Pulsation
Periodic pulsation: one of the brightest features of phaneroplasmodia, an object of intensive study and the main subject of the author's interest.
The pulsation is deeply connected to their movement and physiology in general. Parameters of the pulsation depend on all significant for plasmodium factors: food quantity and quality, illumination, temperature etc.
And it can be observed (and measured!) with a simple equipment.
Simplest example: round plasmodium on a homogenous substrate
An example of photometric measurement of thickness, velocities, periods and amplitudes on a movie of Physarum cinereum.
Photos of plasmodium on a homogeneous substrate were taken in transmitted light every 10 s during 2 hours.
Parameters of pulsation were measured on the ready consequence of frames with home-made software.
left : (first + last frames) / 2
Behaviour of the front edge
measured on the whole edge
(pale blue points − average by cycles)
on separate sectors, indicated by the pink arc
Along big part of the edge (sometimes along all) pulsation is in the same phase. Sometimes obvious beat is seen: interference of waves with different periods, coming from differents places. Since typical period of pulsation is 100 s and period of beating − 1000 s, difference of frequences of these waves is about 0.001 Hz, and difference of their periods − 10 s.
Despite permanent decrease of frequency, velocity of crawling (averaged by cycles) remained roughly constant till all the time.
Pulsation on the whole area
Periods, amplitudes and phases can be measured on the whole area of plasmodium in the same way as on the edge, if you divide the area into many small cells and make the measurements in each one.
Example: a situation in one of such regions:
During the first 3000 s the selected region falls into outer, non-differentiated zone of plasmodium. And periodic changes of period are absent. Later they become very clear.
Actually, this video was divided into 76 thousand cells. (And processing of them took 5 days of computer time.)
Gradual appearing and disappearing of images is a peculiarity of the phase measuring method: phase is determined in interval of the time between first and last extremum, which is different in each cell. Time interval, where measurement of period is made, is even shorter.
Even in absence of any considerable environmental inhomogeneities, different regions of the plasmodium oscillate with significantly different periods, up to 2 times. And the spots of increased/decreased period permanently appear, move to shorter or longer distances and disappear.
You can clearly see a difference between inner and outer zones of plasmodium: outer zone, which is not well differentiated into veins, pulsates almost with the same period and phase along all the edge. Inner veins have very different periods. The waves, when begin on the border of zones, move outwards more slowly then inwards.
Spatiotemporal patterns of pulsation
If you draw an arbitrary line on the frame of movie, straighten it, if curved, and put together such lines from all frames, you will obtain an image of dependency of plasmodium brightness on coordinate and time.
The idea is taken from a paper by Yamada et al. (2007) (see link below)
Such thing can be done with movies of phase, period and amplitude as well as with the original. It is a useful way to watch behaviour of separate veins.
Left and right fragments of the animation show region of plasmodium, centered on the line, where measurements were made, in the first and last frames.
In this example, the line does not follow veins and is parallel to direction of movement. The difference of behaviour of outer and inner zone is seen very clearly: inner zone periodically changes period of pulsation, while outer almost does not. The period of changes is about 1000 s, ten times bigger than period of thickness oscillation.
Here changes of period spread from inside outwards with velocity about 0.02 mm/s. And the waves of thickness can propagate inwards as well as outwards.
Second example
Measurements along line (red), which follows a vein.
Periodic changes of period are easily seen.
The vein has several joints with other big veins. And behaviour of regions between these joints is notably different.
original
period
phase
amplitude
Third example: another thick vein.
Here periodic changes of period are very prominent, except in the outer zone.
Small ripples on a graph of amplitude are an artifact of the measuring method: they appear when maxima and minima of the pulsation have different shape.
original
period
phase
amplitude
Example 4
A closed contour. However, it's parts oscillate differently.
original
period
phase
amplitude
Example 5
A closed contour: ring around the plasmodium at the beginning of time.
The arrow denotes break of the ring (on the top and bottom of the pictures below).
In the first 1000−2000 s the ring falls into the outer zone of plasmodium. So, periods and phases along all the ring are very uniform. Later this region of plasmodium begins to differentiate into veins and the uniformity disappears.
The most interesting is the graph of periods: spots of increased/decreased period appear on the left side of plasmodium, move along it's edge in both directions and disappear on the opposite side. These spots exist for a time, long enough to complete this journey − about an hour. Their velocity is near 0.03 mm/s. Comparing to velocities along veins, it's near the maximum of their range.
So, regularity of the waves of period change seem to be notably stronger than the regularity of the waves of thickness oscillation.
original
period
phase
amplitude
Some links:
Yamada, H.; Nakagaki, T.; Baker, R.E.; Maini, P.K. (2007): Dispersion relation in oscillatory reaction-diffusion systems with self-consistent flow in true slime mold.
Journal of Mathematical Biology, 54(6): 745-760
Takagi, S. (2006): Various rhythmic contraction patterns in the Physarum plasmodium
(on International Symposium on Topological Aspects of Critical Systems and Networks)
(A work on different oscillation patterns of small plasmodia with the visualizations)
www.plasmatracking.de.vu (archive)
(A nice site about a study of shuttle streaming and cytoskeleton. Notice Zytoskelett page with a splendid 3D-video for crossed view.)