Energetics of superhelicity and of B-Z transitions in superhelical DNA

The linking difference, α, imposed upon a superhelically constrained DNA molecule must be partitioned between twisting and bending deformations. Transitions to alternative secondary structures can occur at susceptible sites, altering the local molecular twist by an amount ΔTw _trans. That part of the linking difference not accommodated in this way, the residual linking difference α_res, must be manifested as smooth torsional and flexural deformations of secondary structure. The competition among the alternative ways of accommodating the imposed linking difference α determines a stressed equilibrium state. The superhelical free energy,G(α), is the excess free energy of the equilibrium state at linking difference α above that of the relaxed state under identical conditions. In this paper a method is described by which the free energies associated both to linking,G(α), and to residual linking differences can be determined from data on superhelical conformational transitions. The application of this approach to previously published experimental data on the B-Z transition suggests that the free energy associated with α_res is about 30% larger at substantial superhelicities than it is near the relaxed state. At the onset of transition the functional form ofG(α) is shown to change in a manner dependent upon the length of the Z-susceptible site.     

The Energetics of the B-Z Transition in DNA

Abstract

The paper deals with the energetics of the transition to left-handed Z form in DNA with an arbitrary base sequence. There is a brief outline of the statistical-mechanical model of the B-Z transition allowing for three possible states of each base pair. The parameters of the model can be determined by comparing the theory with experimental data for the B-Z transition in inserts with given sequences in circular DNA The model contains six energy parameters, most of which have been determined before. In order to find the remaining parameters of the model and test its adequacy, a number of oligonucleotide sequences were synthesized and inserted into the pUC 19 plasmid. Two-dimensional gel electrophoresis was used to determine the superhelical density at which the inserts adopt the Z form. A statistical-mechanical treatment of these data yielded a complete set of six energy parameters for the B-Z transition. The theoretical assumption that the free energy of Z-form pairs does not depend on the type of adjacent pairs proved to be in agreement with the experimental data.     

Energetics of the strand separation transition in superhelical DNA.

In this paper the values of three free energy parameters governing the superhelical strand separation transition are determined by analysis of available experimental data. These are the free energy, a, needed to initiate a run of separation, the torsional stiffness, C, associated with interstrand winding of the two single strands comprising a separated site and the coefficient, K, of the quadratic free energy associated to residual linking. The experimental data used in this analysis are the locations and relative amounts of strand separation occurring in the pBR322 DNA molecule and the measured residual linking, both evaluated over a range of negative linking differences. The analytic method used treats strand separation as a heteropolymeric, co-operative, two-state transition to a torsionally deformable alternative conformation, which takes place in a circular DNA molecule constrained by the constancy of its linking number. The values determined for these parameters under the experimental conditions (T = 310 K, pH = 7.0, monovalent cation concentration = 0.01 M) are a = 10.84(+/- 0.2) kcal/mol, C = 2.5(+/- 0.3) x 10(-13) erg/rad2 and K = 2350(+/- 80) RT/N, where N is the molecular length in base-pairs. In order to assess the accuracy of the author's theoretical methods, these free energy parameters are incorporated into the analysis of superhelical strand separation in different molecules and under other conditions than those used in their evaluation. First, the temperature dependence of transition is treated, then superhelical strand separation is analyzed in a series of DNA molecules having systematic sequence modifications, and the results of these theoretical analyses are compared with those from experiments. In all molecules, transition is predicted in the range of linking differences where it is seen experimentally. Moreover, it occurs at the specific sequence locations that the analysis predicts, and with approximately the predicted relative amounts of transition at each location. The known sensitivities of this transition to changes of temperature and to small sequence modifications are predicted in a quantitatively precise manner by the theoretical results. The demonstrated high-level precision of these theoretical methods provides a tool for the screening of DNA sequences for sites susceptible to superhelical strand separation, some of which may have regulatory or other biological significance.     

Energetics of B-Z junction formation in a sixteen base-pair duplex DNA

We report analysis of the NaCl-induced B-Z transition in a 16 base-pair duplex DNA with sequence designed such that when NaCl is increased the left half of the molecule undergoes the B-Z transition while the right half remains in the B-form. An equilibrium thermodynamic model based on the body of available published experimental data and the recent theoretical work of Soumpasis, which indicate, in the salt range above approximately 0.9 M-NaCl, the transition free-energy of B-Z conversion in DNA is a linear function of the NaCl concentration, is employed. Analysis of the B-Z transition of the junction-containing molecule indicates the B-Z junction formed in this 16 base-pair DNA is composed of approximately three base-pairs and has a free energy of formation of approximately 4.7 kcal/mol junction. These values for the junction are in excellent agreement with published estimates of B-Z junction size and energy derived from much longer DNA pieces.     

Competing B-Z and helix-coil conformational transitions in supercoiled plasmid DNA.

The formation of melted regions from A + T-rich sequences and left-handed Z-DNA by alternating purine-pyrimidine sequences will both be facilitated by negative supercoiling, and thus if the sequences are present within the same plasmid molecule they will compete for the free energy of supercoiling. We have studied a series of plasmids that contain either (CG)8 or (TG)12 sequences in either G + C or A + T-rich contexts, by means of two-dimensional gel electrophoresis and chemical modification. We observe both B-Z and helix-coil transitions in all plasmids at elevated temperatures and low ionic strength. The plasmids fall into a number of different classes, in terms of the conformational behavior. As the superhelix density is increased, pCG8/vec ((CG)8 in G + C-rich context) undergoes an initial B-Z transition, followed by melting transitions in sequences remote from the (CG)8 sequence. The two transitions are coupled through the topology of the molecule but are otherwise independent. When the (CG)8 sequence was placed in an A + T-rich context (pCG8/col), the helix-coil transition was perturbed by the presence of the Z-DNA segment. Replacement of the (CG)8 tracts by (TG)12 sequences resulted in a further level of interaction between the transitions. Statistical mechanical modeling of the transitions suggested that at intermediate levels of negative supercoiling the Z-DNA formed by the (TG)12 sequence has a lowered probability due to the helix-coil transition in the A + T-rich sequences. These studies illustrate the complexities of competing conformational equilibria in supercoiled DNA molecules.     

Applying the stochastic difference equation to DNA conformational transitions: a study of B-Z and B-A DNA transitions

Despite the existence of numerous models to account for the B-Z DNA transition, experimenters have not yet arrived at a conclusive answer to the structural and dynamical features of the B-Z transition. By applying the stochastic difference equation to simulate the B-Z DNA transition, we have shown that the stretched intermediate model of the B-Z transition is more probable than other B-Z transition models such as the Harvey model. This is accomplished by comparing potential energy profiles of various B-Z DNA transition models and calculating relative probabilities based on the stochastic difference equation with respect to length (SDEL) formalism. The results garnered in this article allow for new approaches in determining the structural transition of B-DNA to Z-DNA experimentally. We have also simulated the B-A DNA transition using the stochastic difference equation. Unlike the B-Z DNA transition, the mechanism for the B-A DNA transition is well established. The variation in the pseudorotation angle during the transition is in good agreement with experimental results. Qualitative features of the simulated B-A transition also agree well with experimental data. The SDEL approach is thus a suitable numerical technique to compute long-time molecular dynamics trajectory for DNA molecules.     

B-Z DNA junctions contain few, if any, nonpaired bases at physiological superhelical densities

The reactions of bromoacetaldehyde (BAA) with recombinant plasmids that contain sequences which can adopt left-handed Z structures or, at other locations, cruciforms were studied as a function of supercoil density. The sequence in pRW756 that undergoes a supercoil induced transition from a right to left-handed helix was (dC-dG)16 and regions near the replication origin of the pBR322 vector were converted from linearforms to cruciforms. The locations of the most nonpaired structural features were mapped by S1 nuclease cleavage of the "wedged open" duplexes after linearization of the DNAs. Three cruciforms in the pBR322 portions of the plasmids were specifically detected by BAA reaction at physiological supercoil densities (sigma = -0.067). However, the B-Z junctions did not react with BAA under these conditions although the junctions were present since the (dC-dG)16 was shown to be left-handed. Thus, the B-Z junctions have less single-stranded character than the pBR322 cruciforms (3-6 nonpaired bases) and may be fully paired. At much higher superhelical densities (sigma = -0.11-0.12), the B-Z junctions as well as the cruciforms react with BAA indicating a change in the nature of the junctions. Studies were also performed with pRW777 which harbors the mouse kappa immunoglobin sequence (dT-dG)32 . (dC-dA)32 that adopts a left-handed helix under appropriate conditions; the results were similar to those found with pRW756.     

Formation of noncanonical structures in superhelical DNA. Mutual effects of various transitions

This is a theoretical study of the problem of formation of noncanonical structures, cruciforms in palindromic regions and the Z form in purine--pyrimidine sequences, in negatively supercoiled DNA. If two such regions, one palindromic and one purine--pyrimidine, are present in the same DNA molecule of a finite length, then transitions between the regular B form and noncanonical structures in these regions will experience a considerable mutual influence. This takes place because both noncanonical structures compete for the same superhelix energy. A special attention is paid to the case when the probability of the Z form formation nonmonotonously depends on the superhelix density. Such a situation is shown to be possible for some specific interrelation between the DNA length, the length of the palindromic region and the length of the purine--pyrimidine region. The calculations show that in this case the Z form is formed first with the increasing superhelix density, that the cruciform structure is formed whereas the purine--pyrimidine region returns into the B form, and finally, the Z form is formed again. The possibility of experimental observation of such unusual behaviour is discussed.     

The influence of tertiary structural restraints on conformational transitions in superhelical DNA.

This paper examines theoretically the effects that restraints on the tertiary structure of a superhelical DNA domain exert on the energetics of linking and the onset of conformational transitions. The most important tertiary constraint arises from the nucleosomal winding of genomic DNA in vivo. Conformational transitions are shown to occur at equilibrium at less extreme superhelicities in DNA whose tertiary structure is restrained than in unrestrained molecules where the residual linking difference alpha res (that part of the superhelical deformation which is not absorbed by transitions) may be freely partitioned between twisting and bending. In the extreme case of a rigidly held tertiary structure, this analysis predicts that the B-Z transition will occur at roughly half the superhelix density needed to drive the same transition in solution, other factors remaining fixed. This suggests that superhelical transitions may occur at more moderate superhelical deformations in vivo than in solution. The influence on transition behavior of the tertiary structural restraints imposed by gel conditions also are discussed.     

Geometry and mechanics of DNA superhelicity

This paper analyzes the elastic equilibrium conformations of duplex DNA constrained by the constancy of its molecular linking number, Lk. The DNA is regarded as having the mechanical properties of a homogeneous, linearly elastic substance with symmetric cross section. Integral representations of the writhing number Wr and of Lk are developed, in terms of which the equilibria are given as solutions to an isoperimetric problem. It is shown that the Euler angles defining equilibrium conformations must obey equations identical to those governing unconstrained equilibria. A scaling law is developed stating that molecules supercoiled the same amount ΔLk will have geometrically similar elastic equilibria regardless of their length. Thus, comparisons among molecules of properties related to their large-scale tertiary structure should be referred to differences in ΔLk rather than to their superhelix densities. Specific conditions on the elastic equilibrium conformations are developed that are necessary for ring closure. The equilibrium superhelical conformations accessible to closed-ring molecules are shown to approximate toroidal helices. Questions relating to the stability and nonuniqueness of equilibria are treated briefly. A comparison is made between these toroidal conformations and interwound configurations, which are shown to be stable, although they are not equilibria in the present sense. It is suggested that entropic factors are responsible for favouring the toroidal conformation in solution.     

Effects of A:T base pairs on the B-Z conformational transitions of DNA

Effects of A:T base pairs on the propensity of B to Z conformational transitions have been investigated by the CD salt titrations on d(CG)5' d(GC)5' terminal or central A:T replaced decamers, and terminal A:T appended dodecamers. The presence of A:T at the center greatly inhibits the B to Z transition of both G:C decamers. Moderate Z inhibitions are shown by terminal A:T replacements and additions to d(CG)5' with the former exhibiting a stronger effect. In contrast, the addition and replacement with A:T at the terminals of d(GC)5 facilitate the B to Z conversion, with the replacement exhibiting a somewhat more pronounced effect. These results may be rationalized in terms of the number of contigous CG sequences present in an oligomer and the relative inhibitory effects of other dinucleotide sequences. Our results also suggest that some short oligomers with purine at the 5'-end, such as d[A(CG)nT] with n greater than or equal to 2, may likely crystallize as Z conformations.     

Fluctuations in superhelical DNA.

The effect of superhelicity on the base-pair opening probability and on the probability of occurrence of cruciform states in palindromic regions is theoretically treated. The calculations show that below the superhelix density value of -sigma=0.05 superhelicity does not appreciably affect the characteristics of DNA secondary structure fluctuations. In the range of physiological superhelix densities sigma (-sigma=0.05-0.09) the base-pair opening probability markedly increases. However, within this range of sigma the base-pairs are opened only transiently and permanently open regions are not formed. Permanently opened regions appear at higher negative superhelix densities (-sigma greater than 0.10). At the values of -sigma higher than 0.06 a cruciform structure in the palindromic region centred in position 3965 proves to be the most probable fluctuational disturbance in the 0x174 duplex DNA. Different experimental approaches used for probing the fluctuations in superhelical DNA have been analysed. The results suggest that most direct quantitative information can be derived from data on the nicking of closed DNA by single strand-specific endonucleases. Such data (Wang, 1974) accord with the results of theoretical calculations. Calculations show that, due to base-pair opening, the total free energy of superhelical DNA should depend parabolically on sigma only up to some critical value of sigma=sigmac. If negative superhelicity exceeds this critical value, which under physiological conditions proves to be -sigma=0.085, the free energy should increase linearly with -sigma. The biological role of supercoiling is discussed in the light of obtained results.     

Thermostability and superhelicity of plasmid DNA in Bacillus stearothermophilus

Summary The thermostability of the staphylococcal plasmids pC194 and pUB110 and their antibiotic-resistance determinants was examined upon transfer to Bacillus stearothermophilus CU21. Plasmid pGS13, a pUB110 derivative carrying the chloramphenicol acetyltransferase (CAT) gene of pC194, could be maintained up to the maximum growth temperature (68° C) by selection for chloramphenicol resistance. In the absence of selective pressure, pGS13 was lost at temperatures above 60° C. Segregational instability of pGS13 was accompanied by a progressive loss of negative superhelicity at elevated temperatures. Thermostable mutants of pGS13 were isolated by screening for expression of the antibiotic-resistance determinants after growth under non-selective conditions. These mutants were found to contain an insertion of a 1.7 kb DNA sequence derived from the cryptic B. stearothermophilus plasmid pBS02. Increased thermostability correlated with preservation of plasmid superhelicity at elevated temperatures.     

Circular dichroism of superhelical DNA

The circular dichroism (CD) spectra of a number of superhelical DNA's have been measured. The introduction of negative superhelical turns causes an increase in magnitude of the positive band around 280 mμ, while the trough around 250mμ is little affected. For two samples of λb2b5c DNA (20 Mdalton) containing different number of negative superhelical turns, the magnitude of the positive band relative to that of the nicked control increases with increasing number of superhelical turns. In 2M NaCl, the small (1.45 Mdalton) superhelical DNA from E. coli 15 shows an unusually large difference in CD compared with that of the same DNA with a few single-chain scissions per molecule. This large difference is not observed in a medium containing p. 0.11M NaCl. These results indicate that the double helix in a superhelical DNA is perturbed somewhat due to the bending and torsional forces in such a molecule. The magnitude of such structural alteration seems to depend on the number of superhelical turns per unit length, the size of the DNA molecule, as well as the ionic medium.