title: Theoretical investigation of finite size effects at DNA melting.
abstract: We investigated how the finiteness of the length of a sequence affects the phase transition that takes place at the DNA melting temperature. For this purpose, we modified the transfer integral method to adapt it to the calculation of both extensive (partition function, entropy, specific heat, etc.) and nonextensive (order parameter and average separation between paired bases) thermodynamic quantities of finite sequences with open boundary conditions, and applied the modified procedure to two different dynamical models. We characterized in some detail the three effects that take place when the length of the sequence is decreased, namely, (i) the decrease of the critical temperature, (ii) the decrease of the peak values of all quantities that diverge at the thermodynamic limit but remain finite for finite sequences, like the specific heat and the correlation length, and (iii) the broadening of the temperature range over which the transition affects the dynamics of the system. We also performed a finite size scaling analysis of the two models and showed that the singular part of the free energy can indeed be expressed in terms of a homogeneous function. However, Josephson's identity is satisfied for none of the investigated models, so that the derivation of the characteristic exponents which appear, for example, in the expression of the specific heat requires some care.
authors.affiliation: Laboratoire de Spectrométrie Physique (CNRS UMR 5588), Université Joseph Fourier-Grenoble 1, Boîte Postale 87, 38402 St Martin d'Hères, France.
authors.forename: Sahin
authors.initials: S
authors.lastname: Buyukdagli
authors.forename: Marc
authors.initials: M
authors.lastname: Joyeux
mesh_terms: D001482:Base Composition; D001703:Biophysics / Q000379:methods*; D004247:DNA / Q000737:chemistry*; D019277:Entropy; D006358:Hot Temperature; D015233:Models, Statistical; D008962:Models, Theoretical; D009690:Nucleic Acid Conformation; D009691:Nucleic Acid Denaturation; D009841:Oligonucleotides / Q000737:chemistry; D044367:Phase Transition; D013696:Temperature; D013816:Thermodynamics
chemical_list: D009841:Oligonucleotides; D004247:DNA