Length and Statistical Weight of Bubbles in DNA Melting

We present measurements of the length of the bubble versus temperature in the melting transition of DNA oligomers. The sequences are clamped at the ends of GC pairs (strong binding), and have AT rich (weaker binding) middle regions of variable length $B$ relative to the molecule size. We use a quenching technique to trap intermediate states. We find that the average relative bubble size $⟨\ell ⟩$ grows from zero for increasing temperature, but reaches a plateau at a length of order $B$, producing a discontinuous transition with finite bubble size. The statistical weight of the bubble states decreases as $B$ is reduced, the transition becoming more cooperative.

Figure 1

(a) Sketch of the quenching method used to tap intermediate states. The lower part of the figure shows the two sequences used in this study, in the hairpin conformation. (b) Example of a gel, running right to left. The slow (fast) band corresponds to duplexes (hairpins). The temperatures to which the aliquots were heated before quenching are indicated on the lanes. The plot on the right shows the intensity profiles; the numbers are proportional to the areas under the peaks and are used to calculate the fraction of open molecules $p$.

Figure 2

Melting curves for the two sequences; the open circles represent the fraction of open base pairs $f$ (from the UV absorption measurements); the filled circles represent the fraction of open molecules $p$ (from the gels), and the squares represent the average relative length of the bubble $⟨\ell ⟩$, calculated from Eq. (2). (a) $⟨\ell ⟩$ grows smoothly from zero and reaches a plateau for $⟨\ell ⟩\approx 0.6=B$, the relative size of the AT rich middle region for this sequence. (b) With a shorter AT rich middle region ($B=0.42$) the average bubble length reaches a plateau at a correspondingly smaller value $⟨\ell ⟩\approx 0.3$, and the transition is not continuous ($⟨\ell ⟩\ne f$ even before the plateau).

Figure 3

The quantity $\sigma =f-p$, representing the fraction of bases in a bubble state. The statistical weight of intermediate states is smaller for the shorter sequence.