Regulation of Proneural Wave Propagation Through a Combination of Notch-Mediated Lateral Inhibition and EGF-Mediated Reaction Diffusion

2020 ◽  
pp. 77-91 ◽  
Author(s):  
Makoto Sato ◽  
Tetsuo Yasugi
Keyword(s):  
Wave Propagation ◽  
Lateral Inhibition ◽  
Reaction Diffusion

scholarly journals More than Skew: Asymmetric Wave Propagation in a Reaction-Diffusion-Convection System

BIOMATH ◽  
2013 ◽  
Vol 2 (1) ◽  
Author(s):  
Edward H. Flach ◽  
John Norbury ◽  
Santiago Schnell
Keyword(s):  
Wave Propagation ◽  
Reaction Diffusion ◽  
Diffusion Convection ◽  
Asymmetric Wave

scholarly journals Notch-mediated lateral inhibition regulates proneural wave propagation when combined with EGF-mediated reaction diffusion

2016 ◽  
Vol 113 (35) ◽  
pp. E5153-E5162 ◽  
Author(s):  
Makoto Sato ◽  
Tetsuo Yasugi ◽  
Yoshiaki Minami ◽  
Takashi Miura ◽  
Masaharu Nagayama
Keyword(s):  
Notch Signaling ◽  
Cell Fate ◽  
Lateral Inhibition ◽  
Feedback Loop ◽  
Reaction Diffusion ◽  
Signaling Systems ◽  
Visual Center ◽  
Salt And Pepper ◽  
Egf Signaling

Notch-mediated lateral inhibition regulates binary cell fate choice, resulting in salt and pepper patterns during various developmental processes. However, how Notch signaling behaves in combination with other signaling systems remains elusive. The wave of differentiation in the Drosophila visual center or “proneural wave” accompanies Notch activity that is propagated without the formation of a salt and pepper pattern, implying that Notch does not form a feedback loop of lateral inhibition during this process. However, mathematical modeling and genetic analysis clearly showed that Notch-mediated lateral inhibition is implemented within the proneural wave. Because partial reduction in EGF signaling causes the formation of the salt and pepper pattern, it is most likely that EGF diffusion cancels salt and pepper pattern formation in silico and in vivo. Moreover, the combination of Notch-mediated lateral inhibition and EGF-mediated reaction diffusion enables a function of Notch signaling that regulates propagation of the wave of differentiation.

scholarly journals A new scheme for the solution of reaction diffusion and wave propagation problems

2014 ◽  
Vol 38 (23) ◽  
pp. 5651-5664 ◽  
Author(s):  
Ji Lin ◽  
Wen Chen ◽  
C.S. Chen
Keyword(s):  
Wave Propagation ◽  
Reaction Diffusion

scholarly journals Neuronal Calcium Wave Propagation Varies with Changes in Endoplasmic Reticulum Parameters: A Computer Model

2015 ◽  
Vol 27 (4) ◽  
pp. 898-924 ◽  
Author(s):  
Samuel A. Neymotin ◽  
Robert A. McDougal ◽  
Mohamed A. Sherif ◽  
Christopher P. Fall ◽  
Michael L. Hines ◽  
...  
Keyword(s):  
Endoplasmic Reticulum ◽  
Wave Propagation ◽  
Reaction Diffusion ◽  
High Sensitivity ◽  
Apical Dendrite ◽  
Reaction Diffusion Model ◽  
Apparent Diffusion ◽  
Text Density ◽  
Electrochemical Model

Calcium ([Formula: see text]) waves provide a complement to neuronal electrical signaling, forming a key part of a neuron’s second messenger system. We developed a reaction-diffusion model of an apical dendrite with diffusible inositol triphosphate ([Formula: see text]), diffusible [Formula: see text], [Formula: see text] receptors ([Formula: see text]s), endoplasmic reticulum (ER) [Formula: see text] leak, and ER pump (SERCA) on ER. [Formula: see text] is released from ER stores via [Formula: see text]s upon binding of [Formula: see text] and [Formula: see text]. This results in [Formula: see text]-induced-[Formula: see text]-release (CICR) and increases [Formula: see text] spread. At least two modes of [Formula: see text] wave spread have been suggested: a continuous mode based on presumed relative homogeneity of ER within the cell and a pseudo-saltatory model where [Formula: see text] regeneration occurs at discrete points with diffusion between them. We compared the effects of three patterns of hypothesized [Formula: see text] distribution: (1) continuous homogeneous ER, (2) hotspots with increased [Formula: see text] density ([Formula: see text] hotspots), and (3) areas of increased ER density (ER stacks). All three modes produced [Formula: see text] waves with velocities similar to those measured in vitro (approximately 50–90 [Formula: see text]m /sec). Continuous ER showed high sensitivity to [Formula: see text] density increases, with time to onset reduced and speed increased. Increases in SERCA density resulted in opposite effects. The measures were sensitive to changes in density and spacing of [Formula: see text] hotspots and stacks. Increasing the apparent diffusion coefficient of [Formula: see text]  substantially increased wave speed. An extended electrochemical model, including voltage-gated calcium channels and AMPA synapses, demonstrated that membrane priming via AMPA stimulation enhances subsequent [Formula: see text] wave amplitude and duration. Our modeling suggests that pharmacological targeting of [Formula: see text]s and SERCA could allow modulation of [Formula: see text] wave propagation in diseases where [Formula: see text] dysregulation has been implicated.

A level-set approach based on reaction-diffusion equation applied to inversion problems in acoustic wave propagation

2020 ◽  
Author(s):  
Dara Lanzsnaster ◽  
Paulo Bastos de Castro ◽  
Hélio Emmendoerfer Junior ◽  
P T R Mendoca ◽  
Emilio C N Silva ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Diffusion Equation ◽  
Acoustic Wave ◽  
Level Set ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Acoustic Wave Propagation ◽  
Level Set Approach

scholarly journals Gerald Beresford Whitham. 13 December 1927 — 26 January 2014

2015 ◽  
Vol 61 ◽  
pp. 555-577 ◽  
Author(s):  
A. A. Minzoni ◽  
N. F. Smyth
Keyword(s):  
Wave Propagation ◽  
Academic Career ◽  
Applied Mathematics ◽  
Reaction Diffusion ◽  
Nonlinear Wave Propagation ◽  
Research Areas ◽  
California Institute Of Technology ◽  
Pure Mathematics ◽  
Mathematical Techniques ◽  
Institute Of Technology

Gerald Beresford Whitham was one of the leading applied mathematicians of the twentieth century. His original, deep and insightful research into nonlinear wave propagation formed the foundation of and mathematical techniques for much of the current research in this area. Indeed, many of these ideas and techniques have spread beyond wave propagation research into other areas, such as reaction–diffusion, and has influenced research in pure mathematics. His textbook Linear and nonlinear waves , published in 1974, is still the standard reference for the mathematics of wave motion. Whitham was also instrumental in building from scratch the Department of Applied Mathematics at the California Institute of Technology and, through choosing key people in new, promising research areas, in making it into one of the leading centres of applied mathematics in the world, with an influence far beyond its small size. During his academic career, Whitham received major awards and prizes for his research. He was elected a Fellow of the Royal Society in 1965 and a Fellow of the American Academy of Arts and Sciences in 1959, and was awarded the Norbert Wiener Prize for Applied Mathematics in 1980.

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