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Dynamics extracted from fixed cells reveal feedback linking cell growth to cell cycle


Biologists have long been concerned about what constrains variation in cell size, but progress in this field has been slow and stymied by experimental limitations1. Here we describe a new method, ergodic rate analysis (ERA), that uses single-cell measurements of fixed steady-state populations to accurately infer the rates of molecular events, including rates of cell growth. ERA exploits the fact that the number of cells in a particular state is related to the average transit time through that state2. With this method, it is possible to calculate full time trajectories of any feature that can be labelled in fixed cells, for example levels of phosphoproteins or total cellular mass. Using ERA we find evidence for a size-discriminatory process at the G1/S transition that acts to decrease cell-to-cell size variation.

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Figure 1: Dynamic information from static data using ERA.
Figure 2: Calculation of growth as a function of cell cycle progression using ERA.
Figure 3: Rate of cell growth as a function of size and cell cycle.
Figure 4: Effects of drug treatments on size variability at G1 exit.


  1. 1

    Mitchison, J. M. Growth during the cell cycle. Int. Rev. Cytol. 226, 165–258 (2003)

    CAS  Article  Google Scholar 

  2. 2

    Deen, W. M. Analysis of Transport Phenomena 2nd edn (Oxford University Press, 2012)

    Google Scholar 

  3. 3

    Sakaue-Sawano, A. et al. Visualizing spatiotemporal dynamics of multicellular cell-cycle progression. Cell 132, 487–498 (2008)

    CAS  Article  Google Scholar 

  4. 4

    Mitchison, J. M. The Biology of the Cell Cycle 128 (University Press, 1971)

    Google Scholar 

  5. 5

    Popescu, G. et al. Optical imaging of cell mass and growth dynamics. Am. J. Physiol. Cell Physiol. 295, C538–C544 (2008)

    CAS  Article  Google Scholar 

  6. 6

    Mir, M. et al. Optical measurement of cycle-dependent cell growth. Proc. Natl Acad. Sci. USA 108, 13124–13129 (2011)

    ADS  CAS  Article  Google Scholar 

  7. 7

    Son, S. et al. Direct observation of mammalian cell growth and size regulation. Nature Methods 9, 910–912 (2012)

    CAS  Article  Google Scholar 

  8. 8

    Killander, D. & Zetterberg, A. A quantitative cytochemical investigation of the relationship between cell mass and initiation of DNA synthesis in mouse fibroblasts in vitro. Exp. Cell Res. 40, 12–20 (1965)

    CAS  Article  Google Scholar 

  9. 9

    Hendrix, R. W. & Zwaan, J. Cell shape regulation and cell cycle in embryonic lens cells. Nature 247, 145–147 (1974)

    ADS  CAS  Article  Google Scholar 

  10. 10

    Tzur, A., Kafri, R., LeBleu, V. S., Lahav, G. & Kirschner, M. W. Cell growth and size homeostasis in proliferating animal cells. Science 325, 167–171 (2009)

    ADS  CAS  Article  Google Scholar 

  11. 11

    Jacobberger, J. W., Avva, J., Sreenath, S. N., Weis, M. C. & Stefan, T. Dynamic epitope expression from static cytometry data: principles and reproducibility. PLoS ONE 7, e30870 (2012)

    ADS  CAS  Article  Google Scholar 

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We thank A. Klein, Y. Merbl, S. Tal and J. Toettcher for consistent and valuable insights at the beginning of and throughout this project. We thank J. Waters and the staff of The Nikon Imaging Center at Harvard Medical School for help and support. We especially thank R. Ward for her critique of the paper and the National Institute of General Medical Sciences (GM26875) for support of this work.

Author information




R.K. and J.L. developed the method (ERA) for extracting dynamic information and calculating feedback spectra from fixed populations, designed algorithms, wrote all image-processing software and analysed data. R.K. designed all experiments and wrote the manuscript. J.L. contributed significantly to all conceptual challenges and to writing the manuscript. M.B.G. contributed conceptually on levels of the study, made many important measurements and calculations and contributed to the writing of the manuscript. S.O. provided interferometry-derived cell mass measurements. G.L. and M.W.K. contributed to the formulation of the problem, development of the ideas and the writing of the manuscript.

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Correspondence to Marc W. Kirschner.

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The authors declare no competing financial interests.

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This file contains Supplementary Text and Data, which includes Supplementary Figures 1-22 and additional references (see Contents for more details). (PDF 5477 kb)

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Kafri, R., Levy, J., Ginzberg, M. et al. Dynamics extracted from fixed cells reveal feedback linking cell growth to cell cycle. Nature 494, 480–483 (2013).

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