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SUMMARY:The analysis of the effect of cell dynamics on Delta-Notch interac
tion during retina vasculature development
DTSTART;VALUE=DATE-TIME:20180709T094500Z
DTEND;VALUE=DATE-TIME:20180709T100000Z
DTSTAMP;VALUE=DATE-TIME:20240721T131819Z
UID:indico-contribution-287@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Toshiki Oguma (Kyushu University)\nPattern formation
by Delta-Notch interaction has been well studied experimentally and theor
etically. The Delta-Notch system is observed in various pattern formation
process such as somitogenesis\, neuroendocrine cell differentiation in lun
g\, T cell differentiation and blood vessel development. Recent studies ha
ve shown endothelial cell proliferation and movement happen during this pr
ocess. However\, to our knowledge\, there is little theoretical research a
bout the effect of cell dynamics on Delta-Notch interaction.\n\nIn the pre
sent study\, we examined the effect of cell dynamics on Delta-Notch patter
n formation during retina vasculature development. We incorporated cell mo
vement and proliferation to the model for Delta-Notch interaction. Using t
he model\, we analytically derived the instability condition and numerical
ly generated the patterns which have the similarity with the three pattern
s observed in vivo. It is difficult to capture the dynamics of cell moveme
nt and proliferation with standard linear stability analysis of fastest gr
owing wavenumber component. Therefore\, to consider all wavenumber compone
nts\, we introduced the instability index\, $\\Psi(t)$\, as the mean of sq
uare of Delta expression values. Based on Parseval's theorem regarding dis
crete Fourier analysis\, we can derive that $\\Psi(t)$ is equivalent to th
e average of power spectrum. Therefore\, by considering the values of powe
r spectra\, we can evaluate the instability of the system.\n\n$$\\displays
tyle\n{D}_x =\\sum_{m=0}^{n-1} \\delta_k \\mathrm{e}^{ \\lambda_k t + i k
x} \\\\\n\\displaystyle \\Psi(t) := \\frac{1}{n} \\sum_{x=1}^n {D_x}^2 = \
\frac{1}{n} \\sum_{m=0}^{n-1} |\\delta_{\\frac{2\\pi m}{n}}|^2\n$$ \n\n$D_
x$ is the expression values of Delta\, $\\delta_k$ is the discrete Fourier
transform of $D_x$\, $n$ is the number of the cells\, $k=\\frac{2\\pi m}{
n}$.\n\nThese analyses and numerical calculations suggest that the vascula
ture which express homogeneous pattern shows high motility and proliferati
on rate of their endothelial cells. Based on these theoretical results\, w
e experimentally observed cell dynamics during retina vasculature developm
ent by organ culture and immunohistochemistry. The results showed random e
ndothelial cell movements and proliferations happened more frequently in v
ein than in artery\, which are consistent with analytical and numerical re
sults. These results suggest that cell dynamics affect artery-vein differe
ntiation via Delta-Notch interaction.\n\nhttps://conferences.maths.unsw.ed
u.au/event/2/contributions/287/
LOCATION:University of Sydney Holme Building/--The Refectory
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/287/
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