Abstract
We compare free energies of counterion distributions in polyelectrolyte solutions predicted from the cylindrical Poisson-Boltzmann (PB) model and from the counterion condensation theories of Manning: CC1 (Manning, 1969a, b), which assumes an infinitely thin region of condensed counterions, and CC2 (Manning, 1977), which assumes a region of finite thickness. We consider rods of finite radius with the linear charge density of B-DNA in 1-1 valent and 2-2 valent salt solutions. We find that under all conditions considered here the free energy of the CC1 and the CC2 models is higher than that of the PB model. We argue that counterion condensation theory imposes nonphysical constraints and is, therefore, a poorer approximation to the underlying physics based on continuum dielectrics, point-charge small ions, Poisson electrostatics, and Boltzmann distributions. The errors in counterion condensation theory diminish with increasing distance from, or radius of, the polyion.
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Selected References
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- Anderson C. F., Record M. T., Jr The relationship between the poisson-boltzmann model and the condensation hypothesis: an analysis based on the low salt form of the Donnan coefficient. Biophys Chem. 1980 Jun;11(3-4):353–360. doi: 10.1016/0301-4622(80)87008-6. [DOI] [PubMed] [Google Scholar]
- Devore D. I., Manning G. S. Application of polyelectrolyte limiting laws to virial and asymptotic expansions for the Donnan equilibrium. Biophys Chem. 1974 Jun;2(1):42–48. doi: 10.1016/0301-4622(74)80022-0. [DOI] [PubMed] [Google Scholar]
- Fenley M. O., Manning G. S., Olson W. K. Approach to the limit of counterion condensation. Biopolymers. 1990;30(13-14):1191–1203. doi: 10.1002/bip.360301305. [DOI] [PubMed] [Google Scholar]
- Fuoss R. M., Katchalsky A., Lifson S. The Potential of an Infinite Rod-Like Molecule and the Distribution of the Counter Ions. Proc Natl Acad Sci U S A. 1951 Sep;37(9):579–589. doi: 10.1073/pnas.37.9.579. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Manning G. S. Limiting laws and counterion condensation in polyelectrolyte solutions. IV. The approach to the limit and the extraordinary stability of the charge fraction. Biophys Chem. 1977 Sep;7(2):95–102. doi: 10.1016/0301-4622(77)80002-1. [DOI] [PubMed] [Google Scholar]
- Manning G. S. On the application of polyelectrolyte "limiting laws" to the helix-coil transition of DNA. I. Excess univalent cations. Biopolymers. 1972;11(5):937–949. doi: 10.1002/bip.1972.360110502. [DOI] [PubMed] [Google Scholar]
- Manning G. S. The molecular theory of polyelectrolyte solutions with applications to the electrostatic properties of polynucleotides. Q Rev Biophys. 1978 May;11(2):179–246. doi: 10.1017/s0033583500002031. [DOI] [PubMed] [Google Scholar]
- Rae J. L., Dewey J., Rae J. S., Nesler M., Cooper K. Single potassium channels in corneal epithelium. Invest Ophthalmol Vis Sci. 1990 Sep;31(9):1799–1809. [PubMed] [Google Scholar]
- Record M. T., Jr, Anderson C. F., Lohman T. M. Thermodynamic analysis of ion effects on the binding and conformational equilibria of proteins and nucleic acids: the roles of ion association or release, screening, and ion effects on water activity. Q Rev Biophys. 1978 May;11(2):103–178. doi: 10.1017/s003358350000202x. [DOI] [PubMed] [Google Scholar]
- Record M. T., Jr, Lohman M. L., De Haseth P. Ion effects on ligand-nucleic acid interactions. J Mol Biol. 1976 Oct 25;107(2):145–158. doi: 10.1016/s0022-2836(76)80023-x. [DOI] [PubMed] [Google Scholar]
- Schellman J. A. Electrical double layer, zeta potential, and electrophoretic charge of double-stranded DNA. Biopolymers. 1977 Jul;16(7):1415–1434. doi: 10.1002/bip.1977.360160704. [DOI] [PubMed] [Google Scholar]