On the application of polyelectrolyte limiting laws to the helix-coil transition of DNA. III. TDependence of helix stability on excess univalent salt and on polynucleotide phosphate concentration for variable equivalent ratios of divalent metal ion to phosphate.

Using the free energy difference between double-helix and random-coil forms of DNA as a measure of the stability of the double helix, we calculate the dependence of the stability on excess univalent cation concentration and on polynucleotide phosphate concentration, both as functions of the equivalent ratio r of divalent cation-to-phosphate concentrations. The theoretical tool is merely to compare the free energy of one polyelectrolyte solution, characterized by the polyelectrolyte linear charge density, with the free energy of another, characterized by a different value of the charge density. It is assumed only that the charge density of the double helix is greater than that of the coil form. The calculation represents the only molecular theory given to date (for r ≠ O) for these aspects of helix stability. We find that, as excess univalent cation concentration increases, the helix stability increases if r is small but decreases if r is large (i.e., of the order of unity). Moreover, as the concentration of nucleotide phosphate increases, the helix stability does not change for small values of r but increases for large values. For both effects, a continuous transition as a function of r bridges the low-r and high-r behaviour.     

Hydration structure and dynamics of B- and Z-DNA in the presence of counterions via molecular dynamics simulations

Following our previous attempts at understanding the structural and dynamical properties of water and counterions hydrating nucleic acids, we have performed molecular dynamics simulations for B- and Z-DNA. In these simulations, the nucleic acids were held rigid. In the case of B-DNA, one turn of B-DNA double helix was considered in the presence of 1500 water molecules and 20 counterions (K⁺). The simulations were performed for 4.0 ps after equilibrating the system. For Z-DNA, we considered one turn of the double helix in the presence of 1851 water molecules and 24 counterions (K⁺). The simulations were carried out for 3.5 ps after equilibration. The average temperature of these simulations was ～ 360 K for Z-DNA and ～ 345 K for B-DNA. In these simulations the hydrogen atoms were explicitly taken into account. For both simulations, a fifth-order predictor-corrector was used for solving the translational equations of motion. The rotational motion of the water molecules was represented in terms of quaternion algebra and the rotational equations of motion were solved with a second-order quaternion method using a sixth-order predictor-corrector method. A time step of 0.5 · 10^?15 s was used in these simulations. The structural and the dynamical properties of water solvating the counterions, and the phosphate groups of the DNA, were computed to understand the hydration structure. Diffusion coefficients and velocity correlation functions were calculated for both ions and the water molecules. The velocity correlation functions for the ions exhibit a caged behavior. The dipole correlation functions for the water molecules indicate that the water molecules close to the helix retain the memory of their initial orientations for longer periods of time than those away from the helix. During the time period of our simulation (3–4 ps) the ion probability distributions show a well-defined pattern and suggest limited mobility for the ions, being close to the helix.     

On molecular mechanisms of nucleic acid synthesis fidelity aspects. 1. Contribution of base interactions

This paper is concerned with the molecular mechanisms of spontaneous replacements of base pairs in the processes of template synthesis of nucleic acids. The method of atom-atom potential functions was used to calculate the energies of interaction in non-complementary base pairs arranged in a common plane so that the mutual position of the glycosidic bonds does not differ appreciably from their position for Watson-Crick pairs in the DNA double helix. A number of local minima of this energy have been found, which could occur in template synthesis and result in insertion of incorrect bases into the double helix. The calculation results are indicative of formation of purine-purine pairs with one of the purine nucleotides in syn-conformation, which can be regarded as a typical pathway of transversion, and that of wobble-pairs TG and AC, which can be regarded as a typical pathway of transition. The contribution of intramolecular interactions of nucleic acids as well as interactions of polynucleotide chains with an enzyme to the fidelity of template synthesis of nucleic acids is discussed. The calculation results are compared with the experimental data on the frequency of spontaneous mutations and the frequency of errors in template synthesis of nucleic acids in vitro.     

Open states in native polynucleotides. I. Hydrogen-exchange study of adenine-containing double helices.

Since protons that are buried and hydrogen-bonded within nucleic acid double helices exchange readily with solvent protons, it is evident that the native double helix must participate in some kind of reversible opening process. In hydrogen-exchange studies of a number of adenine-containing double helices, the chemical exchange pathways were worked out, and equilibrium and kinetic parameters of the dominant opening reactions were derived. These lead to a picture of the open state that may have implications for DNA recognition processes.     

Nonparametric estimation of 1-dimensional continuous distribution density functions using the continuous LOLINREG approximation

A nonparametric method for estimation of one-dimensional continuous probability distribution functions is presented. Procedures for calculation of estimation of the unknown distribution function and the distribution density will be discussed in their application. 2 items are what type of weight function may be chosen for the proposed local-linear continuous approximation of the empirical distribution function by the least squares method (LOLINREG), and upon what value of bandwidth- or smoothing parameter one optimally should settle. The latter problem is practically very important with respect to the quality of the estimation results. Examples of simulated measurements which come from a standardized normal distribution as random numbers serve to demonstrate the mode of working, the advantages as well as the limits of the presented continuous LOLINREG-approximation.     

Torsional flexibility of B-DNA as revealed by conformational analysis.

The thermal fluctuations of a regular double helix belonging to the B-family were studied by means of atom-atomic potentials method. The winding angle fluctuation was found to be 2.4 degrees for poly(dA):poly(dT) and 3.0 degrees for poly(dG):poly(dC). The reasonable agreement of these estimations with those obtained experimentally reveals the essential role of the small-amplitude torsional vibrations of atoms in the mechanism of the double helix flexibility. The calculated equilibrium winding angle, tau 0, essentially depends on the degree of neutralization of phosphate groups, being about 35.5 degrees for the full neutralization. The deoxyribose pucker is closely related to the tau angle: while tau proceeds from 30 degrees to 45 degrees the pseudorotation phase angle, P, increases from 126 degrees to 164 degrees. Fluctuations of the angles TL and TW, which specify inclination of the bases to the helix axis, were evaluated to be 5 degrees-10 degrees. Possible correlation between conformational changes in the adjacent nucleotides is discussed.     

Theoretical model for the equilibrium behavior of DNA superhelices

A statistical-mechanical model for superhelical DNA is presented. The partition function for a DNA superhelix is written by using a combinatorial approach in order to allow for the known relation between the number of superhelical twists and the states of the base pairs in the double helix. While the theory allows any factors which might contribute to the free energy of superhelical twisting to be included in the statistical weights of the superhelical twists, only the reduction in configurational entropy is considered in this paper. Similarities between an imperfectly matched DNA double helix and a DNA superhelix are used in the derivation of expressions for the entropy of superhelical DNA. Although the partition function is presented in a general form, permitting many equilibrium properties of DNA superhelices to be treated, the application considered in this paper is the calculation of helix–coil transition curves. Several experimentally observed features of such transitions are predicted. For example, the curves are bimodal, with an early and a late transition relative to that of a nicked molecule. The results are very sensitive to the volume within which two parts of the double helix must meet when forming a superhelical twist. The free energy of superhelix formation is calculated, and the results are compared with those obtained from the data of Bauer and Vinograd for ethidium bromide intercalation. In the present model, the free energy increases less sharply with an increase in the number of superhelical twists than observed experimentally, indicating that factors other than configurational entropy probably make important contributions to the free energy of superhelix formation.     

The electrostatic potential and steric accessibility of reactive sites within Z-DNA.

A theoretical study of indices potentially useful for investigation of the reactivity of the recently discovered Z-DNA double helix is presented. The electrostatic potential minima and the steric accessibility of reactive sites are calculated. The effect of screening the phosphate groups by metal cations is investigated. The results are compared with those for the B-DNA double helix.     

The effect of intrinsic curvature on conformational properties of circular DNA.

Both thermal fluctuations and the intrinsic curvature of DNA contribute to conformations of the DNA axis. We looked for a way to estimate the relative contributions of these two components of the double-helix curvature for DNA with a typical sequence. We developed a model and Monte Carlo procedure to simulate the Boltzmann distribution of DNA conformations with a specific intrinsic curvature. Two steps were used to construct the equilibrium conformation of the model chain. We first specified the equilibrium DNA conformation at the base pair level of resolution, using a set of the equilibrium dinucleotide angles and DNA sequence. This conformation was then approximated by the conformation of the model chain consisting of a reduced number of longer, straight cylindrical segments. Each segment of the chain corresponded to a certain number of DNA base pairs. We simulated conformational properties of nicked circular DNA for different sets of equilibrium dinucleotide angles, different random DNA sequences, and lengths. Only random sequences of DNA generated with equal probability of appearance for all types of bases at any site of the sequence were used. The results showed that for a broad range of intrinsic curvature parameters, the radius of gyration of DNA circles should be nearly independent of DNA sequence for all DNA lengths studied. We found, however, a DNA properly that should strongly depend on DNA sequence if the double helix has essential intrinsic curvature. This property is the equilibrium distribution of the linking number for DNA circles that are 300-1000 bp in length. We found that a large fraction of the distributions corresponding to random DNA sequences should have two separate maxima. The physical nature of this unexpected effect is discussed. This finding opens new opportunities for joined experimental and theoretical studies of DNA intrinsic curvature.     

Phosphorus-31 nuclear magnetic resonance of double- and triple-helical nucleic acids. Phosphorus-31 chemical shifts as a probe of phosphorus-oxygen ester bond torsional angles

The temperature dependence to the 31P NMR spectra of poly[d(GC)] . poly [d(GC)],d(GC)4, phenylalanine tRNA (yeast) and mixtures of poly(A) + oligo(U) is presented. The 31P NMR spectra of mixtures of complementary RNA and of the poly d(GC) self-complementary DNA provide torsional information on the phosphate ester conformation in the double, triple, and "Z" helix. The increasing downfield shift with temperature of the single-strand nucleic acids provides a measure of the change in the phosphate ester conformation in the single helix to coil conversion. A separate upfield peak (20-60% of the total phosphates) is observed at lower temperatures in the oligo(U) . poly(A) mixtures which is assigned to the double helix/triple helix. Proton NMR and UV spectra confirm the presence of the multistrand forms. The 31P chemical shift for the double helix/triple helix is 0.2-0.5 ppm upfield from the chemical shift for the single helix which in turn is 1.0 ppm upfield from the chemical shift for the random coil conformation.     

On the mechanism of interaction between histone II B1 and DNA and histone II B2 and DNA

A mechanism is suggested at the molecular level whereby histone IIB₂ can act as a cross-link between two (or possibly three) adjacent and parallel strands of DNA double helix some 40 Å apart. Application of Prothero's rule and the Lewis probability functions indicate the probable locations of three a-helices and a number of β-turns. This, coupled with the requirement that the tertiary conformation of the histone be complementary to the DNA molecules and for as many basic groups as possible to bind to phosphate oxygens, allows us to suggest, on the basis of model building using accurate space-filling (CPK) models, a complex conformation that achieves this.A similar process applied to histone IIB₁, whose complete amino acid sequence is also known, shows the location of five probable a-helices, a number of β-turns, and a segment of β-pleated sheet. The basic amino acids are gathered in four groupings. Model building experiments suggest that histone IIB₁ forms a complex strut joining four parallel strands of DNA double helix that form a diamond with diameters 100 and 40 Å. In both these models the purpose and function of a fair proportion of the individual amino acids can be specified.This paper is the third and last of a series in this Journal in which models are presented for the tertiary conformation and function of all five histones of known (in whole or in part) amino acid sequence. This suggests that all five are concerned in packing the long DNA double helix, which may be in a “square helix” form, into the confined space of the chromosome. The hypotheses may be tested by a direct investigation of nucleoprotein in situ to see if these 40, 70, and 100 Å interhelical distances can be detected by biophysical methods.     

Open states in native polynucleotides. II. Hydrogen-exchange study of cytosine-containing double helices.

Hydrogen-exchange studies of I · C and G · C double helices were carried out to test the generality of conclusions reached previously in studies of adenine-containing polymers (preceding paper). The cytosine amino group shows hydrogen-exchange behavior similar to the analogous group in adenine; a pH-independent pathway and a parallel general catalysis pathway require prior separation of the base-pair and pre-equilibrium protonation at the ring N. The cytosine amino group does, however, display greater sensitivity to specific and to general catalysis than found for adenine. In the G · C helix, the ring NH proton of guanine exchanges at the opening-limited rate, as does the analogous proton in A · U and A · T pairs, while the guanine amino protons exchange without a prior opening of structure. From the observed exchange rates and the known chemistry for the pH-independent reaction, one can calculate equilibrium opening constants of 4 × 10⁻³ for poly(rI) · poly(rC) and perhaps one tenth of that for poly(rG) · poly(rC). Also the opening rate constant for the G · C helix is 0.01 s⁻¹.These results, when applied to published exchange curves for DNA, indicate an equilibrium opening constant of 0.005, an opening rate constant of 0.04 s⁻¹, and a closing rate constant of 10 s⁻¹. (All values refer to studies at 0 °C.) These values point to the same kind of traveling-loop model for base-pair opening discussed previously for the opening reactions in adenine-containing double helices.     

Binding of netropsin to a DNA triple helix.

The interaction of netropsin, a minor groove binding drug, with T-A-T triple helix and A-T double helix was studied using circular dichroism spectroscopy and thermal denaturation. The triple helix was made by an oligonucleotide (dA)12-x-(dT)12-x-(dT)12, where x is a hexaethylene glycol chain bridged between the 3' phosphate of one strand and the 5' phosphate of the following strand. This oligonucleotide is able to fold back on itself to form a very stable triplex. Changing the conditions allows the same oligonucleotide in a duplex form with a (dT)12 dangling arm. Circular dichroism spectroscopy demonstrates that netropsin can bind to the triple helical structure. Spectral analysis shows that the bound drug exhibits a conformation and an environment similar in double-stranded and in triple-stranded structure. However, the binding constant to the triple-stranded structure is found smaller than the binding constant to the double-stranded one. Thermal denaturation experiments demonstrate that netropsin destabilizes the triplex whereas it stabilizes the duplex.     

Steady state and exchange kinetics of pyruvate, phosphate dikinase from Propionibacterium shermanii.

Evidence is presented based on requirements for exchange in the partial reactions, initial velocity and exchange kinetics and product inhibition, that the pyruvate, phosphate dikinase reaction of propionibacteria occurs by a nonclassical Tri Uni Uni Ping Pong mechanism. The mechanism involves a pyrophosphoryl enzyme, a phosphoryl enzyme, and the free enzyme, and three functionally distinct and independent substrate sites. On the first site, there is pyrophosphorylation of the enzyme by ATP with subsequent release of AMP. The pyrophosphoryl moiety then reacts at the second site with Pi yielding the product PPi and the phosphoryl from of the enzyme. At the third site pyruvate is phosphorylated yielding P-enolpyruvate and the free enzyme. The three catalytic sites are proposed to be linked by a histidyl residue which functions as a pyrophosphoyrl- and phosphoryl-carrier between the three sites. This proposal is based on the following observations. (A) The patterns of the double reciprocal plots of the initial velocities were all parallel; (b) product inhibition between each pair of substrates and products of the three partial reactions were competitive, i.e. ATP against AMP, Pi against PPi, and pyruvate against P-enolpyruvate; (c) the other product inhibitions, with one exception, were noncompetitive as required by the nonclassical ping-pong mechanism; (d) ATP or P-enolpyruvate was required for the Pi in equilibrium PPi exchange reaction which is in accord with the participation of a pyrosphosphoryl or phosphoryl form of the enzyme in this exchange; (e) the ATP in equilibrium AMP exchange and pyruvate in equilibrium P-enolpyruvate exchange did not require additional substrates. In addition, the inhibition and participation in the exchange reactions of the alpha,beta and beta,gamma-methylene analogues of ATP and of the methylene analogue of inorganic pyrophosphate were investigated and the results were in accord with the proposed mechanism. The combined evidence provides a well documented example of a three site nonclassical Tri Uni Uni Ping Pong mechanism.     

Orientational and rotational velocity correlation functions for water-hydrating B- and Z-DNA double helices

The molecular dynamics simulations reported earlier for the structure and dynamics of water molecules hydrating B- and Z-DNA double helices are analyzed for the orientational correlation functions and the proton rotational velocity autocorrelation functions. The spectra of the rotational velocity autocorrelation functions obtained from the simulation results are compared with the neutron inelastic scattering experiments on hydrated Na-DNA samples. The results predict a small frequency component associated with water molecules bound to the double helices that disappears for waters away from the double helix.     

Effect of a 5'-phosphate on the stability of triple helix.

An effect of 5'-phosphorylation on the stability of triple helical DNA containing pyrimidine:purine:pyrimidine strands has been demonstrated by both gel electrophoresis and UV melting. A 5'-phosphate on the purine-rich middle strand of a triple helix lowers the stability of triple helix formation by approximately 1 kcal/mol at 25 degrees C. The middle strand is involved in both Watson-Crick and Hoogsteen base pairing. In contrast, a 5'-phosphate on the pyrimidine-rich strands, which are involved in either Watson-Crick or Hoogsteen base pairing, has a smaller effect on the stability of triple helix. The order of stability is: no phosphate on either strand > phosphate on both pyrimidine strands > phosphate on purine strand > phosphate on all three strands. Differential stability of triple helix species is postulated to stem from an increase in rigidity due to steric hindrance from the 5'-phosphate. This result indicates that labelling with 32P affect equilibrium in triplex formation.     

The influence of complementary base pair interactions on secondary structure formation and conformational transitions in polynucleotides]

The calculations have been carried out of interaction energy between complementary base pairs of nucleic acids in the function of conformational parametres of double helix (Arnott's parameters) by the method of atom-atom potential functions. Interaction energy as a function of conformational parametres is valley-like and varies little along the bottom of the valley. The regions of interaction energy minima are compared with experimentally determined conformational parametres of nucleic acid double helices. On the basis of calculation results the pathways of conformational transitions between different forms of double-helical polynucleotides are discussed.     

A stochastic model for a closed biochemical system at equilibrium

This paper presents a stochastic model, a theoretical multi-variate probability function describing concentrations of reactants in a closed biochemical system at equilibrium. The theory applies to the complete range of biochemical systems from single enzyme reactions to combinations of reactions to complete pathways. Prior to examining the general system, probability functions are derived for the following systems as examples: a reaction with a competitive inhibitor, a bisubstrate reaction using the ping-pong mechanism and a series of two mono-substrate reactions. The theory of Markov processes is used to derive the probability functions for each of the example systems and then for the general system which includes the example systems as special cases. The probability function for any appropriate biochemical system proves to be the product of independent Poisson probabilities conditioned on the conservation equations. Finally, the implications of the theory are briefly discussed and possible extensions proposed.     

Strong bending of the DNA double helix

During the past decade, the issue of strong bending of the double helix has attracted a lot of attention. Here, we overview the major experimental and theoretical developments in the field sorting out reliably established facts from speculations and unsubstantiated claims. Theoretical analysis shows that sharp bends or kinks have to facilitate strong bending of the double helix. It remains to be determined what is the critical curvature of DNA that prompts the appearance of the kinks. Different experimental and computational approaches to the problem are analyzed. We conclude that there is no reliable evidence that any anomalous behavior of the double helix happens when DNA fragments in the range of 100 bp are circularized without torsional stress. The anomaly starts at the fragment length of about 70 bp when sharp bends or kinks emerge in essentially every molecule. Experimental data and theoretical analysis suggest that kinks may represent openings of isolated base pairs, which had been experimentally detected in linear DNA molecules. The calculation suggests that although the probability of these openings in unstressed DNA is close to 10⁻⁵, it increases sharply in small DNA circles reaching 1 open bp per circle of 70 bp.     

Ethidium ion binds more strongly to a DNA double helix with a bulged cytosine than to a regular double helix

Thermodynamic parameters for ethidium intercalation were determined for the double helices formed by the oligonucleotides dCA6G + dCT6G, which form a normal helix, and dCA3CA3G + dCT6G, which form a double helix with the middle cytosine bulged outside of the helix. Ethidium intercalation was measured by monitoring the absorbance at 260 and 283 nm as a function of temperature for a number of concentrations of ethidium. The binding to the normal helix occurs equally at all the intercalation sites, with an enthalpy of binding of -8 kcal mol-1, an entropy of binding of -6 eu, and an equilibrium constant at 25 degrees C of 2.2 X 10(4) M-1. The binding to the bulged double helix was considerably stronger and is consistent with a model in which the intercalation sites on either side of the bulged base bind 10 times stronger than the other sites. Thus, there are two strong binding sites on the perturbed helix with equilibrium constants for binding of 2 X 10(5) M-1 at 25 degrees C in addition to five normal sites. Several other binding models were tested but did not fit the data satisfactorily.