Gene-regulatory networks control the establishment and maintenance of alternative gene-expression states during development. A particular challenge is the acquisition of opposing states by two copies of the same gene, as in the case of the long non-coding RNA Xist in mammals at the onset of random X-chromosome inactivation (XCI). The regulatory principles that lead to stable mono-allelic expression of Xist remain unknown. Here, we uncover the minimal regulatory network that can ensure female-specific and mono-alleleic upregulation of Xist, by combining mathematical modeling and experimental validation of central model predictions. We identify a symmetric toggle switch as the basis for random mono-allelic upregulation of Xist, which reproduces data from several mutant, aneuploid and polyploid mouse cell lines with various Xist expression patterns. Moreover, this toggle switch explains the diversity of strategies employed by different species at the onset of XCI. In addition to providing a unifying conceptual framework with which to explore XCI across mammals, our study sets the stage for identifying the molecular mechanisms needed to initiate random XCI.

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Data availability

Source data for Figs. 3c,d, 4b,c,f,g,i, 5d and 6c–f and Supplementary Figs. 1 and 3a,b,d are available with the paper online. Data, code and simulations used in this study are available at https://github.com/verenamutzel/XCI_model under the MIT license. All other data and the cell line TX1072dT generated for this study are available upon reasonable request.

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All code and simulations used in this study are available at https://github.com/verenamutzel/XCI_model under the MIT license.

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We thank A. Wutz (ETH Zürich, Switzerland) for the TXY (Xist-tetOP) and TXY∆A (Xist-∆SX-tetOP) mESC lines. We thank the staff of the Max Planck Institute for Molecular Genetics (MPIMG) and PICTIBiSA@BDD imaging facilities for technical assistance, the MPIMG sequencing core facility of sequencing services and the MPIMG IT facility for support in using the computing cluster. We thank R. Galupa for valuable feedback on the manuscript. This work was funded by a Human Frontier Science Program (HFSP) long-term fellowship (LT000597/2010-L) to E.G.S., a Grant-in-Aid for Specially Promoted Research from the Japan Society for the Promotion of Science (JSPS) (17H06098) to M.S., and by a Japan Science and Technology Agency (JST) Exploratory Research for Advanced Technology (ERATO) grant (JPMJER1104) to M.S., I.O. and M.S., and JSPS KAKENHI grants (25291076 and 18K06030) to I.O. Reseach in the laboratory of E.G.S. is funded by the Max-Planck Research Group Leader program and and the German Ministry of Science and Education (BMBF) through the grant E:bio Module III - Xnet. V.M. is supported by the DFG (GRK1772, Computational Systems Biology). Research in the laboratory of L.G. is funded by an ERC Starting grant (759366).

Author information


  1. Otto Warburg Laboratories, Max Planck Institute for Molecular Genetics, Berlin, Germany

    • Verena Mutzel
    • , Ilona Dunkel
    •  & Edda G. Schulz
  2. Department of Anatomy and Cell Biology, Graduate School of Medicine, Kyoto University, Kyoto, Japan

    • Ikuhiro Okamoto
  3. Japan Science and Technology (JST), Exploratory Research for Advanced Technology (ERATO), Kyoto, Japan

    • Ikuhiro Okamoto
  4. Institute for the Advanced Study of Human Biology (ASHBi), Kyoto University, Kyoto, Japan

    • Mitinori Saitou
  5. Department of Anatomy and Cell Biology, Graduate School of Medicine, Kyoto University, Kyoto, Japan

    • Mitinori Saitou
  6. Center for iPS Cell Research and Application (CiRA), Kyoto University, Kyoto, Japan

    • Mitinori Saitou
  7. Friedrich Miescher Institute for Biomedical Research, Basel, Switzerland

    • Luca Giorgetti
  8. Institut Curie, PSL Research University, CNRS UMR3215, INSERM U934, Paris, France

    • Edith Heard
  9. European Molecular Biology Laboratory (EMBL), Directors’ research unit, Heidelberg, Germany

    • Edith Heard


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E.G.S., E.H. and I.O. conceived the study. V.M. and E.G.S. wrote scripts and performed simulations. V.M., I.O., I.D., L.G. and E.G.S. carried out the experiments. E.G.S. and V.M. wrote the paper with input from E.H. and L.G. E.G.S., E.H. and M.S. supervised the study. E.G.S., E.H., L.G., I.O. and M.S. acquired funding.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Edda G. Schulz.

Integrated supplementary information

  1. Supplementary Figure 1 The cXR-tXA model can reproduce up-regulation of Xist in differentiating mESCs.

    Fraction of cells exhibiting mono-allelic (light grey) and bi-allelic Xist expression (dark grey) during differentiation of mESC line TX1072. Experimental data (circles) is shown together with a simulation using the parameter set that best explains the data. The number of cells analyzed is given on top. The data was pooled from 3 independent experiments. Source data

  2. Supplementary Figure 2 Transient bi-allelic up-regulation of Xist in the cXR-tXA model.

    (a) For all parameter sets that reproduced mono-allelic Xist up-regulation in the cXR-tXA model, the maximal fraction of cells with bi-allelic Xist expression observed during the simulation is shown as a function of the the ratio of switch-ON time (first time point, when Xist levels reach 20% of the high steady state) and tXA silencing delay (siltXA). If Xist up-regulation is slow (high Switch-ON time), it will normally occur one allele at a time. Subsequent silencing will shift the system to the bistable regime (cp. Fig. 2e) and thereby lock in the mono-allelic state before Xist up-regulation from the other X chromosome occurs. This results in a low frequency of bi-allelically expressing cells as observed in mice. If Xist up-regulation is rapid and silencing is slow (long silencing delay siltXA), Xist will initially be expressed from two alleles as observed in rabbit embryos. In this scenario the choice of the inactive X can subsequently occur through mono-allelic silencing of tXA and cXR. Alternatively, silencing of both alleles might reverse Xist up-regulation completely as Xist expression is unstable if both tXA alleles are silenced such that the cell can undertake a second attempt to reach the mono-allelic state. (b) Simulation of bi-allelic expression upon reduced Xist-mediated silencing as observed in human embryos, assuming that in the first 4 days of the simulation either silencing and cXR expression is absent (left) or that cXR is silenced partially (dampening), while tXA is unaffected by Xist (right). Boxplots show the percentage of mono- and bi-allelically expressing cells for 100 randomly chosen parameter sets that can reproduce mono-allelic Xist up-regulation (center line, median; box limits, upper and lower quartiles; whiskers, most extreme data points not considered outliers; points, outliers).

  3. Supplementary Figure 3 Bi-allelic up-regulation of Xist is reversible.

    (a) Simulation of doxycycline treatment one day before the onset of differentiation (linked to Fig. 4a–c). Boxplots show the frequency of mono-allelic (left) and bi-allelic Xist expression (right) in dox-treated (grey) and control cells (black) for 100 parameter sets that could reproduce mono-allelic Xist up-regulation. (b) Boxplots show the simulation results for artificial bi-allelic Xist induction as described in Fig. 4e in the main text, using the same parameters sets as in (a). On each box, the central mark indicates the median, and the bottom and top edges of the box indicate the 25th and 75th percentiles, respectively. The whiskers extend to the most extreme data points not considered outliers, and the outliers are plotted individually. (c, d) Bi-allelic Xist up-regulation is artificially induced by treating TX1072dT cells with doxycycline after 48h of differentiation (cp. Fig. 4e). Cells were treated with EdU to assay proliferation through measuring its incorporation into DNA during replication. EdU was labeled fluorescently through Click-it chemistry and Xist was visualized by RNA FISH. (c) The EdU-positive fraction was quantified at the indicated time points within cells expressing Xist mono- (black) and bi-allelically (grey). Mean and s.d. of n=3 independent experiments are shown, in each replicate at least 50 cells were counted per group, except for bi-allelic cells at 48h. * paired two-sample two-sided T-test. Scale bar indicates 5 μm. Source data

  4. Supplementary Figure 4 Transcriptional interference can generate a precise threshold, which is required for reliable mono-allelic Xist up-regulation.

    (a) Steady state Xist levels simulated deterministically (see Fig. 2e) to indicate that a sharp threshold is required between a single (1x) and a double (2x) tXA dose. (b) Maintenance of the XaXi state was simulated by initiating an allele either from the Xa (light green) or from the Xi state (dark green). For an example parameter set (kT=113 h-1, t1/2repr =0.7 h) mean and standard deviation of Xist expression across 100 cells from the chromosomes that initiated as Xa (light green) and Xi (dark green), respectively, is shown for different values of kX for the full Xist-Tsix model (left) and the reduced model without transcriptional interference (right). The vertical lines indicate the kX threshold value, above which >1 (Thlow, red) or >99 (Thhigh, grey) out of 100 cells up-regulate Xist from the Xa. (c) Distribution of the Thhigh-to-Thlow ratio (red and grey in (b)) across all parameter sets of the Full model (grey) and the reduced model without transcriptional interference (black). Since tXA reduces kX 2-fold upon Xist up-regualtion a threshold ratio of <2 is required to allow reliable Xist up-regulation with a double dose (2x) of tXA and stable maintenance of the XaXi state with a single dose (1x). This is only possible in the Full model with transcriptional interference.

  5. Supplementary Figure 5 Transcriptional interference at the XistTsix locus.

    (a–f) TXY and TXY∆A ESCs were treated with doxycycline for 24 hours and nascent transcription of Xist and Tsix (5′ and 3′) was assessed by RNA FISH. (ac) Quantification of 3 biological replicates, where each dot represents the measured signal intensities of a single allele. Grey lines indicate the detection threshold estimated from negative control regions. (df) Box plots of Tsix signal intensity at Xist+ (green) and Xist- alleles (black) in the two cell lines as indicated for the data shown in (a-c); dotted lines indicate the detection threshold (center line, median; box limits, upper and lower quartiles; whiskers, most extreme data points not considered outliers; points, outliers).

  6. Supplementary Figure 6 Also a reduced overlap between Xist and Tsix as in the human locus allows mono-allelic up-regulation of Xist.

    (a, c) Schematic representation of the Xist-Tsix locus architecture in the mouse (a) and the human (c) genome, respectively. (b, d) Distribution of the mean frequency of mono-allelic Xist up-regulation across all parameter sets tested, in simulations assuming the locus architecture shown in (a) and (c), respectively. For details see Supplementary Note 1 (section 3.5). (e, f) Simulation of Xist up-regulation using the model with the human locus architecture in (c) for one example parameter set, showing three individual cells (e) and a population of 100 cells (f). Light and dark green in (e) represent Xist levels expressed from the two X chromosomes, light and dark grey in (f) represent mono- and bi-allelic Xist expression, as indicated.

Supplementary information

  1. Supplementary Information

    Supplementary Figure 1–6 and Supplementary Notes 1–3

  2. Reporting Summary

  3. Supplementary Table 1

    Reagent Summary. Detailed information on all qPCR and pyrosequencing primers, antibodies, Stellaris FISH probes and amplicons assessed by amplicon sequencing.

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