Conformational Transitions in Supercoiled DNA: Monte Carlo Study
The original problem was to explain the experimental data on the melting behaviour of a form V DNA, an intriguing form of highly supercoiled DNA which has zero linking number. I looked for a method which in addition to giving the overall melting profile, would also give the sequence dependent transformation probabilities of a form V DNA at normal physiological temperature. In the course of investigation, I found that the existing numerical algorithms for tackling such statistical thermodynamic problems involving DNA supercoiling are unsuitable because they become inefficient at high temperature or at high degrees of supercoiling. Monte Carlo method turned out to be free from such deficiencies. In addition it had the advantages of being extremely simple and completely general. At present I am developing the formalism in several steps. In the first step I have shown by comparing with experimental and other theoretical methods that this method gives excellent results for thermal denaturation of supercoiled DNA. This result is now in the process of being extended with the consideration of pH dependent denaturation of supercoiled DNA. In the next step, thermal denaturation and B-Z transition is considered together for a normally supercoiled DNA and compared with experimental data and other theoretical results. This part is almost completed. The final step would be to apply the method to study the behaviour of form V DNA.
The structure of supercoiled DNA displays a host of intriguing features which are quite different from that of linear or relaxed circular DNA. At the tertiary level, supercoiled DNA in solution exhibits a form which has been termed plectonemically interwound. Recently, due to a number of extensive experimental studies, many interesting properties of this type of structure have emerged. It has been found, for example, that the length of the superhelix axis is independent of the linking difference and directly proportional to the contour length of the molecule. A measure of the lateral dimension of the molecule along the superhelix axis, the supercoiling radius, is similarly found to vary hyperbolically with the linking difference and is directly proportional to the length of the molecule. The existing theories, based on the energy minimisation approach, was found to be insufficient for explaining these and other observations, particularly the hyperbolic variation of the supercoiling radius with the degree of supercoiling. In fact, they led to a paradoxical result where at any supercoiling the supercoiling radius tended to zero. To bypass this problem, a finite diameter was ascribed to the double-stranded structure in an ad hoc fashion, which however, did not reproduce the variation of the supercoiling radius with supercoiling.
In my work, the consequences of introducing an entropic term in the supercoiling free energy have been investigated. It was recognised for quite some time that supercoiling involves an entropic cost since the number of configurations available to a supercoiled molecule is much less than that available to a relaxed one. To estimate the entropy change, the supercoiled molecule was imagined to be trapped within a cylinder of radius equal to the supercoiling radius of the molecule. In analogy with a similar problem in polymer physics, one can then calculate the entropy change as a result of this confinement and further calculations showed that with this simple model most of the features in the experimental observations could be explained.
An interesting application of the result of the above study has been to explain the gel electrophoretic mobilities of DNA topoisomers. It has been known for long that in agarose gels of suitable concentration a mixture of DNA topoisomers form a ladder of bands in electrophoresis experiments. However, the resolution of the bands is not uniform but worsens with increasing magnitude of supercoiling. Although the gel electrophoretic behaviour of short stretches of linear DNA has been well explained by the reptation model, it was not clear what mechanism is responsible for the separation of the topoisomers in the gel. In a joint work with Dr. S Sen, we proposed an extension of the reptation model which nicely explained the observed features almost quantitatively. The trick was that, whereas in conventional reptation theory, one dealt with a polymer of negligible thickness, in our case we ascribed a finite thickness to the molecule, the thickness being determined by the supercoiling radius of the molecule. Since a thicker molecule is expected to experience greater friction in the gel matrix, it is easy to see why a more supercoiled molecule (having smaller supercoiling radius) would move faster in the gel. Moreover, since at high levels of supercoiling, the radius decreases asymptotically with increasing degree of supercoiling, the faster moving bands will be poorly resolved. To get an analytical expression for the mobility, we have utilised a relation between the gel mobility of the DNA and the gel concentration. The idea was to replace the picture of a thick molecule in the gel pore by a thin chain molecule in a pore having a reduced dimension (in the same line as the well known Van der Waals correction for the finite size of a gas molecule). Since the gel pore size is dependent on the gel concentration, we were able to relate the mobility with the supercoiling radius, i.e., with the degree of supercoiling.
It is now well established that DNA can exhibit a high degree of structural polymorphism at the secondary structural level. In fact, some of them are stabilised under supercoilng. To understand the connection between supercoiling and DNA secondary structure, it is necessary to derive a general form of supercoiling energy that would be applicable for various types of conformational transitions in the molecule. We have shown that this general form is different from the simple quadratic dependence of the free energy on the total linking difference, particularly when the elastic parameters of the different local conformations differ significantly. Use of this form leads to much improved agreement with experimental data on thermal and alkaline denaturation transitions of supercoiled DNA. Using the properties of supercoiling energy we have also been able to explain the features of denaturation of supercoiled heteropolynucleotides.
Supercoiling is known to affect the regulation of gene function. One possible way by which this can occur is through conformational alterations in some stretches in the molecule and/or through alteration in the binding of regulator molecules to the DNA. I have shown by examining different model systems, how supercoiling energy governs the linkage between ligand binding and conformational transitions in supercoiled DNA. For example, in the presence of Z-specific ligands, the supercoil driven B to Z transition would take place at a much lower magnitude of supercoiling, and I have derived expressions by which this can be calculated. In another type of situation, e.g., with the addition of intercalators like chloroquine, a Z-stretch would revert back to the B state. I have shown that these phenomena can be well described by using such models as the two state allosteric model, and on the basis of it I have derived a modified McGhee-von Hippel equation for ligand binding to supercoiled DNA which can undergo conformational transitions.
Histone H1 is involved in the function and maintenance of higher order chromatin structure in eukaryotes. There has been a lot of study on H1-DNA complexes, but surprisingly no estimate of the binding affinities of the protein for different forms of DNA was available. Using the data of Dr. S. Chaudhuri and Dr. N. P. Bhattacharyya, who were then investigating the binding characteristics of histone H1 to supercoiled DNA by gel retardation technique, I worked out a quantitative method for estimating the binding constant from such data in the non-cooperative binding region.