Loop Dynamics in DNA Denaturation

Abstract

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.PACS numbers: 82.37.-j, 87.14.GgThe thermodynamic properties of DNA near the thermal denaturation transition have been extensively studied during the last few decades [1, 2]. At low temperatures a small fraction of the base pairs are unbound, forming loops of fluctuating lengths. These loops increase in size as the temperature is raised, until the denaturation transition is reached and the two strands separate. Experiments using uv absorption and specific heat measurements have yielded valuable information on equilibrium properties of DNA [2]. Recently, single molecules techniques, most notably Fluorescence Correlation Spectroscopy (FCS) have been used to study dynamical properties such as the temporal behavior of loops [3].The main theoretical approach for studying DNA denaturation has been introduced by Poland and Scheraga (PS) [4] and was used to analyze the case of homopolymers. It was found that the dependence of the entropy of a loop on its length plays a dominant role in determining the thermodynamic behavior near the transition. On general grounds one can argue that the entropy of a loop of length n takes the form S = k B log(Ω(n)), where Ω(n) ∼ s n /n c is the number of loop configurations. Here s is a model-dependent constant and c is a universal exponent whose numerical value has been debated over the years and was found to depend on the degree in which excluded volume interactions are taken into account [4,5,6]. When excluded volume interactions both within a loop and between the loop and the rest of the chain are taken into account one finds c ≃ 2.12 [1,6]. This result, which predicts a first order denaturation transition, has been verified numerically [7]. While numerical studies of the model with excluded volume interaction yield a clear first order transition [8], a direct experimental measurement of c is rather difficult and has not been carried out so far. Theoretical studies of the case of a heteropolymers suggest that disorder makes the transition of order higher than two [9,10].In this paper we analyze the loop dynamics at the denaturation transition. The analysis suggests a method for measuring the exponent c. We focus on predictions for FCS studies [3]. In these experiments one monitors the state of a base pair (whether it is open or closed) as a function of time. The measured quantity is the base pair autocorrelation function C i (t) = u i (0)u i (t) where u i (t) = 1, 0 is a variable which indicates if base pair i is open (1) or closed (0) at time t. By analyzing the loop dynamics using a scaling approach and by di...

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