Counterions Cumulative

Another important component of the analysis phase, and which is especially germane to this chapter, involves assessing the structure of the ion distribution around DNA. > Ensemble averages of the cumulative fraction of the counterions as a function of distance from the global DNA helical axis allow one to estimate the fraction of condensed counterion. (Cumulative fraction is more convenient to compute than a concentration, which would necessitate calculation of the volume of a shell.) When the ions are restrained, this fraction and the concomitant structure will most likely be found to be a function of the restraint parameters. 

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.

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