Ion correlation

It is well known that it is difficult to solve numerically integral equations for models with Coulomb interaction [69,70]. One needs to develop a renormalization scheme for the long-range terms of ion-ion correlations. Here we must do that for ROZ equations. 

Shklovskii BI. 1999. Screening of a macroion by multivalent ions Correlation-induced inversion of charge. Phys Rev E 60 5802-5811. 

One possible explanation for DNA aggregation is ion-ion correlation. A combined theoretical-experimental approach supported this interpretation.40 Monte Carlo simulation and fluorescent imaging of the effects of mixing small polyamines and NaCl with Coliphage T4 DNA concurred in demonstrating that addition of salt expands DNA in the presence of a polyamine, while salt alone causes DNA to contract. 

One of the first studies of multiple ions at the water/solid interface was by Spohr and Heinzinger, who carried out a simulation of a system of 8 Li" and 81" ions dissolved in 200 water molecules between uncharged flat Lennard-Jones walls.However, the issues discussed in their paper involved water structure and dynamics and the single-ion properties mentioned earlier. No attempt was made to consider the ions distributions and ion-ion correlations. This work has recently been repeated using more realistic water-metal potentials. ... 

Another antibody-based immunosorbent assay that can be used to determine HAT activity uses a secondary anti-IgG antibody, which is directed against the primary antibody and is labeled with the lanthanide Europium (Eu). After another washing step that removes all nonbound secondary antibody, one last incubation step is performed, which releases the lanthanide ion from the antibody, so that the final detection of time-resolved fluorescence (340/615 nm) caused by the released metal ion correlates with the acetylation level of the oligepeptide histone substrate, which is correlated with enzymatic activity. So far. 

The interaction of clay crystals within a domain depends upon the DLVO repulsive pressure in the slit-shaped pores and the balance between repulsive pressure [Pr] from counterion hydration and the attractive pressure [Pa] generated by van der Waals forces and the recently discovered ion-ion correlation attraction between the counterions in the confined space of the overlap pores [see Kjellander et al., 1988a, b]. When Ca Is the counterion, the attractive pressure dominates and the overlap pores are stabilized In a primary potential minimum. However, when the crystal... 

Bile Acid Molecular Weight [M-H] Ion Correlation Coefficient (r) Calibration Curve Equation... 

Fig. 3.2 reflects the dependence of benzenoid aromatic ions correlate linearly with the it electron density relative to benzene (Qn = 1)... 

Grange, A. H., and Sovocool, G. W. (2008). Automated determination of precursor ion, product ion, and neutral loss compositions and deconvolution of composite mass spectra using ion correlation based on exact masses and relative isotopic abundances. Rapid Commun. Mass Spectrom. 22 2375-2390. 

MO studies of aromatic nitration cast doubt on the existence of jt-complexes and electron-transfer complexes in liquid-phase nitrations.14 The enthalpy of protonation of aromatic substrates provides a very good index of substrate reactivity to nitration. Coulomb interaction between electrophile and substituent can be a special factor influencing regioselectivity. A detailed DFT study of the reaction of toluene with the nitronium ion has been reported.15 Calculated IR spectra for the Wheland intermediates suggest a classical SE2 mechanism. MO calculations of cationic localization energies for the interaction of monosubstituted benzenes with the nitronium ion correlate with observed product yields.16... 

Defining a Stem layer using hydrated radii of the ions is justified in the P—B framework, since ions must be fully hydrated in order for the uniform dielectric approximation to be valid. If ions were allowed to penetrate this layer, then additional physics would have to be introduced to account for ion—ion correlations, partial dehydration, and other considerations that fall well outside the realm of applicability for standard continuum solvent models. To generalize the P—B framework, new approaches are needed... 

PB equation is based on the mean-field approximation, where ions are treated as continuous fluid-like particles moving independendy in a mean electric potential. The theory ignores the discrete ion properties such as ion size, ion-ion correlation and ion fluctuations. Fail to consider these properties can cause inaccurate predictions for RNA folding, especially in the presence of multivalent ions which are prone to ion correlation due to the strong, long-range Coulomb interactions. For example, PB cannot predict the experimentally observed attractive force between DNA helices in multivalent ion solutions. 

Several attempts have been made to improve the PB by accounting for the effects of ion size, ion correlation, and fluctuations of ion distributions. The resultant modified models have led to improved predictions for the ion effects in RNA/DNA folding stability. 

Recendy, inspired by the experimental findings for the significance of ion size, ion correlation and fluctuations, the TBI model (Tan and Chen, 2005, 2008a) was developed. Comparisons between the TBI theory predictions and the experimental data on ion-binding properties (Stellwagen et al, 2007 ... 

A direct implication of the ion correlation is that the likelihood of finding an ion at a location is sensitive to the locations of other ions. Therefore, to treat the ion correlation effect, we must consider an ensemble of discrete ion distributions (i.e., fluctuations) (Ha and Thirumalai, 2003). In order to enumerate the different distributions for the TBIs, we divide the tightly bound region into discrete phosphate cells, each around a phosphate group. We generate the ensemble of distributions for the TBIs by... 

The TBI model is not based on any of such preassumptions, while other models such as the PB are based on a priori assumptions about the nonexistence of the ion correlation/fluctuation effect. If the ion correlation and fluctuation effects are strong, the TBI model will capture them, otherwise, the model gives identical predictions as other (PB-based) models. Therefore, the TBI model can effectively complement the PB-based methods. 

Both the correlation-corrected DHHC theory as well as the simulations that capture in principle all kinds of ion correlations (see Sect. 2.2) show a decrease in the osmotic coefficient when compared to the prediction of the PB-theory. Since these two totally different approaches agree so well, it becomes clear that they indeed give a good description of the influence of the correlations. However, they do not lower the osmotic coefficient sufficiently to reach full agreement with the experimental data. Moreover, the deviation from the Poisson-Boltzmann curve increases for higher densities, which is true for the DHHC and the simulations as well as for the experiment. This appears plausible if one recalls that correlations become more important at higher densities. 

Since Poisson-Boltzmann theory neglects all ion-ion correlations (see Sect. 2.2) one is tempted to assume that their incorporation into the theoretical treatment would resolve the discrepancy. However, the comparison displayed in Fig. 8 shows clearly that these correlational effects can only be made responsible for a part of the deviations. Since the two different approaches, using a correlation-corrected density functional theory and Molecular Dynamics simulations, agree very well with each other, it becomes obvious that the discrepancy between them and the experiment is not due to the neglect of ionic correlations. 

The correlation of the transverse momenta including or not including the final-state repulsion is investigated theoretically and compared with data for argon in [41]. Including the final-state repulsion yields a good description of the electron-electron correlation, but the electron-ion correlation is outside of the model. 

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