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  • 1
    Electronic Resource
    Electronic Resource
    Monte Carlo determination of the distribution of ions about a cylindrical polyelectrolyte (1984)
    New York : Wiley-Blackwell
    Biopolymers 23 (1984), S. 271-285 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: We report a calculation of the distribution of small ions around a charged cylinder representing a polyelectrolyte molecule in solution. The Monte Carlo method of Metropolis, Rosenbluth, and Teller was used to avoid the inaccuracies known to be associated with the Poisson-Boltzmann equation. The systems examined contained a long polyelectrolyte cylinder with charge parameter, χ, equal to 4.2, corresponding approximately to a DNA molecule. In one model, the cylinder had charges on its axis and an exclusion radius to the center of the small ions equal to 10 Å, while the small ions had various radii in the range from 1 to 10 Å and one or two protonic charges. Various systems were studied; some had one species of small ion alone, others had mixtures of different types. The results showed good agreement with the solution of the Poisson-Boltzmann equation when only the species with 1-Å radius was present, but considerable discrepancies appeared with larger ions as a result of excluded volume interactions between the latter. Deviations from the Poisson-Boltzmann equation also appeared when both positive and negative small ions were present; the deviations were in the direction of a higher concentration of both counter- and co-ions, but particularly co-ions, close to the polyelectrolyte. In another model, the charges were arranged along two helices on the surface of the cylinder; the resulting radial distribution of small ions was not much different from that found when the charges were situated on the axis. In all cases there was a striking accumulation of counterions in a layer of concentration exceeding 1 mol/L at the surface of the polyion.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bip.360230208
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  • 2
    Electronic Resource
    Electronic Resource
    Distribution of counterions around a cylindrical polyelectrolyte and manning's condensation theory (1984)
    New York : Wiley-Blackwell
    Biopolymers 23 (1984), S. 287-312 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The distribution of counterions around a charged polyion cylinder is calculated by several methods. First, the Debye-Hückel approximation is used, and it is shown that Manning's condensation hypothesis is necessry to avoid overneutralization of the polyion charges by the counterions when the linear-charge-density parameter, ξ, of the polyion exceeds the critical value of unity. However, it appears that this method of getting this result involves inconsistent application of Debye-Hückel theory. Therefore, we turn to the analytical solution of the Poisson-Boltzmann equation that was obtained by Alfrey, Berg, and Morawetz for a polyion cylinder plus a neutralizing number of counterions but without added salt. One of the integration constants of this solution is a radius, which we call RM, within which lies precisely the fraction of counterions that Manning assumes to condense in his theory. This radius can be rather large, however, so that the “Manning fraction” of condensed ions actually forms a diffuse cloud whose size varies with the polyelectrolyte concentration; RM varies as κ-1/2, where κ is the Debye-Hückel screening parameter. The Manning fraction, 1 - 1/ξ, and its associated radius are unique in their behavior with dilution; smaller fractions stay within finite radii, while with larger fractions the corresponding radii increase as κ-1. Thus, the condensation hypothesis does have a simple mathematical foundation in the Poisson-Boltzmann equation. Finally, by comparison with numerical solutions, we find that these conclusions are not significantly changed even when salt is added to the polyelectrolyte. A short table of numerical solutions of the Poisson-Boltzmann equation in cylindrical geometry is given, together with tables of coefficients tht enable one to discover the particular solution that applies for a given polyion radius and charge density.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bip.360230209
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Relationship between the energy of superhelix formation, the shear modulus, and the torsional brownian motion of DNA (1978)
    New York : Wiley-Blackwell
    Biopolymers 17 (1978), S. 1939-1955 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The torsional energy of a DNA is the energy involved when the average angle between adjacent base pairs is modified under applied constraints. A relationship is established between the energy of superhelix formation of a upercoiled DNA and its torsional energy. This relationship, valid when the number of the tertiary turns of the supercoiled DNA is small, contains the ratio of the bending to the torsional elastic paramaters of the DNA. From this relationship, the fluctations of the number of tertiary turns of the supercoiled DNA may be compared to those of the DNA with only one sinle-strand scission. An expression for the shear modulus of the DNA is derived from the anisotropy of the fluorescnece of the intercalated ethidium [Wahl et al. (190) Proc. Natl. Acad. Sci. USA 65, 417-421.]. The value of te torsional elastic parameter deduced from these computations is very close to the parameter of the energy of the superhelix formation determined on supercoiled DNAs by different authors. The energy that must be given to twist it. Consequently, the number of crossovers determined using the EM technique should be much less than the value deduced from the amount of ethiium necessary words, the first ethidium cations intercalating into a relaxed, closed double-standard DNA change the twist of the DNA but not its tertiary structure.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bip.1978.360170810
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    Paper (German National Licenses)
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