A simple model for DNA elution from filters

Abstract

DNA chain scission, induced both in vitro and in vivo by various agents, is an event of great biological relevance. The damage is currently evaluated by empirical membrane separation techniques; the results are quite reproducible and the sensitivity higher than 1 single strand break per 10(9) Daltons. We outline a simple theory of the filtration of coiled macrosolutes, having a random size distribution, through porous membranes, considered as being in quasi-steady flow. The basic transport equation Jj = cj (1 - sigma)Jv is solved by considering that the value of sigma j, the reflection coefficient of component j, (1 less than or equal to j less than or equal to N), is given by (1 - KjRj), where Kj is the partition constant between pore and solution, a function of the conformational entropy loss of the coil, and Rj accounts for the frictional force experienced by a particle moving along the pore. The problem of evaluating the volume Vs filled up with solute has been approached according to a simplified theory of the excluded volume for flexible polymers; the result is Vs = sigma nj4/3 pi(rGj)3 where rGj is the jth radius of gyration. The solution of the resulting set of N differential equations gives nj, the number of molecules of component j remaining on the filter, as a function of the elution volume V. The theory demonstrates that the process is governed by the average dimensions of the coil, so affording a universal calibration of filter elution methods, in excellent agreement with the experiments.