Computing numerically the access resistance of a pore

European Biophysics Journal

Volumn 34, Issue 4, 2005, Pages 314-322

  Aguilella Arzo, Marcel ^a   Aguilella, Vicente M ^a   Eisenberg, R S ^b  

^a UNIVERSITAT JAUME I   (Spain)

^b RUSH UNIVERSITY MEDICAL CENTER   (United States)

Author keywords

Access resistance; Channel conductance; Membrane pore; Poisson Nernst Planck equations

Indexed keywords

ION CHANNEL;

ARTICLE; CALCULATION; CONCENTRATION (PARAMETERS); ELECTRICITY; ION CONDUCTANCE; ION CURRENT; MATHEMATICAL COMPUTING; MEMBRANE; POISSON DISTRIBUTION; POROSITY;

BIOLOGICAL TRANSPORT; BIOPHYSICS; CELL MEMBRANE; COMPUTATIONAL BIOLOGY; COMPUTER SIMULATION; DIFFUSION; ELECTRIC CONDUCTIVITY; ELECTRIC IMPEDANCE; ELECTROSTATICS; ION TRANSPORT; IONS; KINETICS; MODELS, BIOLOGICAL; MODELS, MOLECULAR; MODELS, STATISTICAL; POISSON DISTRIBUTION; SALTS; SODIUM CHLORIDE;

EID: 21244485040     PISSN: 01757571     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00249-004-0452-x     Document Type: Article

References (67)

1. Aboud S, Marreiro D, Saraniti M, Eisenberg R (2004) A Poisson P3M force field scheme for particle-based simulations of ionic liquids. J Comput Electron (in press)
2. Aguilella VM, Bezrukov SM (2001) Alamethicin channel conductance modified by lipid charge. Eur Biophys J 30:233-241
3. Allen TW, Andersen OS, Roux B (2003) Structure of gramicidin a in a lipid bilayer environment determined using molecular dynamics simulations and solid-state NMR data. J Am Chem Soc 125:9868-9877
4. Allen TW, Andersen OS, Roux B (2004) Energetics of ion conduction through the gramicidin channel. Proc Natl Acad Sci USA 101:117-122
5. Bank RE, Burgler J, Coughran WM Jr, Fichtner W, Smith RK (1990) Recent progress in algorithms for semiconductor device simulation. Int Ser Num Math 93:125-140
6. Barcilon V (1992) Ion flow through narrow membrane channels: part I. SIAM J Appl Math 52:1391-1404
7. Barcilon V, Chen DP, Eisenberg RS (1992) Ion flow through narrow membrane channels: part II. SIAM J Appl Math 52:1405-1425
8. Bezrukov SM, Vodyanoy I (1993) Probing alamethicin channels with water-soluble polymers. Effect on conductance of channel states. Biophys J 64:16-25
9. Boda D, Gillespie D, Nonner W, Henderson D, Eisenberg B (2004) Computing induced charges in inhomogeneous dielectric media: application in a Monte Carlo simulation of complex ionic systems. Phys Rev E Stat Nonlin Soft Matter Phys 69:046702
10. Cardenas AE, Coalson RD, Kurnikova MG (2000) Three-dimensional Poisson-Nernst-Planck studies. Influence of membrane electrostatics on gramicidin A channel conductance. Biophys J 79:80-93
11. Carneiro CMM, Merzlyak PG, Yuldasheva LN, Silva LG, Thinnes FP, Krasilnikov OV (2003) Probing the volume changes during voltage gating of Porin 31BM channel with nonelectrolyte polymers. Biochim Biophys Acta 1612:144-153
12. Chen DP, Eisenberg RS (1993) Charges, currents and potentials in ionic channels of one conformation. Biophys J 64:1405-1421
13. Chen DP, Barcilon V, Eisenberg RS (1992) Constant field and constant gradients in open ionic channels. Biophys J 61:1372-1393
14. Chung S-H, Kuyucak S (2002) Recent advances in ion channel research. Biochim Biophys Acta 1565:267-286
15. Chung S-H, Allen T, Hoyles M, Kuyucak S (1999) Permeation of ions across the potassium channel: Brownian dynamics studies. Biophys J 77:2517-2533
16. Corry B, Kuyucak S, Chung SH (1999) Test of Poisson-Nernst-Planck theory in ion channels. J Gen Physiol 114(4):597-599
17. Corry B, Kuyucak S, Chung S-H (2000) Tests of continuum theories as models of ion channels. II. Poisson-Nernst-Planck theory versus Brownian dynamics. Biophys J 78:2364-2381
18. Corry B, Kuyucak S, Chung SH (2003) Dielectric self-energy in Poisson-Boltzmann and Poisson-Nernst-Planck models of ion channels. Biophys J 84:3594-3606
19. Damocles (1999) Web address: http://www.research.ibm.com/DAMOCLES/ html_files/sites.html
20. Dieckmann GR, Lear JD, Zhong Q, Klein ML, DeGrado WF, Sharp KA (1999) Exploration of the structural features defining the conduction properties of a synthetic ion channel. Biophys J 76:618-630
21. Edwards S, Corry B, Kuyucak S, Chung SH (2002) Continuum electrostatics fails to describe ion permeation in the gramicidin channel. Biophys J 83:1348-1360
22. Eisenberg RS (1996) Computing the field in proteins and channels. J Membr Biol 150:1-25
23. Eisenberg RS, Engel E (1970) The spatial variation of membrane potential near a small source of current in a spherical cell. J Gen Physiol 55:736-757
24. Engel E, Barcilon V, Eisenberg RS (1972) The interpretation of current-voltage relations recorded from a spherical cell with a single microelectrode. Biophys J 12:384-403
25. Gillespie D, Eisenberg RS (2001) Modified Donnan potentials for ion transport through biological ion channels. Phys Rev E 63:061902-1
26. Gillespie D, Eisenberg RS (2002) Physical descriptions of experimental selectivity measurements in ion channels. Eur Biophys J 31:454-466
27. Graf P, Nitzan A, Kurnikova MG, Coalson RD (2000) A dynamic lattice Monte Carlo model of ion transport in inhomogeneous dielectric environments: method and implementation. J Phys Chem B 104:12324-12338
28. Grasser T, Tang T-W, Kosina H, Selberherr S (2003) A review of hydrodynamic and energy-transport models for semiconductor device simulation. Proc IEEE 91(2):251-274
29. Gray A, Mathews GB (1922) A treatise on Bessel functions and their applications to physics. Dover Publications Inc., New York, p 143 (First published by McMillan and Co., London, 1922)
30. Gummel HK (1964) A self-consistent iterative scheme for one-dimensional steady-state transistor calculations. IEEE Trans Electron Devices 11:445-465
31. Hall JE (1975) Access resistance of a small circular pore. J Gen Phys 66:531-532
32. Hille B (1967) A pharmacological analysis of the ionic channels of nerve. PhD Thesis. The Rockefeller University; University Microfilms, Ann Arbor (Microfilm 68-9584)
33. Hille B (1968) Pharmacological modifications of the sodium channels of frog nerve. J Gen Physiol 51:199-219
34. Hille B (2001) Ionic channels of excitable membranes, 3rd edn. Sinauer Associates Inc., Sunderland
35. Hollerbach U, Chen D, Nonner W, Eisenberg B (1999) Three-dimensional Poisson-Nernst-Planck theory of open channels. Biophys J 76:A205
36. Hollerbach U, Chen D-P, Eisenberg RS (2001) Two- and three-dimensional Poisson-Nernst-Planck simulations of current flow through gramicidin-A. J Comp Sci 16:373-409
37. Im W, Roux B (2001) Brownian dynamics simulations of ions channels: a general treatment of electrostatic reaction fields for molecular pores of arbitrary geometry. Biophys J 115:4850-4861
38. Im W, Roux B (2002) Ion permeation and selectivity of OmpF porin: a theoretical study based on molecular dynamics, Brownian dynamics, and continuum electrodiffusion theory. J Mol Biol 322:851-869
39. Jacoboni C, Lugli P (1989) The Monte Carlo method for semiconductor device simulation. Springer, Berlin Heidelberg New York, pp 1-356
40. Jeans J (1960) The mathematical theory of electricity and magnetism. Cambridge University Press, London, p 195
41. Jerome JW (1995) Mathematical theory and approximation of semiconductor models. Springer, Berlin Heidelberg New York
42. Jerome JW (1996) Analysis of charge transport: a mathematical study of semiconductors. Springer, Berlin Heidelberg New York
43. Kerkhoven T (1998) On the effectiveness of Gummel's method. SIAM J Sci Stat Comp 9:48-60
44. Kerkhoven T, Saad Y (1992) On acceleration methods for coupled nonlinear elliptic systems. Numer Math 57:525-548
45. Kurnikova MG, Coalson RD, Graf P, Nitzan A (1999) A lattice relaxation algorithm for 3D Poisson-Nernst-Planck theory with application to ion transport through the gramicidin A channel. Biophys J 76:642-656
46. Länger P (1976) Diffusion-limited ion flow through pores. Biochim Biophys Acta 455:493-509
47. Levadny V, Aguilella VM, Belaya M (1998) Access resistance of a single conducting membrane channel. Biochim Biophys Acta 1368:338-342
48. Mamonov AB, Coalson RD, Nitzan A, Kurnikova MG (2003) The role of the dielectric barrier in narrow biological channels: a novel composite approach to modeling single-channel currents. Biophys J 84:3646-3661
49. Merzlyak PG, Yuldasheva LN, Rodrigues CG, Carneiro CMM, Krasilnikov OV, Bezrukov SM (1999) Polymeric nonelectrolytes to probe pore geometry: application to the α-toxin transmembrane channel. Biophys J 77:3023-3033
50. Moy G, Corry B, Kuyucak S, Chung S (2000) Tests of continuum theories as models of ion channels. I. Poisson-Boltzmann theory versus Brownian dynamics. Biophys J 78:2349-2363
51. Nadler B, Hollerbach U, Eisenberg RS (2003) Dielectric boundary force and its crucial role in gramicidin. Phys Rev E Stat Nonlin Soft Matter Phys 68:021905
52. Nadler B, Schuss Z, Hollerbach U, Eisenberg RS (2004) Saturation of conductance in single ion channels: the blocking effect of the near reaction field. Phys Rev 70:051912
53. Nadler B, Schuss Z, Singer A, Eisenberg R (2004) Ionic diffusion through confined geometries: from Langevin equations to partial differential equations. J Phys Condens Matter 16:S2153-S2165
54. Nonner W, Eisenberg B (1998) Ion permeation and glutamate residues linked by Poisson-Nernst-Planck theory in L-type calcium channels. Biophys J 75:1287-1305
55. Peskoff A, Bers DM (1988) Electrodiffusion of ions approaching the mouth of a conducting membrane channel. Biophys J 53:863-875
56. Rayleigh JWS (1945) The theory of sound, vol 2, chap XVI. Dover, New York, pp 170-183 (first edition 1878)
57. Romao JD, Price RH (1996) The conical resistor conundrum: a potential solution. Am J Phys 64:1150-1153
58. Rostovtseva TK, Aguilella VM, Vodyanoy I, Bezrukov SM, Parsegian VA (1998) Membrane surface-charge titration probed by gramicidin A channel conductance. Biophys J 75:1783-1792
59. Rostovtseva TK, Nestorovich EM, Bezrukov SM (2002) Partitioning of differently sized poly(ethylene glycol)s into OmpF porin. Biophys J 82:160-169
60. Scharfetter DL, Gummel HK (1969) Large signal analysis of a silicon read diode oscillator. IEEE Trans Electron Devices 16:64-77
61. Schirmer T, Phale PS (1999) Brownian dynamics simulation of ion flow through porin channels. J Mol Biol 294:1159-1167
62. Schuss Z, Nadler B, Eisenberg RS (2001) Derivation of PNP equations in bath and channel from a molecular model. Phys Rev E 64:036116-1
63. Selberherr S (1984) Analysis and simulation of semiconductor devices. Springer, Berlin Heidelberg New York
64. Smart OS, Coates GMP, Sansom MSP, Alder GM, Bashford CL (1998) Structure-based prediction of the conductance properties of ion channels. Faraday Discuss 111:185-189
65. Song J, Minetti CASA, Blake MS, Colombini M (1999) Meningococcal PorA/C1, a channel that combines high conductance and high selectivity. Biophys J 76:804-813
66. Vodyanoy I, Bezrukov SM, Colombini M (1992) Measurement of ion channel access resistance. Biophys J 61:A114
67. Zambrowicz EB, Colombini M (1993) Zero-current potentials in a large membrane channel - a simple theory accounts for complex behavior. Biophys J 65:1093-1100