Universality of clone dynamics during tissue development

Abstract

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 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 disease (1, 2). But what can be learned 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.

Fig. 1. Clonal dynamics during tissue development.

(A) Lineage tracing allows resolving clonal dynamics using a “two-time” measurement in living organisms. (B) Merger and fragmentation of labelled cell clusters occur naturally because of large-scale tissue rearrangements during the growth and development of tissues. (C,D) Illustration of clone fragmentation in mouse during the development of (C) liver and (D) pancreas (collection at post-natal day (P)45 and P14, respectively) following pulse-labelling using, respectively, R26R-CreERT2;Rainbow and R26R-CreERT2; R26-Confetti at E9.5 and E12.5, respectively. Portal tracts (PT) and central veins (CV) are highlighted in white, osteopontin (a ductal marker) is shown in purple and nuclei are marked in blue. Pancreatic ducts are shown in grey. (E) High density (mosaic) labelling of mouse heart using the Mesp1-Confetti system showing the left/right atrium (L/RA), left/right ventricle (L/RV) and the in/out-flow tracts (I/OFT). (F) Distributions of cell cluster sizes on the surface of the developing mouse heart at E12.5 (680 clusters from 4 mice) and P1 (373 clusters from 3 mice). (G) Average cluster sizes in different heart compartments and time points during development. Error bars denote 95% confidence intervals. (H) Rescaled cluster size distributions showing scaling behaviour.

Fig. 2. Origin of scaling and universality in clonal dynamics during development.

(A) Sizes of labelled cell clusters in developing tissues are determined by processes analogous to the kinetics of droplets in aerosols, as depicted. (B) Sketch of the renormalisation flow diagram showing how the relative contributions of different processes to the cluster size distribution evolve during development. At long times and/or larger cluster sizes, the time evolution of the cluster size distribution becomes controlled by three fixed points (dependent on the details of the merging and fragmentation processes), where it acquires a universal scaling dependence (Supplementary Information). The inset shows a schematic of the renormalization process, with the largest cluster sizes (grey) converging more rapidly onto the universal distribution than the smallest cluster sizes (red). (C) Rescaled cluster size distributions for different division modes obtained by numerical simulations (Supplemental Theory) collapse onto a universal log-normal form (grey line).

Fig. 3. Universality of cluster sizes in different tissue types and organisms.

(A-B) Cumulative cluster size distributions obtained from lineage tracing studies of the mouse heart. (C-E) Experimental cumulative cluster size distributions for (C) mouse liver (892 clusters from 4 mice), (D) mouse pancreas (988 clusters from 3 mice), and (E) zebrafish heart (from (20)) collapse onto the predicted universal log-normal dependence fitted by maximum likelihood estimation (grey). Data shown in colour and shading shows 95% Kolmogorov confidence intervals. (F) Experimental cumulative cluster size distributions (solid lines) separated by time, region, cell type labelling strategy collapse onto a universal shape (dashed line) with the exception of a subset of pancreatic acinar cells (inlay).