An energetic model for macromolecules unfolding in stretching experiments

Abstract

We propose a simple approach, based on the minimization of the total (entropic plus unfolding) energy of a two-state system, to describe the unfolding of multidomain macromolecules (proteins, silks, polysaccharides, nanopolymers). The model is fully analytical and enlightens the role of the different energetic components regulating the unfolding evolution. As an explicit example, we compare the analytical results with a titin atomic force microscopy stretch-induced unfolding experiment showing the ability of the model to quantitatively reproduce the experimental behaviour. In the thermodynamic limit, the sawtooth force-elongation unfolding curve degenerates to a constant force unfolding plateau.

Micromechanical model for protein materials: From macromolecules to macroscopic fibers

“…[32,45] and [14], the unfolding energy Q = 550 k B T agrees with the values estimated in Ref. [11]; the number of fibers per unit area N fib = 4.75 × 10 18 (per square meters) reflects the results in Refs. [42,46].…”

“…[11] (this choice allows for analytic computations and keeps the same asymptotic behavior as l → l c of the WLC model):…”

“…The sawtooth shape is due to unfolding of an increasing number of domains with (c) reporting the corresponding total energy minimization approach (see Ref. [11]). (d) Continuum limit approximation with constant unfolding force plateaux.…”

“…Since typically no partial unfolding occurs (either all or none of the domains unfold) following a Griffith-type total energy minimization approach [11], as in Refs. [26] and [35], we model a protein macromolecule as a lattice of n two-states (rigid-folded and entropic-unfolded) domains.…”

“…Specifically, as in Refs. [10] and [11], we consider for the single molecule under assigned elongation a phenomenological Griffith-type approach assuming that the macromolecule unfolds when the energy gain (evaluated as difference of the two force-elongation curves between which the macromolecule jumps) equals a material parameter, representing the energy "dissipated" in the mechanical unfolding of the crystal. The corresponding contour length (hidden length) variations of the macromolecules, which can be also evaluated by the macromolecular stretching experiment, allows to accommodate large stretches (20-40%) with a contemporary high dissipation and toughness.…”