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The emergence of complex organs is driven by the coordinated proliferation, migration and differentiation of precursor cells. The fate behaviour of these cells is reflected in the time
evolution of their progeny, termed clones, which serve as a key experimental observable. In adult tissues, where cell dynamics is constrained by the condition of homeostasis, clonal tracing
studies based on transgenic animal models have advanced our understanding of cell fate behaviour and its dysregulation in disease1,2. But what can be learnt from clonal dynamics in
development, where the spatial cohesiveness of clones is impaired by tissue deformations during tissue growth? Drawing on the results of clonal tracing studies, we show that, despite the
complexity of organ development, clonal dynamics may converge to a critical state characterized by universal scaling behaviour of clone sizes. By mapping clonal dynamics onto a
generalization of the classical theory of aerosols, we elucidate the origin and range of scaling behaviours and show how the identification of universal scaling dependences may allow
lineage-specific information to be distilled from experiments. Our study shows the emergence of core concepts of statistical physics in an unexpected context, identifying cellular systems as
a laboratory to study non-equilibrium statistical physics.
In the version of this Letter originally published, Steffen Rulands was not listed as a corresponding author. This has been corrected in all versions of the Letter.
B.D.S. acknowledges the support of the Wellcome Trust (grant number 098357/Z/12/Z). F.L. is supported by a long-term EMBO fellowship and the postdoctoral fellowship of the FNRS. S.C. is
supported by a FRIA/FNRS fellowship. C.B. is supported by the ULB, a research grant of the FNRS, the Foundation Bettencourt Schueller, the Foundation ULB and the Foundation Baillet Latour.
M.S. is supported by an MRC doctoral training award and A.P. is supported by MRC research grant MR/K018329/1. M.H. is a Wellcome Trust Sir Henry Dale Fellow and is jointly funded by the
Wellcome Trust and the Royal Society (104151/Z/14/Z); M.H. and N.P. are funded by a Horizon 2020 grant (LSFM4LIFE). C.H. was funded by a Cambridge Stem Cell Institute Seed funding award for
interdisciplinary research awarded to M.H. and B.D.S. We are grateful to K. D. Poss and V. Gupta for making a digital version of their data available to us.
Cavendish Laboratory, Department of Physics, JJ Thomson Avenue, University of Cambridge, Cambridge, UK
Steffen Rulands, Christopher J. Hindley & Benjamin D. Simons
The Wellcome Trust/Cancer Research UK Gurdon Institute, University of Cambridge, Cambridge, UK
Steffen Rulands, Christopher J. Hindley, Nicole Prior, Magdalena K. Sznurkowska, Meritxell Huch, Anna Philpott & Benjamin D. Simons
Wellcome Trust Centre for Stem Cell Research, University of Cambridge, Cambridge, UK
Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
Université Libre de Bruxelles, Laboratory of Stem Cells and Cancer, Brussels, Belgium
Department of Oncology, University of Cambridge, Hutchison/MRC Research Centre, Cambridge, UK
S.R. and B.D.S. conceived the project. S.C., F.L., C.J.H., N.P. and M.S. performed the experiments and collected the raw data. M.H. supervised the liver experiments. S.R. developed the
theory, and performed the modelling and statistical analysis. S.R. and B.D.S drafted the manuscript. All authors edited and approved the final manuscript.
We have complied with all relevant ethical regulations. Mesp1-Cre mice colonies were maintained in a certified animal facility in accordance with European guidelines. These experiments were
approved by the local ethical committee under the reference #LA1230332(CEBEA). Research using mice for pancreas and liver samples has been regulated under the Animal (Scientific Procedures)
Act 1986 Amendment Regulations 2012 following ethical review by the University of Cambridge Animal Welfare and Ethical Review Body (AWERB). These experimental data sets were obtained as
by-products from other research projects undertaken by the respective laboratories.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Figs S1 & S2, Supplementary Theory, Supplementary References 1–10
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