Deoxyribonucleic Acid Theory of Techniques for Separation

J. Noolandi, Xerox Research Centre of Canada, Mississauga, Ontario, Canada

Copyright © 2000 Academic Press

Introduction

Separation of biochemical molecules can be carried out in gels or polymer solutions and, in specific cases, in free solution, using constant or variable electric fields. Gels are used primarily in deep-dish containers, submerged in buffer, and polymer solutions are used in glass capillaries, with inner diameters less than 100 |im. Thin gels between two glass plates have been used for separating and sequencing single-stranded DNA molecules. We begin the theoretical discussion by considering the separation of double-stranded DNA molecules (dsDNA) in submarine gels under constant electric field conditions.

Geometrical Sieving Model for Small DNA Molecules in a Constant Electric Field

Ogston was the first to calculate the fractional volume available to a sphere of radius R in a gel of a given concentration. The gel itself was modelled as a random array made up of fibres of radius r. Within this description, a sphere with a radius R»r cannot pass through the network if the sphere is not allowed to deform. This geometrical model predicts that the electrophoretic mobility of DNA molecules, as a result of molecular 'sieving', varies as:

Mo gc exp

where Rg is the radius of gyration of the DNA molecule, ¿u0 is the free solution mobility, a is the average pore size of the gel, and the exponential dependence of the mobility arises from the assumption of Poisson statistics for the distribution of spaces in a random network of straight fibres. This model describes the mobility of small molecules when they first encounter the gel fibres as obstacles to molecular motion. The analysis of experimental data using eqn [1] is highly model dependent, but can provide some guidance for the development of new gel structures for more efficient electrophoretic separations of small molecules.

Entropic Trapping of Small DNA Molecules

For DNA in the entropic size regime, the deformable molecules select the larger pores in order to maximize locally their conformational entropy. However, in order to accomplish this, they must squeeze through the narrow channels connecting the larger pores. The corresponding polyelectrolyte dynamics is dominated by an activation process in this regime, where the electrophoretic mobility is given by an inverse power law ( > 1) over a size range that is larger than for the Ogston regime, but smaller than for the beginning of reptation, which is discussed in the next section.

Gel Electrophoresis of Large DNA Molecules in a Constant Electric Field

Figure 1 shows a schematic picture of a gel matrix, in which a DNA molecule is embedded. For a molecule that is much longer than the average spacing between the chemical cross-links of the gel fibres, the molecule cannot move through the gel as a random coil, rather

Figure 1 Schematic representation of a DNA molecule in a two-dimensional gel (A), in which the open dots represent obstacles corresponding to the gel fibres. (B) Shows how the obstacles hindering the motion ofthe molecule are approximated by a tube and the polymer by a chain of beads; the electric field exerts a force qEon the last bead and orients the segment leaving the tube. The tube is defined by the molecular conformation so that an extended conformation (with less DNA per gel pore) has a longer tube. (C) Charge gradients (C1) along the tube axis, and field-driven tube leakages (C2) are neglected in the biased reptation model.

pore. Under the influence of an electric field, Ma change as a function of time, depending on the stiffness of the molecule, the pore size, the magnitude of the electric field, and other factors. Another important quantity is the scaled effective electric field, Eeff:

eiMaEa 2knT

E Ea

which defines the intrinsic electric field parameter Ea. The net charge per nucleotide for DNA is denoted by ei. This quantity depends on the native charge on the molecule, as well as on the charge screening properties of the buffer solution used for the electrophoretic separation. A simple way of understanding the limitations for separating large molecules in a gel using constant electric fields is as follows.

For constant a and Ma, the electrical force Fl on the molecule in the longitudinal direction (also known as the tube axis, if the molecule is considered to fill a 'tube' made up of occupied gel pores) is:

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