Competition between surface tension and line tension canalizes craniate evolution

doi:10.21203/rs.3.rs-4711361/v1

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Competition between surface tension and line tension canalizes craniate evolution

https://doi.org/10.21203/rs.3.rs-4711361/v1

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It has been suggested for long that physical principles might canalize evolution, especially in the genus homo, where brain size is the largest. However, what physical principle exactly would drive such a progress is unknown. Recent work suggests that there exists a mechanical, built-in, correlation between brain dilation and head flexure in vertebrate morphogenesis. This internal correlation would explain the canalization of evolution towards bigger brains and simultaneously a quite flexed head, with neural tissue curled forward. I report here a detailed study of neural tube flexure and dilation up to day 4 of development in chicken embryos. In vivo time-lapse shows a correlation between brain expansion and head flexure. The early embryo exhibits a biaxial texture in its tissue, in its vascular system and in heart formation, which causes line tensions antagonist to brain dilation. This competition between line tensions and vesicle surface expansion induces a mechanical correlation between brain dilation and flexure. Theoretical modeling reproduces how embryo texture constrains brain expansion and flexure, and how they relate to hemodynamics. This work demonstrates the existence of an internal, textural, correlation between heart morphogenesis, brain dilation and head flexure, which contributes to explaining the origin of humans. To be precise: the physical principle at the origin of humans is a competition between line tension and surface tension.

Biological sciences/Biophysics

Biological sciences/Developmental biology

Biological sciences/Evolution

Physical sciences/Materials science

I.1 Paleontology

It has been suggested for some time that the process of hominization could in part be explained by physical constraints in the biomechanics of the neural tube [1, 2]. A structuralist approach suggests that there exists an internal unknown constraint inside the neural tube which favors a progressive flexure of the neural tube, as the brain dilates, even though mutations are random. In other words, a fundamental law of biomechanics, yet to be discovered, would correlate brain flexure and growth, in a similar way as squeeze in one direction and expansion in the other are correlated by tensorial properties of elastic solids. Although mutations occur randomly, the space of possible forms would be constrained, so that the evolution of the anatomy of the head and neck would remain predictable, genetic mutations working as a diffusive factor rectified by selection in the space of forms. More specifically, brain dilation would be correlated to flexure of the neural tube, and the flexure would also cause a less prognathous face and a verticalization of the spine, leading deterministically to a human-like anatomy. This point of view is known as the Inside story scenario of human origin, as opposed to Eastside or Westside story, as commonly known in paleontology^[1]. One major argument in favor of such an Inside Story, is simply that the biotope only acts a posteriori. Animal forms are generated inside the egg or the uterus, and competition in the biotopes has no effect whatsoever on embryo morphodynamics.

I have proposed that this mechanical constraint is linked to the physical texture of the embryo, and the anisotropy of the associated tensile stress [3]. The work presented here shows that brain dilation and flexure undergo also non-linear twitches related to non-linearity of surface and line tension around sensory organs. Tension in blood vessels plays an important role too. When including the role of heart form and thrust in models of brain expansion, a realistic correlation between brain morphogenesis and head flexure is recovered with basically one parameter: the ratio of surface tension vs line tension, in a predetermined biaxial texture.

I.2 Early brain formation.

The early embryonic brain forms by a process called neurulation, [4] Videos 1–4. Neurulation is a process of roll up of a flat tissue, called blastodisc, caused by cell contraction (Nota Bene : humans and chicken embryos both have a blastodisc stage). This flat tissue is not structure-less. Prior to neurulation, there exists a pattern of rings and rays in the embryonic disc [3, 5, 6], Fig. 1A. Neurulation rolls up the disc dorsally into a tube whose anterior part will form all the head features [6, 7]. Meanwhile, the rays present in the blastodisc are coiled dorsally onto the neural tube around which they form circular belts of cells, Fig. 1B. These denser rings are contractile [3], and they are associated at a molecular level with the presence of a denser actin (Fig. 1C). Each sector defined by the rays is associated to one organ (the palate, the eyes and nose, the mandible and ears). Especially the nasogenian groove (the main groove of the face) is associated to a forward sector which is projected on the neural tube at the eye corner (Videos 3, 4 -arrow [5–7]). In between organs, the early neural tube is coiled with a finite number of belts or collars of cells which strangle it along the shaft [3], Fig. 1A, and behave as snaffle bits. This is why after 3 days of development, an embryonic head is composed of (dorsal) brain vesicles, ballooning out like hernias, and separated by valleys (Fig. 1A). These valleys get progressively relatively sharp, as the rings of cells contract. There exists also a sagittal valley (Fig. 1A, frontal view, Bottom Right)

I.3 Early heart formation.

While the neural primordia form dorsally, the heart forms ventrally during neurulation. Just prior to neurulation, the embryo has a structure in rings and rays forming wedges (Fig. 1A). The main visible wedge in the anterior part of the blastula is called the “cardiac crescent” in classical embryology, because it is associated to heart formation [8]. The ring which delineates the body contour constricts, as neurulation proceeds, so that the neural tube hops over the cardiac crescent (Fig. 2A, Video 3 profile view, Video 5 ventral view). This creates a sigmoid fold [7, 9, 10] with early heart and mouth primordia underneath, and nasal, ocular, otic and brain primordia atop. The organ primordia are delineated by the deformed lines [5, 7]. When the heart is imaged during its morphogenesis, in immuno-fluorescence with a smooth muscle α-actin marker (Fig. 2B), one observes that the contracting ring stains densely for α-actin, and that the wedge pattern exhibits a denser actin too along the rays forming the boundaries of the cardiac crescent or wedge (see also Supp. Figure 1, showing Scanning Electron microscopy of the early heart, reprinted from Ref. 9).

The ring forming the boundary of the cardiac crescent starts to migrate in the caudal direction [9, 10] (Video 6, 7, see also Video 13 in Ref. 7). The contraction of this ring deforms the wedge pattern: the set of lines at right angles (radial and orthoradial) is dragged ventrally in the posterior direction (Fig. 2A, 2C), at a constant speed [10]. The constriction of the circular boundary of the crescent generates the heart, and the radial or wedge part of the crescent generates the venous and arterial tracts (Videos 8, 9). The contraction of the cardiac crescent positions deterministically the aortas in the anterior direction (towards the head), and the venous tract in the medio-lateral direction (Fig. 2C, and Supp. Figure 1 showing an SEM picture of the chiasma formed by the contracted radial and orthoradial lines). To be very clear, the aortas form at the point of insertion of the folded wedge and they follow ventrally the stretched wedge surrounding the mouth primordia (see Video 3 which shows a profile view in which the point of insertion of the wedge is visible, arrow). In Ref. 9 an experiment of incision of the cardiac ring shows that if the cardiac ring is cut, two semi-hearts form, on the left and right side of the body (Video 10, from Ref. 9). During this process the wedge of the heart crescent appears very clearly, and it is located at the apex of the presumptive heart atria from which the aortas emanate (Fig. 2A Right and arrow in Video 10).

Videos 11 and 12 show the exact moment of opening of the aortic tract in ventral view (arrowhead), and Video 13 shows the exact moment of opening of the aortic tract in dorsal view (arrowhead). It is seen that the opening is just below the midbrain, and quite close to the primary palate, at this stage. Video 14 shows a very early stage (end of day 2) of heart beat showing the aortas (white arrows), and the point of flow injection onto the brain vesicle (black arrowhead). Video 15 shows the exact moment of formation of the eyes, in which the aortas are visible (arrows in the first plates) very close to the primary palate. Video 16 shows the heart beat at beginning of day 3, and Video 17 at early day 4. As the heart matures, the aortas take a spear-like structure (Fig. 2), located under the brain vesicles. Later on, secondary arteries follow other textural features. They are known as the aortic arches [11].

In summary the early heart has the shape of a cross, chiasma or hourglass (Fig. 2A), with the narrow part due to contraction of the ventral boundary, and input/output located on either side (anterior and posterior), which follow the texture. All the events described above are chained and propagate dynamically by recruitment of contractile cells along a prepattern (or texture) formed of lines initially at right angles, seeded with actin (Fig. 2B). When heart beat starts and blood stream percolates, the dorsal aortas flush blood in the head in the area of the presumptive mouth corner just below the midbrain (Fig. 2, Videos 11–15, also show the position of the aortas with respect to the primary palate –very close). In this summary, it is assumed that differentiated endothelial cells and cardiomyocytes spontaneously cavitate along the texture, to transform the pattern of rings and rays into lumens, as they do elsewhere to generate the vasculature [12].

I.4 Early vascular network

While the embryonic tissue presents a texture in rings and rays, the blood vessels also follow a texture, which largely mirrors the embryonic form. Indeed, precise in vivo imaging of the vasculature at HH stages 19 and 20 [13] (days 3 to 4), show that the blood vessels present a capillary lattice in the brain shells (Fig. 3A, 3B), and that the blood stream returns to the heart via larger veins which pass through the intervesicle valleys. The brain blood flow is collected by the so-called cardinal veins [11] (Fig. 3A, Video 16). The cardinal veins follow also the body texture. There exist such vessels along the sagittal valley too, which can be imaged in vivo (Fig. 3B, adapted from Ref. 3). The sagittal vessels flow back towards the cardinal veins too by following the intervesicle valleys. By Hamilton and Hamburger [13] stages 19–20 (3rd day) the pattern of blood vessels is composed of small capillary-like vessels in the dilating shells, and of wider vessels in the valleys between dilating brain vesicles. It is observed that the capillary vessels also have a bending oriented in the flow movement (Fig. 3A, Video 17). The flow enters the head through the aortas, and it returns via the cardinal veins which follow the axis of the body. Hence, the vascular texture is determined by the embryonic texture too, and it loops from the heart to the vesicles and back along the texture. It is important to understand that the structure in concentric rings is projected on a body, by ventral contraction of the cardiac crescent, and dorsal contraction of the neural plate. Still, the main lines, although deformed, serve as mechanical cues for establishment of the heart structure and of the vascular pattern. Figure 3C shows immune-fluorescence imaging of typical embryonic vessels (in the CAM). The blood vessels stain for smooth muscle α-actin, except at the very end. This reveals that the blood vessels are more contractile than the capillary bed, with a sharp transition corresponding to cell differentiation to a smooth muscle type (this observation will be important later, to justify the physical modelling).

Keeping this texture in mind, I now present here the analysis of head dilation and flexure at day 3 + of development of the chicken embryo (HH stages 18 to 19). Quantitative data extracted by Time-Lapse video-microscopy finds an almost linear correlation between head flexure and brain dilation, with nevertheless a small anomaly due to eye invagination. Similar contraction twitches causing non-linear behavior of the brain shells were observed during formation of the otic [5] and nasal [6] pits. Also, an acceleration of brain development and flexure is observed when the blood flow percolates, and the heart plays a crucial role in this phenomenon.

II. 1 Non-linear anomaly in brain development, related to eye formation

We first follow chicken embryo development just after neurulation, by (early) day 3 of development. We observe that the embryo head rocks forward and the mouth folds inwardly. Videos 18, 19, 20, show the rotation of the head and the correlative brain expansion (Mag. 1.5X). The videos overlap slightly, but they correspond to increasing times. Figure 4A shows the data extracted from the Videos 18 to 20, which manifest a correlation between brain expansion and head flexure. Figure 4B shows a velocimetry map extracted by the Particle Imaging Velocimetry (PIV) method, which confirms the visual impression that there exists an anterior rotation of the entire head, which makes the mouth primordia less prognathous, while the brain dilates.

While the correlation between head expansion and rotation appears linear in this window of development, an anomaly is observed in the developmental dynamics (Fig. 4A arrows, from Video 19). This anomaly is correlated to eye invagination. Indeed, at one point the eye placode constricts and invaginates, and this causes and inwards centripetal pistoning towards the brain (Videos 15, 18, 21, Fig. 5A and 5B) which correlates with a transient non-linearity in brain development. When filming the eye capsule in time-lapse, one observes that the formation of the eye is accompanied by a back and forth oscillation of the lens ectoderm (Fig. 5C, Video 22). A contractile response of the brain shell is observed (Fig. 5D, Videos 21–23). We therefore ascribe this anomaly to the sudden invagination and contraction caused by eye formation. Invagination causes an inward movement, followed by a contraction of the brain ectoderm which causes an outward movement. This movement is coherent with previous description of the inetarction between surface ectoderm and eye morphogenesis[18]. If it were not for this non-linear event, the correlation between brain dilation and head flexure would appear fairly linear.

II.2 Acceleration of brain development related to blood vessels.

Another non-linearity exists which occurs at the moment of opening of the blood vessels towards the head. In the Videos 18–20 above we followed head dilation and flexure when the head was already rocked in profile view, such that it was possible to measure simultaneously brain dilation and head flexure. However, at earlier stages of development, HH17, the embryo is almost straight and it rests ventrally. Measuring head flexure is difficult, but measuring brain dilation is possible. We observe that the brain dilation accelerates suddenly, as the aortas open (Fig. 6A, Videos 13, 24, 25 and 32). When the embryo is filmed in dual dorso-ventral view (Video 25, Mag. 1.5X), one can observe a snap contraction which encompasses the entire embryo, but more specifically the head territory, which is associated to the opening of the dorsal aortas (arrows in Fig. 6B). At that precise moment the embryo flexes suddenly (Fig. 6B, Video 25, Mag. 1.6X). Video 26 shows a concatenation of dual views of the embryo separated by 3hrs of development to show the effect of the opening of the aortic tract (please play this video several time to identify the opening of the aortas and the head flexure). It is observed that the aortic tract dilates, while the vessels constrict both in diameter and longitudinally. This moment is associated to the onset of head flexure (Fig. 6C), and rapid brain expansion. The opening of the aortas and the onset of flexure can be quantitatively followed in such movies as Video 13, in which the aortic tract appears darker when open (the lumen scatters light less than the surrounding tissue). This allows one to quantify the opening, and the flexure times (Fig. 6C, Left). This shows that the percolation of the blood flow in the head causes an acceleration in brain dilation and simultaneously a tensile response of the vessels which pulls on the head and flexes it. Also, one notices a L-R asymmetry in percolation dynamics.

II.3 Effect of increasing or decreasing tension in the head.

It is classical in medicine to use Mannitol as an osmotic agent causing a decrease in intra cranial pressure [19]. We will therefore use solutions of 3pct Mannitol to induce a decrease in brain tension during ear formation. Conversely, I have shown in Ref. 6, that we can increase tension by electric stimulation. We will therefore use electric stimulation to interfere with sensory organ formation by electric stimulation. Electrodes are approached towards the organ and an electric stimulation of 0. 2V and 1s is applied. These experiments are difficult in that the exact stage of development may differ from embryo to embryo, and the embryos are moving in 3D. However, two results are worth being reported.

II.3.i Ear formation

Firstly, we observe that ear formation is asymmetric: it occurs sooner on the left side of the embryo, Fig. 7A (Video 27 shows the left ear forming, while the right ear is not yet visible, Video 28 shows formation of the right ear, after the left ear pit is well formed). Now, during ear formation the embryo rests on the ventral side, and the presumptive otic pit can be accessed dorsally. When exposing ear formation to a solution of Mannitol, the following effect is observed (N = 5). The entire head shrinks while its volume decreases. During this collapse, the ring of the ear pit closes down onto itself very rapidly, until it vanishes completely, and the forming ear totally disappears (Fig. 7B Top, Video 29). The interpretation is that the tension in the tissue in the shaft is brutally decreased so that the ear pit is no longer stretched out and it collapses or “implodes” onto itself by ring contraction.

II.3.ii Nose formation

As reported earlier, the effect of an electric stimulation in the brain vesicles is to constrict the vesicles and cause a retrograde flexure of the head [6]. When the electric stimulation is performed in the nasal area prior to formation of the presumptive nasal pit (N = 3), a contraction is indeed observed (Fig. 7C). The contraction of the tissue causes a twitch of the entire nasal territory (Fig. 7D, Top, Video 30). The contraction induces rapid nose formation, as it causes the ectoderm to invaginate and form the nasal pit and nare (Fig. 7D Bottom, Video 31). This experiment shows that morphogenesis of a pit can be accelerated by increasing tension in the nasal area, and that nare invagination is associated to a non-linear contraction twitch in the morphogenesis of the nasal vesicle, rather similar to contraction twitches in the eye.

III.1 Neural tube expansion, without heart beat

In order to address the correlation between flexure and dilation, a simple numerical model of growing vesicles was presented in Ref. 3. We shall use again this model here. A finite element calculation is performed (see Materials and Methods section), in which a straight element is composed of successive cavities representing the brain vesicles. Pressure is exerted inside the cavities. Shear forces can be applied also along the boundaries. The cavities are separated by walls, which model the rings existing in the real situation. Figure 8A shows that a series of such vesicles separated by rings will exhibit a forward flexure as the brain dilates. In this situation, when a series of vesicles dilates under internal pressure, anterior vesicles are spontaneously larger, in a self-organized order between the clamped end, and the free end (Video 33). The process shows a non-linear growth with an acceleration (Fig. 8B Left). Most importantly, when the flexure angle is plotted as a function of vesicle diameter, for the 4 vesicles case (which corresponds to the physiological case), one obtains an almost linear relationship between brain dilation and head flexure (Fig. 8B Right). This allometric relationship explains why random mutations drag heads towards bigger and more curled brains, by a process of diffusion in the morphogenetic space.

III.1 Neural tube expansion, with heart beat

However, the model presented in Ref. 3 shows a self-organized gradient of brain vesicles sizes which does not correspond to the observed one. In the real system, the mid-brain vesicle is the largest. While any genetic explanation could be invoked, we remark that the largest vesicle correlates with the presence of a larger return vein, and of an aorta underneath. This suggests that there is globally a higher flux in that vesicle. When observing the position of the heart and the blood flow, it is observed that the heart flushes blood via the aortas right under this vesicle, at the position of the mouth corner (see Videos 11 to 15, especially Video 13 shows very well the opening of the aorta under the midbrain vesicle -arrowhead). This explains why this vesicle is eventually larger. Also, when we observe the capillaries in the biggest vesicle, we see that the capillaries present a bending in the direction of the flow. This is coherent with the “go with the flow” concept of shear flow in vascular morphogenesis, by which shear flow imparts a morphogenetic force on the vessels [15]. The shear stress orients the blood vessels, and reciprocally, the pattern of vessels reflects the field of shear. As a consequence of these observations we may modify the model by hypothesizing a larger hemodynamic pressure close to that vesicle, which gives the pattern in Fig. 9A, for a 60% higher pressure. However, if the blood flow is increased in the aortic tract, so as to increase the equivalent pressure in the mid-brain vesicle, so is the tensile stress in the blood vessels. So when hypothesizing a higher pressure in the mid-brain vesicle one must also take into account a higher shear force in the strands located underneath the neural tube, and oriented towards the heart. This gives the pattern in Fig. 9B, Video 34, which arguably, is much more realistic. Especially, the calculation shows that the nasal vesicle, being at a free end, is more dilated than the forebrain vesicle. Conversely, the forebrain and cerebellum vesicles are squeezed, and dilate less, while the mid brain, being under higher pressure, dilates more and squeezes both cerebellum and forebrain on each side (posterior and anterior). We recover with very simple physical parameters, the distribution of vesicles observed physiologically. In this model, the only parameters are: the bottom-line level of pressure in the vesicles, the surface tension reduction in the midbrain due to blood flow, and the line shear force in the ventral vessels. For a given global fluid pressure, the brain pattern is fixed by the ratio of the surface tension in the midbrain, vs the line tension in the strands or cables (and of course the time of the simulation: the arrest point in our simulations is the instability of the mesh, due to small triangles).

It has been suggested in paleoanthropology that there exists an internal correlation between head flexure and brain dilation [1, 2]. This would explain why the hominins skulls become less prognathous, as the brain expands. Numerical modelling predicts such an internal correlation [3]. Recent experiments of electrical stimulation also show that there exists a correlation between brain dilation and head flexure [3]. It has also been shown that there is a correlation between heart development and head flexure [7, 11]. In Ref. 11, it has been shown that if head flexure is hindered, the heart does not form properly. In Ref. 3 it was shown that if heart tone is decreased or increased, the head development either winds back or forth while it shrinks or dilates correlatively. However, there was no direct in vivo quantitative data supporting the existence of a dynamic internal correlation between head flexure and brain dilation during physiological vertebrate embryo development. We have presented here such dynamic data. It is found that there indeed exists a dynamic correlation between head flexure and brain dilation, after the closure of the neural tube. In Ref. 6 we have shown that brain dilation starts as soon as the neural tube is closed. This would suggest that brain dilation is primarily driven by the internal pressure in the closed neural tube (the ectoderm produces constantly a fluid which accumulates inside the tube as cephalic fluid; conversely, it is a common knowledge that the brain deflates when it is poked during dissection). However, the brain does not simply balloon out, it also flexes, firstly because a series of vesicles in contact tends to flex (Fig. 8). The component of the stress along the Antero-Posterior axis causes a progressive curvature of the head, as it dilates, because the vesicles push against each other while they fight the tension in the vesicle walls, and along the ventral and dorsal lines (Fig. 8). Secondly, there is an increased tension in the tissue which pulls the head and participates to flexure. This pull is associated to heart texture, for the orientation of the pull, and to heart contractile activity, for the magnitude of the effect. But heart activity correlates with brain dilation, since increased blood flow accelerates brain dilation by relieving tensile stress in the brain shell. This explains why there exists a correlation between brain dilation and head flexure. Both the texture and heart activity correlate dilation and flexure. It is classical in condensed material science that textured materials have original mechanical properties, here the property is an internal correlation between dilation and flexure.

However, we also find that there exists an anomaly in the allometric curve, which is related to eye ectoderm invagination. The tension forces in the surface of the brain shell are active, and they are stimulated by the event of eye invagination (and also ear and nose pits invagination). During eye formation, the eye ectoderm flips inwardly and invaginates, much like a buoy valve, which causes a pressure increase by conservation of volume. This may explain naturally the transient small excess of brain dilation (Fig. 5A, arrow), and the twitch in flexure. However, the contraction of the eye invagination triggers a transient contraction in the surrounding tissues, especially the brain shell (Videos 19, 20). A similar behavior was observed during nasal pit formation [6]. By the Laplace relation between surface tension, shell radius and pressure, an increased brain shell contraction amounts to an additional pressure which pushes on the eye outwardly. During eye invagination the behavior of the tissue is therefore complex, with antagonist effects (eye invagination causes an inwards movement, followed by an outwards movement by surface shell contraction and pressure increase) which result in an oscillatory spasm (Fig. 5C) correlated with the transient anomaly in the allometric curve. After this transient event, the data return to an allometric straight line. This movement extends previous knowledge of the effect of surface ectoderm on eye morphogenesis [19].

The electric stimulation of the nare presented above, shows that organogenesis is a latent excitable event, which can be triggered, and that it is indeed associated to a transient contractile twitch of the tissue. The exposure of the ear to osmotic shocks shows that the mechanism of invagination implies a tension of the ridge of the organ, which is antagonist to the tension in the surrounding tissue. The proper invagination of the eye ball, of the otic or nasal pits require a well-tuned fight between the line tension along the round edge of the organ, which attempts to invaginate, and the surface tension in the surrounding cranial surface which hinders invagination. A similar effect was evidenced in brain wound healing experiments in Ref. 3: when a hole is made in the brain, it closes spontaneously by formation of a contractile ring or cable along the edge of the wound. But when tension is increased in the surrounding tissue by electric stimulation, the wound instead opens more [3]. Here we have observed that increasing tension in the forming pit or decreasing tension in the surrounding brain, induce a stronger invagination.

It is also confirmed here that hemodynamics plays an important role in head dilation and flexure. This is particularly visible in the fact that the head is twisted ventrally towards the right side, which correlates with the chiral twist of the heart, and the presence of a bigger aorta along that side. We have shown above that the brain dilation and head twist correlate with percolation of the circulation. However, we have also shown that the pattern of blood vessels mirrors the early embryonic texture. Blood vessels play a role at two stages. During formation of the heart and around the moment of the establishment of the circulation, there is a direct pull by the aortas on the head primordia, which twists and flexes them. The aortas follow the initial boundaries of the cardiac crescent so that the pattern of vessels and force is deterministic. At later stages the blood vessels still mirror the texture of the embryo, as shown by in vivo detailed imaging (Fig. 3). The main vessels follow the valleys in between brain vesicles, and the brain vesicles are covered with a plexus of small capillaries. Flow conservation correlates the tension and shear force exerted along the blood vessels to the pressure in the capillary bed, which contributes to dilating the brain. This creates a torque effect: increase in blood flow causes simultaneous brain dilation by reduction of tensile stress, and also head flexure by increase of tensile stress in larger vessels, inside a general model of vesicle development. Why the tensile stress is reduced in the brain vesicle, while it is increased in the main vessels is related to the differentiation of muscle cells. Figure 3C shows that the capillaries contain much less if any α-actin, while differentiated blood vessels contain much more smooth muscle α-actin. Larger vessels are stronger than smaller ones, also by the presence of more smooth muscle cells. The tensile response of the main vessels to a step in pressure is therefore higher than that of capillaries.

In order to recover the correct distribution of vesicle sizes, we have invoked the reduction of tensile stress by a higher flow in the midbrain (a tensile stress equivalent to a 60% pressure is necessary to recover a realistic vesicle size), which acts as an equivalent increase in pressure working only in the midbrain. Indeed, one cannot obtain such an effect by increasing pressure inside the bulk of the neural tube, instead of the vesicle shell. Since the lumens of the vesicles communicate, by fluid incompressibility, all vesicles should dilate at a similar pace, if only the pressure inside the tube was increased, which is not observed. This shows that the general idea that the brain dilates under the bulk pressure in the cerebral liquid [20] is not completely correct. Something specific must occur inside the very surface of the midbrain, distinct from what occurs in the bulk, and driving dilation. We have shown here that the geometry of the heart position suffices to explain the specific dynamics of the midbrain, by creating a specific dilational effect in that segment of the brain shell.

The reduction of pressure inside the brain shell by Mannitol shows that a reduced tension makes the ear pit edge primordium collapse rapidly onto itself. This shows that the tensile force in the tube outer surface antagonizes ear pit movement. This suggests an explanation to the observation that, physiologically, the head flexes towards the side where ear formation is delayed: increased tension in the tissue causes a progressive contraction and shrinkage of the tissue which flexes and twists the head. But the increased tension tends also to stretch the dorsal surface where ear is forming, and hence, antagonizes the invagination of the ear pit. This delays the morphogenesis of the ear pit. This shows that the difference in time of formation of the left ear vs the right ear should be interpreted not as the ear to the left being ahead, but by the ear to the right being delayed with respect to the left, because of an asymmetric surface tension caused by the presence of the heart underneath. It is remarkable that this delay, which is quite conspicuous at early developmental stages, does not affect the final symmetry of the ears. As shown in Ref. 7, morphogenesis slows down spontaneously, and behaves as a scar. The slowing down of ear organogenesis, to the left, allows the ear to the right to catch it up.

This work confirms the existence of a developmental correlation between brain dilation and head flexure, but points to active actuation of tensions during development, both in tissues (surface shells vs rings) and blood vessels, which are not resolved in classical static stagings. As observed here, all morphogenetic events have an active mechanical component to them, which influences brain dilation and flexure. Especially, the formation of the sensory organs is a non-linear contraction, as confirmed by electric stimulation, which interferes with the otherwise monotonic expansion of the brain, and hemodynamics correlates dilation and flexure at long distance, with a discontinuity related to percolation of the flow, and the associated mechanotransduction.

In summary, there exists a radial and orthoradial texture of rays and wedges in the early blastodisc. This texture serves as cue for filaments or cables formation (contractile cells tend to recruit each other and condense, but along the pre-existing pattern). The pattern of rings and rays is projected onto collars and cables in the dilating neural tube, and ventrally onto forked blood vessels of the heart, which also form by ring contraction. The forked vessels pull directly on the head and flex it. The pattern of cell collars in the valleys constrains the development of the vesicles and causes an additional flexure in the brain. The rays and wedges are also at the origin of the sensory organs [7], of the mouth, and of such landmarks as the nasogenian grooves of the face [6]. There is a correspondence between the valleys in between brain vesicles and the organs seen on the head (including the mouth and jaws).

The neural tube is a dual object submitted to two different physics: the physics of brain shell expansion or contraction, which is a problem of (2D) shells ballooning under pressure, and a physics of (1D) belts or vessels which actively constrict and cause in-line forces.

While collars of cells induce an antagonism between dilation of a tube, and transverse line tension (the collars are around the tube), sensory organ formation corresponds also to an antagonism, but between tube dilation and longitudinal line tension (the rings of the otic pits, nasal pit, and ocular cup are not transverse to the tube axis but along the longitudinal surface of the tube). Hence there is a dual antagonist aspect opposing dilation and contraction, biaxially: longitudinally and transversally. One peculiar case is that of the closure of the neural tube in the anterior end of the neural tube (shutting down the notopore) which is also a matter of ring contraction, although the ring is not complete, and the ring is both transverse and longitudinal (Video 35 and Fig. 6 in Ref.7). Also, the ring around the notopore closes an open tube, so it does not have to fight intra cephalic fluid pressure.

The surface and line contraction duality is inherited from the very fact that cells divide by constriction of a ring of actin. Indeed, in a dividing single cell also, there is an antagonism between dilation of the surface of the cell vs contraction of the ring causing mitosis. The combination of these two physics, one of surface, one of line, is up-scaled in the process of hominization. The collective behavior of cells generates vesicles and rings quite similar to cells in contact. The upscaling of the cellular physics into brain vesicle development is apparent in the fact that the simulations presented in Figs. 8 and 9 could as well be interpreted, modulo a mere change in scale, as the roll up of an epithelium, under cell dilation and basal cortical constriction.

This work supports the idea that human origin is physically constrained ab initio by the texture of cell cleavage in the early embryo, and its mechanism of cleavage by actin-myosin rings. The fundamental competition between surface dilation and line tension is what canalizes evolution. The origin of humans is to be searched inside the embryos [1, 3]; this concept is known as Inside story.

Acknowledgement. I acknowledge the financial support of the anonymous donators of The Fondation CNRS. One set of data (Video 18) was acquired by undergraduate student Olivia Plateau during a Master internship. The confocal images of CAM vessels were obtained by undergraduate student Hany Charara during a Master internship. The Mannitol data were acquired by undergraduate students Marine Pancrazi, Lloyd Kamole-Ghomsi and Elie Abou Zougheib. I am indebted to Charles Dapogny for providing the curvature module for the Freefem++ calculation. The ImageJ software which is used here, was created by Wayne Rasband from the NIH. The Tracking modules for the PIV images were created by Olivier Cardoso and Bérangère Abou. I thank Nicolas Chevalier for stimulating discussions and help with the confocal microscope.

Data availability statement. The datasets, mostly time-lapse videos, used and/or analysed during the current study are available from the corresponding author on reasonable request.

A. Dambricourt-Malassé, Continuity and discontinuity during modalities of hominization, Quat. Interna. 19 85-100 (1993).
A. Dambricourt, Évolution du chondrocrâne et de la face des grands anthropoïdes miocènes jusqu'à Homo sapiens, continuités et discontinuités, C. R. Acad. Sci. Palevol., 5 (1-2) 109-117 (2006).
V. Fleury, Electrical stimulation of chicken embryo development supports the Inside story scenario of human development and evolution, Sci. Rep. 14, 7250 (2024). https://doi.org/10.1038/s41598-024-56686-y.
M. Barresi and S. Gilbert, Developmental Biology, 13^th ed. Oxford UP (2023).
V. Fleury, A. Abourachid, A. Peaucelle, and O. Plateau, Second order division in sectors as a prepattern for sensory organs in vertebrate development, Theory in Biosciences, Special Issue Geometries and phenomenology of the Living (2021).
V. Fleury, Dynamics of early stages of nose morphogenesis, Eu. Phys. J. E 45 93 (2022). doi.org/10.1140/epje/s10189-022-00245-8
V. Fleury, A. Abourachid, A biaxial tensional model for early vertebrate morphogenesis, Eu. Phys. J. E, 45, 31 (2022). doi.org/10.1140/epje/s10189-022-00184-4
V. Fleury, N. Chevalier, F. Furfaro, J.-L. Duband, Buckling along lines of elastic contrast as a mechanism for early vertebrate morphogenesis, Eu. Phys. J. E 38, (6), 1-19 (2015).
V. Fleury, V. A. Murukutla, N. R. Chevalier, B. Gallois, M. Capellazzi-Resta, P. Picquet and A. Peaucelle, Physics of amniote formation, Phys. Rev. E 94, 022426 (2016) doi: https://doi.org/10.1103/PhysRevE.94.022426.
V. Fleury, Dynamic topology of the cephalochordate to amniote morphological transition: A self-organized system of Russian dolls, C. R. Acad. Sci. Biologies 334 (2), 91-99 (2011).
B.M. Carlson, Development of the Vascular System, Reference Module in Biomedical Sciences, Elsevier (2014), doi:10.1016/b978-0-12-801238-3.05459-311.
M. S. Ghasemi Nasab, H. Niroomand-Oscuii, H. Bazmara, M. Soltani, Morphogenetic Mechanisms of Endothelial Cells During Lumen Formation in Sprouting Angiogenesis, Multidisciplinary Cancer Investigation, 6, (2), e-published April 2022. DOI: 10.30699/mci.6.2.523-1
V. Hamburger, H. L. Hamilton, A series of normal stages in the development of the chick embryo, Journal of Morphology 88 (1), 49–92 (1951).
S. Richard, A. Brun, A. Tedesco, B. Gallois, N. Taghi, P. Dantan, J. Seguin, V. Fleury, Direct imaging of capillaries reveals the mechanism of arteriovenous interlacing in the chick chorioallantoic membrane, Commun. Biol. 1, 235 (2018).
F. Le Noble, V. Fleury, A. Pries, P. Corvol, A. Eichmann, S.R. Reneman, Control of arterial branching morphogenesis in embryogenesis: go with the flow, Cardiovasc. Res. 65, 619 (2005).
Hecht, F., New development in FreeFem++, Journal of numerical mathematics, 20, (3) (2012).
J. Männer, W. Seidl and G. Steding, Correlation between the embryonic head flexures and cardiac development, Anat. Embryol. 188, 269–285 (1993). https://doi.org/10.1007/BF00188218
H. S. Hosseini, D.C. Beebe, L. A. Taber, Mechanical effects of the surface ectoderm on optic vesicle morphogenesis in the chick embryo J. Biomech. 47 (16) 3837-46 (2014). doi: 10.1016/j.jbiomech.2014.10.018
J. H. Kim, H. Jeong, et alii, Optimizing Mannitol Use in Managing Increased Intracranial Pressure: A Comprehensive Review of Recent Research and Clinical Experiences, Korean J. Neurotrauma, 19 (2),162-176 (2023) https://doi.org/10.13004/kjnt.2023.19.e25
A. Gato , M. E. Desmond, Why the embryo still matters: CSF and the neuroepithelium as interdependent regulators of embryonic brain growth, morphogenesis and histiogenesis, Dev Biol. 327263–272 (2009).

Eastside story and Westside story refer to the cradle of humanity in Africa, nearing the rift valley, and depending whether one assumes an origin east or west from the rift valley.

No competing interests reported.

SupplementaryFIgure1.jpg
Video1.avi
Video 1 Global view of chicken embryo neurulation (dorsal view, Mag. 4X, duration 10h). Time-Lapse imaging of chicken embryo neurulation in dorsal view, starting from a flat blastodisc,a nd ending with an embryo with eye cups, neural tube and a few somites.
Video2.avi
Video 2 Detail of neurulation in the area of the cardiac crescent showing that the radial lines coincide with kinks in the neural tube (arrows at the beginning, and at the en) (Mag. 10X, duration 4h).
Video3.avi
Video 3 Neurulation profile view, with a visible radial boundary of the cardiac wedge forming the presumptive nasogenian groove. The movie concatenates two different magnifications. The arrow points to the point of insertion of the cardiac wedge along the trunk. ec: eye capsule; bv: brain vesicle; ng: nasogenian groove (Mag. 4X and 10X, duration 10h)
Video4.avi
Video 4 Neurulation ¾ view, with the radial line becoming the nasogenian groove (white arrow). The atrium and ventricle is visible by the end in the bottom left, just below the point of insertion of the cardiac wedge (black arrowhead). The flow of neural crest cells is also visible. (Mag. 4X, duration 8h)
Video5.avi
Video 5 Ventral view of embryo neurulation showing the formation of the ventral pocket. The edge of the pocket constricts and forms the heart. (Mag. 4X, duration 9h)
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Video 6 Time-Lapse of contraction of the cardiac ring seen from the ventral side, and starting when the embryo is flat (Mag. 4X duration 8h).
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Video 7 Time-lapse of contraction of the cardiac ring. The ring constricts at a constant speed. The V-shaped wedge of the cardiac crescent is visible to the left. It is stretched by cardiac morphogenesis but it remains as a physical landmark (arrow); the atria are connected to the point of insertion of the V. The cardiac ring constricts (to the right) and generates the venous tract (arrowheads). Several somites are visible. a: atrium; v: ventricle; s: somite (Mag. 4X, duration 9h).
Video8.avi
Video 8 Later stage of heart formation, one evidences the cardiac flexure, the formation of the venous tract (to the right, white arrowheads), and the early stage of aortic formation in the “top” part of the heart (to the left, black arrow). a: atrium; v: ventricle; ec: eye capsule; s: somite. (Mag. 4X, duration 6h)
Video9.avi
Video 9 Heart formation just prior to opening of the aortas. The beginning of the heart beat is visible and the fork of the aortic tract outside the atria, with one open aorta is visible (arrow). The venous tract is located at the arrowheads. a: atrium; v: ventricle; ec: eye capsule; s: somite. (Mag. 4X).
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SupplementaryMaterial.docx

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Competition between surface tension and line tension canalizes craniate evolution

Status:

Version 1

Abstract

Figures

I. Introduction

I.1 Paleontology

I.2 Early brain formation.

I.3 Early heart formation.

I.4 Early vascular network

II. Results

II. 1 Non-linear anomaly in brain development, related to eye formation

II.2 Acceleration of brain development related to blood vessels.

II.3 Effect of increasing or decreasing tension in the head.

II.3.i Ear formation

II.3.ii Nose formation

III. Modelling

III.1 Neural tube expansion, without heart beat

III.1 Neural tube expansion, with heart beat

IV. Discussion and conclusion

Declarations

References

Footnotes

Additional Declarations

Supplementary Files

Status:

Version 1