Mechanical response of cross-linked actin networks

Sammanfattning: The ability to predict the mechanical properties of cells should be seen in the light of the close connection between abnormal cell states and a change in the cell response to stimuli. For example, it has been found that the stiffness of cancer cells is much lower than their healthy counterparts, influencing metastasis and cell migration. On the contrary, malaria cells have been found to exhibit a significant increase in stiffness.The major structural entity of the cell is called the cytoskeleton, an interior network consisting of three types of protein filaments - actin filaments, intermediate filaments and microtubules. The remodelling ability of the cytoskeleton through polymerisation provides the cell with the ability to adapt its response to external forces accordingly. The properties of interfilament cross-links in terms of stiffness and ability to detach can be expected to influence the mechanical response. The work presented herein focuses on the mechanical response of cross-linked actin networks. The results indicate a strong dependence of the mechanical properties on cross-link dynamics and characteristics.In Paper A, a constitutive model for the response of transiently cross-linked networks is developed using a continuum framework. The deformation is split into viscous (representing sliding of filaments) and elastic deformation. A strain energy function is proposed in the form of a neo-Hookean model, modified in terms of chemically activated cross-links. The disassociation rate constant is modified in terms of an exponential function taking into account the amount of strain energy available to break bonds. The constitutive model was compared with experimental relaxation tests and it was found that the initial region of fast stress relaxation can be attributed to breaking of bonds, and the subsequent slow relaxation to sliding of filaments.In Paper B, a finite element framework was used to assess the influence of numerous geometrical and material parameters on the response of cross-linked actin networks. It was shown that considering the presence of a statistical dispersion in filament lengths has a significant effect on the mechanical properties of the network. Further, the compliance of the crosslinks was shown to influence the stress-strain curve and shift the region of strain hardening. The influence of boundary conditions and the effect of network parameters on experiments in terms of local and global effects were also addressed. Finally, a micromechanically motivated constitutive model in a continuum framework was presented, capturing some essential characteristic features of cross-linked actin networks.