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Diffusion as a Ruler: Modeling Kinesin Diffusion as a Length Sensor for Intraflagellar Transport

Hendel, Nathan L. and Thomson, Matthew and Marshall, Wallace F. (2018) Diffusion as a Ruler: Modeling Kinesin Diffusion as a Length Sensor for Intraflagellar Transport. Biophysical Journal, 114 (3). pp. 663-674. ISSN 0006-3495. PMCID PMC5985012.

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An important question in cell biology is whether cells are able to measure size, either whole cell size or organelle size. Perhaps cells have an internal chemical representation of size that can be used to precisely regulate growth, or perhaps size is just an accident that emerges due to constraint of nutrients. The eukaryotic flagellum is an ideal model for studying size sensing and control because its linear geometry makes it essentially one-dimensional, greatly simplifying mathematical modeling. The assembly of flagella is regulated by intraflagellar transport (IFT), in which kinesin motors carry cargo adaptors for flagellar proteins along the flagellum and then deposit them at the tip, lengthening the flagellum. The rate at which IFT motors are recruited to begin transport into the flagellum is anticorrelated with the flagellar length, implying some kind of communication between the base and the tip and possibly indicating that cells contain some mechanism for measuring flagellar length. Although it is possible to imagine many complex scenarios in which additional signaling molecules sense length and carry feedback signals to the cell body to control IFT, might the already-known components of the IFT system be sufficient to allow length dependence of IFT? Here we investigate a model in which the anterograde kinesin motors unbind after cargo delivery, diffuse back to the base, and are subsequently reused to power entry of new IFT trains into the flagellum. By mathematically modeling and simulating such a system, we are able to show that the diffusion time of the motors can in principle be sufficient to serve as a proxy for length measurement. We found that the diffusion model can not only achieve a stable steady-state length without the addition of any other signaling molecules or pathways, but also is able to produce the anticorrelation between length and IFT recruitment rate that has been observed in quantitative imaging studies.

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Additional Information:© 2017 Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( Submitted June 29, 2017, and accepted for publication November 29, 2017. We thank Greyson Lewis for help with the math and derivations and Ahmet Yildiz for sharing results ahead of publication. This work was supported by National Institutes of Health (NIH) grant GM097017. Author Contributions: N.L.H. wrote the simulations. N.L.H., M.T., and W.F.M. developed ideas and worked out math. N.L.H. and W.F.M. wrote the manuscript.
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Issue or Number:3
PubMed Central ID:PMC5985012
Record Number:CaltechAUTHORS:20180212-080247041
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Official Citation:Nathan L. Hendel, Matthew Thomson, Wallace F. Marshall, Diffusion as a Ruler: Modeling Kinesin Diffusion as a Length Sensor for Intraflagellar Transport, Biophysical Journal, Volume 114, Issue 3, 6 February 2018, Pages 663-674, ISSN 0006-3495, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:84779
Deposited By: Ruth Sustaita
Deposited On:13 Feb 2018 18:42
Last Modified:23 Dec 2020 22:19

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