Theoretical investigation of finite size effects at DNA melting

Abstract

We investigated how the finiteness of the length of the sequence affects the phase transition that takes place at 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 non-extensive (order parameter and correlation length) thermodynamic quantities of finite sequences with open boundary conditions, and applied the modified procedure to two different dynamical models. We showed that rounding of the transition clearly takes place when the length of the sequence is decreased. 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 an homogeneous function. However, both the correlation length and the average separation between paired bases diverge at the melting transition, so that it is no longer clear to which of these two quantities the length of the system should be compared. Moreover, 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.

References in corpus (4)

• Dynamical model based on finite stacking enthalpies for homogeneous and inhomogeneous DNA thermal denaturation
• Bubbles and denaturation in DNA
• Towards more realistic dynamical models for DNA secondary structure
• On scaling laws at the phase transition of systems with divergent order parameter and/or internal length : the example of DNA denaturation

Cited by in corpus (11)

• Physics of base-pairing dynamics in DNA
• Path Integral Method for DNA Denaturation
• Stacking Interactions in Denaturation of DNA Fragments
• Statistical physics of the melting of inhomogeneous DNA
• Twist versus Nonlinear Stacking in Short DNA Molecules
• Dynamical versus statistical mesoscopic models for DNA denaturation
• Thermal and mechanical denaturation properties of a DNA model with three sites per nucleotide
• Coupling between denaturation and chain conformations in DNA: stretching, bending, torsion and finite size effects
• Base pair fluctuations in helical models for nucleic acids
• First-passage probability: a test for DNA Hamiltonian parameters
• On the Pseudo-Schrödinger Equation approximation of the Transfer-Integral operator for 1-dimensional DNA models