$1∕f$ fluctuations of DNA temperature at thermal denaturation

We theoretically investigated the temperature fluctuations of DNA close to denaturation and observed a strong enhancement of these fluctuations at the critical temperature. Although in a much lower frequency range, such a sharp increase was also reported in the recent experimental work of Nagapriya et al. [Phys. Rev. Lett. 96, 038102 (2006)]. We showed that there is instead no enhancement of temperature fluctuations when the dissipation coefficient $\gamma$ in Langevin equations is assumed to be larger than a few tens of ${\mathrm{ps}}^{-1}$, and pointed out the possible role of the solvent in real experiments. We sought for a possible correlation between the growth of large bubbles and the enhancement of temperature fluctuations but found no direct evidence thereof. Finally, we showed that neither the enhancement of fluctuations nor the $1∕f$ dependence are observed at the scale of a single base pair, while these properties show up when summing the contributions of a large number of base pairs. We therefore conclude that both effects result from collective motions that are facilitated by the divergence of the correlation length at denaturation.

Figure 1

(Color online) Log-log plots, at several temperatures, of the SPD of temperature fluctuations for a 2000 bp homogeneous sequence and the PBD model [7]. Melting temperature is about $354\mathrm{K}$. For denaturated sequences, $P\left(f\right)$ is smaller than ${10}^{-12}{\mathrm{K}}^2{\mathrm{Hz}}^{-1}$, so that the corresponding curves do not show up in the figure. Within this model, the configuration of a sequence with $N$ bp is described by $n=N$ coordinates.

Figure 2

(Color online) Log-log plots, at several temperatures, of the SPD of temperature fluctuations for a 2399 bp ATATAT… sequence and the JB model [8]. Melting temperature is about $310\mathrm{K}$. Within this model, the configuration of a sequence with $N$ bp is described by $n=2N$ coordinates.

Figure 3

(Color online) Log-log plots, at several temperatures, of the SPD of temperature fluctuations for the 2399 bp inhibitor [14] and the JB model [8]. Melting temperature is about $335\mathrm{K}$. Within this model, the configuration of a sequence with $N$ bp is described by $n=2N$ coordinates.

Figure 4

(Color online) Log-log plots, at several temperatures, of the SPD of temperature fluctuations for the 1793 bp actin (NCB entry code NM̱001101) and the BSJ model [12]. Melting temperature is about $385\mathrm{K}$. Within this model, the configuration of a sequence with $N$ bp is described by $n=4N$ coordinates.

Figure 5

(Color online) Same as Fig. 3, except that SPD curves were obtained by integrating Langevin’s equations of motion instead of Hamilton’s. A dissipation coefficient $\gamma =5{\mathrm{ns}}^{-1}$ was assumed.

Figure 6

(Color online) Log-log plots, for increasing values of the dissipation coefficient $\gamma$, of the SPD of temperature fluctuations for the 2399 bp inhibitor [14] at $335\mathrm{K}$ (denaturation temperature) and the JB model [8].

Figure 7

(Color online) Top: plot, as a function of their position $k$ in the sequence, of the average distance between paired bases for the 2399 bp inhibitor [14] at 325 and $335\mathrm{K}$ and the JB model [8]. Bottom: plot, as a function of $k$, of the AT percentage averaged over 40 consecutive base pairs of the same sequence.

Figure 8

(Color online) Log-log plots, at the melting temperature $\left(335\mathrm{K}\right)$ and for the JB model, of the product of the SPD times the length $N_j$ of the subsection, for the 11 subsections of the 2399 bp inhibitor [14] (see Fig. 7). The thicker line denotes the curve for subsection B, which is the only closed one at the critical temperature.

Figure 9

(Color online) Time evolution, at 325 and $335\mathrm{K}$ (melting temperature), of the temperature of the 2399 bp inhibitor [14] computed with the JB model [8]. Each pixel corresponds to the temperature averaged over ten successive base pairs and $50\mathrm{ns}$. Temperatures range from $-10\mathrm{K}$ (blue/dark pixels) to $10\mathrm{K}$ (yellow/bright pixels) relative to the average one.

Figure 10

(Color online) Time evolution, at 325 and $335\mathrm{K}$ (melting temperature), of the separation of paired bases for the 2399 bp inhibitor [14] according to the JB model [8]. Each pixel corresponds to separations averaged over ten successive base pairs and $50\mathrm{ns}$. Separations range from $1\mathrm{\AA }$ and less (black pixels) to $20\mathrm{\AA }$ and more (yellow/bright pixels). For this model a base pair is considered to be open if the average separation is larger than about $12\mathrm{\AA }$. Note that this figure was obtained from the same trajectories as Fig. 9.

Figure 11

(Color online) Log-log plots of the SPD of temperature fluctuations for the 2399 bp inhibitor [14] at $335\mathrm{K}$ (melting temperature) and the JB model [8]. Each curve corresponds to a different value of the length $N_j$ of the subsections over which temperature fluctuations are computed.

Figure 12

(Color online) Evolution of the power of temperature fluctuations of the 2399 bp inhibitor [14] as a function of $N_j$ for exponentially increasing frequencies $f$ (2, 20, and $200\mathrm{MHz}$ and $2\mathrm{GHz}$) and three typical temperatures: $315\mathrm{K}$ (double stranded DNA, top plot), $335\mathrm{K}$ (melting temperature, middle plot), and $345\mathrm{K}$ (single stranded DNA, bottom plot).