Mechanisms of scaling in pattern formation

Abstract

Many organisms and their constituent tissues and organs vary substantially in size but differ little in morphology; they appear to be scaled versions of a common template or pattern. Such scaling involves adjusting the intrinsic scale of spatial patterns of gene expression that are set up during development to the size of the system. Identifying the mechanisms that regulate scaling of patterns at the tissue, organ and organism level during development is a longstanding challenge in biology, but recent molecular-level data and mathematical modeling have shed light on scaling mechanisms in several systems, including Drosophila and Xenopus. Here, we investigate the underlying principles needed for understanding the mechanisms that can produce scale invariance in spatial pattern formation and discuss examples of systems that scale during development.

Embryoids, organoids and gastruloids: new approaches to understanding embryogenesis

“…Very different from these examples, it has been shown that the scaling of neural tube pattern in two birds of different size is due to a difference in the threshold at which the cells of the two species respond to signals (Uygur et al, 2016). Other examples and theoretical models exist that further explain the scaling of pattern formation in vivo (Kicheva and Briscoe, 2015;Umulis and Othmer, 2013).…”

Dynamic scaling of morphogen gradients on growing domains

“…a twofold increase in length, indicating that this mechanism is mainly based on an effective increase in the Dpp diffusion coefficient 16 . However, measurements in a range of systems, including the Drosophila wing imaginal disc, show that the (effective) diffusion coefficient of the ligand does not change, even though its gradient scales 15 .…”

“…1b). Different models have been proposed to explain the scaling of morphogen gradients in the various systems where scaling has been analysed [9][10][11][12][13][14][15][16][17] . However, these models have remained controversial because of conflicting experimental observations 16,[18][19][20][21] .…”

“…One such theory proposes that the production rate of the morphogen could be adjusted such that morphogen gradients are higher on larger tissues and thus keep a constant threshold concentration at the particular relative domain position, where the developmental pattern of interest is defined 16 . This model, however, does not apply to the Decapentaplegic (Dpp) gradient in the Drosophila wing and haltere imaginal discs, because measurements show that the gradients indeed widen with the expanding domain 15 .…”

“…These adjustments could be achieved either by passive or active modulators 16 . An active modulation mechanism for the Dpp gradient in the wing imaginal disc has recently been proposed 17 as an extension of a previously proposed expander-repressor scheme 13 .…”