Distinct regimes of elastic response and deformation modes of cross-linked cytoskeletal and semiflexible polymer networks

Abstract

Semiflexible polymers such as filamentous actin (F-actin) play a vital role in the mechanical behavior of cells, yet the basic properties of cross-linked F-actin networks remain poorly understood. To address this issue, we have performed numerical studies of the linear response of homogeneous and isotropic two-dimensional networks subject to an applied strain at zero temperature. The elastic moduli are found to vanish for network densities at a rigidity percolation threshold. For higher densities, two regimes are observed: one in which the deformation is predominately affine and the filaments stretch and compress; and a second in which bending modes dominate. We identify a dimensionless scalar quantity, being a combination of the material length scales, that specifies to which regime a given network belongs. A scaling argument is presented that approximately agrees with this crossover variable. By a direct geometric measure, we also confirm that the degree of affinity under strain correlates with the distinct elastic regimes. We discuss the implications of our findings and suggest possible directions for future investigations.

Stiffest elastic networks

“…Many different elastic systems-such as polymer gels, protein networks, cytoskeletal structures [1][2][3][4][5][6], or wood and bones [7][8][9][10][11]-can be understood as networks of interconnected beams. On a length scale much larger than the typical beam length ('macroscopic' scale), such a network can be viewed as a continuous and homogeneous medium characterized by spatially constant elastic moduli.…”

Anisotropic microsphere-based approach to damage in soft fibered tissue

“…Other models for the failure of fibrils (see e.g Buehler (2008); Tang et al (2010)) use molecular simulations to provides a more detailed insight into the failure process of collagen fibrils, which is basically due to the rupture of the cross-links between the tropocollagen molecules that compose the fibril. In the framework of cytoskeletal and polymers networks, Head et al (2003) presented a different regime of elastic response (affine and non affine) depending of the quality and density of the filament links, leading to an affine response under an unlinked scenario. This is the situation where our model is placed.…”

Shear-induced force transmission in a multicomponent, multicell model of the endothelium

“…However, they assumed that the plasma and nuclear membranes are rigid and immobile, which is unrealistic. Later, more sophisticated models that focused on understanding the rheology of the actin network were presented [45,53,55,56]. The main concern of these studies was to connect these network models to the plasma and nuclear membranes.…”

“…Moreover, several models of the cytoskeleton have been constructed to investigate the hypothesis that this interconnected filamentous structure can act as a mechano-signal transmitter [44][45][46][47][48][49][50][51][52][53][54][55][56]. Shafrir & [46] proposed a two-dimensional model of the cytoskeleton as a random network of rigid rods representing the actin laments and linear Hookean springs representing the actin cross-linkers.…”

“…The activation of signalling pathways by shear forces arises at discrete locations in ECs by force amplification and forceinduced directional biasing of signal propagation [1][2][3][4][10][11][12][16][17][18][20][21][22][23]. Numerous sites have been implicated in transducing mechanical stresses, including the plasma membrane [1,2,5,21,22,24] and its associated glycocalyx [1,5,25 -36], focal adhesions (FAs) [4,7,16,17,37 -43], the nucleus [44,45], the cytoskeleton [4,7,18,19,24,33,38,39,[44][45][46][47][48][49][50][51][52][53][54][55][56], the cortical membrane [1,2,5] and the intercellular junctions …”