The simulation of ionic charge transport in biological ion channels: An introduction to numerical methods

Reviews in Computational Chemistry

Volumn 22, Issue , 2006, Pages 229-293

  Saraniti, Marco ^a   Aboud, Shela ^b   Eisenberg, Robert ^b  

^a Illinois Institute of Technology   (United States)

^b RUSH MEDICAL COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33750034205     PISSN: 10693599     EISSN: None     Source Type: Book Series    
DOI: 10.1002/0471780367.ch4     Document Type: Review

References (205)

1. B. Hille, Ionic Channels of Excitable Membranes, Third Edition, Sinauer, Sunderland, Massachusetts, 2001.
2. E. Neher and B. Sackmann, Nature, 260, 799 (1976). Single-Channel Currents Recorded from Membrane of Denervated Frog Muscle Fibers.
3. B. Sakmann and E. Neher, Eds., Single-Channel Recording, Second Edition, Kluwer Academic, New York, 1995.
4. F. M. Ashcroft, Ion Channels and Disease, Academic Press, San Diego, California, 2000.
5. L.-Q. Gu, O. Braha, S. Conlan, S. Cheley, and H. Bayley, Nature, 398, 686 (1999). Stochastic Sensing of Organic Analytes by a Pore-forming Protein Containing a Molecular Adapter.
6. H. Bayley and P. S. Cremer, Nature, 413, 226 (2001). Stochastic Sensors Inspired by Biology.
7. M. Goryll, S. Wilk, G. M. Laws, T. Thornton, S. Goodnick, M. Saraniti, J. Tang, and R. S. Eisenberg, Superlattices Microstruct., 34(3-6), 451-457 (2003). Silicon-based Ion Channel Sensor.
8. S. Sze, Physics of Semiconductor Devices, Second Edition, John Wiley & Sons, New York, 1981.
9. Semiconductor Industry Association, in International Technology Roadmap for Semiconductors, International SEMATECH, Austin, Texas, 1999, pp. 83-103. Process Integration, Devices, and Structures.
10. E. R. Davidson, in Reviews in Computational Chemistry, Vol. 6, K. B. Lipkowitz and D. B. Boyd, Eds., VHC Publishers, New York, 1990, pp. 373-382. Perspectives on Ab Initio Calculations.
11. H. J. C. Berendsen, in Computational Molecular Dynamics: Challenges, Methods, Ideas, P. Deuflhard, Ed., Springer-Verlag, 1999, pp. 3-36.
12. P. Gibbon and G. Sutmann, in Quantum Simulations of Many-Body Systems: From Theory to Algorithms, Lecture Notes, Vol. 10, J. Grotendorst, D. Marx, and A. Muramatsu, Eds., John von Neumann Institute for Computing, Jülich, Germany, 2002, pp. 467-506.
13. D. E. Elmore and D. A. Dougherty, Biophys. J., 85(3), 1512 (2003). Investigating Lipid Composition Effects on the Mechanosensitive Channel of Large Conductance (MscL) Using Molecular Dynamics Simulations.
14. B. L. de Groot, D. P. Tieleman, P. Pohl, and H. Grubmuller, Biophys. J., 82(6), 2934 (2002). Water Permeation through Gramicidin A: Desformylation and the Double Helix: A Molecular Dynamics Study.
15. W. K. Lee and P. C. Jordan, Biophys. J., 46(6), 805 (1984). Molecular Dynamics Simulation of Cation Motion in Water-Filled Gramicidin like Pores.
16. S. W. Chiu, S. Subramaniam, E. Jakobsson, and J. A. McCammon, Biophys. J., 56(2), 253 (1989). Water and Polypeptide Conformations in the Gramicidin Channel. A Molecular Dynamics Study.
17. B. Roux and M. Karplus, Biophys. J., 59(5), 961 (1991). Ion Transport in a Model Gramicidin Channel. Structure and Thermodynamics.
18. J. A. Szule and R. P. Rand, Biophys. J., 85(3), 1702 (2003). The Effects of Gramicidin on the Structure of Phospholipid Assemblies.
19. T. W. Allen, O. S. Anderson, and B. Roux, Proc. Natl. Acad. Sci. USA, 101(1), 117 (2004). Energetics of Ion Conduction Through the Gramicidin Channel.
20. M. G. Kurnikova, R. D. Coalson, P. Graf, and A. Nitzan, Biophys. J., 76(2), 642 (1999). A Lattice Relaxation Algorithm for Three-Dimensional Poisson-Nernst-Planck Theory with Application to Ion Transport Through the Gramicidin A Channel.
21. U. Hollerbach, D. P. Chen, D. D. Busath, and B. Eisenberg, Langmuir, 16(13), 5509 (2000). Predicting Function from Structure using the Poisson-Nernst-Plank Equations: Sodium Current in the Gramicidin A Channel.
22. U. Hollerbach, D. P. Chen, and R. S. Eisenberg, J. Sci. Comput., 16(4), 373 (2001). Two- and Three-Dimensional Poisson-Nernst-Plank Simulations of Current Flow Through Gramicidin A.
23. S. Edwards, B. Corry, S. Kuyucak, and S.-H. Chung, Biophys. J., 83(3), 1348 (2002). Continuum Electrostatics Fails to Describe Ion Permeation in the Gramicidin Channel.
24. T. W. Allen, T. Bastug, S. Kuyucak, and S.-H. Chung, Biophys. J., 84(4), 2159 (2003). Gramicidin A Channel as a Test Ground for Molecular Dynamics Force Fields.
25. LD Helix.
26. R. R. Ketchem, W. Hu, and T. A. Cross, Science, 261, 1457 (1993). High-Resolution Conformation of Gramicidin A in a Lipid Bilayer by Solid-State NMR.
27. L. E. Townsley, W. Tucker, S. Sham, and J. F. Hinton, Biochemistry, 40, 11676 (2001). Structures of Gramicidin A, B and C Incorporated in Sodium Dodecyl Sulfate Micelles.
28. T. W. Allen, O. S. Andersen, and B. Roux, J. Am. Chem. Soc., 125(32), 9868 (2003). Structure of Gramicidin a in a Lipid Bilayer Environment Determined Using Molecular Dynamics Simulations and Solid-State NMR Data.
29. 1H NMR.
30. R. R. Ketchem, W. Hu, and T. A. Cross, J. Biomol. NMR, 8(1), 1 (1996). Macromolecular Structure Elucidation with Solid-State NMR-Derived Orientation Constraints.
31. T. A. Harroun, W. T. Heller, T. M. Weiss, L. Yang, and H. W. Huang, Biophys. J., 76(6), 3176 (1999). Theoretical Analysis of Hydrophobic Matching and Membrane-Mediated Interactions in Lipid Bilayers Containing Gramicidin.
32. S.-W. Chiu, S. Subramaniam, and E. Jakobsson, Biophys. J., 76(4), 1929 (1999). Simulation Study of a Gramicidin/Lipid Bilayer System in Excess Water and Lipid. I. Structure of the Molecular Complex.
33. T. A. Harroun, W. T. Heller, T. M. Weiss, L. Yang, and H. W. Huang, Biophys. J., 76(2), 937 (1999). Experimental Evidence for Hydrophobic Matching and Membrane-Mediated Interactions in Lipid Bilayers Containing Gramicidin.
34. S.-W. Chiu, S. Subramaniam, and E. Jakobsson, Biophys. J., 76(4), 1939 (1999). Simulation Study of a Gramicidin/Lipid Bilayer System in Excess Water and Lipid. II. Rates and Mechanisms of Water Transport.
35. G. V. Miloshevsky and P. C. Jordan, Biophys. J., 86(1), 92 (2004). Gating Gramicidin Channels in Lipid Bilayers: Reaction Coordinates and the Mechanism of Dissociation.
36. K. M. Armstrong and S. Cukierman, Biophys. J., 82(3), 1329 (2002). On the Origin of Closing Flickers in Gramicidin Channels: A New Hypothesis.
37. G. S. Harms, G. Orr, M. Montal, B. D. Thrall, S. D. Colson, and H. P. Lu, Biophys. J., 85(3), 1826 (2003). Probing Conformational Changes of Gramicidin Ion Channels by Single-Molecule Patch-Clamp Fluorescence Microscopy.
38. D. P. Tieleman, P. C. Bigging, G. R. Smith, and M. S. P. Sansom, Quart. Rev. Biophys., 34(4), 473 (2001). Simulation Approaches to Ion Channel Strucuture-Function Relationships.
39. W. Humphrey, A. Dalke, and K. Schulten, J. Mol. Graphics Model., 14(1), 33 (1996). VMD-Visual Molecular Dynamics.
40. + Conduction and Selectivity.
41. + Channel-Fab Complex at 2.0 A Resolution.
42. Y. Jiang, A. Lee, J. Chen, M. Cadene, B. T. Chait, and R. MacKinnon, Nature, 417, 515 (2002). Crystal Structure and Mechanism of a Calcium-Gated Potassium Channel.
43. G. Yellen, Nature, 419, 35 (2002). The Voltage-Gated Potassium Channels and Their Relatives.
44. + Channel.
45. +-Channel Activation Gating.
46. + Channel.
47. C. A. Ahern and R. Horn, J. Gen. Physiol., 123, 205 (2004). Specificity of Charge-Carrying Residues in the Voltage Sensor of Potassium Channels.
48. + Channel: Electrostatic Stabilization of Monovalent Cations.
49. E. M. Nestorovich, T. K. Rostovtseva, and S. M. Bezrukov, Biophys. J., 85(6), 3718 (2003). Residue Ionization and Ion Transport Through OmpF Channels.
50. S. Varma and E. Jakobsson, Biophys. J., 86(2), 690 (2004). Ionization States of Residues in OmpF and Mutants: Effects of Dielectric Constant and Interactions Between Residues.
51. W. Im and B. Roux, J. Mol. Biol., 322(4), 851 (2002). Ion Permeation and Selectivity of OmpF Porin: A Theoretical Study Based on Molecular Dynamics, Brownian Dynamics, and Continuum Electrodiffusion Theory.
52. W. Im and B. Roux, J. Mol. Biol., 319(5), 1177 (2002). Ions and Counterions in a Biological Channel: A Molecular Dynamics Simulation of OmpF Porin from Escherichia Coli in an Explicit Membrane with 1 M KCl Aqueous Salt Solution.
53. A. Karshikoff, V. Spassov, S. W. Cowan, R. Ladenstein, and T. Schirmer, J. Mol. Biol., 240, 372 (1994). Electrostatic Properties of Two Porin Channels from Escherichia Coli.
54. A. Philippsen, W. Im, A. Engel, T. Schirmer, B. Roux, and D. J. Muller, Biophys. J., 82(3), 1667 (2002). Imaging the Electrostatic Potential of Transmembrane Channels: Atomic Probe Microscopy of OmpF Porin.
55. B. Alberts, D. Bray, A. Johnson, J. Lewis, M. Raff, K. Roberts, and P. Walter, Essential Cell Biology, Garland Publishing, New York, 1998.
56. K. V. Damodaran and K. M. Merz, Jr., in Reviews in Computational Chemistry, Vol. 5, K. B. Lipkowitz and D. B. Boyd, Eds., VHC Publishers, New York, 1994, pp. 269-298. Computer Simulation of Lipid Systems.
57. J. M. Berg, J. L. Tymoczlco, and L. Stryer, Biochemistry, Fifth Edition, W. H. Freeman, New York, 2001.
58. D. P. Tieleman, M. S. P. Sansom, and H. J. C. Berendsen, Biophys. J., 76(1), 40 (1999). Alamethicin Helices in a Bilayer and in Solution: Molecular Dynamics Simulations.
59. J. F. Nagle and S. Trsitram-Nagle, Curr. Opin. Struct. Biol., 10(4), 474 (2000). Lipid Bilayer Structure.
60. H. L. Scott, Curr. Opin. Struct. Biol., 12, 495 (2002). Modeling the Lipid Component of Membranes.
61. U. Essmann and M. L. Berkowitz, Biophys. J., 76(4), 2081 (1999). Dynamical Properties of Phospholid Bilayers from Computer Simulations.
62. E. Lindahl and O. Edholm, Biophys. J., 79(1), 426 (2000). Mesoscopic Undulations and Thickness Fluctuations in Lipid Bilayers from Molecular Dynamics Simulations.
63. I. P. Sugar, T. E. Thompson, and R. L. Biltonen, Biophys. J., 76(4), 2099 (1999). Monte Carlo Simulations of Two-Component Bilayers: DMPC/DSPC Mixtures.
64. A. Smondyrev and M. L. Berkowitz, Biophys. J., 77, 2075 (1999). Structure of Dipalmitoylphosphatidylcholine/Cholesterol Bilayer at Low and High Cholesterol Concentrations: Molecular Dynamics Simulations.
65. S. W. Chiu, E. Jakobsson, and S. Subramaniam, Biophys. J., 77, 2462 (1999). Combined Monte Carlo and Molecular Dynamics Simulation of Fully Hydrated Dioleyl and Palmitoyloleyl Phosphatidylcholine Lipid Bilayers.
66. S. E. Feller, Curr. Opin. Colloid Interface Sci., 5, 217 (2000). Molecular Dynamics Simulations of Lipid Bilayers.
67. E. Jakobsson, Trends Biochem. Sci., 22, 339 (1997). Computer Simulation Studies of Biological Membranes: Progress, Promise and Pittfalls.
68. G. Hummer, L. R. Pratt, and A. E. Garćia, J. Phys. Chem. A, 102(41), 7885 (1998). Molecular Theories and Simulation of Ions and Polar Molecules in Water.
69. J. Bockris and A. K. N. Reddy, Modern Electrochemistry, Second Edition, Vol. I, Ionics, Plenum Press, New York, 1998.
70. S. C. Li, M. Hoyles, S. Kuyucak, and S.-H. Chung, Biophys. J., 74(1), 37 (1998). Brownian Dynamics Study of Ion Transport in the Vestibule of Membrane Channels.
71. J.-P. Simonin, L. Blum, and P. Turq, J. Phys. Chem., 100(18), 7704 (1996). Real Ionic Solutions in the Mean Spherical Approximation. 1. Simple Salts in the Primitive Model.
72. J. M. G. Barthel, H. Krienke, and W. Kunz, in Topics in Physical Chemistry, Vol. 5, Springer, New York, 1998. Physical Chemistry of Electrolyte Solutions.
73. S. Durand-Vidal, J.-P. Simonin, and P. Turq, Electrolytes at Interfaces, Kluwer, Norwell, Massachusetts, 2000.
74. W. Im, M. Feig, and C. L. Brooks, III, Biophys. J., 85(5), 2900 (2003). An Implicit Membrane Generalized Born Theory for the Study of Structure, Stability, and Interactions of Membrane Proteins.
75. D. P. Tieleman, L. R. Forrest, M. S. P. Sansom, and H. J. C. Berendsen, Biochemistry, 37, 17554 (1998). Lipid Properties and the Orientation of Aromatic Residues in OmpF, Influenza M2, and Alamethicin Systems: Molecular Dynamics Systems.
76. T. Schirmer and P. Phale, J. Mol. Biol., 294,1159 (1999). Brownian Dynamics Simulation of Ion Flow Through Porin Channels.
77. T. B. Wolf and B. Roux, Protein: Struct., funct. and Genet., 24(1), 92 (1996). Structure, Energetics, and Dynamics of Lipid-Protein Interactions: A Molecular Dynamics Study of Gramicidin A Channel in a DMPC Bilayer.
78. T. P. Lybrand, in Reviews in Computational Chemistry, Vol. 1, K. B. Lipkowitz and D. B. Boyd, Eds., VHC Publishers, New York, 1990, pp. 295-320. Computer Simulation of Biomolecular Systems Using Molecular Dynamics and Free Energy Perturbation Methods.
79. D. P. Tieteman and H. J. C. Berendsen, Biophys. J., 74(6), 2786 (1998). A Molecular Dynamics Study of the Pores Formed by Escherichia coli OmpF Porin in a Fully Hydrated Palmitoyloleoylphosphatidylcholine Bilayer.
80. L. D. Shen, D. Bassolino, and T. Stouch, Biochemistry, 73, 3 (1997). Transmembrane Helix Structure, Dynamics, and Interactions: Multi-Nanosecond Molecular Dynamics Simulations.
81. P. G. Mezey, in Reviews in Computational Chemistry, Vol. 1, K. B. Lipkowitz and D. B. Boyd, Eds., VHC Publishers, New York, 1990, pp. 265-294. Molecular Surfaces.
82. J. D. Faraldo-Gomez, G. R. Smith, and M. S. P. Sansom, Eur. Biophys. J., 31, 217 (2002). Setting Up and Optimisation of Membrane Protein Simulations.
83. R. W. Hockney and J. W. Eastwood, Computer Simulation Using Particles, Adam Hilger, Bristol, United Kingdom, 1988.
84. D. G. Levitt, Biophys. J., 48(1), 19 (1985). Strong Electrolyte Continuum Theory Solution for Equilibrium Profiles, Diffusion Limitation, and Conductance in Charged Ion Channels.
85. M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids, Clarendon Press, Oxford, United Kingdom, 1987.
86. Y. Georgalis, A. M. Kierzek, and W. Sa, J. Phys. Chem. B, 104, 3405 (2000). Cluster Formation in Aqueous Electrolyte Solutions Observed by Dynamic Light Scattering.
87. C. Jacoboni and P. Lugli, The Monte Carlo Method for Semiconductor Device Equations, Springer-Verlag, NewYork, 1989.
88. P. C. Jordan, Biophys. J., 39(2), 157 (1982). Electrostatic Modeling of Ion Pores. I. Energy Barriers and Electric Field Profiles.
89. P. C. Jordan, Biophys. J., 41(2), 189 (1983). Electrostatic Modeling of Ion Pores. II. Effects Attributable to the Membrane Dipole Potential.
90. M. Cai and P. C. Jordan, Biophys. J., 57(4), 883 (1990). How Does Vestibule Surface Charge Affect Ion Conduction and Toxin Binding in a Sodium Channel?
91. - Pores: Electrostatic Effects of Charged Residues.
92. W. Nonner, D. P. Chen, and B. Eisenberg, Biophys. J., 74(5), 2327 (1998). Anomalous Mole Fraction Effect, Electrostatics, and Binding in Ionic Channels.
93. W. Nonner, L. Catacuzzeno, and B. Eisenberg, Biophys. J., 79(4), 1976 (2000). Binding and Selectivity in L-Type Calcium Channels: A Mean Spherical Approximation.
94. D. Boda, D. D. Busath, D. Henderson, and S. Sokolowski, J. Phys. Chem. B, 104(37), 8903 (2000). Monte Carlo Simulations of the Mechanism for Channel Selectivity: The Competition between Volume Exclusion and Charge Neutrality.
95. D. Boda, D. Gillespie, W. Nonner, D. Henderson, and B. Eisenberg, Phys. Rev. E, 69, 046702 (2004). Computing Induced Charges in Inhomogeneous Dielectric Media: Application in a Monte Carlo Simulation of Complex Ionic Systems.
96. D. Boda, D. Henderson, and D. D. Busath, J. Phys. Chem. B, 105(47), 11574 (2001). Monte Carlo Study of the Effect of Ion and Channel Size on the Selectivity of a Model Calcium Channel.
97. L. Greengard, Science, 265(5174), 909 (1994). Fast Algorithms for Classical Physics.
98. L. Greengard and V. Rokhlin, J. Comput. Phys., 135, 280 (1997). A Fast Algorithm for Particle Simulations.
99. F. S. Lee and A. Warshel, J. Chem. Phys., 97(5), 3100 (1992). A Local Field Method for Fast Evaluation of Long-Range Electrostatic Interactions in Molecular Simulations.
100. P. Ewald, Ann. Phys., 64, 253 (1921). Die Berechnung Optischer und Elektrostatischer Gitterpotentiale.
101. M. Deserno and C. Holm, J. Chem. Phys., 109(18), 7678 (1998). How to Mesh Up Ewald Sums. I. A Theoretical and Numerical Comparison of Various Particle Mesh Routines.
102. J. D.Jackson, Classical Electrodynamics, Second Edition, John Wiley & Sons, New York, 1975.
103. H.-Q. Ding, N. Karasawa, and W. A. Goddard, III, J. Chem. Phys., 97(6), 4309 (1992). Atomic Level Simulations on a Million Particles: The Cell Mulipole Method for Coulomb and London Nonbonded Interactions.
104. J. Shimada, H. Kaneko, and T. Takada, J. Comput. Chem., 15(1), 29 (1994). Performance of Fast Mulipole Methods for Calculating Electrostatic Interactions in Biomacromolecular Simulations.
105. C. A. White and M. Head-Gordon, J. Chem. Phys., 101(8), 6593 (1994). Derivation and Efficient Implementation of the Fast Mulitpole Method.
106. T. Schlick, in Interdisciplinary Applied Mathematics, Vol. 21, Springer, New York, 2000. Molecular Modeling and Simulation: An Interdisciplinary Guide.
107. A. W. Appel, SIAM. Sci. Stat. Comput., 6(1), 85 (1985). An Efficient Program for Many-Body Problems.
108. 3M, FMM, and the Ewald Method for Large Periodic Coulombic Systems.
109. A. R. Leach, Molecular: Modelling Principles and Applications, Second Edition, Prentice-Hall, Harlow, United Kingdom, 2001.
110. P. Crozier, R. L. Rowley, D. Henderson, and D. Boda, Chem. Phys. Lett., 325(5-6), 675 (2000). A Corrected 3D Ewald Calculation of the Low Effective Temperature Properties of the Electrochemical Interface.
111. D. M. Heyes J. Chem. Phys., 74(3), 1924 (1981). Electrostatic Potentials and Fields in Infinite Point Charge Lattices.
112. T. A. Darden, D. York, and L. Pedersen, J. Chem. Phys., 98(12), 10089 (1993). Particle Mesh Ewald: An Nlog(N) Method for Ewald Sums in Large Systems.
113. A. Y. Toukmaji and J. A. Board, Comput. Phys. Commun., 95, 73 (1996). Ewald Summation Techniques in Perspective: A Survey.
114. N. Karasawa and W. A. Goddard, III, J. Phys. Chem., 93, 7320 (1989). Acceleration of Convergence for Lattice Sums.
115. G. Rajagopal and R. M. L. J. Needs, J. Comput. Phys., 115, 399 (1994). An Optimized Ewald Method for Long-Ranged Potentials.
116. U. Essmann, L. Perera, M. L. Berkowitz, T. A. Darden, H. Lee, and L. Pedersen, J. Chem. Phys., 103(19), 8577 (1995). A Smooth Particle Mesh Ewald Method.
117. C. Pommerell and W. Fichtner, SIAM J. Sci. Stat. Comput., 15(2), 460 (1994). Memory Aspects and Performance of Iterative Solvers.
118. D. M. Young, Iterative Solution of Large Linear Systems, Academic Press, New York, 1971.
119. G. Dahlquist and Å. Björck, Numerical Methods, Prentice-Hall, Englewood Cliffs, New Jersey, 1974.
120. P. J. Roache, Computational Fluid Dynamics, Hermosa Publishers, Albuquerque, New Mexico, 1976.
121. B. A. Carré, Comput. J., 4(1), 73 (1961). The Determination of the Optimum Accelerating Factor for Successive Over-Relaxation.
122. L. W. Ehrlich, in Elliptic Problem Solvers, M. H. Schultz, Ed., Academic Press, New York, 1981, pp. 255-259.
123. L. M. Adams and H. F. Jordan, SIAM J. Sci. Stat. Comput., 7(2), 490 (1986). Is SOR Color-Blind?
124. S. Vandewalle, in Parallel Multigrid Waveform Relaxation for Parabolic Problems, B.G. Teubner, Stuttgart, Germany, 1993. Teubner Skripten zur Numerik.
125. W. Hackbush, Multi-Grid Methods and Applications, Springer-Verlag, Berlin, Germany, 1985.
126. A. Brandt, Math. Comput., 31(138), 333 (1977). Multi-Level Adaptive Solutions to Boundary-Value Problems.
127. A. Brandt, in Elliptic Problem Solvers, M. H. Schultz, Ed., Academic Press, New York, 1981, pp. 39-84. Multigrid Solvers on Parallel Computers.
128. P. S. Ramanathan and H. L. Friedman, J. Chem. Phys., 54(3), 1086 (1971). Study of a Refined Model for Aqueous 1-1 Electrolytes.
129. R. S. Berry, S. A. Rice, and J. Ross, Physical Chemistry, Second Edition, Oxford University Press, Oxford, United Kingdom, 2000.
130. W. Im, S. Seefeld, and B. Roux, Biophys. J., 79(2), 788 (2000). A Grand Canonical Monte Carlo-Brownian Dynamics Algorithm for Simulating Ion Channels.
131. + Motion in Water.
132. Y. Yang, D. Henderson, P. S. Crozier, R. L. Rowley, and D, D. Busath, Mol. Phys., 100(18), 3011 (2001). Permeation of Ions Through a Model Biological Channel: Effect of Periodic Boundary Conditions and Cell Size.
133. B. Nadler, T. Nach, and A. Schuss, SIAM J. Appl. Math., 63(3), 850 (2003). Connecting a Discrete Ionic Simulation to a Continuum.
134. B. Corry, M. Hoyles, T. Allen, M. Walker, S. Kuyucak, and S.-H. Chung, Biophys. J., 82(4), 1975 (2002). Reservoir Boundaries in Brownian Dynamics Simulations of Ion Channels.
135. C. K. Birdsall and A. B. Langdon, Plasma Physics via Computer Simulation, Institute of Physics Publishing, Philadelphia, Pennsylvania, 1991.
136. R. S. Eisenberg, J. Membr. Biol., 150(1), 1 (1996). Computing the Field in Proteins and Channels.
137. A. Syganow and E. von Kitzing, Biophys. J., 76(2), 768 (1999). (In)validity of the Constant Field and Constant Currents Assumptions in Theories of Ion Transport.
138. B. Roux and S. Bernéche, Biophys. J., 82(3), 1681 (2002). On the Potential Functions used in Molecular Dynamics Simulations of Ion Channels.
139. D. L. Ermak, J. Chem. Phys., 62(10), 4189 (1975). A Computer Simulation of Charged Particles in Solution. I. Technique and Equilibrium Properties.
140. P. Turq, F. Lantelme, and H. L. Friedman, J. Chem. Phys., 66(7), 3039 (1977). Brownian Dynamics: Its Application to Ionic Solutions.
141. W. F. van Gunsteren and H. J. C. Berendsen, Mol. Phys., 45(3), 637 (1982). Algorithms for Brownian Dynamics.
142. L. Verlet, Phys. Rev., 159(1), 159 (1967). Computer " Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules.
143. E. Jakobsson, Method. Enzymol., 14, 342 (1998). Using Theory and Simulation to Understand Permeation and Selectivity in Ion Channels.
144. P. S. Crozier, D. Henderson, R. L. Rowley, and D. D. Busath, Biophys. J., 81(6), 3077 (2001). Model Channel Ion Currents in NaCl-Extended Simple Point Charge Water Solution with Applied-Field Molecular Dynamics.
145. P. S. Crozier, R. L. Rowley, N. B. Holladay, D. Henderson, and D. D. Busath, Phys. Rev. Lett., 86(11), 2467 (2001). Molecular Dynamics Simulation of Continuous Current Flow Through a Model Biological Membrane Channel.
146. W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W. Impey, and M. L. Klein, J. Chem. Phys., 79(2), 926 (1983). Comparison of Simple Potential Functions for Simulating Liquid Water.
147. A. Wallqvist and R. D. Mountain, in Reviews in Computational Chemistry, Vol. 13, K. B. Lipkowitz and D. B. Boyd, Eds., VHC Publishers, New York, 1999, pp. 183-247. Molecular Models of Water: Derivation and Description.
148. H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, and J. Hermans in Intermolecular Forces, B. Pullman, Ed., Reidel, Dodrecht, the Netherlands, 1981, pp. 331-342. Interaction Models for Water in Relation to Protein Hydration.
149. W. L. Jorgensen, J. Chem. Phys., 77(7), 4156 (1982). Revised TIPS for Simulation of Liquid Water and Aqueous Solutions.
150. H. J. C. Berendsen, J. R. Grigera, and T. P. Straatsma, J. Phys. Chem., 91, 6269 (1987). The Missing Term in Effective Pair Potentials.
151. T. Schlick, in Lecture Notes in Computational Science and Engineering, Vol. 4, P. Deuflhard, J. Hermans, B. Leimkuhler, A. E. Mark, S. Reich, and R. D. Skeel, Eds., Springer, New York, pp. 227-262. Computational Molecular Dynamics: Challenges, Methods, Ideas.
152. M. Tuckerman, B. J. Berne, and G. J. Martyna J. Chem. Phys., 97(3), 1990 (1992). Reversible Multiple Time Scale Molecular Dynamics.
153. X. Qian and T. Schlick, J. Chem. Phys., 116(14), 5971 (2002). Efficient Multiple-Time-Step Integrators with Distance-Based Force Splitting for Particle-Mesh-Ewald Molecular Dynamics Simulations.
154. T. Schlick, in Interdisciplinary Applied Mathematics, Vol. 21, Springer, New York, 2002. Molecular Modeling and Simulation.
155. + Channel in a Bilayer Membrane.
156. + Channel.
157. T. P. Straatsma, in Reviews in Computational Chemistry, Vol. 9, K. B. Lipkowitz and D. B. Boyd, Eds., VHC Publishers, New York, 1996, pp. 81-127. Free Energy by Molecular Simulation.
158. + Channel.
159. S. W. Chiu, J. A. Novotny, and E. Jakobsson, Biophys. J., 64(1), 98 (1993). The Nature of Ion and Water Barrier Crossings in a Simulated Ion Channel.
160. A. B. Mamonov, R. D. Coalson, A. Nitzan, and M. G. Kurnikova, Biophys. J., 84(6), 3646 (2003). The Role of the Dielectric Barrier in Narrow Biological Channels: A Novel Composite Approach to Modeling Single-Channel Currents.
161. B. Roux, Biophys. J., 77(1), 139 (1999). Statistical Mechanical Equilibrium Theory of Selective Ion Channels.
162. G. M. Torrie and J. P. Valleau, J. Comput. Phys., 23, 187 (1977). Nonphysical Sampling Distributions in Monte Carlo Free-energy Estimation: Umbrella Sampling.
163. O. M. Becker, A. D. MacKerell, Jr., B. Roux, and M. Watanabe, Eds., Computational Biochemistry and Biophysics, Marcel Dekker, New York, 2001.
164. D. Beglov and B. Roux, J. Chem. Phys., 100(12), 9050 (1994). Finite Representations of an Infinite Bulk System: Solvent Boundary Potential for Computer Simulations.
165. M. Jalaie and K. B. Lipkowitz, in Reviews in Computational Chemistry, Vol. 14, K. B. Lipkowitz and D. B. Boyd, Eds., Wiley-VCH Publishers, New York, 2000, pp. 441-486. Published Force Field Parameters for Molecular Mechanics, Molecular Dynamics, and Monte Carlo Simulations.
166. T. A. Halgren and W. Damm, Curr. Opin. Struct. Biol., 11(2), 236 (2001). Polarizable Force Fields.
167. S. W. Rick and S. J. Stuart, in Reviews in Computational Chemistry, Vol 18, K. B. Lipkowitz and D. B. Boyd, Eds., Wiley-VHC Publishers, New York, 2002, pp. 89-146. Potentials and Algorithms for Incorporating Polarizability in Computer Simulations.
168. T. Allen, S. Kuyucak, and S.-H. Chung, J. Chem. Phys., 111(17), 7985 (1999). The Effect of Hydrophobic and Hydrophilic Channel Walls on the Structure and Diffusion of Water and Ions.
169. C. Domene and M. S. P. Sansom, Biophys. J., 85(5), 2787 (2003). Potassium Channel, Ions, and Water: Simulation Studies Based on the High Resolution X-Ray Structure of KcsA.
170. S. W. Rick, S. J. Stuart, and B. J. Berne, J. Chem. Phys., 101(7), 6141 (1994). Dynamical Fluctuating Charge Force Fields: Application to Liquid Water.
171. J. L. Banks, G. A. Kaminsky, R. Zhou, D. T. Mainz, B. J. Berne, and R. A. Friesner, J. Chem. Phys., 110(2), 741 (1999). Parametrizing a Polarizable Force Field from Ab Initio Data. I. The Fluctuating Point Charge Model.
172. H. A. Stern, G. A. Kaminski, J. L. Banks, R. Zhou, B. J. Berne, and R. A. Friesner, J. Phys. Chem. B, 103(22), 4730 (1999). Fluctuating Charge, Polarizable Dipole, and Combined Models: Parametrization from Ab Initio Quantum Chemistry.
173. B. W. Arbuckle and P. Clancy, J. Chem. Phys., 116(12), 5090 (2002). Effects of the Ewald Sum on the Free Energy of the Extended Simple Point Charge Model for Water.
174. J. Hermans, H. J. C. Berendsen, W. F. van Gunsteren, and J. P. M. Postma, Biopolymers, 23, 1513 (1984). A Consistent Empirical Potential for Water-Protein Interactions.
175. H. E. Alper and R. M. Levy J. Chem. Phys., 91(2), 1242 (1989). Computer Simulation of the Dielectric Properties of Water: Studies of the Simple Point Charge and Transferrable Intermolecular Potential Models.
176. S.-H. Chiu, E. Jakobsson, S. Subramaniam, and J. A. McCammon, Biophys. J., 60(1), 273 (1991). Time-Correlation Analysis of Simulated Water Motion in Flexible and Rigid Gramicidin Channels.
177. A. Fick, Annalen der Physik und Chemie, 94, 59 (1855). Über Diffusion.
178. C. W. Gardiner, in Springer Series in Synergetics, Vol. 13, Springer, New York, 1983. Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences.
179. P. E. Kloeden and E. Platen, in Applications of Mathematics, Corrected Third Edition, Springer-Verlag, 1999. Numerical Solution of Stochastic Differential Equations.
180. R. S. Eisenberg, M. M. Klosek, and Z. Schuss, J. Chem. Phys., 102(4), 1767 (1995). Diffusion as a Chemical Reaction: Stochastic Trajectories Between Fixed Concentrations.
181. D. A. McQuarrie, Statistical Mechanics, University Science Books, Sausalito, California, 2000.
182. S. A. Rice and P. Gray, in Monographs in Statistical Physics and Thermodynamics, Vol. 8, Wiley Interscience, New York, 1965. The Statistical Mechanics of Simple Liquids.
183. N. W. Ashcroft and N. D. Mermin, Solid State Physics, Holt-Sauders International Editions, Tokyo, 1981.
184. G. Baccarani and M. Wordeman, Solid-State Electron., 28, 407 (1985). An Investigation of Steady State Velocity Overshoot Effects in Si and GaAs Devices.
185. D. P. Chen, R. S. Eisenberg, T. W. Jerome, and C. Shu, Biophys. J., 69, 2304 (1995). Hydrodynamic Model of Temperature Change in Open Ionic Channels.
186. C. M. Snowden, Introduction to Semiconductor Device Modelling, World Scientific Publishing, Singapore, 1986.
187. H. K. Gummel, IEEE Trans. Elect. Dev., ED-11, 455 (1964). A Self-Consistent Iterative Scheme for One-Dimensional Steady State Transistor Calculations.
188. D. L. Sharfetter and H. K. Gummel, IEEE Trans. Elect. Dev., ED-16(1), 64 (1969). Large-Signal Analysis of a Silicon Read Diode Oscillator.
189. J. Molenaar, Multigrid Methods for Semiconductor Device Simulation Technical Report CWI TRACT 100, Center for Mathematics and Computer Science, Amsterdam, the Netherlands, 1993.
190. D. G. Levitt, Biophys. J., 52(3), 455 (1987). Exact Continuum Solution for a Channel that Can be Occupied by Two Ions.
191. A. E. Cardenas, R. D. Coalson, and M. G. Kurnikova, Biophys. J., 79(1), 80 (2000). Three-Dimensional Poisson-Nernst-Planck Theory Studies: Influence of Membrane Electrostatics on Gramicidin A Channel Conductance.
192. T. van der Straaten, S. Varma, S. W. Chiu, J. Tang, N. Aluru, R. S. Eisenberg, U. Ravaioli, and E. Jakobsson, in M. Laudon and B. Romanowicz, Eds., Proceedings of the Second International Conference on Computational Nanoscience and Nanotechnology - ICCN2002, San Juan, Puerto Rico (2002) pp. 60-63.
193. R. S. Eisenberg, J. Membr. Biol., 150, 1 (1996). Computing the Field in Protein and Channels.
194. B. Honig and A. Nichols, Science, 268, 1144 (1995). Classical Electrostatics in Biology and Chemistry.
195. G. Lamm, in Reviews in Computational Chemistry, Vol. 19, K. B. Lipkowitz, R. Larter, and T. R. Cundari, Eds., wiley-VHC Publishers, New York, 2003, pp. 147-365. The Poisson-Boltzmann Equation.
196. T. Weiss, Cellular Biophysics, Vol. 1-2, MIT Press, Cambridge, Massachusetts, 1996.
197. B. Corry, S. Kuyucak, and S.-H. Chung, J. Gen. Physiol., 114, 597 (1999). Test of Poisson-Nernst-Plank Theory in Ion Channels.
198. B. Corry, S. Kuyucak, and S.-H. Chung, Biophys. J., 78(5), 2364 (2000). Tests of Continuum Theories as Models of Ion Channels. II. Poisson-Nernst-Planck Theory versus Brownian Dynamics.
199. G. Moy, B. Corry, S. Kuyucak, and S.-H. Chung, Biophys. J., 78(5), 2349 (2000). Tests of Continuum Theories as Models of Ion Channels. I. Poisson-Boltzmann Theory versus Brownian Dynamics.
200. B. Nadler, U. Hollerbach, and R. S. Eisenberg, Phys. Rev. E, 68, 021905 (2003). Dielectric Boundary Force and Its Crucial Role in Gramicidin.
201. B. Corry, S. Kuyucak, and S.-H. Chung, Biophys. J., 84(6), 3594 (2003). Dielectric Self-Energy in Poisson-Boltzmann and Poisson-Nernst-Planck Models of Ion Channels.
202. R. S. Eisenberg, Proceedings of the Biophysical Society Meeting, Washington, DC (1993). From Structure to Permeation in Open Ionic Channels.
203. R. S. Eisenberg, in Advanced Series in Physical Chemistry, Vol. 7, New Developments and Theoretical Studies of Proteins. World Scientific, London, 1996, pp. 269-358. Atomic Biology, Electrostatics, and Ionic Channels.
204. R. J. Mashl, Y. Tang, J. Schnitzer, and E. Jakobsson, Biophys. J., 81(5), 2473 (2001). Hierarchical Approach to Predicting Permeation in Ion Channels.
205. M. F. Schumaker, R. Pomes, and B. Roux, Biophys. J., 79(6), 2840 (2000). A Combined Molecular Dynamics and Diffusion Model of Single Proton Conduction through Gramicidin.