Force-induced stretched state: Effects of temperature

A model of self-avoiding walks with suitable constraint has been developed to study the effect of temperature on a single-stranded DNA (ssDNA) in the constant force ensemble. Our exact calculations for small chains show that the extension (reaction coordinate) may increase or decrease with the temperature depending on the applied force. The simple model developed here, which incorporates semimicroscopic details of base direction, provides an explanation of the force-induced transitions in ssDNA as observed in experiments.

Figure 1

(Color online) The schematic representation of a ssDNA where bases are on the links of the strand with short stubs representing the direction of the hydrogen bonds. This figure also shows that once two bases are bonded, no further hydrogen bonds can be formed with these bases. The small black circle indicates that one end of the ssDNA is kept fixed while a force $F$ may be applied at the other end.

Figure 2

(Color online) The schematic representation of a ssDNA forming (a) the zipped conformation (dsDNA). In this case, half of the strand is of $\mathbf{A}$ type nucleotides and the other half consists of complementary nucleotides $\mathbf{T}$. (b) A hairpin structure of stems of three bases. (c) shows that by application of a force applied to one end, the system changes from a zipped or hairpin state to an extended state.

Figure 3

Force-temperature diagram for (a) zipped case and (b) DNA hairpin. Solid circles show the crossover regime.

Figure 4

(Color online) The force-extension curve in the constant temperature ensemble for (a) the zipped state and (b) the DNA hairpin. One can see the extension approaching the contour length when the force is varied.

Figure 5

(Color online) Same as Fig. 4 but in the constant force ensemble. The abrupt decrease in the extension is obvious from these plots.

Figure 6

(Color online) Comparison of extension vs temperature curves with and without base-pairing. For the zipped state, the number of base pairs is $N∕2$, while for the hairpin it is 3. $p=0$ corresponds to the noninteracting case.

Figure 7

(Color online) (a) Extension vs temperature curves in 2D for interacting and noninteracting walks of chain length 55 in the constant force ensemble. (b) Extension vs temperature curves for different length ($N=25$, 30, 35, 40, 45, 50, and 55) at $F=1.2$. The collapse of data at low temperature indicates that the chain is in a stretched state.

Figure 8

(Color online) Entropy vs temperature curves in 2D for interacting walks of chain length 55 steps in the constant force ensemble. At high force $F=1.2$ and low temperature, the chain is found to be a stretched state and the entropy of the system is nearly equal to zero. As temperature increases, the system attains a high entropy state. At force equal to zero, one can see that the entropy associated with the globule is higher than the stretched state but much below the extended state. The slight variation in force $F=0.98$ and 1.0 around the phase boundary [23] shows a sharp fall in the entropy from the collapsed state to the extended state. At higher values of $T$, these two curves ($F=1.0$ and 0.98) overlap.