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SKF 2015 16 - 17 Desember 2015, Bandung, lndonesia 1
Model Pergerakan Dua-Dimensi Mikroorganisme dalam Fluida
berbasiskan Butiran
Sparisoma Viridi1* dan Nuning Nuraini2
1Physics Department, Institut Teknologi BandungJalan Ganesha 10, Bandung 40132, Indonesia2Mathematics Department, Institut Teknologi Bandung Jalan Ganesha 10, Bandung 40132, Indonesia*dudung@fi.itb.ac.id
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Outline
• Introduction• Model 1, Results 1, Summary 1• Model 2, Results 2, Summary 2• Model 3, Results 3, Summary 3• Acknowledgements
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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).
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An active fluid
• Turbulence flow can occur in high viscous fluid or in low Reynolds number (Aranson, 2013)
I. Aranson, Physics 6, 61 (2013).
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Motion observations
• Sperm of sea urchin(Psammechinusmiliaris)
• Planar sinusoidalmotion (Keller &Rubinow, 1976)
J. B. Keller, S. I. Rubinow, Biophysical Jounal 16, 151-170 (1976).
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Motion observations (cont.)
• Same motion modewith multipleexposure
J. B. Keller, S. I. Rubinow, Biophysical Jounal 16, 151-170 (1976).
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Prokaryote propulsion data
C. Brennen, H. Winet, Annual Review of Fluid Mechanics 9, 339-398 (1977).
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Prokaryote propulsion data (cont.)
C. Brennen, H. Winet, Annual Review of Fluid Mechanics 9, 339-398 (1977).
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Eukaryote propulsion data
C. Brennen, H. Winet, Annual Review of Fluid Mechanics 9, 339-398 (1977).
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Eukaryote propulsion data (cont.)
C. Brennen, H. Winet, Annual Review of Fluid Mechanics 9, 339-398 (1977).
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Eukaryote propulsion data (cont.)
C. Brennen, H. Winet, Annual Review of Fluid Mechanics 9, 339-398 (1977).
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Brennen, ibid.
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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).
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Self-electrophoretic through membran
• Flow of ions thrusts the microorganism
P. Mitchell, FEBS Letters 28, 1-4 (2012).
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Shrink and swallow model
• Pressure difference can induce motion (Viridi and Nuraini, 2014)
S. Viridi, N. Nuraini, AIP Conference Proceedings 1587, 123-126 (2014).
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Model 1
S. Viridi, N. Nuraini, The International Symposium on BioMathematics (Symomath) 2015, 4-6 November 2015, Bandung, Indonesia
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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 areaρf is fluid density
vf is fluid velocity
fi
fidfi vv
vvCAD
3
21
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Change of spring normal length
• Spring normal length varies with time
Tbridge is oscillation period of bridge between cells
LT
tLlij
12sin
bridge
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Change of drag coefficient
• Both cell can have same or different Cd
i = 1, 2 for each particle
min,max,drag
min,max, 212cos
21, ddddid CC
TtCCC
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Molecular dynamics method
• Newton second law of motion
• Euler method
jijii SD
ma
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 ifTspring ~ Tdrag
• Other than that condition gives zero displace-ment in average for long observation time
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Model 2S. Viridi, F. Haryanto, N. Nuraini, S. N. Khotimah, SEACOMP 2015, 2015, 10-12 December 2015, Yogyakarta, Indonesia
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More complex cell
• A cell could havemore than onelocomotive 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
2Mj
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 0.5000.000 0.500 0.000 0.5000.000 0.500
• 4-dot0.eps 0.000 0.0000.000 0.000
• 4-dot1.eps 0.000 0.0001.000 0.000
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Linear oscillating motion
• 4-lin0.eps 0.0000.000 0.250 0.250
• 4-lin1.eps 0.0000.250 0.250 0.000
• 4-lin2.eps 0.2500.250 0.000 0.000
• 4-lin3.eps 0.2500.000 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
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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
2Mj
j
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Model 3
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Gerak Organ Lokomotif
• Periode sampling berbeda (T): 1, 2, 3, 4
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Gerak Organ Lokomotif (cont.)
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Pengaruh frekuensi sampling
• 1 dan 4 ( fassa ) 2Mj
j
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Frekuensi satu organ saja
• 1, 2, 3, 4 (fasa seperti sebelum
-nya)
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Summary 3
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Summary
• Frekuensi sampling yang sama pada setiap organ lokomotif untuk sebuah gerak hampir melingkar tidak memberikan pengaruh pada mode gerak
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Summary (cont.)
• Gerak hampir melingkar yang memenuhi
φj = 2π/M and
dapat menjadi gerak berarah bila salah satu organ lokomotif memiliki frekuensi sampling berbeda (2, 3, 4, ..)
2Mj
j
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Summary (cont.)
• Sinkronisasi antara panjang pegas dan koefi-sien gesek dalam suatu organ lokomotif i,
berbeda dengan sinkronisasi antar organ loko-motif i dan j agar organisme dapat mengha-silkan gerak berarah
MiTT iidragispring ,,,
kspringjspring TT ,,
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Acknowledgement
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Acknowledgement
• Riset ini didukung oleh Institut Teknologi Bandung, Penelitian Unggulan Perguruan Tinggi – Riset Desentralisasi Dikti bernomor 310i/I1.C01/PL/2015
• Presentasi ini didukung oleh FMIPA dan Panitia SKF 2015
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Thank you