Single molecule statistics and the polynucleotide unzipping transition

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Original entry: Hsin-I Lu, APPHY 225, Fall 2009

"Single molecule statistics and the polynucleotide unzipping transition"

D. K. Lubensky and D. R. Nelson, PRA 65, 031917 (2002)


This paper presents an extensive theoretical investigation of the mechanical unzipping of double-stranded DNA under the influence of an applied force. In the limit of long polymers, there is a thermodynamic unzipping transition at a critical force value of order 10 pN, with different critical behavior for homopolymers and for random heteropolymers. As the applied force approaches the critical value, the double-stranded DNA unravels in a series of discrete, sequence-dependent steps that allow it to reach successively deeper energy minima. Plots of extension versus force thus take the striking form of a series of plateaus separated by sharp jumps. Similar qualitative features should reappear in micromanipulation experiments on proteins and on folded RNA molecules.

Micromanipulation of Single Molecule

Fig. 1: Sketch of the DNA unzipping experiment. Inset: Schematic phase diagram in the temperature– pulling force (<math>T-F</math>) plane of a <math>ds</math>DNA molecule in three dimensions. At low enough T and F, the polymer is in the native, doublestranded phase. At the phase transition line Fc(T), the DNA denatures and the two strands separate. Thermally induced melting occurs at zero force at a temperature Tm . As indicated by the arrow, this paper considers instead the unzipping transition, in which the phase transition line is crossed at nonzero F.

Micromanipulation experiments on single molecules provide the opportunities to measure entire distributions of molecular properties, without the requirement for averaging over a macroscopic sample. The system studied in the paper-the unzipping of double-stranded DNA (<math>ds</math>DNA) shows novel response to force on single molecule level. Fig. 1 shows the system studied in the paper. Two single strands of a double-stranded DNA molecule with a randomly chosen base sequence are pulled apart under the influence of a constant force.

One of the single strands of a dsDNA molecule with a random base sequence is attached by its end to a solid surface, and the other is pulled away from the surface with a constant force F. F could be created, for example, with magnetic tweezers, which have been used to exert constant piconewton-scale forces over hundreds of microns. Optical tweezers or atomic force microscopes (AFM) with appropriate feedback can create a similar effect. As a result, the double strand partially "unzips" or denatures, separating m base pairs (m=2 in the figure). The distance between the ends of the two single strands, or extension, is r.

Fig. 2: Schematic of dsDNA unzipping through a narrow pore. The pore is assumed to be large enough that single-stranded DNA, but not double-stranded DNA, can fit through it. Under the influence of an electric field or comparable force F, one single strand inserts into the channel and is gradually pulled through. As the strand is drawn through the pore, it must unzip from its complementary strand.

The formalism of this study also applies to another method for unzipping DNA (Fig. 2). An electric field is applied to force one of the single strands through a very small pore. If the pore is so narrow that double-stranded DNA cannot fit through it, and if the applied field is strong enough, one of the single strands can enter the pore and be drawn through it, thereby unzipping the duplex.