Counterion accumulation

Thus we have found that the screening should be more efficient than in the Debye-Hiickel theory. The Debye length l//c is shorter by the factor 1 — jl due to the hard sphere holes cut in the Coulomb integrals which reduce the repulsion associated with counterion accumulation. A comparison with Monte Carlo simulation results [20] bears out this view of the ion size effect [19]. 

Figure 20.5 shows the spatial free energy density profiles for the A- and B-form systems, respectively. Counterion densities were visualized by creating free-energy isocontours at —0.5, —1.0, —1.5, and —2.0 kcal/mol intervals, identical to the procedure described in previous work (Chen et al., 2009). The integrated numbers for the cumulative number of counterions accumulated within a free energy interval is calculated as a function of free energy cutoff and plotted in Fig. 20.6. 

Figure 20.6 Comparative cumulative distribution functions to assess the amount of counterion accumulation around the Tar—Tar complex, A-form RNA, and B-form DNA, respectively. Data were obtained from molecular dynamics simulations with explicit representations of water molecules and ions. The ordinate quantifies the number of counterions accumulated around the macroions within contours that have AG less than or equal to the value on the abscissa.

For the Tar—Tar kissing loops, the P—B calculations are unable to discern their propensity to accumulate counterions accumulation at the loop—loop interface (data not shown). This is because the fully hydrated ions as defined by the Stem layer cannot penetrate into the central cation binding pocket (data not shown). Similarly, the axial spine of counterion density observed in the A-RNA helix (Fig. 20.5) is not captured by the P—B calculation (Fig. 20.7). No noticeable sequence specificity is observed in the counterion accumulation patterns in the P—B calculations, even though the sequence effects are explicitly represented in the P—B calculation through the appropriate geometry and assignment of point-charges. This is because the sequence specificity observed in the molecular dynamics simulations usually involves first shell interactions of base moieties with partially dehydrated ions, which cannot be accurately represented in the P—B framework. 

Ion binding around a (polyanionic) nucleic acid structure causes counterion accumulation on the molecular surface. The strong, long-range Coulomb force between the ions cause the ions to become correlated (networked). Mathematically, the strong correlation can be characterized by the large... 

Redispersion of the flocculate and other evidences for the hydrophilic character of the support coated with the adsorbed surfactant in the neighbourhood of the cmc indicate that bilayer coverage represents complete saturation of the surface. Commonly, the term bilayer is applied to an adsorbed structure in which the surfactant molecules are oriented perpendicular to the surface and fully extended [5,9,20,37,81,89]. The hydrocarbon tails of both layers form a hydrophobic core between the heads. At both sides counterions accumulate between the ionic head-groups. The result looks like a lamellar micelle. For certain physical regimes, the adsorbed amount is only a fraction of what is expected for a tightly packed bilayer [37,48] the structure which best fits the experimental data can... 

Gueron, M. Weisbuch, G. Polyelectrolyte theory. I. Counterion accumulation, site-binding, and their insensitivity to polyelectrolyte shape in solutions containing finite salt concentrations. Biopolymers 1980 19 353-382. 

The electrokinetics are a class of several different interfacial effects that become important in micron and submicron dimensions. The most important and widespread categories of the electrokinetic effects are the electroosmosis and the electrophoresis. When the ionized liquids are in contact with stationary charged surfaces, counterions accumulate near the surface and buUd a layer that is called the electric double layer (EDL). The presence of an external electric field moves this layer and consequently generates the bulk flow field in the channels. This effect is named as electroosmosis and the generated flow is electroosmotic or electrokinetic flow. The external electric field also moves charged species and macromolecules in the micro- and nanochaimels which is usually referred to electrophoresis or electrophoretic effect. 

Mills P, Paulsen MD, Anderson CF, Record MX Jr (1986) Monte-Carlo simulations of counterion accumulation near helical DNA. Chem Phys Lett 129 155-158. doi 10.1016/0009-2614(86)80188-9... 

Monte Carlo Simulations of Counterion Accumulation Near Helical DNA. 

M. Gueron and G. Weisbuch, Biopolymers, 19, 353 (1980). Polyelectrolyte Theory. I. Counterion Accumulation, Site-Binding, and Their Insensitivity to Polyelectrolyte Shape in Solutions Containing Finite Salt Concentrations. 

---