Strong effects of molecular topology on diffusion of entangled DNA molecules

Abstract

When long polymers such as DNA are in a highly concentrated state they may become entangled, leading to restricted self-diffusion. Here, we investigate the effect of molecular topology on diffusion in concentrated DNA solutions and find surprisingly large effects, even with molecules of modest length and concentration. We measured the diffusion coefficients of linear and relaxed circular molecules by tracking the Brownian motion of single molecules with fluorescence microscopy. Four possible cases were compared: linear molecules surrounded by linear molecules, circular molecules surrounded by linear molecules, linear molecules surrounded by circles, and circles surrounded by circles. In measurements with 45-kbp DNA at 1 mg/ml, we found that circles diffused Ϸ100 times slower when surrounded by linear molecules than when surrounded by circles. In contrast, linear and circular molecules diffused at nearly the same rate when surrounded by circles, and circles diffused Ϸ10 times slower than linears when surrounded by linears. Thus, diffusion in entangled DNA solutions strongly depends on topology of both the diffusing molecule and the surrounding molecules. This effect also strongly depends on DNA concentration and length. The differences largely disappeared when the concentration was lowered to 0.1 mg/ml or when the DNA length was lowered to 6 kb. Present theories cannot fully explain these effects.polymers ͉ reptation A mong polymers DNA is rather unique in that it is naturally found in a number of different topological forms, including linear, supercoiled circular, relaxed circular, knotted circular, and branched. DNA solutions handled in vitro in molecular biology research are often relatively concentrated (Ϸ1-10 mg/ ml, for example, after lysis of bacterial cells during DNA isolation, or when DNA is redissolved after ethanol precipitation). According to classical theories and experiments in polymer physics, long flexible molecules form random coils that overlap and become entangled as the concentration of solutions is increased (1, 2). In the field of polymer physics and rheology there is considerable fundamental interest in understanding the effect of molecular topology on entangled polymer dynamics (3, 4). In gel electrophoresis it is well known that molecular topology strongly affects the mobility of DNA. However, with few exceptions, most theories and experiments on diffusion in concentrated polymer solutions have examined only linear molecules. Here, we investigate the effect of molecular topology on diffusion of entangled DNA. Although relaxed circular molecules differ from linear molecules only by the presence of one additional pair of phosphodiester bonds (linking head to tail) and diffuse at nearly the same rate in dilute solution (5), we observe large differences in their diffusion rates with molecules of modest size and concentration. ResultsA 45-kbp fosmid DNA construct (pCCFOS1-45) was prepared as described (6). It was treated with topoisomerase I to prepare the relaxed circular form and with ApaI ...

Topological patterns in two-dimensional gel electrophoresis of DNA knots

“…1A). We model the gel as an imperfect cubic mesh (20), where some of the bonds have been cut (see Materials and Methods) to simulate the presence of open strands, or dangling ends, which have been observed in physical agarose gels (21)(22)(23)(24)(25)(26)(27). Our results confirm the linear relation of the electrophoretic mobility with ACN for the first simple knots (we study ACN up to 12) in a sparse gel and under a weak field.…”

Nonequilibrium dynamics and ultraslow relaxation of confined DNA during viral packaging

“…The DNA concentration within phi29, like many other doublestranded DNA bacteriophages, is very high (∼0.5 g/mL), and one would expect excluded volume and chain entanglements to strongly restrict molecular motion (39,47,48). The effect of entanglements on the dynamics of polymers in melts and concentrated solutions has been successfully predicted by reptation models, in which polymer motion is restricted to a tube-shaped region parallel to the chain contour (39,49).…”

Single-Molecule Imaging Reveals Topology Dependent Mutual Relaxation of Polymer Chains

“…4c top), consistent with a previous study. 48 The diffusion of L-L is described by the reptation model…”

“…The motion and conformational relaxation of single polymer chains under the entangled conditions have been studied by using fluorescently-labeled micrometers-long molecules, typically dsDNA molecules. [47][48][49][50] The diffusion rates, 48,49 modes of the chain motion (e.g. reptation motion), 47 and the conformational relaxation of the chain 51,52 have been characterized by SMLT combined with molecular manipulation techniques (e.g.…”