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Volumn 104, Issue 51, 2000, Pages 12324-12338

A dynamic lattice Monte Carlo model of ion transport in inhomogeneous dielectric environments: Method and implementation

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER SIMULATION; CRYSTAL LATTICES; ELECTROSTATICS; IONS; MATHEMATICAL MODELS; MONTE CARLO METHODS; PROTEINS; WATER;

EID: 0034516442     PISSN: 15206106     EISSN: None     Source Type: Journal    
DOI: 10.1021/jp001282s     Document Type: Article
Times cited : (91)

References (67)
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    • DelPhi V3.0; Columbia University, New York
    • Nicholls, A.; Sharp, K. A.; Honig, B. DelPhi V3.0; Columbia University, New York, 1990.
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    • Nicholls, A.1    Sharp, K.A.2    Honig, B.3
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    • and references therein
    • See, e.g., Caillol, J. M. J. Chem. Phys. 1999, 111, 6528, and references therein.
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    • Caillol, J.M.1
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    • describes Brownian dynamics simulations of ion transport through a pore with comparison to mean field (PB and PNP) calculations. Our methodology is different from the approach taken in these papers. Nevertheless our results are consistent with the observations made in these works
    • Three relevant papers have appeared after our paper was submitted, (a) Moy, G.; Corry, B.; Kuyucak, S.; Chung, S.-Ho Biophys. J. 2000, 78, 2349-2363,2364-2381, describes Brownian dynamics simulations of ion transport through a pore with comparison to mean field (PB and PNP) calculations. Our methodology is different from the approach taken in these papers. Nevertheless our results are consistent with the observations made in these works.
    • (2000) Biophys. J. , vol.78 , pp. 2349-2363
    • Moy, G.1    Corry, B.2    Kuyucak, S.3    Chung, S.-H.4
  • 26
    • 0033884302 scopus 로고    scopus 로고
    • describes a Brownian dynamics simulation of ion motion in a Porin channel. In this paper dielectric effects on self-energy and interparticle interactions of mobile ions are disregarded
    • (b) Im, W.; Seefeld, S.; Roux, B. Biophys. J. 2000, 79, 788, describes a Brownian dynamics simulation of ion motion in a Porin channel. In this paper dielectric effects on self-energy and interparticle interactions of mobile ions are disregarded.
    • (2000) Biophys. J. , vol.79 , pp. 788
    • Im, W.1    Seefeld, S.2    Roux, B.3
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    • A description of an equilibrium ionic channel in which the system is separated into an inner and an outer subsystems was recently presented by: Roux, B. Biophys. J. 1999, 77, 139.
    • (1999) Biophys. J. , vol.77 , pp. 139
    • Roux, B.1
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    • In the application of these periodic boundary conditions in the present work the corresponding interion interactions were computed with the minimum image approximation
    • In the application of these periodic boundary conditions in the present work the corresponding interion interactions were computed with the minimum image approximation.
  • 40
    • 0002621511 scopus 로고    scopus 로고
    • For example, composite grids could be used: one grid for the calculation of the electrostatic potential and a different, finer grid to represent ion configuration and ionic motion where the ion occupies more than a single grid cell. For the use of composite grids in electrostatic calculations see: Beck, T. L. J. Comput. Chem. 1999, 20, 1731-1739.
    • (1999) J. Comput. Chem. , vol.20 , pp. 1731-1739
    • Beck, T.L.1
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    • Monte Carlo Investigations of Phase Transitions and Critical Phenomena. Academic Press: New York, Chapter 1
    • See, e.g.: Binder, K. Monte Carlo Investigations of Phase Transitions and Critical Phenomena. Phase Transitions and Critical Phenomena; Academic Press: New York, 1976; Vol. 5b, Chapter 1, pp 1-105.
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    • Binder, K.1
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    • 2/(2a))(1/ε - 1)
    • 2/(2a))(1/ε - 1).
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    • and references therein. Controlling these errors is important in situations where system properties are dominated by the balance between opposing interactions, e.g., Coulombic repulsion vs dielectric attraction in solvated ions of the same charge sign
    • Using Coulomb potentials with a cutoff is a potential source of error. Alternatively, using Ewald summation in inhomogeneous restricted geometry systems (in our case a 2-dimensional Ewald summation is required) is computationally very demanding. Moreover, the inhomogeneous net charge distribution of mobile ions in our system would lead to unphysical interactions between periodic extensions of the system in the Ewald method. There are indications that the errors introduced by using Coulomb interactions with cutoff are not very large for many applications, see, e.g.: Schweighofer, K.; Benjamin, I. J. Chem. Phys. 2000,112, 1474-1482 and references therein. Controlling these errors is important in situations where system properties are dominated by the balance between opposing interactions, e.g., Coulombic repulsion vs dielectric attraction in solvated ions of the same charge sign
    • (2000) J. Chem. Phys. , vol.112 , pp. 1474-1482
    • Schweighofer, K.1    Benjamin, I.2
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    • note
    • c.
  • 47
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    • (0) reflects in the usual way the periodic boundary condition in the x- and y-direction and the finite system size in the z-direction
    • (0) reflects in the usual way the periodic boundary condition in the x- and y-direction and the finite system size in the z-direction.
  • 48
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    • 6
    • 6
  • 49
    • 33646030745 scopus 로고    scopus 로고
    • note
    • The unphysical image of polarization charges, induced by individual ions on the internal dielectric interfaces, on the imposed boundaries is not eliminated by this procedure. If, however, the imposed boundaries are far from the dielectric interfaces the resulting unphysical contribution to the total energy is small.
  • 50
    • 0004179874 scopus 로고
    • Wiley: New York
    • 2 = |r - (0, d)| are the distances between point r and the charges q and q′, respectively. (Note that we compute here only the polarization contribution to the potential Φ. These expressions, which diverge on the interface, become valid far enough (from distances of order a, or our grid spacing) from the interface.
    • (1975) Classical Electrodynamics, 2nd Ed.
    • Jackson, J.D.1
  • 52
    • 33646018762 scopus 로고    scopus 로고
    • As in section 6b, a part that is not eliminated comes from the image of the polarization charges induced at the internal dielectric boundaries; however, this contribution can be made small (see footnote 47)
    • As in section 6b, a part that is not eliminated comes from the image of the polarization charges induced at the internal dielectric boundaries; however, this contribution can be made small (see footnote 47).
  • 53
    • 85088886533 scopus 로고    scopus 로고
    • B = 80 is used in all calculations reported here, because in anticipated applications ions reside in a water environment
    • B = 80 is used in all calculations reported here, because in anticipated applications ions reside in a water environment.
  • 54
    • 0003668078 scopus 로고    scopus 로고
    • Elsevier: Amsterdam, This would, however, raise the issue of validity of the PB approximation for computing solvation energies near a system's boundary
    • An alternative procedure would be to calculate the contribution of the outer medium to the solvation energy of an ion near the boundary using, e.g., a Poisson-Boltzmann description of the outer medium (see, e.g.: Sadus, R. J. Molecular Simulations of Fluids; Elsevier: Amsterdam, 1999). This would, however, raise the issue of validity of the PB approximation for computing solvation energies near a system's boundary.
    • (1999) Molecular Simulations of Fluids
    • Sadus, R.J.1
  • 59
    • 33646070718 scopus 로고    scopus 로고
    • In fact, the correspondence between the two approaches is not complete because the PNP theory disregards the retarding effect of the ionic solvation atmosphere on an ion's motion. This retardation affects the conductivity of a dilute homogeneous electrolyte solution by a few percent
    • In fact, the correspondence between the two approaches is not complete because the PNP theory disregards the retarding effect of the ionic solvation atmosphere on an ion's motion. This retardation affects the conductivity of a dilute homogeneous electrolyte solution by a few percent.
  • 60
    • 85088887536 scopus 로고    scopus 로고
    • R = 0.096 M that correspond to the bulk concentration obtained in the equilibrium DLMC simulation. See Figure 5 and ensuing discussion
    • R = 0.096 M that correspond to the bulk concentration obtained in the equilibrium DLMC simulation. See Figure 5 and ensuing discussion.
  • 62
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    • In realistic biological channels, which may contain internal structural barriers, blocking of ionic motion as a result of ions being trapped for a relatively long time inside the channel may actually lead to a sublinear I/ΔΦ characteristic. See, e.g.: Andersen, O. S. Biophys. J. 1983, 41, 135.
    • (1983) Biophys. J. , vol.41 , pp. 135
    • Andersen, O.S.1


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