Pulling short DNA molecules having defects on different locations

We present a study on the role of defects on the stability of short DNA molecules. We consider short DNA molecules (16 base pairs) and investigate the thermal as well as mechanical denaturation of these molecules in the presence of defects that occur anywhere in the molecule. For the investigation, we consider four different kinds of chains. Not only are the ratios of AT to GC different in these molecules but also the distributions of AT and GC along the molecule are different. With suitable modifications in the statistical model to show the defect in a pair, we investigate the denaturation of short DNA molecules in thermal as well as constant force ensembles. In the force ensemble, we pulled the DNA molecule from each end (keeping other end free) and observed some interesting features of opening of the molecule in the presence of defects in the molecule. We calculate the probability of opening of the DNA molecule in the constant force ensemble to explain the opening of base pairs and hence the denaturation of molecules in the presence of defects.

Figure 1

The on-site potential for the defect in a pair is shown by square symbol and dashed (red) line. The depth of the potential for the bases in a pair is represented by the solid line with black circles. There is no minimum of potential for the defect pair [13].

Figure 2

The melting temperature $T_m$ calculated for different values of upper cutoff ($\delta$) for a homogeneous chain. The best straight line fit for this plot is found for $1/\delta$. The different cutoffs are 8, 10, 20, 50, 100, 200, and 300 Å. The model parameters are $D=0.1\mathrm{eV}$, $a=4.2{\AA }^{-1}$, $\rho =5.0$, $b=0.35{\AA }^{-1}$, and $k=0.021\mathrm{eV}/{\AA }^{-2}$.

Figure 3

The melting temperature $T_m$, calculated by specific heat and fraction of open pairs $\varphi$ for chain 1 (homogeneous) and chain 4 (random). The parameters $p$ and $q$ are adjusted in order to get a precise match with the peak in specific heat. The values are $p=12.0$ and $q=10.0$. The value of $C_v$ is scaled to show that the peak position and 50% of the open pairs meet at the same point (temperature).

Figure 4

The melting temperature $T_m$ for all four chains with different numbers as well as locations of defects along the DNA molecule. Figures in a row are for a chain with different numbers of defects. Figures in a column are for different chains with the same number of defect(s), displayed by $m$.

Figure 5

The value of critical force $F_c$ for different chains having different numbers of defects as well as their location. We show both the cases when force is applied on the $3^{\prime }$ end (solid lines with circle) and on the $5^{\prime }$ end (dashed lines with square). Only for the case when the defect site is in the middle of the chain is there no change in $F_c$ for these two cases. The critical forces for pure chains 1, 2, 3, and 4 are 4.54, 6.96, 6.98, and 6.97 pN respectively.

Figure 6

The density plots to show the difference in the opening of a homogeneous DNA molecule (chain 1 with four defects) when force is applied on the $3^{\prime }$ end. (Left) When defect pairs are 1–4 ($3^{\prime }$ end). (Right) When the four defect pairs are on the $5^{\prime }$ end (13–16). The difference in the critical force $F_c$ for the two cases is observed here (more clearly in the zoomed version). In order to open 50% of the base pairs, the $F_c$ for first case (left) is 2.96 pN while for the second case (right) it is 2.92 pN.