Monte Carlo determination of the distribution of ions about a cylindrical polyelectrolyte

Abstract

SynopsisWe 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, x , 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 A, while the small ions had various radii in the range from 1 to 10 8, 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 1-8, radius was present, but considerable discrepancies appeared with larger ions as a result of excludedvolume 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 molL a t the surface of the polyion.

Effective interaction between helical biomolecules

“…The increase of θ above a certain threshold of salt concentration is mainly due to a counterion accumulation outside the grooves. A similar trend was predicted by PoissonBoltzmann [98] and Monte Carlo [61,47] calculations in different models. More details of the forces and the comparison to linear screening theories are shown in Figures 16, 17 and 18.…”

“…Each charged sphere describes a phosphate group and hence the spheres form a double helix structure. In detail, the effective cylindrical diameter D is commonly chosen to be D = 20Å [61,62,49]. The spheres are monovalent, i.e.…”

Quantitative and Comprehensive Decomposition of the Ion Atmosphere around Nucleic Acids

“…This ensuing limitation of NLPB has been addressed in theoretical studies 15,18,39 . While it has been suggested experimentally that ion size affects electrostatic screening 22,[40][41][42] , the complexity of the systems investigated do not allow a rigorous conclusion to be drawn about the effect of ion size on its occupancy in the ion atmosphere.…”

Electrostatics in soft matter

“…As long as the Coulomb coupling between ions is "fairly" moderate (which is the case for monovalent ions in aqueous solution), the PB theory [4,5,18,19] and even the DH one [20] describe astonishingly well the ion distribution (and hence the thermodynamical system properties) when compared to computer simulations [21,22,23,24,25,26], theories going beyond the mean-field PB level [27], and even experiments [28]. Nonetheless, as soon as ion-ion correlations get relevant, mean field theories such as the PB one [29] or its linearized version (as related above in 2.1) can not explain the experimentally observed relevant effect of overcharging [30,31].…”