Jamming models developed in inanimate matter have been widely used to describe cell packing in tissues1,2,3,4,5,6,7, but predominantly neglect cell diversity, despite its prevalence in biology. Most tissues, animal brains in particular, comprise a mix of many cell types, with mounting evidence suggesting that neurons can recognize their respective types as they organize in space8,9,10,11. How cell diversity revises the current jamming paradigm is unknown. Here, in the brain of the flatworm planarian Schmidtea mediterranea, which exhibits remarkable tissue plasticity within a simple, quantifiable nervous system12,13,14,15,16, we identify a distinct packing state, ‘chromatic’ jamming. Combining experiments with computational modelling, we show that neurons of distinct types form independent percolating networks barring any physical contact. This jammed state emerges as cell packing configurations become constrained by cell type-specific interactions and therefore may extend to describe cell packing in similarly complex tissues composed of multiple cell types.
Subscribe to Journal
Get full journal access for 1 year
only $4.92 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
The datasets generated and analysed within this study can be downloaded from https://github.com/xianshine/cJamming or are available from the corresponding authors on request.
Analysis and simulation codes are available for public access on GitHub (https://github.com/xianshine/cJamming).
Farhadifar, R., Röper, J. C., Aigouy, B., Eaton, S. & Jülicher, F. The influence of cell mechanics, cell-cell interactions, and proliferation on epithelial packing. Curr. Biol. 17, 2095–2104 (2007).
Oswald, L., Grosser, S., Smith, D. M. & Käs, J. A. Jamming transitions in cancer. J. Phys. D 50, 483001 (2017).
Atia, L. et al. Geometric constraints during epithelial jamming. Nat. Phys. 14, 613–620 (2018).
Bi, D., Lopez, J. H., Schwarz, J. M. & Manning, M. L. A density-independent rigidity transition in biological tissues. Nat. Phys. 11, 1074–1079 (2015).
Park, J. A. et al. Unjamming and cell shape in the asthmatic airway epithelium. Nat. Mater. 14, 1040–1048 (2015).
Mongera, A. et al. A fluid-to-solid jamming transition underlies vertebrate body axis elongation. Nature 561, 401–405 (2018).
Schötz, E. M., Lanio, M., Talbot, J. A. & Manning, M. L. Glassy dynamics in three-dimensional embryonic tissues. J. R. Soc. Interface 10, 20130726 (2013).
Chklovskii, D. B., Schikorski, T. & Stevens, C. F. Wiring optimization in cortical circuits. Neuron 34, 341–347 (2002).
Rockhill, R. L., Euler, T. & Masland, R. H. Spatial order within but not between types of retinal neurons. Proc. Natl Acad. Sci. USA 97, 2303–2307 (2000).
Grueber, W. B. & Sagasti, A. Self-avoidance and tiling: mechanisms of dendrite and axon spacing. CSH Perspect. Biol. 2, a001750 (2010).
Fuerst, P. G., Koizumi, A., Masland, R. H. & Burgess, R. W. Neurite arborization and mosaic spacing in the mouse retina require DSCAM. Nature 451, 470–474 (2008).
Newmark, P. A. & Alvarado, A. S. Not your father’s planarian: a classic model enters the era of functional genomics. Nat. Rev. Genet. 3, 210–219 (2002).
Cebrià, F. et al. Dissecting planarian central nervous system regeneration by the expression of neural-specific genes. Dev. Growth Differ. 44, 135–146 (2002).
Takeda, H., Nishimura, K. & Agata, K. Planarians maintain a constant ratio of different cell types during changes in body size by using the stem cell system. Zool. Sci. 26, 805–813 (2009).
Mineta, K. et al. Origin and evolutionary process of the CNS elucidated by comparative genomics analysis of planarian ESTs. Proc. Natl Acad. Sci. USA 100, 7666–7671 (2003).
Rink, J. C. Stem cell systems and regeneration in planaria. Dev. Genes Evol. 223, 67–84 (2013).
Clusel, M., Corwin, E. I., Siemens, A. O. N. & Brujić, J. A ‘granocentric’ model for random packing of jammed emulsions. Nature 460, 611–615 (2009).
Song, C., Wang, P. & Makse, H. A. A phase diagram for jammed matter. Nature 453, 629–632 (2008).
Jorjadze, I., Pontani, L. L., Newhall, K. A. & Brujić, J. Attractive emulsion droplets probe the phase diagram of jammed granular matter. Proc. Natl Acad. Sci. USA 108, 4286–4291 (2011).
O’Hern, C. S., Langer, S. A., Liu, A. J. & Nagel, S. R. Random packings of frictionless particles. Phys. Rev. Lett. 88, 075507 (2002).
Liu, A. J. & Nagel, S. R. Jamming is not just cool any more. Nature 396, 21–22 (1998).
Reese, B. E. & Keeley, P. W. Design principles and developmental mechanisms underlying retinal mosaics. Biol. Rev. 90, 854–876 (2015).
Han, C. et al. Integrins regulate repulsion-mediated dendritic patterning of Drosophila sensory neurons by restricting dendrites in a 2D space. Neuron 73, 64–78 (2012).
Wilson, R. Four Colors Suffice: How the Map Problem Was Solved (Princeton University Press, 2013).
Fraguas, S., Barberán, S., Ibarra, B., Stöger, L. & Cebrià, F. Regeneration of neuronal cell types in Schmidtea mediterranea: an immunohistochemical and expression study. Int. J. Dev. Biol. 56, 143–153 (2012).
Fincher, C. T., Wurtzel, O., de Hoog, T., Kravarik, K. M. & Reddien, P. W. Cell type transcriptome atlas for the planarian Schmidtea mediterranea. Science 360, eaaq1736 (2018).
Agata, K. et al. Structure of the planarian central nervous system (CNS) revealed by neuronal cell markers. Zool. Sci. 15, 433–440 (1998).
Inoue, T. et al. Morphological and functional recovery of the planarian photosensing system during head regeneration. Zool. Sci. 21, 275–283 (2004).
Collins, J. J. et al. Genome-wide analyses reveal a role for peptide hormones in planarian germline development. PLoS Biol. 8, e1000509 (2010).
Duyckaerts, C. & Godefroy, G. Voronoi tessellation to study the numerical density and the spatial distribution of neurons. J. Chem. Neuroanat. 20, 83–92 (2000).
Kay, J. N., Chu, M. W. & Sanes, J. R. MEGF10 and MEGF11 mediate homotypic interactions required for mosaic spacing of retinal neurons. Nature 483, 465–469 (2012).
Wässle, H. & Riemann, H. J. The mosaic of nerve cells in the mammalian retina. Proc. R. Soc. Lond. B 200, 441–461 (1978).
O’Hern, C. S., Silbert, L. E., Liu, A. J. & Nagel, S. R. Jamming at zero temperature and zero applied stress: the epitome of disorder. Phys. Rev. E 68, 011306 (2003).
Stauffer, D. & Aharony, A. Introduction to Percolation Theory (Taylor and Francis, 1994). .
Morita, M. & Best, J. B. Electron microscopic studies of planaria: III. Some observations on the fine structure of planarian nervous tissue. J. Exp. Zool. 161, 391–411 (1966).
Wang, I. E., Lapan, S. W., Scimone, M. L., Clandinin, T. R. & Reddien, P. W. Hedgehog signaling regulates gene expression in planarian glia. eLife 5, e16996 (2016).
Roberts-Galbraith, R. H., Brubacher, J. L. & Newmark, P. A. A functional genomics screen in planarians reveals regulators of whole-brain regeneration. eLife 5, e17002 (2016).
Brandl, H. et al. PlanMine—a mineable resource of planarian biology and biodiversity. Nucleic Acids Res. 44, D764–D773 (2016).
Bonar, N. A. & Petersen, C. P. Integrin suppresses neurogenesis and regulates brain tissue assembly in planarian regeneration. Development 144, 784–794 (2017).
Seebeck, F. et al. Integrins are required for tissue organization and restriction of neurogenesis in regenerating planarians. Development 144, 795–807 (2017).
King, R. S. & Newmark, P. A. In situ hybridization protocol for enhanced detection of gene expression in the planarian Schmidtea mediterranea. BMC Dev. Biol. 13, 8 (2013).
Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995).
We thank Kejia Chen and Ke Chen for help with data analysis, R.H. Roberts-Galbraith and J.J. Collins III for experimental assistance during the early phase of this study and S. Granick, I. Riedel-Kruse, D.M. Sussman and P.N. Newmark for discussions. Plasmids that contain the planarian neuropeptide genes were provided by J.J. Collins III. This work is supported by the Burroughs Wellcome Fund through the CASI programme to B.W.
The authors declare no competing interests.
Peer review information Nature Physics thanks Corey O’Hern and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Khariton, M., Kong, X., Qin, J. et al. Chromatic neuronal jamming in a primitive brain. Nat. Phys. 16, 553–557 (2020). https://doi.org/10.1038/s41567-020-0809-9