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Self-Motion Mechanism of Self-Motion Mechanism of
Chained Spherical Grains Cells
Sparisoma Viridi*,1 dan Nuning Nuraini2
1Nuclear Physics and Biophysics Research Division,
The International Symposium
on BioMathematics
(Symomath) 2013
27-29 October 2013,
Bandung, Indonesia1
Nuclear Physics and Biophysics Research Division,Institut Teknologi Bandung, Bandung 40132, Indonesia2Industrial and Financial Mathematics Research Division,Institut Teknologi Bandung, Bandung 40132, Indonesia*[email protected]
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Outline
• Cell motion
• Problem• Problem
• Cell model
• Prediction
• Parameters
Results• Results
• Summary
The International Symposium
on BioMathematics
(Symomath) 2013
27-29 October 2013,
Bandung, Indonesia2
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Cell motion
• Cytoskeletally driven contractions and
expansions of the cell membrane (Mombach et expansions of the cell membrane (Mombach et
al., 1996)
• Drag from fluid medium (Secomb et al., 1998)
• Rigidity of substrate (Lo et al., 2000)
• Cytoplasmic streaming and membrane • Cytoplasmic streaming and membrane
protrusions and retractions (Alt et al. 1999)
• Myosin-based contractility and transcellular
adhesions (Discher et al., 2005)The International Symposium
on BioMathematics
(Symomath) 2013
27-29 October 2013,
Bandung, Indonesia3
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Problem
• Too complicated
• Is there any way to define a unit of locomotion • Is there any way to define a unit of locomotion
of cell?
• Larger cell will only implement this unit
• Simplify the calculation
The International Symposium
on BioMathematics
(Symomath) 2013
27-29 October 2013,
Bandung, Indonesia4
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Cell model
• L is constant
• Density inside and out• Density inside and out
outside the same
• Area of the cell remains
constant
Force due to pressure from surrounding• Force due to pressure p0
from surrounding
The International Symposium
on BioMathematics
(Symomath) 2013
27-29 October 2013,
Bandung, Indonesia5
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Cell model (cont.)
• Change of grain radius
( )tRR ωδ sin1+=• Relation between grains
( )tRRi ωδ sin10+=
LRLR
LRR i
i
ii −+
− 2222
4
1
2
1
2asin
2
1π
The International Symposium
on BioMathematics
(Symomath) 2013
27-29 October 2013,
Bandung, Indonesia6
cLRLR
LRR j
j
jj
i
=−+
−+
2222
4
1
2
1
2asin
2
1π
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Prediction
• One-grain cell
The International Symposium
on BioMathematics
(Symomath) 2013
27-29 October 2013,
Bandung, Indonesia7
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Prediction (cont.)
• Two-grain cell
The International Symposium
on BioMathematics
(Symomath) 2013
27-29 October 2013,
Bandung, Indonesia8
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Prediction (cont.)
• Three-grain cell
The International Symposium
on BioMathematics
(Symomath) 2013
27-29 October 2013,
Bandung, Indonesia9
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Parameters
And also ω’ = 0.5 ω
The International Symposium
on BioMathematics
(Symomath) 2013
27-29 October 2013,
Bandung, Indonesia10
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Results
• Two-grain cell
The International Symposium
on BioMathematics
(Symomath) 2013
27-29 October 2013,
Bandung, Indonesia11
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Results (cont.)
• Three-grain cell
The International Symposium
on BioMathematics
(Symomath) 2013
27-29 October 2013,
Bandung, Indonesia12
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Summary
• Motion of cell consisted of connected grains
has been simulated.has been simulated.
• One-grain cell shows no motion, two-grain cell
performs oscillation motion, and three-grain
cell exhibits one-direction motion.
• More-grain cell and not-linear combinations • More-grain cell and not-linear combinations
are subject for next investigation.
The International Symposium
on BioMathematics
(Symomath) 2013
27-29 October 2013,
Bandung, Indonesia13
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Thank you
The International Symposium
on BioMathematics
(Symomath) 2013
27-29 October 2013,
Bandung, Indonesia14