Repulsive cues combined with physical barriers and cell–cell adhesion determine progenitor cell positioning during organogenesis

The precise positioning of organ progenitor cells constitutes an essential, yet poorly understood step during organogenesis. Using primordial germ cells that participate in gonad formation, we present the developmental mechanisms maintaining a motile progenitor cell population at the site where the organ develops. Employing high-resolution live-cell microscopy, we find that repulsive cues coupled with physical barriers confine the cells to the correct bilateral positions. This analysis revealed that cell polarity changes on interaction with the physical barrier and that the establishment of compact clusters involves increased cell–cell interaction time. Using particle-based simulations, we demonstrate the role of reflecting barriers, from which cells turn away on contact, and the importance of proper cell–cell adhesion level for maintaining the tight cell clusters and their correct positioning at the target region. The combination of these developmental and cellular mechanisms prevents organ fusion, controls organ positioning and is thus critical for its proper function.

One-color in situ hybridization on wild-type (a-b), clo m39 (a-d) and flh tk241 (e-f) embryos. PGCs are stained with nos3 (a-f, arrows on the left-panel images) and endothelial cells with kdrl probe (a-d, arrowheads in a-b). Despite the lack of endothelial cells, PGCs arrive at the target (c, arrow) and form two separate clusters at 28hpf (d; dotted lines in inset) in clo mutant embryos (number of embryos examined: N=12), similar to wild-type embryos (a-b; N=60). In embryos lacking notochord (flh tk241 ), PGCs form two bilateral clusters at the gonad region at 24hpf (e-f; dotted lines in inset; N=15). Scale bars 50µm. Lateral (left panels) and dorsal (right panels) views are shown. Figure 11. PGC migration at early developmental stages does not require endoderm.

Supplementary
(a, c) Whole-mount in situ hybridization of nos3 as a PGC marker (asterisks) and sox17 as an endodermal marker (blue rim around the yolk in a), both stained in blue. Animal views are shown. (b, d) Hematoxylin and Eosin Counterstained histological sections of embryos following WISH using nos3 (asterisks) and sox17 (blue cells in b) probes. (a-b) Wild-type PGCs migrate in the vicinity of the yolk in close contact with endodermal cells. Number of embryos examined in a: N=20 and b: N=3. (c-d) In sox32 mutant embryos lacking the endoderm PGCs migrate close to the yolk. c: N=20; d: N=10 (e) 3D Confocal Z-stacks of wild-type embryos in the lateral view. Embryos of transgenic fish with EGFP-labeled PGCs are injected with secfp RNA together with an activated taram-A transcript (taram-A*) into one blastomere at 32/ 64-cell stage for endodermal cell labeling, followed by YSL nuclei labeling with h2b-mcherry RNA upon injection into the yolk. PGCs (in green) are positioned among scattered endodermal cells (shown in red) and in the same layer with them, directly above the YSL nuclei (shown in blue) (N=4). Images were processed using Imaris. Scale bars 25µm. Embryos at 70-80% epiboly in all experiments. Figure 12. PGCs are normally specified in embryos lacking the gut tube One color (a and c) or two color (b and d) WISH on wild-type and sox32 ta56 embryos at 24hpf (a and c respectively) or 28hpf (b and d respectively). The gut is stained using foxa1 probe (a-d). In wild-type and sox32 mutant embryos the PGCs (insets) express both the early marker nos3 and the late marker piwil1. Arrowheads indicate the position of the gut (a-b), and no foxa1 expression is detected in the mutants (c-d). Number of embryos examined in a: N=40, b: N=20, c: N=9 and d: N=5. (e-f) PGCs are labeled with vasa-gfp mRNA, showing the characteristic granule formation in PGCs (insets in e and f respectively). e: N=14 and f: N=15. Scale bar 50µm. Dorsal views are shown. Anterior is up. Figure 13. Patterning of the mesodermal tissues adjacent to the gonad is normal in gut-deficient embryos (a-b) Bilateral arrangement of pronephric ducts and the pronephros in embryos deficient for the gut is maintained (pronephric ducts labeled using (Tg(cldnB:egfp)) and pronephros with wt1b probe, green arrows). Anterior is up. (c) Bilateral cxcl12a expression is detected in the somites and lateral plate mesoderm of both control and gut-deficient embryos at 15 and 18hpf. At 24hpf cxcl12a expression at the gonad area is altered in embryos lacking the gut (additional red arrowhead in the cross-section). Green stars indicate cxcl12a expression in the lateral line. The expression of cxcl12a at the gonad region in embryos lacking the gut tube is no longer detected at 28hpf. Scale bars in all panels 50µm.

Supplementary Figure 14. Moderate levels of cell-cell adhesion result in cluster size distribution similar to in vivo values.
The fraction of cells in clusters composed of 3 or more cells as a function of the number of cells within the chamber (gonad region) is presented, for different strengths of cell-cell adhesion and boundary properties (reflective: rb (blue shades) and non-reflective: nrb (green shades)). The experimentally-measured values are presented in red (in vivo). The experimental measurements roughly match the simulation results when employing =0.2 regardless of the boundary conditions. Error bars for the in vivo values are the standard error of the mean, with very rare cases of cell number <11 and >26 having no error bars due to the fact that only one case per cell number was observed. Experimental data derived from 32 embryos (number of PGCs: n=1058).  tyr-sgRNA2-exon1

Amount injected per embryo (pg)
Reference Reference

Calculation of the position distribution for non-interacting particles
Using the simulations in the two-dimensional chamber, under conditions of no adhesion (✏ = 0), we have obtained substantial differences in the distribution of the particles for the two boundary conditions (reflective and non-reflective) (Supplementary Fig. 15). Since the two-dimensional model is not amenable to analytic description, to gain a deeper quantitative understanding we investigated the behavior of a one-dimensional representation (projection) of the full two-dimensional system. This is described below in this supplementary note.

Mapping the 2D system to a 1D approximate model
We attempt to approximate the distribution of the particles along the width of the 2D channel, using a 1D analytical model, for the case of non-interacting particles (✏ = 0). We show that the variance of the obtained approximate distributions for both reflective and non-reflective boundaries is comparable to those of the 2D simulations ( Supplementary Fig. 15).
The two dimensional simulation of the particles, is as follows: Each particle moves due to a constant magnitude motility force, whose direction diffuses with time. The equation of motion of each particle is the overdamped Langevin equation: where v 0 is the self propulsion velocity magnitude,r = (x, y) is the particle's position,n ✓ = (cos ✓, sin ✓) is a unit vector in the direction of the motility force of the particle, and ⌘ is white noise obeying the relations h⌘(t)i = 0, h⌘(t)⌘(t 0 )i = 2D r (t t 0 ). The long axis of the channel geometry used in the simulation is periodic and denoted as the y direction, while in the x direction the region is bounded by hard walls. Since the system is symmetric to translation in the y direction, the particle density is independent of y. We are interested in finding the steady state density of particles along the width of the channel (x). Projecting equation (1a) onto the x axis yields: Next, we perform an approximation, and replace | cos ✓| by its average over all angles h| cos ✓|i = 2 ⇡ (similar to 13 ), to write an approximate one dimensional Langevin equation where v 1 = 2v 0 /⇡ and m(t) stochastically changes value from 1 to -1 and vice versa according to the direction of the particle's motion along the x-axis.

Supplementary Note
The statistics of the flipping times of m(t) (in which m(t) changes sign) are given by the firstpassage problem for the angle ✓ in the interval [0, L], where L = ⇡, with absorbing boundaries. The solution for this problem is found in 14 . The survival probability is dominated by the slowest decaying eigenmode: S(t) / e t ⌧ 1 , with ⌧ 1 = L 2 Dr⇡ 2 = 1/D r . Thus the probability that absorption at one of the boundaries had already occurred at time t (m(t) changed sign) is 1 S(t). Hence the flipping times of m(t) are approximately exponentially distributed with a mean flipping time 1/D r .

Non-reflective boundaries
In this case, particles that hit the boundary remain at the boundary until their motility force rotates away. This causes a discontinuity in the particle density at the boundaries, where particles accumulate. We calculate the density profile of the particles using the one dimensional approximate model. The rate equations which describe the process of particle motion and direction changes of Eq. 3, are the following 15,16 : For d < x < d, where R(x, t), L(x, t) are the local densities of the right/left moving particles respectively. At the boundaries (at x = ±d), we have the following equations for the number of accumulated particles: where N d R is the number of particles at x = d with self-propulstion velocity pointing right, and the notations N d L , N d L , N d R are defined similarly. We also define J R (x) = v 1 R(x) as the current of right moving particles, and J L (x) = v 1 L(x) as the current of left moving particles. The number of particles at the boundaries which move towards the boundary: N d L , N d R increases due to the incoming flux from the bulk, and decreases due to motor flipping of the particles. Since particles whose direction of motion is away from the boundary do not accumulate at the boundary, N d L = N d R = 0. The only extra equation needed to solve for the steady-state particle densities is the conservation of total particle number: and ⇢(x) = R(x) + L(x) is the total particle density in the bulk).
The steady-state solution is: We compare this approximate solution to the simulated particle density distribution from the 2D model in Fig. I. The variance of the distribution for the 2D simulation is 4.18, while for the 1D approximate model we get a variance of 3.98. When comparing to the variance difference between the two boundary conditions, shown in Supplementary Fig. 15, we conclude that the 5% difference between the 2D and 1D models is indeed very small, demonstrating that the 1D approximation provides a reasonable quantitative description.

Reflective boundaries
Here we treat the system with reflecting boundaries using our 1D approximate model. When particles hit the boundary in the 2D simulation, they reorient and leave the boundary in the perpendicular direction. Thus, while particles have an average velocity of v 1 = 2v 0 /⇡ along the x-axis, they have a faster x-velocity of v 0 after being reflected. Such fast (reflected) particles slow down to the normal average x-velocity due to reorientation of their direction of motion: the initial ✓ at the boundary is perpendicular, and it needs to change by ⇡/4 to either side for the particle recover the average x-velocity. This gives an interval of size ⇡/2 in which again we consider a first-passage problem with absorbing boundaries, such that now: ⌧ 1 = 1 4Dr . In this system we expect the density of particles to be close to uniform, and depleted near the boundary over a lengthscale ⇠ v 0 D r . Similar to the case of non-reflective boundaries, we write the 1D equations (as in Eqs. 4), where we add new types of particles that move fast, with velocity v 0 , while the velocity of the "regular" particles is v 1 . A left moving particle (fast or regular) becomes a fast right moving particle upon hitting the left boundary, and similarly for right moving particles hitting the right boundary. Fast particles become regular ones which move in the same direction at rate aD r = 1/⌧ 1 , due to the reasoning above.
The equations are therefore: where R(x, t), L(x, t) are the local densities of the regular right/left moving particles respectively, and R f (x, t), L f (x, t) are the local densities of the faster right/left moving particles that emerge from the reflecting boundaries, respectively. We seek a steady state solution for the particle densities. Equating all RHSs of the equations in (7) to zero, a system of four linear first order differential equations is obtained. Its general solution contains four constants to be determined by the boundary conditions. On the left boundary (x = d), left moving particles become fast right moving particles. Thus the flux of left moving particles is equal to the flux of fast right moving particles at d. A second boundary condition on the left boundary is that right moving particles do not cross the boundary, thus their flux there is zero. These two conditions along with the mirror-symmetrical ones for the right boundary x = d give us the following four boundary conditions: Due to the symmetry of the problem, one of the above conditions is redundant, as it is automatically satisfied when the other three are imposed. Thus we have a remaining constant in the solution, which is determined by the normalization condition: where we define the total particle density ⇢(x) ⌘ L(x) The solution of Eq. (7) with boundary conditions (8) and total particle number conservation normalization condition (9) is: where The density is maximal in the center, and decreases to minima at the edges due to the depletion caused by the reflective boundaries (Fig. II). This reproduces the effect that appears in the simulated 2D system, where a depletion zone with decreased density appears near the edges. We next calculate the variance of the density distribution from the 1D approximate model and compare it to the 2D simulation result. The variance obtained from the 2D simulation is 1.94, while in the 1D model the variance is 1.87. For comparison we note that the variance of a uniform distribution in the same interval is 2.08. We therefore see that the main effect of the reflective boundary on the variance of the density distribution is due to the removal of the particle accumulation at the boundary.

Supplementary Method 1
Two color in situ protocol, See Reference 30 for more details.

Principle of double staining:
A mix of different Dig-labeled and Fluo-labeled probes is used for hybridization.
The antibody-and subsequent staining steps are performed separately for both types of probes. After completion of the first staining reaction the first antibody is removed with acidic solution, followed by the second antibody incubation. The reason for doing so is that both antibodies are coupled to the same enzyme (alkaline phosphatase). This enzyme can be used with different dye combinations, here X-phosphate/NBT and X-phosphate/ INT.

Problems/ considerations:
1 The second staining step is generally less sensitive and, for some probes (like vasa) less reliable than the first one.
2 Fluo-probes tend to be more problematic than Dig-probes. (Fluo-probes often give a weaker signal and more background) 3 Doing the blue staining as a first step has the advantage that the embryos can be cleared in EtOH before the second step. This can strongly reduce dark background in the yolk.
As both antibodies are coupled to the same enzyme cross reactions during the staining take place. Therefore you have to do the blue staining first to avoid unspecific blue staining on top of the red staining.
All principle combinations of probe, dye and first or second step are possible. The best combination should be chosen according to the above mentioned considerations.
For second step staining the probe concentration should be relatively high. For Fluo probes the concentration should be adjusted carefully.
For blue staining as a first step the probe concentration should be low in order to get minimum background.

Examples for probe concentrations: see below
In the following protocol, the first step is blue staining for DIG probes.

Fixation and storage of embryos:
• embryos younger than 24 hrs: fix overnight (not longer than 24 h) at 4°C in 4% PFA in PBS, then rinse 3 times with PBTand then dechorionate by hand/ pronase before transferring to MetOH. • embryos 24hrs and older: remove chorion before fixation by hand/ pronase. Fix overnight at 4°C in 4% PFA in PBS and then rinse 3 times with PBT before transferring to MetOH.
• for very early stages the Proteinase K treatment can be left away

Prehybridization:
Incubate embryos in 300 ml of Hyb buffer, 2 to 5 hrs at hybridization temperature (here: 67°C) in a water bath. The water bath should be warmed before. For shorter probes (300-500bp) one can go to 55-60°C in the water bath.

Hybridization:
Prepare the hybridization mixes (=probes in Hyb buffer) The concentration of the probes depends on the kind and quality of probes and on the stage of the embryos. Heat the hybridization mix to 67°C (water bath) for ca. 10 min.
Remove prehybridization mix and replace with 200 µl of the preheated hybridization mix.
In situ Day 2:

1.Washes:
Leave the tubes with embryos in the water bath. They can usually be left open (Close the lid of the water bath!). Always preheat the washing solutions to hybridization temperature.
Pipetting: with 10 ml pipette like before (Make sure that the pH of SSC 2x and 0.2x is 7.0).
• You can recover the probes: they can be used again (Sometimes they get better) For slowly staining samples: Staining at 4°C overnight is also possible. Next day: go on staining at room temperature.

4.
Stop the reaction by removing the staining solution and washing the embryos 3x in PBT.
To avoid yolk from becoming brown: wash and store in STOP solution. Just before you want to look at the embryos, put them into 80% glycerol + 20% STOP solution.
For one-color staining, after this step you can do the Clearing (go to Day 4, step2) and then store the embryos at 4°C.
In situ Day 4:

(optional) Clearing:
If the yolk turned brownish during the staining procedure with NBT/ X-phosphate, clearing with EtOH gives very good results. After a few days of storage this brown precipitate would turn into a black, stable precipitate that cannot be dissolved away. Therefore, this EtOH treatment has to be done soon after the completion of the staining reaction. This step cannot be performed after the red staining reaction. (The red stain dissolves in ETOH very fast).
-adjust the pH to 7,4 (usually by adding a few drops of 15% HCl) The final pH of Hyb buffer should be 6,0 -6,5 (usually no pH adjustment is required). Store at -20°C.

Method 1
-harvest hundreds of embryos, at different stages.
-fix overnight in 4% PFA in PBS.
-wash embryos 2x in PBT and dechorionate by hand.
-incubate antibody at a dilution of 1:400 on the embryos in BSA, 2mg/ml in PBT. Shake at room temp. for at least 1h. (The embryos can also be smashed prior to incubation. Spin down after incubation and carefully transfer the supernatant to a separate tube before diluting to the final concentration) -Sterile filter using a 0,2 -0,45 µm Cellulose Acetate filter. Best is dilute the antibody to 1: 2000 prior to filtering.
--Keep the antibody at this concentration at 4°C. For storage, add Sodium Azide to 0,02%.

Method 2
Process 50 embryos along with the others (same age) through all the first steps of in situ hybridization except that no probe is used for hybridization of these embryos. during blocking of the others: -block the embryos for preabsorption only 10 min.
-incubate antibody at a dilution of 1:400 on the embryos in BSA, 2mg/ml in PBT at RT for a few hours.

Preadsoption of Abs
Prepare the anti X-AP antibody.
• Make 1:200 dilution of the Ab in blocking solution and pre adsorb it against fixed >MeOH-zebrafish embryos at different stages (primarily 24hrs) over night at 4 degrees on a wheel. (the embryos have to be treated the way those in a real in situ are treated i.e, Prot.K, further fix and blocking.
• Fixed embryos should comprise approximately 10 % of the total volume. This protocol includes a step-by-step procedure for use in the laboratory.

Overview
The RNAscope Multiplex Fluorescent Assay for whole-mount zebrafish embryos can be completed within 2 days, allowing the detection of up to 4 different mRNAs simultaneously in different colors in combination with protein fluorescence.
Before the assay * Unless otherwise mentioned, 0.01% of Tween concentration is used throughout the protocol (in PBT and 0.2X SSCT buffers).

Fixation
Ø Dechorionate embryos manually in PBT (0.1x Tween) in a Petri dish. After dechorionation transfer the embryos to 1.5ml Eppendorf tubes using a glass Pasteur pipette. For embryos younger than 24 hpf, first fix and then dechorionate. 24-hpf embryos and older were fixed without the chorion.
Ø Fix embryos at RT in 1ml freshly prepared or freshly thawed 4% PFA in PBS with the tube positioned on its side.
Fixation time: 4-cells to 8 hpf: 4 hours 12 to 20 hpf: 1 hour 24 hpf to 4 dpf: 30 minutes The optimal fixation times for different stages and specific probes can be further optimized if needed.
Ø Remove the fixation solution and wash 3x5 minutes in 1ml PBT (0.1x Tween) at RT.
Ø Transfer embryos to 100% MeOH for 5 min, replace it with fresh MeOH and store at -20°C for overnight or longer.