Thermal denaturation of fluctuating finite DNA chains: The role of bending rigidity in bubble nucleation

Abstract

Statistical DNA models available in the literature are often effective models where the base-pair state only (unbroken or broken) is considered. Because of a decrease by a factor of 30 of the effective bending rigidity of a sequence of broken bonds, or bubble, compared to the double stranded state, the inclusion of the molecular conformational degrees of freedom in a more general mesoscopic model is needed. In this paper we do so by presenting a 1D Ising model, which describes the internal base pair states, coupled to a discrete worm like chain model describing the chain configurations [J. Palmeri, M. Manghi, and N. Destainville, Phys. Rev. Lett. 99, 088103 (2007)]. This coupled model is exactly solved using a transfer matrix technique that presents an analogy with the path integral treatment of a quantum two-state diatomic molecule. When the chain fluctuations are integrated out, the denaturation transition temperature and width emerge naturally as an explicit function of the model parameters of a well defined Hamiltonian, revealing that the transition is driven by the difference in bending (entropy dominated) free energy between bubble and double-stranded segments. The calculated melting curve (fraction of open base pairs) is in good agreement with the experimental melting profile of polydA-polydT and, by inserting the experimentally known bending rigidities, leads to physically reasonable values for the bare Ising model parameters. Among the thermodynamical quantities explicitly calculated within this model are the internal, structural, and mechanical features of the DNA molecule, such as bubble correlation length and two distinct chain persistence lengths. The predicted variation of the mean-square-radius as a function of temperature leads to a coherent novel explanation for the experimentally observed thermal viscosity transition. Finally, the influence of the DNA strand length is studied in detail, underlining the importance of finite size effects, even for DNA made of several thousand base pairs. Simple limiting formulae, useful for analyzing experiments, are given for the fraction of broken base pairs, Ising and chain correlation functions, effective persistence lengths, and chain mean-square-radius, all as a function of temperature and DNA length.

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

“…term is the spherical Bessel function usually denoted by i (κ) and that we also used the notation e −κ i (κ) = e −G (κ) in Ref. [32]. If f = 0,P is block-diagonal in each ( , m) subspace with matrix elements (we switch to lighter notations):…”

“…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].…”

“…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].…”

“…The partition function is Z = (4π) N ±, (2 + 1)λ N ,± in case of periodic boundary conditions and by Z = (4π) N ,± V |0, ± 2 λ N ,± in case of free ends (where |V is the adequate free-end vector) [32]. Of course, boundary conditions are irrelevant at large N [45], and we have checked that finite size effects are negligible for the DNAs studied in the experiments considered in the following.…”

“…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].…”