Theory of Mechanical Unfolding of Homopolymer Globule: All-or-None Transition in Force-Clamp Mode vs Phase Coexistence in Position-Clamp Mode

Abstract

Equilibrium mechanical unfolding of a globule formed by long flexible homopolymer chain collapsed in a poor solvent and subjected to an extensional force f (force-clamp mode) or extensional deformation D (position-clamp mode) is studied theoretically. Our analysis, like all previous analysis of this problem, shows that the globule behaves essentially differently in two modes of extension. In the force-clamp mode, mechanical unfolding of the globule with increasing applied force occurs without intramolecular microphase segregation, and at certain threshold value of the pulling force the globule unfolds as a whole ("all-or-none" transition). The value of the threshold force and the corresponding jump in the distance between the chain ends increase with a deterioration of the solvent quality and / or with an increase in the degree of polymerization. In the position-clamp mode, the globule unfolding occurs via intramolecular microphase coexistence of globular and extended microphases followed by an abrupt unraveling transition. Reaction force in the microphase segregation regime demonstrates an "anomalous" decrease with increasing extension. Comparison of deformation curves in force and position-clamp modes demonstrates that at weak and strong extensions the curves for two modes coincide, differences are observed in the intermediate extension range. Another unfolding scenario is typical for short globules: in both modes of extension they unfold continuously, without jumps or intramolecular microphase coexistence, by passing a sequence of uniformly elongated configurations. The values of the the critical chain length, Ncr, separating long and short chain behavior are slightly different for two extension modes: N cr,f < Ncr,D.

Unfolding of globular polymers by external force

“…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.…”

“…(24) and (25), we can recover the condition for the thermodynamic transition, f * , found in eqn. (15), which is a reassuring check, since when the energy barriers from the globule state and from the chain state are equal, the two states themselves are equal in energy. This is illustrated in Fig.…”

“…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 .…”

“…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.…”

Force‐induced globule–coil transition in laminin binding protein and its role for viral–cell membrane fusion

“…Analysis of the literature data suggests proposing that we have a case of force-induced globule-coil transition of these species. Such a phenomenon has been first indicated by Halperin and Zhulina (1991) and then has been a subject of a number of theoretical or numerical (e.g., Kreitmeier et al, 1999;Cooke and Williams, 2003;Polotsky et al, 2011) and experimental publications (Haupt et al, 2002;Gunari et al, 2007). The physical essence of this phenomenon is that under weak extension (under the action of relatively small force), some globules in conditions of poor solvability can deform first into an elliptical (and may be also cylindrical) shape structure and then, at a certain critical extension, undergo a sharp transition into a "ball-string" configuration (whence globule-coil transition).…”