Knowledge of the elastic properties of DNA is required to understand the structural dynamics of cellular processes such as replication and transcription. Measurements of force and extension on single molecules of DNA have allowed direct determination of the molecule's mechanical properties, provided rigorous tests of theories of polymer elasticity, revealed unforeseen structural transitions induced by mechanical stresses, and established an experimental and conceptual framework for mechanical assays of enzymes that act on DNA. However, a complete description of DNA mechanics must also consider the effects of torque, a quantity that has hitherto not been directly measured in micromanipulation experiments. We have measured torque as a function of twist for stretched DNA--torsional strain in over- or underwound molecules was used to power the rotation of submicrometre beads serving as calibrated loads. Here we report tests of the linearity of DNA's twist elasticity, direct measurements of the torsional modulus (finding a value approximately 40% higher than generally accepted), characterization of torque-induced structural transitions, and the establishment of a framework for future assays of torque and twist generation by DNA-dependent enzymes. We also show that cooperative structural transitions in DNA can be exploited to construct constant-torque wind-up motors and force-torque converters.

DNA is often modelled as an isotropic rod, but its chiral structure suggests the possible importance of anisotropic mechanical properties, including coupling between twisting and stretching degrees of freedom. Simple physical intuition predicts that DNA should unwind under tension, as it is pulled towards a denatured structure. We used rotor bead tracking to directly measure twist-stretch coupling in single DNA molecules. Here we show that for small distortions, contrary to intuition, DNA overwinds under tension, reaching a maximum twist at a tension of approximately 30 pN. As tension is increased above this critical value, the DNA begins to unwind. The observed twist-stretch coupling predicts that DNA should also lengthen when overwound under constant tension, an effect that we quantitatively confirm. We present a simple model that explains these unusual mechanical properties, and also suggests a possible origin for the anomalously large torsional rigidity of DNA. Our results have implications for the action of DNA-binding proteins that must stretch and twist DNA to compensate for variability in the lengths of their binding sites. The requisite coupled DNA distortions are favoured by the intrinsic mechanical properties of the double helix reported here.

The circular chromosome of Escherichia coli is organized into independently supercoiled loops, or topological domains. We investigated the organization and size of these domains in vivo and in vitro. Using the expression of >300 supercoiling-sensitive genes to gauge local chromosomal supercoiling, we quantitatively measured the spread of relaxation from double-strand breaks generated in vivo and thereby calculated the distance to the nearest domain boundary. In a complementary approach, we gently isolated chromosomes and examined the lengths of individual supercoiled loops by electron microscopy. The results from these two very different methods agree remarkably well. By comparing our results to Monte Carlo simulations of domain organization models, we conclude that domain barriers are not placed stably at fixed sites on the chromosome but instead are effectively randomly distributed. We find that domains are much smaller than previously reported, ∼10 kb on average. We discuss the implications of these findings and present models for how domain barriers may be generated and displaced during the cell cycle in a stochastic fashion.

During the random cyclization of long polymer chains, knots of different types are formed. We investigated experimentally the distribution ofknot types produced by random cyclization of phage P4 DNA via its long cohesive ends. The simplest knots (trefoils) predominated, but more complex knots were also detected. The fraction of knots greatly diminished with decreasing solution Na+ concentration. By comparing these experimental results with computer simulations of knotting probability, we calculated the effective diameter ofthe DNA double helix. This important excluded-volume parameter is a measure of the electrostatic repulsion between segments of DNA molecules. The calculated effective DNA diameter is a sensitive function of electrolyte concentration and is several times larger than the geometric diameter in solutions of low monovalent cation concentration.A classic problem in polymer physics is the probability that the random cyclization of a polymer produces a knot of a particular topology. The issues were formulated more than 30 years ago by Frisch and Wasserman (1) and by Delbruck (2). The initial solution was provided by a Monte Carlo simulation in 1974 (3), and since then several computational analyses of the knotting probability of polymer chains have appeared (reviewed in refs. 4 and 5).Experimental measures of knotting frequency have not been made, however, despite the considerable interest in these forms. Ever since the production oflinked hydrocarbon rings, organic chemists have striven to synthesize knotted molecules. These attempts have recently come to fruition with the elegant and complete synthesis of a hydrocarbon knot by Dietrich-Buchecker and Sauvage (6). A distinct synthetic route based on the properties of nucleic acids has been used by Seeman's group to synthesize different types of knots (7).Knots made of DNA, first identified in 1976 (8), are much easier to synthesize and to analyze than other knotted polymers. Knotted DNA has been identified in numerous in vitro and in vivo experiments (9, 10). The topology of the knots is diagnostic of the mechanism of the enzymes that produce them and of the structure of the DNA substrates (9). The experimental studies of DNA knots have been guided by the development of mathematical methods for analyzing DNA topology (11,12).DNA is thus the most suitable polymer for the experimental investigation of the probability of knotting. The measurement of the probability of knotting duplex DNA is of special interest because it provides an excellent means for determining the effective diameter of DNA. This important parameter characterizes the excluded volume of DNA. The effective diameter of DNA is the diameter of an uncharged polymer chain that mimics the conformational properties of actualThe publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact. electrically charged DNA. Because DNA is a highly charge...

ABSIRATCA target protein for nalidixic and oxolinic acids in Escherichia coli, the nalA gene product (Pnal), was purified to homogeneity as judged by gel electrophoresis, using an in vitro complementation assay. It is a dimer of identical 110,000-dalton subunits. A (2), and ColEl DNA (8) were prepared as described. Relaxed kX174 RF and ColEl DNA were prepared either by nicking with pancreatic DNase followed by sealing with T4 DNA ligase (9) or by relaxation with E. coli w protein (6).Enzyme Assays. The Pnal assay, which will be detailed elsewhere, was essentially that devised by C. Sumida-Yasumoto using a nalAr strain constructed by R. Sternglanz. It is based on the dominant conferral of drug sensitivity by addition of wild-type protein to a 4X174 RFI replication system (2) directed by H560-1 extracts. The reaction mixtures (0.05 ml) contained 1 nmol of OXX174 RFI, 0.1 mg of H560-1 receptor (NH4)2SO4 fraction, 10 jig of Fraction II prepared from H560 infected with 4X174 am3 Pnal, and 30 ,ug/ml of Oxo or 100 ,gg/ml of Nal. One unit of Pnal catalyzes the sensitization of 1 nmol of dTMP incorporation to Nal or Oxo in 30 min at 300.The DNA gyrase assay measures the conversion of relaxed ColEl DNA to the supercoiled form as monitored by agarose gel electrophoresis (3). The reaction mixture (35 ,l) contained 35 mM Tris-HCl at pH 7.6, 6 mM MgCl2, 18 mM potassium phosphate, 5 mM spermidine-HCl, 1.4 mM ATP, yeast tRNA at 90 sg/ml, 5 mM dithiothreitol, bovine serum albumin at 50 Mg/1ml, 0.2 Mg of relaxed DNA, and enzyme. After 60 min at 300, 10 Al of a 25% (vol/vol) glycerol solution containing bromophenol blue at 0.25 mg/ml and either 5% sodium dodecyl sulfate (NaDodSO4), 2.5% Sarkosyl, or 45 mM EDTA was added. The mixture was applied to a 13 X 15 X 0.4 cm slab gel of 1.0% agarose and then subjected to electrophoresis at 40 V for [14][15][16] hr at 230 (3). The gels were stained, destained, and photographed using shortwave ultraviolet light (3). Negatives were traced with a Joyce-Loebl microdensitometer. One unit of DNA gyrase converts 0.1 Mug of relaxed DNA to the superAbbreviations: Nal, nalidixic acid; Oxo, oxolinic acid; Pnal, Nal target protein; N-C, nicking-closing; RF, replicative form; NaDodSO4, sodium dodecyl sulfate. An allele conferring resistance to a drug is indicated by r.