Super-resolution imaging revealed that non-muscle myosin II filaments in adherent cells such as fibroblasts self-organize into 'registered' stacks aligned across neighboring parallel actin bundles over micrometre distances, and that stack formation involves long-range attractive interactions between spatially separated filaments, presumably transmitted elastically through the intervening actin network (Hu et al., Nature Cell Biology 19, 133-141, 2017). The source study left open the quantitative physical characterization of this interaction - its origin, magnitude, range and functional form - and how specific actin regulators (cofilin1, Fmnl3, alpha-actinin-4) act on registry; the same group's follow-up record further developed, as open directions, the construction and validation of a dynamical model coupling myosin mechanochemistry, filament expansion/splitting, actin remodelling and elastic transmission through the disordered network, together with the functional consequences and generality of registered organization (Dasbiswas et al., 2018; Dasbiswas et al., 2019). Follow-up work has produced a force-dipole theory of the ordering, a minimal registry-kinetics model coupling elastic interactions to actin turnover, calculations of dipole interactions in disordered fiber networks, and identification of molecular promoters of stack assembly (myosin-18B, LUZP1, caldesmon); however, no measurement of the interaction in cells, no decisive discrimination between elastic-transmission and molecular-linkage mechanisms, and no validated fully coupled dynamical model exist. The problem of a quantitative, predictive physical account of actin-mediated myosin II stack registry therefore remains open.

Background

Non-muscle cells generate contractile force with the actomyosin cytoskeleton: actin protein filaments are spanned by bipolar filaments of non-muscle myosin II, each an aggregate of roughly 30 myosin molecules with motor domains at both ends, so that one filament can pull two actin filaments toward each other. These actin-myosin units assemble into contractile bundles - ventral stress fibers and transverse arcs - that are anchored to the extracellular matrix at focal adhesions (multiprotein attachment organelles) and generate cellular tension, shape, and mechanosensitive signalling.

In striated muscle, actomyosin is organized into sarcomeres - periodic contractile units - and myofibrils (linear chains of sarcomeres) align laterally 'in registry' across the cell. Whether comparable long-range order exists in non-muscle cells was long unclear, because individual myosin II filaments lie below the resolution limit of conventional light microscopy. Using structured illumination microscopy (SIM), a super-resolution fluorescence technique that roughly doubles the diffraction-limited resolution, Hu et al. (2017) resolved individual myosin II filaments in fibroblasts and found that they are not positioned randomly: filaments align into 'registered' stacks - myosin filaments occupying matching positions across neighboring parallel actin bundles, forming quasi-periodic arrays that span up to several micrometres in the direction orthogonal to the bundles. Kinetic analysis showed that individual myosin filaments turn over rapidly (half-life about 60 s), whereas stack formation proceeds over minutes and requires myosin II motor (ATPase) activity together with actin filament assembly, disassembly and crosslinking - dependent on the actin-nucleating formin Fmnl3, the actin-severing protein cofilin1, and the actin crosslinker alpha-actinin-4. Individual filaments also grow and divide: a bipolar myosin II filament can lengthen ('expand') and can split along its length into separate filaments, so that expansion/splitting denotes the per-filament probability (rate per unit time) of these growth and fission events (Hu et al., 2017; Titus, 2017). Individual filaments were observed to move laterally over long distances toward one another, implying an attractive interaction between spatially separated myosin filaments that the authors proposed is mediated not by direct molecular binding but by mechanical deformation of the intervening actin network (the actin meshwork lying between the bundles).

The physical picture invoked is that of contractile force dipoles in an elastic medium: each actomyosin unit exerts a pair of equal and opposite forces on its surroundings, and two such dipoles interact elastically through the medium - a mechanism previously proposed for the registered alignment of sarcomeres in developing muscle, transmitted there by the extracellular matrix. In a homogeneous elastic continuum such an interaction decays as a power law with separation; the actin cytoskeleton, however, is a disordered, crosslinked, actively remodelling network in which fiber bending can screen long-range force transmission, so the very existence, range, and functional form of the interaction in the cellular network is a nontrivial theoretical and experimental question (Kumar et al., 2023).

Subsequent work built on but did not complete this picture. Dasbiswas et al. (2018) formalized myosin II filaments in the intervening actin network as force dipoles that interact attractively; Dasbiswas et al. (2019) introduced a minimal dynamical model in which these elastic interactions drive mechanosensitive actin turnover and crosslinker remodeling, predicting registry timescales of tens of minutes; Kumar et al. (2023) computed the range and strength of dipole-dipole interactions in elastic fiber networks, finding continuum-like power laws in homogeneous networks but short-ranged, strongly configuration-dependent interactions in dilute networks. On the molecular side, myosin-18B (an unconventional, motor-impaired myosin), LUZP1 (a protein required for the concatenation and persistent association of myosin II filaments), and caldesmon (a protein that dynamically crosslinks myosin II filaments to actin) were identified as promoters or stabilizers of stack assembly and bundle maturation (Jiu et al., 2019; Wang et al., 2024; Kokate et al., 2022), myosin cluster sizes on stress fibers were shown to be controlled by the limiting myosin pool and actin architecture (Chou et al., 2024), and micron-scale supramolecular myosin arrays were reported at epithelial cell-cell (adherens) junctions (Yu-Kemp et al., 2022). Related theory addresses myosin minifilament self-assembly under load (Grewe and Schwarz, 2020), motor- and polarity-driven restructuring of actin bundles (Chandrasekaran et al., 2019; Lenz, 2020), and the physics of sarcomere self-assembly in muscle (Kolley et al., 2024; Kolley-Köchel et al., 2025). Actin bundles need not be uniformly oriented: they can contain filaments of opposite (antiparallel) polarity, and this alternating actin filament polarity - with myosin II filaments associated with the overlap zones between oppositely oriented filaments - is continually rearranged by bundle remodelling (Chandrasekaran et al., 2019; Lenz, 2020). What remains missing is the quantitative core of the original observation: a measurement of the effective interaction between myosin filaments and stacks, an account of how the identified regulators act on it, and a validated dynamical model coupling the full mechanochemistry to network elasticity.

Problem Statement

Establish a quantitative, predictive physical account of the long-range registered self-organization of non-muscle myosin II filaments into stacks in adherent cells, as posed by the source study. The account must jointly deliver: (1) Interaction physics - identify the physical origin of the proposed attractive interaction between spatially separated myosin II filaments and stacks, and determine its magnitude, spatial range, and quantitative functional form; in particular, whether elastic transmission of contractile forces through the intervening actin network suffices, or whether direct molecular linkage is required. (2) Molecular control - establish whether and how the actin regulators cofilin1, Fmnl3, and alpha-actinin-4 act on the probability of myosin filament expansion/splitting, on the elastic properties of the intervening actin network, or on the actin turnover rate. (3) Coupled dynamical model - construct and validate a dynamical model that couples myosin mechanochemistry, filament expansion and splitting, continuous actin remodelling (including alternating actin filament polarities in bundles), and elastic transmission through disordered actin networks, and that predicts both the kinetics of registry and the steady-state registry patterns, including their response to perturbations of motor activity, actin turnover, and crosslinking. Related open directions stated in the same group's follow-up record (Dasbiswas et al., 2018), which complement but are not part of the completion rule, are (4) how the registered organization of myosin II filaments affects overall cell contractility in non-muscle cells, and its function in other actomyosin contexts such as the contractile ring and the adhesion belt, and (5) whether the identified interaction and stacking mechanisms extend across diverse cell types and physiological contexts beyond those examined in the source study. The account is complete when the interaction is quantitatively characterized in cells or derived and validated against the source study's measured filament trajectories (Hu et al., 2017), the regulator effects are mapped onto identified model parameters, and the model reproduces the registry kinetics, steady-state patterns, and perturbation responses reported in Hu et al. (2017).

References

  1. Hu, Shiqiong; Dasbiswas, Kinjal; Guo, Zhenhuan; Tee, Yee-Han; Thiagarajan, Visalatchi; Hersen, Pascal; Chew, Teng-Leong; Safran, Samuel A.; Zaidel-Bar, Ronen; Bershadsky, Alexander D. (2017). Long-range self-organization of cytoskeletal myosin II filament stacks. Nature Cell Biology 19(2), 133-141. DOI: 10.1038/ncb3466. https://doi.org/10.1038/ncb3466
  2. Titus, Margaret A. (2017). Growing, splitting and stacking myosin II filaments. Nature Cell Biology 19(2), 77-79. DOI: 10.1038/ncb3468. https://doi.org/10.1038/ncb3468
  3. Dasbiswas, Kinjal; Hu, Shiqiong; Schnorrer, Frank; Safran, Samuel; Bershadsky, Alexander D. (2018). Ordering of myosin II filaments driven by mechanical forces: experiments and theory. Philosophical Transactions of the Royal Society B 373(1747), 20170114. DOI: 10.1098/rstb.2017.0114. https://doi.org/10.1098/rstb.2017.0114
  4. Dasbiswas, Kinjal; Hu, Shiqiong; Bershadsky, Alexander D.; Safran, Samuel A. (2019). Registry Kinetics of Myosin Motor Stacks Driven by Mechanical Force-Induced Actin Turnover. Biophysical Journal 117(5), 856-866. DOI: 10.1016/j.bpj.2019.07.040. https://doi.org/10.1016/j.bpj.2019.07.040
  5. Kumar, Abhinav; Quint, David A.; Dasbiswas, Kinjal (2023). Range and strength of mechanical interactions of force dipoles in elastic fiber networks. Soft Matter 19(30), 5805-5823. DOI: 10.1039/d3sm00381g. https://doi.org/10.1039/d3sm00381g (preprint: arXiv:2302.12943, https://arxiv.org/abs/2302.12943)
  6. Jiu, Yaming; Kumari, Reena; Fenix, Aidan M.; Schaible, Niccole; Liu, Xiaonan; Varjosalo, Markku; Krishnan, Ramaswamy; Burnette, Dylan T.; Lappalainen, Pekka (2019). Myosin-18B Promotes the Assembly of Myosin II Stacks for Maturation of Contractile Actomyosin Bundles. Current Biology 29(1), 81-92.e5. DOI: 10.1016/j.cub.2018.11.045. https://doi.org/10.1016/j.cub.2018.11.045
  7. Zhao, Shuangshuang; Shi, Xuemeng; Zhang, Yue; Wen, Zeyu; Cai, Jinping; Gao, Wei; Xu, Jiayi; Zheng, Yifei; Ji, Baohua; Cui, Yanqin; Shi, Kun; Liu, Yanjun; Li, Hui; Jiu, Yaming (2020). Myosin-18B Promotes Mechanosensitive CaMKK2-AMPK-VASP Regulation of Contractile Actin Stress Fibers. iScience 23(4), 100975. DOI: 10.1016/j.isci.2020.100975. https://doi.org/10.1016/j.isci.2020.100975
  8. Kokate, Shrikant B.; Ciuba, Katarzyna; Tran, Vivien D.; Kumari, Reena; Tojkander, Sari; Engel, Ulrike; Kogan, Konstantin; Kumar, Sanjay; Lappalainen, Pekka (2022). Caldesmon controls stress fiber force-balance through dynamic cross-linking of myosin II and actin-tropomyosin filaments. Nature Communications 13, 6032. DOI: 10.1038/s41467-022-33688-w. https://doi.org/10.1038/s41467-022-33688-w
  9. Wang, Liang; Tsang, Hoi Ying; Yan, Ziyi; Tojkander, Sari; Ciuba, Katarzyna; Kogan, Konstantin; Liu, Xiaonan; Zhao, Hongxia (2024). LUZP1 regulates the maturation of contractile actomyosin bundles. Cellular and Molecular Life Sciences 81(1), 248. DOI: 10.1007/s00018-024-05294-0. https://doi.org/10.1007/s00018-024-05294-0
  10. Chou, Wen-Hung; Molaei, Mehdi; Wu, Huini; Oakes, Patrick W.; Beach, Jordan R.; Gardel, Margaret L. (2024). Limiting pool and actin architecture controls myosin cluster sizes in adherent cells. Biophysical Journal 123(2), 157-171. DOI: 10.1016/j.bpj.2023.12.004. https://doi.org/10.1016/j.bpj.2023.12.004
  11. Yu-Kemp, Hui-Chia; Szymanski, Rachel A.; Cortes, Daniel B.; Gadda, Nicole C.; Lillich, Madeline L.; Maddox, Amy S.; Peifer, Mark (2022). Micron-scale supramolecular myosin arrays help mediate cytoskeletal assembly at mature adherens junctions. Journal of Cell Biology 221(1), e202103074. DOI: 10.1083/jcb.202103074. https://doi.org/10.1083/jcb.202103074
  12. Vignaud, Timothée; Copos, Calina; Leterrier, Christophe; Toro-Nahuelpan, Mauricio; Tseng, Qingzong; Mahamid, Julia; Blanchoin, Laurent; Mogilner, Alex; Théry, Manuel; Kurzawa, Laetitia (2021). Stress fibres are embedded in a contractile cortical network. Nature Materials 20, 410-420. DOI: 10.1038/s41563-020-00825-z. https://doi.org/10.1038/s41563-020-00825-z
  13. Mao, Qiyan; Acharya, Achyuth; Rodríguez-delaRosa, Alejandra; Marchiano, Fabio; Dehapiot, Benoit; Al Tanoury, Ziad; Rao, Jyoti; Díaz-Cuadros, Margarete; Mansur, Arian; Wagner, Erica; Chardès, Claire; Gupta, Vandana A.; Lenne, Pierre-François; Habermann, Bianca H.; Theodoly, Olivier; Pourquié, Olivier; Schnorrer, Frank (2022). Tension-driven multi-scale self-organisation in human iPSC-derived muscle fibers. eLife 11, e76649. DOI: 10.7554/eLife.76649. https://doi.org/10.7554/eLife.76649
  14. Kolley, Francine; Sidor, Clara; Dehapiot, Benoit; Schnorrer, Frank; Friedrich, Benjamin M. (2024). Mechanisms of Sarcomere Assembly in Muscle Cells Inferred from Sequential Ordering of Myofibril Components. PRX Life 2, 013002. DOI: 10.1103/prxlife.2.013002. https://doi.org/10.1103/prxlife.2.013002
  15. Kolley-Köchel, Francine; Schnorrer, Frank; Friedrich, Benjamin M. (2025). The physical basis of sarcomere self-assembly. Biophysics Reviews 6(4), 041305. DOI: 10.1063/5.0281811. https://doi.org/10.1063/5.0281811
  16. Kruse, Karsten; Berthoz, Rémi; Barberi, Luca; Reymann, Anne-Cécile; Riveline, Daniel (2024). Actomyosin clusters as active units shaping living matter. Current Biology 34(20), R1045-R1058. DOI: 10.1016/j.cub.2024.08.043. https://doi.org/10.1016/j.cub.2024.08.043
  17. Tidei, Joseph J.; Oakes, Patrick W.; Beach, Jordan R. (2025). Myosin 2 - A general contractor for the cytoskeleton. Current Opinion in Cell Biology 94, 102522. DOI: 10.1016/j.ceb.2025.102522. https://doi.org/10.1016/j.ceb.2025.102522
  18. Grewe, Justin; Schwarz, Ulrich S. (2020). Mechanosensitive self-assembly of myosin II minifilaments. Physical Review E 101, 022402. DOI: 10.1103/PhysRevE.101.022402. https://doi.org/10.1103/PhysRevE.101.022402
  19. Chandrasekaran, Aravind; Upadhyaya, Arpita; Papoian, Garegin A. (2019). Remarkable structural transformations of actin bundles are driven by their initial polarity, motor activity, crosslinking, and filament treadmilling. PLoS Computational Biology 15(7), e1007156. DOI: 10.1371/journal.pcbi.1007156. https://doi.org/10.1371/journal.pcbi.1007156
  20. Lenz, Martin (2020). Reversal of contractility as a signature of self-organization in cytoskeletal bundles. eLife 9, e51751. DOI: 10.7554/eLife.51751. https://doi.org/10.7554/eLife.51751