Application of Polyelectrolyte Theory to the Study of the B-Z Transition in DNA (1)

Abstract

We have used the polyelectrolyte theory to study the ionic strength dependence of the B-Z equilibrium in DNA. A DNA molecule is molded as an infinitely long continuously charged cylinder of radius a with reduced linear charge density q. The parameters a and q for the B and Z forms were taken from X-ray data: a _B = 1nm, q _B = 4.2, a _z = 0.9 nm and q _z = 3.9. A simple theory shows that at low ionic strengths (when Debye screening length r _D>>a) the electrostatic free energy difference F ^el _Bz = F ^el _Z - F ^el _B increases with increasing ionic strength since q _B>q_z. At high ionic strengths (when r _D<<a) the F ^el _BZ would go on growing with increasing ionic strength if the inequality q _B/^a _B<q_z/a _z were valid. In the converse case when q _z/q _B<a_z/a _B the F ^el _BZ value decreases with increasing salt concentration at high ionic strength. Since X-ray data correspond to the latter case, theory predicts that the F ^el _BZ value reaches a maximum at an intermediate ionic strength of about 0.1 M (where r _D～a). We also performed rigorous calculations based on the Poisson-Boltzmann equation. These calculations have confirmed the above criterion of nonmonotonous behaviour of the F ^el _BZ value as a function of ionic strength. Different theoretical predictions for the B-Z transition in linear and superhelical molecules are discussed. Theory predicts specifically that at a very low ionic strength the Z form may prove to be more stable than the B form. Thus, one can observe the Z-B-Z transition with increasing ionic strength. In the light of our theoretical findings we discuss numerous experimental data on the B-Z transition in linear and superhelical DNA.     

The energetics of the B-Z transition in DNA

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.     

Thermodynamics of B-Z transition in supercoiled DNA.

The nature of the possible supercoil-induced B-Z transition has been analyzed from the thermodynamical point of view, by taking into account the effects of the twisting as well as the writhing components of the supercoiling free energy. The cooperative aspects of the transition, as predicted by theory, agrees well with the corresponding experimental data.     

Raman spectroscopy study of the B-Z transition in (dG-dC)n.(dG-dC)n and a DNA restriction fragment

The B to Z conformational transition of (dG-dC)n.(dG-dC)n and a 157 bp DNA restriction fragment were followed using Raman spectroscopy. The 157 bp DNA has a 95 bp segment from the E. coli lactose operon sandwiched between 26 and 32 bp of (dC-dG) sequences. Raman spectra of the DNAs were obtained at varying sodium chloride concentrations through the region of the transition. A data analysis procedure was developed to subtract the background curves and quantify Raman vibrational bands. Profiles of relative intensity vs. sodium chloride concentration are shown for bands at 626, 682, 831-833 and 1093 cm-1. Both (dG-dC)n.(dG-dC)n and the 157 bp DNA show changes in the guanine vibration at 682 cm-1 and backbone band at 831-3 cm-1 preceding a highly cooperative change in the 1093 cm-1 PO2- vibration. This result indicates that there are at least two conformational steps in the B to Z conformational pathway. We review the effect of the (dC-dG) portion of the 157 bp DNA on the 95 bp segment. Comparison of Raman spectra of the 157 bp DNA, the 95 bp fragment and (dG-dC)n.(dG-dC)n indicate that in 4.5 M NaCl the (dC-dG) segments are in a Z-conformation. Base stacking in the 95 bp portion of the 157 bp DNA appears to maintain a B-type conformation. However, a substantial portion of this region no longer has a B-type backbone vibration.     

B-Z DNA conformational transition in 1:1 electrolytes: dependence upon counterion size

We have studied the B-Z transition of poly[d(G-C)] in the presence of alkali metal, tetramethylammonium and tetraethylammonium chlorides at room temperature. The measured critical salt concentrations increase in the order Na, K, Rb, TMA, Cs and are in good agreement with the theoretical values predicted from a statistical-mechanical treatment of the transition.     

A unified theory of the B-Z transition of DNA in high and low concentrations of multivalent ions

We showed recently that the high-salt transition of poly[d(G-C)]. poly[d(G-C)] between B-DNA and Z-DNA (at [NaCl] = 2.25 M or [MgCl(2)] = 0.7 M) can be ascribed to the lesser electrostatic free energy of the B form, due to better immersion of the phosphates in the solution. This property was incorporated in cylindrical DNA models that were analyzed by Poisson-Boltzmann theory. The results are insensitive to details of the models, and in fair agreement with experiment. In contrast, the Z form of the poly[d(G-m5C)] duplex is stabilized by very small concentrations of magnesium. We now show that this striking difference is accommodated quantitatively by the same electrostatic theory, without any adjustable parameter. The different responses to magnesium of the methylated and nonmethylated polymers do not come from stereospecific cation-DNA interactions: they stem from an experimentally derived, modest difference in the nonelectrostatic component of the free energy difference (or NFED) between the Z and B forms. The NFED is derived from circular DNA measurements. The differences between alkaline earth and transition metal ions are explained by weak coordination of the latter. The theory also explains the induction of the transition by micromolar concentrations of cobalt hexammine, again without specific binding or adjustable parameters. Hence, in the case of the B-Z transition as in others (e.g., the folding of tRNA and of ribozymes), the effect of multivalent cations on nucleic acid structure is mediated primarily by nonspecific ion-polyelectrolyte interactions. We propose this as a general rule for which convincing counter-examples are lacking.     

The stretched intermediate model of B-Z DNA transition

There have been numerous attempts to describe the mechanism of B-Z transition. Our simulations based on the stochastic difference equation with length algorithm show that a short DNA oligomer will tend to unwind and overstretch during the transition. The overstretching of DNA is then understood from the Zhou, Zhang, and Ou-Yang model. Unlike the Harvey model, the stretched intermediate model does not pose any steric dilemma; we are able to show that the chain sense reversal progresses spontaneously using the stretched intermediate model. A nonlinear DNA model is used to describe the origins and mechanism of base rotation in the stretched intermediate state of DNA. We also propose an experiment that can verify the existence of a stretched intermediate state during B-Z transition, thus opening up fresh grounds for experimentation in this field.     

Application of conductivity studies and polyelectrolyte theory to the conformation and order-disorder transition of xanthan polysaccharide

The conductivity of xanthan (extracellular polysaccharide from Xanthomonas campestris) in the potassium salt form has been studied over the temperature range 5–80°C spanning the order-disorder conformational transition. In salt-free solution data analysis using Manning's polyelectrolyte-conductivity theory gives a charge spacing, b, of 0.58±0.04 nm for the low temperature ordered form, consistent with a single rather than a double helix (b=0.58 and 0.29 nm respectively). In solutions with 0.01 M added KBr the increase in counterion condensation on conformational ordering is found from conductivity studies to be — ^–1= 0.20 ± 0.02, in good agreement with the value 0.20±0.02 using polyelectrolyte-equilibrium theory for the variation of transition-midpoint temperature with added salt determined from opticalrotation data.     

Cooperative chiral order in the B-Z transition in random sequences of DNA.

We present a theory for cooperative chiral order in the transition between right-handed B-DNA and left-handed Z-DNA. This theory, based on the random-field Ising model, predicts the characteristic length scale of Z-DNA segments. This length scale depends on whether the DNA is a homopolymer or a random sequence: it is approximately 4000 nucleotides in a homopolymer but only approximately 25 nucleotides in a random sequence. These theoretical results are consistent with experiments on DNA homopolymers and random sequences.     

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.     

Composite cylinder models of DNA: application to the electrostatics of the B-Z transition.

We develop and test a Poisson-Boltzmann model of the electrostatics of the B-Z transition of DNA. Starting from the detailed geometries of the two forms, we compute at each radius the fractions of DNA matter, of volume forbidden (for nonpoint-like ions), and of volume accessible to the center of ions. These radial distributions are incorporated in a composite cylinder model; availability to ions (porosity) and the dielectric constant at each radial distance are then obtained. The phosphate charge is distributed with cylindrical symmetry on two layers at the appropriate radial distances. The porous sheath, between the axis and the charge distribution, provides much more room for ions in B-DNA than in Z-DNA. By using previously developed methods, the Poisson-Boltzmann problem of such cylinders is easily solved. The computational load is small, so that results can be obtained for a large set of salt concentrations and for a number of ionic radii. The variation of the electrostatic free energy difference with salt concentration compares favorably with the experimental value (it is half as large). There is also qualitative agreement with experiments on supercoiled DNA, including a maximum of the free energy difference at submolar salt concentrations. The results for this cylinder with porous sheath are in line with those of the earlier simple planar model and of a plain cylinder with sheath, which is also presented here. They are thus insensitive to details of the model. They support the proposition that the main electrostatic feature of the B-Z transition is the better immersion of the B-DNA phosphates into the solution. They also give confidence in the validity of the Poisson-Boltzmann approach, despite the large salt concentrations involved. Prior studies using an approach based on the potential of mean force are discussed.     

The B-Z transition in supercoiled DNA depends on sequence beyond nearest-neighbors.

In order to examine sequence-dependent structural effects in DNA, the ability of alternating purine-pyrimidine fragments to undergo a B-Z transition when cloned in a supercoiled plasmid was determined solely as a function of sequence, with base and nearest-neighbor composition held constant. Sequences of 22 GC and 2 AT base pairs were synthesized such that the AT base pairs varied between contiguous placement and separation by eight GC base pairs. Results show, surprisingly, that the ease of the B-Z transition varies with the position of the two AT base pairs, occurring at lower superhelical densities when AT base pairs are contiguous, and at higher torsional strain when the AT base pairs are moved further apart.     

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.     

B-Z transition in poly(dG-dC).poly(dG-dC) in the presence of formaldehyde amino derivatives

It was shown by circular dichroism that the B-Z transition of poly(dG-dC).poly(dG-dC) in high NaCl concentrations occurred more rapidly in the presence of formaldehyde and Tris. The product of formaldehyde and glycine interaction induces changes in the poly(dG-dC).poly(dG-dC) CD spectral characteristics of a 'B-like' conformation. It is supposed that the B-Z transition occurs without large-scale hydrogen bond breakage.     

9-aminoacridine inhibits the B-Z transition of poly(dA-dT).

9-Aminoacridine is the parent compound of a family of pharmacologically active model substances that bind to DNA through intercalation between base pairs. In the present study we show that 9-aminoacridine inhibits the B-to-Z isomerization of poly(dA-dT) in conditions that otherwise cause it to occur (5 M NaCl and 123 mM Ni(ClO4)2). Higher concentrations of Ni(ClO4)2 (155 mM) are able to induce the Z-form due to the disruption of the drug-polynucleotide interaction by the metal ion. Additionally, the dye reverses the Z-form in certain conditions. Thus, the data from this study indicate that 9-aminoacridine binds preferentially to the B-form of poly(dA-dT).     

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.