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Theory for Coexistence and Selection of Branched Actin Networks in a Shared and Finite Pool of Monomers

Valentin Wössner, Falko Ziebert, and Ulrich S. Schwarz*

  • *Contact author: schwarz@thphys.uni-heidelberg.de

PRX Life 4, 033020 – Published 26 August, 2026

DOI: https://doi.org/10.1103/wmcg-9rq7

Abstract

Biological cells contain actin structures of different types and sizes, but all of them are continuously turned over. Since they all compete for a shared pool of actin monomers, the question arises how they can coexist in these dynamic steady states. Recently, the coexistence of branched actin networks with different densities growing in a shared and finite pool of purified proteins has been demonstrated in a biomimetic bead assay. However, theoretical work in the context of organelle size regulation has mainly been focused on linear architectures, such as single filaments and bundles, and thus is not able to explain this observation. Here we show theoretically that the local depletion of actin monomers caused by the growth of a branched network naturally gives rise to a negative feedback loop between network density and growth rate and that this competition is captured by one central ordinary differential equation. A comprehensive bifurcation analysis shows that the theory leads to well-defined steady states even in the case of multiple networks sharing the same pool of monomers, without any need for specific molecular processes. Under increasing competition strength, coexistence is replaced by selection. We also show that our theory is in excellent agreement with spatiotemporal simulations, implemented in a finite element framework, and that local depletion even occurs in the presence of a large pool of nonpolymerizable actin. In summary, our work suggests that local monomer depletion is the decisive and universal factor controlling growth of branched actin networks.

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References (74)

  1. L. Blanchoin, R. Boujemaa-Paterski, C. Sykes, and J. Plastino, Actin dynamics, architecture, and mechanics in cell motility, Physiol. Rev. 94, 235 (2014).
  2. P. Lappalainen, T. Kotila, A. Jégou, and G. Romet-Lemonne, Biochemical and mechanical regulation of actin dynamics, Nat. Rev. Mol. Cell Biol. 23, 836 (2022).
  3. B. L. Goode, J. Eskin, and S. Shekhar, Mechanisms of actin disassembly and turnover, J. Cell Biol. 222, e202309021 (2023).
  4. S. Banerjee, M. L. Gardel, and U. S. Schwarz, The actin cytoskeleton as an active adaptive material, Annu. Rev. Condens. Matter Phys. 11, 421 (2020).
  5. M. Théry and L. Blanchoin, Reconstituting the dynamic steady states of actin networks in vitro, Nat. Cell Biol. 26, 494 (2024).
  6. A. Wegner, Head to tail polymerization of actin, J. Mol. Biol. 108, 139 (1976).
  7. M.-F. Carlier and S. Shekhar, Global treadmilling coordinates actin turnover and controls the size of actin networks, Nat. Rev. Mol. Cell Biol. 18, 389 (2017).
  8. Y.-H. M. Chan and W. F. Marshall, How cells know the size of their organelles, Science 337, 1186 (2012).
  9. D. S. Banerjee and S. Banerjee, Design principles and feedback mechanisms in organelle size control, Curr. Opin. Cell Biol. 95, 102533 (2025).
  10. N. W. Goehring and A. A. Hyman, Organelle growth control through limiting pools of cytoplasmic components, Curr. Biol. 22, R330 (2012).
  11. J. D. Rotty and J. E. Bear, Competition and collaboration between different actin assembly pathways allows for homeostatic control of the actin cytoskeleton, BioArchitecture 5, 27 (2015).
  12. R. S. Kadzik, K. E. Homa, and D. R. Kovar, F-actin cytoskeleton network self-organization through competition and cooperation, Annu. Rev. Cell Dev. Biol. 36, 35 (2020).
  13. D. Raz-Ben Aroush, N. Ofer, E. Abu-Shah, J. Allard, O. Krichevsky, A. Mogilner, and K. Keren, Actin turnover in lamellipodial fragments, Curr. Biol. 27, 2963 (2017).
  14. L. Mohapatra, T. J. Lagny, D. Harbage, P. R. Jelenkovic, and J. Kondev, The limiting-pool mechanism fails to control the size of multiple organelles, Cell Syst. 4, 559 (2017).
  15. D. S. Banerjee and S. Banerjee, Size regulation of multiple organelles competing for a limiting subunit pool, PLoS Comput. Biol. 18, e1010253 (2022).
  16. L. Mohapatra, B. L. Goode, P. Jelenkovic, R. Phillips, and J. Kondev, Design principles of length control of cytoskeletal structures, Annu. Rev. Biophys. 45, 85 (2016).
  17. A. Rosario, S. G. McInally, P. R. Jelenkovic, B. L. Goode, and J. Kondev, Universal length fluctuations of actin structures found in cells, eLife 12, 91574 (2023).
  18. S. G. McInally, A. J. B. Reading, A. Rosario, P. R. Jelenkovic, B. L. Goode, and J. Kondev, Length control emerges from cytoskeletal network geometry, Proc. Natl. Acad. Sci. USA 121, e2401816121 (2024).
  19. S. A. Momin, M. Cohen, and L. Mohapatra, Quantitative signatures of disassembly mechanisms modulating filament and bundle assembly in a shared pool, bioRxiv (2025), https://doi.org/10.1101/2025.05.24.655867.
  20. C. Guérin, A.-B. N'Diaye, L. Gressin, A. Mogilner, M. Théry, L. Blanchoin, and A. Colin, Balancing limited resources in actin network competition, Curr. Biol. 35, 500 (2025).
  21. M. Mund, J. A. van der Beek, J. Deschamps, S. Dmitrieff, P. Hoess, J. L. Monster, A. Picco, F. Nédélec, M. Kaksonen, and J. Ries, Systematic nanoscale analysis of endocytosis links efficient vesicle formation to patterned actin nucleation, Cell 174, 884 (2018).
  22. M. Akamatsu, R. Vasan, D. Serwas, M. A. Ferrin, P. Rangamani, and D. G. Drubin, Principles of self-organization and load adaptation by the actin cytoskeleton during clathrin-mediated endocytosis, eLife 9, e49840 (2020).
  23. K. Popov, J. Komianos, and G. A. Papoian, MEDYAN: Mechanochemical simulations of contraction and polarity alignment in actomyosin networks, PLoS Comput. Biol. 12, e1004877 (2016).
  24. J. Liman, C. Bueno, Y. Eliaz, N. P. Schafer, M. N. Waxham, P. G. Wolynes, H. Levine, and M. S. Cheung, The role of the Arp2/3 complex in shaping the dynamics and structures of branched actomyosin networks, Proc. Natl. Acad. Sci. USA 117, 10825 (2020).
  25. S. L. Freedman, S. Banerjee, G. M. Hocky, and A. R. Dinner, A versatile framework for simulating the dynamic mechanical structure of cytoskeletal networks, Biophys. J. 113, 448 (2017).
  26. K.-C. Lee and A. J. Liu, New proposed mechanism of actin-polymerization-driven motility, Biophys. J. 95, 4529 (2008).
  27. I. V. Maly and G. G. Borisy, Self-organization of a propulsive actin network as an evolutionary process, Proc. Natl. Acad. Sci. USA 98, 11324 (2001).
  28. J. Weichsel and U. S. Schwarz, Mesoscopic model for filament orientation in growing actin networks: The role of obstacle geometry, New J. Phys. 15, 035006 (2013).
  29. J. Mueller, G. Szep, M. Nemethova, I. de Vries, A. D. Lieber, C. Winkler, K. Kruse, J. V. Small, C. Schmeiser, K. Keren, R. Hauschild, and M. Sixt, Load adaptation of lamellipodial actin networks, Cell 171, 188 (2017).
  30. R. M. Garner and J. A. Theriot, Leading edge maintenance in migrating cells is an emergent property of branched actin network growth, eLife 11, e74389 (2022).
  31. A. Mogilner and L. Edelstein-Keshet, Regulation of actin dynamics in rapidly moving cells: A quantitative analysis, Biophys. J. 83, 1237 (2002).
  32. H. Boukellal, O. Campás, J.-F. Joanny, J. Prost, and C. Sykes, Soft Listeria: Actin-based propulsion of liquid drops, Phys. Rev. E 69, 061906 (2004).
  33. E. Paluch, J. van der Gucht, J.-F. Joanny, and C. Sykes, Deformations in actin comets from rocketing beads, Biophys. J. 91, 3113 (2006).
  34. A. E. Carlsson, Disassembly of actin networks by filament severing, New J. Phys. 9, 418 (2007).
  35. P. J. Michalski and A. E. Carlsson, The effects of filament aging and annealing on a model lamellipodium undergoing disassembly by severing, Phys. Biol. 7, 026004 (2010).
  36. P. J. Michalski and A. E. Carlsson, A model actin comet tail disassembling by severing, Phys. Biol. 8, 046003 (2011).
  37. A. Manhart, T. A. Icheva, C. Guerin, T. Klar, R. Boujemaa-Paterski, M. Thery, L. Blanchoin, and A. Mogilner, Quantitative regulation of the dynamic steady state of actin networks, eLife 8, e42413 (2019).
  38. R. Boujemaa-Paterski, C. Suarez, T. Klar, J. Zhu, C. Guérin, A. Mogilner, M. Théry, and L. Blanchoin, Network heterogeneity regulates steering in actin-based motility, Nat. Commun. 8, 655 (2017).
  39. A. E. Carlsson, Growth velocities of branched actin networks, Biophys. J. 84, 2907 (2003).
  40. J. Weichsel and U. S. Schwarz, Two competing orientation patterns explain experimentally observed anomalies in growing actin networks, Proc. Natl. Acad. Sci. USA 107, 6304 (2010).
  41. R. D. Mullins, P. Bieling, and D. A. Fletcher, From solution to surface to filament: Actin flux into branched networks, Biophys. Rev. 10, 1537 (2018).
  42. L. Cassimeris, D. Safer, V. T. Nachmias, and S. H. Zigmond, Thymosin beta 4 sequesters the majority of G-actin in resting human polymorphonuclear leukocytes, J. Cell Biol. 119, 1261 (1992).
  43. A. L. Goldstein, E. Hannappel, and H. K. Kleinman, Thymosin β4: Actin-sequestering protein moonlights to repair injured tissues, Trends Mol. Med. 11, 421 (2005).
  44. T. P. Loisel, R. Boujemaa, D. Pantaloni, and M.-F. Carlier, Reconstitution of actin-based motility of Listeria and Shigella using pure proteins, Nature (London) 401, 613 (1999).
  45. M. A. Wear, D. A. Schafer, and J. A. Cooper, Actin dynamics: Assembly and disassembly of actin networks, Curr. Biol. 10, R891 (2000).
  46. T. D. Pollard, Rate constants for the reactions of ATP- and ADP-actin with the ends of actin filaments., J. Cell Biol. 103, 2747 (1986).
  47. P. Bieling, T.-D. Li, J. Weichsel, R. McGorty, P. Jreij, B. Huang, D. A. Fletcher, and R. D. Mullins, Force feedback controls motor activity and mechanical properties of self-assembling branched actin networks, Cell 164, 115 (2016).
  48. T. M. Svitkina, Ultrastructure of the actin cytoskeleton, Curr. Opin. Cell Biol. 54, 1 (2018).
  49. D. Pantaloni, R. Boujemaa, D. Didry, P. Gounon, and M.-F. Carlier, The Arp2/3 complex branches filament barbed ends: Functional antagonism with capping proteins, Nat. Cell Biol. 2, 385 (2000).
  50. S. Wiesner, E. Helfer, D. Didry, G. Ducouret, F. Lafuma, M.-F. Carlier, and D. Pantaloni, A biomimetic motility assay provides insight into the mechanism of actin-based motility, J. Cell Biol. 160, 387 (2003).
  51. A. Colin, T. Kotila, C. Guérin, M. Orhant-Prioux, B. Vianay, A. Mogilner, P. Lappalainen, M. Théry, and L. Blanchoin, Recycling of the actin monomer pool limits the lifetime of network turnover, EMBO J. 42, EMBJ2022112717 (2023).
  52. A. Michelot, J. Berro, C. Guérin, R. Boujemaa-Paterski, C. J. Staiger, J.-L. Martiel, and L. Blanchoin, Actin-filament stochastic dynamics mediated by ADF/cofilin, Curr. Biol. 17, 825 (2007).
  53. D. Pavlov, A. Muhlrad, J. Cooper, M. Wear, and E. Reisler, Actin filament severing by cofilin, J. Mol. Biol. 365, 1350 (2007).
  54. C. Chan, C. C. Beltzner, and T. D. Pollard, Cofilin dissociates Arp2/3 complex and branches from actin filaments, Curr. Biol. 19, 537 (2009).
  55. J. Plastino, I. Lelidis, J. Prost, and C. Sykes, The effect of diffusion, depolymerization and nucleation promoting factors on actin gel growth, Eur. Biophys. J. 33, 310 (2004).
  56. P. Bleicher, A. Sciortino, and A. R. Bausch, The dynamics of actin network turnover is self-organized by a growth-depletion feedback, Sci. Rep. 10, 6215 (2020).
  57. A. van Oudenaarden and J. A. Theriot, Cooperative symmetry-breaking by actin polymerization in a model for cell motility, Nat. Cell Biol. 1, 493 (1999).
  58. J. Weichsel, K. Baczynski, and U. S. Schwarz, Unifying autocatalytic and zeroth-order branching models for growing actin networks, Phys. Rev. E 87, 040701(R) (2013).
  59. J. Roland, J. Berro, A. Michelot, L. Blanchoin, and J.-L. Martiel, Stochastic severing of actin filaments by actin depolymerizing factor/cofilin controls the emergence of a steady dynamical regime, Biophys. J. 94, 2082 (2008).
  60. C. S. Peskin, G. M. Odell, and G. F. Oster, Cellular motions and thermal fluctuations: The Brownian ratchet, Biophys. J. 65, 316 (1993).
  61. A. Mogilner and G. Oster, Cell motility driven by actin polymerization, Biophys. J. 71, 3030 (1996).
  62. V. C. Abraham, V. Krishnamurthi, D. L. Taylor, and F. Lanni, The actin-based nanomachine at the leading edge of migrating cells., Biophys. J. 77, 1721 (1999).
  63. A. Kawska, K. Carvalho, J. Manzi, R. Boujemaa-Paterski, L. Blanchoin, J.-L. Martiel, and C. Sykes, How actin network dynamics control the onset of actin-based motility, Proc. Natl. Acad. Sci. USA 109, 14440 (2012).
  64. D. Stauffer and M. Sahimi, Scaling theory of percolation clusters, in Complex Media and Percolation Theory, edited by M. Sahimi and A. G. Hunt (Springer, New York, 2021), pp. 49–60.
  65. R. Dominguez and K. C. Holmes, Actin structure and function, Annu. Rev. Biophys. 40, 169 (2011).
  66. N. Selve and A. Wegner, Rate constant for capping of the barbed ends of actin filaments by the gelsolin-actin complex, Eur. J. Biochem. 155, 397 (1986).
  67. E. Doedel, A. Champneys, T. Fairgrieve, Y. Kuznetsov, B. Sandstede, and X. Wang, AUTO 97: Continuation and Bifurcation Software for Ordinary Differential Equations (with HomCont) (Concordia University, Montreal, 1999).
  68. V. Wössner, F. Ziebert, and U. S. Schwarz, Code for “Theory for coexistence and selection of branched actin networks in a shared and finite pool of monomer”, GitHub, San Francisco, 2025, https://github.com/vwoessner/actin-networks-limited-pool.
  69. A. Dedner, R. Klöfkorn, M. Nolte, and M. Ohlberger, A generic interface for parallel and adaptive discretization schemes: Abstraction principles and the dune-fem module, Computing 90, 165 (2010).
  70. J. K. Au, A. O. Olivares, A. Henn, W. Cao, D. Safer, and E. M. De La Cruz, Widely distributed residues in thymosin β4 are critical for actin binding, Biochemistry 47, 4181 (2008).
  71. A. Mogilner, On the edge: Modeling protrusion, Curr. Opin. Cell Biol. 18, 32 (2006).
  72. P. Bastian, M. Blatt, A. Dedner, N.-A. Dreier, C. Engwer, R. Fritze, C. Gräser, C. Grüninger, D. Kempf, R. Klöfkorn, M. Ohlberger, and O. Sander, The Dune framework: Basic concepts and recent developments, Comput. Math. Appl. 81, 75 (2021).
  73. C. Geuzaine and J.-F. Remacle, Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities, Int. J. Numer. Methods Eng. 79, 1309 (2009).
  74. C. C. Beltzner and T. D. Pollard, Pathway of actin filament branch formation by Arp2/3 complex, J. Biol. Chem. 283, 7135 (2008).

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