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School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel
Correspondence: Address reprint requests to David Andelman, School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel 69978. Tel.: 972-3-640-7239; Fax: 972-3-642-2979; E-mail: andelman{at}post.tau.ac.il.
We address theoretically aggregation of DNA segments by multivalent polyamines such as spermine and spermidine. In experiments, the aggregation occurs above a certain threshold concentration of multivalent ions. We demonstrate that the dependence of this threshold on the concentration of DNA has a simple form. When the DNA concentration cDNA is smaller than the monovalent salt concentration, the threshold multivalent ion concentration depends linearly on cDNA, having the form
cDNA + ß. The coefficients
and ß are related to the density profile of multivalent counterions around isolated DNA chains, at the onset of their aggregation. This analysis agrees extremely well with recent detailed measurements on DNA aggregation in the presence of spermine. From the fit to the experimental data, the number of condensed multivalent counterions per DNA chain can be deduced. A few other conclusions can then be reached: 1), the number of condensed spermine ions at the onset of aggregation decreases with the addition of monovalent salt; 2), the Poisson-Boltzmann theory overestimates the number of condensed multivalent ions at high monovalent salt concentrations; and 3), our analysis of the data indicates that the DNA charge is not overcompensated by spermine at the onset of aggregation.
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