Anomalies in sedimentation: IV. Decrease in sedimentation coefficients of chains at high fields

Abstract

A theory is presented for the decrease of sedimentation coefficient at high centrifugal fields recently reported for samples of DNA by Rubenstein and Leighton and others. The theory uses the model of a chain of beads and springs to represent the molecule. Kirkwood's approximation is used for the sedimentation coefficient. The decrease in sedimentation coefficient with field comes about as a result of the uneven frictional forces in the chain, which on the average are less on segments near the center of the chain than on those near the ends. As a result the ends of the chain tend to drag behind the center, and the average intersegment distances are increased; consequently the hydrodynamic shielding of one segment by another is reduced, and the average friction is increased. The effect is thus characteristic of single molecules; intermolecular interaction is not involved. The sedimentation coefficient, S, varies as a power series in a parameter y that measures the distortion produced by the uneven friction: S = S 0(1− D 2 y 2 + D 4 y 4 − ·). where S 0 is the limiting value of S at zero centrifugal field and D 2 and D 4 are constants; y is proportional to the cen speed squared tunes the molecular weight squared divided by S 0. It has been observed that the effects of centrifuge speed on S are negligible below certain critical values of the speed and molecular weight, but increase dramatically immediately above these values; this follows naturally from the high powers of the speed and molecular weight that appear in the above equation.