Bubble statistics and dynamics in double-stranded DNA

The dynamical properties of double-stranded DNA are studied in the framework of the Peyrard-Bishop-Dauxois model using Langevin dynamics. Our simulations are analyzed in terms of two distribution functions describing localized separations (“bubbles”) of the double strand. The result that the bubble distributions are more sharply peaked at the active sites than thermodynamically obtained distributions is ascribed to the fact that the bubble lifetimes affect the distributions. Certain base-pair sequences are found to promote long-lived bubbles, and we argue that this is a result of length scale competition between the nonlinearity and disorder present in the system.

Figure 1

(Color) Bubble probability ${\sum }_{\mathit{tr}=1.5\mathrm{\AA }}^{\infty }{P}_n(l,\mathit{tr})$ for the 69-base-pair homogeneous A-T sequence (upper) and for the periodic ${\mathrm{G}}_5{\mathrm{A}}_5$ sequence (lower).

Figure 2

(Color) Bubble probability ${\sum }_{\mathit{tr}=1.5\mathrm{\AA }}^{\infty }{P}_n(l,\mathit{tr})$ for the 69-base-pair AAV P5 promoter (see Ref. 4), with $t_s=2$ nsec and $M=800$ simulations.

Figure 3

(Color) Bubble probability ${\sum }_{\mathit{tr}=1.5\mathrm{\AA }}^{\infty }{P}_n(l,\mathit{tr})$ for a mutated AVV P5 sequence (see text).

Figure 4

(Color) Average bubble duration time ${\sum }_{\mathit{tr}=4.5\mathrm{\AA }}^{\infty }ABD(n,l,\mathit{tr})$ for AAV P5 (upper) and for mutated AVV P5 (lower) sequences.

Figure 5

(Color online) Bubble length probability (log scale) ${\sum }_{n=-46}^{23}{\sum }_{\mathit{tr}=1.5\mathrm{\AA }}^{\infty }{P}_n(l,\mathit{tr})$ (upper) and bubble amplitude probability (log scale) ${\sum }_{n=-46}^{23}{\sum }_{l=3bp}^{\infty }{P}_n(l,\mathit{tr})$ (lower). The insets compare these for AAV P5 at $1\mathrm{nsec}$ and $2\mathrm{nsec}$ simulation times.