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Register a new userDenaturation of Circular DNA: Supercoils and Overtwist
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The denaturation transition of circular DNA is studied within a Poland-Scheraga type approach, generalized to account for the fact that the total linking number (LK), which measures the number of windings of one strand around the other, is conserved. In the model the LK conservation is maintained by invoking both overtwisting and writhing (supercoiling) mechanisms. This generalizes previous studies which considered each mechanism separately. The phase diagram of the model is analyzed as a function of the temperature and the elastic constant $kappa$ associated with the overtwisting energy for any given loop entropy exponent, $c$. As is the case where the two mechanisms apply separately, the model exhibits no denaturation transition for $c le 2$. For $c>2$ and $kappa=0$ we find that the model exhibits a first order transition. The transition becomes of higher order for any $kappa>0$. We also calculate the contribution of the two mechanisms separately in maintaining the conservation of the linking number and find that it is weakly dependent on the loop exponent $c$.
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The linking number (topological entanglement) and the writhe (geometrical entanglement) of a model of circular double stranded DNA undergoing a thermal denaturation transition are investigated by Monte Carlo simulations. By allowing the linking number to fluctuate freely in equilibrium we see that the linking probability undergoes an abrupt variation (first-order) at the denaturation transition, and stays close to 1 in the whole native phase. The average linking number is almost zero in the denatured phase and grows as the square root of the chain length, N, in the native phase. The writhe of the two strands grows as the square root of N in both phases.
The dynamics of a loop in DNA molecules at the denaturation transition is studied by scaling arguments and numerical simulations. The autocorrelation function of the state of complementary bases (either closed or open) is calculated. The long-time decay of the autocorrelation function is expressed in terms of the loop exponent c both for homopolymers and heteropolymers. This suggests an experimental method for measuring the exponent c using florescence correlation spectroscopy.
Poland-Scheraga models were introduced to describe the DNA denaturation transition. We give a rigorous and refined discussion of a family of these models. We derive possible scaling functions in the neighborhood of the phase transition point and review common examples. We introduce a self-avoiding Poland-Scheraga model displaying a first order phase transition in two and three dimensions. We also discuss exactly solvable directed examples. This complements recent suggestions as to how the Poland-Scheraga class might be extended in order to display a first order transition, which is observed experimentally.
We study the effect of the composition of the genetic sequence on the melting temperature of double stranded DNA, using some simple analytically solvable models proposed in the framework of the wetting problem. We review previous work on disorder
We propose a statistical mechanics model for DNA melting in which base stacking and pairing are explicitly introduced as distinct degrees of freedom. Unlike previous approaches, this model describes thermal denaturation of DNA secondary structure in the whole experimentally accessible temperature range. Base pairing is described through a zipper model, base stacking through an Ising model. We present experimental data on the unstacking transition, obtained exploiting the observation that at moderately low pH this transition is moved down to experimentally accessible temperatures. These measurements confirm that the Ising model approach is indeed a good description of base stacking. On the other hand, comparison with the experiments points to the limitations of the simple zipper model description of base pairing.
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