The mechanosensitive model quantitatively phenocopies experimental apex constriction dynamics

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Quantitative phenocopy of experimental constriction dynam-ics by in silico modelling

We succeeded to reproduce the constriction transition experimentally observed, characterized by a transient regime during which cells oscillate typically twice, before the emergence of a subsequent regime of collective stable constriction at 2–3 min (77 Kam et al 1991, 78 Martin et al 2009)(Figure 13).
Figure 13: (A) 1D 300 cell chain patterned by 50 Snail and Fog expressing cells in the : of the mesoderm (green), two ventro-lateral mesoderm domains of 25 cells each expressing only Fog (red), and two lateral domains of 100 ectoderm cells each expressing neither Snail nor Fog (blue). Snail-dependent single cell oscillations of 0.25% of amplitude lead to collective movements characterized by pulses of apex size of 5% that activate the Fog-dependent active collective constriction after two cycles of oscillations (120 s), as observed in vivo (Martin et al 2009). Collective constriction is complete at 400 s, as observed in vivo ((8) Kam et al 1991). Note that in addition to the phase, the initial size of the cells was also randomized with an amplitude of 0.1% in the simulation, to add stochasticity in the active fluctuations. (B) Similar results were obtained taking into account the fact that con-tractile ventro-lateral cells are delayed in constriction compared to (A) (mostly red Fog expressing cells) because they are submitted to curvature constraints preventing them from constricting (see the text), (C) as well as with a reduced number of cells reflecting anisotropic constriction along the dorso-ventral axis (see the text). Experi-mental apex cell diameter length (dotted line) was calculated on the basis of lexp = 2∗(A/π)1/2 where A is the area of the cell apex from experimental data of reference (Martin et al 2009), approximating the cell as cylin-ders with apexes as disks. Simulation results are robust and representative of all simulations tested with the same set of parameters (at least three times for each set of parameters).
Interestingly, in Figure 13 A, we observe that the cells expressing only Fog (in red) constrict in response to Snail dependent oscillations. In a 3D geometry they should not been able to do it because of the high curvature im-posed on the ventro-lateral cells by the invagination of the most central mesodermal cells expressing both Snail and Fog (in green). We then suggested that even though activated, the lateral mesodermal cell expressing Fog only cannot contract because of such curvature. This feature was thus mimicked in the simulation by prevent-ing constriction in the lateral cells expressing Fog only. As a result, the simulation showed a dynamics of con-striction that fits with the experimental curve (black circles) for an individual constricting cell (Figure 13B), for an arbitrary number of 100 cells. Figure 13C represents the same conditions with the smaller number of cells characterizing quantitatively the real number of cells of a dorso-ventral cross section. Within this condition, we find a behaviour of constricting cells in good quantitative agreement again with the dynamics of experimental individual cell constriction.

Passive and active collective behaviours

Interestingly, here we find that the amplitude of the individual excitation is of 0.25%, namely significantly smaller than the 5% critical length activating the contractile Fog signalling pathway, by a factor of 20. There-fore, collective movements emerging from mechanical coupling between individual cells are in this simulation necessary to transiently generate single cell oscillations of amplitude larger than the critical length activating the constriction.
In addition, once activated in a single cell, the Fog signalling pathway generates a stable active constriction that dilates neighbouring cells. Then, the probability for those neighbouring cell apex sizes to become larger than the critical size increases. As a consequence, neighbouring cells constrict in response to the first cell con-striction, leading, in turn, to the constriction of their own neighbouring cells. The involvement of such a collec-tive effect of active constriction was verified by impairing cell–cell mechanical interaction by introducing a coupling constant At in front of the first and third terms of the second member of equation (4), and putting At=0. In this case, no cell constricts because collective movements are missing and do not allow anymore to reach the 5% required for the active constriction to be triggered (Figure 14 A). Interestingly, full deletion of adhesive properties between cells would be required to test such prediction of the model, partial adhesion inhibition still allowing tension to be transmitted between cells and leading to membrane tension through strong membrane tethering (Martin et al 2010).
This result suggests that the collective passive response of the mechanically coupled cells to the Snail-dependent active excitation could be necessary for individual cells to attempt the critical size activating the Fog-dependent contraction, in a configuration for which individual uncoupled cell oscillation amplitudes would not be sufficient. The activation of the constriction could, in turn, propagate from cell to cell and lead to the coordinated active constriction necessary for mesoderm invagination.

A critical role for the frequency of Snail dependent pulsations

Then, I decided to modify the excitation frequency to study the sensitivity of the system response to the dy-namics of its excitation. Due to the viscoelasticity, changing the excitation frequency of individual cells should change the oscillation amplitude of the cells. This is due to the fact that high frequencies do not let the time to collective modes to explore the full amplitude it could explore without viscosity, because of to the viscosity medium. Indeed, doubling the frequency of the Snail dependent oscillations decreased the amplitude of oscilla-tion of the connected cells in response to the solicitation, thereby leading to a loss of the collective constriction phase (Figure 14 B).
In contrast, if we half the frequency, we observe an increase of oscillation amplitude that is much bigger than in the case reflecting endogenous frequency (Figure 14C). This is because in that case we let more time to col-lective modes to explore the amplitude it could explore fully without viscosity, due to the lower viscosity of the medium. In this case collective constriction occurs, but do phenocopy experimental data with less quantitative accuracy Strikingly, mutants of Snail effectively show experimentally a doubling of the frequency of excitation compared to Twist mutants or wild types, with amplitude of fluctuations significantly reduced, and a lack of transition (13 Martin et al 2009). This result suggests that in addition to the amplitude of the excitation, the frequency of the Snail-dependent excitation might also be a critical parameter leading to the activation of the Fog-dependent constriction wave.

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The alternative hypothesis of a mean field hydrostatic pres-sure

In the model just presented, the mechanical strain activating one cell is due to the constriction of the neigh-bouring cell. An alternative possibility would be that membrane tension leading to the inhibition of Fog endocy-tosis is triggered by hydrostatic pressure increase in the mesoderm due to the cells having already constricted. In this model all the cells would interact together through a mean field pressure generated by cell shape changes (Figure 15).
During the Snail-dependent apex oscillations, individual cells transiently take trapezoidal shapes due to the decrease of the apex surface. Such shape change decreases the total surface of the apex at constant volume, possibly leading to an increase of hydrostatic pressure inside the cell. Hydrostatic pressure should propagate immediately along the mesoderm through lateral cell plasma membrane deformations, and increase the mean internal pressure in all mesodermal cells. As a consequence, membrane tension should increase in all cells. In response to the increase of membrane tension, Fog endocytosis would be inhibited, thereby activating the downstream pathway leading to Myo-II apical attraction. We have added in this simulation a mean field pres-sure proportional to the number of cells constricted and critical pressure activation to activate the constriction. Within these conditions, the transition was found to be much more sudden than the transition predicted by cell–cell local interactions, with all cells following the same dynamics of constriction at the same time (Figure 15 A). The same result was obtained in the absence or in the presence of adherens junctions (At = 1) with im-mediate activation of all contractile cells. By decreasing Kfog by a factor of 2, the simulation dynamics better fits the observations, except that the ratchet steps were delayed in amplitude and time (Figure 15 B). By playing with the characteristic time scale of the ratchet, the ratchet events could be located at correct characteristic amplitude, but not at correct characteristic time, and diverged from the experimental curve after one step (Figure 15 C). It was not possible to find a set of parameters correctly fitting both the long mean and short ratchet dynamics of the constriction using the hydrodynamics model. This suggested that cell–cell mechanical interactions leading to active constriction could be viscoelastic and local through apex–apex interactions, ra-ther than hydrostatic and non-local through cell–cell pressure interactions across the mesoderm.

Table of contents :

1- Mechanics in development
a- Forces in biology
b- Forces of embryonic development
2- Mechanotransduction
I – Mechanotransduction in Drosophila embryo mesoderm invagination: transition from individual pulsating to collective constriction apex behaviour
1- Introduction
a- Drosophila embryo mesoderm invagination
b- Existing models of gastrulation
2 – The Snail/Fog patterned mechanosensitive model: a 1 Dimension model
3- Simulation’s results
a- Quantitative phenocopy of experimental constriction dynamics by in silico modelling
b- Passive and active collective behaviours
c- A critical role for the frequency of Snail dependent pulsations
d- The alternative hypothesis of a mean field hydrostatic pressure
4- Conclusion
a- The mechanosensitive model quantitatively phenocopies experimental apex constriction dynamics
b- Physiological function of collective constriction transition
c- Constriction transition leading to mesoderm invagination as emerging from ‘mechano-genetic’ coupling in development
5- Perspectives
II- Evolutionary conservation of early mesoderm specification by mechanotransduction in Bilateria
1- Introduction
a- Zebrafish development
2- notail induction at the onset of epiboly
a- notail expression is β-cat dependent
b- β-cat -dependent notail expression is Wnt-independent
3- Mechanical induction of β-cat nuclear translocation in mesoderm cells
4- Mechanical induction of notail expression
5- Mechanical induction of β-cat dependent ntl expression by magnetic forces quantitatively mimicking the onset of epiboly dynamics
6- Mechanical induction of β-cat molecular translocation and of ntl expression by Y667 β-cat phosphorylation
7- Pathways synergising with Y667-β-cat mechanically induced phosphorylation
a- Bmp and Nodal
b- Mapk and phospho-GSK3β
8- Comparison with Drosophila and evolutionary consequences
a- Mechanical induction of Twist expression by Armadillo/ β-cat nuclear translocation
b- Mechanical induction of Y667 β-cat phosphorylation
9- Conclusion: a mechanotransductive origin of mesoderm emergence in the common ancestor of bilaterians ?
10- Perspectives
III- Mechanically Induced Heritable Modulation of Developmental Biochemical Regulation
1- Introduction
a- Epigenetics in Drosophila
b- The pi-RNA transposon repressing complex
c- The checkpoints DNA integrity guardians
2- Mechanically induced herited early developmental phenotypic defects
a- Mortality and morphological approach to study the progeny
b- Inheritance of anomalies in the progeny of indented embryos
c- Microscope analysis
3- Hypothesis: the dorsalised phenotype as induced by checkpoint activation
a- Dorsalized ventro-dorsal gradient of Dorsal nuclear translocation
b- Testing the inhibition of the check point phenotype by indenting p53 and Check-2 mutants
4- Testing the transposon activation hypothesis
a- Candidate approach
b- Non-candidate screening approach
5- Conclusion
a- Genetic transmission
b- Epigenetic transmission
6- Perspectives
a- Transposon activation
b- Individual flies sequencing
c- Physical characterization of the underlying mechanotranductive process
d- Putative speciation process
General conclusion


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