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. 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
- 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-Taix辿 et al., 2010) L. Leal-Taix辿, M. Heydt, S. Weie, 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
- 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 =
- 11. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones11 Fluid drag force Drag force Cd is drag constant A is cross sectional area f is fluid density vf is fluid velocity ( ) fi fi dfi vv vv CAD 駕 駕 = 3 2 1
- 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 留 留 + 錚 錚 錚 錚 錚 錚 錚 錚 = 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 + 錚 錚 錚 錚 錚 錚 錚 錚 =
- 14. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones14 Molecular dynamics method Newton second law of motion Euler method 錚 錚 錚 錚 錚 錚 錚 錚 += j ijii SD m a 駕駕 1 ( ) ( ) tatvttv iii +=+ 駕駕 ( ) ( ) ( ) ttvtrttr ii +=+ 駕駕
- 15. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones15 Comprehensive view of the model
- 16. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones16 Results 1
- 17. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones17 Displacement
- 18. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones18 Same drag constant Cd = 0.1, Cd = 0.1
- 19. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones19 Same drag constant (cont.) Cd = 0.1, Cd = 0.4
- 20. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones20 Same drag constant (cont.) Cd = 0.4, Cd = 0.1
- 21. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones21 Same drag constant (cont.) Cd = 0.4, Cd = 0.4
- 22. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones22 Influence of frequency Tbridge = 2
- 23. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones23 Influence of frequency Tbridge = 2.5
- 24. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones24 Oscillating drag constant Tbridge = 1, Tdrag = 0.5
- 25. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones25 Oscillating drag constant (cont.) Tbridge = 1, Tdrag = 1
- 26. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones26 Oscillating drag constant (cont.) Tbridge = 1, Tdrag = 1.5
- 27. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones27 Summary 1
- 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. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones29 Model 2
- 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. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones31 More complex cell (cont.) Or just four organs
- 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 慮 2 M j j =
- 33. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones33 Synchronization (cont.) And have initial phase j But with same period T Resultant motion is simple sum of each locomotive organ
- 34. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones34 Results 2
- 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. 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. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones37 Circular motion j = 2/M 1 2 3 4 5 6 7 8
- 38. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones38 M = 4, j / 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. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones39 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 j = 2/M and No motion can produced if all organs have the same initial phase 慮 2 M j j =
- 41. SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndones41 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