Abstract:A fundamental problem in developmental biology is understanding how complex patterns and organised tissues develop from a small group of nearly identical cells. A wealth of experimental data has exposed the complexity of the molecular networks guiding cellular decisions of organisation and patterning – networks whose output evolves over space and time as development progresses. Integrating this data into reaction–diffusion (RD) mathematical models that describe the spatiotemporal dynamics of molecular species … Show more
“…There are at least two mechanisms of active transport: vesicle-based transport, including transcytosis and migrasomes, in which morphogen ligands are shuttled across tissue via repeated cycles of receptor-mediated endo- and exocytosis (reviewed by Erban and Othmer, 2014 ; González-Gaitán and Jäckle, 1999 ; Greco et al, 2001 ; Jiang et al, 2019 ; Kicheva et al, 2007 ; Othmer et al, 1988 ; Panáková et al, 2005 ; reviewed by Restrepo et al, 2014 ), and cytoneme-mediated transport, in which extensive actin-based filopodial networks act as direct conduits for morphogen transmission to target cells ( Ramírez-Weber and Kornberg, 1999 ). Other non-directional forms of active transport, such as transcytosis or transport on microtubule-based motor proteins, can be modeled mathematically as diffusion-like (reviewed by Bollenbach et al, 2005 ; Thompson et al, 2018 ). Fig.…”
Section: Forming Bmp Gradientsmentioning
confidence: 99%
“…Reaction-diffusion mathematical models, which are distinct to Turing's reaction-diffusion mechanism of patterning, can be used to describe the spatiotemporal dynamics of BMP in terms of experimentally observable biophysical rates ( Box 1 ). Integrating quantitative biophysical experiments with mathematical modeling provides a rigorous approach to test the plausibility of hypothesized mechanisms guiding pattern formation (reviewed by Thompson et al, 2018 ). Importantly, analysis through a reaction-diffusion modeling framework can remain somewhat agnostic of the class of gradient formation and can account for differences between these mechanisms ( Box 1 ).…”
Section: Forming Bmp Gradientsmentioning
confidence: 99%
“… Box 1. Reaction-diffusion model framework Within this framework, reviewed at length in Thompson et al (2018) , the ‘Production’ term reflects both the spatial extent of the ligand expression domain, as well as the rate of ligand production. Clearance of BMP ligand via receptor-mediated internalization and interactions with extracellular regulators are accounted for within the ‘Reaction’ term.…”
Pattern formation by bone morphogenetic proteins (BMPs) demonstrates remarkable plasticity and utility in several contexts, such as early embryonic development, tissue patterning and the maintenance of stem cell niches. BMPs pattern tissues over many temporal and spatial scales: BMP gradients as short as 1-2 cell diameters maintain the stem cell niche of the Drosophila germarium over a 24-h cycle, and BMP gradients of several hundred microns establish dorsal-ventral tissue specification in Drosophila, zebrafish and Xenopus embryos in timescales between 30 min and several hours. The mechanisms that shape BMP signaling gradients are also incredibly diverse. Although ligand diffusion plays a dominant role in forming the gradient, a cast of diffusible and non-diffusible regulators modulate gradient formation and confer robustness, including scale invariance and adaptability to perturbations in gene expression and growth. In this Review, we document the diverse ways that BMP gradients are formed and refined, and we identify the core principles that they share to achieve reliable performance.
“…There are at least two mechanisms of active transport: vesicle-based transport, including transcytosis and migrasomes, in which morphogen ligands are shuttled across tissue via repeated cycles of receptor-mediated endo- and exocytosis (reviewed by Erban and Othmer, 2014 ; González-Gaitán and Jäckle, 1999 ; Greco et al, 2001 ; Jiang et al, 2019 ; Kicheva et al, 2007 ; Othmer et al, 1988 ; Panáková et al, 2005 ; reviewed by Restrepo et al, 2014 ), and cytoneme-mediated transport, in which extensive actin-based filopodial networks act as direct conduits for morphogen transmission to target cells ( Ramírez-Weber and Kornberg, 1999 ). Other non-directional forms of active transport, such as transcytosis or transport on microtubule-based motor proteins, can be modeled mathematically as diffusion-like (reviewed by Bollenbach et al, 2005 ; Thompson et al, 2018 ). Fig.…”
Section: Forming Bmp Gradientsmentioning
confidence: 99%
“…Reaction-diffusion mathematical models, which are distinct to Turing's reaction-diffusion mechanism of patterning, can be used to describe the spatiotemporal dynamics of BMP in terms of experimentally observable biophysical rates ( Box 1 ). Integrating quantitative biophysical experiments with mathematical modeling provides a rigorous approach to test the plausibility of hypothesized mechanisms guiding pattern formation (reviewed by Thompson et al, 2018 ). Importantly, analysis through a reaction-diffusion modeling framework can remain somewhat agnostic of the class of gradient formation and can account for differences between these mechanisms ( Box 1 ).…”
Section: Forming Bmp Gradientsmentioning
confidence: 99%
“… Box 1. Reaction-diffusion model framework Within this framework, reviewed at length in Thompson et al (2018) , the ‘Production’ term reflects both the spatial extent of the ligand expression domain, as well as the rate of ligand production. Clearance of BMP ligand via receptor-mediated internalization and interactions with extracellular regulators are accounted for within the ‘Reaction’ term.…”
Pattern formation by bone morphogenetic proteins (BMPs) demonstrates remarkable plasticity and utility in several contexts, such as early embryonic development, tissue patterning and the maintenance of stem cell niches. BMPs pattern tissues over many temporal and spatial scales: BMP gradients as short as 1-2 cell diameters maintain the stem cell niche of the Drosophila germarium over a 24-h cycle, and BMP gradients of several hundred microns establish dorsal-ventral tissue specification in Drosophila, zebrafish and Xenopus embryos in timescales between 30 min and several hours. The mechanisms that shape BMP signaling gradients are also incredibly diverse. Although ligand diffusion plays a dominant role in forming the gradient, a cast of diffusible and non-diffusible regulators modulate gradient formation and confer robustness, including scale invariance and adaptability to perturbations in gene expression and growth. In this Review, we document the diverse ways that BMP gradients are formed and refined, and we identify the core principles that they share to achieve reliable performance.
“…The subject of mechanisms forming morphogen gradients in diverse systems has been reviewed extensively (a sample of such reviews [40][41][42][43][44][45][46] ). In Drosophila development, the transport of the BMP homolog Dpp is shown to fit a power-law curve from a source along the dorsal midline 47 and exponential decay in the wing imaginal disc 48 .…”
Positional information encoded in signaling molecules is essential for early patterning in the prosensory domain of the developing cochlea. The cochlea contains an exquisite repeating pattern of sensory hair cells and supporting cells. This requires precision in the morphogen signals that set the initial radial compartment boundaries, but this has not been investigated. To measure gradient formation and morphogenetic precision in developing cochlea, we developed a quantitative image analysis procedure measuring SOX2 and pSMAD1/5/9 profiles in mouse embryos at embryonic day (E)12.5, E13.5, and E14.5. Intriguingly, we found that the pSMAD1/5/9 profile forms a linear gradient in the medial ~75% of the PSD during E12.5 and E13.5. This is a surprising activity readout for a diffusive BMP4 ligand secreted from a tightly constrained lateral region since morphogens typically form exponential or power-law gradient shapes. This is meaningful for gradient interpretation because while linear profiles offer the theoretically highest information content and distributed precision for patterning, a linear morphogen gradient has not yet been observed. In addition to the information-optimized linear profile, we found that while pSMAD1/5/9 is stable during this timeframe, an accompanying gradient of SOX2 shifts dynamically. Third, we see through joint decoding maps of pSMAD1/5/9 and SOX2 that there is a high-didelity mapping between signaling activity and position in the regions soon to become Kolliker's organ and the organ of Corti, where radial patterns are more intricate than lateral regions. Mapping is ambiguous in the prosensory domain precursory to the outer sulcus, where cell fates are uniform. Altogether, this research provides new insights into the precision of early morphogenetic patterning cues in the radial cochlea prosensory domain.
“…One of the fundamental problems in developmental biology is how complex patterns in organisms emerge from a group of nearly identical cells. A major tool in understanding such complex pattern emergence is to use reaction-diffusion mathematical models which model how molecular organization changes over space and time [1]. Three major components of reaction-diffusion models are molecular transport, production and clearance.…”
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