Unfolding of globular polymers by external force

Abstract

We examine the problem of a polymer chain, folded into a globule in poor solvent, subjected to a constant tensile force. Such a situation represents a Gibbs thermodynamic ensemble and is useful for analysing force-clamp atomic force microscopy measurements, now very common in molecular biophysics. Using a basic Flory mean-field theory, we account for surface interactions of monomers with solvent. Under an increasing tensile force, a first-order phase transition occurs from a compact globule to a fully extended chain, in an "all-or-nothing" unfolding event. This contrasts with the regime of imposed extension, first studied by Halperin and Zhulina [Europhys. Lett. 15, 417 (1991)], where there is a regime of coexistence of a partial globule with an extended chain segment. We relate the transition forces in this problem to the solvent quality and degree of polymerisation, and also find analytical expressions for the energy barriers present in the problem. Using these expressions, we analyse the kinetic problem of a force-ramp experiment and show that the force at which a globule ruptures depends on the rate of loading.

Globule–stretch transition of a self-attracting chain in the repulsive active particle bath

“…The folding and unfolding processes have been well studied in the case of a polymer chain in poor solvent and subjected to a tensile force [29][30][31][32]. The phenomenon of hysteresis has also been observed, but the mechanism is due to the nucleation barrier between the globule and stretch states [29,30], different from the "sticky"-particleinduced dynamic barrier in our system. Such hysteresis is not as definite as in our system, i.e.…”

Non-exponential kinetics of unfolding under a constant force

“…where A(x) is the surface area of the deformed globule, and b is the monomer size. Following an earlier work 11 , for efficient analytical treatment we take the shape of the globule to be a spherocylinder (see Fig. 1), with a constant volume N g b 3 .…”

“…In force-clamp experiments, biomolecules typically show all-or-nothing transitions between folded and unfolded states 7,8 , meaning that denaturation occurs abruptly and completely once a critical force is reached in the case of force-ramp, or a characteristic time is reached if a constant force is applied. The transition from stable to metastable configurations with increasing applied force has been treated theoretically, and indeed found to be first order [9][10][11] .…”

“…Hence we will take a polymer chain with N = 100 residues, as a value close to the above proteins. Since the minimal force these authors were using was ∼ 90 pN, and we have earlier obtained the theoretical value for the critical unfolding force f * in this regime 11 , quite a reasonable value of the globule 'hydrophobic strength' u = 5k B T has to be chosen (assuming the characteristic size of an amino acid residue is b ∼ 0.3 nm); at this strength of globule the critical force for a homopolymer would be f * ≈ 4.48(k B T /b) = 59.7 pN, acceptably slightly below what was used in experiment.…”

Mapping a single-molecule folding process onto a topological space

“…There have been a number of numerical and analytical studies on stretching globular homopolymers under a controlled constant force or a constant unwinding velocity. [28][29][30][31][32][33] However, they all lack information on how the internal organization and structure of the polymer changes during folding to the final compact globular state. Here, we provide the first circuit topological mapping of a folding process and search for the determinants of fold topology during the folding process and of the final ''native'' structure.…”