A. V. Lukashin

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.

Fluctuational opening of the double helix as revealed by theoretical and experimental study of DNA interaction with formaldehyde.

It follows from the theory of helix-coil transition that local opening of the double helix due to thermal fluctuations must take place at temperatures well below the melting range. Provided that formaldehyde can not react with hydrogen-bonded bases and can react only with the exposed ones, such fluctuational opening of base-pairs may be probed by formaldehyde. To test the adequacy of the theory for describing the fluctuational opening of the double helix, the process of DNA interaction with formaldehyde has been simulated by the Monte Carlo method with the aid of a computer. On the basis of kinetic constants for the forward and reverse reactions of formaldehyde with all four nucleotides measured by McGhee & von Hippel (1975 a,b ), the kinetic curves of DNA unwinding by formaldehyde have been calculated theoretically without the use of any adjustable parameter. The calculations have demonstrated that the highly reversible but very fast reaction of formaldehyde with the imino group of thymine plays a very important role in the process of DNA unwinding by formaldehyde have been compared with experimental data obtained for bacteriophage T7 DNA for different values of pH, temperature and concentration of formaldehyde. This comparison leads to the conclusion that the theory offers a correct general description of fluctuational opening of the double helix. The main characteristics of this process calculated by the theory are as follows. At room temperatures only individual base-pairs are opened and the mean distance between adjacent unpaired bases is as great as 2×10 5 base-pairs. Each A·T pair is shown to be opened with frequency about 10 2 s −1 and each G·C pair with a frequency about 10 s −1 . At elevated temperatures, in the DNA premelting region, the probability of fluctuational opening, as well as the average number of base-pairs in an opened region, increases considerably. A possible role of the results obtained from an analysis of the processes of DNA function in the cell is discussed.

Neural Network Models for Promoter Recognition

The problem of recognition of promoter sites in the DNA sequence has been treated with models of learning neural networks. The maximum network capacity admissible for this problem has been estimated on the basis of the total of experimental data available on the determined promoter sequences. The model of a block neural network has been constructed to satisfy this estimate and rules have been elaborated for its learning and testing. The learning process involves a small (of the order of 10%) part of the total set of promoter sequences. During this procedure the neural network develops a system of distinctive features (key words) to be used as a reference in identifying promoters against the background of random sequences. The learning quality is then tested with the whole set. The efficiency of promoter recognition has been found to amount to 94 to 99%. The probability of an arbitrary sequence being identified as a promoter is 2 to 6%.

On the ability of neural networks to perform generalization by induction

The ability of neural networks to perform generalization by induction is the ability to learn an algorithm without the benefit of complete information about it. We consider the properties of networks and algorithms that determine the efficiency of generalization. These properties are described in quantitative terms. The most effective generalization is shown to be achieved by networks with the least admissible capacity. General conclusions are illustrated by computer simulations for a three-layered neural network. We draw a quantitative comparison between the general equations and specific results reported here and elsewhere.

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

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: aB = 1nm, qB = 4.2, aZ = 0.9 nm and qZ = 3.9. A simple theory shows that at low ionic strengths (when Debye screening length rD much greater than a) the electrostatic free energy difference FelBZ = FelZ - FelB increases with increasing ionic strength since qB greater than qZ. At high ionic strengths (when rD much less than a) the FelBZ would go on growing with increasing ionic strength if the inequality qB/aB greater than qZ/aZ were valid. In the converse case when qZ/qB greater than aZ/aB the FelBZ value decreases with increasing salt concentration at high ionic strength. Since X-ray data correspond to the latter case, theory predicts that the FelBZ value reaches a maximum at an intermediate ionic strength of about 0.1 M (where rD approximately a). We also performed rigorous calculations based on the Poisson-Boltzmann equation. These calculations have confirmed the above criterion of nonmonotonous behaviour of the FelBZ 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.(ABSTRACT TRUNCATED AT 250 WORDS)

Comparison of different approaches for calculation of polyelectrolyte free energy.

We consider the problem of the mean field (Poisson-Boltzmann) calculation of the electrostatic free energy for a strongly charged polyelectrolyte such as DNA in a salt solution. We compare two approaches to calculate the free energy: (i) direct one starting from the statistical-mechanical expression for the electrostatic free energy and (ii) the polyion charge variation method. In the infinite dilution limit (in respect to polyion) and in excess salt (IDLES) the two approaches are fully equivalent. This is shown by straight forward algebra. We have performed specific calculations of the free energy difference for the case of B-Z transition in DNA as a function of ionic strength. As expected, the two approaches led to identical results. The ionic strength dependence of the B-to-Z free energy proves to be concaved up and as a result Z-DNA is stabilized at low ionic concentration as well as at high salt, in full agreement with our previous results (M.D.Frank-Kamenetskii et al., J. Biomol. Struct. Dyn. 3, 35-42 (1985]. Our data quantitatively agree with the results of Soumpasis (D.M.Soumpasis, J. Biomol. Struct. Dyn. 6, 563-574 (1988]. However, his claim about the absence of the effect of stabilization of Z-DNA at low salt proves to be groundless, and the criticism of our earlier approach seems to be irrelevant.

Towards an exact theory of polyelectrolytes

Abstract Within the framework of the gas approximation an exact method is developed for calculating the electric potential distribution around a polyion. The polyion is modelled as an infinitely long impermeable cylinder and the mobile ions are assumed to be impermeable spheres. Equations are derived for two potentials ψ min and ψ max so that the genuine potential ψ lies in between. The equations are numerically solved for different parameter values. The results are compared with data obtained on the basis of the standard Poisson-Boltzmann equation.

Allowance for spatial dispersion of dielectric permittivity in polyelectrolyte model of DNA.

In order to allow for real dielectric properties of a solvent in calculating of electrostatic characteristics of strongly charged polyions such as DNA in salt solution we consider a simple model of linear dielectric response of a medium. The interactions between charged particles are treated in the framework of self-consistent-field approximation. The basic characteristic of the problem, electrostatic potential, can be found from the solution of non-linear integro-differential equation. Specifically we consider so-called quasimacroscopic model where dielectric response of a medium depends only on the distance from the polyion. Application of the approach for calculating of the B-to-Z free energy qualitatively retains the main conclusion obtained previously within the model with fixed dielectric constant: non-monotonous behavior of the free energy differences as a function of ionic strength. At the same time, essential sensitivity of the results to specific values of dielectric parameters is observed.

Theory of co-operative formation of defects in DNA molecule under ultraviolet irradiation

Abstract The process of thymine dimers formation in DNA under the action of ultraviolet irradiation has been analyzed theoretically taking into account the long range transfer of electronic excitation along the molecule. First, for the case of homopolymer (poly dA.dT) an exact analytical solution of the problem has been obtained. For the case of random walks of excitation as well as for the case of its directional motion the distribution functions of undamaged regions on their lengths have been calculated. These functions turned out to differ drastically from a trivial exponential distribution taking place without excitations transfer. At the same time the transfer of excitation leads to the effect of thymine dimers clustering—the new dimers are formed mainly in the vicinity of dimers formed earlier. The degree of clustering γ (the mean number of dimers per cluster) depends quadratically on the concentration of clusters C in the homopolymer for the case of random walks of excitation. For the case of a heteropolymer having inhomogeneous distribution of potential dimers (two thymines situated one by one in the same strand) a machine algorithm for numerical solution of the problem by the Monte-Carlo method has been proposed. Calculations for the heteropolymer with a random sequence of bases have shown that in this case the curve γ(c) is S-shaped and its form agrees with the experimental one obtained by Shafranovskaya, Trifonov, Lazurkin & Frank-Kamenetskii (1972) . The values of parameters providing the best agreement between theory and experiment have been obtained. Using these values of parameters the calculations of distribution function of undamaged regions and curves γ(c) for different concentrations of AT-pairs in DNA have been performed. These calculations show that the degree of clustering γ rises dramatically with increasing concentration of AT-pairs in DNA. Theoretical predictions which can be tested experimentally have been summarized.