Abstract
This paper studies the mechanical properties of a chain of bistable elements that interact with each other, such as a molecular chain of folding and unfolding units. The authors observe that for a small number of elements the thermodynamic limit is not reached, and the behavior depends on the boundary conditions. The results are compared to experimental observations in stretching biological systems.
Highlights
The thorough understanding and the tuning of the physical properties of bistable and cooperative systems are the object of extensive research activity [1, 2]
We suppose to embed the system in a thermal bath at the temperature T, we consider the system at thermodynamic equilibrium and we study the effects of the Ising interactions on the mechanical and configurational behavior within the Gibbs or the Helmholtz ensembles
We investigated the properties of a chain of two-state units coupled through an Ising interaction scheme, providing a paradigmatic description of the effects of bistability and cooperativity in biological and artificial microand nano-systems
Summary
The thorough understanding and the tuning of the physical properties of bistable and cooperative systems are the object of extensive research activity [1, 2]. Previous attempts to integrate Ising chains in mechanical systems only concerned the dynamics of a single harmonic oscillator coupled to a linear chain of spins [72, 73] and the analysis of ripples in strings [74] To complement this picture, our analysis fully describes the (entropic and/or enthalpic) elastic response and the units transitions in small systems, within both the Helmholtz and the Gibbs ensembles of the statistical mechanics. From the historical point of view, the first model based on a discrete quantity, similar to a spin variable, has been performed to predict the response of skeletal muscles [77, 78] This method has been recently applied to different two-state systems and molecular chains as well [79,80,81,82].
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