 9. doi: 10.1186/2046-1682-5-9
[28]	W. Rocchia, S. Sridharan, A. Nicholls, E. Alexov, A. Chiabrera, B. Honig, Rapid grid-based construction of the molecular surface and the use of induced surface charge to calculate reaction field energies: Applications to the molecular systems and geometric objects, J. Comput. Chem., 23 (2002), 128-137. doi: 10.1002/jcc.1161
[29]	W. M. Botello-Smith, X. Liu, Q. Cai, Z. Li, H. Zhao, R. Luo, Numerical Poisson-Boltzmann model for continuum membrane systems, Chemi. Phys. Lett., 555 (2013), 274-281. doi: 10.1016/j.cplett.2012.10.081
[30]	Y. Zhou, S. Zhao, M. Feig, G. W. Wei, High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources, J. Comput. Phys., 213 (2006), 1-30. doi: 10.1016/j.jcp.2005.07.022
[31]	E. Jurrus, D. Engel, K. Star, K. Monson, J. Brandi, L. E. Felberg, et al., Improvements to the APBS biomolecular solvation software suite, Protein Sci., 27 (2018), 112-128. doi: 10.1002/pro.3280
[32]	A. H. Boschitsch, M. O. Fenley, A new outer boundary formulation and energy corrections for the nonlinear Poisson-Boltzmann equation, J. Comput. Chem., 28 (2007), 909-921. doi: 10.1002/jcc.20565
[33]	A. H. Boschitsch, M. O. Fenley, Hybrid boundary element and finite difference method for solving the nonlinear Poisson-Boltzmann equation, J. Comput. Chem., 25 (2004), 935-955. doi: 10.1002/jcc.20000
[34]	C. Li, Z. Jia, A. Chakravorty, S. Pahari, Y. Peng, S. Basu, et al., DelPhi Suite: New Developments and Review of Functionalities, J. Comput. Chem., 40 (2019), 2502-2508. doi: 10.1002/jcc.26006
[35]	I. Klapper, R. Hagstrom, R. Fine, K. Sharp, B. Honig, Focusing of electric fields in the active site of Cu-Zn superoxide dismutase: Effects of ionic strength and amino-acid modification, Proteins: Struct., Funct., Bioinf., 1 (1986), 47-59. doi: 10.1002/prot.340010109
[36]	W. Im, D. Beglov, B. Roux, Continuum solvation model: computation of electrostatic forces from numerical solutions to the Poisson-Boltzmann equation, Comput. Phys. Commun., 111 (1998), 59-75. doi: 10.1016/S0010-4655(98)00016-2
[37]	W. Rocchia, E. Alexov, B. Honig, Extending the applicability of the nonlinear Poisson- Boltzmann equation: multiple dielectric constants and multivalent ions, J. Phys. Chem. B, 105 (2001), 6507-6514. doi: 10.1021/jp010454y
[38]	B. A. Luty, M. E. Davis, J. A. McCammon, Solving the finite-difference non-linear Poisson-Boltzmann equation, J. Comput. Chem., 13 (1992), 1114-1118. doi: 10.1002/jcc.540130911
[39]	M. J. Holst, F. Saied, Numerical solution of the nonlinear Poisson-Boltzmann equation: developing more robust and efficient methods, J. Comput. Chem., 16 (1995), 337-364. doi: 10.1002/jcc.540160308
[40]	Q. Cai, M. J. Hsieh, J. Wang, R. Luo, Performance of nonlinear finite-difference Poisson- Boltzmann solvers, J. Chem. Theory Comput., 6 (2010), 203-211. doi: 10.1021/ct900381r
[41]	A. Shestakov, J. Milovich, A. Noy, Solution of the nonlinear Poisson-Boltzmann equation using pseudo-transient continuation and the finite element method, J. Colloid Interface Sci., 247 (2002), 62-79. doi: 10.1006/jcis.2001.8033
[42]	A. Sayyed-Ahmad, K. Tuncay, P. J. Ortoleva, Efficient solution technique for solving the Poisson-Boltzmann equation, J. Comput. Chem., 25 (2004), 1068-1074. doi: 10.1002/jcc.20039
[43]	W. Geng, S. Zhao, Fully implicit ADI schemes for solving the nonlinear Poisson-Boltzmann equation, Comput. Math. Biophys., 1 (2013), 109-123. doi: 10.2478/mlbmb-2013-0006
[44]	A. Nicholls, B. Honig, A rapid finite difference algorithm, utilizing successive over-relaxation to solve the Poisson-Boltzmann equation, J. Comput. Chem., 12 (1991), 435-445. doi: 10.1002/jcc.540120405

mbe-17-06-331-Supplementary.pdf

Reader Comments

Your name:*

Email:*
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)