Condensation of DNA by multivalent cations: considerations on mechanism.

DNA is generally found within viruses and cells in a tightly packaged state, typically occupying only 10(-4)-10(-6) of the volume of the uncondensed DNA wormlike coil. Condensation can be induced in vitro at low salt by the naturally occurring polyamines spermidine3+ and spermine4+, by hexammine cobalt(III), and even by Mg2+ in methanol-water mixtures. These condensates generally have an orderly, toroidal, or rodlike shape and size similar to that of DNA gently lysed from phage heads. It is also striking that the condensate size distribution is independent of DNA molecular length from 400 to 40,000 base pairs (bp), but that shorter DNA molecules (e.g., 150-bp mononucleosomal DNA) cannot condense in this fashion. We have constructed a successive association equilibrium theory to attempt to explain these results, using an equation devised by Tanford for micelle formation. Most of the obvious attractive and repulsive free energy contributions (mixing, bending, hydration, and other nearest-neighbor interactions) are linear in the amount of DNA incorporated, but the net attractive delta G0 grows nonlinearly because of the increasing average number of nearest neighbors of each duplex as the particle grows. In order that the size distribution have a maximum, a quadratic repulsive free energy is also required, arising from the electrostatic self-energy of the incompletely neutralized particles. The net attractive free energy per base pair interaction is tiny, on the order of 10(-3) kT. Despite the apparent generally correct order of magnitude of the various free energy terms, the calculated size distribution is smaller and narrower than observed experimentally. It appears that the size distribution of condensed particles is determined kinetically rather than thermodynamically. Very short DNA molecules cannot nucleate stable aggregates because they cannot develop adequate overlap, either internally or intermolecularly. A substantial fraction of rodlike condensates is observed in aqueous solutions only with a rather inefficient condensing agent, permethylated spermidine. This suggests that slow condensation kinetics may be required to overcome the high activation energy of highly distorted DNA bends or kinks at the turning points of rods. Evidence is reviewed that condensation may be associated with localized helix structure distortion provoked by condensing agents.