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

Abstract

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.

Thermal control of nucleation and propagation transition stresses in discrete lattices with non-local interactions and non-convex energy

“…[48], involves important novelties compared to the case with identical constants. Indeed, when the folded and unfolded elastic constants are equal (α = 1), the conformational transitions correspond to a temperature independent average plateau force [54,[67][68][69][70][71][72]. This result can be simply explained in the framework of the Bell relation f = ∆E/∆x, discovered in the context of cell adhesion [62,78,79].…”

“…The first theoretical ideas introducing this technique can be found in the early models of the bio-mechanical response of skeletal muscles [19,20]. This technique has been further generalized to study different multistable systems [22-25, 54, 65, 66], and macromolecular chains [67][68][69][70][71][72]. This approach is based on the introduction of a series of discrete variables (the so-called spin variables), which are able to identify the state of the units.…”

“…Moreover, from a theoretical point of view, the comparison of the force-extension response within different ensembles is an important point useful to understand the concept of ensembles equivalence in the thermodynamic limit, as discussed below. The spin variable method has been successfully used to study the nanomechanics of macromolecules [67][68][69][70][71][72], the denaturation of macromolecules [73,74], the non-local or cooperative effects [54,64], skeletal muscles [22][23][24][25], and systems with transitions between unbroken and broken states [65,66,[75][76][77].…”

Temperature controlled decohesion regimes of an elastic chain adhering to a fixed substrate by softening and breakable bonds

“…The introduction of the spin variables frequently simplifies the calculation of the partition function and the analysis of the corresponding averaged thermodynamic quantities. This technique has been largely exploited to investigate bistable systems with transitions between ground and metastable states, with important applications to nanomechanics [82][83][84][85][86][87][88][89]. Similarly, this approach has been considered for breakable materials with the spin variable distinguishing broken and unbroken units to study debonding processes in biological materials [27][28][29]80].…”

Role of temperature in the decohesion of an elastic chain tethered to a substrate by onsite breakable links

“…The first models based on this technique have been developed for describing the response of skeletal muscles [27,28]. More recently, this approach has been generalized to study different allosteric systems [30][31][32][33] and macromolecular chains [71][72][73][74][75][76]. The main idea consists in introducing a series of discrete (spin) variables to identify the state of the system units.…”