Skip to main content
Log in

Charge density distributions derived from smoothed electrostatic potential functions: design of protein reduced point charge models

  • Published:
Journal of Computer-Aided Molecular Design Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

To generate reduced point charge models of proteins, we developed an original approach to hierarchically locate extrema in charge density distribution functions built from the Poisson equation applied to smoothed molecular electrostatic potential (MEP) functions. A charge fitting program was used to assign charge values to the so-obtained reduced representations. In continuation to a previous work, the Amber99 force field was selected. To easily generate reduced point charge models for protein structures, a library of amino acid templates was designed. Applications to four small peptides, a set of 53 protein structures, and four KcsA ion channel models, are presented. Electrostatic potential and solvation free energy values generated by the reduced models are compared with the corresponding values obtained using the original set of atomic charges. Results are in closer agreement with the original all-atom electrostatic properties than those obtained with a previous reduced model that was directly built from the smoothed MEP functions [Leherte and Vercauteren in J Chem Theory Comput 5:3279–3298, 2009].

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Abbreviations

AA:

Amino acid

AMBER:

Assisted model building and energy refinement

APBS:

Adaptive Poisson-Boltzmann Solver

CD:

Charge density

CG:

Coarse grain(ed)

COM:

Center of mass

DNA:

Desoxyribonucleic acid

ECEPP:

Empirical conformational energy program for peptides

ED:

Electron density

FF:

Force field

GA:

Genetic algorithm

LJ:

Lennard-Jones

MC:

Monte Carlo

MD:

Molecular dynamics

MM:

Molecular mechanics

MEP:

Molecular electrostatic potential

PB:

Poisson-Boltzmann

PDB:

Protein data bank

rmsd:

Root mean square deviation

SA:

Simulated annealing

SLIRP:

Structural library of intrinsic residue propensities

SMMP:

Simple molecular mechanics for proteins

3D:

Three-dimensional

References

  1. Kahraman A, Morris RJ, Laskowski RA, Favia AD, Thornton JM (2010) On the diversity of physicochemical environments experienced by identical ligands in binding pockets of unrelated proteins. Proteins 78:1120–1136

    Article  CAS  Google Scholar 

  2. Dell’Orco D, Xue W-F, Thulin E, Linse S (2005) Electrostatic contributions to the kinetics and thermodynamics of protein assembly. Biophys J 88:1991–2002

    Article  Google Scholar 

  3. Kumar S, Wolfson HJ, Nussinov R (2001) Protein flexibility and electrostatic interactions. IBM J Res Dev 45:499–512

    Article  CAS  Google Scholar 

  4. Strickler SS, Gribenko AV, Gribenko AV, Keiffer TR, Tomlinson J, Reihle T, Loladze VV, Makhatadze GI (2006) Protein stability and surface electrostatics: a charged relationship. Biochemistry 45:2761–2766

    Article  CAS  Google Scholar 

  5. Boiteux C, Kraszewski S, Ramseyer C, Girardet C (2007) Ion conductance vs. pore gating and selectivity in KcsA channel: modeling achievements and perspectives. J Mol Model 13:699–713

    Article  CAS  Google Scholar 

  6. Azia A, Levy Y (2009) Nonnative electrostatic interactions can modulate protein folding: molecular dynamics with a grain of salt. J Mol Biol 393:527–542

    Article  CAS  Google Scholar 

  7. Reif MM, Kräutler V, Kastenholz MA, Daura X, Hünenberger PH (2009) Molecular dynamics simulations of a reversibly folding β-heptapeptide in methanol: influence of the treatment of long-range electrostatic interactions. J Phys Chem B 113:3112–3128

    Article  CAS  Google Scholar 

  8. Camacho CJ, Ma H, Champ PC (2006) Scoring a diverse set of high-quality docked conformations: a metascore based on electrostatic and desolvation interactions. Proteins 63:868–877

    Article  CAS  Google Scholar 

  9. Corrêa F, Salinas RK, Bonvin AMJJ, Farah CS (2008) Deciphering the role of the electrostatic interactions in the α-tropomyosin head-to-tail complex. Proteins 73:902–917

    Article  Google Scholar 

  10. Garden DP, Zhorov BS (2010) Docking flexible ligands in proteins with a solvent exposure- and distance-dependent dielectric function. J Comput Aided Mol Des 24:91–105

    Article  CAS  Google Scholar 

  11. Vizcarra CL, Mayo SL (2005) Electrostatics in computational protein design. Curr Opin Chem Biol 9:622–626

    Article  CAS  Google Scholar 

  12. Boas FE, Harbury PB (2007) Potential energy functions for protein design. Curr Opin Struct Biol 17:199–204

    Article  CAS  Google Scholar 

  13. Lippow SM, Tidor B (2007) Progress in computational protein design. Curr Opin Biotech 18:1–7

    Article  Google Scholar 

  14. Liang S, Li L, Hsu W-L, Pilcher MN, Uversky V, Zhou Y, Dunker AK, Meroueh SO (2009) Exploring the molecular design of protein interaction sites with molecular dynamics simulations and free energy calculations. Biochemistry 48:399–414

    Article  CAS  Google Scholar 

  15. Hildebrandt A, Blossey R, Rjasanow S, Kohlbacher O, Lenhof H-P (2007) Electrostatic potentials of proteins in water: a structured continuum approach. Bioinformatics 23:e99–e103

    Article  CAS  Google Scholar 

  16. Dong F, Olsen B, Baker NA (2008) Computational methods for biomolecular electrostatics. Methods Cell Biol 84:843–870

    Article  CAS  Google Scholar 

  17. Papazyan A, Warshel A (1997) Continuum and dipolar lattice models of solvation. J Phys Chem B 101:11254–11264

    Article  CAS  Google Scholar 

  18. Koehl P, Delarue M (2010) AQUASOL: an efficient solver for the dipolar Poisson-Boltzmann-Langevin equation. J Chem Phys 132:064101–1/064101–16

    Google Scholar 

  19. Voth GA (ed) (2009) Coarse-graining of condensed phase and biomolecular systems. CRC Press, Boca Raton

    Google Scholar 

  20. Hills RD Jr, Lu L, Voth GA (2010) Multiscale coarse-graining of the protein energy landscape. PLoS Comput Biol 6:e1000827/1–e1000827/12

    Article  Google Scholar 

  21. Bereau T, Deserno M (2009) Generic coarse-grained model for protein folding and aggregation. J Chem Phys 130:235106/1–235106/15

    Article  CAS  Google Scholar 

  22. Moritsugu K, Smith JC (2009) REACH: a program for coarse-grained biomolecular simulation. Comput Phys Commun 180:1188–1195

    Article  CAS  Google Scholar 

  23. Marrink SJ, Risselada HJ, Yefimov S, Tieleman DP, de Vries AH (2007) The MARTINI forcefield: coarse-grained model for biomolecular simulations. J Phys Chem B 111:7812–7824

    Article  CAS  Google Scholar 

  24. Basdevant N, Borgis D, Ha-Duong T (2007) Coarse-grained protein-protein potential derived from an all-atom force field. J Phys Chem B 111:9390–9399

    Article  CAS  Google Scholar 

  25. Pizzitutti F, Marchi M, Borgis D (2007) Coarse-graining the accessible surface and the electrostatics of proteins for protein-protein interactions. J Chem Theory Comput 3:1867–1876

    Article  CAS  Google Scholar 

  26. Monticelli L, Kandasamy SK, Periole X, Larson RG, Tieleman DP, Marrink SJ (2008) The MARTINI coarse-grained forcefield: extension to proteins. J Chem Theory Comput 4:819–834

    Article  CAS  Google Scholar 

  27. DeVane R, Shinoda W, Moore PB, Klein ML (2009) Transferable coarse grain nonbonded interaction model for amino acids. J Chem Theory Comput 5:2115–2124

    Article  CAS  Google Scholar 

  28. Liwo A, Czaplewski C, Oldziej S, Rojas AV, Kazmierkiewicz R, Makowski M, Murarka RK, Sheraga HA (2009) In: Voth GA (ed) Coarse-graining of condensed phase and biomolecular systems. CRC Press, Boca Raton

    Google Scholar 

  29. Zacharias M (2003) Protein-protein docking with a reduced protein model accounting for side chain flexibility. Prot Sci 12:1271–1282

    Article  CAS  Google Scholar 

  30. Fujitsuka Y, Takada S, Luthey-Schulten ZA, Wolynes PG (2004) Optimizing physical energy functions for protein folding. Proteins 54:88–103

    Article  CAS  Google Scholar 

  31. Curcó D, Nussinov R, Alemán C (2007) Coarse-grained representation of β-helical protein building blocks. J Phys Chem B 111:10538–10549

    Article  Google Scholar 

  32. Hori N, Chikenji G, Berry RS, Takada S (2009) Folding energy landscape and network dynamics of small globular proteins. Proc Natl Acad Sci USA 106:73–78

    Article  CAS  Google Scholar 

  33. Zhang Z, Lu L, Noid WG, Krishna V, Pfaendtner J, Voth GA (2008) A systematic methodology for defining coarse-grained sites in large biomolecules. Biophys J 95:5073–5083

    Article  CAS  Google Scholar 

  34. Gabdoulline RR, Wade RC (1996) Effective charges for macromolecules in solvent. J Phys Chem 100:3868–3878

    Article  CAS  Google Scholar 

  35. Berardi R, Muccioli L, Orlandi S, Ricci M, Zannoni C (2004) Mimicking electrostatic interactions with a set of effective charges: a genetic algorithm. Chem Phys Lett 389:373–378

    Article  CAS  Google Scholar 

  36. Skepö M, Linse P, Arnebrant T (2006) Coarse-grained modeling of proline rich protein 1 (PRP-1) in bulk solution and adsorbed to a negatively charged surface. J Phys Chem B 110:12141–12148

    Article  Google Scholar 

  37. Cascella M, Neri MA, Carloni P, Dal Peraro M (2008) Topologically based multipolar reconstruction of electrostatic interactions in multiscale simulations of proteins. J Chem Theory Comput 4:1378–1385

    Article  CAS  Google Scholar 

  38. Ha-Duong T (2010) Protein backbone dynamics simulations using coarse-grained bonded potentials and simplified hydrogen bonds. J Chem Theory Comput 6:761–773

    Article  Google Scholar 

  39. Ayton GS, Noid WG, Voth GA (2007) Multiscale modeling of biomolecular systems: in serial and in parallel. Curr Opin Struct Biol 17:192–198

    Article  CAS  Google Scholar 

  40. Yang L-W, Chng C-P (2008) Coarse-grained models reveal functional dynamics–I. Elastic network models–theories, comparisons and perspectives. Bioinf Biol Insights 2:25–45

    CAS  Google Scholar 

  41. Chng C-P, Yang L-W (2008) Coarse-grained models reveal functional dynamics–II. Molecular dynamics simulation at the coarse-grained level–Theories and biological applications. Bioinf Biol Insights 2:171–185

    CAS  Google Scholar 

  42. Clementi C (2008) Coarse-grained models of protein folding: toy models or predictive tools? Curr Opin Struct Biol 18:10–15

    Article  CAS  Google Scholar 

  43. Kamerlin SCL, Vicatos S, Dryga A, Warshel A (2011) Coarse-grained (Multiscale) simulations in studies of biophysical and chemical systems. Annu Rev Phys Chem 62:41–64

    Article  CAS  Google Scholar 

  44. Wu C, Shea J-E (2011) Coarse-grained models for protein aggregation. Curr Opin Struct Biol 21:209–220

    Article  CAS  Google Scholar 

  45. Leherte L, Allen FH (1994) Shape information from critical point analyses of calculated electron density maps: application to DNA-drug systems. J Comput Aided Mol Des 8:257–272

    Article  CAS  Google Scholar 

  46. Becue A (2004) Development of an original genetic algorithm method dedicated to complementarity studies between protein-protein and protein-nucleic acid macromolecular partners. Ph.D. Thesis, University of Namur

  47. Becue A, Meurice N, Leherte L, Vercauteren DP (2004) Evaluation of the protein solvent-accessible surface using reduced representations in terms of critical points of the electron density. J Comput Chem 25:1117–1126

    Article  CAS  Google Scholar 

  48. Becue A, Meurice N, Leherte L, Vercauteren DP (2008) In: Boeyens JCA, Ogilvie JF (eds) Models, mysteries, and magic of molecules. Springer, Dordrecht

    Google Scholar 

  49. Leherte L, Guillot B, Vercauteren DP, Pichon-Pesme V, Jelsch C, Lagoutte A, Lecomte C (2007) In: Matta CF, Boyd RJ (eds) The quantum theory of atoms in molecules—from solid state to dna and drug design. Wiley-VCH, Weinheim

    Google Scholar 

  50. Leherte L (2004) Hierarchical analysis of promolecular full electron-density distributions: description of protein structure fragments. Acta Crystallogr D 60:1254–1265

    Article  Google Scholar 

  51. Leherte L, Vercauteren DP (2009) Coarse point charge models for proteins from smoothed molecular electrostatic potentials. J Chem Theory Comput 5:3279–3298

    Article  CAS  Google Scholar 

  52. Baker NA, Sept D, Joseph S, Holst MJ, McCammon JA (2001) Electrostatics of nanosystems: application to microtubules and the ribosome. Proc Natl Acad Sci USA 98:10037–10041

    Article  CAS  Google Scholar 

  53. APBS—Adaptive Poisson-Boltzmann Solver (APBS) (2011) Software for evaluating the electrostatic properties of nanoscale biomolecular systems. http://www.poissonboltzmann.org/apbs/. Accessed 3 January 2011

  54. Wang J, Cieplak P, Kollman PA (2000) How well does a restrained electrostatic potential (RESP) model perform in calculating conformational energies of organic and biological molecules. J Comput Chem 21:1049–1074

    Article  CAS  Google Scholar 

  55. Berman HM, Westbrook J, Feng Z, Gilliland G, Bhat TN, Weissig H, Shindyalov IN, Bourne PE (2000) The protein data bank. Nucleic Acids Res 28:235–242

    Article  CAS  Google Scholar 

  56. RCSB PDB Protein Data Bank (2009) http://www.rcsb.org/pdb. Accessed 3 January 2011

  57. Tjong H, Zhou H-X (2008) On the dielectric boundary in Poisson-Boltzmann calculations. J Chem Theory Comput 4:507–514

    Article  CAS  Google Scholar 

  58. Hart RK, Pappu RV, Ponder JW (2000) Exploring the similarities between potential smoothing and simulated annealing. J Comput Chem 21:531–552

    Article  CAS  Google Scholar 

  59. Leung Y, Zhang JS, Xu Z-B (2000) Clustering by scale-space filtering. IEEE T Pattern Anal 22:1396–1410

    Article  Google Scholar 

  60. Borodin O, Smith GD (2011) Force Field Fitting Toolkit, The University of Utah. http://www.eng.utah.edu/~gdsmith/fff.html. Accessed 3 January 2011

  61. Dolinsky TJ, Nielsen JE, McCammon JA, Baker NA (2004) PDB2PQR: an automated pipeline for the setup of Poisson-Boltzmann electrostatics calculations. Nucl Acids Res 32:W665–W667

    Article  CAS  Google Scholar 

  62. PDB2PQR, An Automated Pipeline for the Setup, Execution, and Analysis of Poisson-Boltzmann Electrostatics Calculations (2007) SourceForge Project Page. http://pdb2pqr.sourceforge.net/. Accessed 3 January 2011

  63. Eisenmenger F, Hansmann UHE, Hayryan S, Hu C-K (2006) An enhanced version of SMMP-open-source software package for simulation of proteins. Comput Phys Comm 174:422–429

    Article  CAS  Google Scholar 

  64. Simple Molecular Mechanics for Proteins. http://www.smmp05.net/. Accessed 3 January 2011

  65. Nemethy G, Gibson KD, Palmer KA, Yoon CN, Paterlini G, Zagari A, Rumsey S, Scheraga HA (1992) Energy parameters in polypeptides. 10. Improved geometrical parameters and nonbonded interactions for use in the ECEPP/3 algorithm, with application to proline-containing peptides. J Phys Chem 96:6472–6484

    Article  CAS  Google Scholar 

  66. Simms AM, Toofanny RD, Kehl C, Benson NC, Daggett V (2008) Dynameomics: design of a computational lab workflow and scientific data repository for protein simulations. Prot Eng Des Sel 21:369–377

    Article  CAS  Google Scholar 

  67. DYNAMEOMICS (2007) The Daggett Group at the University of Washington. http://www.dynameomics.org/. Accessed 3 January 2011

  68. Heisterberg DJ (1990), Technical report, Ohio Supercomputer Center, Translation from FORTRAN to C and Input/Output by Labanowski J, Ohio Supercomputer Center

  69. CCL quaternion-mol-fit (1999) Computational Chemistry List, ltd. http://www.ccl.net/cca/software/SOURCES/C/quaternion-mol-fit/. Accessed 3 January 2011

  70. Exner TE, Mezey PG (2002) Ab initio-quality electrostatic potentials for proteins: an application of the ADMA approach. J Phys Chem A 106:11791–11800

    Article  CAS  Google Scholar 

  71. Bliznyuk AA, Rendell AP, Allen TW, Chung S-H (2001) The potassium ion channel: comparison of linear scaling semiempirical and molecular mechanics representations of the electrostatic potential. J Phys Chem B 105:12674–12679

    Article  CAS  Google Scholar 

  72. Gascon JA, Leung SSF, Batista ER, Batista VS (2006) A Self-consistent space-domain decomposition method for QM/MM computations of protein electrostatic potentials. J Chem Theory Comput 2:175–186

    Article  CAS  Google Scholar 

  73. Warshel A, Kato M, Pisliakov AV (2007) Polarizable force fields: history, test cases, and prospects. J Chem Theory Comput 3:2034–2045

    Article  CAS  Google Scholar 

  74. Piccinini E, Ceccarelli M, Affinito F, Brunetti R, Jacoboni C (2008) Biased molecular simulations for free-energy mapping: a comparison on the KcsA channel as a test case. J Chem Theory Comput 4:173–183

    Article  CAS  Google Scholar 

  75. Bond PJ, Sansom MSP (2006) Insertion and assembly of membrane proteins via simulation. J Am Chem Soc 128:2697–2704

    Article  CAS  Google Scholar 

  76. Bond PJ, Holyoake J, Ivetac A, Khalid S, Sansom MSP (2007) Coarse-grained molecular dynamics simulations of membrane proteins and peptides. J Struct Biol 157:593–605

    Article  CAS  Google Scholar 

  77. Leherte L, Vercauteren DP (2010) In: Collett CT, Robson CD (eds) Handbook of computational chemistry research. Nova Science Publishers, New York

    Google Scholar 

  78. Maciejczyk M, Spasic A, Liwo A, Scheraga HA (2010) Coarse-grained model of nucleic acid bases. J Comput Chem 31:1644–1655

    CAS  Google Scholar 

Download references

Acknowledgments

The authors thank the referees for very useful comments. They also acknowledge Profs. E. Clementi and M. Sansom for very fruitful discussions, as well as Prof. N. Baker for APBS assistance. The ‘‘Fonds National de la Recherche Scientifique’’ (FNRS-FRFC), the ‘‘Loterie Nationale’’ (convention no. 2.4578.02), and the ‘‘Facultés Universitaires Notre-Dame de la Paix’’ (FUNDP), are gratefully acknowledged for the use of the Interuniversity Scientific Computing Facility (ISCF) Center.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Laurence Leherte.

Electronic supplementary material

Rights and permissions

Reprints and permissions

About this article

Cite this article

Leherte, L., Vercauteren, D.P. Charge density distributions derived from smoothed electrostatic potential functions: design of protein reduced point charge models. J Comput Aided Mol Des 25, 913–930 (2011). https://doi.org/10.1007/s10822-011-9471-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10822-011-9471-8

Keywords

Navigation