Accueil du site > Publications > Publications 2008 > Thermal denaturation of fluctuating finite DNA chains : the role of bending rigidity in bubble nucleation

John Palmeri, Manoel Manghi, Nicolas Destainville

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, - 19 septembre 2007

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.