Incollection,
The melting phase transition of homogeneous and heterogeneous DNA
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Abstract
Our work aims at studying the non-linear
dynamics and statistical properties of DNA in order to better
understand the denaturation mechanism essential for the
transcription process. It is well known that the dissociation of DNA
is associated with a phase transition which is of first order
according to the experimental data.
Recently we have proposed a non-linear DNA model which takes into
account the finitness of stacking interactions between base pairs as
well as the stiffness of phosphate-sugar backbones1,2.
We will first investigate the critical behaviour of the model in the
thermodynamical limit. According to Landau's theory, close to the
critical temperature thermodynamical quantities (specific heat,
order parameter, correlation length...) obey power laws, that is,
there are critical exponents which characterize their singular
behaviour. These exponents are related by polynomial relations, the
so-called scaling laws. Using the transfer integral (TI) method, we
computed critical exponents for two realistic DNA models, including the one proposed in 1, checked scaling laws and showed that two of them are not satisfied3. This is because some suppositions necessary to derive these scaling laws are not valid for one dimensional systems with a divergent internal
degree of freedom, as is the case for a one dimensional DNA chain.
The second part of the presentation will be devoted to finite size
effects at DNA thermal denaturation. Experiments dealing with DNA
molecules are carried out with several sequence lengths $L$.
However, it is well known that the finiteness of the system size
lets the critical singularities disappear and smears out the phase
transition. Using an extended version of the TI method, we performed
a finite size scaling analysis4. We studied the evolution of this
rounding phenomenon and the approach to the thermodynamical limit
($L\toınfty$) with respect to the sequence length. The obtained
results are in concordance with our previous conclusion3 relating
the breakdown of Josephson's identity to the divergence of the order
parameter.
Finally some results concerning the melting of DNA with sequence
disorder will be presented. By adapting the TI method to
finite-length heterogeneous DNA chains, we were able to reproduce
smooth curves (without noise) for thermodynamical quantities such as
entropy and specific heat as well as for melting profiles. Using
this data, we will show that sequence disorder may induce several
phase transitions characterized by distant critical temperatures.
1) M. Joyeux and S. Buyukdagli,
Phys. Rev. E, 72, 051902 (2005)\\
2) S. Buyukdagli, M. Sanrey, M.
Joyeux, Chem. Phys. Lett. 419, 434 (2006)\\
3) S. Buyukdagli and M. Joyeux, Phys.
Rev. E, 73, 051910 (2006)\\
4) S. Buyukdagli and M. Joyeux,
arXiv:physics/0703082v1
submitted to Phys. Rev. E
