1. Physics of Living Systems
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Diffusion vs direct transport in the precision of morphogen readout

  1. Sean Fancher  Is a corresponding author
  2. Andrew Mugler  Is a corresponding author
  1. University of Pennsylvania, United States
  2. Purdue University, United States
Research Article
  • Cited 2
  • Views 716
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Cite this article as: eLife 2020;9:e58981 doi: 10.7554/eLife.58981


Morphogen profiles allow cells to determine their position within a developing organism, but not all morphogen profiles form by the same mechanism. Here we derive fundamental limits to the precision of morphogen concentration sensing for two canonical mechanisms: the diffusion of morphogen through extracellular space and the direct transport of morphogen from source cell to target cell, e.g., via cytonemes. We find that direct transport establishes a morphogen profile without adding noise in the process. Despite this advantage, we find that for sufficiently large values of profile length, the diffusion mechanism is many times more precise due to a higher refresh rate of morphogen molecules. We predict a profile lengthscale below which direct transport is more precise, and above which diffusion is more precise. This prediction is supported by data from a wide variety of morphogens in developing Drosophila and zebrafish.

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All data used in this study is simulated via computational methods outlined in the manuscript and appendices.

Article and author information

Author details

  1. Sean Fancher

    Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, United States
    For correspondence
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-8701-192X
  2. Andrew Mugler

    Department of Physics and Astronomy, Purdue University, West Lafayette, United States
    For correspondence
    Competing interests
    The authors declare that no competing interests exist.


Simons Foundation (376198)

  • Sean Fancher
  • Andrew Mugler

Simons Foundation (568888)

  • Sean Fancher

National Science Foundation (PHY-1945018)

  • Andrew Mugler

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

Reviewing Editor

  1. Raymond E Goldstein, University of Cambridge, United Kingdom

Publication history

  1. Received: May 15, 2020
  2. Accepted: October 13, 2020
  3. Accepted Manuscript published: October 14, 2020 (version 1)
  4. Version of Record published: November 4, 2020 (version 2)
  5. Version of Record updated: November 6, 2020 (version 3)


© 2020, Fancher & Mugler

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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Further reading

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    1. Developmental Biology
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    Yonghyun Song, Changbong Hyeon
    Research Article Updated

    Spatial boundaries formed during animal development originate from the pre-patterning of tissues by signaling molecules, called morphogens. The accuracy of boundary location is limited by the fluctuations of morphogen concentration that thresholds the expression level of target gene. Producing more morphogen molecules, which gives rise to smaller relative fluctuations, would better serve to shape more precise target boundaries; however, it incurs more thermodynamic cost. In the classical diffusion-depletion model of morphogen profile formation, the morphogen molecules synthesized from a local source display an exponentially decaying concentration profile with a characteristic length λ. Our theory suggests that in order to attain a precise profile with the minimal cost, λ should be roughly half the distance to the target boundary position from the source. Remarkably, we find that the profiles of morphogens that pattern the Drosophila embryo and wing imaginal disk are formed with nearly optimal λ. Our finding underscores the cost-effectiveness of precise morphogen profile formation in Drosophila development.