Gel mobilities of linking-number topoisomers and their dependence on DNA helical repeat and elasticity

Abstract

Agarose-gel electrophoresis has been used for more than thirty years to characterize the linking-number (Lk) distribution of closed-circular DNA molecules. Although the physical basis of this technique remains poorly understood, the gel-electrophoretic behavior of covalently closed DNAs has been used to determine the local unwinding of DNA by proteins and small-molecule ligands, characterize supercoiling-dependent conformational transitions in duplex DNA, and to measure helical-repeat changes due to shifts in temperature and ionic strength. Those results have been analyzed by assuming that the absolute mobility of a particular topoisomer is mainly a function of the integral number of superhelical turns, and thus a slowly varying function of plasmid molecular weight. In examining the mobilities of Lk topoisomers for a series of plasmids that differ incrementally in size over more than one helical turn, we found that the size-dependent agarose-gel mobility of individual topoisomers with identical values of Lk (but different values of the excess linking number, DeltaLk) vary dramatically over a duplex turn. Our results suggest that a simple semi-empirical relationship holds between the electrophoretic mobility of linking-number topoisomers and their average writhe in solution.

Fig 1

(A) Plasmid constructs used in the present study. Variable-length regions are indicated by the thicker arc segment between recombination target sites (gray arrows). (B) Example of the “cleavage-end repair-ligation” procedure used to construct several plasmids. Action of a restriction endonuclease at its cleavage sites (arrowheads) generates a pair of M-nt 5′ overhangs (red) that are filled by the Klenow fragment of E. coli DNA polymerase I in the presence of dNTPs (green). The plasmid is then cyclized by blunt-end ligation using T4 ligase, thereby extending the DNA duplex by M bp. (C) Gel-electrophoretic characterization of native (superhelix density ≈ −0.055) pFS2.Xd plasmids in a 0.8% agarose gel run in TBE buffer containing 0.5 µg mL⁻¹ chloroquine. Lanes 1–9 correspond to the pFS2.Xd plasmids given in Table 1 in order of increasing plasmid size. (D) Gel-electrophoretic separation of pFS2.Xd plasmids under conditions identical to those in (C) after relaxation to equilibrium with topoisomerase I as described in Materials and Methods. Gel lanes are labeled as in (C). Note the linear dependence of topoisomer mobility on construct size, highlighted by the red diagonal boxes in the figure. Bands corresponding to nicked forms are located within the blue rectangle.

Fig 2

Analysis of topoisomer mobilities. (A) Line scan of intensity along a gel lane obtained by horizontal averaging of pixel intensities across the image of a gel lane. Positions of the centers of each topoisomer band are indicated by vertical arrows. Bands correspond to topoisomers with increasing values of Lk from left to right; $L{k\prime }_0$ denotes the (integer) Lk value closest to Lk₀. The peak corresponding to the nicked form is indicated by oc. (B) Gel mobilities of topoisomers with identical values of Lk for plasmids of different size. Bands corresponding to the same topoisomer are indicated by the diagonal boxed regions. (C) Set of line scans corresponding to the left-hand portion of (B).

Fig 3

Theoretical estimates of Wr distributions, Wr variance, and <Wr>as functions of Lk based on Metropolis Monte Carlo simulations of a 3000-bp plasmid. (A) The Wr probability density for ΔLk = −10 computed over 1·10⁷ trial moves is shown along with a Gaussian fit to this distribution. (B) Normalized Monte Carlo Wr distributions for topoisomers having ΔLk values between −20 and −10. Note the progressive narrowing of the distribution with increasing values of −ΔLk (C) Metropolis Monte Carlo Wr variance for supercoiled DNAs as a function of −ΔLk and comparison with the analysis of Levene and Crothers [48]. The solid line is a least-squares fit to the variance over the range −12 ≤ ΔLk ≤ 2. (D) Average Wr, <Wr>, as a function of −ΔLk determined by Metropolis Monte Carlo simulations. The solid curve is a linear fit to the data with slope 0.73.

Fig 4

Fitting of topoisomer gel-mobility data according to Eq. (1). (A) pCS2.Xd mobilities in TAE buffer. (B) pCS2.Xd mobilities in TBE buffer. (C) pFS2.Xd in TBE buffer. Individual topoisomers are identified by their Lk values in legends located to the right of each figure. The value $L{k\prime }_0$ corresponds to the most-probable topoisomer for each distribution and is the nearest integral Lk value to Lk₀. Best-fit values of adjustable parameters are given in Table 3.