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Experimental observation of a quadrupolar flow in
early chicken gastrulation
Vincent Fleury and Nicolas Chevalier
Laboratoire Matière et Systèmes Complexes
Université Paris Diderot
10 rue Alice Domont et Léonie Duquet 75013 Paris
France
Abstract.
Animal morphogenesis, including that of vertebrates, consists of a series of complex movements.
In amniotes (e.g. chicken) early ontogeny starts by large rotatory movements on a flat blastula. We
suggest as a model of this movement a quadrupolar movement initiated by one ring of cells at the
periphery of the blastula. Three consequences of this model are that 1-The movement should start
at the edge. 2-The blastula should extend posteriorly in a predictable way. 3-Contra-rotatory
vortices in the blastula should be observed at the posterior end. The purpose of this article is to
present the corresponding observations, confirming the existence of a visco-elastic quadrupolar
flow at the beginning of vertebrate morphogenesis.
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Introduction
Animal ontogeny comprises a complex series of movements. The nature of these
movements is hardly rendered by the classical staging of embryos at frozen stages1. In order
to understand development, each step has to be carefully and dynamically, analyzed. In
vertebrates, the earliest morphogenetic movements, at the blastula stage, are composed of
large-scale rotatory movements. These movements have been known since the original work
of Wetzel2. They have been revisited experimentally recently3. Since these movements are
akin to large vortex flows, one of us proposed in 20054 a physico-mathematical model to
explain why such vortices should be observed. Basically, the early round blastula5 is
subdivided in several rings, each exhibiting a different average cell size. This structure has
been inherited from previous divisions. As the cells at the periphery exert a pull, a
quadrupolar flow is generated by viscous shear, which convects dynamically the entire
embryonic tissue. The latter is considered as a visco-elastic paste.
In this article we present 3 observations, based on actual predictions of the model. Indeed,
the model predicts that if the movement is caused by the peripheral cells, then it should
start at the periphery, and next propagate “internally” towards the inside of the blastula.
Second, the model predicts that the early blastula should form a pointed feature in the
posterior area, with a quadrupolar contour. Finally, the model predicts a posterior winding
of the tissue, rotating in the opposite direction as the main vortices seen in the main part of
the blastula. We show here that these three predictions are confirmed by experimental
observation. These observations are based on time-lapse imaging as performed following
the method described in Materials and Methods Section.
Results. Initial rotatory movements. While initially round and flat (Fig. 1), the embryo
exhibits circular rings, associated to different cell types5. The most external ring is called
Zona Opaca in classical embryology6. More internally one finds the Zona Pellucida. Both the
Zona Opaca and the Zona Pellucida are presumptive extra-embryonic territories. Centrally,
one finds the disc of cells called Blastoderm, which is the future embryonic territory.
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Figure 1. Outline of the main regions of the embryo before it starts revolving in
vortex movements.
Time-lapse imaging of the early rotatory movements indicate that the embryo movement is
stirred by a traction force exerted along the boundary of the zona pellucida5. Typical velocity
fields as for example Fig. 2 (From Movie 1) show consistently that the embryo is stirred
tangentially (= orthoradially), at the border of the future embryo body, in the area of its
posterior pole. The maximal speed is 3m/minutes. Assuming that inner forces are
generated at positions where shear force is the greatest, the profile of shear (gradient of
speed) by the edge indeed indicates that it is the Zona Pellucida that drags the
morphogenetic movement.
Figure 2(A)
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Figure 2(B)
Figure 2(C)
Figure 2. The early movements display a rotatory movement in the main part of the
blastula (esp. in the blastoderm which will form the embryo). Figure 2(A)Left:
average of the plates in Movie 1 during a 120 minute movement.Movie 1 actually
concatenates a moie at Mag 4X, and next the same embryo at Mag 10X. . Fig.
2(A)Right : projection of maximal pixel values of the plates during that time, with
the Z-project tool in ImageJ (ImageJ software, courtesy of Wayne Rasband). Flow
trajectories are obtained by this method, as cell nuclei scatter more light. The
trajectories are clearly seen. Figure 2(B) : Particle Imaging Velocimetry analysis of
the vortex flow, in the entire blastula. Figure 2(C): cross-section across the center of
the left vortex (the two vortices are slightly offset, so a cut across the blastula does
not pass simultaneously through the two cores. It is observed that the maximal
value of the speeds is at the periphery, in the zona pellucida. The shear is also the
greatest there (shear is the gradient of speed, measured by the slope of the black
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curve formed by the speeds, shear is highest in the are pointed by the arrow). This
suggests that the force is exerted at the periphery.
However, since the shear by the edge induces eventually a strong flow “inside”, it is
not obvious in steady-state that the drag is by the edge. A better way to confirm
that the movement is exerted nearby the edge, consists in studying the transient
régime of flow establisment : by viscous diffusion, if the cause of the movement is
near the edge, then the movement should propagate from the edge, inwards. This
is indeed what is observed. Fig. 3 shows the displacement as a function of time
along the edge, and more in the centre of the blastula shown in Movie 2 which
encompasses the onset of the rotatory movement. The plate shows the
displacement as a function of time for points along the boundary, and for points
more in the centre of the blastula (for the sake of clarity, the curves are slightly
offset). The speed is the gradient of the data in the charts. Points along the
boundary already have a significant speed (negative as they move to the left in the
plates), while the points along the median axis are first static, until they start to
move (to the right, this is why they have positive speeds). It is observed that there is
already a strong movement of the edge, while the central part is static, and it is only
after approx. 2hrs of movement along the edge, that the movement has propagated
to the centre of the blastula, and that the flow is “injected” inwards along the
median axis (as the flow is a vortex flow, the movements are in opposite direction
along the edge and in the centre). This confirms that the cause of the movement is
located at the periphery of the blastula; not strictly at the edge (the Zona Opaca),
but slightly internally over the Zona Pellucida.
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Figure 3
Figure 3. The ring associated to the Zona Pellucida is already moving at a time
when the tissue located along the median axis is still static (the typical speeds of
the cell flow by the edge is 2m/min). The charts to the left show the component
of the speed oriented perpendicular to the blue line. Top is for points near the
edge, bottom is for points in the center. The points by the edge already move,
while the central part of the blastula is still static. The flow starts brutally in the
center after about 2hrs of movement at the edge. To the right, snapshots of the
blastula at several times. (PS: primitive streak, ZO: Zona Opaca). A separatrix
forms, separating the vortices oriented anteriorly, from the ones oriented
posteriorly, and converging to a saddle-point.
Observation 2. Posterior vortices. A second prediction of the model4 is that there should
exist posterior vortices. This deserves a preliminary explanation. There are obvioulsy vortices
in early chicken gastrulation. Cellular flows rotating in vortical patterns (eddies) cannot
follow simple gradients of chemotactants. The appearance of these vortices can hardly be
explained by an attraction mediated by chemotactants, as their distribution would have to
be very contrived to reproduce a vortex motion. A simple physical view is to assume that
cells pull themselves together from a well-defined initial distribution. The initial distribution
of cells forms circular lines in the blastula5. When lines of cells pull themselves forward,
vortices are naturally generated, which come in pairs. The tissue revolves in antagonist
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directions on either side of the cell movement (so called dipolar flow). The model presented
in Ref.4 assumes that only a line of cells located at the periphery, drags the blastula flow.
The model predicts vortices in the anterior part, but also a spontaneous recirculation in the
posterior area, revolving in the opposite direction. The vortices arise as natural
consequences of physical conservation laws. Complex pool of chemotactants organized in
dipoles are not required to explain the existence of such antagonist eddies. Since the source
of force is located at the edge of the blastula, the posterior vortices should be very small. We
now show that such vortices are indeed observed.
Indeed, a detailed examination of the posterior area of embryos (Fig. 4, from Movies 3, 4)
reveals a recirculation forming two posterior vortices rotating in the opposite direction of
the two main vortices. These vortices are extremely difficult to image, because they are
small and are localized quite peripherally, close to the Zona Opaca, where yolk droplets tend
to resist rinsing and alter image quality. The diameter of the posterior vortices is about 4
times smaller than the diameter of the main vortices. Movie 4 shows the vortices at a cell
resolved scale. Absolute values of the speeds are larger through the Zona Pellucida, where
shear is also stronger (middle of the box in Fig. 4 (B), see also Fig. 2(C)), oriented towards the
median axis, the shear force generates rotatory flows (dipolar vortices). The collision of the
right and left pairs of vortices forms a global quadrupolar flow, with four vortices.
Figure 4(A)
Figure 4(B)
Figure 4(C)
Figure 4. After a transient time of establishment, the movement exhibits a
quadrupolar component of flow in the posterior pole with contra-rotative vortices
in the most posterior area. Fig. 4(A), a wide field view of the blastula, with
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trajectories obtained by simply projecting the maximal value in the plates (Mag
x4, from Movie 3). Fig. 4(B), the Particle Imaging Velocimetry (Tracker Module of
ImageJ, courtesy of Olivier Cardoso) tracking. Fig. 4(C) Pattern of vortices
obtained by adding the plates (Mag. X10, Movie 4) which evidences quite clearly
the retrograde vortex observed to the bottom right of the blastula. (Movie 4 is
the continuation of the same blastula as in Movie 3, observed at higher
magnification).
Observation 3. Posterior extension of the embryo. As the embryo is flexible, it deforms selfconsistently under the influence of the quadrupolar flow observed above. In a first phase of
posterior deformation, the blastula acquires a pointed feature in the posterior pole (Movie 5
and Fig. 5). This pointed feature can be quantitatively fitted (Fig. 5) by following the
deformation of a circle in a viscous flow generated by a quadrupole of force located
posteriorly. Indeed, in thin films, and in presence of shear on the substrate, an
incompressible liquid has a Poiseuille-like profile of displacement across the plane4.
Therefore, for a thin film dragged by an in-plane force, both the displacement and the
displacement rate follow a classical equation4. With or without dissipation, a small step of inplane displacement into a quadrupolar flow, of a disk of radius R and of thickness h can be
calculated approximately at first order (in ratio of h/R, the in-plane shear is neglected with
respect to the transverse shear). To do so, the stream (x,y) is introduced, such that
V(x,y)=curl((0,0,(x,y))
Equ. [1]
 is the classical Poiseuille prefactor fh2/12, for a viscous flow of viscosity dragged by a
force f, or 3fh2/4E for an elastic model with Young modulus E. The stream function for a
dipole located at (0,0) is :
(x,y)=y/((x)2+y2 )
And the stream function for a quadrupole is obtained by combining two dipolar terms
located at x=+p and x=-p, corresponding to the pulling zone located at a stagnation point Y 0
along the A-P axis (see Ref. 4) :
(x,y)=(y- Y0)/((x-p)2+(y-Y0)2 )- y/( (x+p) 2+(y-Y0)2)
Equ. [2]
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From Equ. [1] and Equ. [2] the initial quadrupolar deformation of a disc advected in such a
flow, can be calculated, with the position of the stagnation point as an adjustable parameter.
It is assumed that the stress generated by this deformation is dissipated at long time, so that
the deformation becomes irreversible. This is the calculation which was performed in Ref.4,
and which we here fit to the experimental shape of the blastula in Fig. 5. This calculation
shows that a mere quadrupolar flow fits the first stages of deformation of the blastula,
without invoking complex material properties or distributions of chemotactants.
Figure 5. To the left the calculation of the deformation, to the right the fit with
the blastula in Movie 5. A careful observation of this blastula shows that it also
has contra-rotative vortices in the posterior area. The round line which seems not
to fit the boundary, in the upper part is a line where the blastula is not fully
delaminated yet. The top part of the calculated boundary does pass along the
border of the zona opaca/zona pellucida.
Conclusion.
The work presented here complements and supports experimentally the theoretical model
presented in Ref.4. It supports the concept that the early developmental movements are
physical in nature, dragged by an outer rim of cells, and that they initially have a quadrupolar
flow pattern.
Considerable work has been dedicated to staining molecular expressions in early blastulas7-9,
resulting in entire data bases10. It has long been observed that several molecular markers
follow the external ring of cells described here. However, these stainings hardly explain the
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pattern of the flow field and its robustness. An alternative view is to observe that, once the
physical distribution of cells exhibits such rings, a localized contraction will spontaneously,
(and quite simply from physics principles), generate the observed flow pattern. This is to say
that the pattern of the movement, fixed by physics, might actually be decoupled from the
fuel of the movement. Such a decoupling would explain why it is apparently easy to induce
a gastrulation movement in chicken with chemical artefacts8 which do not actually provide a
complete geometrical information about the long range velocity field. Also, it is a classical
observation that gastrulation resumes normally even after massive rinsing of the blastula.
This is naturally explained by the fact that the structure of the movement is “carved” in the
structure of the blastula itself. Since the blastula structure has a pre-pattern consisting of
rings of different cells encased one inside the other, when a contractile molecule is added by
hand to the preparation, the blastula constricts with a force term oriented along the rings
and therefore forms spontaneously a movement which is physically quadrupolar. By this
mechanism, the pattern of movement is robust, and not dependent on complex molecular
feedbacks which would “draw” a quadrupolar field of speeds.
Materials and methods
Embryos are purchased from Centre Avicole d’Ile de France. The embryo is gently cut off from the
vitelline membrane with scissors. It is transferred to a Petri dish with a spoon. In the Petri dish, most
if not all yolk is rinsed away by washing away with PBS and a Pasteur pipette. The embryos are
transferred with the albumin gel and the vitelline membrane, all the yolk being rinsed away. Embryos
are put to incubate in a standard Minitüb incubator at 37°C. A Schott Fiber lamp is used with dichroic
light. For time-lapse imaging at low resolution, a Leica Macrofluo was used. The high resolution cellresolved time-lapse movies of Fig. 2(A), and Fig. 4(C) were taken with an upright microscope from
Nikon, Eclipse, with the 4X, 10X objectives with long working distance.
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