메뉴 건너뛰기




Volumn 230, Issue 13, 2011, Pages 5239-5262

Second-order Poisson-Nernst-Planck solver for ion transport

Author keywords

Dirichlet to Neumann mapping; Gramicidin A; Ion channels; Matched interface and boundary; Poisson Nernst Planck equations

Indexed keywords

COMPUTATION THEORY; CONTINUUM MECHANICS; GEOMETRY; IONS; ITERATIVE METHODS; NONLINEAR EQUATIONS; PROTEINS;

EID: 79955476670     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2011.03.020     Document Type: Article
Times cited : (111)

References (81)
  • 1
    • 66549111828 scopus 로고    scopus 로고
    • Asymptotic expansions of I-V relations via a Poisson-Nernst-Planck system
    • Abaid N., Eisenberg R.S., Liu W.S. Asymptotic expansions of I-V relations via a Poisson-Nernst-Planck system. SIAM J. Appl. Dyn. Syst. 2008, 7(4):1507-1526.
    • (2008) SIAM J. Appl. Dyn. Syst. , vol.7 , Issue.4 , pp. 1507-1526
    • Abaid, N.1    Eisenberg, R.S.2    Liu, W.S.3
  • 2
    • 0035723018 scopus 로고    scopus 로고
    • Electrostatic potential inside ionic solutions confined by dielectrics: a variational approach
    • Allen R., Hansen J.-P., Melchionna S. Electrostatic potential inside ionic solutions confined by dielectrics: a variational approach. Phys. Chem. Chem. Phys. 2001, 3:4177-4186.
    • (2001) Phys. Chem. Chem. Phys. , vol.3 , pp. 4177-4186
    • Allen, R.1    Hansen, J.-P.2    Melchionna, S.3
  • 3
    • 0000024779 scopus 로고
    • The finite element method for elliptic equations with discontinuous coefficients
    • Babuška I. The finite element method for elliptic equations with discontinuous coefficients. Computing 1970, 5:207-213.
    • (1970) Computing , vol.5 , pp. 207-213
    • Babuška, I.1
  • 4
    • 0026930493 scopus 로고
    • Ion flow through narrow membran channels: part I
    • Barcilon V. Ion flow through narrow membran channels: part I. SIAM J. Appl. Math. 1992, 52(5):1391-1404.
    • (1992) SIAM J. Appl. Math. , vol.52 , Issue.5 , pp. 1391-1404
    • Barcilon, V.1
  • 5
    • 0026929304 scopus 로고
    • Ion flow through narrow membrane channels: Part ii
    • Barcilon V., Chen D., Eisenberg R. Ion flow through narrow membrane channels: Part ii. SIAM J. Appl. Math. 1992, 52:1405-1425.
    • (1992) SIAM J. Appl. Math. , vol.52 , pp. 1405-1425
    • Barcilon, V.1    Chen, D.2    Eisenberg, R.3
  • 7
    • 67650932053 scopus 로고    scopus 로고
    • Geometric and potential driving formation and evolution of biomolecular surfaces
    • Bates P.W., Chen Z., Sun Y.H., Wei G.W., Zhao S. Geometric and potential driving formation and evolution of biomolecular surfaces. J. Math. Biol. 2009, 59:193-231.
    • (2009) J. Math. Biol. , vol.59 , pp. 193-231
    • Bates, P.W.1    Chen, Z.2    Sun, Y.H.3    Wei, G.W.4    Zhao, S.5
  • 8
    • 38349095051 scopus 로고    scopus 로고
    • Minimal molecular surfaces and their applications
    • Bates P.W., Wei G.W., Zhao S. Minimal molecular surfaces and their applications. J. Comput. Chem. 2008, 29(3):380-391.
    • (2008) J. Comput. Chem. , vol.29 , Issue.3 , pp. 380-391
    • Bates, P.W.1    Wei, G.W.2    Zhao, S.3
  • 9
    • 42749109091 scopus 로고    scopus 로고
    • Diffuse-charge dynamics in electrochemical systems
    • Bazant M.Z., Thornton K., Ajdari A. Diffuse-charge dynamics in electrochemical systems. Phys. Rev. E 2004, 70:021506.
    • (2004) Phys. Rev. E , vol.70 , pp. 021506
    • Bazant, M.Z.1    Thornton, K.2    Ajdari, A.3
  • 10
    • 42749100087 scopus 로고    scopus 로고
    • Computing induced charges in inhomogeneous dielectric media: application in a Monte Carlo simulation of complex ionic systems
    • Boda D., Gillespie D., Nonner W., Henderson D., Eisenberg B. Computing induced charges in inhomogeneous dielectric media: application in a Monte Carlo simulation of complex ionic systems. Phys. Rev. E, Stat. Nonlinear Soft Matter Phys. 2004, 69:046702.
    • (2004) Phys. Rev. E, Stat. Nonlinear Soft Matter Phys. , vol.69 , pp. 046702
    • Boda, D.1    Gillespie, D.2    Nonner, W.3    Henderson, D.4    Eisenberg, B.5
  • 12
    • 34548717678 scopus 로고    scopus 로고
    • Steric selectivity in Na channels arising from protein polarization and mobile side chains
    • Boda D., Nonner W., Valisko M., Henderson D., Eisenberg B., Gillespie D. Steric selectivity in Na channels arising from protein polarization and mobile side chains. Biophys. J. 2007, 93(6):1960-1980.
    • (2007) Biophys. J. , vol.93 , Issue.6 , pp. 1960-1980
    • Boda, D.1    Nonner, W.2    Valisko, M.3    Henderson, D.4    Eisenberg, B.5    Gillespie, D.6
  • 13
    • 34247260951 scopus 로고    scopus 로고
    • The combined effect of pore radius and protein dielectric coefficient on the selectivity of a calcium channel
    • Boda D., Valisko M., Eisenberg B., Nonner W., Henderson D., Gillespie D. The combined effect of pore radius and protein dielectric coefficient on the selectivity of a calcium channel. Phys. Rev. Lett. 2007, 98:168102.
    • (2007) Phys. Rev. Lett. , vol.98 , pp. 168102
    • Boda, D.1    Valisko, M.2    Eisenberg, B.3    Nonner, W.4    Henderson, D.5    Gillespie, D.6
  • 14
    • 3042835846 scopus 로고    scopus 로고
    • Monte carlo simulation study of a system with a dielectric boundary: application to calcium channel selectivity
    • Boda D., Varga T., Henderson D., Busath D., Nonner W., Gillespie D., Eisenberg B. Monte carlo simulation study of a system with a dielectric boundary: application to calcium channel selectivity. Mol. Simul. 2004, 30:89-96.
    • (2004) Mol. Simul. , vol.30 , pp. 89-96
    • Boda, D.1    Varga, T.2    Henderson, D.3    Busath, D.4    Nonner, W.5    Gillespie, D.6    Eisenberg, B.7
  • 15
    • 21444439361 scopus 로고    scopus 로고
    • A finite element method for interface problems in domains with smooth boundaries and interfaces
    • Bramble J., King J. A finite element method for interface problems in domains with smooth boundaries and interfaces. Adv. Comput. Math. 1996, 6:109-138.
    • (1996) Adv. Comput. Math. , vol.6 , pp. 109-138
    • Bramble, J.1    King, J.2
  • 16
    • 0043239420 scopus 로고    scopus 로고
    • Three-dimensional Poisson-Nernst-Planck theory studies: influence of membrane electrostatics on Gramicidin A channel conductance
    • Cardenas A.E., Coalson R.D., Kurnikova M.G. Three-dimensional Poisson-Nernst-Planck theory studies: influence of membrane electrostatics on Gramicidin A channel conductance. Biophys. J. 2000, 79:80-93.
    • (2000) Biophys. J. , vol.79 , pp. 80-93
    • Cardenas, A.E.1    Coalson, R.D.2    Kurnikova, M.G.3
  • 17
  • 18
    • 45849096468 scopus 로고    scopus 로고
    • Piecewise-polynomial discretization and Krylov-accelerated multigrid for elliptic interface problems
    • Chen T., Strain J. Piecewise-polynomial discretization and Krylov-accelerated multigrid for elliptic interface problems. J. Comput. Phys. 2008, 16:7503-7542.
    • (2008) J. Comput. Phys. , vol.16 , pp. 7503-7542
    • Chen, T.1    Strain, J.2
  • 19
    • 77956414486 scopus 로고    scopus 로고
    • Differential geometry based solvation models I: Eulerian formulation
    • Chen Z., Baker N.A., Wei G.W. Differential geometry based solvation models I: Eulerian formulation. J. Comput. Phys. 2010, 229:8231-8258.
    • (2010) J. Comput. Phys. , vol.229 , pp. 8231-8258
    • Chen, Z.1    Baker, N.A.2    Wei, G.W.3
  • 20
    • 12344297727 scopus 로고    scopus 로고
    • An accurate and efficient empirical approach for calculating the dielectric self-energy and ion-ion pair potential in continuum models of biological ion channels
    • Cheng M.H., Coalson R.D. An accurate and efficient empirical approach for calculating the dielectric self-energy and ion-ion pair potential in continuum models of biological ion channels. J. Phys. Chem. B 2005, 109(1):488-498.
    • (2005) J. Phys. Chem. B , vol.109 , Issue.1 , pp. 488-498
    • Cheng, M.H.1    Coalson, R.D.2
  • 21
    • 78649979016 scopus 로고    scopus 로고
    • Molecular dynamics and Brownian dynamics investigation of ion permeation and anesthetic halothane effects on a proton-gated ion channel
    • Cheng M.H., Coalson R.D., Tang P. Molecular dynamics and Brownian dynamics investigation of ion permeation and anesthetic halothane effects on a proton-gated ion channel. J. Am. Chem. Soc. 2010, 132(46):16442-16449.
    • (2010) J. Am. Chem. Soc. , vol.132 , Issue.46 , pp. 16442-16449
    • Cheng, M.H.1    Coalson, R.D.2    Tang, P.3
  • 22
    • 33846682092 scopus 로고    scopus 로고
    • Accurate evaluation of electrostatics for macromolecules in solution
    • Chern I.L., Liu J.-G., Weng W.-C. Accurate evaluation of electrostatics for macromolecules in solution. Methods Appl. Anal. 2003, 10(2):309-328.
    • (2003) Methods Appl. Anal. , vol.10 , Issue.2 , pp. 309-328
    • Chern, I.L.1    Liu, J.-G.2    Weng, W.-C.3
  • 24
    • 0037064260 scopus 로고    scopus 로고
    • Recent advances in ion channel research
    • Chung S.-H., Kuyucak S. Recent advances in ion channel research. Biochim. Biophys. Acta 2002, 1565:267-286.
    • (2002) Biochim. Biophys. Acta , vol.1565 , pp. 267-286
    • Chung, S.-H.1    Kuyucak, S.2
  • 25
    • 15244344856 scopus 로고    scopus 로고
    • Poisson-Nernst-Planck theory approach to the calculation of current through biological ion channels
    • Coalson R.D., Kurnikova M.G. Poisson-Nernst-Planck theory approach to the calculation of current through biological ion channels. IEEE Trans. Nanobiosci. 2005, 4(1):81-93.
    • (2005) IEEE Trans. Nanobiosci. , vol.4 , Issue.1 , pp. 81-93
    • Coalson, R.D.1    Kurnikova, M.G.2
  • 26
    • 0036788529 scopus 로고    scopus 로고
    • Noncontact dipole effects on channel permeation. vi. 5f- and 6F-Trp gramicidin channel currents
    • Cole C.D., Frost A.S., Thompson N., Cotten M., Cross T.A., Busath D.D. Noncontact dipole effects on channel permeation. vi. 5f- and 6F-Trp gramicidin channel currents. Biophys. J. 2002, 83:1974-1986.
    • (2002) Biophys. J. , vol.83 , pp. 1974-1986
    • Cole, C.D.1    Frost, A.S.2    Thompson, N.3    Cotten, M.4    Cross, T.A.5    Busath, D.D.6
  • 27
    • 34547559704 scopus 로고    scopus 로고
    • PDB2PQR: expanding and upgrading automated preparation of biomolecular structures for molecular simulations
    • Dolinsky T.J., Czodrowski P., Li H., Nielsen J.E., Jensen J.H., Klebe G., Baker N.A. PDB2PQR: expanding and upgrading automated preparation of biomolecular structures for molecular simulations. Nucl. Acids Res. 2007, 35(S2):W522-W525.
    • (2007) Nucl. Acids Res. , vol.35 , Issue.S2
    • Dolinsky, T.J.1    Czodrowski, P.2    Li, H.3    Nielsen, J.E.4    Jensen, J.H.5    Klebe, G.6    Baker, N.A.7
  • 29
    • 77956944534 scopus 로고    scopus 로고
    • Energy variational analysis of ions in water and channels: field theory for primitive models of complex ionic fluids
    • Eisenberg B., Hyon Y., Liu C. Energy variational analysis of ions in water and channels: field theory for primitive models of complex ionic fluids. J. Chem. Phys. 2010, 133(104104).
    • (2010) J. Chem. Phys. , vol.133 , pp. 104104
    • Eisenberg, B.1    Hyon, Y.2    Liu, C.3
  • 30
    • 34548804174 scopus 로고    scopus 로고
    • Poisson-Nernst-Planck systems for ion channels with permanent charges
    • Eisenberg B., Liu W.S. Poisson-Nernst-Planck systems for ion channels with permanent charges. SIAM J. Appl. Dyn. Syst. 2006, 38(6):1932-1966.
    • (2006) SIAM J. Appl. Dyn. Syst. , vol.38 , Issue.6 , pp. 1932-1966
    • Eisenberg, B.1    Liu, W.S.2
  • 31
    • 4243514587 scopus 로고
    • Poisson-Nernst-Planck (PNP) theory of an open ionic channel
    • Eisenberg R., Chen D. Poisson-Nernst-Planck (PNP) theory of an open ionic channel. Biophys. J. 1993, 64:A22.
    • (1993) Biophys. J. , vol.64
    • Eisenberg, R.1    Chen, D.2
  • 32
    • 0029876860 scopus 로고    scopus 로고
    • Computing the field in proteins and channels
    • Eisenberg R.S. Computing the field in proteins and channels. J. Membrane Biol. 1996, 150:1-25.
    • (1996) J. Membrane Biol. , vol.150 , pp. 1-25
    • Eisenberg, R.S.1
  • 33
    • 0346837922 scopus 로고    scopus 로고
    • A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
    • Fedkiw R.P., Aslam T., Merriman B., Osher S. A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method). J. Comput. Phys. 1999, 152:457-492.
    • (1999) J. Comput. Phys. , vol.152 , pp. 457-492
    • Fedkiw, R.P.1    Aslam, T.2    Merriman, B.3    Osher, S.4
  • 35
    • 34648817162 scopus 로고    scopus 로고
    • Treatment of charge singularities in implicit solvent models
    • Geng W., Yu S., Wei G.W. Treatment of charge singularities in implicit solvent models. J. Chem. Phys. 2007, 127:114106.
    • (2007) J. Chem. Phys. , vol.127 , pp. 114106
    • Geng, W.1    Yu, S.2    Wei, G.W.3
  • 36
    • 38949090423 scopus 로고    scopus 로고
    • Energetics of divalent selectivity in a calcium channel: the ryanodine receptor case study
    • Gillespie D. Energetics of divalent selectivity in a calcium channel: the ryanodine receptor case study. Biophys. J. 2008, 94(4):1169-1184.
    • (2008) Biophys. J. , vol.94 , Issue.4 , pp. 1169-1184
    • Gillespie, D.1
  • 37
    • 26444537377 scopus 로고    scopus 로고
    • Density functional theory of the electrical double layer: the RFD functional
    • Gillespie D., Valisko M., Boda D. Density functional theory of the electrical double layer: the RFD functional. J. Phys.: Condens. Matter 2005, 17:6609-6626.
    • (2005) J. Phys.: Condens. Matter , vol.17 , pp. 6609-6626
    • Gillespie, D.1    Valisko, M.2    Boda, D.3
  • 38
    • 84916430884 scopus 로고
    • A self-consistent iterative scheme for the one-dimensional steady-state transistor calculations
    • Gummel H.K. A self-consistent iterative scheme for the one-dimensional steady-state transistor calculations. IEEE Trans. Electron Dev. 1964, 11:455-465.
    • (1964) IEEE Trans. Electron Dev. , vol.11 , pp. 455-465
    • Gummel, H.K.1
  • 40
    • 0000381967 scopus 로고    scopus 로고
    • Two- and three-dimensional Poisson-Nernst-Planck simulations of current flow through Gramicidin A
    • Hollerbach U., Chen D.P., Eisenberg R.S. Two- and three-dimensional Poisson-Nernst-Planck simulations of current flow through Gramicidin A. J. Sci. Comput. 2002, 16(4):373-409.
    • (2002) J. Sci. Comput. , vol.16 , Issue.4 , pp. 373-409
    • Hollerbach, U.1    Chen, D.P.2    Eisenberg, R.S.3
  • 41
    • 85189839931 scopus 로고
    • The Poisson-Boltzmann equation: analysis and multilevel numerical solution, PhD Thesis, California Institute of Technology
    • M. Holst, The Poisson-Boltzmann equation: analysis and multilevel numerical solution, PhD Thesis, California Institute of Technology, 1994.
    • (1994)
    • Holst, M.1
  • 42
    • 38049129674 scopus 로고    scopus 로고
    • Incorporation of inhomogeneous ion diffusion coefficients into kinetic lattice grand canonical Monte Carlo simulations and application to ion current calculations in a simple model ion channel
    • Hwang H., Schatz G.C., Ratner M.A. Incorporation of inhomogeneous ion diffusion coefficients into kinetic lattice grand canonical Monte Carlo simulations and application to ion current calculations in a simple model ion channel. J. Phys. Chem. A 2007, 111(49):12506-12512.
    • (2007) J. Phys. Chem. A , vol.111 , Issue.49 , pp. 12506-12512
    • Hwang, H.1    Schatz, G.C.2    Ratner, M.A.3
  • 43
    • 0036389892 scopus 로고    scopus 로고
    • Ion permeation and selectivity of OmpF porin: a theoretical study based on molecular dynamics, Brownian dynamics, and continuum electrodiffusion theory
    • Im W., Roux B. Ion permeation and selectivity of OmpF porin: a theoretical study based on molecular dynamics, Brownian dynamics, and continuum electrodiffusion theory. J. Mol. Biol. 2002, 322:851-869.
    • (2002) J. Mol. Biol. , vol.322 , pp. 851-869
    • Im, W.1    Roux, B.2
  • 46
    • 72049087484 scopus 로고    scopus 로고
    • A computational study of ion conductance in the KcsA K+ channel using a Nernst-Planck model with explicit resident ions
    • Jung Y.W., Lu B.Z., Mascagni M. A computational study of ion conductance in the KcsA K+ channel using a Nernst-Planck model with explicit resident ions. J. Chem. Phys. 2009, 131(215101).
    • (2009) J. Chem. Phys. , vol.131 , pp. 215101
    • Jung, Y.W.1    Lu, B.Z.2    Mascagni, M.3
  • 47
    • 0033032906 scopus 로고    scopus 로고
    • A lattice relaxation algorithm for three-dimensional Poisson-Nernst-Planck theory with application to ion transport through the Gramicidin A channel
    • Kurnikova M.G., Coalson R.D., Graf P., Nitzan A. A lattice relaxation algorithm for three-dimensional Poisson-Nernst-Planck theory with application to ion transport through the Gramicidin A channel. Biophys. J. 1999, 76:642-656.
    • (1999) Biophys. J. , vol.76 , pp. 642-656
    • Kurnikova, M.G.1    Coalson, R.D.2    Graf, P.3    Nitzan, A.4
  • 49
    • 0028485385 scopus 로고
    • The immersed interface method for elliptic equations with discontinuous coefficients and singular sources
    • LeVeque R.J., Li Z.L. The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal. 1994, 31:1019-1044.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 1019-1044
    • LeVeque, R.J.1    Li, Z.L.2
  • 50
    • 0022522698 scopus 로고
    • Interpretation of biological ion channel flux data-reaction-rate versus continuum theory
    • Levitt D.G. Interpretation of biological ion channel flux data-reaction-rate versus continuum theory. Annu. Rev. Biophys. Biophys. Chem. 1986, 15:29-57.
    • (1986) Annu. Rev. Biophys. Biophys. Chem. , vol.15 , pp. 29-57
    • Levitt, D.G.1
  • 51
    • 0033010064 scopus 로고    scopus 로고
    • Modeling of ion channels
    • Levitt D.G. Modeling of ion channels. J. Gen. Physiol. 1999, 113(6):789-794.
    • (1999) J. Gen. Physiol. , vol.113 , Issue.6 , pp. 789-794
    • Levitt, D.G.1
  • 52
    • 0036208213 scopus 로고    scopus 로고
    • Maximum principle preserving schemes for interface problems with discontinuous coefficients
    • Li Z.L., Ito K. Maximum principle preserving schemes for interface problems with discontinuous coefficients. SIAM J. Sci. Comput. 2001, 23:339-361.
    • (2001) SIAM J. Sci. Comput. , vol.23 , pp. 339-361
    • Li, Z.L.1    Ito, K.2
  • 54
    • 21244486362 scopus 로고    scopus 로고
    • Geometric singular perturbation approach to steady-state Poisson-Nernst-Planck systems
    • Liu W.S. Geometric singular perturbation approach to steady-state Poisson-Nernst-Planck systems. SIAM J. Appl. Math. 2005, 65(3):754-766.
    • (2005) SIAM J. Appl. Math. , vol.65 , Issue.3 , pp. 754-766
    • Liu, W.S.1
  • 55
    • 0001491689 scopus 로고    scopus 로고
    • A boundary condition capturing method for Poisson's equation on irregular domains
    • Liu X.D., Fedkiw R.P., Kang M. A boundary condition capturing method for Poisson's equation on irregular domains. J. Comput. Phys. 2000, 160:151-178.
    • (2000) J. Comput. Phys. , vol.160 , pp. 151-178
    • Liu, X.D.1    Fedkiw, R.P.2    Kang, M.3
  • 57
    • 33750621301 scopus 로고    scopus 로고
    • Diffusion constant of K+ inside Gramicidin A: a comparative study of four computational methods
    • Mamonov A.B., Kurnikova M.G., Coalson R.D. Diffusion constant of K+ inside Gramicidin A: a comparative study of four computational methods. Biophys. Chem. 2006, 124:268-278.
    • (2006) Biophys. Chem. , vol.124 , pp. 268-278
    • Mamonov, A.B.1    Kurnikova, M.G.2    Coalson, R.D.3
  • 58
    • 0000323669 scopus 로고    scopus 로고
    • Ab initio molecular dynamics: theory and implementation
    • John von Neumann Institute for Computing, Jülich, J. Grotendorst (Ed.) Modern Methods and Algorithms of Quantum Chemistry
    • Marx D., Hutter J. Ab initio molecular dynamics: theory and implementation. NIC Series 2000, vol. 3:329-477. John von Neumann Institute for Computing, Jülich. J. Grotendorst (Ed.).
    • (2000) NIC Series , vol.3 , pp. 329-477
    • Marx, D.1    Hutter, J.2
  • 59
    • 67049160490 scopus 로고    scopus 로고
    • A multigrid method for the Poisson-Nernst-Planck equations
    • Mathur S.R., Murthy J.Y. A multigrid method for the Poisson-Nernst-Planck equations. SIAM J. Appl. Math. 2009, 52(17-18):4031-4039.
    • (2009) SIAM J. Appl. Math. , vol.52 , Issue.17-18 , pp. 4031-4039
    • Mathur, S.R.1    Murthy, J.Y.2
  • 60
    • 0021417514 scopus 로고
    • The fast solution of Poisson's and the biharmonic equations on irregular regions
    • Mayo A. The fast solution of Poisson's and the biharmonic equations on irregular regions. SIAM J. Numer. Anal. 1984, 21:285-299.
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 285-299
    • Mayo, A.1
  • 61
    • 33750614424 scopus 로고    scopus 로고
    • A cartesian grid finite volume method for elliptic equations with variable coefficients and embedded interfaces
    • Oevermann M., Klein R. A cartesian grid finite volume method for elliptic equations with variable coefficients and embedded interfaces. J. Comput. Phys. 2006, 219:749-769.
    • (2006) J. Comput. Phys. , vol.219 , pp. 749-769
    • Oevermann, M.1    Klein, R.2
  • 62
    • 0017424014 scopus 로고
    • Numerical analysis of blood flow in the heart
    • Peskin C.S. Numerical analysis of blood flow in the heart. J. Comput. Phys. 1977, 25(3):220-252.
    • (1977) J. Comput. Phys. , vol.25 , Issue.3 , pp. 220-252
    • Peskin, C.S.1
  • 64
    • 0017429069 scopus 로고
    • Areas, volumes, packing, and protein structure
    • Richards F.M. Areas, volumes, packing, and protein structure. Annu. Rev. Biophys. Bioeng. 1977, 6(1):151-176.
    • (1977) Annu. Rev. Biophys. Bioeng. , vol.6 , Issue.1 , pp. 151-176
    • Richards, F.M.1
  • 65
    • 3142652094 scopus 로고    scopus 로고
    • Theoretical and computational models of biological ionchannels
    • Roux B., Allen T., Berneche S., Im W. Theoretical and computational models of biological ionchannels. Q. Rev. Biophys. 2004, 7(1):1-103.
    • (2004) Q. Rev. Biophys. , vol.7 , Issue.1 , pp. 1-103
    • Roux, B.1    Allen, T.2    Berneche, S.3    Im, W.4
  • 67
    • 0030040323 scopus 로고    scopus 로고
    • Reduced surface: an efficient way to compute molecular surfaces
    • Sanner M.F., Olson A.J., Spehner J.C. Reduced surface: an efficient way to compute molecular surfaces. Biopolymers 1996, 38:305-320.
    • (1996) Biopolymers , vol.38 , pp. 305-320
    • Sanner, M.F.1    Olson, A.J.2    Spehner, J.C.3
  • 68
    • 0035441903 scopus 로고    scopus 로고
    • Derivation of Poisson and Nernst-Planck equations in a bath and channel from a molecular model
    • Schuss Z., Nadler B., Eisenberg R. Derivation of Poisson and Nernst-Planck equations in a bath and channel from a molecular model. Phys. Rev. E, Stat. Nonlinear Soft Matter Phys. 2001, 64:036116.
    • (2001) Phys. Rev. E, Stat. Nonlinear Soft Matter Phys. , vol.64 , pp. 036116
    • Schuss, Z.1    Nadler, B.2    Eisenberg, R.3
  • 69
    • 23844506931 scopus 로고    scopus 로고
    • Limitations of atom-centered dielectric functions in implicit solvent models
    • Swanson J.M.J., Mongan J., McCammon J.A. Limitations of atom-centered dielectric functions in implicit solvent models. J. Phys. Chem. B 2005, 109(31):14769-14772.
    • (2005) J. Phys. Chem. B , vol.109 , Issue.31 , pp. 14769-14772
    • Swanson, J.M.J.1    Mongan, J.2    McCammon, J.A.3
  • 70
    • 77951687164 scopus 로고    scopus 로고
    • An iterative, fast, linear-scaling method for computing induced charges on arbitrary dielectric boundaries
    • Tyagi S., Suzen M., Sega M., Barbosa M., Kantorovich S.S., Holm C. An iterative, fast, linear-scaling method for computing induced charges on arbitrary dielectric boundaries. J. Chem. Phys. 2010, 132(15):154112-154119.
    • (2010) J. Chem. Phys. , vol.132 , Issue.15 , pp. 154112-154119
    • Tyagi, S.1    Suzen, M.2    Sega, M.3    Barbosa, M.4    Kantorovich, S.S.5    Holm, C.6
  • 71
    • 77955229645 scopus 로고    scopus 로고
    • Differential geometry based multiscale models
    • Wei G.W. Differential geometry based multiscale models. Bull. Math. Biol. 2010, 72:1562-1622.
    • (2010) Bull. Math. Biol. , vol.72 , pp. 1562-1622
    • Wei, G.W.1
  • 72
    • 36749034166 scopus 로고    scopus 로고
    • A new minimization protocol for solving nonlinear Poisson-Boltzmann mortar finite element equation
    • Xie D., Zhou S.Z. A new minimization protocol for solving nonlinear Poisson-Boltzmann mortar finite element equation. BIT Numer. Math. 2007, 47:853-871.
    • (2007) BIT Numer. Math. , vol.47 , pp. 853-871
    • Xie, D.1    Zhou, S.Z.2
  • 73
    • 34547352376 scopus 로고    scopus 로고
    • Treatment of geometric singularities in implicit solvent models
    • Yu S., Geng W., Wei G.W. Treatment of geometric singularities in implicit solvent models. J. Chem. Phys. 2007, 126:244108.
    • (2007) J. Chem. Phys. , vol.126 , pp. 244108
    • Yu, S.1    Geng, W.2    Wei, G.W.3
  • 74
    • 35348917599 scopus 로고    scopus 로고
    • Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities
    • Yu S., Wei G.W. Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities. J. Comput. Phys. 2007, 227:602-632.
    • (2007) J. Comput. Phys. , vol.227 , pp. 602-632
    • Yu, S.1    Wei, G.W.2
  • 75
    • 34248596727 scopus 로고    scopus 로고
    • Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces
    • Yu S., Zhou Y., Wei G.W. Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces. J. Comput. Phys. 2007, 224(2):729-756.
    • (2007) J. Comput. Phys. , vol.224 , Issue.2 , pp. 729-756
    • Yu, S.1    Zhou, Y.2    Wei, G.W.3
  • 76
    • 4544354197 scopus 로고    scopus 로고
    • High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces
    • Zhao S., Wei G.W. High-order FDTD methods via derivative matching for Maxwell's equations with material interfaces. J. Comput. Phys. 2004, 200(1):60-103.
    • (2004) J. Comput. Phys. , vol.200 , Issue.1 , pp. 60-103
    • Zhao, S.1    Wei, G.W.2
  • 77
    • 64049109900 scopus 로고    scopus 로고
    • Matched interface and boundary (MIB) for the implementation of boundary conditions in high order central finite differences
    • Zhao S., Wei G.W. Matched interface and boundary (MIB) for the implementation of boundary conditions in high order central finite differences. Int. J. Numer. Methods Eng. 2009, 77:1690-1730.
    • (2009) Int. J. Numer. Methods Eng. , vol.77 , pp. 1690-1730
    • Zhao, S.1    Wei, G.W.2
  • 78
    • 37649005586 scopus 로고    scopus 로고
    • Highly accurate biomolecular electrostatics in continuum dielectric environments
    • Zhou Y.C., Feig M., Wei G.W. Highly accurate biomolecular electrostatics in continuum dielectric environments. J. Comput. Chem. 2008, 29:87-97.
    • (2008) J. Comput. Chem. , vol.29 , pp. 87-97
    • Zhou, Y.C.1    Feig, M.2    Wei, G.W.3
  • 79
    • 33750356476 scopus 로고    scopus 로고
    • On the fictitious-domain and interpolation formulations of the matched interface and boundary (MIB) method
    • Zhou Y.C., Wei G.W. On the fictitious-domain and interpolation formulations of the matched interface and boundary (MIB) method. J. Comput. Phys. 2006, 219(1):228-246.
    • (2006) J. Comput. Phys. , vol.219 , Issue.1 , pp. 228-246
    • Zhou, Y.C.1    Wei, G.W.2
  • 80
    • 31744448526 scopus 로고    scopus 로고
    • High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources
    • Zhou Y.C., Zhao S., Feig M., Wei G.W. High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources. J. Comput. Phys. 2006, 213(1):1-30.
    • (2006) J. Comput. Phys. , vol.213 , Issue.1 , pp. 1-30
    • Zhou, Y.C.1    Zhao, S.2    Feig, M.3    Wei, G.W.4
  • 81
    • 85033849708 scopus 로고    scopus 로고
    • Finite-difference solution of the Poisson-Boltzmann equation: complete elimination of self-energy
    • Zhou Z., Payne P., Vasquez M., Kuhn N., Levitt M. Finite-difference solution of the Poisson-Boltzmann equation: complete elimination of self-energy. J. Comput. Chem. 1996, 17:1344-1351.
    • (1996) J. Comput. Chem. , vol.17 , pp. 1344-1351
    • Zhou, Z.1    Payne, P.2    Vasquez, M.3    Kuhn, N.4    Levitt, M.5


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.