Fig. 6.
Artificial and biological programs for controlling filament behaviors. (A) Demonstration of filament homing using (i) amplitude or (ii) frequency-modulated signals. Overlay of filament center lines at the start (green) and end (red) of 50 cycles of activity starting from 100 random filament shapes. Time evolution of the filament base-tip angle for (iii) amplitude and (iv) frequency modulation. (B) Programming local and global sampling of the filament tip using alternating periods of low- and high-frequency activity. (i) Filament shapes during low- and high-frequency states shown in red and blue, respectively, with the tip trajectory (dashed line). (ii) Plotting the tip speed reveals that the filament dwells in a local region during high-frequency states and rapidly moves across space during the low-frequency state. (iii) Zoomed in view of a local sampling trajectory. (C) Biological activity “programs” extracted from experimental data of L. olor as a time sequence of extension and compression phases (Top, sample time trace). (i) Representative images of L. olor during compression and extension phases. (ii) Distributions of extension and compression phases for N = 7 cells and 200 activity cycle events. The line shows a log-normal fit of the underlying data. (iii) Simulation search clouds of filaments with a Lacrymaria-like activity distribution and log-normal activity profile. (iv) Experimental search clouds for L. olor from ref. 7. (v and vi) Search dynamics of the filament tip for simulations and experiments. In (v), symbols are simulations, and lines are theoretical fits to Eq. 4. In (v) and (vi) cycle counts are estimated by rescaling time by the mean cycle duration <τa> in simulations and experiments, respectively.