Force Propagation in Active Cytoskeletal Networks
Conventional materials science establishes clear structure-function relationships: grain boundaries modulate strength by blocking dislocations, and defect density limits conductivity through electron scattering. Active matter presents a fundamentally different challenge, components continuously consume energy to generate forces, creating a dual identity as both structural elements and force-generating machines. This material-machine duality raises a fundamental question: which structural parameters govern functional behavior in systems where constituents actively generate forces rather than merely responding to external inputs? Here we demonstrate that percolation is the critical mechanism that transforms active cytoskeletal networks from energy-dissipating materials into work-performing machines. Using light-controlled microtubule-kinesin networks, we show that increasing bundle length from 0.9 {micro}m to 5 {micro}m triggers a percolation transition that enables global force organization. Networks below the threshold remain incapable of performing coordinated work, while networks above it develop correlation lengths exceeding 240 {micro}m, generate 25-fold stronger forces, and extract 1000-fold more mechanical work, powering transport of live cells across 800 {micro}m distances. Network simulations reveal that introducing just 5-10% longer bundles creates a connected component containing 90% of microtubules, establishing the precise threshold that drives this material-to-machine transition. Our findings establish percolation as the fundamental mechanism governing whether active matter systems function as passive materials or as coordinated machines--providing design principles for both synthetic and biological systems. increasing bundle length from 0.9 {micro}m to 5 {micro}m increasing bundle length from 0.9 {micro}m to 5 {micro}m