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Scaling of embryonic patterning based on phase-gradient encoding


A fundamental feature of embryonic patterning is the ability to scale and maintain stable proportions despite changes in overall size, for instance during growth1,2,3,4,5,6. A notable example occurs during vertebrate segment formation: after experimental reduction of embryo size, segments form proportionally smaller, and consequently, a normal number of segments is formed1,7,8. Despite decades of experimental1,7 and theoretical work9,10,11, the underlying mechanism remains unknown. More recently, ultradian oscillations in gene activity have been linked to the temporal control of segmentation12; however, their implication in scaling remains elusive. Here we show that scaling of gene oscillation dynamics underlies segment scaling. To this end, we develop a new experimental model, an ex vivo primary cell culture assay that recapitulates mouse mesoderm patterning and segment scaling, in a quasi-monolayer of presomitic mesoderm cells (hereafter termed monolayer PSM or mPSM). Combined with real-time imaging of gene activity, this enabled us to quantify the gradual shift in the oscillation phase and thus determine the resulting phase gradient across the mPSM. Crucially, we show that this phase gradient scales by maintaining a fixed amplitude across mPSM of different lengths. We identify the slope of this phase gradient as a single predictive parameter for segment size, which functions in a size- and temperature-independent manner, revealing a hitherto unrecognized mechanism for scaling. Notably, in contrast to molecular gradients, a phase gradient describes the distribution of a dynamical cellular state. Thus, our phase-gradient scaling findings reveal a new level of dynamic information-processing, and provide evidence for the concept of phase-gradient encoding during embryonic patterning and scaling.

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Figure 1: An ex vivo cell culture model for gene activity oscillations.
Figure 2: Molecular and morphological analysis of the ex vivo cell culture model using in situ hybridization after 18–24 h of culture.
Figure 3: Quantification of segment sizes and oscillation dynamics reveals scaling behaviour due to a fixed phase gradient amplitude.
Figure 4: Phase-gradient scaling does not rely on sensing global size cues.


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We thank members of the Aulehla laboratory for discussion and comments on the manuscript. We thank M. Snaebjornsson for providing Supplementary Video 1. We thank F. Peri, D. Gilmour, T. Hiiragi and F. Spitz for comments on the manuscript and P. Riedinger for artwork. This work was supported by EMBL Imaging and Laboratory animal resource core facilities. The Mesp2-GFP line was provided by Y. Saga. P.F. was supported by Natural Science and Engineering Research Council of Canada (NSERC), Discovery Grant program RGPIN 401950-11, Regroupement Québécois pour les matériaux de pointe (RQMP) and McGill University.

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Authors and Affiliations



V.M.L. developed the ex vivo culture system, performed the experiments and analysed the data; C.D.T. performed the experiments, analysed the data and developed the oscillation-phase quantification; P.F. developed and wrote the mathematical model; A.A. designed and supervised the project and wrote the manuscript. All authors discussed and contributed to the manuscript.

Corresponding author

Correspondence to Alexander Aulehla.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Figures 1-8 Supplementary Text that contains the derivation of our mathematical model explaining segment and phase-gradient scaling and we discuss different possible biochemical implementations and Supplementary references. (PDF 7915 kb)

In vivo PSM imaging of gene activity oscillations

Two-photon time-lapse imaging of PSM of LuVeLu transgenic embryos; side view on the PSM, merged YFP and brightfield channel. Real-time recordings reveal oscillatory patterns of gene activity (Venus channel), sweeping from posterior to anterior PSM as periodic, kinematic waves. Simultaneously, segment formation occurs in the anterior PSM. (MOV 19833 kb)

Oscillatory gene activity patterns visualized in the ex vivo cell culture assay

The video shows time-lapse imaging of LuVeLu reporter activity (YFP/Venus channel) in a monolayer PSM (mPSM). This reveals oscillatory gene activity patterns that over time resemble concentric waves that sweep across the mPSM in a central–peripheral direction. Tail bud mesoderm from an E10.5 LuVeLu-transgenic reporter mouse embryo was used to establish the cell culture. Snapshots from this video are represented in Fig. 1d and the corresponding kymograph in Fig. 1f. (MOV 15989 kb)

Spreading of primary mesoderm cells in the ex vivo cell culture assay

Brightfield channel of supplementary video 2, showing spreading of tailbud mesoderm. (MOV 18557 kb)

Morphological segment formation in the ex vivo cell culture assay

Tailbud mesoderm derived from an E10.5 mouse embryo double heterozygous for the LuVeLu transgene and for the targeted Mesp2-GFP allele, a marker for segment formation. Supplementary video 4 (brightfield channel) shows an ex vivo culture at later stages, during which morphological segment formation becomes visible. (MOV 14195 kb)

Oscillatory gene activity patterns at stages of segment formation in the ex vivo cell culture

Tailbud mesoderm derived from a 10.5 mouse embryo double heterozygous for the LuVeLu transgene and for the targeted Mesp2-GFP allele, a marker for segment formation. Supplementary video 5 shows LuVeLu reporter activity (Venus channel) from the same sample as shown in supplementary videos 4, 6 & 7, central-peripheal waves are visualized. To exclude bleedthrough from the Mesp2-GFP signal into the YFP channel, the GFP signal was subtracted from the YFP-channel. A maximum intensity projection of a z-stack blurred with a 3x3 median filter is shown. (MOV 10982 kb)

Real-time imaging of Mesp2 activation during segment formation in the ex vivo cell culture

Tailbud mesoderm derived from an E10.5 mouse embryo double heterozygous for the LuVeLu transgene and for the targeted Mesp2-GFP allele, a marker for segment formation. Supplementary video 6 shows Mesp2-GFP fluorescence from the same sample as shown in supplementary videos 4, 5 & 7. Video shown is a maximum intensity projection of a z-stack. (MOV 14331 kb)

Segment boundaries form where gene oscillation waves come to halt

Supplementary video 7 shows merged channels of GFP, YFP and brightfield from sample shown in supplementary videos 4-6. Brightness and contrast of the brightfield channel have been adjusted linearly to allow a better recognition of the overlaying Mesp2-GFP (shown in red) and LuVeLu (shown in green) fluorescence. (MOV 19560 kb)

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Lauschke, V., Tsiairis, C., François, P. et al. Scaling of embryonic patterning based on phase-gradient encoding. Nature 493, 101–105 (2013).

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