A Hierarchy of Instabilities in an Active Material

The cellular cytoskeleton possesses the remarkable ability to self-organize in space and time into cellular-scale structures that perform biological functions crucial for survival. These structures are composed of polar filaments and molecular motor proteins, which crosslink and exert forces on the filaments, driving the system out of equilibrium. Understanding how the collective dynamics and architecture of these structures arise from the interactions between motor proteins and filaments is an open question not fully addressed for any cytoskeletal system. Here, we consider a system of stabilized microtubules and the motor protein XCTK2, a member of the Kinesin-14 family. We show that these networks undergo a spontaneous bulk contraction on the millimeter length scale, followed by extension leading to a buckling instability with wavelength independent of motor concentration. By combining fluorescence and nonlinear optical techniques, we can measure the microtubule density, motor density, nematic order parameter, and scalar polar order in these networks as a function of space and time and make comparisons with an active fluid model. We find a hierarchy of instabilities in this system, with density buildup followed by alignment, which precedes buckling and polar ordering.