Analyzing ion distributions around DNA

Abstract

We present a new method for analyzing ion, or molecule, distributions around helical nucleic acids and illustrate the approach by analyzing data derived from molecular dynamics simulations. The analysis is based on the use of curvilinear helicoidal coordinates and leads to highly localized ion densities compared to those obtained by simply superposing molecular dynamics snapshots in Cartesian space. The results identify highly populated and sequence-dependent regions where ions strongly interact with the nucleic and are coupled to its conformational fluctuations. The data from this approach is presented as ion populations or ion densities (in units of molarity) and can be analyzed in radial, angular and longitudinal coordinates using 1D or 2D graphics. It is also possible to regenerate 3D densities in Cartesian space. This approach makes it easy to understand and compare ion distributions and also allows the calculation of average ion populations in any desired zone surrounding a nucleic acid without requiring references to its constituent atoms. The method is illustrated using microsecond molecular dynamics simulations for two different DNA oligomers in the presence of 0.15 M potassium chloride. We discuss the results in terms of convergence, sequence-specific ion binding and coupling with DNA conformation.

Figure 1.

Left: Schematic view of the curvilinear helicoidal coordinates (CHC). An ion (red dot) is described by a distance D along the curved helical axis (black line), a radial distance R from the axis and an angle A from a reference vector which tracks the helical twist of the nucleic acid. At the base pair levels, this vector corresponds approximately to the long axis of the base pairs and points toward the 5′-3′ strand. Consequently, A ≈ 90° places an ion in the minor groove and A ≈ 270° places an ion in the major groove. Right: Isodensity surfaces (red) for the phosphorus atoms of the AGCT oligomer analyzed in the CHC system, then mapped into Cartesian space using the average helical axis of the oligomer (black line). The nucleotides are colored to indicate the base sequence (G: blue, C: green, A: red, T: orange). All isodensity plots were obtained using Chimera (39,40).

Figure 2.

Root mean square fluctuations (Å) for the phosphorus atoms of the AGCT oligomer are smaller when calculated using the CHC analysis mapped into Cartesian space (black lines), than when simply superposing snapshots from the molecular dynamics simulation (red lines). Note that phosphates belonging to the two strands are shown consecutively in the 5′-3′ direction.

Figure 3.

Average phosphorus distributions calculated using CHC for the 1 μs AGCT trajectory and plotted in various planes: DA (top left), DR (top right), RA (bottom left). The bottom right plot shows the RA plane for the sugar C1′ atoms from the same trajectory. The blue to red color scale represents increasing molarity. DR and RA plots show the average radius of the phosphorus atoms from the helical axis as a white line and as a white circle, respectively. The DA and RA plots show the minor groove limits, defined by the average C1′ positions, as a white line and as white radial vectors, respectively. RA plots also have a vertical radial vector indicating the center of the major groove.

Figure 4.

Time-averaged K⁺ populations within the DNA grooves for the unique base pair steps (T8pA9, A9pG10, G10pC11) belonging to the central tetranucleotide of the AGCT oligomer for increasing durations (ns) of the molecular dynamics trajectory.

Figure 5.

Averaged conformation of the AGCT oligomer (black line drawing) and the associated average locations of the K⁺ (blue spheres) and Cl⁻ (green spheres) ions calculated for increasing durations of the molecular dynamics trajectory.

Figure 6.

1D K⁺ distributions averaged over the 1 μs AGCT trajectory. The vertical line in the R plot indicates the radial position of the phosphorus atoms, while the shorter distance between the two vertical lines in the A plot delimits the minor groove using the angular position of the sugar C1′ atoms (see Figure 3).

Figure 7.

2D K⁺ distributions averaged over the 1 μs AGCT trajectory: DA plane (top left), DR plane (top right), RA plane (bottom). The results are plotted as molarities as shown by the color bars, with a blue to red scale indicating increasing values.

Figure 8.

3D K⁺ distributions obtained by mapping CHC analysis of the 1 μs AGCT trajectory into Cartesian space with respect to the average DNA structure, shown as a line drawing on the left (G: blue, C: green, A: red, T: orange) and as a gray solvent accessible surface on the right. Molarity isodensity surfaces for potassium ions are plotted at 15 M (solid red) and 5 M (green mesh).

Figure 9.

2D RA K⁺ distributions for various dinucleotide steps within the central tetranucleotides of the AGCT and ATGC oligomers, averaged over the corresponding 1 μs trajectories. The blue to red color scale indicates increasing molarity values. In each plot, the numbers in the upper and lower semicircles indicate the average K⁺ occupancy in the major and minor grooves, respectively.

Figure 10.

Variations in K⁺ molarity along the DNA grooves (solid lines) of the AGCT oligomer. Values are averaged over the 1 μs AGCT trajectory and compared with variations in groove width (dotted lines). Groove width variations are plotted in Å with respect to the respective minimal values (major: 10.0 Å, minor: 3.5 Å) on the same scale as the molarities. Left: major groove. Right: minor groove.