How to assemble a scale-invariant gradient

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Abstract

Intracellular protein gradients serve a variety of functions, such as the establishment of cell polarity or to provide positional information for gene expression in developing embryos. Given that cell size in a population can vary considerably, for the protein gradients to work properly they often have to be scaled to the size of the cell. Here we examine a model of protein gradient formation within a cell that relies on cytoplasmic diffusion and cortical transport of proteins toward a cell pole. We show that the shape of the protein gradient is determined solely by the cell geometry. Furthermore, we show that the length scale over which the protein concentration in the gradient varies is determined by the linear dimensions of the cell, independent of the diffusion constant or the transport speed. This gradient provides scale-invariant positional information within a cell, which can be used for assembly of intracellular structures whose size is scaled to the linear dimensions of the cell, such as the cytokinetic ring and actin cables in budding yeast cells.

Data availability

All data generated or analysed during this study are included in the manuscript and supporting files. Source Code is available at https://github.com/gnick08/cell-gradients.

The following data sets were generated

1. Ghosh S
(2021) How to assemble a scale-invariant gradient
GitHub.

https://github.com/gnick08/cell-gradients

Article and author information

Author details

Arnab Datta

Department of Physics, Brandeis University, Waltham, United States

Competing interests
The authors declare that no competing interests exist.
Sagnik Ghosh

Department of Physics, Brandeis University, Waltham, United States

For correspondence
sagnik@brandeis.edu

Competing interests
The authors declare that no competing interests exist.

"This ORCID iD identifies the author of this article:" 0000-0001-7174-8479
Jane Kondev

Department of Physics, Brandeis University, Waltham, United States

Competing interests
The authors declare that no competing interests exist.

"This ORCID iD identifies the author of this article:" 0000-0001-7522-7144

Funding

National Science Foundation (DMR-1610737)

Arnab Datta
Sagnik Ghosh
Jane Kondev

Brandeis University (MRSEC - DMR-548 2011846)

Arnab Datta
Sagnik Ghosh
Jane Kondev

Simons Foundation

Arnab Datta
Sagnik Ghosh
Jane Kondev

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

Copyright

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.