Dynamical model based on finite stacking enthalpies for homogeneous and inhomogeneous DNA thermal denaturation

We present a nonlinear dynamical model for DNA thermal denaturation, which is based on the finite stacking enthalpies used in thermodynamical nearest-neighbor calculations. Within this model, the finiteness of stacking enthalpies is shown to be responsible for the sharpness of calculated melting curves. Transfer-integral and molecular dynamics calculations are performed to demonstrate that the proposed model leads to a good agreement with known experimental results for both homogeneous and inhomogeneous DNA.

Figure 1

(Color online) Plot of the stacking energy $W(y_n,y_{n+1})$ (in eV) as a function of $y_n-y_{n+1}$ (in Å).

Figure 2

(Color online) Variation of the mean bond length $⟨y⟩$ vs temperature. Scattered symbols show the results of TI calculations in the thermodynamic limit of infinitely long chains for the harmonic PB model [4] (crosses), the anharmonic PB model [5] (squares), and the model of Eq. (3) (circles). The solid line shows the result of MD simulations for the model of Eq. (3) and a $2399\mathrm{bp}$ sequence with periodic boundary conditions.

Figure 3

(Color online) Denaturation curves, averaged over 4 MD runs, for the model of Eq. (4) and three $2399\mathrm{bp}$ sequences with open ends: an ATATAT⋯ sequence (left), an inhomogeneous sequence with 61% GC base pairs [13] (middle), and a GCGCGC⋯ sequence (right). The vertical scale indicates the probability $p(u_n-v_n>15\mathrm{\AA })$ in percents.

Figure 4

(Color online) (Top) plot for increasing temperatures of $⟨y_n⟩$ as a function of the site number $n$ for a $1793\mathrm{bp}$ inhomogeneous sequence found in the literature (NCBI entry code NM 001101). (Bottom) plot as a function of $n$ of the AT percentage averaged over 40 consecutive base pairs of the same sequence.

Figure 5

(Color online) Variation of the entropy per site $s$ and the specific heat $c_V$ (both in $k_B$ units) vs temperature, obtained from TI calculations in the thermodynamic limit of infinitely long chains. Shown are the results for the harmonic PB model [4] (crosses), the anharmonic PB model [5] (squares), and the model of Eq. (3) (circles).

Figure 6

(Color online) Variation of the specific heat $c_V$ (in $k_B$ units) vs temperature for the model of Eq. (3). Circles show the result of TI calculations in the thermodynamic limit of infinitely long chains, the solid line the result of MD simulations applied to a $2399\mathrm{bp}$ sequence with periodic boundary conditions (average over 4 runs), and the dashed line the result of MD simulations applied to a $100\mathrm{bp}$ sequence with open ends (average over 80 runs).