The ionic atmosphere around A-RNA: Poisson-Boltzmann and molecular dynamics simulations

Abstract

The distributions of different cations around A-RNA are computed by Poisson-Boltzmann (PB) equation and replica exchange molecular dynamics (MD). Both the nonlinear PB and size-modified PB theories are considered. The number of ions bound to A-RNA, which can be measured experimentally, is well reproduced in all methods. On the other hand, the radial ion distribution profiles show differences between MD and PB. We showed that PB results are sensitive to ion size and functional form of the solvent dielectric region but not the solvent dielectric boundary definition. Size-modified PB agrees with replica exchange molecular dynamics much better than nonlinear PB when the ion sizes are chosen from atomistic simulations. The distribution of ions 14 Å away from the RNA central axis are reasonably well reproduced by size-modified PB for all ion types with a uniform solvent dielectric model and a sharp dielectric boundary between solvent and RNA. However, this model does not agree with MD for shorter distances from the A-RNA. A distance-dependent solvent dielectric function proposed by another research group improves the agreement for sodium and strontium ions, even for shorter distances from the A-RNA. However, Mg(2+) distributions are still at significant variances for shorter distances.

Figure 1

(a) Schematic illustration of cylindrical layer ΔV(r) = 2πrdΔr, around A-RNA. The height of the cylinder d is 78 Å while the duplex length is 74 Å. Top (b) and side (c) views of a snapshot from the MD simulations of sodium. (Blue points) Na⁺ ions deep in the grooves. (Red points) Na⁺ ions on the outer surface of the RNA. Molecular rendering is done with the ZMoil visualization software MOIL (http://clsb.ices.utexas.edu/prebuilt/).

Figure 2

Radial distribution of sodium ions around A-RNA computed with NLPB, SMPB, and MD simulations. (a) The dielectric constant of A-RNA and solvent is set to 1 and 78.5, respectively (Option 1). (b) The solvent dielectric constant given by Eq. 8 (Option 2). (Black circles with solid lines) MD simulation results. (Blue dashed line) NLPB using a Stern layer (width = 2.4 Å). (Red dotted line) SMPB with SES with probe radius 1.4 Å. (Green dashed-dotted line) SMPB with vdW. The Na⁺ ion radius is set to 2.4 Å and Cl⁻ to 4 Å. (Thin dotted line in orange) SMPB with SES with 4.8Å ion size.

Figure 3

Radial distribution of strontium ions around the A-RNA computed with NLPB, SMPB, and MD simulations. (a) The dielectric model Option 1. (b) Option 2. (Black circles with solid lines) MD results. (Blue dashed line) NLPB using Stern layer of 2.3 Å. (Red dotted line and green dashed-dotted lines) Results for SMPB using SES and vdW, respectively, to determine the dielectric boundary.

Figure 4

Radial distribution function of magnesium ions around the A-RNA duplex computed with NLPB, SMPB, and MD simulations. (a) The dielectric model Option 1 and (b) Option 2. (Black circles with solid lines) MD simulation. (Blue dashed line) NLPB using Stern layer width of 4.2 Å. (Red dotted and green dashed-dotted lines) Result for SMPB using the SES and vdWs, respectively, to determine the dielectric boundary separating the solute and solvent dielectric regions. We used 4.2 Å for Mg²⁺ ion radius.

Figure 5

Radial distribution of a mixture of Na⁺ and Mg⁺², computed with NLPB, SMPB, and MD simulations. The distance-dependent dielectric function is used (Option 2). (Black circles with solid lines) MD simulation. (Blue dashed line) NLPB with a Stern layer width adjusted to ion sizes. (Red dotted line) Result for SMPB with 1.4 Å SES. (Black dashed-dotted line) Result of the same method when magnesium ion size is reduced to 1.4 Å. (a) Magnesium ion profile. (b) Sodium ion.

Figure 6

Comparison of the number of bound ions around A-RNA computed by MD (⊙), NLPB (+), SMPB with a fixed solvent dielectric constant (×), and SMPB when a distance-dependent solvent dielectric function is used (□). One pure (Na/Mg) salt solution and three salt mixtures of Na⁺ and Mg²⁺ with varying ratios are compared. (Black dashed line) Guide to the eye to show the number of Na⁺; (red solid line) number of Mg²⁺.