Modeling Shape and Rupture of Filament Networks

The actin cytoskeleton is a biopolymer network that provides spatial coordination and mechanical strength to biological cells. Due to the asymmetric mechanical response of polymers under tension versus compression, it behaves like a mechanical network of cables. In addition, it actively contracts through the continuous action of myosin molecular motors. Here we investigate theoretical models on the cellular scale which incorporate these special properties. In the first part of this work we model cells adherent to discrete adhesion sites on planar surfaces. We compare the shape and force distribution in contracted networks of Hookean springs and cables. We find that only active cable networks can correctly predict the experimentally observed cell shape. In the second part we apply the active cable network to experimental data. We combine this model with contractile actin bundles and find that this combination leads to surprisingly good predictions for the traction force pattern of adherent cells on soft elastic substrates. Because cellular forces can lead to failure of the network, in the third part we investigate bond rupture in mechanical networks. Here, bonds stochastically rupture with rates that grow exponentially with force. We study the statistical properties of networks under constant strain and strain which linearly increases in time. The results are compared to traditional fracture mechanics which are dominated by stability thresholds

Sarcomeric Pattern Formation by Actin Cluster Coalescence

Contractile function of striated muscle cells depends crucially on the almost crystalline order of actin and myosin filaments in myofibrils, but the physical mechanisms that lead to myofibril assembly remains ill-defined. Passive diffusive sorting of actin filaments into sarcomeric order is kinetically impossible, suggesting a pivotal role of active processes in sarcomeric pattern formation. Using a one-dimensional computational model of an initially unstriated actin bundle, we show that actin filament treadmilling in the presence of processive plus-end crosslinking provides a simple and robust mechanism for the polarity sorting of actin filaments as well as for the correct localization of myosin filaments. We propose that the coalescence of crosslinked actin clusters could be key for sarcomeric pattern formation. In our simulations, sarcomere spacing is set by filament length prompting tight length control already at early stages of pattern formation. The proposed mechanism could be generic and apply both to premyofibrils and nascent myofibrils in developing muscle cells as well as possibly to striated stress-fibers in non-muscle cells

Filament turnover stabilizes contractile cytoskeletal structures

Vital cellular processes depend on contractile stresses generated by the actin cytoskeleton. Commonly, the turnover of actin filaments in the corresponding structures is large. We introduce a mesoscopic theoretical description of motor-filament systems that accounts for filament nucleation, growth, and disassembly. To analyze the dynamic equations, we introduce an expansion of the filament densities in terms of generalized Laguerre polynomials. We find that filament turnover significantly stabilizes contractile structures against rupture. Finally, we relate the mesoscopic description to a phenomenological theory of cytoskeletal dynamics