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Open Access Publications from the University of California

A Mathematical Model of Diffusion as a Length Sensor in Intraflagellar Transport

  • Author(s): Hendel, Nathan Lawrence
  • Advisor(s): Marshall, Wallace F
  • et al.

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 just 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 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. An analytical formulation of the model predicts the effect that physical parameters have on length, motivating experiments that can validate or disprove the model.

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