Bubble generation in a twisted and bent DNA-like model

The DNA molecule is modeled by a parabola embedded chain with long-range interactions between twisted base pair dipoles. A mechanism for bubble generation is presented and investigated in two different configurations. Using random normally distributed initial conditions to simulate thermal fluctuations, a relationship between bubble generation, twist and curvature is established. An analytical approach supports the numerical results.

Figure 1

DNA chain embedded on a parabola in the $xy$ plane. Sites $(x_n,y_n)$ with $y_n=(\kappa ∕2){(x_n-\gamma )}^2$, indicated by light gray dots. Base pair dipoles, orthogonal to the parabola, shown as dark gray arrows. Curvature $\kappa =2$ and twist $\tau =1$. The $z$-axis (not shown) forms a right-handed system with $x$ and $y$ axes. Left, the on-site case, $\gamma =0$. Right, the intersite case, $\gamma =1∕2$.

Figure 2

The Morse potential $V_{\mathrm{Morse}}\left(u_n\right)={\left(e^{-u_n}-1\right)}^2$ (solid curve). Effective potential, Eq. (9), in the analytical approximation (dashed curve).

Figure 3

(Color online) The twist angle, ${\varphi }_n$, for various values of the twist, $\tau$, around the chain center. On-site case, $\gamma =0$; intersite case, $\gamma =1∕2$.

Figure 4

Evolution of the center site amplitude for $\kappa =1.0$ and $\tau =6$ (dashed curve) and $\tau =4$ (solid curve) for an on-site case.

Figure 5

Region of bubble generation in the on-site case. Light gray region, bubble generation. Dark gray region, transition region indicating the uncertainty of the simulations. White region, no bubble generation. Insets show the displacement, $u_n$, versus site, $n$, at the points (a) and (b) at simulation times (a) $t=51$ and (b) $t=100$ for the same initial condition.

Figure 6

Region of bubble generation in the intersite case. Light gray region, bubble generation. Dark gray region, transition region indicating the uncertainty of the simulations. White region, no bubble generation. Insets show the displacement, $u_n$, versus site, $n$, at the points (a) and (b) at simulation time (a) $t=45$ and (b) $t=100$ for the same initial condition.

Figure 7

Effective potential $V_n-V_{\infty }$ for constant curvature $\kappa =1.0$. (a) On-site case. (b) Intersite case.

Figure 8

Effective potential $V_n-V_{\infty }$ for constant twist. (a) On-site case, $\tau =6$. (b) Intersite case, $\tau =2$.