Agent-based simulations and theory (Banerjee, Freedman, Murrell and Banerjee, Cytoskeleton 81:409-419, 2024) showed that actin-like filaments growing rapidly from a shared, limiting monomer pool in a crowded environment collectively bend and become kinetically trapped in long-lived, high-curvature configurations organized around nematic topological defects, suggesting a route to shape memory in cytoskeletal networks. The model deliberately assumes nucleator-seeded nucleation with no spontaneous nucleation, no molecular motors, no ATP-hydrolysis-driven turnover, and actin-like filament mechanics. The open problem is the robustness and generality of growth-induced kinetic trapping: determine how the emergent trapped morphology - the extent of collective bending, the trapping lifetime, the nematic order, and the defect organization - changes when each of these simplifications is relaxed, that is, under spontaneous nucleation and the resulting filament-length heterogeneity, under motor activity interacting with growth-generated topological defects, under treadmilling and severing, and under microtubule-, intermediate-filament-, or FtsZ-like filament mechanics. The overarching question is whether shape memory is a robust, general consequence of filament growth in crowded, resource-limited environments or an artifact of the idealized model. No published work is known to extend the model along any of these axes; adjacent lines of work on actin assembly in protein condensates, motor-driven active-gel theories, renewable-active-matter hydrodynamics, and FtsZ treadmilling leave this core open.

Background

Actin, the main structural protein of the eukaryotic cell cortex (the contractile polymer network beneath the cell membrane), assembles from globular monomers (G-actin) into polar helical filaments (F-actin). In cells, actin structures grow while competing for a shared, limiting pool of monomers, in a crowded environment imposed by neighboring filaments. Experiments on biomimetic cortices (Yadav et al., 2019, Advanced Functional Materials) showed that filament nucleation tunes mechanical memory: at an intermediate nucleation density, polymerization-induced filament bending energy accumulates roughly a hundredfold, high-curvature filaments act as templates for further assembly, and vortex-like topological defects stabilize.

To explain the physical origin of these observations, Banerjee, Freedman, Murrell and Banerjee (2024, Cytoskeleton 81:409-419) built a minimal agent-based model within the AFINES simulation framework (Freedman et al., 2017). Filaments are polar worm-like chains - elastic rods whose bending modulus κ\kappa defines a persistence length Lp=κ/kBTL_p=\kappa/k_\mathrm{B}T, the length over which thermal fluctuations decorrelate the filament direction - that grow stochastically from a shared limiting monomer pool (Gillespie algorithm), interact sterically through volume-exclusion potentials, and can be connected by crosslinkers modeled as Hookean springs. They found that rapid growth in crowded conditions produces correlated, collective bending of filaments that becomes kinetically trapped, meaning long-lived non-equilibrium configurations that cannot relax on accessible timescales, organized around half-integer nematic defects (singular points of the nematic director field - the local average filament direction - carrying topological charge ±1/2\pm 1/2, as in liquid crystals). The stability of the defects and the extent of trapping are amplified by a larger actin monomer pool and by crosslinking; structural relaxation occurs only at moderate actin densities and for long filaments, where the timescale of bending relaxation competes with growth. These findings were proposed as a route to program shape memory in actin networks, consistent with the in vitro trends of Yadav et al. (2019) for actin and of Dunajova et al. (2023, Nature Physics) for the bacterial division protein FtsZ.

The model excludes four ingredients central to real cytoskeletons, and the source paper itself lists them as its main limitations and future directions. First, spontaneous nucleation: all filaments are seeded by a fixed number of pre-set nucleators, whereas spontaneous nucleation in a limiting pool is known to produce broad, heterogeneous exponential filament-length distributions (Banerjee and Banerjee, 2022, Biophysical Journal); in cells, nucleation is regulated by nucleators such as the Arp2/3 complex (a branching nucleator) and formins (processive elongation factors). Second, molecular motors: myosin motors, which walk along actin filaments and generate contractile stresses, are absent, although topological defects in actin networks are implicated in morphogenesis and in motor-driven force generation and contractility. Third, ATP-hydrolysis-driven turnover: neither treadmilling (growth at the fast-growing barbed end with simultaneous shrinkage at the pointed end) nor ADF/cofilin-mediated severing (nucleotide-state-dependent cutting of filaments) is included; the paper conjectures that severing may act analogously to extra nucleation and that treadmilling may enhance polarity sorting and the motility of nematic defects. Fourth, filament-type specificity: all parameters are actin-like, whereas microtubules (tubulin polymers) are far more rigid, intermediate filaments are more flexible and apolar, and FtsZ filaments are short and treadmill during bacterial division-ring formation. Whether growth-induced kinetic trapping and shape memory survive these relaxations - separately and jointly - is the open problem.

Problem Statement

Within the growth-induced kinetic-trapping framework established by Banerjee et al. (2024) - filaments modeled as polar worm-like chains that grow by polymerization from a shared limiting monomer pool, interact through steric volume exclusion, and may be crosslinked - determine whether the emergent trapped morphology (extent of correlated collective bending, kinetic-trapping lifetime, nematic order, and the number, charge, and stability of topological defects) is robust to the four simplifications of the minimal model, addressing each axis and their interplay:

  1. Nucleation and length heterogeneity: allow spontaneous (or otherwise heterogeneous) nucleation of new filaments during growth, producing broad filament-length distributions that compete for the depleting monomer pool, and characterize how the resulting length heterogeneity modifies collective bending, trapping, and defect organization relative to the nucleator-seeded baseline.

  2. Motor activity: incorporate molecular motors (e.g., myosin) that bind, walk, and generate contractile stresses on the growing network, and determine how motor-generated stresses interact with growth-generated topological defects - whether motors anneal, anchor, convect, or nucleate defects - and with what consequences for force generation and contractility.

  3. ATP-hydrolysis-driven turnover: include treadmilling and nucleotide-state-dependent severing (ADF/cofilin-like), and quantify how turnover reshapes the kinetics of trapping and the structural relaxation of high-curvature morphologies, testing the paper's conjectures that severing acts analogously to extra nucleation and that treadmilling enhances polarity sorting and defect motility.

  4. Filament-type generality: determine whether growth-induced collective bending and kinetic trapping arise for non-actin filament mechanics (microtubule-like rigidity, intermediate-filament-like flexibility and apolarity, FtsZ-like short treadmilling filaments), identifying the dimensionless regimes (growth rate versus bending relaxation rate, crowding strength, persistence length versus system size) in which trapping occurs.

The common objective uniting these axes is to establish whether growth-induced kinetic trapping and the associated shape memory are robust, general consequences of filament growth in crowded, resource-limited environments - as the source conjectures - or artifacts of the idealized actin-like, nucleator-seeded, motor-free, non-turning model. Each numbered axis is an independently refutable sub-claim; a complete determination addresses all four axes and their interplay, so resolving a subset narrows but does not by itself settle the overarching question. Here "robust" means that the trapped-state observables - the extent of collective bending, the trapping lifetime, the nematic order, and the number, charge, and stability of defects - survive the relaxation in question, that is, the network remains kinetically trapped rather than relaxing to an untrapped, weakly ordered state.

References

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  2. Yadav V, Banerjee DS, Tabatabai AP, Kovar DR, Kim T, Banerjee S, Murrell MP (2019). Filament nucleation tunes mechanical memory in active polymer networks. Advanced Functional Materials 29(49):1905243. DOI: 10.1002/adfm.201905243. https://doi.org/10.1002/adfm.201905243
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