메뉴 건너뛰기




Volumn 7, Issue 4, 2008, Pages 1507-1526

Asymptotic expansions of I-V relations via a Poisson-Nernst-Planck system

Author keywords

I V relations; Matched asymptotic expansion; Singular perturbation

Indexed keywords

ASYMPTOTIC EXPANSION; BISTABLE STRUCTURES; DEBYE LENGTH; DEGENERATE CASE; FIRST ORDER; HIGHER ORDER; HIGHER ORDER TERMS; HODGKIN-HUXLEY MODELS; I-V RELATIONS; ION CHANNEL; ION SPECIES; MATCHED ASYMPTOTIC EXPANSION; NARROW CHANNEL; REAL ROOTS; SECOND ORDERS; SECOND-ORDER CORRECTION; SINGULAR PERTURBATIONS; SINGULARLY PERTURBED SYSTEMS; SPECIAL STRUCTURE;

EID: 66549111828     PISSN: None     EISSN: 15360040     Source Type: Journal    
DOI: 10.1137/070691322     Document Type: Article
Times cited : (67)

References (51)
  • 1
    • 33750606030 scopus 로고    scopus 로고
    • Molecular dynamics-Potential of mean force calculations as a tool for understanding ion permeation and selectivity in narrow channels
    • T. W. ALLEN, O. S. ANDERSEN, AND B. ROUX, Molecular dynamics-Potential of mean force calculations as a tool for understanding ion permeation and selectivity in narrow channels, Biophys. Chem., 124 (2006), pp. 251-267.
    • (2006) Biophys. Chem. , vol.124 , pp. 251-267
    • Allen, T.W.1    Andersen, O.S.2    Roux, B.3
  • 3
    • 0026930493 scopus 로고
    • Ion flow through narrow membrane channels: Part i
    • V. BARCILON, Ion flow through narrow membrane channels: Part I, SIAM J. Appl. Math., 52 (1992), pp. 1391-1404.
    • (1992) SIAM J. Appl. Math. , vol.52 , pp. 1391-1404
    • Barcilon, V.1
  • 4
    • 0026929304 scopus 로고
    • Ion flow through narrow membrane channels: Part II
    • V. BARCILON, D.-P. CHEN, AND R. S. EISENBERG, Ion flow through narrow membrane channels: Part II, SIAM J. Appl. Math., 52 (1992), pp. 1405-1425.
    • (1992) SIAM J. Appl. Math. , vol.52 , pp. 1405-1425
    • Barcilon, V.1    Chen, D.-P.2    Eisenberg, R.S.3
  • 5
    • 0031166471 scopus 로고    scopus 로고
    • Qualitative properties of steady-state Poisson-Nernst-Planck systems: Perturbation and simulation study
    • V. Barcilon, D.-P. Chen, R. S. Eisenberg, and J.W. Jerome, Qualitative properties of steady-state Poisson-Nernst-Planck systems: Perturbation and simulation study, SIAM J. Appl. Math., 57 (1997), pp. 631-648.
    • (1997) SIAM J. Appl. Math. , vol.57 , pp. 631-648
    • Barcilon, V.1    Chen, D.-P.2    Eisenberg, R.S.3    Jerome, J.W.4
  • 6
    • 34548270391 scopus 로고    scopus 로고
    • Inverse problems related to ion channel selectivity
    • M. Burger, R. S. Eisenberg, and H. W. Engl, Inverse problems related to ion channel selectivity, SIAM J. Appl. Math., 67 (2007), pp. 960-989.
    • (2007) SIAM J. Appl. Math. , vol.67 , pp. 960-989
    • Burger, M.1    Eisenberg, R.S.2    Engl, H.W.3
  • 7
    • 0036710071 scopus 로고    scopus 로고
    • Translocation mechanism of long sugar chains across the maltoporin membrane channel
    • R. Dutzler, T. Schirmer, M. Karplus, and S. Fischer, Translocation mechanism of long sugar chains across the maltoporin membrane channel, Structure, 10 (2002), pp. 1273-1284.
    • (2002) Structure , vol.10 , pp. 1273-1284
    • Dutzler, R.1    Schirmer, T.2    Karplus, M.3    Fischer, S.4
  • 8
    • 0003255784 scopus 로고
    • Asymptotic analysis of singular perturbations
    • North-Holland, Amsterdam, New York
    • W. Eckhaus, Asymptotic Analysis of Singular Perturbations, Stud. Math. Appl. 9, North-Holland, Amsterdam, New York, 1979.
    • (1979) Stud. Math. Appl. , vol.9
    • Eckhaus, W.1
  • 9
    • 0028494718 scopus 로고
    • Fundamental concepts of matching
    • W. Eckhaus, Fundamental concepts of matching, SIAM Rev., 36 (1994), pp. 431-439.
    • (1994) SIAM Rev. , vol.36 , pp. 431-439
    • Eckhaus, W.1
  • 10
    • 34548804174 scopus 로고    scopus 로고
    • Poisson-Nernst-Planck systems for ion channels with permanent charges
    • B. Eisenberg and W. Liu, Poisson-Nernst-Planck systems for ion channels with permanent charges, SIAM J. Math. Anal., 38 (2007), pp. 1932-1966.
    • (2007) SIAM J. Math. Anal. , vol.38 , pp. 1932-1966
    • Eisenberg, B.1    Liu, W.2
  • 11
    • 0028901238 scopus 로고
    • Sodium in gramicidin: An example of a permion
    • R. Elber, D. Chen, D. Rojewska, and R. S. Eisenberg, Sodium in gramicidin: An example of a permion, Biophys. J., 68 (1995), pp. 906-924.
    • (1995) Biophys. J. , vol.68 , pp. 906-924
    • Elber, R.1    Chen, D.2    Rojewska, D.3    Eisenberg, R.S.4
  • 13
    • 0037175732 scopus 로고    scopus 로고
    • Coupling Poisson-Nernst-Planck and density functional theory to calculate ion flux
    • D. Gillespie, W. Nonner, and R. S. Eisenberg, Coupling Poisson-Nernst-Planck and density functional theory to calculate ion flux, J. Phys. Condens. Matter, 14 (2002), pp. 12129-12145.
    • (2002) J. Phys. Condens. Matter , vol.14 , pp. 12129-12145
    • Gillespie, D.1    Nonner, W.2    Eisenberg, R.S.3
  • 14
    • 0242493974 scopus 로고    scopus 로고
    • Density functional theory of charged, hard-sphere fluids
    • D. Gillespie, W. Nonner, and R. S. Eisenberg, Density functional theory of charged, hard-sphere fluids, Phys. Rev. E, 68 (2003), pp. 1-10.
    • (2003) Phys. Rev. E , vol.68 , pp. 1-10
    • Gillespie, D.1    Nonner, W.2    Eisenberg, R.S.3
  • 15
    • 0019441262 scopus 로고
    • Improved patch-clamp techniques for high-resolution current recording from cells and cell-free membrane patches
    • O. P. Hamill, A. Marty, E. Neher, B. Sakmann, and F. J. Sigworth, Improved patch-clamp techniques for high-resolution current recording from cells and cell-free membrane patches, Pflugers Arch., 391 (1981), pp. 85-100.
    • (1981) Pflugers Arch. , vol.391 , pp. 85-100
    • Hamill, O.P.1    Marty, A.2    Neher, E.3    Sakmann, B.4    Sigworth, F.J.5
  • 16
    • 0014969006 scopus 로고
    • Discreteness of conductance change in bimolecular lipid membranes in the presence of certain antibiotics
    • S. B. Hladky and D. A. Haydon, Discreteness of conductance change in bimolecular lipid membranes in the presence of certain antibiotics, Nature, 225 (1970), pp. 451-453.
    • (1970) Nature , vol.225 , pp. 451-453
    • Hladky, S.B.1    Haydon, D.A.2
  • 17
    • 0037198211 scopus 로고    scopus 로고
    • Concentration-dependent shielding of electrostatic potentials inside the gramicidin A channel
    • U. Hollerbach and R. Eisenberg, Concentration-dependent shielding of electrostatic potentials inside the gramicidin A channel, Langmuir, 18 (2002), pp. 3262-3631.
    • (2002) Langmuir , vol.18 , pp. 3262-3631
    • Hollerbach, U.1    Eisenberg, R.2
  • 18
    • 0022107831 scopus 로고
    • Consistency of semiconductor modeling: An existence/stability analysis for the stationary Van Roosbroeck system
    • J. W. Jerome, Consistency of semiconductor modeling: An existence/stability analysis for the stationary Van Roosbroeck system, SIAM J. Appl. Math., 45 (1985), pp. 565-590.
    • (1985) SIAM J. Appl. Math. , vol.45 , pp. 565-590
    • Jerome, J.W.1
  • 19
    • 0026139032 scopus 로고
    • A finite element approximation theory for the drift diffusion semiconductor model
    • J. W. Jerome and T. Kerkhoven, A finite element approximation theory for the drift diffusion semiconductor model, SIAM J. Numer. Anal., 28 (1991), pp. 403-422.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 403-422
    • Jerome, J.W.1    Kerkhoven, T.2
  • 20
    • 0036708441 scopus 로고    scopus 로고
    • Trial by ordeal: Ionic free energies in gramicidin
    • P. C. Jordan, Trial by ordeal: Ionic free energies in gramicidin, Biophys. J., 83 (2002), pp. 1235-1236.
    • (2002) Biophys. J. , vol.83 , pp. 1235-1236
    • Jordan, P.C.1
  • 21
    • 0003413399 scopus 로고    scopus 로고
    • Mathematical physiology, interdisciplinary
    • Springer-Verlag, New York
    • J. Keener and J. Sneyd, Mathematical Physiology, Interdisciplinary Appl. Math. 8, Springer-Verlag, New York, 1998.
    • (1998) Appl. Math. , vol.8
    • Keener, J.1    Sneyd, J.2
  • 22
    • 0003244685 scopus 로고
    • Perturbation methods in applied mathematics
    • Springer-Verlag, New York, Berlin
    • J. Kevorkian and J. D. Cole, Perturbation Methods in Applied Mathematics, Appl. Math. Sci. 34, Springer-Verlag, New York, Berlin, 1981.
    • (1981) Appl. Math. Sci. , vol.34
    • Kevorkian, J.1    Cole, J.D.2
  • 23
    • 0003324745 scopus 로고    scopus 로고
    • Multiple scale and singular perturbation methods
    • Springer-Verlag, New York
    • J. Kevorkian and J. D. Cole, Multiple Scale and Singular Perturbation Methods, Appl. Math. Sci. 114, Springer-Verlag, New York, 1996.
    • (1996) Appl. Math. Sci. , vol.114
    • Kevorkian, J.1    Cole, J.D.2
  • 24
    • 0036154083 scopus 로고    scopus 로고
    • Transport of maltodextrins through maltoporin: A single-channel study
    • L. Kullman, M. Winterhalter, and S. M. Bezrukov, Transport of maltodextrins through maltoporin: A single-channel study, Biophys. J., 82 (2002), pp. 803-812.
    • (2002) Biophys. J. , vol.82 , pp. 803-812
    • Kullman, L.1    Winterhalter, M.2    Bezrukov, S.M.3
  • 25
    • 0033032906 scopus 로고    scopus 로고
    • A lattice relaxation algorithm for 3D Poisson-Nernst-Planck theory with application to ion transport through the gramicidin A channel
    • M. G. Kurnikova, R. D. Coalson, P. Graf, and A. Nitzan, A lattice relaxation algorithm for 3D Poisson-Nernst-Planck theory with application to ion transport through the gramicidin A channel, Biophys. J., 76 (1999), pp. 642-656.
    • (1999) Biophys. J. , vol.76 , pp. 642-656
    • Kurnikova, M.G.1    Coalson, R.D.2    Graf, P.3    Nitzan, A.4
  • 27
    • 21244486362 scopus 로고    scopus 로고
    • Geometric singular perturbation approach to steady-state Poisson-Nernst-Planck systems
    • W. Liu, Geometric singular perturbation approach to steady-state Poisson-Nernst-Planck systems, SIAM J. Appl. Math., 65 (2005), pp. 754-766.
    • (2005) SIAM J. Appl. Math. , vol.65 , pp. 754-766
    • Liu, W.1
  • 28
    • 78650206858 scopus 로고    scopus 로고
    • Steady-state Poisson-Nernst-Planck systems for ion channels with multiple ion species
    • Submitted
    • W. Liu, Steady-state Poisson-Nernst-Planck systems for ion channels with multiple ion species, J. Differential Equations, submitted.
    • J. Differential Equations
    • Liu, W.1
  • 29
    • 78650197681 scopus 로고    scopus 로고
    • Poisson-Nernst-Planck Systems for narrow tubular-like membrane channels
    • Submitted
    • W. Liu and B. Wang, Poisson-Nernst-Planck Systems for narrow tubular-like membrane channels, Trans. Amer. Math. Soc., submitted.
    • Trans. Amer. Math. Soc.
    • Liu, W.1    Wang, B.2
  • 30
    • 0020180752 scopus 로고
    • An example of nonuniqueness of stationary solutions in device models
    • M. S. Mock, An example of nonuniqueness of stationary solutions in device models, COMPEL, 1 (1982), pp. 165-174.
    • (1982) COMPEL , vol.1 , pp. 165-174
    • Mock, M.S.1
  • 31
    • 0017258698 scopus 로고
    • Single channel currents recorded from the membrane of denervated muscle fibers
    • E. Neher and B. Sakmann, Single channel currents recorded from the membrane of denervated muscle fibers, Nature, 260 (1976), pp. 799-802.
    • (1976) Nature , vol.260 , pp. 799-802
    • Neher, E.1    Sakmann, B.2
  • 32
    • 0031682987 scopus 로고    scopus 로고
    • Ion permeation and glutamate residues linked by Poisson-Nernst-Planck theory in L-type calcium channels
    • W. Nonner and R. S. Eisenberg, Ion permeation and glutamate residues linked by Poisson-Nernst-Planck theory in L-type calcium channels, Biophys. J., 75 (1998), pp. 1287-1305.
    • (1998) Biophys. J. , vol.75 , pp. 1287-1305
    • Nonner, W.1    Eisenberg, R.S.2
  • 33
    • 0003329938 scopus 로고
    • Singular perturbation methods for ordinary differential equations
    • Springer-Verlag, New York
    • R. E. O'Malley, Jr., Singular Perturbation Methods for Ordinary Differential Equations, Appl. Math. Sci. 89, Springer-Verlag, New York, 1991.
    • (1991) Appl. Math. Sci. , vol.89
    • O'Malley Jr., R.E.1
  • 34
    • 0031164174 scopus 로고    scopus 로고
    • Qualitative properties of steady-state Poisson-Nernst-Planck systems: Mathematical study
    • J.-H. Park and J. W. Jerome, Qualitative properties of steady-state Poisson-Nernst-Planck systems: Mathematical study, SIAM J. Appl. Math., 57 (1997), pp. 609-630.
    • (1997) SIAM J. Appl. Math. , vol.57 , pp. 609-630
    • Park, J.-H.1    Jerome, J.W.2
  • 35
    • 78650223340 scopus 로고
    • Matched asymptotic expansions of the Green's function for the electric potential in an infinite cylindrical cell
    • A. Peskoff, R. S. Eisenberg, and J. D. Cole, Matched asymptotic expansions of the Green's function for the electric potential in an infinite cylindrical cell, SIAM J. Appl. Math., 30 (1976), pp. 222-239.
    • (1976) SIAM J. Appl. Math. , vol.30 , pp. 222-239
    • Peskoff, A.1    Eisenberg, R.S.2    Cole, J.D.3
  • 36
    • 33748583013 scopus 로고
    • Ion transport in a gramicidin-like channel: Dynamics and mobility
    • B. Roux and M. Karplus, Ion transport in a gramicidin-like channel: Dynamics and mobility, J. Phys. Chem., 95 (1991), pp. 4856-4868.
    • (1991) J. Phys. Chem. , vol.95 , pp. 4856-4868
    • Roux, B.1    Karplus, M.2
  • 37
    • 0025882246 scopus 로고
    • Ion transport in a model gramicidin channel: Structure and thermodynamics
    • B. Roux and M. Karplus, Ion transport in a model gramicidin channel: Structure and thermodynamics, Biophys. J., 59 (1991), pp. 961-981.
    • (1991) Biophys. J. , vol.59 , pp. 961-981
    • Roux, B.1    Karplus, M.2
  • 38
    • 0023431121 scopus 로고
    • Multiple steady states in one-dimensional electrodiffusion with local electroneutrality
    • I. Rubinstein, Multiple steady states in one-dimensional electrodiffusion with local electroneutrality, SIAM J. Appl. Math., 47 (1987), pp. 1076-1093.
    • (1987) SIAM J. Appl. Math. , vol.47 , pp. 1076-1093
    • Rubinstein, I.1
  • 39
    • 0010996524 scopus 로고
    • Electro-diffusion of ions
    • SIAM, Philadelphia
    • I. Rubinstein, Electro-Diffusion of Ions, SIAM Stud. Appl. Math. 11, SIAM, Philadelphia, 1990.
    • (1990) SIAM Stud. Appl. Math. , vol.11
    • Rubinstein, I.1
  • 41
    • 0028946962 scopus 로고
    • Structural basis for sugar translocation through maltoporin channels at 3.1 resolution
    • R. H. Schirmer, T. A. Keller, Y. F. W., and J. P. Rosenbusch, Structural basis for sugar translocation through maltoporin channels at 3.1 resolution, Science, 267 (1995), pp. 512-514.
    • (1995) Science , vol.267 , pp. 512-514
    • Schirmer, R.H.1    Keller Y F W, T.A.2    Rosenbusch, J.P.3
  • 42
    • 0035441903 scopus 로고    scopus 로고
    • Derivation of Poisson and Nernst-Planck equations in a bath and channel from a molecular model
    • Z. Schuss, B. Nadler, and R. S. Eisenberg, Derivation of Poisson and Nernst-Planck equations in a bath and channel from a molecular model, Phys. Rev. E, 64 (2001), pp. 1-14.
    • (2001) Phys. Rev. E , vol.64 , pp. 1-14
    • Schuss, Z.1    Nadler, B.2    Eisenberg, R.S.3
  • 43
    • 50849111742 scopus 로고    scopus 로고
    • A Poisson-Nernst-Planck model for biological ion channels-An asymptotic analysis in a 3-D narrow funnel
    • A. Singer and J. Norbury, A Poisson-Nernst-Planck model for biological ion channels-An asymptotic analysis in a 3-D narrow funnel, European J. Appl. Math., 19 (2008), pp. 541-560.
    • (2008) European J. Appl. Math. , vol.19 , pp. 541-560
    • Singer, A.1    Norbury, J.2
  • 45
    • 0024926244 scopus 로고
    • Asymptotic analysis of the current-voltage curve of a pnpn semiconductor device
    • H. Steinrück, Asymptotic analysis of the current-voltage curve of a pnpn semiconductor device, IMA J. Appl. Math., 43 (1989), pp. 243-259.
    • (1989) IMA J. Appl. Math. , vol.43 , pp. 243-259
    • Steinrück, H.1
  • 46
    • 0042714350 scopus 로고
    • A bifurcation analysis of the one-dimensional steady-state semiconductor device equations
    • H. Steinrück, A bifurcation analysis of the one-dimensional steady-state semiconductor device equations, SIAM J. Appl. Math., 49 (1989), pp. 1102-1121.
    • (1989) SIAM J. Appl. Math. , vol.49 , pp. 1102-1121
    • Steinrück, H.1
  • 47
    • 33645459327 scopus 로고    scopus 로고
    • Negative incremental resistance induced by calcium in asymmetric nanopores
    • Z. Siwy, M. R. Powell, E. Kalman, R. D. Asumian, and R. S. Eisenberg, Negative incremental resistance induced by calcium in asymmetric nanopores, Nano Lett., 6 (2006), pp. 473-477.
    • (2006) Nano Lett. , vol.6 , pp. 473-477
    • Siwy, Z.1    Powell, M.R.2    Kalman, E.3    Asumian, R.D.4    Eisenberg, R.S.5


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.