Kinetics of Morphogen Gradient Formation

Science ◽  
2007 ◽  
Vol 315 (5811) ◽  
pp. 521-525 ◽  
Author(s):  
A. Kicheva ◽  
P. Pantazis ◽  
T. Bollenbach ◽  
Y. Kalaidzidis ◽  
T. Bittig ◽  
...  
Keyword(s):  
Morphogen Gradient ◽  
Gradient Formation ◽  
Kinetics Of

MATHEMATICAL MODELS OF RECEPTOR-MEDIATED TRANSPORT OF MORPHOGENS

2010 ◽  
Vol 20 (11) ◽  
pp. 2021-2052 ◽  
Author(s):  
PIOTR KRZYŻANOWSKI ◽  
PHILIPPE LAURENÇOT ◽  
DARIUSZ WRZOSEK
Keyword(s):  
Degenerate Parabolic Equation ◽  
Intracellular Transport ◽  
Binding Kinetics ◽  
Morphogen Gradient ◽  
Reversible Binding ◽  
Numerical Tests ◽  
Gradient Formation ◽  
Degenerate Parabolic ◽  
Morphogen Transport ◽  
Kinetics Of

Two models of receptor-mediated morphogen transport in a biological tissue are proposed to investigate morphogen gradient formation. The first model concerns intracellular transport of morphogen molecules, while the second describes transport along the cell surface. Both models couple via diffusivity a quasilinear degenerate parabolic equation describing the transport of the morphogens with an ordinary differential equation describing reversible binding kinetics of receptors. A detailed study of the steady states is provided, together with numerical tests which compare the models with experimental data.

scholarly journals Cyto-architecture constrains the spread of photoactivated tubulin in the syncytial Drosophila embryo

2020 ◽  
Vol 64 (4-5-6) ◽  
pp. 275-287
Author(s):  
Sameer Thukral ◽  
Bivash Kaity ◽  
Bipasha Dey ◽  
Swati Sharma ◽  
Amitabha Nandi ◽  
...  
Keyword(s):  
Plasma Membrane ◽  
Nuclear Division ◽  
The Body ◽  
Drosophila Embryo ◽  
Morphogen Gradient ◽  
Cytoplasmic Domains ◽  
Microtubule Network ◽  
Drosophila Embryogenesis ◽  
Gradient Formation ◽  
Kinetics Of

Drosophila embryogenesis begins with nuclear division in a common cytoplasm forming a syncytial cell. Morphogen gradient molecules spread across nucleo-cytoplasmic domains to pattern the body axis of the syncytial embryo. The diffusion of molecules across the syncytial nucleo-cytoplasmic domains is potentially constrained by association with the components of cellular architecture. However, the extent of restriction has not been examined. Here we use photoactivation (PA) to generate a source of cytoplasmic or cytoskeletal molecules in order to monitor the kinetics of their spread in the syncytial Drosophila embryo. Photoactivated PA-GFP and PA-GFP-Tubulin generated within a fixed anterior area diffused along the antero-posterior axis. These molecules were enriched in the cortical cytoplasm above the yolk-filled center, suggesting that the cortical cytoplasm is phase separated from the yolk-filled center. The length scales of diffusion were extracted using exponential fits under steady state assumptions. PA-GFP spread a greater distance as compared to PA-GFP-Tubulin. Both molecules were more restricted when generated in the center of the embryo. The length scale of spread for PA-GFP-Tubulin increased in mutant embryos containing short plasma membrane furrows and a disrupted tubulin cytoskeleton. PA-GFP spread was unaffected by cyto-architecture perturbation. Taken together, these data show that PA-GFP-Tubulin spread is restricted by its incorporation in the microtubule network and intact plasma membrane furrows. This photoactivation based analysis of protein spread allows for interpretation of the dependence of gradient formation on syncytial cyto-architecture.

scholarly journals Cyto-architecture constrains a photoactivation induced tubulin gradient in the syncytial Drosophila embryo

2019 ◽  
Author(s):  
Sameer Thukral ◽  
Bivash Kaity ◽  
Bipasha Dey ◽  
Swati Sharma ◽  
Amitabha Nandi ◽  
...  
Keyword(s):  
Plasma Membrane ◽  
Nuclear Division ◽  
The Body ◽  
Drosophila Embryo ◽  
Morphogen Gradient ◽  
Cytoplasmic Domains ◽  
Microtubule Network ◽  
Cellular Architecture ◽  
Gradient Formation ◽  
Kinetics Of

AbstractDrosophila embryogenesis begins with nuclear division in a common cytoplasm forming a syncytial cell. Morphogen gradient molecules spread across nucleo-cytoplasmic domains to pattern the body axis of the syncytial embryo. The diffusion of molecules across the syncytial nucleo-cytoplasmic domains is potentially constrained by association with the components of cellular architecture, however the extent of restriction has not been examined so far. Here we use photoactivation (PA) to generate a source of cytoplasmic or cytoskeletal molecules in order to monitor the kinetics of their spread in the syncytial Drosophila embryo. Photoactivated PA-GFP and PA-GFP-Tubulin within a fixed anterior area diffused along the antero-posterior axis. These molecules were enriched in cortical cytoplasm above the yolk-filled center suggesting that the cortical cytoplasm is phase separated from the yolk-filled center. The length scales of diffusion were extracted using exponential fits under steady state assumptions. PA-GFP spread to greater distance as compared to PA-GFP-Tubulin. Both gradients were steeper and more restricted when generated in the center of the embryo probably due to a higher density of nucleo-cytoplasmic domains. The length scale of diffusion for PA-GFP-Tubulin gradient increased in mutant embryos containing short plasma membrane furrows and disrupted tubulin cytoskeleton. The PA-GFP gradient shape was unaffected by cyto-architecture perturbation. Taken together, these data show that PA-GFP-Tubulin gradient is largely restricted by its incorporation in the microtubule network and intact plasma membrane furrows. This photoactivation based analysis of protein spread across allows for interpretation of the dependence of gradient formation on the syncytial cyto-architecture.

scholarly journals Kinetics of receptor occupancy during morphogen gradient formation

2013 ◽  
Vol 138 (24) ◽  
pp. 244105 ◽  
Author(s):  
Alexander M. Berezhkovskii ◽  
Stanislav Y. Shvartsman
Keyword(s):  
Receptor Occupancy ◽  
Morphogen Gradient ◽  
Gradient Formation ◽  
Kinetics Of

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
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