Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-10T14:35:42.824Z Has data issue: false hasContentIssue false
  • English
  • Français

Between Algorithm and Model: Different Molecular Surface Definitions for the Poisson-Boltzmann Based Electrostatic Characterization of Biomolecules in Solution

Published online by Cambridge University Press:  03 June 2015

Sergio Decherchi ,
Jose Colmenares ,
Chiara Eva Catalano ,
Michela Spagnuolo ,
Emil Alexov  and
Walter Rocchia
Sergio Decherchi*
Affiliation:
Department of Drug Discovery and Development, Istituto Italiano di Tecnologia, via Morego, 30, 16163 Genova, Italy
Jose Colmenares*
Affiliation:
Department of Drug Discovery and Development, Istituto Italiano di Tecnologia, via Morego, 30, 16163 Genova, Italy
Chiara Eva Catalano*
Affiliation:
Institute for Applied Mathematics and Information Technologies, National Research Council of Italy, Genoa, Italy
Michela Spagnuolo*
Affiliation:
Institute for Applied Mathematics and Information Technologies, National Research Council of Italy, Genoa, Italy
Emil Alexov*
Affiliation:
Department of Physics, Clemson University, Clemson, South Carolina, USA
Walter Rocchia*
Affiliation:
Department of Drug Discovery and Development, Istituto Italiano di Tecnologia, via Morego, 30, 16163 Genova, Italy
*
Email:sergio.decherchi@iit.it
Email:jose.colmenares@iit.it
Email:chiara@ge.imati.cnr.it
Email:michela.spagnuolo@ge.imati.cnr.it
Email:ealexov@clemson.edu
Corresponding author.Email:walter.rocchia@iit.it
Get access

Abstract

The definition of a molecular surface which is physically sound and computationally efficient is a very interesting and long standing problem in the implicit solvent continuum modeling of biomolecular systems as well as in the molecular graphics field. In this work, two molecular surfaces are evaluated with respect to their suitability for electrostatic computation as alternatives to the widely used Connolly-Richards surface: the blobby surface, an implicit Gaussian atom centered surface, and the skin surface. As figures of merit, we considered surface differentiability and surface area continuity with respect to atom positions, and the agreement with explicit solvent simulations. Geometric analysis seems to privilege the skin to the blobby surface, and points to an unexpected relationship between the non connectedness of the surface, caused by interstices in the solute volume, and the surface area dependence on atomic centers. In order to assess the ability to reproduce explicit solvent results, specific software tools have been developed to enable the use of the skin surface in Poisson-Boltzmann calculations with the DelPhi solver. The results indicate that the skin and Connolly surfaces have a comparable performance from this last point of view.

Keywords

65D1865Z0592-0835Q9278A70Molecular surfaceConnolly surfaceblobby surfaceskin surfacePoisson-Boltzmann
Type
Research Article
Information
Communications in Computational Physics , Volume 13 , Issue 1 , January 2013 , pp. 61 - 89
Copyright
Copyright © Global Science Press Limited 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Fogolari, F., Brigo, A., and Molinari, H.The Poisson-Boltzmann equation for biomolecular electrostatics: A tool for structural biology. J. Mol. Recognit., 15: 377–392, 2002.Google Scholar
[2]Onufriev, A., Bashford, D., and Case, D.A.Effective born radii in the generalized born ap-proximation: The importance of being perfect. J. Comp. Chem., 23(14): 1297–1304, 2002.Google Scholar
[3]Lee, B. and Richards, F.M.The interpretation of protein structures: Estimation of static accessibility. J. Mol. Biol., 55: 379–400, 1971.Google Scholar
[4]Connolly, M.L.Analytical molecular surface calculation. J. Appl. Cryst., 16: 548–558, 1983.CrossRefGoogle Scholar
[5]Sanner, M. F., Olson, A. J., and Spehner, J.C.Reduced surface: An efficient way to compute molecular surfaces. Biopolymers, 38: 305–320, 1996.Google Scholar
[6]Rocchia, W., Sridharan, S., Nicholls, A., Alexov, E., Chiabrera, A., and Honig, B.Rapid grid-based construction of the molecular surface for both molecules and geometric objects: Applications to the finite difference Poisson-Boltzmann method. J. Comp. Chem., 23: 128–137, 2002.Google Scholar
[7]Totrov, M. and Abagyan, R.The contour-buildup algorithm to calculate the analytical molecular surface. J. Struct. Biol., 116: 138–143, 1996.Google Scholar
[8]Masunov, A. and Lazaridis, T.Potentials of mean force between ionizable amino acid side chains in water. J. Am. Chem. Soc., 125: 1722–1730, 2003.Google Scholar
[9]Swanson, J.M.J., Mongan, J., and McCammon, A.Limitations of atom-centered dielectric functions in implicit solvent models. J. Phys. Chem. B, 109: 14769–14772, 2005.Google Scholar
[10]Rocchia, W., Alexov, E., and Honig, B.Extending the applicability of the nonlinear Poisson-Boltzmann equation: Multiple dielectric constants and multivalentions. J. Phys. Chem. B, 105(28): 6507–6514, 2001.Google Scholar
[11]Xu, D. and Zhang, Y.Generating triangulated macromolecular surfaces by euclidean distance transform. PLoS One, 4, 2009.Google Scholar
[12]Can, T., Chen, C., and Wang, Y.F.Efficient molecular surface generation using level-set methods. J. Mol. Graph. Model., 25: 442–454, 2006.CrossRefGoogle ScholarPubMed
[13]Bardhan, J.P., Altman, M.D., Willis, D.J., Lippow, S.M., Tidor, B., and White, J.K.Numerical integration techniques for curved-element discretizations of molecule-solvent interfaces. J. Chem. Phys., 127: 014701, 2007.CrossRefGoogle ScholarPubMed
[14]Bajaj, C., Lee, H., Merkert, R., and Pascucci, V.Nurbs based b-rep models from macromolecules and their properties. In Fourth Symposium on Solid Modeling and Applications, pages 217–228, 1997.CrossRefGoogle Scholar
[15]Liang, J., Edelsbrunner, H., Fu, P., Sudhakar, P.V., and Subramaniam, S.Analytical shape computation of macromolecules: Molecular area and volume through alpha shape. Proteins, 33: 1–17, 1998.Google Scholar
[16]Ryua, J., Park, R., and Kimb, D.S.Molecular surfaces on proteins via beta shapes. Comput. Aided Des., 39: 1042–1057, 2007.Google Scholar
[17]Lu, Q. and Luo, R.A Poisson-Boltzmann dynamics method with nonperiodic boundary condition. J. Chem. Phys., 119: 11035–11047, 2003.CrossRefGoogle Scholar
[18]Vorobjev, Y.N. and Hermans, J.Sims: Computation of a smooth invariant molecular surface. Biophys. J., 73: 722–732, 1997.Google Scholar
[19]Bates, P.W., Wei, G.W., and Zhao, S.Minimal molecular surfaces and their applications. J. Comp. Chem., 29(3): 380–391, 2008.Google Scholar
[20]Lorensen, W.E. and Cline, H.E.Marching cubes: A high resolution 3D surface construction algorithm. Comp. Graph., 21(4): 163–169, 1987.CrossRefGoogle Scholar
[21]Grant, J.A., Pickup, B.T., and Nicholls, A.A smooth permittivity function for Poisson-Boltzmann solvation methods. J. Comp. Chem., 22(6): 608–640, 2001.Google Scholar
[22]Im, W., Beglov, D., and Roux, B.Continuum solvation model: Computation of electrostatic forces from numerical solutions to the Poisson-Boltzmann equation. Comput. Phys. Commun., 111(59): 59–75, 1998.Google Scholar
[23]Edelsbrunner, H.Deformable smooth surface design. Discrete Comput. Geom., 21(1): 87–115, 1999.Google Scholar
[24]Blinn, J.F.A generalization of algebraic surface drawing. ACM T. Graph., 1(3): 235–256, 1982.Google Scholar
[25]Zhang, Y., Xu, G., and Bajaj, C.Quality meshing of implicit solvation models of biomolecular structures. Comput. Aided Geom. Des., 23: 510–530, 2006.CrossRefGoogle ScholarPubMed
[26]Cheng, H.L. and Shi, X.Quality mesh generation for molecular skin surfaces using restricted union of balls. In IEEE Visualization, page 51, 2005.Google Scholar
[27]Kruithof, N.G.H. and Vegter, G.Meshing skin surfaces with certified topology. Comp. Geom-Theor. Appl., 36(3): 166–182, 2007.Google Scholar
[28]Chavent, M., Levy, B., and Maigret, B.Metamol: High quality visualization of molecular skin surface. J. Mol. Graph. Model., 27(2): 209–216, 2008.Google Scholar
[29]Lindow, N., Baum, D., Prohaska, S., and Hege, H.C.Accelerated visualization of dynamic molecular surfaces. In Eurographics/IEEE-VGTC Symposium on Visualization, volume 29, pages 943–951, 2010.Google Scholar
[30]Holst, M. and Saied, F.Multigrid solution of the Poisson-Boltzmann equation. J. Comp. Chem., 14: 105–113, 1993.Google Scholar
[31]D’Agostino, D., Decherchi, S., Galizia, A., Colmenares, J., Quarati, A., Rocchia, W., and Clematis, A.Cuda accelerated blobby molecular surface generation. In Accepted at PPAM, 2011.Google Scholar
[32]Bashford, D.An object-oriented programming suite for electrostatic effects in biological molecules, an experience report on the mead project. In Scientific Computing in Object-Oriented Parallel Environments, Lecture Notes in Computer Science, volume 1343, pages 233–240, 1997.Google Scholar
[33] C.L. Bajaj, Pascucci, V., Shamir, A., Holt, R.J., and Netravali, A.N.Dynamic maintenance and visualization of molecular surfaces. Discrete Appl. Math., 127(1), 2003.Google Scholar
[34]Rashin, A.A., Iofin, M., and Honig, B.Internal cavities and buried waters in globular proteins. Biochemistry, 25(12): 3619–3625, 1986.Google Scholar
[35]Cheng, H.L., Dey, T.K., Edelsbrunner, H., and Sullivan, J.Dynamic skin triangulation. Discrete Comput. Geom., 25: 525–568, 2001.Google Scholar
[36]Rycroft, C.H.Voro++: A three-dimensional voronoi cell library in c++. Chaos, 19(4): 041111, 2009.Google Scholar
[37]Eberly, D. Distance from point to a general quadratic curve or a general quadric surface. Geometric Tools, http://www.geometrictools.com/.Google Scholar
[38]Kazhdan, M., Bolitho, M., and Hoppe, H.Poisson surface reconstruction. In Eurographics Symposium on Geometry Processing, Polthier, K. and Sheffer, A. (Eds.), pages 61–70, 2006.Google Scholar
[39]Desbrun, M., Meyer, M., Schroder, P., and Barr, A.H.Discrete differential-geometry operators for triangulated 2-manifolds. 2002.Google Scholar
[40]Dey, T.K. and Sun, J.An adaptive MLS surface for reconstruction with guarantees, In Eurographics Symposium on Geometry Processing, Desbrun, M., Pottmann, H. (Eds.), 2005.Google Scholar
[41]Attene, M. and Falcidieno, B.ReMESH: An interactive environment to edit and repair triangle meshes, In IEEE International Conference on Shape Modeling and Applications 2006, page 41, 2006.CrossRefGoogle Scholar
[42]Cignoni, P., Rocchini, C., and Scopigno, R.Metro: Measuring error on simplified surfaces. Comput. Graph. Forum, 17(2): 167–174, 1998.CrossRefGoogle Scholar
[43]Pietrucci, F., Broglia, R.A., Bonomi, M., Branduardi, D., Bussi, G., Camilloni, C., Provasi, D., Raiteri, P., Donadio, D., Marinelli, F., and Parrinello, M.Plumed: A portable plugin for free energy calculations with molecular dynamics. Comput. Phys. Commun., 180(1961), 2009.Google Scholar
[44]Pettitt, B.M. and Rossky, P.J.Alkali halides in water: Ion-solvent correlations and ionion potentials of mean force at infinite dilution. J. Chem. Phys., 84(5836), 1986.Google Scholar
[45]Lennerz, C. and Schömer, E.Efficient distance computation for quadratic curves and surfaces. In Proceedings of the Geometric Modeling and Processing – Theory and Applications (GMP’02), IEEE Computer Society, pages 60–72, 2002.Google Scholar