Molecular Dynamics Simulation of Multivalent-Ion Mediated Attraction between DNA Molecules

All atom molecular dynamics simulations with explicit water were done to study the interaction between two parallel double-stranded DNA molecules in the presence of the multivalent counterions putrescine ($2+$), spermidine ($3+$), spermine ($4+$) and cobalt hexamine ($3+$). The inter-DNA interaction potential is obtained with the umbrella sampling technique. The attractive force is rationalized in terms of the formation of ion bridges, i.e., multivalent ions which are simultaneously bound to the two opposing DNA molecules. The lifetime of the ion bridges is short on the order of a few nanoseconds.

Figure 1

(a) Top view of the simulation box with two parallel DNA decamers and ten Sm counterions in the initial configuration. The box has a transverse dimension of $7\times 7{\mathrm{nm}}^2$ and 3.4 nm height. (b) Snapshot illustrating ion bridge formation.

Figure 2

Illustration of the cross section of the simulation box and how the two external springs pull the two DNA duplexes in opposite directions in the transverse plane.

Figure 3

Fluctuation in interduplex spacing of Sm-DNA. (a) simulation without springs; (b) as in (a) but with two springs centered at $(\pm x,\pm y)=(0.95,0.95)\mathrm{nm}$.

Figure 4

(a) Interaction potential versus interduplex distance for Pu, Sd, and Sm-DNA. ▿: no springs. With springs $(\pm x,\pm y)=(0.90,0.90)$, +; (0.95, 0.95), ▵; (1.00, 1.00), *; (1.05, 1.05), ○ nm. (b) Force-separation curve for Sm-DNA. The dots are obtained from the spring extensions as described in the text.

Figure 5

(a) Time-evolution of the number of ion bridges in the Sm-DNA simulation with $(\pm x,\pm y)=(0.90,0.90)\mathrm{nm}$ (rebinned in 0.1 ns intervals). (b) Average number of ion bridges vs interduplex distance.: ○, Co-DNA; ▵, Sm-DNA; ▿, Sd-DNA; □, Pu-DNA.