Model for melting of confined DNA

When DNA molecules are heated they denature. This occurs locally so that loops of molten single DNA strands form, connected by intact double-stranded DNA pieces. The properties of this “melting” transition have been intensively investigated. Recently there has been a surge of interest in this question, in part caused by experiments determining the properties of partially bound DNA confined to nanochannels. But how does such confinement affect the melting transition? To answer this question we introduce and solve a model predicting how confinement affects the melting transition for a simple model system by first disregarding the effect of self-avoidance. We find that the transition is smoother for narrower channels. By means of Monte Carlo simulations we then show that a model incorporating self-avoidance shows qualitatively the same behavior and that the effect of confinement is stronger than in the ideal case.

Figure 1

(a) Conformation of a partially molten DNA molecule confined to a channel of width $D=14{\ell }_{\mathrm{K}}$. Shown is a snapshot obtained from computer simulations of the model described in the text. The parameters of the simulation are $N=400$, $r={\ell }_{\mathrm{K}}$, $a=0.63{\ell }_{\mathrm{K}}$, $E_{\mathrm{b}}=2.4$. The beads of diameter $a$ are not drawn. Color code: Molten parts (loops) are light red, intact parts are dark blue. (b) Schematic illustration of the three-dimensional model of a confined double-stranded chain that is used in the Monte Carlo simulations; see text. Note that the two strands are clamped at the ends.

Figure 2

A sketch of the first-return probability $f\left(m\right)$. Dashed line: $f\left(m\right)$ for an unconfined DNA molecule. Solid line: $f\left(m\right)$ for ideal DNA confined to a square channel of size $D\gg {\ell }_{\mathrm{K}}$.

Figure 3

Effect of confinement upon the melting transition, ideal case. (a) Binding probability as a function of monomer number, for an ideal chain with binding energy $E_{\mathrm{b}}=0.78$, at different levels of confinement: $D/{\ell }_{\mathrm{K}}=8$ (blue, upper curve), $D/{\ell }_{\mathrm{K}}=14$ (red, middle curve), and unconfined (green, lower curve). $N=400$, $a=0$, $r={\ell }_{\mathrm{K}}$ (b) Order parameter $p_{\mathrm{b}}(N/2)$ as a function of the binding energy, for different channel sizes as in panel (a). Solid lines: Fits to a solution of Eqs. (3); see text for details.

Figure 4

Effect of confinement upon the melting transition, self-avoiding case. (a) Binding probability as a function of monomer number, for a self-avoiding chain with binding energy $E_{\mathrm{b}}=2.33$, at different levels of confinement: $D/{\ell }_{\mathrm{K}}=8$ (blue, upper curve), $D/{\ell }_{\mathrm{K}}=14$ (red, middle curve), unconfined (green, lower curve). $N=400$, $a=0.63{\ell }_{\mathrm{K}}$, $r={\ell }_{\mathrm{K}}$ (b) Order parameter $p_{\mathrm{b}}(N/2)$ as a function of the binding energy, for different channel sizes as in panel (a).