DNA charge neutralisation by linear polymers I: irreversible binding

We develop a deterministic mathematical model to describe the wayin which polymers bind to DNA by considering the dynamics of thegap distribution that forms when polymers bind to a DNA plasmid.In so doing, we generalise existing theory to account for overlapsand binding cooperativity whereby the polymer binding rate dependson the size of the overlap The proposed mean-field models are thensolved using a combination of numerical and asymptotic methods. Wefind that overlaps lead to higher coverage and hence higher chargeneutralisations, results which are more in line with recentexperimental observations. Our work has applications to genetherapy where polymers are used to neutralise the negative chargesof the DNA phosphate backbone, allowing condensation prior todelivery into the nucleus of an abnormal cell