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.

Disentangling DNA molecules.

The widespread circular form of DNA molecules inside cells creates very serious topological problems during replication. Due to the helical structure of the double helix the parental strands of circular DNA form a link of very high order, and yet they have to be unlinked before the cell division. DNA topoisomerases, the enzymes that catalyze passing of one DNA segment through another, solve this problem in principle. However, it is very difficult to remove all entanglements between the replicated DNA molecules due to huge length of DNA comparing to the cell size. One strategy that nature uses to overcome this problem is to create the topoisomerases that can dramatically reduce the fraction of linked circular DNA molecules relative to the corresponding fraction at thermodynamic equilibrium. This striking property of the enzymes means that the enzymes that interact with DNA only locally can access their topology, a global property of circular DNA molecules. This review considers the experimental studies of the phenomenon and analyzes the theoretical models that have been suggested in attempts to explain it. We describe here how various models of enzyme action can be investigated computationally. There is no doubt at the moment that we understand basic principles governing enzyme action. Still, there are essential quantitative discrepancies between the experimental data and the theoretical predictions. We consider how these discrepancies can be overcome.

Topological Behavior of Plasmid DNA.

The discovery of the B-form structure of DNA by Watson and Crick led to an explosion of research on nucleic acids in the fields of biochemistry, biophysics, and genetics. Powerful techniques were developed to reveal a myriad of different structural conformations that change B-DNA as it is transcribed, replicated, and recombined and as sister chromosomes are moved into new daughter cell compartments during cell division. This article links the original discoveries of superhelical structure and molecular topology to non-B form DNA structure and contemporary biochemical and biophysical techniques. The emphasis is on the power of plasmids for studying DNA structure and function. The conditions that trigger the formation of alternative DNA structures such as left-handed Z-DNA, inter- and intra-molecular triplexes, triple-stranded DNA, and linked catenanes and hemicatenanes are explained. The DNA dynamics and topological issues are detailed for stalled replication forks and for torsional and structural changes on DNA in front of and behind a transcription complex and a replisome. The complex and interconnected roles of topoisomerases and abundant small nucleoid association proteins are explained. And methods are described for comparing in vivo and in vitro reactions to probe and understand the temporal pathways of DNA and chromosome chemistry that occur inside living cells.

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.

Bending of short DNA helices.

In their recent Science paper, Vafabakhsh and Ha claim that DNA duplexes at the range of 100 bp experience anomalous flexibility, much greater than the flexibility of large DNA molecules. ( 1) However, careful reevaluation of their data leads to the conclusion that the presented data do not warrant the authors' claim.

Unlinking of supercoiled DNA catenanes by type IIA topoisomerases.

It was found recently that DNA catenanes, formed during replication of circular plasmids, become positively (+) supercoiled, and the unlinking of such catenanes by type IIA topoisomerases proceeds much more efficiently than the unlinking of negatively (-) supercoiled catenanes. In an attempt to explain this striking finding we studied, by computer simulation, conformational properties of supercoiled DNA catenanes. Although the simulation showed that conformational properties of (+) and (-) supercoiled replication catenanes are very different, these properties per se do not give any advantage to (+) supercoiled over (-) supercoiled DNA catenanes for unlinking. An advantage became evident, however, when we took into account the established features of the enzymatic reaction catalyzed by the topoisomerases. The enzymes create a sharp DNA bend in the first bound DNA segment and allow for the transport of the second segment only from inside the bend to its outside. We showed that in (-) supercoiled DNA catenanes this protein-bound bent segment becomes nearly inaccessible for segments of the other linked DNA molecule, inhibiting the unlinking.

Temperature dependence of DNA persistence length.

We have determined the temperature dependence of DNA persistence length, a, using two different methods. The first approach was based on measuring the j-factors of short DNA fragments at various temperatures. Fitting the measured j-factors by the theoretical equation allowed us to obtain the values of a for temperatures between 5°C and 42°C. The second approach was based on measuring the equilibrium distribution of the linking number between the strands of circular DNA at different temperatures. The major contribution into the distribution variance comes from the fluctuations of DNA writhe in the nicked circular molecules which are specified by the value of a. The computation-based analysis of the measured variances was used to obtain the values of a for temperatures up to 60°C. We found a good agreement between the results obtained by these two methods. Our data show that DNA persistence length strongly depends on temperature and accounting for this dependence is important in quantitative comparison between experimental results obtained at different temperatures.

Sequence dependence of DNA bending rigidity.

For many aspects of DNA-protein interaction, it is vital to know how DNA bending rigidity (or persistence length, a) depends on its sequence. We addressed this problem using the method based on cyclization of short DNA fragments, which allows very accurate determination of a. Our approach was based on assigning specific values of a to each of 10 distinct dinucleotide steps. We prepared DNA fragments, each about 200 bp in length, with various quasi-periodic sequences, measured their cyclization efficiencies (j factors), and fitted the data by the theoretical equation to obtain the values of a for each fragment. From these data, we obtained a set of a for the dinucleotide steps. To test this set, we used it to design DNA sequences that should correspond to very low and very high values of a, prepared the corresponding fragments, and determined their values of a experimentally. The measured and calculated values of a were very close to one another, confirming that we have found the correct solution to this long-standing problem. The same experimental data also allowed us to determine the sequence dependence of DNA helical repeat.

Tightness of knots in a polymer chain.

It was predicted recently that sufficiently complex knots on a linear wormlike chain can have a metastable size, preventing their spontaneous expansion. We tested this prediction via computer simulations for 7(1) and 10(151) knots. We calculated the equilibrium distributions of knot size S for both knots. By using the umbrella sampling, we were able to obtain the distributions over a wide range of S values. The distributions were converted into the dependencies of the free energy on the knot size. The obtained free energy profiles have no pronounced local minima, so there are no metastable knot sizes for these knots. We also performed Brownian dynamics simulation of 7(1) knot relaxation that started from a very tight knot conformation. The simulation showed that knot expansion is a fast process compared to knot displacement along the chain contour by diffusion.

DNA supercoiling helps to unlink sister duplexes after replication.

DNA supercoiling is one of the mechanisms that can help unlinking of newly replicated DNA molecules. Although DNA topoisomerases, which catalyze the strand passing of DNA segments through one another, make the unlinking problem solvable in principle, it remains difficult to complete the process that enables the separation of the sister duplexes. A few different mechanisms were developed by nature to solve the problem. Some of the mechanisms are very intuitive while the others, like topology simplification by type II DNA topoisomerases and DNA supercoiling, are not so evident. A computer simulation and analysis of linked sister plasmids formed in Escherichia coli cells with suppressed topoisomerase IV suggests an insight into the latter mechanism.

Determining protein-induced DNA bending in force-extension experiments: theoretical analysis.

Computer simulations were used to investigate the possibility of determining protein-induced DNA bend angles by measuring the extension of a single DNA molecule. Analysis of the equilibrium sets of DNA conformations showed that shortening of DNA extension by a single protein-induced DNA bend can be as large as 35 nm. The shortening has a maximum value at the extending force of approximately 0.1 pN. At this force, the DNA extension experiences very large fluctuations that dramatically complicate the measurement. Using Brownian dynamics simulation of a DNA molecule extended by force, we were able to estimate the observation time needed to obtain the desired accuracy of the extension measurement. Also, the simulation revealed large fluctuations of the force, acting on the attached magnetic bead from the stretched DNA molecule.

Theoretical models of DNA topology simplification by type IIA DNA topoisomerases.

It was discovered 12 years ago that type IIA topoisomerases can simplify DNA topology--the steady-state fractions of knots and links created by the enzymes are many times lower than the corresponding equilibrium fractions. Though this property of the enzymes made clear biological sense, it was not clear how small enzymes could selectively change the topology of very large DNA molecules, since topology is a global property and cannot be determined by a local DNA-protein interaction. A few models, suggested to explain the phenomenon, are analyzed in this review. We also consider experimental data that both support and contravene these models.

Theoretical analysis of disruptions in DNA minicircles.

Under sufficient bending stress, which appears in DNA minicircles and small DNA loops, the double helix experiences local disruptions of its regular structure. We developed a statistical-mechanical treatment of the disruptions in DNA minicircles, studied experimentally by Du et al. The model of disruptions used in our Monte Carlo simulation of minicircle conformations specifies these conformations by three parameters: DNA bend angle at the disruption, theta(d); local DNA unwinding caused by the disruption; and the free energy associated with the disruption in the unstressed double helix, G(d). The model is applicable to any structural type of disruption, kinks or opening of single basepairs. The simulation shows that accounting for both torsional and bending deformation associated with the disruptions is very important for proper analysis. We obtained a relationship between values of G(d) and theta(d) under which the simulation results are compatible with the experimental data. The relationship suggests that the free energy of basepair opening, which includes flipping out both bases, is significantly higher than the generally accepted value. The model is also applied to the analysis of j-factors of very short DNA fragments.

Simulation of DNA catenanes.

DNA catenanes are important objects in biology, foremost as they appear during replication of circular DNA molecules. In this review we analyze how conformational properties of DNA catenanes can be studied by computer simulation. We consider classification of catenanes, their topological invariants and the methods of calculation of these invariants. We briefly analyze the DNA model and the simulation procedure used to sample the equilibrium conformational ensemble of catenanes with a particular topology. We consider how to avoid direct simulation of many DNA molecules when we need to account for the linking-unlinking process. The simulation methods and their comparisons with experiments are illustrated by some examples. We also describe an approach that allows simulating the steady state fraction of DNA catenanes created by type II topoisomerases.

Kinking the double helix by bending deformation.

DNA bending and torsional deformations that often occur during its functioning inside the cell can cause local disruptions of the regular helical structure. The disruptions created by negative torsional stress have been studied in detail, but those caused by bending stress have only been analyzed theoretically. By probing the structure of very small DNA circles, we determined that bending stress disrupts the regular helical structure when the radius of DNA curvature is smaller than 3.5 nm. First, we developed an efficient method to obtain covalently closed DNA minicircles. To detect structural disruptions in the minicircles we treated them by single-strand-specific endonucleases. The data showed that the regular DNA structure is disrupted by bending deformation in the 64-65-bp minicircles, but not in the 85-86-bp minicircles. Our results suggest that strong DNA bending initiates kink formation while preserving base pairing.

Probability of the site juxtaposition determines the rate of protein-mediated DNA looping.

Numerous biological processes are regulated by DNA elements that communicate with their targets over a distance via formation of protein-bridged DNA loops. One of the first questions arising in studies of DNA looping is whether the rate of loop formation is limited by diffusion of the DNA sites. We addressed this question by comparing the in vitro measured rates of transcription initiation in the NtrC-glnAp2 enhancer-dependent transcription initiation system with predictions of two different theoretical models. The promoter and enhancer were in a 7.6-kb plasmid and separated by 2.5 kb. The measurements were performed for different values of the plasmid superhelix density, from 0 to -0.07. Earlier theoretical analysis, based on the Monte Carlo simulation of DNA conformations, showed that if the rate of loop formation is determined by the equilibrium probability of juxtaposition of the DNA sites, the rate should be approximately 100 times higher in supercoiled than in relaxed DNA. On the other hand, Brownian dynamics simulation showed that if the rate of loop formation is limited by the site diffusion, it should be nearly independent of DNA supercoiling. We found that efficiency of the transcription initiation increases by nearly two orders of magnitude as a result of the corresponding increase of the template supercoiling. This clearly shows that the rate of bridging in the enhancer-promoter system is not limited by diffusion of the DNA sites to one another. We argue that this conclusion derived for the specific system is likely to be valid for the great majority of biological processes involving protein-mediated DNA looping.