Ultrafast reversible self-assembly of living tangled matter

Abstract

Tangled active filaments are ubiquitous in nature, from chromosomal DNA and cilia carpets to root networks and worm collectives. How activity and elasticity facilitate collective topological transformations in living tangled matter is not well understood. We studied California blackworms ( Lumbriculus variegatus ), which slowly form tangles in minutes but can untangle in milliseconds. Combining ultrasound imaging, theoretical analysis, and simulations, we developed and validated a mechanistic model that explains how the kinematics of individual active filaments determines their emergent collective topological dynamics. The model reveals that resonantly alternating helical waves enable both tangle formation and ultrafast untangling. By identifying generic dynamical principles of topological self-transformations, our results can provide guidance for designing classes of topologically tunable active materials.

Worm blobs as entangled living polymers: from topological active matter to flexible soft robot collectives

“…The chirality number, therefore provides a mechanism for controlling the emergent topology of a worm collective. 15 Multi-filament 3D numerical simulations of elastic filaments confirm that the chirality of worm trajectories determines the emergent topological state formed (Fig. 6(d)).…”

“…1a and d). Topological complexity can be captured using the linking number, Lk O , which can be defined for open curves 14,15 γ 1 ( s ) and γ 2 ( σ ), by integrating the function Γ ( s , σ ) = ( γ 1 ( s ) − γ 2 ( σ ))/| γ 1 ( s ) − γ 2 ( σ )|Although not strictly a topological quantity, 14,16,17 the open linking number has emerged as a tool for quantifying such entangled interactions, separating simple interlocking (Fig. 1(a) and (b)) from more intricate intertwining (Fig.…”

“…1a and d). Topological complexity can be captured using the linking number, Lk O , which can be defined for open curves 14,15 g 1 (s) and g 2 (s), by integrating the function G(s,s) = (g 1 (s) À g 2 (s))/|g 1 (s) À g 2 (s)|…”

“…Fig.6Topological structure and topological dynamics of worm blobs15 (a) ultrasound reconstruction of a living worm blob enables key topological interactions to be identified. Scale bar 5 mm.…”

Entanglement in living systems

“…These branched treelike organisms often wind around themselves or others, thus becoming visually tangled (Figure 1). This physical phenomenon, called "entanglement", is well-studied in non-living materials [1][2][3][4][5][6][7][8][9][10], and has recently become a topic of interest in active systems [11][12][13]. Entanglement provides these systems unique and potentially useful material properties.…”