Mechanical Unfolding of a Homopolymer Globule: Applied Force versus Applied Deformation

Abstract

Summary:We propose the quantitative mean-field theory of mechanical unfolding of a globule formed by long flexible homopolymer chain collapsed in poor solvent and subjected to an extensional force We show that with an increase in the applied force the globule unfolds as a whole without formation of an intermediate state. The value of the threshold force and the corresponding jump in the distance between chain ends increase with a deterioration of the solvent quality and / or with an increase in the degree of polymerization. This way of globule unfolding is compared with that in the D-ensemble, when the distance between chain ends is imposed.

Unfolding of globular polymers by external force

“…imposing a fixed extension in the Helmholtz thermodynamic ensemble), the collapsed polymer globule undergoes a transition to an extended chain through a gradual release of chain from the globule. In contrast, in the constant-force Gibbs ensemble the forceclamp transition is not gradual, but instead has 'all-ornothing' nature (as has been seen in lattice simulations in 27 , in 15,16 , and elsewhere). The globule undergoes a discontinuous jump in extension at a threshold force, and we show that it depends on the kinetics of the experiment.…”

“…There is an important difference with the earlier work of Polotsky et al 15,16 , who have only considered weak globules and small forces (to Taylor-expand their expressions) and effectively remained in the quadratic region G eq ∼ −f 2 in Fig. 6.…”

“…This is in contrast to a fully expanded polymer coil where monomers are well separated from each other and are all equally surrounded by solvent, where we take the enthalpic part of the free energy to be zero in spite of the unfavourable contact between the polymer and the solvent, simply because there are no effective pair interactions between monomers left. The same argument could be phrased via the Flory model of coil-globule collapse, which would express the value of monomer enthalpy u via the Flory χ-parameter, as is done in 15,16 .…”

“…(17) and 22, we see that u 2 ≥ u * , and so it is clear from eqs. (16) and (21) that f 2 ≥ f * , with equality holding only at N → ∞. More generally, and noting that N g = N − N c , we can find an expression for the number of monomers in the globule at the free energy maximum, N * g , by solving the effective quadratic eqn.…”

“…Later, simple models were able to account for internal properties of the globule: either the bending rigidity or specific bonding between its units (replicating the protein morphology) 14 . There has been previous theoretical work on the force-clamp mode for poor solvents 15,16 . Polotsky et al used self-consistent field modelling and verified an 'allor-nothing' transition in this regime.…”