Ionic atmosphere of rodlike polyelectrolytes. A hypernetted chain study

Bacquet, Russell J.; Rossky, Peter J.

doi:10.1021/j150656a046

Cited by 105 publications

(54 citation statements)

References 13 publications

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“…Such finitesize effects at low ξ are also observed in previous numerical studies, which have devised simulations in linear scale and thus considered only small confinement volumes per polymer (typically ∆ < 10) [24,26,64,65,66]. In some studies [72], these effects have been interpreted as an evidence for counterion condensation at small ξ, leading to the incorrect conclusion that no condensation transition exists.…”

Section: Simulation Results In 3dmentioning

confidence: 69%

Scaling and universality in the counterion-condensation transition at charged cylinders

2006

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Counterions at charged rod-like polymers exhibit a condensation transition at a critical temperature (or equivalently, at a critical linear charge density for polymers), which dramatically influences various static and dynamic properties of charged polymers. We address the critical and universal aspects of this transition for counterions at a single charged cylinder in both two and three spatial dimensions using numerical and analytical methods. By introducing a novel Monte-Carlo sampling method in logarithmic radial scale, we are able to numerically simulate the critical limit of infinite system size (corresponding to infinite-dilution limit) within tractable equilibration times. The critical exponents are determined for the inverse moments of the counterionic density profile (which play the role of the order parameters and represent the inverse localization length of counterions) both within mean-field theory and within Monte-Carlo simulations. In three dimensions, we demonstrate that correlation effects (neglected within mean-field theory) lead to an excessive accumulation of counterions near the charged cylinder below the critical temperature (condensation phase), while surprisingly, the critical region exhibits universal critical exponents in accord with the mean-field theory. Also in contrast with the typical trend in bulk critical phenomena, where fluctuations are strongly enhanced in lower dimensions, we demonstrate, using both numerical and analytical approaches, that the mean-field theory becomes exact for the 2D counterion-cylinder system at all temperatures (Manning parameters), when number of counterions tends to infinity. For finite particle number, however, the 2D problem displays a series of peculiar singular points (with diverging heat capacity), which reflect successive de-localization events of individual counterions from the central cylinder. In both 2D and 3D, the heat capacity shows a universal jump at the critical point, and the energy develops a pronounced peak. The asymptotic behavior of the energy peak location is used to locate the critical point, which is also found to be universal and in accordance with the mean-field prediction.

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Section: Simulation Results In 3dmentioning

confidence: 69%

Scaling and universality in the counterion-condensation transition at charged cylinders

2006

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“…None of the studies reported to date covers the range of salt concentrations we have explored, and except for two cases (16,17) the papers published were concerned exclusively with the B form of DNA modeled as an unstructured infinite charged cylinder (12)(13)(14)(15). For the Poisson-Boltzmann treatments based on realistic B DNA structural models similar to that presented here (16,17), quantitative results comparable, for example, to the cylindrically averaged distributions given in Fig.…”

Section: Methodsmentioning

confidence: 73%

“…The treatments have substantial differences in the structural modeling of DNA and the use of statistical approximations. If one pictures a DNA structure as an infinitely long uniformly charged cylinder, it is straightforward to compute the average cylindrically symmetric ionic distributions through the numerical solution of the Poisson-Boltzmann (10-12) and hypernetted chain equations (13,14) This brief overview clearly shows that a general, fairly accurate, computationally efficient method to approximately solve the problem at hand for arbitrarily complex biomolecular structures over a wide range of bulk ionic concentrations is highly desirable but has been previously unavailable. We present here an approach based on the potentials of mean force framework (19-21) that emphasizes the role of realistic structural modeling and effective ionic interactions and has been found to describe simple salt effects on DNA structure and structural transitions very well (19)(20)(21)(22)(23)(24)(25).…”

mentioning

confidence: 99%

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confidence: 99%

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Computation of ionic distributions around charged biomolecular structures: results for right-handed and left-handed DNA.

Klement

Soumpasis

Jovin

1991

Proc. Natl. Acad. Sci. U.S.A.

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We introduce an efficient computational methodology employing the potentials of mean force approach for estimating the detailed three-dimensional ionic distributions around arbitrarily complex charged biomolecular structures for all monovalent salt concentrations of practical interest (e.g., 0.1-5.0 M NaCl). Such distributions are required for specifying thermodynamic and structure-specific features of ion-mediated interactions of charged proteins, DNA and RNA, membranes, and macromolecular assemblies. As a first application, we present results for distributions around the B and Z, conformers of the DNA oligomer d(C-G)j8sd(C-G)js. The ionic microenvironment depends strongly on the DNA conformation, sequence, and bulk salt concentration.The computation of ionic distributions around highly charged biomolecules has been a subject ofcontinuous interest for the past 20 years due to the importance of the ionic environment for structural stability and transitions as well as for intermolecular.interactions and binding equilibria. For example, in the case of DNA, ionic effects play a central role in the extensively studied B -+ Z transition (for recent reviews, see refs. 1 and 2), at all levels of DNA structural organization (refs. 3 and 4 and references therein), and in ligand-DNA binding equilibria (5).The approaches proposed to date for computing ionic distributions around DNA vary widely with respect to (i) the structural modeling of the DNA-water-ions system, (ii) the statistical approximations employed, (iii) the computational complexity, (iv) the range of bulk ionic concentrations, and (v) the DNA conformations studied. If the water, ions, and DNA components are described microscopically, the only currently feasible way to determine ionic distributions is by large-scale computer simulations (i.e., Monte Carlo and molecular dynamics), as reported by Clementi and Corongiu (6-8) and more recently by van Gunsteren et al. (9). These calculations are extremely costly and can only be performed practically in the absence of added salt. For example, to simulate a 0.1 M NaCl electrolyte around DNA, one has to consider at least 50 anion-cation pairs and 25,000 water molecules in the central simulation box, an effort that is at present impossible.In previous studies water has been represented as a dielectric continuum and the ions have been considered either as hard or soft spheres or simply point particles. The treatments have substantial differences in the structural modeling of DNA and the use of statistical approximations. If one pictures a DNA structure as an infinitely long uniformly charged cylinder, it is straightforward to compute the average cylindrically symmetric ionic distributions through the numerical solution of the Poisson-Boltzmann (10-12) and hypernetted chain equations (13,14) This brief overview clearly shows that a general, fairly accurate, computationally efficient method to approximately solve the problem at hand for arbitrarily complex biomolecular structures over a wide range of bulk ionic ...

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“…3, where u (r) accounts for the exclusion of small ions from the interior of the polyion. For a "hard" polyion, ui(r) =00 if r < a, and ui(r) = 0 if r -a. Alternatively, for a "soft" polyion, ur) 0.8 kBT (alr)9 (40). Fig.…”

Section: Rationalementioning

confidence: 99%

Distribution of ions around DNA, probed by energy transfer.

Wensel¹,

Meares²,

Vlachy³

et al. 1986

Proc. Natl. Acad. Sci. U.S.A.

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Measurements of the effect of DNA on rates of bimolecular energy transfer between ions provide a direct indication of how cations cluster in regions near DNA and how anions are repelled from the same regions. Energy transfer from luminescent lanthanide ions (in the "rapid-diffusion" limit) probes collision frequencies that are dependent on the equilibrium spatial distributions of ions. The addition of 1 mM DNA (phosphate) to a 2 mM salt solution increases the overall collision frequency between monovalent cations by a factor of 6 ± 1.5; it increases the divalent-monovalent cation collision frequency by a factor of 29 ± 3; and it decreases the divalent cation-monovalent anion collision frequency by a factor of 0.24 ± 0.03. Comparisons are made with the changes in collision frequencies predicted by several different theoretical descriptions of ion distributions. The closest agreement with experimental results for monovalent ions at 1 mM DNA is obtained with a static accessibility-modified discrete charge calculation, Theoretical calculations of the electrostatic potential and the distribution ofions around DNA have been carried out by many authors (e.g., refs. 6-14). On the other hand, experimental techniques for studying these properties usually have been limited to observing either the effect of DNA on bulk thermodynamic properties of the solution (6,(15)(16)(17) or the dependence of ligand binding on electrolyte concentration (18,19). NMR spectroscopy of 23Na+ can report directly on ions near DNA, but interpretation is complicated because of the mechanisms of nuclear relaxation involved (20)(21)(22)(23)(24).In principle, the effect of a polyelectrolyte on ion-ion collision frequencies can be used to test theoretical descriptions of the distribution of ions around the polyion (25). However, despite numerous reports concerning the effects of polyelectrolytes on bimolecular chemical reaction rates (refs. 26 and 27 and references therein), quantitative comparisons with theory are lacking.The experimental measurement and analysis of interactions between ions in solution is straightforward using energy transfer in the rapid-diffusion limit (28-30). With terbium chelates as donors, and simple transition-metal complexes as acceptors, the energy transfer rate depends on the donoracceptor collision frequency (30). Ion-ion energy-transfer rates in the presence of a polyelectrolyte like DNA depend directly on the spatial distribution of the ions around each DNA molecule. For example, adding DNA should enhance the rate of energy transfer from one cation to another, due to clustering of cations near DNA. RATIONALERelation Between Ion Distributions and Energy-Transfer Measurements. Energy transfer in the rapid-diffusion limit can be used to probe equilibrium properties of solutions, such as ion distributions, because the lifetime of the observed luminescence (-1 msec) is very long compared to the time required for an ion to diffuse through a representative sample of the solution. As a consequence, all energy donors ...

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Ionic atmosphere of rodlike polyelectrolytes. A hypernetted chain study

Cited by 105 publications

References 13 publications

Scaling and universality in the counterion-condensation transition at charged cylinders

Scaling and universality in the counterion-condensation transition at charged cylinders

Computation of ionic distributions around charged biomolecular structures: results for right-handed and left-handed DNA.

Distribution of ions around DNA, probed by energy transfer.

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