Cellular growth is the result of passive physical constraints and active biological processes. Their interplay leads to the appearance of robust and ubiquitous scaling laws relating linearly cell size, dry mass, and nuclear size. Despite accumulating experimental evidence, their origin is still unclear. Here, we show that these laws can be explained quantitatively by a single model of size regulation based on three simple, yet generic, physical constraints defining altogether the Pump-Leak model. Based on quantitative estimates, we clearly map the Pump-Leak model coarse-grained parameters with the dominant cellular components. We propose that dry mass density homeostasis arises from the scaling between proteins and small osmolytes, mainly amino-acids and ions. Our model predicts this scaling to naturally fail, both at senescence when DNA and RNAs are saturated by RNA polymerases and ribosomes respectively, and at mitotic entry due to the counterion release following histone tail modifications. Based on the same physical laws, we further show that nuclear scaling results from a osmotic balance at the nuclear envelope and a large pool of metabolites, which dilutes chromatin counterions that do not scale during growth.

Data availability

All data analysed during this study are included in the manuscript and supporting file; Source Data files have been provided for Figures 2 and 4.Figure 2 - Source Data 1 to 4 contain the experimental data used to fit and validate our theory in the panels B to E of Figure 2. These data are extracted from Neurohr et al, Cell 2019.Figure 4 - Source Data 1 contains the experimental data used to fit and validate our theory in the panel D of Figure 4. These data are extracted from Finan et al, Ann Biomed Eng., 2009

Article and author information

Author details

  1. Romain Rollin

    PSL Research University, Institut Curie, CNRS UMR168, Paris, France
    For correspondence
    Competing interests
    No competing interests declared.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-6042-234X
  2. Jean-François Joanny

    PSL Research University, Institut Curie, CNRS UMR168, Paris, France
    For correspondence
    Competing interests
    No competing interests declared.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-6966-3222
  3. Pierre Sens

    PSL Research University, Institut Curie, CNRS UMR168, Paris, France
    For correspondence
    Competing interests
    Pierre Sens, Reviewing editor, eLife.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0003-4523-3791


Programme d'investissements d'avenir (ANR-11-LABX-0038)

  • Romain Rollin

Programme d'investissements d'avenir (ANR-10-IDEX-0001-02)

  • Romain Rollin

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Reviewing Editor

  1. Ariel Amir, Harvard University, United States

Publication history

  1. Received: August 5, 2022
  2. Accepted: April 28, 2023
  3. Accepted Manuscript published: May 2, 2023 (version 1)


© 2023, Rollin et al.

This article is distributed under the terms of the Creative Commons Attribution License permitting unrestricted use and redistribution provided that the original author and source are credited.


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  1. Romain Rollin
  2. Jean-François Joanny
  3. Pierre Sens
Physical basis of the cell size scaling laws
eLife 12:e82490.

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