How to assemble a scale-invariant gradient

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.

All-optical mapping of cAMP transport reveals rules of sub-cellular localization

“…The effects of surface-to-volume ratio discussed here apply broadly to other small molecules and to systems where interacting partners are localized differentially on the membrane versus in the bulk (46,53,54). An important goal for future research will be to characterize the diffusion coefficients, length constants, and time constants for other signaling molecules.…”

Geometric control of intracellular patterning

“…Many models have been constructed that generate positional information fields. In the recommended paper, Arnab Datta, Sagnik Ghosh and Jane Kondev add to this list of models [2]. Their model is distinguished by three features: i) a parsimonious list of requirements, ii) a close matching to the experimental situation in many biological contexts, and iii) a purely geometric control of patterning in cells and tissues.…”

“…In this model, synthesis and degradation are both linked to diffusive capture. Moreover, the typical rate at which molecules diffuse from the bulk to the surface of a cell of radius R gives the capture or degradation rate 𝑘 = 𝐷 𝑅 2 ⁄ . Since the decay length scale 𝜆 = √𝐷 𝑘 ⁄ , the resulting concentration profile along the axis of polarization is an exponential with a decay length 𝜆~𝑅.…”