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The slime mold Physarum polycephalum exhibits well-known oscillations of its vein network, which drive the so-called shuttle streaming of endoplasmic fluid within the veins. These oscillations are already visible in microplasmodia, which are precursors of extended networks. We present a correlation analysis of single microplasmodia monitored in bright field. We measure the cross-sectional area and calculate the spatio-temporal velocity map of the cellular edge. We find fast oscillations with a period of 1-2 minutes superimposed on slow oscillations with a period of 20 minutes. Amplitude and period of the fast oscillations correlate with the phase of the slow oscillations. In addition, we find lateral contraction waves running along the cellular circumference with a speed of 10 microns per second.
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C.T. Lim and J.C.H. Goh (Eds.): WCB 2010, IFMBE Proceedings 31, pp. 1133–1136, 2010.
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Microplasmodium Dynamics of Physarum Polycephalum
E. Bernitt
1,2,*
, C. Oettmeier
1,2,*
, and H.-G. Döbereiner
1,2
1
Institut für Biophysik, Universität Bremen, Germany
2
Research Center of Excellence in Mechanobiology, National University of Singapore, Singapore
AbstractThe slime mold Physarum polycephalum exhibits
well-known oscillations of its vein network, which drive the so-
called shuttle streaming of endoplasmic fluid within the veins.
These oscillations are already visible in microplasmodia, which
are precursors of extended networks. We present a correlation
analysis of single microplasmodia monitored in bright field.
We measure the cross-sectional area and calculate the spatio-
temporal velocity map of the cellular edge. We find fast oscilla-
tions with a period of 1-2 minutes superimposed on slow oscil-
lations with a period of 20 minutes. Amplitude and period of
the fast oscillations correlate with the phase of the slow oscilla-
tions. In addition, we find lateral contraction waves running
along the cellular circumference with a speed of 10 microns
per second.
Keywords— Slime mold, oscillations, active gels, mechano-
biology, cell motility.
I. INTRODUCTION
The plasmodial slime mold Physarum polycephalum has
been the working horse of cell motility from the 60´s to the
early 80´s [1]. In the following years, the focus of attention
shifted gradually to the cellular slime mold Dictyostelium
discoideum as a model organism. Finally, during the last two
decades, mouse cells became the dominant system studied.
Recently, however, there has been revived interest in the
pattern [2] and network [3,4] forming properties of Physa-
rum. Remarkably, the unicellular (but multi-nucleated) organ-
ism Physarum can solve minimization problems with its
network of veins, which can grow to considerable size of
square centimeters or even square meters. At the basis of this
complex behavior are the intracellular regulatory mecha-
nisms, which consist of coupled biochemical and mechanical
oscillators [5]. The most prominent mechanical feature is the
rhythmic shuttle streaming of endoplasm in the veins [6].
This streaming is caused by oscillatory contractions of acto-
myosin sheets and fibrils forming an ectoplasmic tube. The
network of streaming endoplasm, which provides a long-
range coupling of distant parts of the organism, is part of the
information processing system of Physarum. Utilizing these
mechanobiological mechanisms, Physarum can anticipate
periodic events and mechanically react to them by memoriz-
ing timed stimuli [7].
Paramount for early events in network formation is the
dynamic behavior of microplasmodia from which extended
vein networks develop. Even though there is a body of lit-
erature on Physarum oscillations, high-resolution experi-
mental data on the spatio-temporal dynamics are rare. In
this contribution, we concentrate on the dynamic boundary
conditions of oscillating internal pattern formation: We
report on the time dependent morphology and front velocity
of a single microplasmodium.
F
ig. 1 Oscillating microplasmodium. The solid red and dashed blue con-
tour lines represent shapes 10 minutes apart and correspond to minimal and
maximal area in terms of 20 minutes oscillations (see arrows in Fig. 2A.)
II. MATERIAL AND METHODS
A. Preparation of Microplasmodia
Slime molds of the species Physarum polycephalum were
grown from spherules, which were kindly provided by the
group of W. Marwan, Magdeburg, Germany. Filter paper
containing spherules was placed on petri dishes with SDM-
agar [8] and a tiny drop of distilled water was added. After
one to two days, small yellow plasmodia emerged from the
filter paper and continued to grow. Plasmodia were further
cultivated on medium containing 1.7% of SDM-agar. Pro-
longed culturing of plasmodia was achieved by transferring
small cut-out pieces to new agar plates. When they had
Anlage A3
1134 E. Bernitt, C. Oettmeier, and H.-G. Döbereiner
IFMBE Proceedings Vol. 31
developed into well-defined, large networks covering the
6 cm diameter petri dish, they were submerged in growth
medium and left for one to five minutes. After submersion,
some plasmodial strands let go and could easily be sucked
from the agar surface using a pipette. The fragments were
then transferred into 500 ml Erlenmeyer flasks containing
100 ml of growth medium. The liquid culture was main-
tained at 24°C and submitted to an orbital shaking of 150
rpm. Under these conditions, microplasmodia with a diame-
ter on the order of 100 micron were formed by shear forces
from the larger fragments. For observation, microplasmodia
were placed in petri dishes (3.5 cm diameter) filled with a
thin layer of SDM-agar and placed over an inverted light
microscope (Zeiss Observer) equipped with an environ-
mental chamber. A constant temperature of 24°C and excess
nutrient conditions were maintained throughout the experi-
ment. Petri dishes were closed in order to avoid drying of
the agar.
B. Recording of Time Series
Images of oscillating microplasmodia were taken every 5
seconds in bright field at a magnification of 2.5x with a 12
bit AxioCam MRm
camera. Time series were recorded for
several hours under low light conditions as Physarum is
photosensitive. Accordingly, we used an exposure time of
926 ms. Exposure time and frame rate were chosen as to
minimize photo effects and, at the same time, sample the
one-minute area oscillations. Single microplasmodia of
interest were identified and movies cropped to appropriate
size.
C. Image Analysis
All image processing was done with Mathwork's Matlab
using the image processing toolbox. Given the high contrast
of the images, see Fig. 1, segmentation was straightforward
by application of an intensity threshold filter. From the
F
ig. 2 Area and velocity of microplasmodium shown in Fig.1. A) Area as a function of time. Arrows denote the position of the two contours shown in Fig.1
Time points of periodically occurring minima are indicated by vertically dashed lines. B) Normal velocity map of contours for the first 40 minutes. Red and
blue stripes denote contour extension and retraction respectively. C) Histogram of velocity distribution gathered for positive/negative curvature regions in
between inflection points of smoothed area in panel A
A
B
C
Microplasmodium Dynamics of Physarum Polycephalum 1135
IFMBE Proceedings Vol. 31
segmented image the object area can simply be calculated as
the sum of object pixels, see Fig. 2A, scaled with the spatial
resolution. Contour data were then obtained by morphologi-
cal operations on the binary images [9].
A global description of membrane edge dynamics can be
achieved using velocity charts. A velocity chart contains a
membrane edge velocity value for every point on the con-
tour of every frame. Each velocity value was calculated as
follows: For a contour point of a frame the distance to all
points of the next frame was calculated and stored. Thereaf-
ter the angles between straight lines connecting the point
with all other points of the next contour and normal direc-
tion of the contour were also calculated and stored. The
velocity was calculated as the length of the line with mini-
mal angle below a certain threshold distance divided by the
time between the two frames. When applied to all contour
points of all frames and scaled to the actual distance in
space and time this results in a complete velocity chart as
shown in Fig. 2B.
III. RESULTS
Microplasmodia were of different sizes ranging from 50
to 1000 micron in diameter. The small ones usually had an
uneven surface. We choose medium-size quasi-spherical
microplasmodia with a smooth surface for further analysis.
We encountered a variety of morphologies. Besides the
quasi-spherical shapes, which are the focus of this paper, we
found dumbbells and more complicated arrays of spherical
objects connected by small tubes. Dumbbells exhibited
oscillating exchange of protoplasm from one sphere into the
other [10]. Occasionally, we observed fusion of two isolated
quasi-spherical microplasmodia into a peanut-shaped mor-
phology. Opposing microplasmodia would correlate their
area oscillations, develop flattened juxtaposed regions,
adhere to one another, and finally fuse via retraction of the
equatorial double membrane. A detailed study of this phe-
nomenon is underway in our laboratory. In the following,
we present the dynamics of one single microplasmodium in
order to exemplify our data.
As shown in Fig. 2A, we observed a strikingly regular
20-minute-oscillation of equatorial area of the microplas-
modium. Superimposed are faster oscillations which shift in
amplitude. The Fourier spectrum of area oscillations (data
not shown) exhibits peaks at 19.2 (slow oscillation) and 9.6
(modulation of amplitude in fast oscillation) minutes, as
well as a cluster of seven peaks ranging from 1.0 to 1.7
minutes (fast oscillation). Close inspection shows that the
fast area oscillations tend to have a smaller amplitude and
larger period in the minima of the 20 minute variations.
This is most clearly seen in the velocity map shown in
Fig. 2B, where consecutive bands of positive and negative
contour velocity are grouped into larger and faster as well as
smaller and slower oscillations.
We have analyzed these regions by gathering velocity
values separately for negative (maxima) and positive (min-
ima) curvature of the smoothed area in Fig. 2A. Histograms
of both regions are shown in Fig 2C. Small area regions
have a narrower distribution than large area regions, reflect-
ing the different parts of the velocity map. For the standard
A
B
D
C
Fig. 3 Autocorrelation of velocity map (whole data set). Panels A & B
shows correlations for large area, Panel C & D for small area regions.
Panels A & B give the time cuts at zero space lag of the full spatio-
temporal correlation map shown in panels B & C. Correlation maxima fo
r
large area are at 0.92, 1.75, 2.33, 3.17, and 4.10 min time lag; maxima fo
r
small area are at 1, 1.5, 2.75, 3.33 and 4.58 min
1136 E. Bernitt, C. Oettmeier, and H.-G. Döbereiner
IFMBE Proceedings Vol. 31
deviations we find 390 nm/s and 540 nm/s, respectively.
Both mean values are smaller than 10 nm/s, i.e. we have
pure oscillations, no growth.
Consecutive velocity bands exhibit lateral waves running
along the circumference as well as standing wave patterns.
These special features of the velocity map are visible at the
positions marked with arrows. The horizontal arrow points
at two lateral contractions waves with opposite speeds,
annihilating at the marked point. For these waves, we find a
speed of (13.8 ± 3.4) µm/s. The two vertical arrows point at
nodes of standing waves. Note the change of color/contrast
from above to below the node. The oscillating black region
on top of the velocity map corresponds to variations in the
equatorial contour length of the microplasmodium.
In order to characterize the stochastic process behind the
morphological oscillations, we have calculated the autocor-
relation function of the velocity map for the large and small
area regions separately, as shown in Fig. 3. Generally, cor-
relation maps average out noise present in the data and
reveal information about the regulating parameters of the
underlying stochastic process. The transition from faster to
slower temporal oscillations is clearly visible when compar-
ing panels 3A/B with 3C/D. There is some crosstalk be-
tween the regions, but the overall trend is evident. The stan-
ding wave pattern, visible in the velocity map Fig. 2B,
shows up in the correlation map Fig. 3B as a shift in the
correlation bands at a space lag of 600 µm (see dashed li-
ned) compared to zero lag.
IV. DISCUSSION AND CONCLUSION
We have found a coupling of global area oscillations to
local contour oscillations of microplasmodia. This is in
accord with a recent model proposing a coupling of local
oscillators via the plasma pressure field [5]. Assuming vol-
ume conservation of the microplasmodia, a change in area
implies a change in the height profile, which will affect
pressure distribution. In turn, the change in pressure affects
amplitude and phase of the actomyosin contractions possi-
bly via stretch-activated Ca
++
channels. More detailed
measurements and imaging of calcium density fields are
clearly needed to support this conjecture.
Further, we found lateral waves of contractile activity
with a speed on the order of 10 µm/s. This is much faster
than in mouse embryonic fibroblasts or wings disks cells of
Drosophila melanogaster where one observes speeds of 0.4
µm/s and 0.1 µm/s, respectively [11]. Presumably this is
mainly due to the different sizes of the acto-myosin gel
masses. Whereas the lamellipodia in fibroblasts have an
extension on the order of 1 µm, the contractile region in a
microplasmodium [12] is on the order of the size of the cell
itsself, i.e., in our case about 100 µm. Indeed, this explains
the two order of magnitude difference in speed observed.
In summary, we have introduced spatio-temporal analy-
sis of the dynamic behavior of single microplasmodia.
Autocorrelation maps of local front velocity and its cross-
correlation with global geometry allow detailed comparison
with theoretical models of Physarum motility.
ACKNOWLEDGMENT
We thank W. Marwan for providing us with Physarum
spherules. We enjoyed the hospitality of Mike Sheetz and
the RCE in Mechanobiology where this paper was written.
HGD thanks K. Brix for getting him interested in Physa-
rum.
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Corresponding author: H.-G. Döbereiner. Email: hgd@uni-bremen.de
* These authors contributed equally to the work.
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The plasmodia of Physarum polycephalum show different oscillatory phenomena (time period approximately 1.3 min) in their contraction behaviour and their protoplasmic flow. The force generating system for these phenomena is cytoplasmic actomyosin. The biochemical nature and location(s) of the oscillator(s), i.e. the clock governing these phenomena are unknown. The following locations are discussed as possible sites of the oscillator: (1) cytoplasmic actomyosin, (2) the energy supply system, (3) inner Ca2+ stores, and (4) the plasmalemma, which must be involved at least in modulating the force generated by the contractile machinery during a chemotactic response. The following oscillatory phenomena were used to assess the effects of externally and internally applied substances (e.g. calcium antagonistic drugs, caffeine, D2O) on oscillating force output: (1) persistance of longitudinal contractile activity of veins (for external application of test substances), (2) persistance of radial activity of veins (for internal application of the test substances), (3) de novo generation of contractile activity in protoplasmic drops (external application). The data seem to exclude rhythmical Ca2+, Na+ or K+ transport across the plasmalemma as a triggering function for the oscillation. Contractile activity seems to represent a spontaneous, endogeneous oscillation which can be modulated via the plasmalemma during chemotaxis.
Article
Depending on the conditions of the axenic shuttle culture, microplasmodia of the acellular slime mold Physarum polycephalum can be subdivided into three classes regarding fine structural organization and protoplasmic streaming activity: (1) spherical and rod-shaped types, (b) ameboid types, and (c) symmetrical types. In ameboid microplasmodia, the motive force for the irregular protoplasmic streaming activity is generated by alternative contraction and relaxation of a membrane-associated layer, morphologically consisting exclusively of thin filaments (probably actin). The protoplasm flows along a hydraulic pressure gradient produced by the filament layer within limited regions of the cell periphery. In dumbbell-shaped microplasmodia the motive force for the regular protoplasmic shuttle streaming between the two spherical heads is generated both by volume changes of the peripheral cell region (caused by the contractile activity of the membrane-associated filament layer), and by volume changes of the internal cell membrane invagination system (caused by fibrils attached to the basal region of the invaginations). The development from the unordered protoplasmic streaming pattern and less complicated fine structural organization in ameboid microplasmodia to the highly organized protoplasmic shuttle streaming and the more complicated morphology in dumbbell-shaped microplasmodia can be explained by intermediate stages. Whereas the motive force for the transport of smaller amounts of protoplasm can be generated by the exclusive action of a cortical filament layer, the existence of a filament cortex, the display of cytoplasmic fibrils, and the development of plasma membrane invaginations appear to be a necessary precondition for the transport of large amounts of protoplasm.
Article
SUMMARY A wild strain of the multinucleate plasmodial myxomycete Physarum poly- cephalum was isolated in pure culture and grown on a medium consisting of 1 yo (w/v) Tryptone, 1% (w/v) glucose, 0.15% (w/v) yeast extract, 0.3% (w/v) CaCO,, inorganic salts and a small amount of chick embryo extract. The organism may be grown with this medium either as a single large plasmodium on surface culture, or as a suspension of tiny plasmodia in submerged culture. From an initial inoculum of 1 ml. of a %day culture, the average plasmodial yield in a submerged culture was about 80 mg. dry weight/20 ml. medium at 72 hr. Growth occurred only in the presence of small amounts of an unidentified factor which was present particularly in chick embryo extract and foetal calf serum. An isolate of P. polycephalum was grown continuously on this medium for over four years without an appreciable decrease in growth rate. Under proper conditions a suspension of tiny plasmodia from shaken culture will fuse to form a single large surface plasmodium which exhibits syn- chronous mitosis.
Article
The plasmodium of the true slime mold Physarum polycephalum is a large amoeboid organism that displays "smart" behavior such as chemotaxis and the ability to solve mazes and geometrical puzzles. These amoeboid behaviors are based on the dynamics of the viscoelastic protoplasm and its biochemical rhythms. By incorporating both these aspects, we constructed a mathematical model for the dynamics of the organism as a first step towards understanding the relation between protoplasmic movement and its unusual abilities. We tested the validity of the model by comparing it with physiological observation. Our model reproduces fundamental characteristics of the spatio-temporal pattern of the rhythmic movement: (1) the antiphase oscillation between frontal tip and rear when the front is freely extending; (2) the asynchronous oscillation pattern when the front is not freely extending; and (3) the formation of protoplasmic mounds over a longer time scale. Both our model and physiological observation suggest that cell stiffness plays a primary role in plasmodial behaviors, in contrast to the conventional theory of coupled oscillator systems.
Article
When plasmodia of the true slime mold Physarum were exposed to unfavorable conditions presented as three consecutive pulses at constant intervals, they reduced their locomotive speed in response to each episode. When the plasmodia were subsequently subjected to favorable conditions, they spontaneously reduced their locomotive speed at the time when the next unfavorable episode would have occurred. This implied the anticipation of impending environmental change. We explored the mechanisms underlying these types of behavior from a dynamical systems perspective.