The pulling force of a single DNA molecule condensed by spermidine

In a recent experiment, a single DNA double helix is stretched and relaxed in the presence of spermidine, a short positive polyelectrolyte, and the pulling force is measured as a function of DNA extension. In a certain range of spermidine concentration, a force plateau appears whose value shows maximum as a function of spermidine concentration. We present a quantitative theory of this plateau force based on the theory of reentrant condensation and derive almost parabolic behavior of the plateau force as a function of the logarithm of the spermidine concentration in the range of condensation. Our result is in good agreement with experimental data. DNA condensation by strongly positively charged proteins , histones, is used by nature for compaction of DNA in cell nucleus (DNA is strongly negatively charged). Positive proteins, protamines, are used for additional compaction of DNA in the sperm [1]. Gene therapy uses complexes of DNA with long positive polyelectrolytes or other macrocations. The net charge of these complexes can be positive and therefore they are not repelled by negative cell membrane in the course of gene delivery. Thus, condensation of DNA by positive macrocations is an extremely important physical phenomenon. It is intensively studied in the model system of double helix DNA with spermidine, a flexible polymer with length 15Å and charge +3. It is known that in a dilute DNA solution at some concentration of spermidine, s = s c , each long DNA molecule self-condenses into a toroid [2]. When s grows farther, at a much larger concentration, s = s d , DNA dissolves back [3]. This phenomenon is called reentrant condensation and has got theoretical explanations [4, 5]. f f Bead Bead x L FIG. 1: Schematic illustration of the experimental setup. Partly condensed long DNA is pulled by two beads. Recently, a new single molecule technique has been used to measure the force necessary to pull a single DNA double helix from a toroidal condensate of DNA [6] (Fig. 1). In the experiment, extremely small concentration of DNA (2 nM of nucleotides) is dissolved in water with certain concentrations of spermidine (varying from 200 µM to 200 mM). Dual-trap tweezers are used to stretch a single DNA molecule tethered between two protein-coated polystyrene beads. DNA is first stretched and then relaxed. During these processes, the pulling force f is measured. Experiments are repeated at various spermidine concentrations. It is observed that …