Thermal Denaturation of Fluctuating DNA Driven by Bending Entropy

Abstract

A statistical model of homopolymer DNA, coupling internal base pair states (unbroken or broken) and external thermal chain fluctuations, is exactly solved using transfer kernel techniques. The dependence on temperature and DNA length of the fraction of denaturation bubbles and their correlation length is deduced. The thermal denaturation transition emerges naturally when the chain fluctuations are integrated out and is driven by the difference in bending (entropy dominated) free energy between broken and unbroken segments. Conformational properties of DNA, such as persistence length and mean-square-radius, are also explicitly calculated, leading, e.g., to a coherent explanation for the experimentally observed thermal viscosity transition.PACS numbers: 87.10.+e, 87.15.Ya, 82.39.Pj Double-stranded DNA (dsDNA) is made up of two intertwined interacting semi-flexible single-strand DNA (ssDNA) chains. Over fifty years ago it was recognized that the intracellular unwinding of DNA at physiological temperature has as counterpart the thermally induced denaturation above physiological temperature of purified DNA solutions where dsDNA completely separates into two ssDNA. Despite the differences between the two mechanisms, this observation has led to an intensive study of thermal denaturation [1,2]. The stability of dsDNA at physiological temperature is due to the selfassembly of neighboring base pairs within a same strand via base-stacking interactions and of both strands via hydrogen bonds between complementary bases. The bonding energy is, however, on the order of k B T (thermal energy) [3] and thermal fluctuations can lead, even at physiological temperature, to local and transitory unzipping of dsDNA [1]. The cooperative opening of consecutive base pairs leads to denaturation bubbles and the melting temperature, T m , above which bubbles proliferate, depends on sequence, chain length, and ionic strength. Experiments show, for example, that there exist a bubble initiation barrier of ∼ 10k B T and free energy cost of ∼ 0.1k B T for breaking an additional base pair in an existing A-T bubble [4]. A detailed understanding of equilibrium [1] and dynamical [5] properties of DNA in solution is still being sought and a consensus concerning the physical mechanism behind the denaturation transition has not yet been reached.A variety of mesoscopic models have been proposed to account for the thermodynamical properties of denaturation bubbles in DNA. They range from i) simple effective Ising-like two-state models [1] to more detailed ones such as ii) loop entropy models (with or without chain selfavoidance) [1,2,6,7], and iii) non-linear phonon models, where the shape of the interaction potential between base pairs is more precisely taken into account [8,9]. To get a transition in models i) and ii), an effective temperature dependent base-pair chemical potential must be inserted by hand. For finite chains, type (ii) models simply refine the sharpness of the transition [1], but do not attempt to provide a deeper explanation of the ...

Mesoscopic models for DNA stretching under force: New results and comparison with experiments

“…This allows us to write an effective Ising model since Eqs. (30,31) do not depend on t anymore. Hence, coming back to Eq.…”

“…We use a Ising-Heisenberg coupled model, which has already been used by us for the theory of DNA denaturation [31,32]. Other works have used such types of models [24,25].…”

“…(30,31) are negligible and thus assume that they are equal to 1 for all the parameter values. This allows us to write an effective Ising model since Eqs.…”

“…is the internal Ising free energy associated with base pair i and its interaction with base pair i + 1 (2µ is the energy necessary to break one base-pair and 2J is the energy of a domain wall) [31,32].…”

“…This is a coupled Ising/Heisenberg model which is an extension of the mesoscopic model that we had introduced in 2007 for the description of temperatureinduced melting of dsDNA [31,32]. This model is first solved exactly in Section III A using pseudo-analytic transfer matrix calculations, following the same formalism as Rahi et al [33].…”