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SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones1
Molecular Dynamics Simulation of
Microorganism Motion in Fluid Ba...
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones2
Outline
• Introduction
• Model 1
• Results 1
• Summary 1
• Model ...
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones3
Introduction
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones4
Motion patterns of microorganism
• The patterns are unique: (1) o...
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones5
An active fluid
• Turbulence flow can occur in high viscous fluid...
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones6
Flagella as thruster
• Flagella introduces force and torque to th...
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones7
Shrink and swallow model
• Pressure difference can induce motion ...
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones8
Model 1
S. Viridi, N. Nuraini, The International Symposium on Bio...
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones9
Two grain model
• Two spherical particles as cells, which are
con...
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones10
Push and pull spring force
• Spring force
lij is normal length o...
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones11
Fluid drag force
• Drag force
Cd is drag constant
A is cross sec...
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones12
Change of spring normal length
• Spring normal length varies wit...
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones13
Change of drag coefficient
• Both cell can have same or differen...
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones14
Molecular dynamics method
• Newton second law of motion
• Euler ...
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones15
Comprehensive view of the model
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones16
Results 1
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones17
Displacement
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones18
Same drag constant
• Cd = 0.1, Cd = 0.1
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones19
Same drag constant (cont.)
• Cd = 0.1, Cd = 0.4
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones20
Same drag constant (cont.)
• Cd = 0.4, Cd = 0.1
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones21
Same drag constant (cont.)
• Cd = 0.4, Cd = 0.4
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones22
Influence of frequency
• Tbridge = 2
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones23
Influence of frequency
• Tbridge = 2.5
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones24
Oscillating drag constant
• Tbridge = 1, Tdrag = 0.5
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones25
Oscillating drag constant (cont.)
• Tbridge = 1, Tdrag = 1
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones26
Oscillating drag constant (cont.)
• Tbridge = 1, Tdrag = 1.5
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones27
Summary 1
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones28
Summary
• Microorganism motion can be modeled by
oscillating spr...
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones29
Model 2
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones30
More complex cell
• A cell could have
more than one
locomotive o...
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones31
More complex cell (cont.)
• Or just four organs
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones32
Synchronization
• Each locomotive organ should have certain
init...
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones33
Synchronization (cont.)
• And have initial phase φj
• But with s...
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones34
Results 2
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones35
No motion
• 8-dot0.eps 0.000 0.000 0.000 0.000 0.000
0.000 0.000...
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones36
Linear oscillating motion
• 4-lin0.eps 0.000
0.000 0.250 0.250
•...
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones37
Circular motion φj = 2π/M
1 2 3 4
5 6 7 8
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones38
M = 4, φj / T = 0.3, 0.4, 0.5, 0.6
0.3 0.4
0.5 0.6
4-cur0.eps
0....
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones39
Summary 2
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones40
Summary
• Synchronization of locomotive organs can
produce inter...
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones41
Acknowledgement
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones42
Acknowledgement
• This work is supported by Institut Teknologi
B...
SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones43
Thank you
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Molecular Dynamics Simulation of Microorganism Motion in Fluid Based on Granular Model in the Case of Multiple Simple Push-Pull Filaments

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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.

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Molecular Dynamics Simulation of Microorganism Motion in Fluid Based on Granular Model in the Case of Multiple Simple Push-Pull Filaments

  1. 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. 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. 3. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones3 Introduction
  4. 4. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones4 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. 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. 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. 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. 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. 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
  10. 10. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones10 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−−= 
  11. 11. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones11 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. 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. 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. 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 ∆+=∆+ 
  15. 15. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones15 Comprehensive view of the model
  16. 16. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones16 Results 1
  17. 17. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones17 Displacement
  18. 18. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones18 Same drag constant • Cd = 0.1, Cd = 0.1
  19. 19. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones19 Same drag constant (cont.) • Cd = 0.1, Cd = 0.4
  20. 20. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones20 Same drag constant (cont.) • Cd = 0.4, Cd = 0.1
  21. 21. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones21 Same drag constant (cont.) • Cd = 0.4, Cd = 0.4
  22. 22. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones22 Influence of frequency • Tbridge = 2
  23. 23. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones23 Influence of frequency • Tbridge = 2.5
  24. 24. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones24 Oscillating drag constant • Tbridge = 1, Tdrag = 0.5
  25. 25. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones25 Oscillating drag constant (cont.) • Tbridge = 1, Tdrag = 1
  26. 26. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones26 Oscillating drag constant (cont.) • Tbridge = 1, Tdrag = 1.5
  27. 27. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones27 Summary 1
  28. 28. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones28 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
  29. 29. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones29 Model 2
  30. 30. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones30 More complex cell • A cell could have more than one locomotive organ, e.g. eight organs
  31. 31. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones31 More complex cell (cont.) • Or just four organs
  32. 32. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones32 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 =
  33. 33. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones33 Synchronization (cont.) • And have initial phase φj • But with same period T • Resultant motion is simple sum of each locomotive organ
  34. 34. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones34 Results 2
  35. 35. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones35 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
  36. 36. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones36 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
  37. 37. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones37 Circular motion φj = 2π/M 1 2 3 4 5 6 7 8
  38. 38. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones38 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
  39. 39. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones39 Summary 2
  40. 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 =
  41. 41. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones41 Acknowledgement
  42. 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. 43. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones43 Thank you

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