Path Integral Method for DNA Denaturation

TL;DR

This paper uses a path integral approach to model DNA denaturation, revealing it as a cooperative, second-order phase transition with continuous entropy growth and a peak in specific heat at the denaturation temperature.

Contribution

It introduces a novel path integral formalism to analyze DNA denaturation, capturing cooperative effects and thermodynamic properties without significant size dependence.

Findings

Denaturation behaves as a second order phase transition.

Entropy increases smoothly with temperature.

Specific heat peaks at the denaturation temperature.

Abstract

The statistical physics of homogeneous DNA is investigated by the imaginary time path integral formalism. The base pair stretchings are described by an ensemble of paths selected through a macroscopic constraint, the fulfillement of the second law of thermodynamics. The number of paths contributing to the partition function strongly increases around and above a specific temperature $T^*_c$ whereas the fraction of unbound base pairs grows continuosly around and above $T^*_c$. The latter is identified with the denaturation temperature. Thus, the separation of the two complementary strands appears as a highly cooperative phenomenon displaying a smooth crossover versus $T$. The thermodynamical properties have been computed in a large temperature range by varying the size of the path ensemble at the lower bound of the range. No significant physical dependence on the system size has been envisaged. The entropy grows continuosly versus $T$ while the specific heat displays a remarkable peak at $T^*_c$. The location of the peak versus $T$ varies with the stiffness of the anharmonic stacking interaction along the strand. The presented results suggest that denaturation in homogeneous DNA has the features of a second order phase transition. The method accounts for the cooperative behavior of a very large number of degrees of freedom while the computation time is kept within a reasonable limit.