Molecular motors stiffen non-affine semiflexible polymer networks

Abstract

Reconstituted filamentous actin networks with myosin motor proteins form active gels, in which motor proteins generate forces that drive the network far from equilibrium. This motor activity can also strongly affect the network elasticity; experiments have shown a dramatic stiffening in in vitro networks with molecular motors. Here we study the effects of motor generated forces on the mechanics of simulated 2D networks of athermal stiff filaments. We show how heterogeneous internal motor stresses can lead to stiffening in networks that are governed by filament bending modes. The motors are modeled as force dipoles that cause muscle like contractions. These contractions "pull out" the floppy bending modes in the system, which induces a cross-over to a stiffer stretching dominated regime. Through this mechanism, motors can lead to a nonlinear network response, even when the constituent filaments are themselves purely linear. These results have implications for the mechanics of living cells and suggest new design principles for active biomemetic materials with tunable mechanical properties.The mechanics of living cells is largely governed by the cytoskeleton, a complex assembly of various filamentous proteins. Cross-linked networks of actin filaments form one of the major structural components of the cytoskleton. However, this cytoskeleton is driven far from equilibrium by the action of molecular motors that can generate stresses within the meshwork of filaments [1][2][3]. Such motor activity plays a key role in various cellular functions, including morphogenesis, division and locomotion. The nonequilibrium nature of motor activity has been demonstrated in simplified reconstituted filamentous actin networks with myosin motors [4][5][6][7][8]. Even in the absence of motor proteins, such in vitro networks of cytoskeletal filaments already constitute a rich class of soft matter systems that exhibit unusual material properties, including a highly nonlinear elastic response to external stress [9][10][11][12][13][14][15]. This nonlinear response can be exploited using molecular motors [4,7]; the network stiffness can be varied by orders of magnitude, depending on motor activity. A quantitative understanding of such active biological matter poses a challenge for theoretical modeling [3,[16][17][18][19][20][21].The nonlinear mechanical response of reconstituted biopolymer networks in many cases reflects the nonlinear force-extension behavior of the constituting cross-links or filaments [9-11, 14, 22]. For such networks, there is both theoretical and experimental evidence that internal stress generation by molecular motors can result in network stiffening in direct analogy to an externally applied uniform stress [4,7,[18][19][20]23]. However, the mechanical response of semiflexble polymers is highly anisotropic and is typically much softer to bending than to stretching. In some cases, this renders the network deformation highly non-affine with most of the energy stored in bending modes [24][25][26][27][28]. Such non-affinel...

The role of structure in the nonlinear mechanics of cross-linked semiflexible polymer networks

“…Future work can be aimed at elucidating the individual roles of fiber properties (e.g., d, L, l p , and E) and cross-linker properties (e.g., k cl and r 0 ), which will enable more quantitative comparison to other experimental and theoretical works. 22,24,28,51 These properties, or the distribution thereof, 21,52,53 are likely to affect the structural network response by varying the length-scale difference between the heterogeneous and the homogeneous scales.…”

Strain-driven criticality underlies nonlinear mechanics of fibrous networks

“…In fact forκ 10 −3 , the critical strain obtained in this way is practically constant. Moreover, the range of 10 −5 κ 10 −3 is the experimentally relevant range [24,33]. In particular, the central-force limit is not achievable experimentally.…”

“…Fibers are arranged on a triangular lattice (2D) or a facecentered cubic lattice (3D) of linear dimension W . In 2D, we randomly select two of the three fibers at each vertex on which we form a binary cross-link, i.e., enforcing local fourfold connectivity of the network in which the third fiber does not interact with the other two [24]. Similarly, in 3D, where there are six fibers crossing at a point, we randomly connect three separate pairs of fibers at each vertex with binary cross-links to enforce local fourfold connectivity [25].…”

“…We model lattice-based networks [24][25][26] in 2D and 3D. Fibers are arranged on a triangular lattice (2D) or a facecentered cubic lattice (3D) of linear dimension W .…”

Stability and anomalous entropic elasticity of subisostatic random-bond networks

“…Beyond this, theoretical work has shown that there are numerous ways of stabilizing a network, and therefore tuning its rigidity, below the isostatic point [15]. Examples include the addition of a bending stiffness to the model filaments [16][17][18] by applying stress [19] either internally via molecular motors [20,21] or externally by placing the network under tension by applying a bulk strain to the system [22][23][24]. It has been shown that a network's rigidity point can be shifted from the Maxwell point by adding these interactions and forces to the system.…”