Elastic Response of Single DNA Molecules Exhibits a Reentrant Collapsing Transition

We measured the elastic response of single DNA molecules at various concentrations of the trivalent cation, spermidine. When added spermidine caused the DNA to collapse, the force-extension curves showed either plateaus or stick-release patterns depending on the concentration. The periodic stick-release response determines a characteristic length, which may reflect toroidal supercoiling. At high concentrations of spermidine, we observed the reelongation of single molecules of collapsed DNA. Thus condensation occurs between lower and upper critical concentrations, verifying that the transition is reentrant as theoretically predicted.

Figure 1

$F\mathrm{\text{−}}x$ curves at various SPD concentrations. $N=500\mu \mathrm{M}$ (a), 1 mM (b), 10 mM (c), 100 mM (d). ○: $N=0\mathrm{m}\mathrm{M}$ (before solution exchange), ■: first relaxation after solution exchange, □: first stretching, ▲: second relaxation, △: second stretching, ▼: third relaxation, and ▽: third stretching (data not shown for the third stretching and relaxation for $N=500\mu \mathrm{M}$ and 100 mM). Each data point is the average value of 20 measurements completed within 10 sec. After solution exchange, DNA molecules were initially relaxed except for $N=10\mathrm{m}\mathrm{M}$.

Figure 2

Dependence of the width of the force plateau on the SPD concentration. Each point averages the force across each plateau during relaxation. The error bar is the standard deviation, for 51 points ($500\mu \mathrm{M}$), 74 points (1 mM), 42 points (2 mM), 200 points (10 mM), 22 points (50 mM), and 62 points (100 mM). The width of the force plateau is maximal between 1 and 10 mM.

Figure 3

Histogram of the distance between force peaks during extension. We measured the peak-peak distance for stick release for $1\mathrm{m}\mathrm{M}\le N\le 100\mathrm{m}\mathrm{M}$. We counted 64 peak-peak distances for seven stick-release curves.

Figure 4

(a) Evolution of the force during solution exchange at 200 mM SPD. We measured the force every 0.33 sec. After the first abrupt increase and decrease of force (A), the value stayed almost constant (B), then decreased (C). Solution exchange ended at 600 sec. (b) The elastic response of a reelongated DNA molecule. ○: Before solution exchange. ■: First stretching after solution exchange; □: first relaxation after solution exchange. The solid and dotted lines describe the WLC of Eq. (1) with $P=39\mathrm{n}\mathrm{m}$, $L=5.2\mu \mathrm{m}$ and with $P=25\mathrm{n}\mathrm{m}$, $L=5.2\mu \mathrm{m}$, respectively.