16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012
Micro PIV Measurements of the Internal Flow of an Amoeba proteus
Elka Lobutova1, Ling Li1, Danja Voges2, Christian Resagk1,*
1: Institute Thermodynamics and Fluid Mechanics, Ilmenau University of Technology, Ilmenau, Germany
2: Department of Biomechatronics, Ilmenau University of Technology, Ilmenau, Germany
* correspondent author: [email protected]
Abstract We report about the investigation of the amoeboid locomotion at Amoeba proteus. Based on the
detailed experimental study of the internal cytoplasm flow and the variation of the contour of the amoeba
with optical flow measurement techniques like particle image velocimetry (PIV) we found characteristic
velocity fields and motions of the center of mass. As result we got local cytoplasm velocities in the range
between 0.3 µm/s and 10 µm/s and the averaged maximum velocity is up to four times higher than the
motion speed of the amoeba’s centroid. The velocity time series at several points in the cytoplasm show a
fluctuating internal flow with times scales between 1s and 10 s.
1. Introduction
Amoeba proteus is the classic specimen to study amoeboid movement. The genus Amoeba (aquatic
or parasitic) is a representative unicellular organism with a cell membrane, a thick cortical gel layer
(ectoplasm), an endoplasm (sol) and many endogenous particles like lipid bodies or food vacuoles.
Amoeboid movement is ubiquitary in the animal kingdom (protozoa, slime molds, leukocytes…). It
is the most common type of movement characterised by cytoplasmic streaming and continuous
hanging the body shape, let’s call it shape variability. Three main phases of amoeboid locomotion
can be defined: a) protrusion (extension of pseudopodia), b) attachment (connection to substratum),
and c) traction (forward movement of body) [Condeelis 1993, Rogers et al. 2008, Stossel 1993].
Pseudopodia (number not fixed) can build at any region of the body (Fig. 1.1). This is a continuous
process which can in general be described by local changes in the mechanical compliance of the cell
cortex.
Fig. 1.1: Amoeba proteus.
Since more than 200 years scientists explore the phenomenon of cytoplasmic streaming, its reasons
and physical mechanism. Obviously involved is an interaction of the actin-myosin-complex,
calcium-ions, actin-binding proteins, osmotic pressure and the sol-gel transformation during
crawling of amoeba [Mitchison et al. 1996, Patrick et al. 1995, Pomorski et al. 2007]. Less
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16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012
described in detail in the literature are the properties of the cytoplasmic streaming. In this work we
will take a look at the amoeba from the fluid mechanical point of view in order to find new motion
parameters and fluid properties for the modelling of the amoeboid locomotion and for the
development of prototypes for robotic applications [Alt et al. 2012].
2. Investigation of the amoeboid movement using micro particle image
velocimetry (µPIV)
2.1. Materials, methods and experimental setup
A. proteus was ordered from science Supply Company and carried in a laboratory in mineral water
with pH 7.0 and 2% soil water medium. Amoeba is fed on Chilomonas. Individuals were
transferred to a micro-slide together with some drops of the original culture medium. The IBIDI
µ-slide was then placed on the stage of the microscope ready for the experiment and left for about
10 min before the beginning of the observations. This allowed the amoeba to adapt to the new
conditions.
Common micro particle image velocimetry (µPIV) is used to measure the cytoplasmic streaming
and the movement of the amoeba. With this optical flow measurement technique a thin plane of the
fluid with tracer particles is illuminated and the images of the tracer particles are recorded by a
digital camera through an optical imaging system. From the cross-correlation function of image
pairs with known temporal displacement the velocity of the tracer particles can be reconstructed
resulting in a 2D vector plot of the fluid velocity field [Raffel et al. 1997].
In our case we used an inverted microscope in the phase-contrast mode as the imaging system and
the microscope’s own halogen lamp for the illumination. Dependent on the depth of field of the
microscope lens the measurement volume had a height of less than 10 microns. The granules of the
cytoplasm are best suited as natural tracer particles. Their size is about 5 µm. Videos were taken by
a 1.4 Mpix monochrome microscope camera at a rate of 12 frames per second.
The experimental setup of the µPIV measurement is shown in Fig. 2.1. It consists of a MOTIC
AE31 inverted microscope in the phase contrast mode, an IBIDI µ-slide with 50x50x0.4 mm3 size
and a MOTICAMPRO 1.4 Mpix CCD camera. A desktop computer with ILA VidPIV software was
used for image processing and PIV analysis. A dc power supply provides the voltage to two
platinum electrodes at both ends of the water-filled µ-slide and a current meter is used to control the
electrical field in the slide.
4
1
2
6
3
5
Fig. 2.1: Experimental setup for the µPIV measurements in a micro-channel applying a dc electric
field. 1 – MOTIC AE31 phase contrast inverted microscope, 2 – MOTICAM PRO 385C 1.4 Mpix
ccd camera, 3 - IBIDI µ-slide 50x5x0.4 mm3, 4 – Platinum electrodes for applying a dc electric
field, 5 – dc source, 6 – data processing
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16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012
2.2. Results
A. proteus is moving using pseudopodia. Normally there is more than one pseudopodium at the
same time. The movement is not intense and has not preferred direction. In order to stimulate the
movement of the amoeba in a certain direction, it was exposed to dc electric field during the
measurements. A comparison between free moving amoeba and amoeba in electric field is shown in
Fig. 2.2.
Exposed to dc electric field amoeba typically migrate towards the cathode [Korohoda et al. 2000,
Teixeira-Pinto et al. 1960]. The strength of the electric field was estimated with a method
commonly used in research involving cell electrophoresis in cylindrical or rectangular chambers
[Abramson et al. 1942, Seaman 1965]. The field strength E = I / σA, where I is the current in
Amperes [A], σ is the electrical conductivity of the medium in Siemens per centimetre [Scm-1] and
A is the cross-section area of the chamber in cm2. The current intensity used in our experiments was
in the range of 0.026 mA – 0.029 mA. And the resulting field strength 6.5 Vcm-1 – 7.25 Vcm-1.
(a)
(b)
Fig. 2.2: Comparison between microscope image of Amoeba proteus with horizontal electric field
(a) and without electric field (b)
However we observed that there is no change in the velocity field in the cytoplasm at different
strengths of the electric field until the damage threshold leading to a galvanic disruption of the
amoeba. The presence of electric field influenced only the direction of the internal cytoplasm flow.
Fig. 2.3 and Fig. 2.4 show the magnitude of flow velocity in amoeba without and with an applied
electric field. The strength of the field is 6.5 Vcm-1 and will be used as a boundary condition for all
further discussion in this contribution.
400
(a)
y [µm]
300
Absolute velocity [mms-1]
8.00
6.06
4.59
3.48
2.64
2.00
200
100
100
200
300
400
500
600
x [µm]
Fig. 2.3: Magnitude of the cytoplasm velocity in the amoeba without electric field, in the x-y plane.
The velocity field is averaged over 98 single frames.
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16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012
400
(b)
y [µm]
300
200
Absolute velocity [mms-1]
7.00
6.00
5.00
4.00
3.00
2.00
1.00
Field direction
100
300
400
500
600
x [µm]
700
800
900
Fig. 2.4: Magnitude of the cytoplasm velocity in the amoeba with electric field, in the x-y-plane.
The strength of the field is 6.5 Vcm-1. The velocity field is averaged over 98 single frames.
Using µPIV we successfully measured the whole velocity field within a crawling amoeba, see Fig.
2.5. The spatial resolution of the measurement is 4 µm and the temporal resolution is 83 ms. The
velocity profiles from different cross-sections show the intersection of the inner liquid part of the
cytoplasm (endoplasm) and the outer viscoelastic layer of the cytoplasm (ectoplasm), Fig. 2.6 c and
d. In contrast to the velocity profiles in the front part the profiles in the rear part of the amoeba are
more flat, and there is no clear boundary line between liquid and viscous layers, Fig. 2.6 a, b, e and
f. If we compare the velocity magnitude of the cytoplasm flow in the front and in the rear part of the
amoeba (Fig. 2.3 – Fig. 2.6) we observe a much lower velocity in the rear part. With 3 µms-1 it is
only half as large the cytoplasm flow in the front section. The higher cytoplasm velocity in front of
the moving amoeba can be explained with the development of a pseudopod. Therefore the amoeba
needs to pump cytoplasm from the rear part to the front part using a kind of hydrostatic pump. This
pumping mechanism is thought to be based on a sol-gel transformation in the cytoplasm, inducing
the formation of a viscoelastic contractile actin cortex “gel” at the lateral and rearward boundaries
and a simultaneous forward flow of the bulk “sol” fluid.
y [µm]
400
300
200
300
400
500
600
x [µm]
700
800
900
Fig. 2.5: Vector field of the cytoplasm flow of an amoeba. It is averaged over 98 single frames.
The velocity profile averaged over 400 single frames at the central part of the amoeba shows, in
agreement with the findings from Rogers et al. 2008, a parabolic profile in the inner part of the
cross section and constant velocity in the outer part (Fig. 2.7a). The latter we can explain a slow
forward movement of the viscoelastic ectoplasm (cortex).
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16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012
We measured not only the internal flow of the cytoplasm but also studied the movement of the
amoeba body using image processing methods. In Fig. 2.7b the movement of the centre of mass of
the amoeba exposed to the electric field is plotted over the time. As result we see a strongly linear
movement with a velocity of 3 µms-1. This velocity is half as large as the maximum internal
instantaneous velocities and 66% of the averaged cytoplasm velocity at the center of the amoeba.
In Fig. 2.8 time series of the maximum cytoplasm velocity at different positions of the center line
are plotted. We find velocity fluctuations up to 10 µms-1, especially in the front part of the amoeba
where a pseudopod is developing. Less fluctuations in the rear part are indicating a higher
hydrostatic pressure during the pumping process.
(a)
5
0
x=452µm
-50
v [µm/s]
v [µm/s]
x=352µm
0
xa [µm]
50
(b)
5
0
-50
0
xa [µm]
0
x=652µm
v [µm/s]
v [µm/s]
x=552µm
5
(c)
-50
0
xa [µm]
50
(d)
5
0
-50
0
xa [µm]
0
(e)
-50
0
xa [µm]
50
x=852µm
v [µm/s]
v [µm/s]
x=752µm
5
50
50
5
0
(f)
-50
0
xa [µm]
50
Fig. 2.6: Velocity profiles at different cross-sections of an amoeba. The profiles are extracted from
the 2d vector plot in Fig. 2.4.
(a)
(b) 30
x=648µm
s [µm]
v [µm/s]
4
2
0
-50
0
xa [µm]
20
10
0
50
0
2
4
6
8
10
t [s]
Fig. 2.7: Velocity profile from the central part of the amoeba averaged over 400 single frames (a).
Path of the center of mass of the amoeba (b).
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16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012
0
0
2
4
6
t [s]
x=552µm
8
10
0
0
2
4
6
t [s]
x=752µm
8
10
0
0
2
4
t [s]
6
8
vmax [µm/s]
10
vmax [µm/s]
x=452µm
vmax [µm/s]
vmax [µm/s]
vmax [µm/s]
vmax [µm/s]
x=352µm
10
0
0
2
4
6
t [s]
x=652µm
8
0
2
4
6
t [s]
x=852µm
8
0
2
10
0
10
0
4
t [s]
6
8
Fig. 2.8: Time series of the maximum cytoplasm velocity at different positions.
3. Summary
We studied the internal flow of the cytoplasm inside Amoeba proteus using µPIV. The onedimensional movement of the amoeba was controlled by a weak external electric field applied
trough platinum wires in the water-filled µ-slide. We observed that the magnitude of the internal
flow velocity field is not dependent on the external field but with field the generation of pseudopods
occurs only in the direction of the field and the amoeba's body is aligned parallel to the streamlines.
From the PIV measurements we calculated time-dependent velocity plots, time-averaged velocity
profiles and velocity time series. In agreement with the findings of Rogers et al. 2008 the flow in
the cytoplasm is similar to a viscose pipe flow of a Newtonian fluid with a parabolic profile at a
Reynolds number of Re = 10-4. The maximum velocity in the centre of the amoeba varies between
0.3 and 10 µms-1. The specific flow rate (per height) of the cytoplasm in the 40 µm wide cytoplasm
channel is in the order of Q/h = 80 µm2s-1. Furthermore, we quantified the linear movement of
Amoeba proteus in an external electric field. In further investigations we want to systemically study
the cytoplasm flow under different boundary conditions like external surface and volume forces. To
get more knowledge about the variations in cytoplasmic viscosity, the local concentration of
Calcium ions or other stained regulatory proteins could be measured by fluorescence microscopy.
4. References
Abramson, HA, Moyer, LS, Gorin, MH (1942) Electrophoresis of proteins and the chemistry of cell
surfaces. Reinhold, New York
Alt, W, Böhm, V, Kaufhold, T, Lobutova, E, Resagk, C, Voges, D, Zimmermann, K (2012)
Theoretical and Experimental Investigations of Amoeboid Movement and First Steps of
Technical Realisation. Notes on Numerical Fluid Mechanics and Multidisciplinary Design,
Nature-Inspired Fluid Mechanics, Vol. 119, 3-23, C. Tropea, H. Bleckmann (Eds.), Springer
Condeelis, J (1993) Life at the leading edge: formation of cell protrusion. Annu. Rev. Cell. Biol. 9:
414-440
Korohoda, W, Mycielska, M, Janda, E, Madeja, Z (2000) Immediate and long-term galvanotactic
responses of amoeba proteus to electric fields. Cell Motil. Cytoskeleton 45: 10-26
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16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012
Mitchison, TJ, Cramer, LP (1996) Actin-based cell motility and cell locomotion. Cell 84: 371-379
Patrick, YJ, Peter, AP, Scott, AW, Elliot, LE (1995) A mechanical function of myosin II in cell
motility. J. of Cell Sci. 108: 387-393
Pomorski, P, Krzeminski, A, Wasik, A, Wierzbicka, K, Baranska, J, Klopocka, W (2007) Actin
dynamics in Amoeba proteus motility. Protoplasma 231: 31-41
Raffel, M, Willert, CE, Kompenhans, J (1997) Particle Image Velocimetry: A Practical Guide.
Springer, Berlin Heidelberg New York
Rogers, SS, Waigh, ThA, Lu, JR (2008) Intracellular microrheology of motile Amoeba proteus.
Biophys. J. 94: 3313-3322
Seaman, GVF (1965) Electrophoresis using a cylindrical chamber. In: Ambrose, E.J. (ed.) Cell
electrophoresis, pp. 4-21. J&A. Churchill Ltd, London
Stossel, ThP (1993) On the crawling of animal cells. Science 260: 1086-1094
Teixeira-Pinto, AA, Nejelski, JR, Cutler, JL, Heller, JH (1960) The behaviour of unicellular
organisms in an electromagnetic field. Exp. Cell Res. 20: 548-564
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