Spatiotemporal Analysis of Different Mechanisms for Interpreting Morphogen Gradients

Abstract

During development, multicellular organisms must accurately control both temporal and spatial aspects of tissue patterning. This is often achieved using morphogens, signaling molecules that form spatially varying concentrations and so encode positional information. Typical analysis of morphogens assumes that spatial information is decoded in steady state by measuring the value of the morphogen concentration. However, recent experimental work suggests that both pre-steadystate readout and measurement of spatial and temporal derivatives of the morphogen concentration can play important roles in defining boundaries. Here, we undertake a detailed theoretical and numerical study of the accuracy of patterning-both in space and time-in models where readout is provided not by the morphogen concentration but by its spatial and temporal derivatives. In both cases we find that accurate patterning can be achieved, with sometimes even smaller errors than directly reading the morphogen concentration. We further demonstrate that such models provide other potential benefits to the system, such as the ability to switch on and off gene response with a high degree of spatiotemporal accuracy. Finally, we discuss how such derivatives might be calculated biologically and examine these models in relation to Sonic Hedgehog signaling in the vertebrate central nervous system. We show that, when coupled to a downstream transcriptional network, pre-steady-state measurement of the temporal change in the Shh morphogen is a plausible mechanism for determining precise gene boundaries in both space and time.

Fold-change detection and scale invariance of cell–cell signaling in social amoeba

“…A case in point is the collective oscillations of NADH in yeast cell suspension whose amplitude and frequency are conserved for three orders of magnitude in cell density (54). In higher organisms, morphogen fields are dynamic and their temporal changes appear to be read out to regulate cell fates (10,55). Traveling waves are also prevalent in embryonic development (56,57).…”

Morphogen rules: design principles of gradient-mediated embryo patterning

“…Behavior consistent with this has been suggested for TGFβ ( Sorre et al, 2014 ) and Dpp ( Wartlick et al, 2011 ). This could result in more accurate patterning than that achieved by mechanisms based on simply interpreting absolute morphogen concentration ( Richards and Saunders, 2015 ). Mechanistically, the way cells ‘calculate’ a derivative or integral would probably rely on the downstream transcriptional network.…”

New Model for Understanding Mechanisms of Biological Signaling: Direct Transport via Cytonemes

“…4,5,[8][9][10] Despite common use of the SDD model and related approaches for many biological systems, there is a growing number of experimental observations, suggesting that the indirect delivery of the morphogens via diffusion might not be the only mechanism in the transportation of morphogenetic signals. 6,22,23,34 It has been argued that the complex environment of the embryo systems might prevent the passive free diffusion from establishing distinguishable morphogen gradients at different regions. 6,22 An alternative direct delivery mechanism of signaling molecules that employs cytonemes has been proposed.…”