Mechanics of collective unfolding

Abstract

Mechanically induced unfolding of passive crosslinkers is a fundamental biological phenomenon encountered across the scales from individual macro-molecules to cytoskeletal actin networks. In this paper we study a conceptual model of athermal load-induced unfolding and use a minimalistic setting allowing one to emphasize the role of long-range interactions while maintaining full analytical transparency. Our model can be viewed as a description of a parallel bundle of N bistable units confined between two shared rigid backbones that are loaded through a series spring. We show that the ground states in this model correspond to synchronized, single phase configurations where all individual units are either folded or unfolded. We then study the fine structure of the wiggly energy landscape along the reaction coordinate linking the two coherent states and describing the optimal mechanism of cooperative unfolding. Quite remarkably, our study shows the fundamental difference in the size and structure of the folding-unfolding energy barriers in the hard (fixed displacements) and soft (fixed forces) loading devices which persists in the continuum limit. We argue that both, the synchronization and the non-equivalence of the mechanical responses in hard and soft devices, have their origin in the dominance of long-range interactions. We then apply our minimal model to skeletal muscles where the power-stroke in acto-myosin crossbridges can be interpreted as passive folding. A quantitative analysis of the muscle model shows that the relative rigidity of myosin backbone provides the long-range interaction mechanism allowing the system to effectively synchronize the power-stroke in individual crossbridges even in the presence of thermal fluctuations. In view of the prototypical nature of the proposed model, our general conclusions pertain to a variety of other biological systems where elastic interactions are mediated by effective backbones

Rigidity generation by nonthermal fluctuations

“…The proposed mechanism of rigidity generation requires a finite distance from equilibrium and is therefore different from the more conventional entropic stabilization [18]. The possibility of actively tunable rigidity opens interesting prospects not only in biomechanics [19] but also in engineering design incorporating negative stiffness [20] or aiming at synthetic materials stabilized dynamically [21,22].We illustrate our idea on a simple bi-stable mechanical system described by a single collective variable: the negative stiffness is viewed as a result of coarse-graining in a microscopic system with domineering long range interactions [23]. We assume that this 'snap-spring' is exposed to both thermal and correlated noises and acts against a linear spring which qualifies it as a molecular motor operating in stall conditions [24].…”

“…We illustrate our idea on a simple bi-stable mechanical system described by a single collective variable: the negative stiffness is viewed as a result of coarse-graining in a microscopic system with domineering long range interactions [23]. We assume that this 'snap-spring' is exposed to both thermal and correlated noises and acts against a linear spring which qualifies it as a molecular motor operating in stall conditions [24].…”

Illuminating Origins of Impact Energy Dissipation in Mechanical Metamaterials

“…Yet, the presence of buckling members induces non-affine response at the microscale, so that clear understanding of the exact energy dissipation mechanisms remains clouded. [18][19][20][21] Yet, a common vision for elastomeric mechanical metamaterials is to mitigate impact, in which case high strain rates are induced. By illuminating the dynamic distribution of strain in the metamaterial, the authors uncover a rational way to program the macroscopic deformation and enhance impact mitigation properties.…”

“…Recent attention has turned to buckling-based material system concepts, whereby elastic and/or plastic buckling structural members on a microscale level [3][4][5][6][7] are harnessed to absorb shock at the system level. [18][19][20][21] Yet, a common vision for elastomeric mechanical metamaterials is to mitigate impact, in which case high strain rates are induced. [8][9][10][11][12] Under low frequency cycling of applied strain or stress, these new generations of cellular materials [13] are shown to exhibit exceptional elastic energy dissipation properties [14][15][16] due to a "reversible plasticity" effect [17] that has an analogy to energy management in cytoskeletal actin networks.…”

“…[8][9][10][11][12] Under low frequency cycling of applied strain or stress, these new generations of cellular materials [13] are shown to exhibit exceptional elastic energy dissipation properties [14][15][16] due to a "reversible plasticity" effect [17] that has an analogy to energy management in cytoskeletal actin networks. [18][19][20][21] Yet, a common vision for elastomeric mechanical metamaterials is to mitigate impact, in which case high strain rates are induced. In this light, experimental evidence suggests these metamaterials are effective to dissipate sudden accelerations [9] and shocks, [11] although the exact energy mitigation mechanisms are unknown.…”