Opposing Effects of Multivalent Ions on the Flexibility of DNA and RNA

Increasing the concentration of counterions (salt) is known to reduce the bending persistence length of DNA. Here we use atomistic molecular dynamics simulations to predict that multivalent counterions have the opposite effect on double-stranded RNA, increasing its bending rigidity by at least 30%. This counterintuitive effect is observed for various tri- and tetravalent ions alike, and is robust to methodological details and the RNA sequence. In contrast to DNA, multivalent counterions bind inside the RNA major groove, causing significant contraction of the molecule along its helical axis—as a result, its further deformation due to bending becomes energetically more expensive compared to bending without bound multivalent ions. Thus, the relationship between mechanical properties of a charged polymer and its ionic atmosphere may be richer than previously thought.

Figure 1

Estimation of the bending persistence length $L_p$ of the DNA duplex with (red) and without (blue) ${\mathrm{CoHex}}^{3+}$ counterions. $L_p$ is estimated by fitting (dashed lines) the data points to Eq. (3); each point represents a value of $-\ln [P(\theta ,l)/\sin \theta ]$ averaged over the $\sim 0.008$ interval of $\theta$.

Figure 2

In DNA (left), multivalent counterions (illustrated for ${\mathrm{CoHex}}^{3+}$, green) bind mostly externally [16] onto the negatively charged phosphates (red), with little effect on the DNA structure. The binding reduces the effective electrostatic repulsion along the helix, which in turn decreases the helix bending rigidity. In contrast, the same ions bind deep inside the RNA major groove (right) [16], causing the double helix to contract and significantly stiffen its internal structure. This leads to an overall increase of the RNA bending rigidity—the pull of the ions works as taut bicycle spokes that tighten the wheel. The distributions (not shown) of bound ${\mathrm{s}\text{permine}}^{4+}$ around DNA and RNA are similar to the above.