Buckling transition for filamentous bundles under constant strain

The structure and dynamics of the cytoskeleton dictate the stability and motility of the cell, but a full understanding of how the global behavior of the network is influenced by the detailed microscopic interactions remains lacking. In particular, the ability of the cytoskeletal network to support a compressive load, necessary for both growth and response to external stimulation, depends strongly on the statistics of the individual filaments and the crosslinks between them. Using a mean field approach, I identify a critical strain at which buckling will occur for a single filament. Strongly bent configurations are predicted to be stable for compressions beyond this critical strain. The mean compressive force required to attain these strains is also computed, with the filament unable to support greater applied forces. I further show that a pair of filaments crosslinked by passive linkers (modeled as permanent harmonic interactions) can be treated on the mean field level as well, and determine the buckling transition for these bundles in two dimensions. These predictions give greater quantitative insight into how the topology of the passive crosslinking between filaments can affect the strength of the system.