Hindbrain neuropore tissue geometry determines asymmetric cell-mediated closure dynamics in mouse embryos

Significance Failure to biomechanically close the embryonic neural tube in the developing brain causes fatal anencephaly. Despite their clinical importance, which cellular force-generating mechanisms close the neural tube remains poorly understood. This interdisciplinary study combines morphometric analysis, mouse embryo live imaging, and in silico modeling to formally identify cellular behaviors which complete midbrain/hindbrain closure. Two cellular force-generating behaviors not previously appreciated to act in this context are identified: contractility of supracellular actomyosin purse strings around the gap and directional movement of cells toward the gap. Both these mechanisms are required to describe gap closure, and their resulting dynamics are substantially impacted by morphogenetically imposed tissue geometry. This work provides a broadly applicable biophysical framework underlying fatal failures of midbrain/hindbrain closure.


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Appendix References
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Appendix Methods-Page 3
Appendix Table S1

Immunofluorescence, image acquisition and analysis
Images were captured on a Zeiss Examiner LSM 880 confocal using 10 x/NA 0.5 or 20 x/NA 1.0 Plan Apochromat dipping objectives. Whole HNP images were captured with x/y pixel sizes of 0.42-0.59 μm and z-step of 0.8-2.44 μm (speed, 8; bidirectional imaging, 1024×1024 pixels). Images were processed with Zen 2.3 software and visualised as maximum projections in Fiji (1). To visualise the surface ectoderm, the z-stacks were first surface subtracted as previously described (2) to only show the apical 2-3 μm of tissue.
For morphometric analysis, HNP length and width were calculated by annotating the HNP rim and then measuring the major and minor axis using the fit ellipse function in Fiji. To quantify the distance of each zipper from the otic vesicles, reflection images were captured using the 10 x/NA 0.5 dipping objective (633 nm wavelength, x/y pixel size 2.44, z step 3.33 μm). The z stacks were 3D rotated and visualised as maximum projections. For 3D visualisation of reflection images (Fig 2A, E), z-stacks were despeckled in Fiji, filtered with a Kuwahara filter (sampling window width of 5) and opened with the 3D viewer plugin.

Live imaging
Live imaging datasets were 3D registered in Fiji using the Correct 3D Drift plugin (3). They were then deconvolved using the Richardson-Lucy algorithm (5 iterations) in DeconvolutionLab2 (4). All sequences were surface subtracted (macro above) in order to enable visualisation of surface ectoderm cell borders. Cell migration analysis was done in Fiji using the manual tracking plugin along with the 'chemotaxis and Migration tool' plugin (ibidi).
Particle Image Velocimetry (PIV) analysis was performed in Fiji using the in-built Iterative PIV (Cross-correlation) plugin (32 pixel final interrogation window size, normalise median test noise = 1 and threshold = 5). Images were Gaussian-filtered (radius = 2 pixels) before applying PIV.

Laser ablations
After removal of the extraembryonic membranes, embryos were stained with 1:500 CellMask Deep Red plasma membrane (C10046 Invitrogen) in DMEM at 37 o C for 5 min. They were then positioned on agarose plates using microsurgical needles and moved to the microscope stage (heated at 37 o C). Tissue-level (5) and cable (6) laser ablations were performed as previously described using a Mai Tai laser (SpectraPhysics Mai Tai eHP DeepSee multiphoton laser).
For cable ablations, a 0.1 μm-wide line was cut using 710 nm wavelength at 100% laser power (0.34 μs pixel dwell time for 10 iterations, 20X/NA 1 Plan Apochromat dipper). One ablation was analysed per embryo. Cable recoil was calculated by measuring the immediate displacement of cell landmarks perpendicular to the ablation.
For tissue-level zippering point ablations, a pre-and post-ablation z-stack was obtained using 10X magnification at 633 nm. Total acquisition time for each stack was ~3 min. The ablations were performed using 800 nm wavelength at 100% laser power (65.94 μs pixel dwell time for 1 iteration, 10X/NA 0.5 Plan Apochromat dipper). The zippering point was ablated using narrow rectangular ROIs, moving sequentially in z to ensure the tissue was ablated.

Computational Model
To model neural tube closure, we use the vertex model for epithelia (7,8). The apical surface of the tissue is modelled by a network of connected edges, with cells described as the polygons and cell-cell junctions as the edges. The tissue mechanical energy given by: where indicates the sum over all cells. The first term represents cell area elasticity, with elastic modulus , cell area and preferred area 0 . The second term represents a combination cytoskeletal contractility and interfacial adhesion energy, where is the contractility, the cell perimeter, and 0 the preferred perimeter. When adhesion dominates over contractility, 0 will be large as cells aim to increase contact length with their neighbours.
The mechanical force acting on vertex is given by = − / , where is the position of the vertex. Assuming that the system is over-damped, the equation of motion is given by: where is the drag coefficient.
To model the closure forces acting on the border cells at the gap, we implement an increased tension for edges on the gap representing the purse-string (9, 10). The purse-string tension is chosen such that the total tension of the junction is equal to 5 times the mean tissue tension.
The tension within the tissue is given by 2Γ( − 0 ), where is the mean cell perimeter, since two cells contribute to a single junction, and at the wound edge by Γ( − 0 ) + Λ . Thus, we calculate Λ = 9Γ( − 0 ).
Each cell in the tissue may also crawl, with a polarity vector which determines the direction of crawling forces. The crawling applies an additional force to all vertices of that cell, equal to 0 , where 0 is the cell crawl speed. Cells around the gap have a polarity vector equal to the unit vector perpendicular to their edge on the gap (9). Cells within the bulk of the tissue then align polarity with their neighbours, subject to a decay: where the sum is over all neighbouring cells indexed by , is the polarity alignment rate, and is the polarity decay rate. The resulting effect is that all cells will crawl towards the gap, but with less speed as distance to the gap increases.

Model implementation
The model is implemented using Surface Evolver (11). We generate an initial tissue configuration using data from experiments. Given a set of cell centers, and boundary points for the gap and border of the tissue, we generate a Voronoi diagram, giving us the cell shapes. The tissue is then relaxed, with the gap edges fixed to maintain its shape, to a mechanical equilibrium before simulating closure. In experiments, the tissue curves around but is free to deform, thus we use free boundary conditions on the external edges. If an edge shrinks below a critical value, 1 , the edge undergoes a rearrangement, or T1 transition, in which a new edge is formed perpendicular to the original junction. The equations are solved numerically by discretizing the equation of motion: ( + ) = ( ) + / , where is the time step.

Model parameters
We non-dimensionalise length by 0 1/2 and energy by / 0 2 , giving us a normalized mechanical energy of The purse-string tension chosen so that the total tension on the gap edges is five times greater than the mean edge tension, to match experimental recoil rates after laser ablation. The tension on an edge has contributions from the two cells connected to it, giving a mean tension of 2( ̅ − 0 ), where ̅ is the mean cell perimeter. Since the gap has contributions from one cell, the purse-string tension satisfies + ( ̅ − 0 ) = 10( ̅ − 0 ). Cell crawl speed is chosen to maintain a constant gap aspect ratio over time.