Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Constitutive splicing and economies of scale in gene expression

Abstract

In eukaryotic cells, many introns are constitutively, rather than alternatively, spliced and therefore do not contribute to isoform diversification. It has remained unclear what functional roles such constitutive splicing provides. To explore this issue, we asked how splicing affects the efficiency with which individual pre-messenger RNA transcripts are productively processed across different gene expression levels. We developed a quantitative single-molecule fluorescence in situ hybridization-based method to quantify splicing efficiency at transcription active sites in single cells. We found that both natural and synthetic genes in mouse and human cells exhibited an unexpected ‘economy of scale’ behavior in which splicing efficiency increased with transcription rate. Correlations between splicing efficiency and spatial proximity to nuclear speckles could explain this counterintuitive behavior. Functionally, economy of scale splicing represents a non-linear filter that amplifies the expression of genes when they are more strongly transcribed. These results indicate that constitutive splicing plays an active functional role in modulating gene expression.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Splicing efficiency requires single-cell measurement.
Fig. 2: Experimental method for quantifying splicing efficiency at the TAS in individual cells.
Fig. 3: Quantification of single-transcript intensity units in multiple channels.
Fig. 4: Splicing efficiency increases with transcript level, exhibiting ‘economy of scale’ behavior, for the two tested genes, Gli1 induced by Shh in 3T3 cells and the Tet-off minigene RG6 induced by dox in HEK293 cells.
Fig. 5: Phenomenological model for ‘economy of scale’ behavior.
Fig. 6: Splicing can act as a gene expression ‘filter’.

Similar content being viewed by others

Data availability

Source data for Figs. 2, 3d,e, 4 and 5d are available online. All other original data, Matlab code, DNA constructs and cell lines are available upon request.

References

  1. Wang, E. T. et al. Alternative isoform regulation in human tissue transcriptomes. Nature 456, 470–476 (2008).

    Article  CAS  Google Scholar 

  2. Papasaikas, P. & Valcárcel, J. Evolution. Splicing in 4D. Science 338, 1547–1548 (2012).

    Article  Google Scholar 

  3. Black, D. L. Mechanisms of alternative pre-messenger RNA splicing. Annu. Rev. Biochem. 72, 291–336 (2003).

    Article  CAS  Google Scholar 

  4. Barbosa-Morais, N. L. et al. The evolutionary landscape of alternative splicing in vertebrate species. Science 338, 1587–1593 (2012).

    Article  CAS  Google Scholar 

  5. Kalsotra, A. & Cooper, T. A. Functional consequences of developmentally regulated alternative splicing. Nat. Rev. Genet. 12, 715–729 (2011).

    Article  CAS  Google Scholar 

  6. Nilsen, T. W. & Graveley, B. R. Expansion of the eukaryotic proteome by alternative splicing. Nature 463, 457–463 (2010).

    Article  CAS  Google Scholar 

  7. Chen, F.-C., Wang, S.-S., Chen, C.-J., Li, W.-H. & Chuang, T.-J. Alternatively and constitutively spliced exons are subject to different evolutionary forces. Mol. Biol. Evol. 23, 675–682 (2006).

    Article  Google Scholar 

  8. Brinster, R. L., Allen, J. M., Behringer, R. R., Gelinas, R. E. & Palmiter, R. D. Introns increase transcriptional efficiency in transgenic mice. Proc. Natl Acad. Sci. USA 85, 836–840 (1988).

    Article  CAS  Google Scholar 

  9. Westholm, J. O. & Lai, E. C. Mirtrons: microRNA biogenesis via splicing. Biochimie 93, 1897–1904 (2011).

    Article  CAS  Google Scholar 

  10. Filipowicz, W. & Pogacić, V. Biogenesis of small nucleolar ribonucleoproteins. Curr. Opin. Cell Biol. 14, 319–327 (2002).

    Article  CAS  Google Scholar 

  11. Rearick, D. et al. Critical association of ncRNA with introns. Nucleic Acids Res. 39, 2357–2366 (2011).

    Article  CAS  Google Scholar 

  12. Gilbert, W. Why genes in pieces? Nature 271, 501 (1978).

    Article  CAS  Google Scholar 

  13. Lev-Maor, G. et al. The ‘alternative’ choice of constitutive exons throughout evolution. PLoS Genet. 3, e203 (2007).

    Article  Google Scholar 

  14. Bentley, D. L. Coupling mRNA processing with transcription in time and space. Nat. Rev. Genet. 15, 163–175 (2014).

    Article  CAS  Google Scholar 

  15. Das, R. et al. SR proteins function in coupling RNAP II transcription to pre-mRNA splicing. Mol. Cell 26, 867–881 (2007).

    Article  CAS  Google Scholar 

  16. Rosonina, E. & Blencowe, B. J. Gene expression: the close coupling of transcription and splicing. Curr. Biol. 12, R319–R321 (2002).

    Article  CAS  Google Scholar 

  17. Green, M. R. Biochemical mechanisms of constitutive and regulated pre-mRNA splicing. Annu. Rev. Cell Biol. 7, 559–599 (1991).

    Article  CAS  Google Scholar 

  18. Reed, R. Mechanisms of fidelity in pre-mRNA splicing. Curr. Opin. Cell Biol. 12, 340–345 (2000).

    Article  CAS  Google Scholar 

  19. Houseley, J. & Tollervey, D. The many pathways of RNA degradation. Cell 136, 763–776 (2009).

    Article  CAS  Google Scholar 

  20. Boutz, P. L., Bhutkar, A. & Sharp, P. A. Detained introns are a novel, widespread class of post-transcriptionally spliced introns. Genes Dev. 29, 63–80 (2015).

    Article  Google Scholar 

  21. Khodor, Y. L., Menet, J. S., Tolan, M. & Rosbash, M. Cotranscriptional splicing efficiency differs dramatically between Drosophila and mouse. RNA 18, 2174–2186 (2012).

    Article  CAS  Google Scholar 

  22. Khodor, Y. L. et al. Nascent-seq indicates widespread cotranscriptional pre-mRNA splicing in Drosophila. Genes Dev. 25, 2502–2512 (2011).

    Article  CAS  Google Scholar 

  23. Carrillo Oesterreich, F., Preibisch, S. & Neugebauer, K. M. Global analysis of nascent RNA reveals transcriptional pausing in terminal exons. Mol. Cell 40, 571–581 (2010).

    Article  CAS  Google Scholar 

  24. Lipp, J. J., Marvin, M. C., Shokat, K. M. & Guthrie, C. SR protein kinases promote splicing of nonconsensus introns. Nat. Struct. Mol. Biol. 22, 611–617 (2015).

    Article  CAS  Google Scholar 

  25. Katz, Y., Wang, E. T., Airoldi, E. M. & Burge, C. B. Analysis and design of RNA sequencing experiments for identifying isoform regulation. Nat. Methods 7, 1009–1015 (2010).

    Article  CAS  Google Scholar 

  26. Neugebauer, K. M. On the importance of being co-transcriptional. J. Cell Sci. 115, 3865–3871 (2002).

    Article  CAS  Google Scholar 

  27. Churchman, L. S. & Weissman, J. S. Nascent transcript sequencing visualizes transcription at nucleotide resolution. Nature 469, 368–373 (2011).

    Article  CAS  Google Scholar 

  28. Herzel, L., Straube, K. & Neugebauer, K. M. Long-read sequencing of nascent RNA reveals coupling among RNA processing events. Genome Res. 28, 1008–1019 (2018).

    Article  CAS  Google Scholar 

  29. Raj, A. & van Oudenaarden, A. Nature, nurture, or chance: stochastic gene expression and its consequences. Cell 135, 216–226 (2008).

    Article  CAS  Google Scholar 

  30. Waks, Z., Klein, A. M. & Silver, P. A. Cell-to-cell variability of alternative RNA splicing. Mol. Syst. Biol. 7, 506 (2011).

    Article  Google Scholar 

  31. Larson, D. R. et al. Direct observation of frequency modulated transcription in single cells using light activation. eLife 2, e00750 (2013).

    Article  Google Scholar 

  32. Raj, A., Peskin, C. S., Tranchina, D., Vargas, D. Y. & Tyagi, S. Stochastic mRNA synthesis in mammalian cells. PLoS Biol. 4, e309 (2006).

    Article  Google Scholar 

  33. Vargas, D. Y. et al. Single-molecule imaging of transcriptionally coupled and uncoupled splicing. Cell 147, 1054–1065 (2011).

    Article  CAS  Google Scholar 

  34. Martin, R. M., Rino, J., Carvalho, C., Kirchhausen, T. & Carmo-Fonseca, M. Live-cell visualization of pre-mRNA splicing with single-molecule sensitivity. Cell Rep. 4, 1144–1155 (2013).

    Article  CAS  Google Scholar 

  35. Coulon, A. et al. Kinetic competition during the transcription cycle results in stochastic RNA processing. eLife 3, e03939 (2014).

    Article  Google Scholar 

  36. Raj, A., van den Bogaard, P., Rifkin, S. A., van Oudenaarden, A. & Tyagi, S. Imaging individual mRNA molecules using multiple singly labeled probes. Nat. Methods 5, 877–879 (2008).

    Article  CAS  Google Scholar 

  37. Zenklusen, D., Larson, D. R. & Singer, R. H. Single-RNA counting reveals alternative modes of gene expression in yeast. Nat. Struct. Mol. Biol. 15, 1263–1271 (2008).

    Article  CAS  Google Scholar 

  38. Femino, A. M., Fay, F. S., Fogarty, K. & Singer, R. H. Visualization of single RNA transcripts in situ. Science 280, 585–590 (1998).

    Article  CAS  Google Scholar 

  39. Stetson, P. B. DAOPHOT: a computer program for crowded-field stellar photometry. Publ. Astron. Soc. Pac. 99, 191–222 (1987).

    Article  Google Scholar 

  40. Orengo, J. P., Bundman, D. & Cooper, T. A. A bichromatic fluorescent reporter for cell-based screens of alternative splicing. Nucleic Acids Res. 34, e148 (2006).

    Article  Google Scholar 

  41. Munding, E. M., Shiue, L., Katzman, S., Donohue, J. P. & Ares, M. Jr. Competition between pre-mRNAs for the splicing machinery drives global regulation of splicing. Mol. Cell 51, 338–348 (2013).

    Article  CAS  Google Scholar 

  42. Li, P. et al. Morphogen gradient reconstitution reveals Hedgehog pathway design principles. Science 360, 543–548 (2018).

    Article  CAS  Google Scholar 

  43. Elowitz, M. B., Levine, A. J., Siggia, E. D. & Swain, P. S. Stochastic gene expression in a single cell. Science 297, 1183–1186 (2002).

    Article  CAS  Google Scholar 

  44. Park, T. et al. Bayesian estimation of hardness ratios: modeling and computations. Astrophys. J. 652, 610–628 (2006).

    Article  CAS  Google Scholar 

  45. Coath, C. D., Steele, R. C. J. & Fred Lunnon, W. Statistical bias in isotope ratios. J. Anal. Spectrom. 28, 52–58 (2013).

    Article  CAS  Google Scholar 

  46. Lamond, A. I. & Spector, D. L. Nuclear speckles: a model for nuclear organelles. Nat. Rev. Mol. Cell Biol. 4, 605–612 (2003).

    Article  CAS  Google Scholar 

  47. Misteli, T., Cáceres, J. F. & Spector, D. L. The dynamics of a pre-mRNA splicing factor in living cells. Nature 387, 523–527 (1997).

    Article  CAS  Google Scholar 

  48. Phair, R. D. & Misteli, T. High mobility of proteins in the mammalian cell nucleus. Nature 404, 604–609 (2000).

    Article  CAS  Google Scholar 

  49. Quinodoz, S. A. et al. Higher-order inter-chromosomal hubs shape 3D genome organization in the nucleus. Cell 174, 744–757.e24 (2018).

    Article  CAS  Google Scholar 

  50. Wahl, M. C., Will, C. L. & Lührmann, R. The spliceosome: design principles of a dynamic RNP machine. Cell 136, 701–718 (2009).

    Article  CAS  Google Scholar 

  51. Luco, R. F., Allo, M., Schor, I. E., Kornblihtt, A. R. & Misteli, T. Epigenetics in alternative pre-mRNA splicing. Cell 144, 16–26 (2011).

    Article  CAS  Google Scholar 

  52. Colgan, D. F. & Manley, J. L. Mechanism and regulation of mRNA polyadenylation. Genes Dev. 11, 2755–2766 (1997).

    Article  CAS  Google Scholar 

  53. Shatkin, A. J. & Manley, J. L. The ends of the affair: capping and polyadenylation. Nat. Struct. Biol. 7, 838–842 (2000).

    Article  CAS  Google Scholar 

  54. Jensen, T. H., Jacquier, A. & Libri, D. Dealing with pervasive transcription. Mol. Cell 52, 473–484 (2013).

    Article  CAS  Google Scholar 

  55. Eldar, A. & Elowitz, M. B. Functional roles for noise in genetic circuits. Nature 467, 167–173 (2010).

    Article  CAS  Google Scholar 

  56. Losick, R. & Desplan, C. Stochasticity and cell fate. Science 320, 65–68 (2008).

    Article  CAS  Google Scholar 

  57. Beyer, A. L. & Osheim, Y. N. Splice site selection, rate of splicing, and alternative splicing on nascent transcripts. Genes Dev. 2, 754–765 (1988).

    Article  CAS  Google Scholar 

  58. Rosenberg, A. B., Patwardhan, R. P., Shendure, J. & Seelig, G. Learning the sequence determinants of alternative splicing from millions of random sequences. Cell 163, 698–711 (2015).

    Article  CAS  Google Scholar 

  59. Wong, M. S., Kinney, J. B. & Krainer, A. R. Quantitative activity profile and context dependence of all human 5′ splice sites. Mol. Cell 71, 1012–1026.e3 (2018).

    Article  CAS  Google Scholar 

  60. Wieringa, B., Hofer, E. & Weissmann, C. A minimal intron length but no specific internal sequence is required for splicing the large rabbit beta-globin intron. Cell 37, 915–925 (1984).

    Article  CAS  Google Scholar 

  61. Graveley, B. R., Hertel, K. J. & Maniatis, T. A systematic analysis of the factors that determine the strength of pre‐mRNA splicing enhancers. EMBO J. 17, 6747–6756 (1998).

    Article  CAS  Google Scholar 

  62. Girard, C. et al. Post-transcriptional spliceosomes are retained in nuclear speckles until splicing completion. Nat. Commun. 3, 994 (2012).

    Article  Google Scholar 

  63. Lubeck, E., Coskun, A. F., Zhiyentayev, T., Ahmad, M. & Cai, L. Single-cell in situ RNA profiling by sequential hybridization. Nat. Methods 11, 360–361 (2014).

    Article  CAS  Google Scholar 

  64. Shah, S., Lubeck, E., Zhou, W. & Cai, L. In situ transcription profiling of single cells reveals spatial organization of cells in the mouse hippocampus. Neuron 92, 342–357 (2016).

    Article  CAS  Google Scholar 

  65. Zahler, A. M., Lane, W. S., Stolk, J. A. & Roth, M. B. SR proteins: a conserved family of pre-mRNA splicing factors. Genes Dev. 6, 837–847 (1992).

    Article  CAS  Google Scholar 

  66. Engreitz, J. M. et al. Local regulation of gene expression by lncRNA promoters, transcription and splicing. Nature 539, 452–455 (2016).

    Article  CAS  Google Scholar 

  67. La Manno, G. et al. RNA velocity of single cells. Nature 560, 494–498 (2018).

    Article  Google Scholar 

  68. Chen, K. H., Boettiger, A. N., Moffitt, J. R., Wang, S. & Zhuang, X. RNA imaging. Spatially resolved, highly multiplexed RNA profiling in single cells. Science 348, aaa6090 (2015).

    Article  Google Scholar 

Download references

Acknowledgements

We thank T. Cooper for DNA constructs of minigene RG6, P. Li for providing Gli1 inducible protocol, Z. Singer and Y. Antebi for technical assistance, M. Guttman, C. Su, H. Klumpe, M. Budde and L. Bintu for critical feedbacks on the manuscript. We also thank M. Guttman, G. Seelig, D. Black, D. Baltimore, M. Moore, J.G. Ojalvo and N. Wingreen for discussion and feedback on the project. The work was funded by a Fellowship from the Schlumberger Foundation, by the Gordon and Betty Moore Foundation through Grant GBMF2809 to the Caltech Programmable Molecular Technology Initiative and the Institute for Collaborative Biotechnologies through grant W911NF-09-0001 from the U.S. Army Research Office. The content of the information does not necessarily reflect the position or the policy of the Government, and no official endorsement should be inferred. M.B.E. is a Howard Hughes Medical Institute Investigator.

Author information

Authors and Affiliations

Authors

Contributions

F.D. conceived of the project. F.D. and M.B.E. designed experiments. F.D. performed experiments, analyzed data and did mathematical modeling. F.D. and M.B.E. wrote the manuscript.

Corresponding author

Correspondence to Michael B. Elowitz.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Integrated supplementary information

Supplementary Figure 1 Detailed workflow for quantifying the number of transcripts at the TAS.

(a) The expanded version of Fig. 2b. (b) The z-axis max projection of confocal images represents the intensity of the fluorescent FISH dots. (c) We fit the dot intensity by a fit-subtraction loop. (1) Fit the dot with a 2D Gaussian intensity distribution; (2) Subtract the fitting from the original image and obtain a new image; (3) Fit the new image with another 2D Gaussian; (4) Subtract this new fitting from the new images. This fit-subtraction loop continues until the intensity of the new 2D Gaussian fitting falls below 10% of the first integrated dot intensity. Finally, the original image is fit by the sequential 2D Gaussian fit together, whose positions are constrained. (d) Analysis of dots co-occurring in multiple channels provides an alternative estimate of the single-molecule fluorescence unit. Here, each histogram includes only dots that appear in two or more channels. Poisson fitting of these intensity distributions generates similar single-molecule fluorescence units as in Fig. 3b. Color is labeled as in Fig. 2a.

Supplementary Figure 2 Splicing efficiency increases with transcription level for RG6 genes induced by dox in HEK293 cells.

Each dot is the measurement of a single TAS. Colors and labels are as in Fig. 4.

Supplementary Figure 3 DNA-FISH verifies the ‘economy of scale’ observation for Gli1.

(a) We first performed RNA-FISH, labeling intron, Exon1, and Exon2, and then ran DNA-FISH in the same cells (see SI Materials and Methods for details). In the example image, DNA-FISH identified two genomic loci, while only one has co-localized dots in the RNA-FISH images. These results indicate that one locus (circled in white) is not active, while the other one (circled in blue) is active. (b) ‘Economy of scale’ observation based only on RNA-FISH images (n = 1430). (c) The ‘economy of scale’ effect remains when considering only the TASs overlapping with DNA-FISH dots across three fluorescent channels (n = 92). Note that we have significantly fewer measurements in this plot, due to the technical difficulty of combining DNA-FISH with RNA-FISH. Data are representative of two independent experiments.

Supplementary Figure 4 Hardness of ratio correction.

(a) False-positive ‘economy of scale’ for both splicing efficiency and control measurements, due to the putative correlation between denominator and numerator, that is 1 – NI/NE1 versus NE1. (b) Mathematical methods can correct this hardness of ratio with a = 4.3. The control measurements are, as expected, constant, while splicing efficiency still maintains the ‘economy of scale’ trend. See SI text for more details.

Supplementary Figure 5

(a) Measurement of the distance between a TAS and the nearest speckle. We first defined a set of fixed distances from the TAS. Specifically, we defined distance in units of pixels. Each circle (center panel) represents a defined distance from the TAS. Then, we measured the maximum fluorescent intensity at fixed distances. Finally, we plotted the maximum intensity versus the distance and found the minimum distance where the intensity reaches a pre-set threshold (right panel). (b) Raw data (n = 2421) for Fig. 5d. Error bars represent standard error of the mean. (c) The spatial distribution of splicing factors positively correlates with nascent splicing targets in HEK293 cells. Top: Splicing factors in the nucleus by citrine labeling Serine/arginine-rich splicing factor 1 (SRSF1); Bottom: RNA from transient transfection in the nucleus by FISHing intron. The cells have stably integrated citrine labelled SRSF1 gene and transiently transfected RNA (a synthetic SRSF1 targeted transcript, see Materials and Methods). The transient transfection generates multiple transcription active sites in the nucleus. As shown in the figure, the activities of these TASs are positively correlated with the proximity to speckles: every TAS is co-localized with a speckle and higher expressed TASs are with higher amount of splicing factors. Notice that some speckles do not have correlated TAS. This is because there are other TASs in the cell apart from the transiently transfected RNAs.

Supplementary Figure 6 A phenomenological mathematical model of the ‘economy of scale’ behavior.

(a) Purple curve represents classical Michaelis-Menten model with uniform enzyme accessibility (that is constant kon). Orange curve represents the modified model in which kon is proportional to the available pre-mRNA concentration. For the classical model (purple curve), the splicing efficiency is close to 1 at low transcription levels (box 1), where enzyme levels are not limiting, and then decline at higher transcription levels (box 3) due to saturation. By comparison, for the modified model (orange curve), the splicing efficiency is close to 0 at low expression levels (box 2), where pre-mRNA concentrations are too low to recruit splicing machinery. As the transcription level increases (box 4), enzyme accessibility increases, and splicing efficiency increases to 1. This represents the observed ‘economy of scale’ effect. Further increases of transcription level eventually saturate the splicing machinery, reducing splicing efficiency (box 5). (b) ‘Economy of scale’ behavior is robust across different residence time (that is different degradation rate of unspliced and spliced isoforms, gu and gm respectively). Parameter values used here: ku = 0.1, km = 0.12, rD = 100, E0 = 1000 and K = 0.5. (c) ‘Economy of scale’ occurs across a wide range of parameters. The color scale, Δefficiency/Δb, represents the slope of splicing efficiency versus transcription level evaluated between b = 1 and b = 10. Pink to yellow (right) shows positive slope, that is ‘economy of scale’; purple to blue (left) shows negative slope, that is ‘diminishing returns.’

Supplementary Figure 7 The induction of promoter primarily affects transcriptional burst size.

The synthetic mini-gene RG6 under Tet-on CMV was induced by 32 ng/ml (left panel) and 100 ng/ml (right panel) 4-Epidoxycycline (an analogue of Doxycycline). The distribution of mRNA expression (that is the number of smFISH dots) was fit by a previous published stochastic model (Raj, A., et al., Nat. Methods 5, 877–879 2008).

Supplementary Figure 8 Examples of different TASs.

For the TAS in the bottom cell, transcripts are spreading out from the TAS, while for the TAS in the top cell, no obvious transcripts are seen in the neighborhood. Note that the two TASs have similar intensity (that is similar transcription level).

Supplementary Figure 9

(a) Ratio of the mean underestimates splicing efficiency. We calculated 1 - <Intron>/<Exon> (that is ratio of the mean) in black, as a comparison to the original 1 - <Intron/Exon> (that is mean of the ratio), same color as in Fig. 4. Averaging over heterogeneous cells mildly distorts splicing efficiency (as illustrated in Fig. 1), reducing the apparent magnitude of the ‘economy of scale’ effect. (b) Population-based measurements show the ‘economy of scale’ trend. We used qPCR to quantify the amounts of unspliced and spliced transcripts for RG6 (see Materials and Methods). Because qPCR does not provide absolute transcript abundances, we analyzed the ratio of unspliced to spliced abundances (each relative to a control gene) as a function of the relative abundance of spliced transcripts. Multiple curves represent repeats using different two different cell clones and multiple primer sets.

Supplementary Figure 10 Examples of co-localization of Exon1 and Exon2 probes.

Top: Unprocessed images of both channels. Middle: all classified dots that co-localize in both channels are marked with white boxes. Bottom: Dots that were detected in only a single channel. Overall, the fraction of all dots that were co-localized between channels is ~ 90%.

Supplementary information

Supplementary Information

Supplementary Figs 1–10, Supplementary Tables 1 and 2, Supplementary Notes 1–4

Reporting Summary

Source data

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ding, F., Elowitz, M.B. Constitutive splicing and economies of scale in gene expression. Nat Struct Mol Biol 26, 424–432 (2019). https://doi.org/10.1038/s41594-019-0226-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41594-019-0226-x

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing