Structure and energy of a DNA dodecamer under tensile load

Abstract

In the last decade, methods to study single DNA molecules under tensile load have been developed. These experiments measure the force required to stretch and melt the double helix and provide insights into the structural stability of DNA. However, it is not easy to directly relate the shape of the force curve to the structural changes that occur in the double helix under tensile load. Here, state-of-the-art computer simulations of short DNA sequences are preformed to provide an atomistic description of the stretching of the DNA double helix. These calculations show that for extensions larger that approximately 25% the DNA undergoes a structural transformation and a few base pairs are lost from both the terminal and central part of the helix. This locally melted DNA duplex is stable and can be extended up to approximately 50-60% of the equilibrium length at a constant force. It is concluded that melting under tension cannot be modeled as a simple two-state process. Finally, the important role of the cantilever stiffness in determining the shape of the force-extension curve and the most probable rupture force is discussed.

Figure 1

(a) Plot of the PMF (kcal mol⁻¹) versus extension (nm) as determined by a weighted histogram analysis of the five umbrella sampling simulations (solid line), or from the three AFM pulling simulations using the Jarzynski equality (dashed line). (b) Plot of the force (pN) versus extension (nm). Forces have been obtained as the derivative of the PMF calculated from the umbrella sampling (cross) or the pulling simulations (plus).

Figure 2

Number of Watson–Crick base pairs as a function of the d(ACTG)₃–(CAGT)₃ extension (nm). The presence of a base pair is assumed when the N₁–N₃ distance for A:T or G:C is <0.4 nm. The values reported here are averages over all the conformations sampled in the umbrella sampling and AFM pulling simulations.

Figure 3

DNA energy as a function of extension. The DNA energy (blue) was obtained as the sum of the internal energy, solvation free energy and conformational entropy. The internal plus solvation energies (green) were calculated with the GB/SA approximation (41). The internal entropy contribution TS_∞ (red) was calculated from the mass-weighted covariance matrix using a harmonic approximation (40).

Figure 4

Rupture probability as a function of extension (nm) for each base pair of the d(ACTG)₃–(CAGT)₃ dodecamer. Probabilities are indicated in white (40%), light gray (60%), dark gray (80%) and black (>80%). The presence of a base pair is assumed when the N₁–N₃ distance for A:T or G:C is <0.4 nm. The values reported here are averages over all the conformations sampled in the umbrella sampling and AFM pulling simulations.

Figure 5

Umbrella sampling simulation of d(ACTG)₃–(CAGT)₃. Structures obtained from simulation u4 at 5.0 nm (a) and 6.5 nm (b) of extension. The bond of the DNA molecules are represented as sticks colored according to the atoms participating in a bond (carbon—cyan, oxygen—red, nitrogen—blue, phosphorous—green). The Na⁺ counterions are represented as balls. Water molecules and hydrogen atoms are not shown for the sake of clarity.

Figure 6

AFM pulling simulations of d(A)_n–d(T)_n and d(C)_n–d(G)_n. Number of broken Watson–Crick base pairs as a function of extension for the terminal A:T base pairs (solid line), the internal A:T base pairs (dashed line), the terminal C:G base pairs (dotted line) and the internal C:G base pairs (dashed-dotted line).

Figure 7

Two-state model representation of the DNA double helix under tensile load. An analytical expression for the force required to stretch the bound (solid line) and the overstretched (dashed line) states was obtained by fitting to a third-degree polynomial the forces calculated from the umbrella sampling simulation u5 (crosses) at low (from 3.5 to 5.0 nm) and moderate (from 5.5 to 6.8 nm) extensions, respectively.

Figure 8

Numerical simulation of an AFM pulling experiment. (a) Force versus time plots for experiments performed with a soft (20 pN nm⁻¹—solid line) and a stiff (200 pN nm⁻¹—dashed line) cantilever. The loading rate in both experiments is 1000 pN s⁻¹. (b) Loading rate dependence of the most probable rupture force for experiments performed with a soft (20 pN nm⁻¹—squares) and a stiff (200 pN nm⁻¹—diamonds) cantilever. Averages and SDs for each data point were calculated from the result of 30 numerical experiments performed with different initial velocities.