molecular dynamics simulation of microorganism motion in fluid based on granular model in the case...

SEACOMP 2015 10 - 12 December 2015, Yogyakarta, lndonesia

1

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

1Physics Department, Institut Teknologi BandungJalan Ganesha 10, Bandung 40132, Indonesia2Mathematics Department, Institut Teknologi Bandung Jalan Ganesha 10, Bandung 40132, Indonesia*[email protected]


2

Outline

• Introduction• Model 1• Results 1• Summary 1• Model 2• Results 2• Summary 2• Acknowledgements


3

Introduction


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

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

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

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

Model 1

S. Viridi, N. Nuraini, 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

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

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


12

Change of spring normal length

• Spring normal length varies with time

Tbridge is oscillation period of bridge between cells

LT

tLlij

12sin

bridge


13

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


14

Molecular dynamics method

• Newton second law of motion

• Euler method

jijii SD

ma

1

tatvttv iii

ttvtrttr ii


15

Comprehensive view of the model


16

Results 1


17

Displacement


18

Same drag constant

• Cd = 0.1, Cd = 0.1


19

Same drag constant (cont.)

• Cd = 0.1, Cd = 0.4


20


• Cd = 0.4, Cd = 0.1


21


• Cd = 0.4, Cd = 0.4


22

Influence of frequency

• Tbridge = 2


23

Influence of frequency

• Tbridge = 2.5


24

Oscillating drag constant

• Tbridge = 1, Tdrag = 0.5


25

Oscillating drag constant (cont.)

• Tbridge = 1, Tdrag = 1


26

Oscillating drag constant (cont.)

• Tbridge = 1, Tdrag = 1.5


27

Summary 1


28

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


29

Model 2


30

More complex cell

• A cell could havemore than onelocomotive organ,e.g. eight organs


31

More complex cell (cont.)

• Or just four organs


32

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


33

Synchronization (cont.)

• And have initial phase φj

• But with same period T

• Resultant motion is simple sum of each locomotive organ


34

Results 2


35

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


36

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


37

Circular motion φj = 2π/M

1 2 3 4

5 6 7 8


38

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

Summary 2


40

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


41

Acknowledgement


42

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

Thank you

molecular dynamics simulation of microorganism motion in fluid based on granular model in the case...

Science