Matrix topology guides collective cell migration in vivo

Diverse modes of cell migration shape organisms in health and disease and much research has focused on the role of intracellular and extracellular components in different cell migration phenomena. What is less explored, however, is how the arrangement of the underlying extracellular matrix that many cells move upon in vivo influences migration. Combining novel transgenic lines and image analysis pipelines, reveals that during zebrafish optic cup formation cells use cryptopodia-like protrusions to migrate collectively and actively over a topologically changing matrix. These changing topologies correspond to different cell-matrix interactions. Interference with matrix topology results in loss of cryptopodia and inefficient migration. Thus, matrix topology influences the efficiency of directed collective cell migration during eye morphogenesis, a concept likely conserved in other developmental and disease contexts. One-Sentence Summary Dynamic cell-matrix interactions, crucial for successful collective rim cell migration, rely on extracellular matrix topologies during optic cup development in vivo.


Abstract:
Diverse modes of cell migration shape organisms in health and disease and much research has focused on the role of intracellular and extracellular components in different cell migration phenomena. What is less explored, however, is how the arrangement of the underlying extracellular matrix that many cells move upon in vivo influences migration.
Combining novel transgenic lines and image analysis pipelines, reveals that during zebrafish optic cup formation cells use cryptopodia-like protrusions to migrate collectively and actively over a topologically changing matrix. These changing topologies correspond to different cellmatrix interactions. Interference with matrix topology results in loss of cryptopodia and inefficient migration. Thus, matrix topology influences the efficiency of directed collective cell migration during eye morphogenesis, a concept likely conserved in other developmental and disease contexts.
One-Sentence Summary: Dynamic cell-matrix interactions, crucial for successful collective rim cell migration, rely on extracellular matrix topologies during optic cup development in vivo.
Main Text: During organogenesis and in homeostasis, cells often actively move to the location where they later function (1,2). Further, many cancers are worsened when cell migration causes metastasis (3).
So far, most studies have focused on understanding cell migration during development, as findings are often translatable to disease states (4). Cell migration during development occurs via distinct modes broadly classified as single or collective cell migration (5). Singly migrating cells show the intrinsic ability to move in a certain direction as shown for primordial germ cell migration (1) or neuronal migration (6). Collectively migrating cells move as a cohesive group in which they maintain contact with each other to coordinate their movements while they are additionally steered by environmental factors (4,7). Examples of collective cell migration include follicle epithelial cells that shape the Drosophila egg chamber (8) or the migrating lateral line primordium in zebrafish (9).
All types of cell migration depend on both intrinsic and extrinsic factors for directionality and migration efficiency. The role of cell intrinsic factors like adherens junctions, cytoskeletal elements, and basal focal adhesions (FA) have been studied in depth and shown to be essential to facilitate cell migration in numerous contexts (10,11). Further, cell extrinsic factors like growth factors or guiding chemokines provide directionality for long-range single and collective cell migration (1,9).
In addition to cell intrinsic factors and extrinsic chemical signaling, it is now clear that physical parameters like tissue stiffness, substrate density, or topology (12,13) can also be instructive for cell migration. However, here, many details are still unknown. In particular, the role of the extracellular matrix (ECM), that is encountered by many migrating cells in vivo is still underexplored (14). To understand how the ECM could influence collective cell migration, in vitro studies in which the density, stiffness and arrangement patterns of the ECM mimicked the in vivo situation have revealed a spectrum of possibilities by which ECM properties can influence cell migration. This has included ECM stiffness (15,16) and topology, which involves the porosity, alignment and density of the matrix (17). So far, however, the extent to which ECM properties affect cell migration in vivo is not yet fully explored. One reason is that here the dynamic visualization of cell-matrix interactions has been challenging due to the lack of appropriate tools.
The developing optic cup in zebrafish is a model that allows for such visualization as it is situated at the outside of the developing embryo and is approachable to quantitative long-term imaging. During optic cup formation (OCF), collectively migrating rim cells move within a continuous epithelium to shape the hemispherical tissue (18,19). Rim cells require an intact ECM and cell-matrix interactions for successful migration (18) but the exact interplay between ECM and rim cells is unknown. We investigate this phenomenon by introducing tools to visualize the ECM in vivo, combined with new analysis pipelines to quantify cell-matrix interactions. We find that rim cells migrate collectively over a uniformly compressible ECM.
The topology of the matrix varies along the migration path and influences cell-matrix interactions and migration dynamics. These interactions rely on basal cryptopodia-like protrusions, basal protrusions that extend beneath the next cell along the direction of migration.
When the topology of the matrix is perturbed, these cryptopodia are lost and migrating rim cells become less directed. Thus, we directly link matrix topology to the guidance of collective cell migration in vivo generating an important reference to investigate similar phenomena in other developmental and disease contexts.

Laminin does not undergo diffusive turnover in the optic cup ECM
To reveal possible interactions between collectively migrating rim cells and the underlying matrix, we generated markers to visualize the ECM during OCF in vivo. As laminin knockdown impairs efficient rim migration (18), transgenic laminin lines were generated using a bacterial artificial chromosome (BAC) containing the laminin -1 gene along with its native gene regulatory elements (lama1 in zebrafish) and a large upstream region to preserve possible regulatory elements (for details see Materials and Methods). This ensured close-to-endogenous expression of laminin. Laminin was tagged with the fluorescent proteins sf-GFP, mKate2 and photoconvertible dendra (Fig. 1A and fig. S1B). Expression of these constructs matched laminin -1 antibody staining (Fig. 1B). Further, transplantation of Tg(lama1:lama1-sfGFP) cells into Tg(lama1:lama1-mKate2) showed that mKate2 and GFP expression colocalize ( fig.   S1C). Transplantations also revealed that the laminin deposited around the optic cup arises from more than one tissue as even when transplanted cells only appeared outside of the optic cup, they contributed to laminin in the optic cup ECM (fig. S1C and Table S6, N = 3/4 embryos).
Time lapse imaging of Tg(lama1:lama1-sfGFP) between 16hpf and 19hpf, the stages at which OCF occurs, revealed that the ECM surrounding the optic cup undergoes frequent deformations ( Fig. 1D and movie S1) indicating some matrix dynamicity. To understand whether these deformations are accompanied by matrix turnover, fluorescence recovery after photobleaching (FRAP) was performed. Over short time spans (5min imaged at 50ms intervals) the intensity of laminin did not recover ( Fig. 1, E to H, fig. S1D and movie S2). Over longer time periods in the range of hours however, a gradual recovery of laminin was observed, most likely due to the deposition of new protein into the matrix ( fig. S1, E to G and movie S3).
Thus, laminin does not freely diffuse in the optic cup ECM over short time scales and can be deposited by cells outside the optic cup.

Rim cells actively migrate over the underlying ECM using cryptopodia like protrusions
The low laminin turnover rate suggested that this structure served as a stable scaffold for rim cells to actively move over. Another possibility was that the whole matrix was moving towards the retinal neuroepithelium (RNE) thereby passively dragging rim cells with it, as seen previously in other contexts (20). To differentiate between these two possibilities, Tg(lama1:lama1-dendra) embryos ( Fig. 1I and fig. S1H) were photoconverted in the rim region ( Fig. 1, J to K) and focal adhesions (FAs) were labeled by Integrin beta1b-EGFP. This allowed the tracking of rim cells relative to matrix movements (movie S4) and showed that rim cells moved actively over the matrix (Fig. 1K). The same experiment was conducted at earlier stages of OCF (13hpf -14hpf), revealing that even before obvious RNE invagination onset, rim and proximal cells showed active movement over the matrix towards the prospective RNE ( Fig. 1L, fig. S1I and movie S4).
As it was shown that rim cell migration correlated with protrusive activity (18), we investigated the ultrastructure of the protrusions involved through transmission electron microscopy (TEM).
We found that protrusions did not resemble filopodia or lamellipodia as seen for other collectively migrating cells (11,21) but instead showed cryptopodia characteristics as they extended beneath the cell in front, along the direction of migration (22). Such cryptopodia have previously been shown to direct collective cell migration in vitro, in systems that lack a leading edge or leader cells (23) similar to the optic cup (7). Interestingly, the cryptopodia-like protrusions are less extended in cells already positioned close to the distal side of the tissue.
Further, cells in the RNE no longer extended cryptopodia in any particular direction ( Fig. 2A to C and fig. S2E).
Thus, active rim cell movement starts at very early stages of OCF, before the onset of tissue invagination and rim migration and is accompanied by cryptopodia formation with different morphologies depending on rim cell location.

Rim cells exhibit different focal adhesion dynamics in different regions of the migratory path
We speculated that the different morphologies of basal cryptopodia along the path of migration were linked to different cell interactions with the underlying ECM and tested this idea via live imaging. Mosaic labeling of the FA proteins paxillin (Paxillin-mKate2) or integrin (Integrin beta1b-EGFP, Integrin beta1b-mKate2) in combination with the transgenic laminin lines revealed that FA behavior changed from dynamic to more stable once rim cells reached the inner side of the neuroepithelium (movie S5). In particular, FA interactions with the underlying matrix changed along the migration path and could be divided into three categories ( To analyze FA dynamics in more quantitative detail, a segmentation and tracking tool was set up (24) that allowed the segmentation of only the FA signal that colocalized with the underlying laminin matrix (see Materials and Methods) (movie S6). This tool enabled the calculation of the time averaged mean square displacement (tamsd) and velocity autocorrelation, allowing for the analysis of directionality and persistence of FA movements. The positive curvature of the tamsd graphs showed that FAs of migrating cells close to the RPE and in the rim region underwent directed movements (Fig. 2, F to G and fig. S2, F to G). Interestingly, FAs of migrating cells close to the RNE displayed less directed movements and migrated in the least persistent manner (Fig. 2, H to I and fig. S2H). This is in line with the qualitative analysis that showed that these cells step back more often than migrating cells in the rim region and near the RPE ( fig. S2D).
Overall, qualitative and quantitative evaluation of FA dynamics over the matrix showed that rim cells transition from directed to less directed movement prior to stopping when entering the RNE ( fig. S2, B to C and fig. S2I).

Changing focal adhesion dynamics are accompanied by changes in laminin topology
In vitro studies showed that changes of ECM properties like stiffness, density and arrangement of fibrils can result in changing FA dynamics (17,25,26). Thus, we characterized and quantified matrix properties in the different migratory zones.
To assess matrix compressibility, Brillouin microscopy, a non-invasive method that measures High resolution confocal imaging of laminin -1 staining revealed that laminin arrangements differed between the rim and RNE regions. While laminin in the RNE region appeared as aligned fibrils, in the rim region laminin was more porous and the fibrils less aligned (Fig. 3A).
We thus asked whether overall matrix topology could influence rim migration as changes in substrate topology and density have the ability to influence FA dynamics in vitro (17,25,26).
To investigate the topology of the matrix, we established image analysis pipelines (for details refer to Materials and Methods) that quantified the arrangement, porosity and intensity of laminin in different optic cup regions. This analysis showed that the orientation of laminin fibrils was more coherent in the RNE region compared to the rim region ( lines concurred with the porosity measurements as laminin intensity was the highest in the RNE and lowest in the rim region at 18hpf (Fig. 3B and fig. S3F).
Overall, this showed that the topology of laminin is spatially distinct in different regions of the optic cup suggesting a possible link between matrix topology and the different FA dynamics observed.

Differences in topology result in changing physical properties of laminin
Changes in matrix arrangement can lead to changing mechanical properties of the matrix, which in turn influence cell-matrix interactions and cell migration as shown in vitro and in vivo (28, 26). While we did not see significant changes in overall compressibility between the rim-ECM and RNE-ECM, different laminin topologies could nevertheless result in local changes in mechanical properties. To explore this idea initially theoretically, we modeled the laminin matrix as a hexagonal spring lattice with a fixed boundary (29) (see Materials and Methods for a detailed description of the model). The topology of the matrix was then varied by changing the degrees of porosity in the lattice. Mapping the distribution of local tensions in the network revealed that with an increase in porosity, regions with higher tensions appeared (Fig. 4, A to   B). In addition, using a simple theoretical model of a string under tension, we found that it should be harder to deform the string in the orthogonal direction as the tension in the string increases ( Fig. 4, C to D). To test this idea experimentally, we made use of the fact that mitotic cells in the optic cup deform the underlying laminin when rounding apically (Fig 4,C).
Analyzing laminin deformations indued by these mitotic cells, we found that in accordance the model they induce smaller deformations in the porous rim regions compared to the RNE region where laminin is less porous (Fig. 4, E to F and movie S7).
Thus, our theoretical model and experiments indicate that network topology can influence the distribution of local stresses within the network resulting in changing mechanical properties of the lamina.

Focal adhesion dynamics and rim cell migration are less directed upon interference with laminin topology
Our theoretical model predicted that after a certain threshold of node removal and increasing porosity, large circular breaks should appear that distort the topology of the network nearby ( fig. S4A). To test this prediction experimentally, the laminin structure was disrupted using a verified laminin -1 morpholino (18, 30) to downregulate laminin. Morpholino treatment was preferred over a full mutant as it allowed the creation of varying phenotypes from mild disturbance to full ECM rupture, depending on morpholino concentration.
Embryos injected with 0.4ng/embryo of laminin -1 MO into the Tg(lama1:lama1-sfGFP) or Tg(lama1:lama1-mKate2) lines showed severe laminin downregulation resulting in large laminin pores and breaks in the structure that were usually more severe in the rim region than the RNE (Fig. 5A yellow asterisks). Interestingly, the shape of the breaks and the topology of the surrounding laminin, strongly resembled the distorted topology observed on drastically increasing porosity in the theoretical lattice ( fig. S5A).
Next, we aimed to test whether disrupting the laminin topology influenced cell behavior. We imaged the FA dynamics along with laminin in laminin morphants and noted that rim cells started blebbing basally as reported previously (18) instead of throwing podia in the direction of movement. These blebs hindered migration and often extended through the laminin breaks ( Fig. 5B). In most instances (7/9 cells) rim cells were stuck in the same position, unable to retract the blebs extending through the matrix (Fig. 5B, fig. S5D and movie S8). In regions where laminin structures were still more intact, cells did not get stuck but focal adhesions nevertheless exhibited less directed movements and cells migrated over shorter distances than We additionally perturbed laminin arrangements without interfering directly with the protein's expression by downregulating the matrix cross linker protein nidogen (29), known to be required for OCF (31, 32), using established morpholinos against nidogen 1a and nidogen 1b (see Materials and Methods). This condition phenocopied laminin knockdown and resulted in breaks with increased pore sizes in the laminin structure around the optic cup (Fig. 5A). We again observed rim cells blebbing through the laminin structure (Fig. 5, F to G and movie S9).
Further, this condition led to cells with less directed focal adhesion dynamics (2/7cells) (Fig 5, F to G yellow arrow and fig. S5G). Milder perturbations in which the laminin matrix did not present as large breaks but was less organized, showed rim cells that migrated without blebs but stepped backwards more often than in controls (3/7 cells) ( fig. S5G).
To understand how these conditions influenced the cells' protrusive activity at the structural level, we imaged embryos injected with 0.4ng/embryo of laminin -1 MO using TEM. We found that rim cells showed less or no cryptopodia-like protrusions (Fig. 5C). Instead, bleblike structures were observed (Fig. 5C red arrow and fig. S5C), suggesting that disrupting the topology of laminin directly affects rim cell protrusion dynamics.
Our experiments show that downregulating laminin results in the disruption of laminin topology, confirming the prediction of the model. Additionally, we found that disrupting laminin topology leads to less efficient rim cell migration presenting a direct link between matrix topology and rim cell migration efficiency.

Discussion
The use of new tools to label the ECM component laminin in vivo in combination with sophisticated image analysis pipelines enabled us to show that matrix topology guides collective cell migration in vivo during OCF. During zebrafish OCF, cell matrix interactions depend on basal cryptopodia and their dynamics change with differing matrix topology.
Changing this topology upon genetic interference results in less directed migration. This and our photoconversion experiments reveal that rim cells are not dragged passively into the neuroepithelium as suggested previously (19) but actively migrate towards it. This active rim migration is driven by cryptopodia, which are defined as basal protrusions that extend beneath the next cell along the direction of migration (22). These have so far mainly been reported in vitro (22,23) but recently they have also been suspected to be involved in some types of collective cell migration in vivo (33, 34). In 'closed' epithelial structures in vitro that lack a free edge or clearly defined leader and follower cells, the direction and angle of contact of cryptopodia with the underlying substrate predetermines the overall direction of migration (23).
A similar mechanism could operate in the optic cup which resembles a closed epithelium, in 13 which cryptopodia could act to break symmetry and define the direction of migration. The finding that FA movements over the matrix are seen as early as 13hpf before the onset of RNE invagination ( Fig. 1L and fig. S1I), strengthens this idea. Interestingly, at these timepoints laminin is already differentially enriched in the RNE region ( fig. S3G). However, the hierarchies between the timing of cryptopodia polarization, changes in matrix topology and rim migration onset need to be further explored, taking other cell behaviors that occur during OCF into account (35).
Rim cells migrate over changing laminin topologies, with laminin porosity being the highest in the center of the migration path which corresponds to the rim region (see schematic in Fig.   5H). This strongly suggests that rim migration is driven by topotaxis, a phenomenon not yet widely reported in vivo, where cells can migrate toward denser or sparser topological features (17). Since topotaxis is regulated by the intrinsic stiffness of the migrating cell, it will be important to understand how cell mechanics and matrix topology influence each other during OCF. We observed that cells on very large laminin breaks are unable to maintain their shape and display extremely 'floppy' behavior (fig. S5, E to F and movie S10), possibly indicating that they become 'softer'. This implies a link between cell stiffness and matrix topology as shown in vitro (17). Investigating the relation and interplay between matrix topology and physical properties of the cell will be exciting areas to study in the future, comparing in vitro and in vivo data.
It will further be interesting to probe how cell-matrix interactions themselves could reorganize the matrix. In vitro it has been shown that endothelial cells rearrange the matrix to mimic the overlying branched EC network (36) and in the Drosophila egg chamber migrating follicle cells influence the progressive alignment of matrix fibrils (8). We also observe that during OCF, laminin becomes progressively aligned in the RNE where tissue invagination occurs (fig. S3, I to J), indicating a role for cell-matrix interactions in matrix arrangement.
Importantly, in addition to the developmental context, the arrangement of matrix molecules is crucial to wound healing and is disrupted in diseased states like cancer (17) and fibrosis (37).
Thus, understanding the interplay between matrix topology, cell behavior and the factors that regulate ECM arrangement during development will facilitate the understanding of factors underlying diverse severe disease states. Such findings will also help create better in vitro environments for organoids, which are emerging as useful tools to understand human development and regeneration.          1). BAC clones were first transformed with pSC101-BAD-gbaA-tet-plasmid which expresses the lRed operon proteins upon induction with the L-arabinose enzyme. The plasmid also contains a temperature sensitive replicon pSC101 and tetracycline (tet) selection marker.
The lama1 gene was tagged on the c-terminal with fluorescent proteins super folded GFP (sf-GFP), mKate2 and the photoconvertible dye dendra (Table S2). These tags contained a kanamycin selection marker that was flanked by FRT sites. These FRT sites can be removed by site specific Flp/FRT recombination. R6K plasmids carrying the respective tags were used to amplify 50bp of 5' and 3' homology arms to the lama1 gene using specific oligos (Table S3). In order to tag the  Table   S4 for antibiotic concentrations). Cells were grown on plates with and without kanamycin to test for sensitivity towards the antibiotic. E.coli colonies that only grew on plates that lacked kanamycin were selected.

Zebrafish transgenesis
The BAC plasmid was injected at 0.1ng/embryo along with 0.3 -0.6ng/embryo of transposase2 enzyme mRNA into the cell of 1 cell staged WT embryo. F0 embryos were screened at 24 hpf for fluorescence signal using a fluorescence stereoscope and positive embryos were selected and grown. F0 adults were outcrossed to WT fish and the progeny was screened for positive fluorescence signal and by PCR on the whole genome (Table S5). The enzyme emerald was used in the PCR reaction to amplify the GFP sequence in the whole genome sample. F0 progeny that expressed GFP were selected and grown. Fluorescence recovery after photobleaching analysis The same ROIs as specified during photobleaching were used to track the recovery of fluorescence.
For the analysis, time points during the bleaching event were not considered for all the embryos in the rim and RNE regions. The fluorescence recovery intensity was normalized against the noise in the image and against acquisition bleaching (45). The ROI to correct for acquisition bleaching was specified in the ventricle where a stable laminin signal was observed. The position of the ROI was corrected in case of drift in the image. Normalized fluorescence recovery intensity was plotted for 3 minutes after bleaching (Fig. 1, G to H and fig. S1D).

Quantifying laminin turnover (hours)
An ROI of 19x21 pixels was specified in the center of the photobleached region in the rim and RNE region (see fig. S1E). Imaging was done over 34.3 m (step size 0.7 m) and the intensity of fluorescence recovery was measured over a volume of 3.5 -4.9 m within the rim and RNE region covering 2-3 slices above and below the bleached region over 1 -2 hours. The intensity was normalized to eliminate background noise and acquisition bleaching as mentioned above.
Tracking and quantifying focal adhesion (FA) dynamics A novel image analysis pipeline was used to segment the FA sites on curved surfaces (here: laminin structure) (24). We created a binary mask using the watershed algorithm to select the membrane with FAs to be segmented and to eliminate additional membranes before applying the pipeline.
Each movie was treated separately with parameters fine-tuned for optimal segmentation of the FA.
The centroid of the segmented FA was then tracked (46)  ) also known as coherency is defined within boxes of size 21x21 pixels from the -tensor as twice its larger eigenvalue 2 √ 2 + 2 , a quantity which is also known as scalar nematic order parameter. Averaging across all 21x21 boxes fully contained within the foreground, defined as the convex hull of the binarized image after smoothing with a Gaussian of kernel radius 5px, yields the mean local coherency (Fig. 3D and fig. S3J).

Laminin intensity measurements
The mean intensity of laminin was measured in different regions of the optic cup over several microns in depth in live Tg(lama1:lama1-sfGFP) and Tg(lama1:lama1-mKate2) embryos at 17.9hpf (115 minutes from 16hpf). The mean intensity was sampled 14 m from the dorsal most part of the optic cup to 49 -56 m in depth with an interval of 7 m. The mean intensity of laminin in the different regions were normalized to the RNE region at each depth and was always found to be <1. These normalized intensities were then plotted and statistically analyzed (Fig. 3B).
Laminin deformation measurements: The deformation observed in laminin on apical division in different regions of the optic cup was measured using the angle tool in Fiji. The quantification was done on maximum intensity projected time lapse images covering the entire region of laminin that was deformed by the dividing cell.
These movies were sometimes corrected for noise by subtracting the background signal using a rolling ball radius of 500 pixels and adding a gaussian filter of sigma 0.2 m radius to visualize the laminin better.

Montage of time lapse images
Montage of time lapse images tracking FA dynamics in WT and morpholino conditions was done from maximum intensity projections of cropped movies that were manually registered and drift corrected using a Fiji plugin (http://imagej.net/Manual_drift_correction_plugin) developed by Benoit Lombardot (Scientific Computing Facility, MPI-CBG). In addition, the images were corrected for noise by subtracting the background signal using a rolling ball radius of 500 pixels and adding a gaussian filter of sigma 0.2 m radius.

Statistical analysis
Statistical analysis was done on GraphPad Prism 9 software. Confidence intervals of 95% and above were used. Detailed description of the tests and p values can be found in the respective figure legends. The table of replicates can be found in Table 6. To test the significance of the Brillouin shift between the rim and RNE across replicates, we used a linear mixed effects model, with a random intercept and region slope across replicates. The model was fitted using the python package statsmodels version 0.12.2.
General description of the spring network model Generating hexagonal lattice with pores: We model the laminin network as a hexagonal lattice of springs. For this we first generate a perfect hexagonal lattice consisting of 5200 vertices. Next, in order to generate pores, we randomly delete n vertices and their edges. We ensure that none of the vertices that are on the boundary are deleted.
This leads to some vertices that have less than three neighbors ( fig. S6A). We wish to generate a network where every vertex has only three neighbors, similar to the laminin network (29). Hence, we go through each remaining vertex and delete any vertex that has one or fewer neighbors.
Vertices which have only two edges are deleted and the neighbors are connected if they are closer than twice the lattice edge length. Again, we do not delete any vertex that is on the boundary of the network. This algorithm gives us a lattice where every vertex that is not on the boundary has three neighbors ( fig. S6B). We define the porosity of our lattice as the ratio between the number of vertices deleted and the number of vertices before generating pores (5200). For a given n, we generate ten networks using different random seeds. This gives us networks of very similar porosity values.
Implementing stress on the network: Each spring in the network has a spring constant, k, and a preferred rest length, lo. We keep the value of lo to be the same as the edge length of a perfect hexagonal lattice without pores. Also, the spring constant for all springs is given a value of 1. Next, we place the vertices of the network such that the whole network is uniformly stretched in all directions by a factor of s and fix the boundary vertices at their new positions. The rest of the vertices are then moved in discrete timesteps until a force balance is achieved.
In order to move the vertices, we assume overdamped dynamics which implies that the vertices have no inertia. After a given discrete timestep ∆t, the new position vector of a vertex α, x α , is given by where ⟨αβ⟩ represents the force exerted by the spring connecting vertex α with its neighbor β. γ represents the friction coefficient and is kept as 1 arbitrarily. The force on the spring is computed as follows Where ̂⟨ αβ⟩ = ( α − β )/ ⟨αβ⟩ and ⟨αβ⟩ = | α − β |.
Calculating the normalized tension in the springs: In order to quantify the amount of stretch and compression in the networks after achieving equilibrium, we compute for each spring a normalized tension. This is the ratio between the signed scalar force in springs and the expected force in springs of a perfect hexagonal lattice with no pores. The normalized tension for a spring connecting vertices α and β is given by This quantity is a scalar dimensionless quantity computed for each spring. We observe that on achieving force balance, the pores in the network take up circular shapes ( fig.   S7). Moreover, for networks with very high porosity, we see small pores elongating along the larger pores that look similar to the pores observed in the laminin structures in embryos treated with 0.05ng/embryo of laminin -1 MO (fig. S5A).
We also observe that with increase in porosity up to an extent, we see more stretched springs appearing. This can be observed as a new peak in the distribution plots of the normalized tensions ( fig. S8). We also observe a very slight but consistent increase in the mean normalized tensions with increase in porosity. However, on increasing the porosity value beyond 0.2, we start seeing a slight decrease in the mean normalized tension and the distribution starts to flatten out ( fig. S9A).
More stretched springs take up more space in the network than less stretched springs. In order to quantify the space of the network that 'appears' stretched to the cell, we quantified the length weighted normalized tension. Here again, we see a slight but consistent increase in the mean value with increase in porosity, except for networks with very high porosity ( fig. S9B). It should be noted that these simulations with high porosity (>0.2) qualitatively look much more porous than the images of the laminin network in the optic cup in wild type conditions.    Laminin modeled as a hexagonal lattice with a three-point vertex. Color bar indicates values of normalized tension (tension in porous lattices /tension in a non-porous lattice). Porosity is defined as the ratio of (number of nodes removed/total number of nodes in the network).      Table S1. Primers to sequence the lama1 BAC Table S2. Fluorescent protein tags used to label the lama1gene Table S3.
Oligos used for tagging cassettes Table S4.
List of antibiotics used at the respective concentrations