Onset of DNA Aggregation in Presence of Monovalent and Multivalent Counterions

TL;DR

This paper presents a theoretical analysis of DNA aggregation induced by multivalent ions, showing a linear relationship between the threshold ion concentration and DNA concentration, and compares predictions with experimental data.

Contribution

It introduces a simple model relating aggregation threshold to ion density profiles and validates it against recent experimental measurements.

Findings

Threshold multivalent ion concentration depends linearly on DNA concentration.

Number of condensed spermine ions decreases with added monovalent salt.

Poisson-Boltzmann theory overestimates condensed ions at high salt levels.

Abstract

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 c_DNA is smaller than the monovalent salt concentration, the threshold multivalent ion concentration depends linearly on c_DNA, having the form alpha c_DNA + beta. The coefficients alpha and beta 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: i) the number of condensed spermine ions at the onset of aggregation decreases with the addition of monovalent salt; ii) the Poisson-Boltzmann theory over-estimates the number of condensed multivalent ions at high monovalent salt concentrations; iii) our analysis of the data indicates that the DNA charge is not over-compensated by spermine at the onset of aggregation.