Model of microorganism using contracting spring as locomotive organ is presented in this work. A simple molecular dynamics method implementing Euler algorithm is used in the simulation.

1. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones1
Molecular Dynamics Simulation of
Microorganism Motion in Fluid Based
on Granular Model in the Case of
Multiple Simple Push-Pull Filaments
S. Viridi1*
, F. Haryanto1
, N. Nuraini2
, S. N. Khotimah1
1
Physics Department, Institut Teknologi Bandung
Jalan Ganesha 10, Bandung 40132, Indonesia
2
Mathematics Department, Institut Teknologi Bandung
Jalan Ganesha 10, Bandung 40132, Indonesia
*
dudung@fi.itb.ac.id

2. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones2
Outline
• Introduction
• Model 1
• Results 1
• Summary 1
• Model 2
• Results 2
• Summary 2
• Acknowledgements

3. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones3
Introduction

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Motion patterns of microorganism
• The patterns are unique: (1) orientation, (2)
wobbling, (3) gyration, and (4) intensive
surface probing (Leal-Taixé et al., 2010)
L. Leal-Taixé, M. Heydt, S. Weiße, A. Rosenhahn, B. Rosenhahn, Pattern
Recognition 6376, 283-292 (2010).

5. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones5
An active fluid
• Turbulence flow can occur in high viscous fluid
or in low Reynolds number (Aranson, 2013)
I. Aranson, Physics 6, 61 (2013).

6. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones6
Flagella as thruster
• Flagella introduces force and torque to the
fluid (Yang et al., 2012)
C. Yang, C. Chen, Q. Ma, L. Wu, T. Song, Journal of Bionic Engineering 9,
200-210 (2012).

7. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones7
Shrink and swallow model
• Pressure difference can induce motion (Viridi
and Nuraini, 2014)
S. Viridi, N. Nuraini, AIP Conference Proceedings 1587, 123-126 (2014).

8. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones8
Model 1
S. Viridi, N. Nuraini, The International Symposium on BioMathematics
(Symomath) 2015, 4-6 November 2015, Bandung, Indonesia

9. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones9
Two grain model
• Two spherical particles as cells, which are
connected by a spring
mi
mj
kij

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Push and pull spring force
• Spring force
lij is normal length of the spring
kij is spring constant
rij is distance between mass mi and mj
( ) ijijijijij rlrkS ˆ−−=


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Fluid drag force
• Drag force
Cd is drag constant
A is cross sectional area
ρf is fluid density
vf is fluid velocity
( )
fi
fi
dfi
vv
vv
CAD 


−
−
−=
3
2
1
ρ

12. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones12
Change of spring normal length
• Spring normal length varies with time
Tbridge is oscillation period of bridge between
cells
( )L
T
t
Llij α
π
α −+








= 1
2
sin
bridge

13. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones13
Change of drag coefficient
• Both cell can have same or different Cd
i = 1, 2 for each particle
( ) ( )min,max,
drag
min,max,
2
12
cos
2
1
, ddddid CC
T
t
CCC +








−=
π

14. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones14
Molecular dynamics method
• Newton second law of motion
• Euler method








+= ∑j
ijii SD
m
a
 1
( ) ( ) tatvttv iii ∆+=∆+

( ) ( ) ( ) ttvtrttr ii ∆+=∆+


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Comprehensive view of the model

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Results 1

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Displacement

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Same drag constant
• Cd = 0.1, Cd = 0.1

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Same drag constant (cont.)
• Cd = 0.1, Cd = 0.4

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Same drag constant (cont.)
• Cd = 0.4, Cd = 0.1

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Same drag constant (cont.)
• Cd = 0.4, Cd = 0.4

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Influence of frequency
• Tbridge = 2

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Influence of frequency
• Tbridge = 2.5

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Oscillating drag constant
• Tbridge = 1, Tdrag = 0.5

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Oscillating drag constant (cont.)
• Tbridge = 1, Tdrag = 1

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Oscillating drag constant (cont.)
• Tbridge = 1, Tdrag = 1.5

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Summary 1

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Summary
• Microorganism motion can be modeled by
oscillating spring normal length and drag
constant
• Noticeable displacement is observed if
Tspring ~ Tdrag
• Other than that condition gives zero displace-
ment in average for long observation time

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Model 2

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More complex cell
• A cell could have
more than one
locomotive organ,
e.g. eight organs

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More complex cell (cont.)
• Or just four organs

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Synchronization
• Each locomotive organ should have certain
initial phase in order the organism to have
directional motion
• Supposed there is M locomotive organs
• Assumed that each is positioned at
πθ 2
M
j
j =

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Synchronization (cont.)
• And have initial phase φj
• But with same period T
• Resultant motion is simple sum of each
locomotive organ

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Results 2

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No motion
• 8-dot0.eps 0.000 0.000 0.000 0.000 0.000
0.000 0.000 0.000
• 8-dot1.eps 0.000 0.500
0.000 0.500 0.000 0.500
0.000 0.500
• 4-dot0.eps 0.000 0.000
0.000 0.000
• 4-dot1.eps 0.000 0.000
1.000 0.000

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Linear oscillating motion
• 4-lin0.eps 0.000
0.000 0.250 0.250
• 4-lin1.eps 0.000
0.250 0.250 0.000
• 4-lin2.eps 0.250
0.250 0.000 0.000
• 4-lin3.eps 0.250
0.000 0.000 0.250
01
23

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Circular motion φj = 2π/M
1 2 3 4
5 6 7 8

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M = 4, φj / T = 0.3, 0.4, 0.5, 0.6
0.3 0.4
0.5 0.6
4-cur0.eps
0.000 0.000
0.250 0.500

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Summary 2

40. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones40
Summary
• Synchronization of locomotive organs can
produce interesting motion
• Circular-like motion must obey that
φj = 2π/M and
• No motion can produced if all organs have the
same initial phase
πθ 2
M
j
j =

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Acknowledgement

42. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones42
Acknowledgement
• This work is supported by Institut Teknologi
Bandung, and Ministry of Higher Education
and Research, Indonesia, through the scheme
Penelitian Unggulan Perguruan Tinggi – Riset
Desentralisasi Dikti with contract number
310i/I1.C01/PL/2015
• Presentation of this work is supported by
Committee of SEACOMP 2015

43. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones43
Thank you