Unfolding of a polymer globule: sequence of intra-molecular conformational transitions

Alexey Polotsky, Sérvice de Physique de l'Etat Condensé CEA/Saclay, France

A particular interest to globular state of individual macromolecules and to collapse-to-swelling or unfolding conformational transitions in individual polymer chain is motivated by existing physical analogy between globules of synthetic polymers stabilized by attractive interactions between the monomer units in poor solvent and compact structures biopolymers, e.g., globular proteins. Experiments on single molecules subjected to extensional force (or to extensional deformation) have become possible recently due to development of such techniques as AFM single molecule force spectroscopy or optical tweezers. The single molecule AFM force spectroscopy, enables one to obtain equilibrium or out-of-equilibrium force-deformation curves. An ultimate goal of the theory is to establish relation between the shape of the force-deformation spectra, 3D spatial organization and primary chemical sequence of (bio)polymers. It has been shown in experiments on unfolding of proteins that the force versus deformation curves may exhibit quite complex patterns and are essentially non-monotonic, thus suggesting possibility of intra-molecular microphase separation and coexistence upon unfolding.

We propose a quantitative mean-field theory of unfolding of a globule formed by long flexible homopolymer chain collapsed in poor solvent and subjected to extensional deformation. In contrast to predictions of classical scaling theory (A.Halperin and E.Zhulina, Europhys. Lett.1991, v.15, p. 417), our results indicate occurrence of two jump-wise conformational transitions to occur in course of the globule deformation: the first one is from weakly elongated (ellipsoidal) globule to the microphase separated tadpole structure and the second one is from the tadpole to the uniformly extended chain conformation. We anticipate that both transitions should manifest in the experimental force-deformation curves in the experimentally relevant range of the molecular weight. The theoretical force-deformation curves are obtained as a function of the solvent strength. The conformational transitions are analyzed in detail, the dependences of critical extension, conformational characteristics, and restoring force in the transition points as functions of the solvent strength and degree of polymerization are obtained analytically for long chains.