Figure 6. Comparison of the self-organization and buckling mechanisms (relevant for actin).

(a) At length scales of the order of the distance between consecutive motors and crosslinks (i.e., much smaller than those considered in the main text), filament buckling can generate an additional source of bundle contraction (Lenz et al., 2012a) (b). Specifically, the random juxtaposition of motors and crosslinks within a bundle create regions of alternating compressive and extensile stresses along individual filaments, which can result in filament buckling if the compressive forces exceed the buckling threshold of a filament section. Following buckling, the bent part of the filament becomes essentially irrelevant elastically and the tensile force $F_s$ exerted by the motor on the non-buckled filament sets the tension of the bundle. (b) Tension per filament induced by the self-organization mechanism and (c) the buckling mechanism. Note that $𝒯$ can take both positive and negative values, denoting contraction and extension respectively, while ${𝒯}_{\text{buckling}}$ is always positive. We set ${𝒯}_{\text{buckling}}$ to zero outside of the interval ${\mathrm{\ell }}_0^{-}<{\mathrm{\ell }}_0<{\mathrm{\ell }}_0^{+}$ where buckling is allowed. (d) Bounds of the interval where buckling is allowed (purple line) and the parameter regimes where $|𝒯|>{𝒯}_{\text{buckling}}$ (light blue region).