Spin-oscillator model for DNA/RNA unzipping by mechanical force

Abstract

We model unzipping of DNA/RNA molecules subject to an external force by a spin-oscillator system. The system comprises a macroscopic degree of freedom, represented by a one-dimensional oscillator, and internal degrees of freedom, represented by Glauber spins with nearest-neighbor interaction and a coupling constant proportional to the oscillator position. At a critical value $F_c$ of an applied external force $F$, the oscillator rest position (order parameter) changes abruptly and the system undergoes a first-order phase transition. When the external force is cycled at different rates, the extension given by the oscillator position exhibits a hysteresis cycle at high loading rates whereas it moves reversibly over the equilibrium force-extension curve at very low loading rates. Under constant force, the logarithm of the residence time at the stable and metastable oscillator rest position is proportional to $(F-F_c)$ as in an Arrhenius law.

arXiv comment9 pages, 6 figures, submitted to PRE

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• Bifurcation analysis and phase diagram of a spin-string model with buckled states
• Derivation of a Langevin equation in a system with multiple scales: the case of negative temperatures
• Buckling in a rotationally invariant spin-elastic model