Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Mechanical feedback drives asynchronous cell divisions during embryogenesis

Abdul N. Malmi-Kakkada1,2,*,†, Sumit Sinha3,*,‡,§, and D. Thirumalai3,4,∥

  • *These authors contributed equally to this work.
  • †Contact author: amalmikakkada@towson.edu
  • ‡Present address: Applied Mathematics (SEAS, Harvard University) & Data Science (Dana Farber Cancer Institute).
  • §Contact author: ssinha@g.harvard.edu
  • ∥Contact author: dave.thirumalai@gmail.com

Phys. Rev. Research 7, 043027 – Published 7 October, 2025

DOI: https://doi.org/10.1103/z4y9-5f9f

Abstract

The initial stage of zebrafish morphogenesis is characterized by a synchronous to asynchronous transition (SAT) in cell divisions. The cells divide in unison in the synchronous phase, unlike in the asynchronous phase. Despite the widespread observation of SAT in multiple organisms, there is no theoretical framework to predict the critical number of cell cycles n* that mark the beginning of asynchronous division. Here, by probabilistically modeling cell cycle progression under the assumption that the distribution of cell division times is broadened, we predict the value of n* and the time at which the SAT occurs. The theory, supplemented by agent-based simulations, supports the hypothesis that the SAT emerges as a consequence of biomechanical feedback on cell division. Our results are in excellent agreement with experiments while also explaining the cell cycle lengthening that arises as a result of biomechanical feedback. The emergence of the asynchronous phase is due to increasing fluctuations in the cell cycle times with each round of cell division. We also make several testable predictions that further shed light on the role of biomechanical feedback in growing multicellular systems, such as during tissue and tumor growth.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (40)

  1. J. T. Enright, Temporal precision in circadian systems: A reliable neuronal clock from unreliable components? Science 209, 1542 (1980).
  2. R. E. Mirollo and S. H. Strogatz, Synchronization of pulse-coupled biological oscillators, SIAM J. Appl. Math. 50, 1645 (1990).
  3. A. Sherman, J. Rinzel, and J. Keizer, Emergence of organized bursting in clusters of pancreatic beta-cells by channel sharing, Biophys. J. 54, 411 (1988).
  4. T. J. Walker, Acoustic synchrony: Two mechanisms in the snowy tree cricket, Science 166, 891 (1969).
  5. H. M. Smith, Synchronous flashing of fireflies, Science 82, 151 (1935).
  6. R. Sarfati, J. C. Hayes, and O. Peleg, Self-organization in natural swarms of Photinus carolinus synchronous fireflies, Sci. Adv. 7, eabg9259 (2021).
  7. D. A. Kane and C. B. Kimmel, The zebrafish midblastula transition, Development 119, 447 (1993).
  8. S. F. Gilbert, An introduction to early developmental processes, in Developmental Biology, edited by C. Wigg, 7th ed. (Sinauer Associates, Sunderland, MA, 2000), p. 191.
  9. G. A. Anderson, L. Gelens, J. C. Baker, and J. E. Ferrell, Desynchronizing embryonic cell division waves reveals the robustness of Xenopus laevis development, Cell Rep. 21, 37 (2017).
  10. M. C. Gibson, A. B. Patel, R. Nagpal, and N. Perrimon, The emergence of geometric order in proliferating metazoan epithelia, Nature (London) 442, 1038 (2006).
  11. D. W. Thompson, On Growth and Form (Cambridge University Press, New York, 1942).
  12. T. J. Shaw and P. Martin, Wound repair at a glance, J. Cell Sci. 122, 3209 (2009).
  13. G. M. Cooper, The nucleus during mitosis, in The Cell: A Molecular Approach, edited by K. W. Adams, 9th ed. (Oxford University Press, New York, 2000), pp. 598–600.
  14. C. R. Samarage et al., Cortical tension allocates the first inner cells of the mammalian embryo, Dev. Cell 34, 435 (2015).
  15. J.-L. Maître et al., Asymmetric division of contractile domains couples cell positioning and fate specification, Nature (London) 536, 344 (2016).
  16. P. Gross, K. V. Kumar, and S. W. Grill, How active mechanics and regulatory biochemistry combine to form patterns in development, Annu. Rev. Biophys. 46, 337 (2017).
  17. B. I. Shraiman, Mechanical feedback as a possible regulator of tissue growth, Proc. Natl. Acad. Sci. USA 102, 3318 (2005).
  18. P. J. Keller, A. D. Schmidt, J. Wittbrodt, and E. H. Stelzer, Reconstruction of zebrafish early embryonic development by scanned light sheet microscopy, Science 322, 1065 (2008).
  19. See Supplemental Material at http://link.aps.org/supplemental/10.1103/z4y9-5f9f for details of the theoretical model of synchronous to asynchronous transition, description of the simulation of two-dimensional cell aggregates with no size growth, and details of the simulation of three-dimensional cell aggregates with cell size growth.
  20. A. Puliafito et al., Collective and single cell behavior in epithelial contact inhibition, Proc. Natl. Acad. Sci. USA 109, 739 (2012).
  21. J. Smith and L. Martin, Do cells cycle? Proc. Natl. Acad. Sci. U. S. A. 70, 1263 (1973).
  22. O. Sandler et al., Lineage correlations of single cell division time as a probe of cell-cycle dynamics, Nature (London) 519, 468 (2015).
  23. C. B. Kimmel, W. W. Ballard, S. R. Kimmel, B. Ullmann, and T. F. Schilling, Stages of embryonic development of the zebrafish, Dev. Dyn. 203, 253 (1995).
  24. K. D. Irvine and B. I. Shraiman, Mechanical control of growth: Ideas, facts and challenges, Development 144, 4238 (2017).
  25. A. N. Malmi-Kakkada, S. Sinha, X. Li, and D. Thirumalai, Adhesion strength between cells regulate nonmonotonic growth by a biomechanical feedback mechanism, Biophys. J. 121, 3719 (2022).
  26. B. G. Godard and C.-P. Heisenberg, Cell division and tissue mechanics, Curr. Opin. Cell Biol. 60, 114 (2019).
  27. H. Eagle and E. M. Levine, Growth regulatory effects of cellular interaction, Nature (London) 213, 1102 (1967).
  28. M. Pavel et al., Contact inhibition controls cell survival and proliferation via YAP/TAZ-autophagy axis, Nat. Commun. 9, 2961 (2018).
  29. R. K. Jain, J. D. Martin, and T. Stylianopoulos, The role of mechanical forces in tumor growth and therapy, Annu. Rev. Biomed. Eng. 16, 321 (2014).
  30. A. N. Malmi-Kakkada, X. Li, H. S. Samanta, S. Sinha, and D. Thirumalai, Cell growth rate dictates the onset of glass to fluidlike transition and long time superdiffusion in an evolving cell colony, Phys. Rev. X 8, 021025 (2018).
  31. S. Sinha and D. Thirumalai, Self-generated persistent random forces drive phase separation in growing tumors, J. Chem. Phys. 153, 201101 (2020).
  32. S. Sinha and A. N. Malmi-Kakkada, Inter-particle adhesion regulates the surface roughness of growing dense three-dimensional active particle aggregates, J. Phys. Chem. B 125, 10445 (2021).
  33. S. Sinha, H. Samanta, and D. Thirumalai, Observe without disturbing: Tracer particles sense local stresses in cell collectives without affecting the cancer cell dynamics, Soft Matter 19, 5385 (2023).
  34. C. L. Marchant, A. N. Malmi-Kakkada, J. A. Espina, and E. H. Barriga, Cell clusters softening triggers collective cell migration in vivo, Nat. Mater. 21, 1314 (2022).
  35. G. Zills, T. Datta, and A. N. Malmi-Kakkada, Enhanced mechanical heterogeneity of cell collectives due to temporal fluctuations in cell elasticity, Phys. Rev. E 107, 014401 (2023).
  36. S. R. Lish, L. Hupe, R. Golestanian, and P. Bittihn, Isovolumetric dividing active matter, arXiv:2409.20481.
  37. J. A. Farrell and P. H. O'Farrell, From egg to gastrula: How the cell cycle is remodeled during the Drosophila mid-blastula transition, Annu. Rev. Genet. 48, 269 (2014).
  38. P. H. O'Farrell, How metazoans reach their full size: The natural history of bigness, Cell Growth Control of Cell Size, edited by M. N. Hall, M. Raff, and G. Thomas (Cold Spring Harbor Laboratory Press, Cold Spring Harbor, NY, 2004), pp. 1–11.
  39. S. Sinha, A. N. Malmi-Kakkada, X. Li, H. S. Samanta, and D. Thirumalai, Spatially heterogeneous dynamics of cells in a growing tumor spheroid: Comparison between theory and experiments, Soft Matter 16, 5294 (2020).
  40. https://github.com/naseermk/2D_no_size_growth.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation