Extension of Rod-Coil Multiblock Copolymers and the Effect of the Helix-Coil Transition

Abstract

The extension elasticity of rod-coil mutliblock copolymers is analyzed for two experimentally accessible situations. In the quenched case, when the architecture is fixed by the synthesis, the force law is distinguished by a sharp change in the slope. In the annealed case, where interconversion between rod and coil states is possible, the resulting force law is sigmoid with a pronounced plateau. This last case is realized, for example, when homopolypeptides capable of undergoing a helix-coil transition are extended from a coil state. Both scenarios are relevant to the analysis and design of experiments involving single molecule mechanical measurements of biopolymers and synthetic macromolecules.PACS numbers: 61.25. Hq, 61.41.+e, 87.15.He With the advent of single molecule mechanical measurements it became possible to study the force laws characterizing the extension of individual macromolecules [1]. In turn, these provide a probe of internal degrees of freedom associated with intrachain self assembly or with monomers that can assume different conformational states. A molecular interpretation of the force laws thus obtained requires appropriate theoretical models allowing for the distinctive "internal states" of each system. The formulation of such models is a challenging task in view of the complexity and diversity of the systems investigated. These include DNA [2], the muscle protein titin [3] and the extracellular matrix protein tenascin [4], the polyscharides dextran [5] and xanthan [6] as well as the synthetic polymer poly(ethelene-glycol) [7].In this letter we consider two unexplored yet accessible systems where a detailed confrontation between theory and experiment is possible. In particular, we present a theory for the extension force law of multiblock copolymers consisting of alternating rod and coil blocks. Two scenarios are considered, both focusing on the equilibrium force law of long chains undergoing quasistatic extension. In one, the architecture is "quenched" that is, the block structure is set by the chemistry and no interconversion is possible. Such is the case, for example, for segmented polyurethans [8]. In the second scenario the monomers can interconvert between coil and rod states. The "annealed" architecture is realized, for instance, in homopolypeptides capable of undergoing a cooperative helix-coil transition [9][10][11]. In this system, the highly rigid helical domains play the part of the rod blocks. As we shall see, the two scenarios lead to distinctive force laws (Figure). The force law of the quenched case is characterized by an abrupt change of slope. This arises because the rod blocks are more susceptible to orientation by the applied tension. In the annealed scenario, the extension of a chain that is initially in a coil state leads to a sigmoid force profile exhibiting a pronounced plateau. The plateau is traceable to a one dimensional coexistence of helical and coil domains where the chain extension favors the helical state because of its low configurational entropy. These res...

Competition for hydrogen-bond formation in the helix-coil transition and protein folding

“…They have explicitly added extension force into the Zimm and Bragg description. In one of their papers a step-like behavior of helicity degree versus normalised force has been reported [60], without any model for solvent. A thorough study of Tamashiro and Pincus reported no step-like behavoir of helicity degree within the same model [61].…”

An energetic model for macromolecules unfolding in stretching experiments

“…In the following, we assume, as in [30], that the penalizing term J dominates this effect, so that we always consider single folded domain configurations (thus we assume n b f ¼ 1: di-block approximation). This hypothesis is supported by the MD simulations [22] showing an unfolding strategy with always one single connected internal unfolded domain inside two boundary-folded domains.…”

“…Here, Q is the unfolding energy for a single domain and J is a penalizing 'interfacial' energy term (measuring the loss of internal energy owing to the unbind terminal hydrogen bonds of each contiguous folded domain [30]). …”

“…In the field of protein mechanics, on the basis of the approach proposed in [30], an important step in the comprehension of the energy competition between the unfolding and entropic energy terms, has been delivered in [32]. In this paper, the author models the unfolding of a biomacromolecule as a chain composed of folded and unfolded domains, both elastic with Gaussian type response, combined with an Ising-type unfolding energy.…”

“…Based on previous considerations and inspired by the model in [2,29], where the authors describe the hysteresis of filled polymers and spider silks, here we propose an energetic approach and describe the unfolding macromolecule as a two-state material. Similarly, a two-state energetic approach was proposed in [30] to describe the helix ! coil transition of polypeptide chains regulating the damage of multi-block copolymers.…”