Strain stiffening induced by molecular motors in active crosslinked biopolymer networks

Abstract

We have studied the elastic response of actin networks with both compliant and rigid crosslinks by modeling molecular motors as force dipoles. Our finite element simulations show that for compliant crosslinkers such as filamin A, the network can be stiffened by two orders of magnitude while stiffening achieved with incompliant linkers such as scruin is significantly smaller, typically a factor of two, in excellent agreement with recent experiments. We show that the differences arise from the fact that the motors are able to stretch the compliant crosslinks to the fullest possible extent, which in turn causes to the deformation of the filaments. With increasing applied strain, the filaments further deform leading to a stiffened elastic response. When the crosslinks are incompliant, the contractile forces due to motors do not alter the network morphology in a significant manner and hence only small stiffening is observed.The mechanical properties of plant and animal cells are governed by the cytoskeleton, a flexible and dynamic network of biopolymer fibers combined with a group of associated regulatory and crosslinking proteins 1,2 . One of the key aspects of the mechanical behaviour of these networks is their highly nonlinear elastic response to applied stresses 3 , in particular their ability to strain stiffen by orders of magnitude when subject to large stresses. Cells also employ molecular motors to convert chemical energy into mechanical work 1 . Motors generate internal stress in the networks even in the absence of external loading 1,4 . In this manner, cells can regulate their mechanical properties by using both active and passive components.While the mechanical behavior of semiflexible polymer networks with compliant and rigid crosslinks has been studied in detail both experimentally and theoretically 5-10 , the interplay between active mechanisms of stress generation through motor activity and passive strain hardening properties of crosslinks has only been considered very recently 4,7 . In this regard, reconstituted actin networks can be particularly useful, since the density of crosslinks and motors can be varied in a desired manner to gain insights into the mechanisms of strain hardening and nonlinear elastic response. Indeed, recent experiments on networks that consist of actin filaments crosslinked by filamin A (FLNa) and bipolar filaments of muscle myosin II show that in 0 * a School of Engineering, Brown University, Providence, RI 02912, USA. Email:Vivek Shenoy@brown.edu the absence of any applied loads 7 , the motors stiffen the network by about two orders of magnitude. The degree of stiffening was found to increase with increasing density of myosin motors. Another key observation from this study relates to the magnitude of stiffening caused by compliant and incompliant crosslinks. While FLNa is a large, highly flexible dimer that promotes orthogonal F-actin crosslinking, scruin is an incompliant crosslink. Interestingly, it was found that in distinct contrast to FLNa, scruin does not promote activ...

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