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.     

Left-handed Z form in superhelical DNA: a theoretical study

This is a comprehensive statistical mechanical treatment of the Z form formation in purinepyrimidine stretches of different length inserted into superhelical DNA. The B-Z transition for short inserts is shown to follow the "all-or-none" principle. Over some critical value of the insert length n, the B-Z transition in the insert proceeds in two stages. The flipping of m base pairs into the Z form is followed by a gradual growth of the Z-form stretch until it occupies the whole insert. By fitting the theoretical transition curves to experimental ones the fundamental thermodynamic parameters of the B-Z transition have been determined: the B-Z junction energy Fj = 4-5kcal.mol-1 and the free energy change delta FBZ = 0.5-7.0 kcal.mol-1 under standard salt conditions. Calculations show that the B-Z transition in short purinepyrimidine inserts may be seriously affected by cruciform formation in the carrier DNA.     

Left-handed Z Form in Superhelical DNA: A Theoretical Study

Abstract

This is a comprehensive statistical mechanical treatment of the Z form formation in purine- pyrimidine stretches of different length inserted into superhelical DNA. The B-Z transition for short inserts is shown to follow the “all-or-none” principle. Over some critical value of the insert length n, the B-Z transition in the insert proceeds in two stages. The flipping of m base pairs into the Z form is followed by a gradual growth of the Z-form stretch until it occupies the whole insert. By fitting the theoretical transition curves to experimental ones the fundamental thermodynamic parameters of the B-Z transition have been determined: the B-Z junction energy Fj = 4–5kcal?mol^?1 and the free energy change ΔF_B-Z = 0.5–0.7 kcal?mol^?1 under standard salt conditions. Calculations show that the B-Z transition in short purine-pyrimidine inserts may be seriously affected by cruciform formation in the carrier DNA.     

A model of the strain-induced B-Z transition

The B-to-Z transition in supercoiled circular DNA is modeled as a strain-induced nonlinear excitation process. Using a model, in which DNA is regarded as a chain of units with a bistable energy function along the twisting coordinate together with a harmonic inter-unit interaction, we show that a Z region and the accompanying two B-Z junctions of finite width appear naturally as a solution of nonlinear equations, when the strain exceeds a critical value. We examine the B-Z transition behaviour as a function of twist under various situations. We also analyse available experimental results on B-Z transition in supercoiled plasmid with G-C insertions by this mechanistic model in order to estimate the magnitude of model parameters. The energy barrier of the B-Z transition is estimated to be of the order of 1 kcal/mole per base pair. The analysis shows that if the length of the insertion is less than a certain value, the entire insertion converts to Z form at a transition point, but if the insertion is much longer, the B-Z transition exhibits a different behavior, in which part of the insertion flips to Z form and the Z region expands linearly upon changing linking number.     

A Model of the Strain-induced B-Z Transition

Abstract

The B-to-Z transition in supercoiled circular DNA is modeled as a strain-induced nonlinear excitation process. Using a model, in which DNA is regarded as a chain of units with a bistable energy function along the twisting coordinate together with a harmonic inter-unit interaction, we show that a Z region and the accompanying two B-Z junctions of finite width appear naturally as a solution of nonlinear equations, when the strain exceeds a critical value. We examine the B-Z transition behaviour as a function of twist under various situations. We also analyse available experimental results on B-Z transition in supercoiled plasmid with G-C insertions by this mechanistic model in order to estimate the magnitude of model parameters. The energy barrier of the B-Z transition is estimated to be of the order of 1 kcal/mole per base pair. The analysis shows that if the length of the insertion is less than a certain value, the entire insertion converts to Z form at a transition point, but if the insertion is much longer, the B-Z transition exhibits a different behavior, in which part of the insertion flips to Z form and the Z region expands linearly upon changing linking number.     

Methylation of cytosine in the 5-position alters the structural and energetic properties of the supercoil-induced Z-helix and of B-Z junctions

The structural and energetic consequences of cytosine methylation in the 5-position on the supercoil-dependent B-Z equilibrium in alternating dC-dG sequences cloned into recombinant plasmids were investigated. The helical parameters determined with the band shift method for right-handed [10.7 base pairs (bp)/turn] and left-handed (12.8 bp/turn) 5MedC-dG inserts were different from the helical repeat values for unmethylated dC-dG inserts (10.5 bp/turn in the right-handed and 11.5 bp/turn in the left-handed form). We analyzed the thermodynamic parameters delta GBZ (free energy difference per base pair between right-handed and left-handed helix structure), delta Gjx (free energy for formation of one B-Z junction), and b (helix unwinding at a junction region) for varying lengths of dC-dG inserts by two-dimensional gel electrophoresis and application of a statistical mechanics model. A comparison of plasmids fully methylated in vitro with HhaI methylase and their unmethylated counterparts revealed that delta Gjx is not significantly changed by cytosine methylation. However, this base modification results in an approximate 3-fold decrease of delta GBZ and an approximate 2-fold decrease of the unwinding b at B-Z junction regions. Analysis of a pair of related plasmids, each containing two dC-dG blocks, revealed qualitatively different transition behaviors. When the two dC-dG blocks were separated by 95 bp of a mixed sequence, they underwent independent B to Z transitions with separate nucleation events and junction formations. When the two blocks were separated by only a 4 bp GATC sequence, only one nucleation event was necessary, and the Z-helix spread across the nonalternating GATC region.(ABSTRACT TRUNCATED AT 250 WORDS)     

Theoretical model of the B-Z transition in DNA with an arbitrary sequence

A statistical-mechanical model is suggested that makes it possible to describe the B-Z transition in DNA with an arbitrary sequence of nucleotides. The key point consists in allowance for the fact that each base pair can assume one of the two states with different energies. One of these states corresponds to the standard Z-form with purines in the syn conformation and pyrimidines in the anti conformation. However, in natural DNA sequences such standard base-pair conformations should be interrupted by energetically unfavorable conformations (syn for pyrimidines and anti for purines). Open regions and cruciform structures are also allowed for in the model. The probabilities of formation of the Z-form stretches, open regions and cruciform structures have been calculated for different values of parameters for pBR322 and pAO3 DNA.     

Allosteric conversion of Z DNA to an intercalated right-handed conformation by daunomycin

Absorbance and fluorescence methods were used to measure the binding of the anticancer drug daunomycin to poly (dGdC) under ionic conditions that initially favor the left-handed Z conformation of the polymer. Drug binding was cooperative under these conditions and may be fully accounted for by an allosteric model in which the drug binds preferentially (but not exclusively) to the right-handed B conformation and shifts the polymer from the Z to an intercalated right-handed conformation. Quantitative analysis of binding isotherms in terms of the allosteric model allowed for estimation of the equilibrium constants for the conversion of a base pair at a B-Z interface from the Z to the B conformation and for the formation of a base pair in the B conformation within a stretch of helix in the Z conformation. The free energy of the Z to B conversion of a base pair was calculated from this data and ranges from +0.03 to +0.3 kcal/mol over the NaCl range of 2.4-3.5 M. The free energy for the formation of a B-Z junction was nearly constant at +4.0 kcal/mol over the same range of NaCl concentrations. The salt dependence of the free energy of the Z to B transition indicates preferential Na+ binding to the Z form and that there is a net release of Na+ upon conversion of a base pair from the Z to the B conformation. The energetically unfavorable Z to B transition was found by this analysis to be driven by coupling to the energetically favorable interaction of daunomycin with B form DNA. In 3.5 M NaCl, for example, the free energy change for the overall reaction (Z DNA base pairs) + (daunomycin) in equilibrium with (right-handed complex) is -7.0 kcal/mol, nearly all of which is contributed by the binding of drug to B DNA. Analysis using the allosteric model also shows that the number of base pairs converted from the Z to the B conformation per bound drug molecule is salt dependent and provides evidence that drug molecules partition into regions of the polymer in the right-handed conformation.     

B-Z cooperativity and kinetics of poly(dG-m5dC) are controlled by an unfavorable B-Z interface energy

Thermodynamic and kinetic properties of the B-Z transition of poly(dG-m5dC) were investigated using polynucleotide samples ranging in length from 11000 to 300 base pairs. Van't Hoff enthalpy values increase with increasing polymer length for the B-Z transition in 0.35 mM MgCl2, 50 mM NaCl, 5 mM TRIS, pH 8. Rates of the B to Z transition increase with increasing polymer length for a jump of 0 to 3 mM MgCl2 in 50 mM NaCl, 5 mM TRIS, pH 8. The activation energy of the B to Z transition equals 7.9 +/- 0.3 kcal/mol and is length independent. Thermodynamic and kinetic data were fit to a model that simulates distribution of B- and Z-form tracts at the midpoint of B-Z equilibrium as a function of polymer length. A cooperative length of 1000 +/- 200 base pairs is estimated for the B-Z transition. A direct relationship between rates of the B to Z transition and the square of the van't Hoff enthalpy values of the B-Z transition reflects a dependence of kinetics and cooperativity upon the energy of the nucleation event. Faster B to Z transition rates with increasing polymer length can be explained by a mechanism rate limited by nucleation within the polymer instead of the ends.     

B-Z Cooperativity and Kinetics of Poly(dG-m5dC) are Controlled by an Unfavorable B-Z Interface Energy

Abstract

Thermodynamic and kinetic properties of the B-Z transition of poly(dG-m⁵dC) were investigated using polynucleotide samples ranging in length from 11000 to 300 base pairs. Van't Hoff enthalpy values increase with increasing polymer length for the B-Z transition in 0.35 mM MgCl₂, 50 mM NaCl, 5 mM TRIS, pH 8. Rates of the B to Z transition increase with increasing polymer length for a jump of 0 to 3 mM MgCl, in 50 mM Nad, 5 mM TRIS, pH 8. The activation energy of the B to Z transition equals 7.9 ± 0.3 kcal/mol and is length independent Thermodynamic and kinetic data were fit to a model that simulates distribution of B- and Z-form tracts at the midpoint of B-Z equilibrium as a function of polymer length. A cooperative length of 1000 ± 200 base pairs is estimated for the B-Z transition. A direct relationship between rates of the B to Z transition and the square of the van't Hoff enthalpy values of the B-Z transition reflects a dependence of kinetics and cooperativity upon the energy of the nucleation event Faster B to Z transition rates with increasing polymer length can be explained by a mechanism rate limited by nucleation within the polymer instead of the ends.     

1H NMR and circular dichroism studies of the B and Z conformations of the self-complementary deoxyhexanucleotide d(m5C-G-C-G-m5-C-G): mechanism of the Z-B-coil transitions

The double-helical conformations of d(m5-C-G-C-G-m5-C-G) in aqueous solution were studied by circular dichroism and 1H NMR spectroscopy. In 0.1 M NaCl, only the B form is detected whereas the Z form is strongly predominant in 3 M NaCl. In the presence of 2 M NaCl, two resonance signals corresponding to the B and Z duplexes were observed for each proton below 50 degrees C, indicating a slow exchange between B and Z. However, the B-Z exchange becomes intermediate or fast in the 55-80 degrees C temperature interval. By contrast the exchange between B helix and single-stranded (or coil) forms is much faster for the same temperature conditions. The Z form is only detectable when the coil form is practically absent. With decreasing temperature the B form decreases in favor of the Z form. From proton line-width measurements under various experimental conditions, it was also shown that Z exchanges only with B, while the latter also exchanges with the single-stranded form (S): Z in equilibrium B in equilibrium S. The enthalpy value is about 8 +/- 1 kcal/mol for the B-Z transition and about 40 +/- 2 kcal/mol for the B-S dissociation (2 M NaCl solution). The activation energy is about 47 +/- 2 kcal/mol for the Z----B and 39 +/- 2 kcal/mol for the B----Z reaction. Very good agreement between the experimental results and computed data (based on the above kinetic reaction model) was found for the B, Z, and coil proportions. The B-Z transition of methylated d(C-G)n oligomers is only possible when the Watson-Crick hydrogen bonds between the CG base pairs are firmly maintained; otherwise, the transformation from B to Z would not occur, and B-S dissociation would take place instead.     

A theoretical study of formation of DNA noncanonical structures under negative superhelical stress

The development of statistical mechanical models of the formation of noncanonical structures in circular DNA and the finding of the energy parameters for these models made it possible to predict the appearance of such structures in a DNA with any given sequence. It does not seem feasible, however, to perform such calculations for DNA sequences of considerable length by allowing for all the possible states. We propose a special algorithm for calculating the thermodynamic characteristics of various conformational rearrangements in DNA that occur under negative supercoilings, allowing for several possible states of each base pair in the chain. Calculations have been performed for a number of natural DNAs. According to these calculations, the most likely noncanonical structures in DNA under normal conditions are cruciform structures and the Z form. The results of the calculations are compared with the experimental data reported in the literature. State diagrams have been computed for a number of inserts in circular DNA that can adopt both the cruciform conformation and the left-handed helical Z form.     

Effects of 5 cytosine methylation on the B-Z transition in DNA restriction fragments and recombinant plasmids

Alternating (dC-dG)n regions in DNA restriction fragments and recombinant plasmids were methylated at the 5 position of the cytosine residues by the HhaI methylase. Methylation lowers the concentration of NaCl or MgCl2 necessary to cause the B-Z conformational transition in these sequences. Ionic strengths higher than physiological conditions are required to form the Z conformation when the methylated (dC-dG)n tract is contiguous with regions that do not form Z structures, in contrast to the results with the DNA polymer poly(m5dC-dG) . poly(m5dC-dG). In supercoiled plasmids containing (dC-dG)n sequences, methylation reduces the number of negative supercoils necessary to stabilize the Z conformation. Calculations of the observed free energy contributions of the B-Z junction and cytosine methylation suggest that two junctions offset the favorable effect of methylation on the Z conformation in (dC-dG)n sequences (about 29 base-pairs in length). Studies with individual methylated topoisomers demonstrate that increasing Na+ concentration up to approximately 0.2 M inhibits the formation of the Z conformation in the (m5dC-dG)n region of supercoiled plasmids. The results suggest that methylation may serve as a triggering mechanism for Z DNA formation in supercoiled DNAs.     

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.     

A Theoretical Study of Formation of DNA Noncanonical Structures Under Negative Superhelical Stress

Abstract

The development of statistical mechanical models of the formation of noncanonical structures in circular DNA and the finding of the energy parameters for these models made it possible to predict the appearance of such structures in a DNA with any given sequence. It does not seem feasible, however, to perform such calculations for DNA sequences of considerable length by allowing for all the possible states. We propose a special algorithm for calculating the thermodynamic characteristics of various conformational rearrangements in DNA that occur under negative supercoilings, allowing for several possible states of each base pair in the chain. Calculations have been performed for a number of natural DNAs. According to these calculations, the most likely noncanonical structures in DNA under normal conditions are cruciform structures and the Z form. The results of the calculations are compared with the experimental data reported in the literature. State diagrams have been computed for a number of inserts in circular DNA that can adopt both the cruciform conformation and the left-handed helical Z form.     

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.     

Comparison of the reactivity of B-DNA and Z-DNA with two isosteric chemical carcinogens: 2-N,N-acetoxyacetylaminofluorene and 3-N,N-acetoxyacetylamino-4,6-dimethyldipyrido-[1,2-a:3'',2'' -d] imidazole.

The reactivity of nucleic acids in various conformations and two isosteric chemical carcinogens 2-N,N-acetoxyacetylaminofluorene (N-AcO-AAF) and 3-N,N-acetoxyacetylamino-4,6-dimethyldipyrido [1,2-a:3',2'-d] imidazole (N-AcO-AGlu-P-3) have been studied. Both carcinogens bind covalently to poly(dG-dC).poly(dG-dC) (B form) and to poly(dG-br5C).poly(dG-br5dC) (Z form). They also bind covalently to (dC-dG)16 and to (dG-dT)15 sequences inserted in plasmids when the inserts are in the B form but they do not bind to the inserts in the Z form. The reactivity of guanine residues at the B-Z junctions depends upon the superhelical density of the plasmids and upon the base sequences at the junction. The distribution of AGlu-P-3 modified guanines in a restriction fragment of pBR322 is not uniform and is different from that of AAF-modified guanines. The conclusion is that N-AcO-Glu-P-3 as N-AcO-AAF can probe at the nucleotide level the polymorphism of DNA. On the other hand, the non-reactivity of both chemical carcinogens and Z-DNA and the hyperreactivity of some junctions might have some importance in the understanding of chemical carcinogenesis.     

Chemical Probing of the B-Z Transition in Negatively Supercoiled DNA

Abstract

An analysis of the B-to-Z transition as a function of supercoiling for a natural Z-DNA- forming sequence found in plasmid pBR322 is presented at nucleotide resolution. The analysis is based on reactivity to four chemical probes which exhibit hyperreactivity in the presence of Z-DNA: hydroxylamine, osmium tetroxide, diethyl pyrocarbonate and dimethyl sulfate. We find that the initial transition occurs largely within a 14 base pair region which is mostly alternating purines and pyrimidines. With increasing negative supercoiling, Z-DNA extends into flanking regions having less and less alternating character, first in one direction and then in the other. Evidence of B-Z junctions is seen at four sites bracketing these three adjacent regions. One of these Z-forming regions contains the non-alternating sequence CTCCT, suggesting that such sequences can form Z-DNA without great difficulty if they are adjacent to alternating sequences. A plasmid containing three copies of a 61 base pair fragment bearing the entire Z-forming region shows equal reactivity of all three copies at any given superhelical density, implying that they compete equally and independently for the torsional strain energy which promotes the B-Z transition, and are unaffected by adjacent sequences more than 20–30 base pairs away.     

The in-vivo occurrence of Z DNA

The energetics of the B-Z transition of two different types of cloned alternating purine/pyrimidine DNA sequences have been analysed by a two dimensional electrophoretic technique. Since the transition between right handed and left handed forms of these polymers is detected by alterations of electrophoretic mobilities of topoisomers of the plasmid DNA molecules, the method is not dependent on Z-DNA binding ligands. The measurements reflect intrinsic properties of the DNA unperturbed by the free energy of binding such a ligand. Direct evidence from the analysis of topoisomer distributions is presented which shows that d(GC)n.d(GC)n sequence elements within an E. coli plasmid will adopt a Z conformation in-vivo under conditions of blocked protein synthesis. Evidence for the in-vivo occurrence of Z-DNA was not detected in plasmid DNA isolated from bacterial cells growing in the absence of protein synthesis inhibitors. A model is proposed for a function for the B-Z transition in ensuring the correct pairing of homologous chromosomes during meiosis.