DNA ELECTROPHORESIS IN POLYMER-SOLUTIONS - OGSTON SIEVING, REPTATION AND CONSTRAINT RELEASE

The electrophoresis of long polyelectrolytes is considered theoretical ly, with special attention to duplex DNA. We first discuss quantitativ e approaches to determine unambiguously the entanglement properties of polymer solutions. Following an idea proposed by Grossman and Soane, we then assume that the ''mesh'' size of the solution plays the role o f a dynamic ''pore size'' in order to apply theories for gel electroph oresis. In the framework of the Ogston model, we predict that duplex D NA up to 1 kb or more should be separable in dilute (i. c. nonentangle d) solutions of high molecular weight polymers. In an entangled soluti on, and for DNA larger than the pore size, we use a recently developed fluctuation-reptation model to predict the range of sizes in which se paration should be possible as a function of electric field E and pore size xi(b). For xi(b) larger than the Kuhn length of DNA, we predict a separation up to a size Nscaling as E-1xi(b)-1. For xi(b) smaller t han the Kuhn length, two different regimes are expected. For small ele ctric fields (typically of the order of 10 V/cm), Nshould be proporti onal to E-1xi(b)-3/2, whereas for high electric fields such as encount ered in capillary electrophoresis, we expect that Nis proportional to E-2/5xi(b)-12/5. These predictions are qualitatively different from e arlier ones. Finally, we demonstrate that the finite lifetime of the ' 'pores'' in an entangled solution (as opposed to a gel) may lead to a new migration mechanism by constraint release, which is not size-depen dent. In contrast with earlier suggestions, we show that, in general, the concentration should be raised above a minimal value significantly higher than the entanglement threshold cin order to separate large D NA molecules. We propose expressions for this minimal concentration as a function of DNA and polymer sizes. This model suggests that, for a given high molecular weight polymer, the size of the largest DNA that can be separated increases roughly linearly with the viscosity of the solution.