Direct vs. Synaptic Coupling in a Mathematical Model of Cytoneme-Based Morphogen Gradient Formation

2018 ◽  
Vol 78 (5) ◽  
pp. 2323-2347 ◽  
Author(s):  
Hyunjoong Kim ◽  
Paul C. Bressloff
Keyword(s):  
Mathematical Model ◽  
Morphogen Gradient ◽  
Synaptic Coupling ◽  
Gradient Formation

scholarly journals Systems biology derived source-sink mechanism of BMP gradient formation

eLife ◽  
2017 ◽  
Vol 6 ◽  
Author(s):  
Joseph Zinski ◽  
Ye Bu ◽  
Xu Wang ◽  
Wei Dou ◽  
David Umulis ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Systems Biology ◽  
Bmp Signaling ◽  
Morphogen Gradient ◽  
Wild Type ◽  
Morphogenetic Protein ◽  
Gradient Formation ◽  
Source Sink ◽  
Bmp Antagonist ◽  
Prevailing View

A morphogen gradient of Bone Morphogenetic Protein (BMP) signaling patterns the dorsoventral embryonic axis of vertebrates and invertebrates. The prevailing view in vertebrates for BMP gradient formation is through a counter-gradient of BMP antagonists, often along with ligand shuttling to generate peak signaling levels. To delineate the mechanism in zebrafish, we precisely quantified the BMP activity gradient in wild-type and mutant embryos and combined these data with a mathematical model-based computational screen to test hypotheses for gradient formation. Our analysis ruled out a BMP shuttling mechanism and a bmp transcriptionally-informed gradient mechanism. Surprisingly, rather than supporting a counter-gradient mechanism, our analyses support a fourth model, a source-sink mechanism, which relies on a restricted BMP antagonist distribution acting as a sink that drives BMP flux dorsally and gradient formation. We measured Bmp2 diffusion and found that it supports the source-sink model, suggesting a new mechanism to shape BMP gradients during development.

scholarly journals Dally regulates Dpp morphogen gradient formation by stabilizing Dpp on the cell surface

2008 ◽  
Vol 313 (1) ◽  
pp. 408-419 ◽  
Author(s):  
Takuya Akiyama ◽  
Keisuke Kamimura ◽  
Cyndy Firkus ◽  
Satomi Takeo ◽  
Osamu Shimmi ◽  
...  
Keyword(s):  
Cell Surface ◽  
Morphogen Gradient ◽  
Gradient Formation

Fractional calculus and morphogen gradient formation

2012 ◽  
Author(s):  
Santos Bravo Yuste ◽  
Enrique Abad ◽  
Katja Lindenberg
Keyword(s):  
Fractional Calculus ◽  
Morphogen Gradient ◽  
Gradient Formation

scholarly journals CRITICAL TIMESCALES AND TIME INTERVALS FOR COUPLED LINEAR PROCESSES

2013 ◽  
Vol 54 (3) ◽  
pp. 127-142 ◽  
Author(s):  
MATTHEW J. SIMPSON ◽  
ADAM J. ELLERY ◽  
SCOTT W. MCCUE ◽  
RUTH E. BAKER
Keyword(s):  
Differential Equations ◽  
Applied Mathematics ◽  
Finite Measure ◽  
Single Species ◽  
Diffusion Reaction ◽  
Morphogen Gradient ◽  
Time Intervals ◽  
Linear Processes ◽  
Gradient Formation ◽  
Time Required

AbstractIn 1991, McNabb introduced the concept of mean action time (MAT) as a finite measure of the time required for a diffusive process to effectively reach steady state. Although this concept was initially adopted by others within the Australian and New Zealand applied mathematics community, it appears to have had little use outside this region until very recently, when in 2010 Berezhkovskii and co-workers [A. M. Berezhkovskii, C. Sample and S. Y. Shvartsman, “How long does it take to establish a morphogen gradient?”Biophys. J. 99(2010) L59–L61] rediscovered the concept of MAT in their study of morphogen gradient formation. All previous work in this area has been limited to studying single-species differential equations, such as the linear advection–diffusion–reaction equation. Here we generalize the concept of MAT by showing how the theory can be applied to coupled linear processes. We begin by studying coupled ordinary differential equations and extend our approach to coupled partial differential equations. Our new results have broad applications, for example the analysis of models describing coupled chemical decay and cell differentiation processes.

scholarly journals Morphogen Gradient Formation Unraveled Using In Vivo Three-dimensional Single Molecule Microscopy

2009 ◽  
Vol 96 (3) ◽  
pp. 33a ◽  
Author(s):  
Laurent Holtzer ◽  
Anna Kicheva ◽  
Marcos Gonzalez-Gaitan ◽  
Thomas Schmidt
Keyword(s):  
Single Molecule ◽  
Three Dimensional ◽  
Morphogen Gradient ◽  
Single Molecule Microscopy ◽  
Gradient Formation

scholarly journals Internalization and end flux in morphogen gradient formation

2006 ◽  
Vol 190 (1-2) ◽  
pp. 232-251 ◽  
Author(s):  
A.D. Lander ◽  
Q. Nie ◽  
F.Y.M. Wan
Keyword(s):  
Morphogen Gradient ◽  
Gradient Formation

scholarly journals Morphogen gradient formation and action

Fly ◽  
2011 ◽  
Vol 5 (3) ◽  
pp. 242-246 ◽  
Author(s):  
Junbo Liu ◽  
Feng He ◽  
Jun Ma
Keyword(s):  
Morphogen Gradient ◽  
Gradient Formation

scholarly journals Dorsal/NF-κB exhibits a dorsal-to-ventral mobility gradient in the Drosophila embryo

2018 ◽  
Author(s):  
Hadel Al Asafen ◽  
Natalie M. Clark ◽  
Thomas Jacobsen ◽  
Rosangela Sozzani ◽  
Gregory T. Reeves
Keyword(s):  
Dna Binding ◽  
Nuclear Export ◽  
Developmental Process ◽  
Ventral Side ◽  
Correlation Spectroscopy ◽  
Drosophila Embryo ◽  
Morphogen Gradient ◽  
Biophysical Parameters ◽  
Quantitative Measurements ◽  
Gradient Formation

AbstractMorphogen-mediated patterning is a highly dynamic developmental process. To obtain an accurate understanding of morphogen gradients, biophysical parameters such as protein diffusivities must be quantified in vivo. The dorsal-ventral (DV) patterning of early Drosophila embryos by the NF-κB homolog Dorsal (Dl) is an excellent system for understanding morphogen gradient formation. Dl gradient formation is controlled by the inhibitor Cactus/IκB (Cact), which regulates the nuclear import and diffusion of Dl protein. However, quantitative measurements of spatiotemporal Dl movement are currently lacking. Here, we use scanning fluorescence correlation spectroscopy to quantify the mobility of Dl. We find that the diffusivity of Dl varies along the DV axis, with lowest diffusivities on the ventral side, and the DV asymmetry in diffusivity is exclusive to the nuclei. Moreover, we also observe that nuclear export rates are lower in the ventral and lateral regions of the embryo. Both cross correlation spectroscopy measurements and a computational model of Dl/DNA binding suggest that DNA binding of Dl, which is more prevalent on the ventral side of the embryo, is correlated to a lower diffusivity and nuclear export rate. We propose that the variation in Dl/DNA binding along the DV axis is dependent on Cact binding Dl, which prevents Dl from binding DNA in dorsal and lateral regions of the embryo. Thus, our results highlight the complexity of morphogen gradient dynamics and the need for quantitative measurements of biophysical interactions in such systems.

scholarly journals Shuttling of Dorsal by Cactus: mechanism and implications

2019 ◽  
Author(s):  
Allison E. Schloop ◽  
Sophia Carrell-Noel ◽  
Gregory T. Reeves
Keyword(s):  
Cell Types ◽  
Bmp Signaling ◽  
Previous Literature ◽  
Drosophila Embryo ◽  
Morphogen Gradient ◽  
Facilitated Diffusion ◽  
Morphogen Gradients ◽  
Binding Partner ◽  
Early Drosophila Embryo ◽  
Gradient Formation

AbstractIn a developing animal, morphogen gradients act to pattern tissues into distinct domains of cell types. However, despite their prevalence in development, morphogen gradient formation is a matter of debate. In our recent publication, we showed that the Dorsal/NF-κB morphogen gradient, which patterns the DV axis of the early Drosophila embryo, is partially established by a mechanism of facilitated diffusion. This mechanism, also known as “shuttling,” occurs when a binding partner of the morphogen facilitates the diffusion of the morphogen, allowing it to accumulate at a given site. In this case, the inhibitor Cactus/IκB facilitates the diffusion of Dorsal/NF-κB. In the fly embryo, we used computation and experiment to not only show that shuttling occurs in the embryo, but also that it enables the viability of embryos that inherit only one copy of dorsal maternally. Here we further discuss our evidence behind the shuttling mechanism, the previous literature data explained by the mechanism, and how it may also be critical for robustness of development. Finally, we describe an interaction between Dorsal and BMP signaling that is likely affected by shuttling.

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