Symomath 2015 Microorganism Motion Simulation
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This document summarizes a presentation given at the International Symposium on BioMathematics in 2015 in Bandung, Indonesia. The presentation models the motion of microorganisms using a granular model that represents cells as connected spherical particles subjected to oscillating spring and drag forces from the surrounding fluid. Simulation results show noticeable displacement occurs when the oscillation periods of the spring and drag forces are similar, while other conditions produce little average displacement over time. The model provides insight into how microorganism motion can arise from interactions between an organism's shape changes and fluid forces.
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Symomath 2015 Microorganism Motion Simulation
- 1. The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 1 Simulation of Microorganism Motion in Fluid Based on Granular Model Sparisoma Viridi1 and Nuning Nuraini2 1 Physics Department, Institut Teknologi Bandung 2 Mathematics Department, Institut Teknologi Bandung Jalan Ganesha 10, Bandung 40132, Indonesia 1 dudung@fi.itb.ac.id, 2 nuning@math.itb.ac.id
- 2. The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 2 Outline • Introduction • Model • Results • Summary
- 3. The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 3 Introduction
- 4. The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 4 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. The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 5 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. The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 6 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. The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 7 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. The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 8 Model
- 9. The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 9 Two grain model • Two spherical particles as cells, which are connected by a spring mi mj kij
- 10. The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 10 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. The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 11 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. The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 12 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. Change of drag coefficient • Both cell can have same or different Cd i = 1, 2 for each particle The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 13 ( ) ( )min,max, drag min,max, 2 12 cos 2 1 , ddddid CC T t CCC + −= π
- 14. The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 14 Molecular dynamics method • Newton second law of motion • Euler method += ∑j ijii SD m a 1 ( ) ( ) tatvttv iii ∆+=∆+ ( ) ( ) ( ) ttvtrttr ii ∆+=∆+
- 15. The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 15 Results
- 16. The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 16 Displacement
- 17. Same drag constant • Cd = 0.1, Cd = 0.1 The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 17
- 18. Same drag constant (cont.) • Cd = 0.1, Cd = 0.4 The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 18
- 19. Same drag constant (cont.) • Cd = 0.4, Cd = 0.1 The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 19
- 20. Same drag constant (cont.) • Cd = 0.4, Cd = 0.4 The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 20
- 21. Influence of frequency • Tbridge = 2 The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 21
- 22. Influence of frequency • Tbridge = 2.5 The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 22
- 23. Oscillating drag constant • Tbridge = 1, Tdrag = 0.5 The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 23
- 24. Oscillating drag constant (cont.) • Tbridge = 1, Tdrag = 1 The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 24
- 25. Oscillating drag constant (cont.) • Tbridge = 1, Tdrag = 1.5 The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 25
- 26. The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 26 Summary
- 27. The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 27 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
- 28. The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 28 Acknowledgement
- 29. 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 The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 29
- 30. The International Symposium on BioMathematics (Symomath) 2015 4-6 November 2015, Bandung, Indonesia 30 Thank you