Victor A. Bloomfield

In the presence of multivalent cations, high molecular weight DNA undergoes a dramatic condensation to a compact, usually highly ordered toroidal structure. This review begins with an overview of DNA condensation: condensing agents, morphology, kinetics, and reversibility, and the minimum size required to form orderly condensates. It then summarizes the statistical mechanics of the collapse of stiff polymers, which shows why DNA condensation is abrupt and why toroids are favored structures. Various ways to estimate or measure intermolecular forces in DNA condensation are discussed, all of them agreeing that the free energy change per base pair is very small, on the order of 1% of thermal energy. Experimental evidence is surveyed showing that DNA condensation occurs when about 90% of its charge is neutralized by counterions. The various intermolecular forces whose interplay gives rise to DNA condensation are then reviewed. The entropy loss upon collapse of the expanded wormlike coil costs free energy, and stiffness sets limits on tight curvature. However, the dominant contributions seem to come from ions and water. Electrostatic repulsions must be overcome by high salt concentrations or by the correlated fluctuations of territorially bound multivalent cations. Hydration must be adjusted to allow a cooperative accommodation of the water structure surrounding surface groups on the DNA helices as they approach. Undulations of the DNA in its confined surroundings extend the range of the electrostatic forces. The condensing ions may also subtly modify the local structure of the double helix.

We used a force-measuring laser tweezers apparatus to determine the elastic properties of lambda-bacteriophage DNA as a function of ionic strength and in the presence of multivalent cations. The electrostatic contribution to the persistence length P varied as the inverse of the ionic strength in monovalent salt, as predicted by the standard worm-like polyelectrolyte model. However, ionic strength is not always the dominant variable in determining the elastic properties of DNA. Monovalent and multivalent ions have quite different effects even when present at the same ionic strength. Multivalent ions lead to P values as low as 250-300 A, well below the high-salt "fully neutralized" value of 450-500 A characteristic of DNA in monovalent salt. The ions Mg2+ and Co(NH3)63+, in which the charge is centrally concentrated, yield lower P values than the polyamines putrescine2+ and spermidine3+, in which the charge is linearly distributed. The elastic stretch modulus, S, and P display opposite trends with ionic strength, in contradiction to predictions of macroscopic elasticity theory. DNA is well described as a worm-like chain at concentrations of trivalent cations capable of inducing condensation, if condensation is prevented by keeping the molecule stretched. A retractile force appears in the presence of multivalent cations at molecular extensions that allow intramolecular contacts, suggesting condensation in stretched DNA occurs by a "thermal ratchet" 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.

Providing a comprehensive account of the structures and physical chemistry properties of nucleic acids, with special emphasis on biological function, this text is for those with only a basic understanding of physical chemistry and molecular biology.