A. V. Vologodskii

Computer Simulation of DNA Supercoiling

We treat supercoiled DNA within a wormlike model with excluded volume. A modified Monte Carlo approach has been used, which allowed computer statistical-mechanical simulations of moderately and highly supercoiled DNA molecules. Even highly supercoiled molecules do not have a regular shape, though with an increase in writhing the chains look more and more like branched interwound helixes. The averaged writhing (Wr) approximately 0.7 delta Lk. The superhelical free energy F is calculated as a function of the linking number. Lk. The calculations have shown that the generally accepted quadratic dependence of F on Lk is valid for a variety of conditions, though it is by no means universal. Significant deviations from the quadratic dependence are expected at high superhelical density under ionic conditions where the effective diameter of DNA is small. The results are compared with the available experimental data.

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.

Allowance for Heterogeneous Stacking in the DNA Helix-Coil Transition Theory

Melting profiles of eight DNA molecules with lengths ranging from 849 to 4362 bp have been measured in an SSC buffer where the melting is an equilibrium process up to complete strand separation. A theoretical analysis shows that the melting profiles depend on only eight invariants that are linear combinations of 10 original stacking parameters. As a result it is impossible to determine the 10 parameters from the melting profiles. The 8 variants have been determined by fitting theoretical profiles to experimental ones for two fragments. Then theoretical and experimental profiles are compared for those 6 fragments that were not used in the fitting procedure. This comparison demonstrates that allowance for heterogeneous stacking considerably improves the agreement between theory and experiment. The values of invariants have proved to be small. This confirms the previous conclusion that heterogeneous stacking interactions produce only small corrections to the major effect of the difference in the mean stabilities of AT and GC pairs. Some discrepancy between theory and experiment that remains after the allowance for heterogeneous stacking is probably due to even finer effects of long-range interactions.

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.

Direct comparison of theoretical and experimental melting profiles for RF II phiX174 DNA.

The determination by Sanger et al. of the complete nucleotide sequence for ΦX174 DNA has made it possible for the first time to compare directly theoretical and experimental DNA melting profiles. The comparison shows that the theory predicts the observed shape of the differential melting curve surprisingly well. Calculation of the denaturation maps allows the peaks on the curve to be correlated with cooperative melting out of concrete regions on the sequence of nucleotides.

Modeling supercoiled DNA.

Publisher Summary Numerous structural methods, such as X-ray crystallography and NMR, make it possible to elucidate the local DNA structure. However, for DNA molecules comprising hundreds of base pairs, the global structure is of great importance. The global structure arises because of the accumulation of minute changes in local structure, and it cannot be detected by structural methods used to detect the local structure. Special methods, which are sensitive to the global structure, are used. Among the global DNA features, the most significant is DNA supercoiling. Supercoiling entails the topological restrictions arising in closed circular DNA molecules. A statistical-mechanical approach described in this chapter makes it possible to obtain, first, the images of superhelical DNA conformations in three dimensions. These images can be compared to the data obtained by electron microscopy and cryoelectron microscopy. The approach is also very useful in interpreting numerous experimental data obtained by different indirect techniques, such as hydrodynamic methods and static and dynamic light scattering. Among other things, it permits the calculation of the superhelix free energy as a function of superhelical density.

Laplace operator and random walk on one-dimensional nonhomogeneous lattice

A classical result of probability theory states that under suitable space and time renormalization, a random walk converges to Brownian motion. We prove an analogous result in the case of nonhomogeneous random walk on onedimensional lattice. Under suitable conditions on the nonhomogeneous medium, we prove convergence to Brownian motion and explicitly compute the diffusion coefficient. The proofs are based on the study of the spectrum of random matrices of increasing dimension.

The Effect of Sequence Heterogeneity on DNA Melting Kinetics

We consider kinetics of the cooperative melting of DNA sections situated at the edge of the helix. Accurate calculations based on the real sequences of such sections demonstrate that their internal heterogeneity has a drastic effect on the melting kinetics. Allowance for the internal heterogeneity increases the relaxation time by several orders of magnitude as compared with a model based on the assumption of equal base-pair stability within a section. The relaxation times obtained are in good agreement with the experimental data of Suyama and Wada (A. Suyama and A. Wada, Biopolymers, 23, 409 (1984)). An analysis of the melting process revealed some simple sequence characteristics that determine its rate. An examination of the temperature dependence of the relaxation time led to a distinct interpretation of the apparent activation energies of the denaturation and renaturation. The relaxation time proved to reach its maximum near the equilibrium melting point of the section examined.

Theoretical study of DNA unwinding under the action of formaldehyde

A consistent theory of DNA unwinding under the action of formaldehyde which makes possible calculation of all characteristics of the process based on a given nucleotide sequence has been developed. The kinetic parameters are obtained with the use of the theory of helix-coil transition in DNA. These parameters are then employed for obtaining the final characteristics of the unwinding process by formaldehyde, the kinetic curves of unwinding (and their anamorphoses) and the maps of denaturation. The calculations which were performed for heteropolynucleotides with random sequences and with different concentrations of defects revealed that a simple theory previously developed for the homopolymer case, is also valid for the heteropolymer. This result agrees with the experimental data and justifies, from the theoretical point of view, applications of the kinetic formaldehyde method to the natual DNAs. Denaturation maps have also been calculated which demonstrated that a purely random sequence proved to give only slightly noticeable singularities. However, the insertion of the AT clusters (the regions consisting of 20–40 AT pairs) into the random sequence gives rise to the clear-cut peaks on the maps. The magnitude of such a peak drops sharply if only a few GC pairs are present within the AT cluster. Electron microscopic mapping data obtained by the Inman method, have been discussed on the basis of the above theoretical results. This consideration allows one to attribute the sharp peaks on the denaturation maps to T7 phage DNA as originated from the AT clusters.

DNA melting and energetics of the double helix

Studying melting and energetics of the DNA double helix has been one of the major topics of molecular biophysics over the past six decades. The main objective of this article is to overview the current state of the field and to emphasize that there are still serious gaps in our understanding of the issue. We start with a concise description of the commonly accepted theoretical model of the DNA melting. We then concentrate on studies devoted to the comparison with experiment of theoretically predicted melting profiles of DNAs with known sequences. For long DNA molecules, such comparison is significant from the basic-science viewpoint while an accurate theoretical description of melting of short duplexes is necessary for various very important applications in biotechnology. Several sets of DNA melting parameters, proposed within the framework of the nearest neighbor model, are compared and analyzed. The analysis leads to a conclusion that in case of long DNA molecules the consensus set of nearest neighbor parameters describes well the experimental melting profiles. Unexpectedly, for short DNA duplexes the same set of parameters hardly yields any improvement as compared to the simplest model, which completely ignores the effect of heterogeneous stacking. Possible causes of this striking observation are discussed. We then overview the issue of separation of base-pairing and base-stacking contributions into the double helix stability. The recent experimental attempts to solve the problem are extensively analyzed. It is concluded that the double helix is essentially stabilized by stacking interaction between adjacent base pairs. Base pairing between complementary pairs does not appreciably contribute into the duplex stability. In the final section of the article, kinetic aspects of the DNA melting phenomenon are discussed. The main emphasis is made on the hysteresis effects often observed in melting of long DNA molecules. It is argued that the phenomenon can be well described via an accurate theoretical treatment of the random-walk model of melting kinetics of an isolated helical segment in DNA.