The rate dependent response of a bistable chain at finite temperature

Benichou, Itamar; Zhang, Yaojun; Dudko, Olga K.; Givli, Sefi

doi:10.1016/j.jmps.2016.05.001

Cited by 35 publications

(36 citation statements)

References 87 publications

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“…As a matter of fact, the quadratic potentials and the associated spin variables are not sufficient to describe the dynamic regime since the relaxation times of the system strongly depend on the energy barriers between the potential wells, which are neglected within our approach. This is a well-known result, encoded within the Kramers rate formula, originally formulated to study chemical reactions [85], and recently generalized for arbitrary systems with nonconvex energy landscapes [86,87].…”

Section: The Systemmentioning

confidence: 93%

Isotensional and isometric force-extension response of chains with bistable units and Ising interactions

Benedito

Giordano

2018

Phys. Rev. E

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The combination of bistability and cooperativity plays a crucial role in several biological and artificial micro-and nano-systems. In particular, the exhaustive understanding of the mechanical response of such systems under the effect of thermal fluctuations is essential to elucidate a rich variety of phenomena. Here, a linear chain composed of elastic units, which are bistable (folded or unfolded) and coupled through an Ising-like interaction, is selected as a case study. We assess the macroscopic thermoelastic response of this chain in terms of its microscopic description. For small systems, far from the thermodynamic limit, this response depends on the applied isometric or isotensional boundary conditions, which correspond to the Helmholtz or Gibbs ensembles of the statistical mechanics, respectively. The theoretical analysis is conducted through the spin variables approach, based on a set of discrete quantities able to identify the folded or unfolded state of the chain units. Eventually, this technique yields closed form expressions for the force-extension curves and the average number of unfolded units, as function of the applied fields. In addition, it allows to unveil a critical behavior of such systems, characterizing the operating regions with negative differential stiffness (spinoidal phase).

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Section: The Systemmentioning

confidence: 93%

Isotensional and isometric force-extension response of chains with bistable units and Ising interactions

Benedito

Giordano

2018

Phys. Rev. E

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“…This is a wellknown result, encoded within the Kramers rate formula, originally formulated to study chemical reactions 78 and recently generalized for arbitrary systems with nonconvex energy landscapes. 79,80 Concerning the two-state freely jointed chain with extensibility, we have here generalized a recent result obtained for the same system without extensibility. 76 It is important to remark that the finite elastic constant of the units plays a crucial role in defining the force-extension response in both isotensional and isometric ensembles.…”

Section: Introductionmentioning

confidence: 59%

“…78 Finally, it is interesting to remark that the statistical mechanics and the dynamics of systems with multi-well energy are useful to model other physical situations including, but not limited to, cell adhesion, macromolecular hairpins, skeletal muscles, ferromagnetic alloys, nano-indented substrates, and plastic materials. 71,75,77,80…”

Section: Concerning the Hard Devices The Following Issues Clarify Thmentioning

confidence: 99%

Thermodynamics of small systems with conformational transitions: The case of two-state freely jointed chains with extensible units

Benedito

Giordano

2018

The Journal of Chemical Physics

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Several experimental methods are usually applied for stretching single molecules and provide valuable insights about the static and dynamic responses induced by externally applied forces. This analysis is even more important for macromolecules exhibiting conformational transitions, thereby corresponding to folding/unfolding processes. With the aim of introducing the statistical mechanics of such phenomena, we apply here the spin variables approach based on a set of discrete quantities able to identify the folded or unfolded state of the chain units. First, we obtain the macroscopic thermodynamics of the chain from its microscopic description. For small systems, far from the thermodynamic limit, this result depends on the applied boundary condition (e.g., isometric or isotensional), which corresponds to the considered statistical ensemble. Then, we develop the theory for the two-state extensible freely jointed chain, where the elastic constant of the units, a property often neglected, plays a central role in defining the force-extension curve. For this system, the partition function of the isometric ensemble can be written in closed form in terms of the natural generalization of the Hermite polynomials, obtained by considering negative indices. These results are relevant for the interpretation of stretching experiments, operated from the entropic regime up to the unfolding processes.

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“…This approach has generated a powerful class of approximated results, which are of simple application in many different regimes and configurations [67][68][69][70][71][72][73].…”

Section: Introductionmentioning

confidence: 99%

Rate-dependent force–extension models for single-molecule force spectroscopy experiments

Benedito¹,

Manca²,

Palla³

et al. 2020

Phys. Biol.

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Single-molecule force spectroscopy (SMFS) techniques allow for the measurements of several static and dynamic features of macromolecules of biological origin. In particular, the atomic force microscopy (AFM), used with a variable pulling rate, provides valuable information on the folding/unfolding dynamics of proteins. We propose here two different models able to describe the out-of-equilibrium statistical mechanics of a chain composed of bistable units. These latter represent the protein domains, which can be either folded or unfolded. Both models are based on the Langevin approach and their implementation allows for investigating the effect of the pulling rate and of the device intrinsic elasticity on the chain unfolding response. The theoretical results (both analytical and numerical) have been compared with experimental data concerning the unfolding of the titin and filamin proteins, eventually obtaining a good agreement over a large range of the pulling rates.

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The rate dependent response of a bistable chain at finite temperature

Cited by 35 publications

References 87 publications

Isotensional and isometric force-extension response of chains with bistable units and Ising interactions

Isotensional and isometric force-extension response of chains with bistable units and Ising interactions

Thermodynamics of small systems with conformational transitions: The case of two-state freely jointed chains with extensible units

Rate-dependent force–extension models for single-molecule force spectroscopy experiments

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