Fig. 2: The transition from an in-plane to out-of-plane instability is set by the ratio of active motors to passive crosslinkers.

Blurriness B as a function of a ATP concentration: increasing [ATP] leads to a transition from an out-of-plane (B > 0) to an in-plane (B = 0) instability ([motor cluster] = 30 nM, [PRC1 crosslinker] = 100 nM); b PRC1 crosslinker concentration: increasing [PRC1 crosslinker] leads to a transition from an in-plane to an out-of-plane instability ([ATP] = 40 μM, [motor cluster]=60 nM). c Motor clusters concentration: increasing [motor clusters] can induce a re-entrant transition when [ATP] is low ([ATP] = 15 μM, [PRC1 crosslinker] = 100 nM). d Average microtubules’ length ([ATP]=8 μM, [motor cluster] = 15 nM, [PRC1 crosslinker] = 100 nM). In a–d, the color map indicates the mean blurriness B, and the error bars represent the standard deviation of the blurriness over at least three independent replicates. e Schematics of an active network where the ratio of active motors to passive crosslinkers or the polymers’ length are changed. Orange motor clusters are ATP-bound (aka active), while green motor clusters are passively crosslinking microtubules. f Theoretical phase diagram showing how the interplay between activity \(\zeta\) and shear modulus \(\mu\) of a thin active elastomer sheet sets the direction of the most unstable mode. The sheet spontaneously deforms in 3D along the direction of the most unstable mode. In-plane deformations spontaneously grow only for \(\zeta /\mu \, > \, 1\) (continuous line) while the out-of-plane modes are always unstable. Source data are provided in the Source data file.