Torsional and bending rigidity of the double helix from data on small DNA rings

We have calculated the variance of equilibrium distribution of a circular wormlike polymer chain over the writhing number, [Wr)2), as a function of the number of Kuhn statistical segments, n. For large n these data splice well with our earlier results obtained for a circular freely jointed polymer chain. Assuming that [delta Lk)2) = [delta Tw)2) we have compared our results with experimental data on the chain length dependence of the [delta Lk)2) value recently obtained by Horowitz and Wang for small DNA rings. This comparison has shown an excellent agreement between theory and experiment and yielded a reliable estimate of the torsional and bending rigidity parameters. Namely, the torsional rigidity constant is C = 3.0.10(-19) erg cm, and the bending rigidity as expressed in terms of the DNA persistence length is a = 500 A. The obtained value of C agrees well with earlier estimates by Shore and Baldwin as well as by Horowitz and Wang whereas the a value is in accord with the data of Hagerman. We have found the data of Shore and Baldwin on the chain length dependence of the [delta Lk)2) value to be entirely inconsistent with our theorectical results.     

Effect of nucleosome distortion on the linking deficiency in relaxed minichromosomes

The wrapping of closed circular DNA on a protein surface, followed by relaxation with a topoisomerase and removal of proteins, produces a characteristic DNA linking deficiency, delta Lk. We show that the magnitude of delta Lk depends upon the surface shape, and we calculate changes in delta Lk caused by particular distortions of the protein wrapping surface. If the DNA remains attached to the surface during distortion, the DNA winding number, phi, is not altered. The change in delta Lk is then equal to the change in the surface linking number, SLk, which is a straightforward measure of the wrapping of the DNA around the surface. For left-handed wrapping, as in a nucleosome, SLk = -n, the number of times that the DNA axis winds around the axis of the protein complex. We calculate values of SLk for the helical wrapping of a constant length of DNA on protein surfaces having the shapes of cylinders and of ellipsoids and hyperboloids of revolution. If the equatorial radius of the protein is fixed, change in shape from a cylinder to a hyperboloid increases SLk, while the corresponding change to an ellipsoid reduces SLk. We apply the general results to the interpretation of experiments in which minichromosomes are relaxed with topoisomerase at various temperatures and delta Lk is determined. The result is that a distortion of the nucleosome core by at most 5% (the change in the radius at the axial extremity relative to the equator) is sufficient to explain the observed delta Lk changes.     

The influence of salt on the structure and energetics of supercoiled DNA.

We present a detailed computational study of the influence of salt on the configurations, energies, and dynamics of supercoiled DNA. A potential function that includes both elastic and electrostatic energy components is employed. Specifically, the electrostatic term, with salt-dependent coefficients, is modeled after Stigter's pioneering work on the effective diameter of DNA as a function of salt concentration. Because an effective charge per unit length is used, the electrostatic formulation does not require explicit modeling of phosphates and can be used to study long DNAs at any desired resolution of charge. With explicit consideration of the electrostatic energy, an elastic bending constant corresponding to the nonelectrostatic part of the bending contribution to the persistence length is used. We show, for a series of salt concentrations ranging from 0.005 to 1.0 M sodium, how configurations and energies of supercoiled DNA (1000 and 3000 base pairs) change dramatically with the simulated salt environment. At high salt, the DNA adopts highly compact and bent interwound states, with the bending energy dominating over the other components, and the electrostatic energy playing a minor role in comparison to the bending and twisting terms. At low salt, the DNA supercoils are much more open and loosely interwound, and the electrostatic components are dominant. Over the range of three decades of salt examined, the electrostatic energy changes by a factor of 10. The buckling transition between the circle and figure-8 is highly sensitive to salt concentration: this transition is delayed as salt concentration decreases, with a particularly sharp increase below 0.1 M. For example, for a bending-to-twisting force constant ratio of A/C = 1.5, the linking number difference (delta LK) corresponding to equal energies for the circle and figure-8 increases from 2.1 to 3.25 as salt decreases from 1.0 to 0.005 M. We also present in detail a family of three-lobed supercoiled DNA configurations that are predicted by elasticity theory to be stable at low delta Lk. To our knowledge, such three-dimensional structures have not been previously presented in connection with DNA supercoiling. These branched forms have a higher bending energy than the corresponding interwound configurations at the same delta Lk but, especially at low salt, this bending energy difference is relatively small in comparison with the total energy, which is dominated by the electrostatic contributions. Significantly, the electrostatic energies of the three-lobed and (straight) interwound forms are comparable at each salt environment.(ABSTRACT TRUNCATED AT 400 WORDS)     

Atomistic simulations reveal bubbles, kinks and wrinkles in supercoiled DNA

Although DNA is frequently bent and supercoiled in the cell, much of the available information on DNA structure at the atomistic level is restricted to short linear sequences. We report atomistic molecular dynamics (MD) simulations of a series of DNA minicircles containing between 65 and 110 bp which we compare with a recent biochemical study of structural distortions in these tight DNA loops. We have observed a wealth of non-canonical DNA structures such as kinks, denaturation bubbles and wrinkled conformations that form in response to bending and torsional stress. The simulations show that bending alone is sufficient to induce the formation of kinks in circles containing only 65 bp, but we did not observe any defects in simulations of larger torsionally relaxed circles containing 110 bp over the same MD timescales. We also observed that under-winding in minicircles ranging in size from 65 to 110 bp leads to the formation of single stranded bubbles and wrinkles. These calculations are used to assess the ability of atomistic MD simulations to determine the structure of bent and supercoiled DNA.     

Brownian dynamics simulations of supercoiled DNA with bent sequences.

The recently presented Brownian dynamics model for superhelical DNA is extended to include local curvature of the DNA helix axis. Here we analyze the effect of a permanent bend on the structure and dynamics of an 1870-bp superhelix with delta Lk = -10. Furthermore, we define quantitative expressions for computing structural parameters such as loop positions, superhelix diameter, and plectonemic content for trajectories of superhelical DNA, and assess the convergence toward global equilibrium. The structural fluctuations in an interwound superhelix, as reflected in the change in end loop positions, seem to occur by destruction/creation of loops rather than by a sliding motion of the DNA around its contour. Their time scale is on the order of 30-100 microseconds. A permanent bend changes the structure and the internal motions of the DNA drastically. The position of the end loop is fixed at the permanent bend, and the local motions of the chain are enhanced near the loops. A displacement of the bend from the end loop to a position inside the plectonemic part of the superhelix results in the formation of a new loop and the disappearance of the old one; we estimate the time involved in this process to be about 0.5 ms.     

Condensin pinches a short negatively supercoiled DNA loop during each round of ATP usage

Condensin, an SMC (structural maintenance of chromosomes) protein complex, extrudes DNA loops using an ATP‐dependent mechanism that remains to be elucidated. Here, we show how condensin activity alters the topology of the interacting DNA. High condensin concentrations restrain positive DNA supercoils. However, in experimental conditions of DNA loop extrusion, condensin restrains negative supercoils. Namely, following ATP‐mediated loading onto DNA, each condensin complex constrains a DNA linking number difference (∆Lk) of −0.4. This ∆Lk increases to −0.8 during ATP binding and resets to −0.4 upon ATP hydrolysis. These changes in DNA topology do not involve DNA unwinding, do not spread outside the condensin‐DNA complex and can occur in the absence of the condensin subunit Ycg1. These findings indicate that during ATP binding, a short DNA domain delimited by condensin is pinched into a negatively supercoiled loop. We propose that this loop is the feeding segment of DNA that is subsequently merged to enlarge an extruding loop. Such a “pinch and merge” mechanism implies that two DNA‐binding sites produce the feeding loop, while a third site, plausibly involving Ycg1, might anchor the extruding loop.     

Probing the elastic limit of DNA bending

Sharp bending of double-stranded DNA (dsDNA) plays an essential role in genome structure and function. However, the elastic limit of dsDNA bending remains controversial. Here, we measured the opening rates of small dsDNA loops with contour lengths ranging between 40 and 200 bp using single-molecule Fluorescence Resonance Energy Transfer. The relationship of loop lifetime to loop size revealed a critical transition in bending stress. Above the critical loop size, the loop lifetime changed with loop size in a manner consistent with elastic bending stress, but below it, became less sensitive to loop size, indicative of softened dsDNA. The critical loop size increased from ∼60 bp to ∼100 bp with the addition of 5 mM magnesium. We show that our result is in quantitative agreement with the kinkable worm-like chain model, and furthermore, can reproduce previously reported looping probabilities of dsDNA over the range between 50 and 200 bp. Our findings shed new light on the energetics of sharply bent dsDNA.     

DNA Topological Context Affects Access to Eukaryotic DNA Topoisomerase I

Abstract

We have analyzed the reactivity of a 217 base pair segment of the intrinsically curved Crithidia fasciculata kinetoplast DNA towards eukaryotic DNA topoisomerase I. The substrates were open [linear fragment and nicked circle] and closed minidomains [closed relaxed circle and circles with linking differences of ?1 and ?2], We interpreted the results with the aid of a model that was used to predict the structures of the topoisomers. The modelling shows that the ΔLk(?l) form is unusually compact because of the curvature in the DNA. To determine the role of sequence-directed curvature in both the experimental and modeling studies, controls were examined in which the curved Crithidia sequence was replaced by an uncurved sequence obtained from the plasmid pBR322.

Reactivity of the Crithidia DNA [as analyzed both by the cleavage and the topoisomerization reactions] markedly varied among the DNA forms: (i) the hierarchy of overall reactivity observed is: linear fragment > nicked circular, closed circular [ΔLk(O)], interwound [ΔLk(?2)] > bent interwound [ΔLk(?l)]; (ii) the intensity of several cleavage positions differs among DNA forms.

The results show that eukaryotic DNA topoisomerase I is very sensitive to the conformation of the substrates and that its reactivity is modulated by the variation of the compactness of the DNA molecule. The C. fasciculata sequence contains a highly curved segment that determines the conformation of the closed circle in a complex way.     

Temperature dependence of the gel electrophoretic mobility of superhelical DNA.

We have determined the gel electrophoretic behavior of closed circular plasmid pSM1 DNA (5420 bp) as a function of both temperature and of linking number (Lk). At temperatures below 37 degrees, the electrophoretic mobility first increases, then becomes constant as Lk is decreased below that of the relaxed closed DNA. As the temperature is increased above 37 degrees the electrophoretic mobility first increases as Lk decreases and then varies in a cyclic manner with further decreases in Lk. As the temperature is increased over the range 37 degrees - 65 degrees the cyclic behavior is manifested at progressively smaller decreases in Lk and the amplitude of the cycles increases. We interpret the results in terms of the early melting of superhelical DNA, in which the free energy associated with superhelix formation is progressively transferred to local denaturation. Using a two state approximation, we estimate the free energy change in the first cyclic transition to be 35 Kcal/mole DNA at 37 degrees and to decrease linearly with temperature. The free energy becomes equal to zero at a temperature of 71.6 degrees, which lies within 3 degrees of the melting temperature for the corresponding nicked circular DNA. From the slope of this relationship we estimate the apparent entropy and enthalpy of the first mobility transition to be 6.0 Kcal/mole base pair and 17.3 cal/mole base pair/degree, values consistent with duplex melting.     

Cooperative kinking at distant sites in mechanically stressed DNA

In cells, DNA is routinely subjected to significant levels of bending and twisting. In some cases, such as under physiological levels of supercoiling, DNA can be so highly strained, that it transitions into non-canonical structural conformations that are capable of relieving mechanical stress within the template. DNA minicircles offer a robust model system to study stress-induced DNA structures. Using DNA minicircles on the order of 100 bp in size, we have been able to control the bending and torsional stresses within a looped DNA construct. Through a combination of cryo-EM image reconstructions, Bal31 sensitivity assays and Brownian dynamics simulations, we have been able to analyze the effects of biologically relevant underwinding-induced kinks in DNA on the overall shape of DNA minicircles. Our results indicate that strongly underwound DNA minicircles, which mimic the physical behavior of small regulatory DNA loops, minimize their free energy by undergoing sequential, cooperative kinking at two sites that are located about 180° apart along the periphery of the minicircle. This novel form of structural cooperativity in DNA demonstrates that bending strain can localize hyperflexible kinks within the DNA template, which in turn reduces the energetic cost to tightly loop DNA.     

Torsional and Bending Rigidity of the Double Helix from Data on Small DNA Rings

Abstract

We have calculated the variance of equilibrium distribution of a circular wormlike polymer chain over the writhing number, ?(Wr)²?, as a function of the number of Kuhn statistical segments, n, For large n these data splice well with our earlier results obtained for a circular freely jointed polymer chain. Assuming that ?(ΔLk)²? = ?(ΔTw)²? + ?(Wr)²? we have compared our results with experimental data on the chain length dependence of the ?(ΔLk) ²? value recently obtained by Horowitz and Wang for small DNA rings. This comparison has shown an excellent agreement between theory and experiment and yielded a reliable estimate of the torsional and bending rigidity parameters. Namely, the torsional rigidity constant is C = 3.0·10^?19 erg cm, and the bending rigidity as expressed in terms of the DNA persistence length is a = 500 A. The obtained value of C agrees well with earlier estimates by Shore and Baldwin as well as by Horowitz and Wang whereas the a value is in accord with the data of Hagerman. We have found the data of Shore and Baldwin on the chain length dependence of the ?(ΔLk) ²? value to be entirely inconsistent with our theoretical results.     

Energetics of DNA twisting. II. Topoisomer analysis

A gel electrophoresis method has been developed for resolving small (approximately equal to 250 bp DNA topoisomers. In this size range only one major topoisomer band is observed, except for ligase closure conditions in which the probabilities are nearly equal for circularization by untwisting and overtwisting the corresponding linear DNA. The two probabilities are nearly equal when delta Tw is close to 0.5, if the mean helical twist of the linear DNA is n + delta Tw, where n is an integer and delta Tw is the fractional twist. We determine delta Tw of the linear DNA in standard conditions (20 degrees C, no ethidium) by titration experiments in which delta Tw is varied at the time of ligase closure, either by changing temperature or ethidium concentration. The endpoint (delta Tw = 0.5) is found when the two topoisomers formed by untwisting and overtwisting are present at equal concentrations. This analysis assumes that the net writhe is zero and the DNA helix is isotropically bendable. The results confirm the analysis of cyclization probabilities given in the preceding paper: delta Tw = 0 at the two maxima in the curve of j-factor versus DNA length and delta Tw = 0.5 at the minimum. Consequently, we can determine the DNA lengths at which Tw takes on integral values and use them to measure precisely the average helix repeat. From the difference between the delta Tw values of DNAs with 237 and 247 bp, we obtain an approximate value for the helix repeat of h = 10.4 +/- 0.1 bp/turn, in good agreement with earlier values found by the band-shift and nuclease-cutting methods. The twist is integral at 250.8 +/- 0.4 bp and from h = 10.4 +/- 0.1 we find n = 24; then 250.8/24 gives h = 10.45 +/- 0.02 bp/turn. The mean linking number (Lk) changes in a stepwise manner as delta Tw is varied for 250 bp DNAs. This result is expected when the free energy of twisting half a turn becomes large compared to thermal fluctuations. In these experiments, it is possible to obtain the mean Tw value from the mean Lk value only when delta Tw = 0.5, and consequently the mean Lk value is not simply related to DNA length for 250 bp DNAs except when delta Tw = 0.5.(ABSTRACT TRUNCATED AT 400 WORDS)     

Modulation of intramolecular interactions in superhelical DNA by curved sequences: a Monte Carlo simulation study.

A Monte Carlo model for the generation of superhelical DNA structures at thermodynamic equilibrium (Klenin et al., 1991; Vologodskii et al., 1992) was modified to account for the presence of local curvature. Equilibrium ensembles of a 2700-bp DNA chain at linking number difference delta Lk = -15 were generated, with one or two permanent bends up to 120 degrees inserted at different positions. The computed structures were then analyzed with respect to the number and positions of the end loops of the interwound superhelix, and the intramolecular interaction probability of different segments of the DNA. We find that the superhelix structure is strongly organized by permanent bends. A DNA segment with a 30 degrees bend already has a significantly higher probability of being at the apex of a superhelix than the control, and for a 120 degrees bend the majority of DNAs have one end loop at the position of the bend. The entropy change due to the localization of a 120 permanent bend in the end loop is estimated to be -17 kJ mol-1 K-1. When two bends are inserted, the conformation of the superhelix is found to be strongly dependent on their relative positions: the straight interwound form dominates when the two bends are separated by 50% of the total DNA length, whereas the majority of the superhelices are in a branched conformation when the bends are separated by 33%. DNA segments in the vicinity of the permanent bend are strongly oriented with respect to each other.     

Spontaneous sharp bending of double-stranded DNA

Sharply bent DNA is essential for gene regulation in prokaryotes and is a major feature of eukaryotic nucleosomes and viruses. The explanation normally given for these phenomena is that specific proteins sharply bend DNA by application of large forces, while the DNA follows despite its intrinsic inflexibility. Here we show that DNAs that are 94 bp in length-comparable to sharply looped DNAs in vivo-spontaneously bend into circles. Proteins can enhance the stability of such loops, but the loops occur spontaneously even in naked DNA. Random DNA sequences cyclize 10(2)-10(4) times more easily than predicted from current theories of DNA bending, while DNA sequences that position nucleosomes cyclize up to 10(5) times more easily. These unexpected results establish DNA as an active participant in the formation of looped regulatory complexes in vivo, and they point to a need for new theories of DNA bending.     

A Characteristic Bent Conformation of RNA Pseudoknots Promotes –1 Frameshifting during Translation of Retroviral RNA

The structures of four different RNA pseudoknots that provide one of the signals required for ribosomal frameshifting in mouse mammary tumor virus have been determined by NMR. The RNA pseudoknots have similar sequences and assume similar secondary structures, but show significantly different frameshifting efficiencies. The three-dimensional structures of one frameshifting and one non-frameshifting RNA pseudoknot had been determined previously by our group. Here we determine the structures of two new RNA pseudoknots, and relate the structures of all four pseudoknots to their frameshifting abilities. The two efficient frameshifting pseudoknots adopt characteristic bent conformations with stem 1 bending towards the major groove of stem 2. In contrast, the two poor frameshifting pseudoknots have structures very different from each other and from the efficient frameshifters. One has linear, coaxially stacked stems, the other has stems twisted and bent, but in the opposite direction to the efficient frameshifters. Changes in loop size that favor bending (shorter loops) increase frameshifting efficiency; longer loops that allow linear arrangement of the stems decrease frameshifting. Frameshifting pseudoknots in feline immunodeficiency virus and simian retrovirus have different loop sequences, but the sequences at their stem junctions imply the same bent conformation as in the mouse mammary tumor viral RNA. The requirement for a precise pseudoknot conformation for efficient frameshifting strongly implies that a specific interaction occurs between the viral RNA pseudoknot and the host protein-synthesizing machinery.