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Attractive Forces between Cation Condensed DNA Double Helices

Brian A. Todd ^*, V. Adrian Parsegian ^*, Akira Shirahata , T. J. Thomas  and Donald C. Rau ^*

^* Laboratory of Physical and Structural Biology, National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20892-0924; Department of Biochemistry and Cellular Physiology, Josai University, Saitama, Japan; and Department of Medicine, University of Medicine and Dentistry of New Jersey-Robert Wood Johnson Medical School, Piscataway, New Jersey 08903

Correspondence: Address reprint requests to Brian A. Todd, E-mail: toddba{at}mail.nih.gov.

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 measurements of several different cations, we identify two invariant properties of multivalent cation-mediated DNA interactions: repulsive forces decay exponentially with a 2.3 ± 0.1 Å characteristic decay length and the attractive component of the free energy is always 2.3 ± 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 ± 0.5 Å characteristic decay length for intermolecular attractions between condensed DNA molecules.