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.