Attractive forces between cation condensed DNA double helices

ABSTRACT By combining single-molecule magnetic tweezers and osmotic stress on DNA assemblies, we separate attractive and repulsive components of the total intermolecular interaction between multivalent cation condensed DNA. Based on mea-surements of several different cations, we identify two invariant properties of multivalent cation-mediated DNA interactions: re-pulsive forces decay exponentially with a 2.3 6 0.1 A ̊ characteristic decay length and the attractive component of the free energy is always 2.3 6 0.2 times larger than the repulsive component of the free energy at force-balance equilibrium. These empirical constraints are not consistent with current theories that attribute DNA-DNA attractions to a correlated lattice of counterions. The empirical constraints are consistent with theories for Debye-Hückel interactions between helical line charges and with the order-parameter formalism for hydration forces. Each of these theories posits exponentially decaying attractions and, if we assume this form, our measurements indicate a cation-independent, 4.8 6 0.5 A ̊ characteristic decay length for intermolecular attractions between condensed DNA molecules