A self-generated Toddler gradient guides mesodermal cell migration

The sculpting of germ layers during gastrulation relies on the coordinated migration of progenitor cells, yet the cues controlling these long-range directed movements remain largely unknown. While directional migration often relies on a chemokine gradient generated from a localized source, we find that zebrafish ventrolateral mesoderm is guided by a self-generated gradient of the initially uniformly expressed and secreted protein Toddler/ELABELA/Apela. We show that the Apelin receptor, which is specifically expressed in mesodermal cells, has a dual role during gastrulation, acting as a scavenger receptor to generate a Toddler gradient, and as a chemokine receptor to sense this guidance cue. Thus, we uncover a single receptor–based self-generated gradient as the enigmatic guidance cue that can robustly steer the directional migration of mesoderm through the complex and continuously changing environment of the gastrulating embryo.


Supplementary movie legends
Movie S1 | Internalized wild-type cells polarize and extend actin-rich lamellipodia towards the animal pole. Light sheet time-lapse imaging (time interval: 1 min) of LifeAct-GFP-labelled wild-type cells transplanted to the margin of a wild-type host embryo. Establishment of a polymerized actin network and lamellipodia is marked by accumulation of LifeAct-GFP at the front of the cell. The movie starts after cells have successfully internalized, confirming that cells were of either mesodermal or endodermal cell fate, and shows efficient animal-pole directed migration of these cells. Each frame is a maximum intensity projection of a z-stack. Animal pole is to the top. Scale bar, 10 µm. Right: Aplnr-deficient cells (grey) are placed next to a Toddler-overexpressing source (red). Mesodermal and source cells are labelled with LifeAct-GFP and Dextran-AlexaFluore568, respectively. Each frame is a maximum projection of a z-stack. Source is located towards the top. Scale bar, 20 µm.

Computational modeling
Here, we provide additional details for the modelling of self-generated Toddler gradients during zebrafish gastrulation.

Position of the problem
We write the conservation equation for the concentration of mesoderm cells ( , ) and secreted Toddler ( , ) as a function of time and position along the animal-vegetal axis (where = 0 is the position of the margin, and where we restrict ourselves to a one-dimensional description thanks to the radial symmetry of the problem): In this description, mesodermal cell concentration can change from i) free diffusion and ii) directional motion at speed , while Toddler concentration can change from i) free diffusion, ii) production (from ectoderm cells), iii) intrinsic degradation and iv) mesoderm consumption. We have denoted " and $ as the diffusion coefficient of mesoderm cells (in the absence of directed motion) and Toddler molecules, respectively, % ( ) as the target concentration of Toddler (which can be spatially modulated) in the absence of any mesoderm consuming it, $ as the timescale of intrinsic Toddler degradation and as the consumption rate of Toddler from mesoderm cells (larger density of mesoderm cells signifying more receptor density for Toddler degradation -note that this implicitly assumes that receptor density per cell is constant, an assumption that we relax below). For this equation we must additionally specify a dependency between directed cell migration velocity and Toddler concentration. How cells sense gradients is an area of active study, and different non-linear as well as adaptative responses have been uncovered in particular while interpreting GPCR signalling gradients (see for instance review by Jin (56)). Here, we explored two simple limits of gradient sensing: = # (i.e. cells move up an absolute gradient of Toddler) or = & ! $ $ (i.e. cells move up a relative gradient in Toddler) -with denoting in each case the strength of the coupling. We also note that this equation makes the important approximation (which we will come back to below in fig. S3C) that Toddler gradients only impacts the average "advective" velocity of cells and not their random motility coefficient " . This is a coarse-grained description which can be made because the cell velocity in response to a Toddler gradient does not necessarily require a Toddler-dependent change of the instantaneous cell speed, but can arise from a partial bias in their random walk that is caused by a more persistent directionality in cell polarity triggered by the local Toddler gradient. Similarly, in our Finally, we specify boundary and initial conditions for this problem at the margin: the Toddler protein and mesodermal cells cannot escape at the margin, leading to no-flux boundary conditions # ( = 0) = 0 and # ( = 0) = 0. While the initial conditions for Toddler are largely irrelevant and given its continuous production simplest defined as ( , 0) = % , they are key for mesoderm specification. We therefore first assume that the mesodermal cell number is fixed and initially concentrated very close to the margin: ( , 0) = % ( , 0).

Key length and timescales in the problem
From these equations, two natural scales emerge: a time scale $ , which represents the timescale of Toddler turnover, and a length scale = = $ $ , which represents the distance at which Toddler produced by a localized source is degraded. This is, for instance, important during our rescue experiments, during which we place Toddler-expressing cells at the animal pole (Fig. 4A, forth from the right): Toddler is predicted to decay exponentially from the source cell location, at a length scale of .  . S4F-G). This showed a roughly exponential decay, as predicted by our linear model, and from which we could extract $ ≈ 120 min ( fig. S4F-G). We also compared this exponential to a linear fit 1 − / $ , and used Akaike Information Next, we examined the movements of toddler -/cells transplanted into a toddler -/background. As these cells show no measurable directed motion ( = 0), we reasoned we could use these experiments to constrain the value of free cell diffusion " . We found that these cells diffused on a length scale of approximately 25 from the margin during the 30 min of the timescale ( fig. S4K-L), leading us to a rough estimate of " ≈ 20 ' . () .

Parameter constraints, fitting and non-dimensionalization
Once we rescale all time scales by $ , all length scales by : that this neglects advective terms in the Toddler equation (for instance cell/fluid movements transporting Toddler). This is a safe assumption given the order of magnitude difference between the two. Estimating a Peclet number yields / $ ≈ 0.04, so that free diffusion is largely dominant. We can further rescale Toddler by its maximal concentration % , and mesoderm by its initial total amount % leading to

Thus, in addition to the length and time scales (which have been independently measured), this
shows that the problem now only depends on 3 rescaled parameters: the relative diffusion coefficients of mesoderm and Toddler . These two last parameters are harder to independently measure and should therefore be considered as fitting parameters in the theory.
Importantly, however, analysis of the system of equations above finds that these last two parameters can largely be coarse-grained into a single one, with their product being the most relevant parameter: this is because controls how strong of a gradient of Toddler is created, and how strongly this gradient is interpreted, so that high -low and low -high give rise to similar velocities. Numerical simulations keeping the product constant, but changing each by several orders of magnitude confirmed this (see fig. S4C where we multiply by 5 and divide by 5, giving nearly identical results to fig. S4A), although this effect would break down at very high (when mesoderm consumption of Toddler would be so strong that the Toddler concentration reaches values close to zero).
Another approximation of the model that we wished to verify was that the random motility of cells (represented by the diffusion coefficient " ) was unaffected by the local Toddler gradient. To verify this, we quantitatively analyzed the experiments in which cells with or without Aplnr were transplanted at a distance from Toddler-secreting or Toddler-deficient cells ( Fig. 2A-C). We quantified the average displacement of cells over 15 min, either in the direction of the source (y-axis) or perpendicular to it (xaxis), and generated probability distributions for each case. As expected from a purely random and diffusive process in the x-direction, all three conditions displayed Gaussian distributions in step size centered around zero average displacement ( fig. S3C). Importantly, the standard deviation (proportional to " ) was nearly identical in all three cases, arguing that random motility is unaffected by either the presence of a Toddler gradient or Apelin receptor expression. Interestingly, when looking at the same distribution in the y-direction (towards the source), we found again that the standard deviation of the displacement was comparable between conditions (and also to its value in the xdirection, as expected from a random walk, fig. S3C). The only difference for the Toddler-Apelin receptor pair was that the best-fit Gaussian distribution was not centered around 0, but instead around a non-zero average velocity value of 0.3 / -as expected for a biased random walk and our model in which Toddler gradients only act on the advective velocity v (fig. S3C, see legends for detailed statistics and fitting).
Finally, although the model as defined above assumes that all cells internalize at the same time (initial Delta function at x=0 in the initial condition ( , 0) = % ( , 0)), the experimental situation is more gradual, with numbers of internalizing cells showing a broad temporal peak with typical variance of an hour (13). This can easily be taken into account by assuming that the initial condition is now  (13). Although these are the parameters that we show in Fig. 3, we also ran simulations with the previous initial condition (synchronous internalization of all mesendoderm cells) and found very similar results for both wild type and toddler -/simulations (see fig. S4A-E).
Thus, in the following, we only fit in the theory (simulations from main text are made for % = 1).
is essentially proportional to the speed of migrating cells up a self-generated gradient. As we found an average speed of ≈ 0.08 / , this means ≈ 10 . in our unit simulations.
With the model fully parametrized in this manner, we turned to its predictions on a number of nontrivial features, such as the spatiotemporal density/velocity profiles of mesoderm migration in wild type and toddler -/mutant, or transplantation assays (Fig. 3, S5D, S7A,B).

Model predictions
We first consider the case of toddler -/-, in which directed cell migration is negligible ( = 0). Because the margin constitutes a hard boundary, internalized cells are expected to still migrate upwards to some degree according to a diffusive process with coefficient " . Given our estimate of " from shortterm trajectories, we thus asked how much cells were predicted to travel by pure diffusion (1D along the animal-vegetal axis) in the Δ =3.5 hours between internalization and the 75% epiboly stage. These simulations predicted around 200 µm, compared to 600 µm for wild type ( fig. S4H). To confirm these predictions experimentally, we measured the intensity profiles of mesoderm markers (aplnrb) by in situ hybridization assays in toddler -/compared to the wild-type embryos along the animal-vegetal axis as a proxy for the mesoderm concentration ( fig. S4I-J). We found that the mesoderm concentration profile in toddler -/embryos decayed around twice as fast as in wild-type embryos. It is important to note that uncertainty in the exact diffusion coefficient of mesoderm cells, or the possibility of small, residual, non-zero directionality in the migration of toddler -/cells could explain the slightly stronger phenotype in the model.
In the presence of self-generated gradients, the system organizes into a travelling-wave solution, as expected from the literature (23), where cells adopt a non-zero net polarity/velocity towards the animal pole, as observed experimentally ( Fig. 2B-C,E). Although this self-organized collective migration is robust to the details of the parameters, such as the effective diffusion length scale L for Toddler, such parameters do have an effect on the detailed spatiotemporal profiles of mesoderm migration. For very local Toddler diffusion (small ), only a few cells at the very edge sense the selfgenerated gradient, which causes them to initially migrate very fast (see fig. S4D for a simulation with $ = 10 , so that the length scale is around 20 µm, i.e. the cell size). However, this creates a concentration gradient of mesoderm cells, which in turn causes a concentration gradient of Toddler, which does not stem from diffusion, but rather the differential degradation of Toddler caused by the spatial differences in mesoderm density. Thus, cells can still migrate in a self-generated manner, although the cellular density gradient is more pronounced than the "front-like" solutions shown in Fig.   3 (limit of large effective Toddler diffusion relevant here as the length scale is of the order of the embryo size as described above).
Comparing these predictions to our tracking data of mesoderm cells (marked by drl:GFP) undergoing migration towards the animal pole after internalization, we found similar qualitative features, with cells at the edge displaying the largest velocity, which decreased both as a function of time and distance from the edge. More quantitatively, we compared kymographs for the cellular velocity as a function of position, which equals the distance from margin and time (Fig. 3H). It is important to note that in the kymographs we show the total effective cell velocity as measured by cell tracking, which represents the sum of the advective velocity and the diffusive flux, which can have directional contribution in the presence of a density gradient. The total flux of cells reads as !/! = # − " # , in which the first term is the advective contribution proportional to the local Toddler gradient, and the second is the diffusive flux. We thus define !/! = !/! / = # − " # / as the total average velocity of mesodermal cells at position x, which is plotted in Fig. 3H.
Importantly, while we predict that the contribution of diffusion is rather small compared to advection (see fig. S4E for a simulation with zero mesendoderm free diffusion, " = 0) in wild type, the latter becomes dominant in toddler -/-, in which advection is close to zero.

Effect of number of transplanted cells on the resulting dynamics
As discussed in the main text, the mechanism of self-generated gradients that we propose relies ## % (i.e. no directed migration term). As we show in fig. S5D, simulating transplants of small numbers of wild-type cells in aplnr MO embryos (large % density, low density) resulted in little migration, while transplants of small numbers of wild-type cells in wild-type density was effectively the same as regular wild-type migration (as transplanted cells are identical to the surroundings). On the other hand, simulating large clusters of wild-type cells in aplnr MO embryos (large % density, intermediate density) resulted in an intermediary phenotype ( fig. S5D), as seen in the data (Fig. 4).

Overexpression of Toddler and Apelin receptor
We next consider the effect of overexpression of Toddler, which has shown to give rise to defects in upward migration (10). This is modelled by a change in the baseline production of Toddler % : where previously we had non-dimensionalized the problem to % = 1. When considering different % , the assumption of absolute vs. relative gradient sensing (resp. = # or = & ! $ $ ) does impact the resulting prediction: for absolute gradient sensing, the gradient (and thus migration) increases with % , whereas it is almost insensitive to % for relative gradient sensing. However, it should be noted that the equation above implicitly assumes that mesoderm cells (via their Apelin receptors) can take up arbitrary amounts of Toddler ligand. Although this may be correct for the wild-type condition, this situation might not generally hold true for overexpression phenotypes, especially as Apelin receptors are internalized with Toddler, which might result in not enough Apelin receptor left on membranes to sense and uptake Toddler. To take this latter feature of GPCR signalling into account, we between cells, although they are "transported" spatially together with the movements of mesoderm cells (advective term putting in the co-moving frame of cells). This first-order equation assumes that there is a baseline equilibrium of Apelin receptor at the membrane (time scale of recycling 0 , equilibrium concentration % ), but that each event of Toddler internalization also removes an Apelin receptor. This is the same sink term as in the Toddler equation, now rewritten to depend also on :