Brandeis physicists propose theoretical model for how cells form consistent gradients

How does the cell, the building block of all living organisms, “know” how to arrange its internal parts or how to cells know how to differentiate into an overall body plan?

Three researchers from the Brandeis University physics department have worked out a hypothesis that they think can shed important light on this long standing question in biology. Their study, titled “How to assemble a scale-invariant gradient,” appears March 21 in the online journal eLife.

Their approach draws on the physical concept of gradient, a variation over space of the concentration or intensity of some substance or force.

As the authors note, “The living cell is not a well-mixed bag of chemicals. Different parts of the cell have different chemical composition and these spatial inhomogeneities are critical to life.”

Protein gradients

Not just embryos but much smaller cells like budding yeast, for example, exhibit varying patterns and concentrations of proteins at different locations. 

When cells divide they typically form a structure known as a cytokinetic ring, a collection of proteins that assemble at a specific location. In symmetrically dividing cells this ring assembles at the middle of the cell. But “how does the cell ‘know’ where its middle is?” the authors ask. 

A remarkable recent discovery shows that yeast cells of different sizes assemble their cytokinetic rings in such a way that the diameter of the rings scales with the diameter of the cell. 

This feature of “scale invariance” suggested to the physicists examining the problem to think of it as an engineering problem in which the cell finds some way to set up a coordinate system that specifies positional information. The key, they thought, must be the varying gradients of chemical concentrations within the cell. 

Bicoid protein in fruit flies

Studies over recent decades have shown how intracellular gradients are involved in the development of the fruit fly embryo. In the fruit fly, the variations in the concentration of the so-called Bicoid protein at different parts of the embryo provide the cue for cell growth. The gradient comes about by the simple act of degradation of the protein with distance from its point of origin. The Bicoid protein forms at the anterior of the embryo and diffuses through the cell, degrading with time and distance. 

In other types of organisms, different proteins may carry out this coordinate-setting function which enables the parts of the cell to “know” where to form. 

A general principle for "how to assemble a scale-invariant gradient"

Here, the authors develop a theoretical model where the shape of the gradient is determined solely by the cell’s shape. Their model may help us better understand different biological gradient formation and scaling. In this model, the “protein gradient formation within a cell [...] relies on cytoplasmic diffusion and cortical transport of proteins toward a cell pole.”

It is the biophysical properties of having “diffusion of proteins in the cytoplasm coupled to polar transport along the cell surface, which can be driven by motor transport,” that allows for the scale-invariant gradient formation in their model.

They say, “In the case of a spherical cell, the gradient is approximately exponential with a decay length set by the cell’s radius. In a cylindrically shaped cell, where the transport is along the long axis, the gradient is exponential with a decay length set by the radius, mostly independent of the length of the cell.”

Although the solution so far is purely theoretical, the editors of the journal eLife conclude that it holds promise for future work. 

“While there are no experiments available to date to directly probe the proposed mechanism,” they write, “it could be achieved through several biochemical implementations and can inspire experimental studies."

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A Datta et al. How to assemble a scale-invariant gradient. eLife (2022). DOI: 10.7554/eLife.71365

https://elifesciences.org/articles/71365

Scanning electron microscope of yeast cells (Saccharomyces cerevisiae).