Conditions of double-stranded DNA precipitation by the polyamines spermidine and spermine have been determined experimentally and compared to theoretical predictions. The influence of the concentrations of DNA and added monovalent salt, and of the DNA length has been investigated in a systematic manner. Three regimes of DNA concentrations are observed. We clarify the dependence of these regimes on the monovalent salt concentration and on the DNA length. Our observations make possible a rationalization of the experimental results reported in the literature. A comparison of the precipitation conditions of different kinds of polyelectrolytes suggests a general process. Our experimental data are compared to the "ion-bridging" model based on short-range electrostatic attractions. By starting from the spinodal equation, predicted by this model, and using the limiting form of Manning's fractions of condensed counterions, analytical expressions of the precipitation conditions have been found in the three regimes. Experimental and theoretical results are in good agreement.

We have studied the precipitation of short DNA molecules by the polycations spermidine, spermine, and cobalthexamine. The addition of these cations to a DNA solution leads first to the precipitation of the DNA; further addition resolubilizes the DNA pellet. The multivalent salt concentration required for resolubilization is essentially independent of the DNA concentration (between 1 g/ml and 1 mg/ml) and of the monovalent cation concentration present in the DNA solution (up to 100 mM). The DNA aggregates are anisotropic; those obtained in the presence of the polyamines spermidine and spermine generally contain a cholesteric liquid crystalline phase that flows spontaneously. In contrast this phase is never seen in the presence of cobalthexamine. We propose that the ability of polyamines to condense DNA in fluid structures is an essential feature of their biological functions.Multivalent cations with a charge of 3ϩ or greater induce the condensation of DNA in aqueous solution (reviewed in Ref. 1). In extremely dilute DNA solutions, one can observe the monomolecular collapse of long chains; with more concentrated DNA solutions (of short or long chains), aggregation sets in. Electrostatic forces appear to be predominant in DNA condensation. For highly charged polyelectrolytes there is a strong electrostatic repulsion between the chains. One expects the addition of multivalent cations to decrease this repulsion. DNA condensation by multivalent cations has been analyzed within the framework of the counterion condensation theory developed by Manning (2). This theory predicts the fraction of the DNA charges neutralized by a given cation: a saturating trivalent cation for instance should neutralize 92% of the DNA charges. It has been shown experimentally that approximately 90% of the DNA charges must be neutralized before DNA condensation can occur (3, 4). In addition, mono-and divalent cations compete with multivalent cations in the condensation process, in agreement with the proposal that the interactions are predominantly electrostatic. It is known, however, that a purely electrostatic model is insufficient to account for the experimental data; cobalthexamine is for instance five times more efficient as a condensing agent than spermidine, although these compounds have the same charge (3ϩ) (4).DNA condensation has been studied with the naturally occurring polyamines spermidine (3ϩ) and spermine (4ϩ), as well as with the inorganic cation cobalthexamine (3ϩ). Experimental data indicate that condensation is usually coupled with an isotropic to an anisotropic transition. In particular, high molecular weight DNA aggregates formed by spermidine, spermine, or cobalthexamine give a strong equatorial reflection when analyzed by x-ray diffraction (5, 6). Based on these data, several types of crystalline and liquid crystalline structures have been suggested for these DNA aggregates (5, 7). We have recently undertaken a study of these DNA aggregates using short (about 150 base pairs long) DNA molecules (8). In the case of the triv...