slide viridi et_al_20131028_0

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*dudung@gmail.com

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

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

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(Symomath) 2013

27-29 October 2013,

Bandung, Indonesia3

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

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on BioMathematics

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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

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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

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cLRLR

LRR j

j

jj

i

=−+

−+

2222

4

1

2

1

2asin

2

1π

Prediction

• One-grain cell

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Prediction (cont.)

• Two-grain cell

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Prediction (cont.)

• Three-grain cell

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Parameters

And also ω’ = 0.5 ω

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Results

• Two-grain cell

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Results (cont.)

• Three-grain cell

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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.

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on BioMathematics

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27-29 October 2013,

Bandung, Indonesia13

Thank you

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on BioMathematics

(Symomath) 2013

27-29 October 2013,

Bandung, Indonesia14