Opening of DNA chain due to force applied on different locations

We consider a homogeneous DNA molecule and investigate the effect of random force applied on the unzipping profile of the molecule. How the critical force varies as a function of the chain length or number of base pairs is the objective of this study. In general, the ratio of the critical forces that is applied on the middle of the chain to that which is applied on one of the ends is two. Our study shows that this ratio depends on the length of the chain. This means that the force which is applied to a point can be experienced by a section of the chain. Beyond a length, the base pairs have no information about the applied force. In the case when the chain length is shorter than this length, this ratio may vary. Only in the case when the chain length exceeds a critical length, this ratio is found to be two. Based on the de Gennes formulation, we developed a method to calculate these forces at zero temperature. The exact results at zero temperature match numerical calculations.

Figure 1

The specific heat as a function of applied force at different locations in the chain. The distribution of the critical forces (peak in specific heat) is shown along the chain for finite and infinite chains. Panel (a) is for chain of 400 base pairs, while panel (b) is for 600 base pairs chain and (c) is for 1000 base pairs chain.

Figure 2

Values of the critical forces for increasing chain lengths when force is applied at the different sites along the chain. The points in the plot correspond to the point of force location in the chain. The figure in the inset shows the results in terms of the fraction of site index, $s$. Here $s=i/N$, where $i$ is the site index where the force is applied, while $N$ is the number of base pairs in a chain.

Figure 3

The distribution of the critical forces along the chain for short and long chains. The force is applied to the chain in a section of 25 base pairs, and force is randomly distributed over these 25 sites. Again the subfigures (a), (b), and (c) are for the chains of 400 base pairs, 600 base pairs, and 1000 base pairs, respectively.

Figure 4

Values of the critical forces along applied force locations for a long chain. The points correspond to the applied force locations. When force is applied to 25 sites, the point is shown by the middle number of that section.

Figure 5

Saturation length at different temperatures calculated through the numerical calculations using the PBD model. From the fitted data we find that the saturation length at zero temperature is approximately 52 base pairs.

Figure 6

The average separation, $\langle y_j\rangle$, of base pairs at a force of 50 pN for the three cases, (a) when the force is applied on the end, (b) when the force is applied on the $100\mathrm{th}$ site, and (c) when the force is applied on the $300\mathrm{th}$ site (the mid point of the chain). The plots are for a chain of 600 base pairs.

Figure 7

Plot of $\langle y\rangle$ for a chain of 600 base pairs below and above the critical force ($\sim 41.5$ pN). The upper four figures display the deformation due to a force (from left to right) of 30, 35, 40, and 45 pN. The lower four figures are the zoomed version of the respective upper four figures.

Figure 8

Schematic representation of DNA ladder structure when the strands are pulled in opposite directions from an end. The displacements of the complementary bases are presented by $u_i$ and $v_i$.

Figure 9

The distribution of the critical forces along the chain for a chain length of 1000 base pairs. From the inset figure, we find that, for $\chi =0.155$, the saturation length is approximate 52 base pairs. A similar length is found from the numerical calculations at zero temperature.