Supplementary Material
Hydra molecular network reaches criticality at the symmetry-breaking,
axis defining moment
J. Soriano, C. Colombo, and A. Ott.
1. Methods
We provide additional information on the experimental procedures, biological
protocols and data analysis.
1.1. Animals.
Strains of Hydra Vulgaris (provided by T. Bosch, U. Kiel, Germany) were used in all
experiments. The animals were cultured at 18 °C in Hydra medium (1.0 mM CaCl2,
1.5 mM NaHCO3, 0.1 mM MgCl2, 0.08 mM MgSO4, and 0.03 mM KNO3) and fed
regularly four times a week. Animals were starved for 24-48 h before an experiment.
1.2. Hydra spheres preparation.
Spheres made of small fragments of tissue were prepared as described in Ref. [1] by
first cutting a thin disc of tissue from the central part of the body column of an adult
Hydra. The disc was next divided into four to eight fragments to select different sizes,
and left unperturbed for 2 h at 20 °C. During this time the fragments close and heal at
the edges, forming hollow spheres made of a cell-bilayer with typical radii between
100 and 250 µm.
Spheres made of aggregates of dissociated single cells were prepared as follows. After
removal of head and foot, a group of 3-10 adult animals was cut into small fragments
and treated with dissociation medium (3.6 mM KCl; 6 mM CaCl2; 1.2 mM MgSO4; 6
mM sodium citrate; 6 mM sodium pyruvate; 6 mM glucose; 12.5 mM TES; and 50
mg/ml rifampicin, pH 6.9) for 2-4 h at 4 °C. During this time repeated pipetting of the
suspension, periodic cycles of filtering, centrifugation, and resuspension in fresh
dissociation medium were applied to improve the dissociation. A compact aggregate
of cells was obtained by centrifugation of the final solution for 10 min at 10g, the
aggregate was left to stabilize in 50% dissociation medium / 50% hydra medium for 2
h at 20 °C, and finally transferred to 100 % hydra medium. A hollow sphere emerged
from the aggregate of cells within 4-6 h. Different sphere sizes were obtained by
splitting the cell suspension into populations of different sizes before the final
centrifugation step.
1.3. In situ hybridization. We follow the standard procedure described in Ref [2]
with minimal modifications. RNA labelling was performed using the dioxygeninlabelling kit (Roche). A detailed description of the in situ hybridization protocol is
described in Appendix A. Spheres were prepared and cultured at 20 ºC.
1.4. Ks1 expression patterns analysis. In-situ hybridization images of the Hydra
spheres were obtained with a CCD camera mounted in a microscope Zeiss Axiovert
25 with 10X magnification, which provided a final spatial resolution of 1.33
µm/pixel. The images were thresholded to obtain binary files of the ks1 patterns (0 for
absence of expression, 1 for presence), as shown in Figs. S1a and S1b. The patterns
were subsequently analyzed to extract their size (fraction of cells expressing ks1
respect to the total number of cells in the sphere), the distribution of spot sizes, and
the perimeter and area fractal dimensions. For each pattern we studied the effect of
using different pixel resolutions and thresholds, and observed that for an individual
pattern the variation in the results was negligible compared to the variation from
pattern to pattern.
Fig S1. (a) Original ks1 pattern, in color and grey-scale. Culture time, 20 h. (b) Pattern analyzed with
different threshold levels (top), showing the corresponding contours (bottom). Threshold level 1 is the
one systematically used in all patterns. (c) Perimeter fractal dimension of the thresholded contours,
compared with the perimeter fractal dimension of a circle. Lines are least square fits.
The fractal analysis of the patterns was performed using the grid (or box-counting)
method. It is based on counting the number N of boxes of lateral size required to
cover the perimeter or area of the pattern. The process is repeated for gradually higher
values of . In our analysis we chose an initial value of  close to the typical size of
the hydra cells (about 5 m in diameter) and then increased  in factors of 2. The
fractal dimension D is finally obtained as log(N) ~ - D log(). Fig. S1c shows an
example of the analysis of the perimeter fractal dimension for a pattern analyzed with
different thresholds. The results are compared with the perimeter area dimension of a
compact pattern, in this case a circle, which has been analyzed using the same
procedure as the ks1 patterns. Compact patterns give D=1, and the deviation from this
value provides an estimation of the errors due to pixelization. The analysis of the
patterns with different thresholds shows that the patterns keep the fractal structure
even for high threshold values, with D=1.18 for threshold level 1, and D=1.13 for
level 4. This gives a variation of about 4%, compared with a variation of about 8%
from pattern to pattern with the same culture time.
From the thresholded patterns, we also obtained the cumulative distribution of ks1
spot sizes, P(s ≥), by counting the number of spots of size equal or larger than s (in
cells expressing ks1). After normalization, P(s ≥) gives the probability that a cell
belongs to a spot of size equal or larger than s. The probability distribution was then
averaged over the probability distributions of other patterns with the same culture
time to obtain the distributions shown in Fig. 3 (which are vertically shifted for
clarity). At the critical point, P(s ≥) scales as P(s ≥) ~ s – (  – 2 ), and the frequency of
occurrence of spots of size s, n(s), scales as n(s) ~ s –. The exponent  can be then
derived immediately from P(s ≥), providing  = -2.8  0.1. The analysis of the
patterns for different thresholds shows that P(s ≥) is sensitive to changes in the
threshold level of the pattern, which affect particularly the smallest spots. However,
we have verified that the difference in distributions from one pattern to another (with
the same culture time) is more significant than the variations of P(s ≥) with different
thresholds of the same pattern.
Note that close to the critical state a noticeable increase of variation on the individual
patterns will result from a minor variation of the “control parameter”, the
“excitability” of the cells. Therefore these differences in distribution only strengthen
our interpretation.
1.5. Organizer insertion into aggregates. The head of an adult hydra was removed
and left to regenerate for 1 h at room temperature. Then, a community of about 50
cells was excised from the tip of the regenerating head. For staining the cells, they are
immersed for 1 minute into a fluorescent solution that contains 1 part of 1,1'dioctadecyl-3,3,3',3'-tetramethylindocarbocyanine perchlorate (Dil) and 9 parts of 70
mM sucrose solution in hydra medium, following the same procedure described in
Ref. [3]. Then, the stained cell cluster is inserted into an aggregate of hydra cells. The
Hydra cell aggregate forms a hollow sphere in about 2 h. The stained cell cluster
forms a compact spot on the sphere, which can be easily identified. The evolution of
the sphere is observed during two days, while the position of the stained cells is
monitored. Control experiments are performed by cutting, staining and inserting a
small group of cells from the body column into the aggregate to verify that the
fluorescent dye does not affect the regeneration process.
2. Experimental setup and procedure
The spheres, formed either from a small fragment of tissue or from an aggregate of
dissociated cells, are transferred immediately after preparation into a chamber filled
with hydra medium that contains a series of 10 wells made of solidified agarose gel,
as shown in Figs. S2a and S2b. The wells are 1 mm in diameter, the separation
distance is 1 mm (Fig S2c). The wells reduce convection, keep the hydra in the field
of observation and prevent interaction between animals; the agarose gel reduces
further convection in the chamber. The observation chamber is sealed to prevent
evaporation, with glasses at the top and at the bottom. Hydra cells quickly stick to the
glass bottom, which prevents them from turning and moving with respect to the
gradient. Convection was suppressed by increasing the viscosity of the hydra medium
by 500 times with 0.5 % Methyl Cellulose. Control experiments at room temperature
were performed with and without Methyl Cellulose to verify that it had no effect on
the regeneration process. Additional control experiments were carried out to exclude
effects of the viscous medium on Hydra regeneration. As any type of steel was found
to be incompatible with hydra regeneration, the temperature gradient in the
observation chamber was controlled via two sapphire plates inserted into a Teflon
holder, the observation chamber. The plates are inserted into the same holder and
sealed with Eccobond industrial glue.
Fig S2. (a) and (b) Sketch of the experimental setup. (c) Example of two hydra spheres inside the wells
(top view). (d) The orientation of the hydra axis after regeneration is measured as the angle between the
direction of the temperature gradient and the head-pointing axis of the animal.
The observation chamber is mounted on a x-y stage of a home built microscope
equipped with a 5X Zeiss Epifluar objective. Images of the evolution of 10 hydra
spheres are recorded with a CCD camera with a size of 574 x 512 pixels at 3 minutes
interval during 2 days. A computer controls the acquisition of the images, which are
synchronized with the movement of the x-y stage. The spheres are kept in darkness
and illuminated only during image acquisition.
The observation chamber temperature gradient can be set by two independent closed
loop thermal feedback controls, which heat or cool each sapphire plate via a peltier
element to the desired temperature, within a precision of 0.1 °C measured in the
center of the plates. All experiments at constant temperature were carried out at 20
°C. For the experiments with a temperature gradient, the thermal control was set to
provide 20 °C at the center of the chamber. At the end of the experiment the images
are analyzed to retrieve the in-plane contour of the hydra ball, the orientation of the
foot-head axis and other relevant information.
For hydra balls obtained from small fragments of tissue, t=0 is defined as the moment
at which the fragment is excised. For aggregates of cells, t=0 corresponds to the last
centrifugation. The mechanical changes of the hydra ball during regeneration are
studied either with the volume or the radius of the sphere. The volume of the sphere at
time t is determined by assuming that the animal is a revolution ellipsoid with major
axis a and minor axis b, which are obtained directly from the analyzed contour. The
radius is obtained as r = (A/)1/2, where A is the area enclosed by the contour of the
sphere. The orientation of the hydra axis after regeneration is defined as the angle
between the direction of the temperature gradient and the head-pointing axis of the
animal, as shown in Fig. S2d.
3. Evidences of elastic anisotropy after symmetry-breaking
With respect to [1], we have carried out an additional analysis that provides
experimental evidences of changes in the elastic properties of the hydra ball after
symmetry-breaking,
As first part of the analysis we measured the swelling (or inflation) rate of the hydra
ball during phase I and II. Since the radius increases linearly with time during the
inflation stages, the swelling rate is measured as the slope dr/dt. The distribution of
the slopes for 200 phase I cycles and 150 phase II cycles is shown in Fig. S3a. The
results show that the swelling rate becomes larger and shifts to higher values after axis
formation, from an average value of 7.2 m/h to 10.5 m/h. Since the swelling rate
can be expected to depend on the elastic properties of the hydra ball, this increase
suggests that some regions of the hydra ball have increased the elasticity and offer
less resistance to swelling.
As second part of the analysis we conducted a detailed inspection of the evolving
contour of the hydra ball during regeneration. For the cases in which hydra exactly
regenerates parallel to the plane of observation, it is possible to study local changes in
the shape of the animal by comparing consecutive contours. This analysis is shown in
Fig. S3b. Before symmetry-breaking, the hydra ball shows isotropic inflation and
collapse while, just at the onset of axis establishment, the collapse and future
oscillations are anisotropic. Oscillations are more pronounced along the axis of the
animal.
Fig S3. (a) Distribution of swelling rates during phase I and II. (b) Analysis of the relative change
between consecutives contours. Blue and red indicate inflation and deflation, respectively. The
thickness of the color band is proportional to the variation between the contours. The top plot shows
the position of the analyzed contours along the regeneration process.
4. Mechanical oscillations and the presence of initial asymmetries.
We have performed a series of additional experiments to verify the relation between
the mechanical oscillations and symmetry-breaking. On one hand, we observed that
the insertion of an organizer into an aggregate of hydra cells defines the axis position
of the regenerated animal and shortens phase I oscillations. On the other, spheres with
an already defined axis lack phase I oscillations, regenerate faster, and their
regeneration is insensitive to a temperature gradient.
These results show that phase I motion is a signature of initial isotropy of the cell ball,
and that phase II motion is an indication of the formation and irreversible locking of
the axis.
4.1. Cells from the organizer inserted into a hydra sphere define the axis.
The cells located at the tip of a regenerating head have a strong competence for head
formation [4]. This group of cells constitute an organizer. For instance, their insertion
into the body column of an adult hydra induces the formation of a new head. We
performed experiments in which we inserted a group of organizer cells into an
aggregate of hydra cells (see Methods) and observed the evolution of the sphere. The
results (Fig. S4a, sphere 2) show that these spheres reduce the amplitude of
oscillations much earlier than normal ones (Fig. S4a, sphere 1). The position of the
head coincides with the position of the inserted cells, revealing that the organizer
defines the position of the axis. We have also studied the temporal evolution of the
period of the oscillations for 6 spheres with an organizer inserted. The results (Fig.
S4b) show that phase I motion is considerably shortened (the drop in the period of the
oscillations takes place earlier) compared to normal spheres by about 50%. Spheres
with an organizer inserted also show faster regeneration.
4.2. Hydra spheres with an axis already defined lack phase I oscillations.
Fragments, about 10-20 times larger than the ones normally studied, retain the
original axis and develop according to it. They lack phase I motion (Fig. S4a, sphere
3) and the regeneration time is reduced accordingly.
Budding is the asexual form of reproduction in hydra, consisting of the development
of clones in the body column of an adult animal that grow in size and finally de-attach
from the parent. Buds have an organizer constituted from the very beginning [5].
Excised buds, even very small, retain the original axial information and develop
according to it. They do not show any sign of phase I motion (Fig. S4a, sphere 4) and
the regeneration time is substantially shorter than normal (isotropic) spheres of similar
size (Fig. S4b).
Fig S4. (a) Examples of the effect of initial developmental asymmetries on the mechanical oscillations
of hydra spheres.1: (control) isotropic sphere made of a small fragment of hydra tissue or an aggregate
of dissociated cells; 2: sphere with an organizer inserted; 3: large fragments; 4: excised buds. AF: axis
formation. (b) Temporal evolution of the period of the oscillations,, from sphere formation to
regeneration.  is re-scaled by the number of cells in the sphere, S0, to reduce the effect of different
sphere sizes. The top plot compares normal spheres (20 samples) with spheres with an organizer
inserted (6). The bottom plot compares normal spheres with big fragments (18 samples) and buds (10).
____________________________________________
References:
[1] C. Fütterer, C. Colombo, F. Jülicher and A. Ott. Europhys. Lett. 64, 137 (2003).
[2] D.E. Martinez, M.-L. Dirksen, P.M. Bode, M. Jamrich, R.E. Steele & H.R. Bode
Dev. Biol. 192, 523-536 (1997).
[3] Y. Kishimoto, M. Murate, and T. Sugiyama. J. Cell Sci. 109, 763 (1996).
[4] U. Technau, C. C. von Laue, F. Rentzsch, S. Luft, B. Hobmayer, H. R. Bode, and
T. W. Holstein. Proc. Natl. Acad. Sci. U.S.A. 97, 12127 (2000).
[5] U. Technau and H.R. Bode. Development 126, 999 (1999).
Appendix A. In-situ Hybridization with Hydra
The different steps described below are performed in a 12 Well Cell Culture Cluster (Corning
Incorporated) for fixation, washings, and staining; and in 1 ml Eppendorf tubes for
Hybridization and final washings. The protocol applies for both adult animals and spheres.
For the steps carried out in cell culture wells, the animals are placed inside a plastic basket
with a 50 m nylon mesh at the bottom. The basket is transferred from one culture well to the
next during the different steps. Two groups of animals are manipulated in parallel, one that
will contain the ks1 sense probe, and a second one containing the anti-sense (control) probe.
The whole protocol is completed in 4 days.
Day 1:
Relax starved (24 - 48 h) Hydras in 2% urethane in hydra medium for 2 min. .1
Fix animals (overnight at 4ºC) with 4% paraformaldehyde (pH 7.4) in hydra medium. .2
Day 2 (8-9 hours):
Treat samples with 99% EtOH for 10 min. .3
Rehydrate samples: .4
75% EtOH / 25% H2O for 5 min, room temperature (RT). o
50% EtOH / 50% PBT or H2O for 5 min, RT. o
25% EtOH / 75% PBT for 5 min, RT. o
Wash with PBT, 3 x 10 min, RT. RNA amplification and labeling is started here (see .5
later), and it is completed in 3 hours.
Treat samples with Proteinase K in PBT for 20 min, RT (10 l of Proteinase K per ml of .6
PBT).
Short wash with Glycine solution (1x). RT. .7
Wash with Glycine solution (1x), 10 min. RT. .8
Wash with PBT, 3 x 10 min, RT. .9
Wash with Triethanolamine pH 7.8, 2 x 10 min. RT. .11
Exchange Triethanolamine by Acteic anhydride (2.5 l of Acteic anhydride per ml of .11
Triethanolamine). Wait 5 min and add 2.5 l more of Acteic anhydride.
Wash with PBT, 3 x 5 min, RT. .12
Refix with 4% Paraformaldehyde in PBT for 1 h, at RT. .13
Wash with PBT, 3 x 10 min, RT. .14
Wash with 2xSSC, 2 x 10 min, RT. .15
At the end of the washing the animals are transferred to Eppendorf tubes using Pasteur .16
pipettes.
Heat the animals by putting 500 l of 2xSSC (at 70ºC) in each Eppendorf tube and .17
incubate at 70ºC for 15 min. Prepare Hybridization Solution (HS) during this step and
heat it up to 57 ºC (hybridization temperature).
Prepare a solution containing 50% 2xSSC and 50% Hybridization Solution. Wash the .18
animals in this solution for 10 min at RT.
Prehybridize for 2 h in Hybridization Solution + tRNA. We prepare a tube with HS (at .19
the hybridization temperature, 57 ºC) and place 20 l of tRNA per ml of HS. We put
500 l of this solution to the Eppendorfs containing the animals. Then we keep the
Eppendorf tubes at 57ºC with moderate shaking.
Denature the RNA Probes for 10 min at 70 ºC. The probes were prepared before, diluted, .21
and stored at -20 ºC. We put in new Eppendorf tubes 2 l of probe and 50 l of HS. Each
tube contains, respectively, the sense and anti-sense (control) probes diluted in HS. Then
we incubate the tubes at 70 ºC for 10 min.
We transfer the denatured probes to the Eppendorf tubes containing the animals. .21
Hybridize overnight at 57ºC with moderate shaking. Seal the Eppendorf tubes with .22
parafilm to avoid evaporation.
--------------------------------------------------------------------------------------------------------------RNA amplification
Using the RNA labeling kit specifications, we put the necessary volume of original probe to
have 1 g of DNA sample into a small microfuge tube. Then we add DEPC-water to have a
final volume of 13 l. Next, we add 2 l of DIG RNA labeling mix, 2 l 10*Transcription
buffer, 1 l RNAse inhibitor, and finally 2 l of the RNA polymerases T7 (sense) and SP6
(anti-sense).
The microfuge tubes are incubated at 37 ºC for 2-4 h. Then, 2 l of DNAse-I, RNAse free is
added and probes incubated again at 37ºC for 15 min. This step eliminates the template DNA.
The reaction is finally stopped with 2 l EDTA.
The probes are diluted a factor 10 to have them ready for hybridization. In new microfuge
tubes we add 4 l of the concentrated probe and 40 l of DEPC water. 2 l of this diluted
probe will be used during hybridization
---------------------------------------------------------------------------------------------------------------
Day 3: (6-7 hours)
We start by washing away the probe. This procedure is carried out at hybridization .23
temperature and with moderate shaking.
100% HS (without tRNA), 10 min. o
75% HS / 25% 2xSSC, 10 min. o
50% HS / 50% 2xSSC, 10 min. o
25% HS / 75% 2xSSC, 10 min. o
Now we incubate in 2xSSC + 0.1 % CHAPS for 2 x 30 min at Hybridization .24
temperature.
We wash with MAB, for 2 x 10 min at RT. During this process we prepare MAB + 1% .25
BSA (Bovine Serum fraction V).
We wash with MAB + BSA (MABB) for 1 h. RT. .26
Now we prepare Blocking solution, prepared with MABB + sheep serum, in a ratio of 80 .27
% MABB / 20 % sheep serum. We wash the samples for 2 h. at 4 ºC.
Staining with antibodies. We will use Dioxygenin AP in 1:2000 concentration. We .28
incubate overnight at 4ºC.
Day 4: (6-7 hours)
Wash with MAB (or Blocking solution) for 2 x 45 min, RT. .29
Wash with MAB 6 x 45 min, RT. .31
Wash with NTMT for 5 min. RT. At the end of this washing the animals are manipulated .31
again in 12-well cell cultures.
Wash with NTMT/Levamisole (1mM) for 5 min. We prepare NTMT and add stock .32
solution of Levamisole in a concentration of 1:1000.
During this washing we prepare the staining solution. We put in a tube 1 ml of NTMT .33
times the number of samples and we add NBT/BCIP (the staining reagent) in a
concentration of 12.5 l per ml of NTMT. Store in the dark until the solution is used.
Discard the NTMT/Levamisole solution and add 1 ml of staining solution. Incubate at .34
37ºC in the dark.
Check the animals in the microscope in 5 min intervals. .35
As soon as the staining reaction is detected, the animals are washed in DEPC-water to .36
stop the reaction, 3 x 1 min.
Incubate in Methanol to remove unspecific staining; a first washing of 5 min with 50% .37
methanol / 50% DEPC-water, and a second washing with 100% methanol.
Embed animals in Euparol. .38