Diffusion vs. direct transport in the precision of morphogen readout

Abstract

Morphogen profiles allow cells to determine their position within a developing organism, but not all morphogen profiles form by the same mechanism. Here we derive fundamental limits to the precision of morphogen concentration sensing for two canonical mechanisms: the diffusion of morphogen through extracellular space and the direct transport of morphogen from source cell to target cell, e.g., via cytonemes. We find that direct transport establishes a morphogen profile without adding noise in the process. Despite this advantage, we find that for sufficiently large values of profile length, the diffusion mechanism is many times more precise due to a higher refresh rate of morphogen molecules. We predict a profile lengthscale below which direct transport is more precise, and above which diffusion is more precise. This prediction is supported by data from a wide variety of morphogens in developing Drosophila and zebrafish.

Diversity and robustness of bone morphogenetic protein pattern formation

“…Related studies are needed to better determine robustness and fragility of BMP systems with hindered feedback. Intriguingly, recent modeling work in the Drosophila wing imaginal disc indicates that cytonemes may allow for gradient formation without the addition of extrinsic noise, suggesting a potential division of labor between cytoneme-and diffusion-based mechanisms, depending on the noise sensitivity of a given patterning niche (Fancher and Mugler, 2020). Perhaps the prevalence and complexity of feedback loops in a given patterning niche may be indicative of the relative role of diffusion and cytonemes in gradient formation.…”

Tuning the diffusion constant to optimize the readout of positional information of spatial concentration patterns

“…[1] To provide positional information, spatial concentration patterns such as morphogen gradients are often employed. [2][3][4][5][6][7] Generally, in the presence of a spatially heterogeneous concentration distribution of a certain molecule such as a morphogen, cells can infer their positions based on the readout of the local concentration of such a molecule. [1,2,[8][9][10][11] Various mechanisms for establishing nonuniform distribution of molecules have been extensively studied, e.g., the Turing mechanism, [12,13] the wave-pinning (WP) model, [14] the active transport (AT) model, [15][16][17] and the synthesis-degradationdiffusion (SDD) model.…”

“…[1,2,[8][9][10][11] Various mechanisms for establishing nonuniform distribution of molecules have been extensively studied, e.g., the Turing mechanism, [12,13] the wave-pinning (WP) model, [14] the active transport (AT) model, [15][16][17] and the synthesis-degradationdiffusion (SDD) model. [4,7,18] The Turing mechanism usually involves two mutually interacting molecular species with strong nonlinearity and distinct diffusion constants, leading to the Turing instability, i.e., the destabilization of uniform concentration distribution. [12,13] As a result, the system spontaneously resides into a stable and usually spatially periodic concentration distribution.…”

“…The SDD model is one of the most studied mechanisms for morphogen gradients. [4,7,18] It involves the synthesis, degradation, and passive diffusion of one molecular species. The synthesis term is usually considered as a spatially fixed source.…”

“…[13,22] However, it is well known that the Tur-ing instability necessitates the involvement of diffusion, implying that such randomness could induce global order, resembling the theory of stochastic resonance. [23][24][25][26] Nonetheless, how diffusion affects the positional information of spatial concentration patterns in general, especially for mechanisms other than the Turing mechanism, [7,13,19,20,22] remains to be explored. Therefore, this study focuses on the other three representative models: the AT, SDD, and WP models.…”