Lage Clara

Pustelnik Nelly

Arbona Jean-Michel

Audit Benjamin

Space-Scale Hybrid Continuous-Discrete Sliding Frank-Wolfe Method

In this work, we focus on the challenging problem of designing an off-the-grid method for dictionaries involving both positional and scale shifts. To tackle this challenge, we introduce a novel algorithm inspired by the Sliding Frank-Wolfe approach. In our proposed algorithm, positions are treated as continuous variables, whereas scales are discretized. Such a strategy eliminates numerical instabilities inherent to the direct application of Sliding Frank-Wolfe. We successfully apply this algorithm to the study of DNA replication data.

Introduction

Formally, sparse coding methods consist in approximating a signal z P L 2 pX q, in a vector space X , by a finite linear combination of atoms selected from the dictionary D " tφp¨; θq P L 2 pX q : θ P Θu, where φ is a continuous mapping. The objective is to estimate the underlying unknown parameters θ1 , ..., θK P Θ, and amplitudes ᾱ1 , ..., ᾱK P R modeling the signal z as:

z " F ˜K ÿ k"1 ᾱk φp¨; θk q ¸,
where F denotes a stochastic degradation. This problem can be solved by different optimization techniques of sparse approximation [START_REF] Natarajan | Sparse Approximate Solutions to Linear Systems[END_REF][START_REF] Tibshirani | Regression Shrinkage and Selection via the Lasso[END_REF][START_REF] Mallat | Matching pursuits with time-frequency dictionaries[END_REF].

Traditionally, sparse coding methods rely on the discretization of the parameter set Θ, corresponding to a set of r K atoms tφ k " φp¨; θ k qu Ă K k"1 , from which a small subset of K ą 0 atoms must by chosen. In this context, LASSO (Least Absolute Shrinkage and Selection Operator, [START_REF] Tibshirani | Regression Shrinkage and Selection via the Lasso[END_REF]) is a well accepted method that uses the ℓ 1 norm as a measure of sparsity. Numerically, the signal is a vector z P R N as well as the atoms φ k P R N and the LASSO is written as:

p a P Argmin a }z ´Ă K ÿ k"1 a k φ k } 2 2 `λ}a} 1 , (1)
where λ ą 0, impacts the number of non-zero components of a " pâ k q 1ďkď Ă K P R K . In this work, we focus on atoms φ for which the parametrization Θ is associated to dilatation and translation of a reference atom, forming a space ˆscale dictionary. We investigate how this type of dictionary interacts with sparse coding methods. As the translation of an atom can be expressed using a convolution kernel it gives rise to a variety of numerical methods. Particularly when Θ is discrete, these methods are called convolutional sparse coding and have been applied in audio processing and other fields [START_REF] Dragoni | Spike sorting for massive neurophysiological datasets : sliding window working set strategy for the estimation of convolutional models in high dimension[END_REF][START_REF] Zhu | Convolutional Sparse Coding for Trajectory Reconstruction[END_REF][START_REF] Schmidt | Shift Invariant Sparse Coding of Image and Music Data[END_REF][START_REF] Kwong R. Grosse | Shift-Invariant Sparse Coding for Audio Classification[END_REF]. The popularity of these methods comes from (i) the possibility of providing a compact representation of a large dictionary, and (ii) the efficient computation of convolutions via FFTs.

Another objective of sparse coding methods is to increase the accuracy in the estimation of parameters. For this purpose, continuous sparse coding methods have shown significant advantages compared to traditional discretized formulations [START_REF] Blanc-Féraud | Off-The-Grid Variational Sparse Spike Recovery: Methods and Algorithms[END_REF][START_REF] Clément | OMP and Continuous Dictionaries: Is k-step Recovery Possible?[END_REF]. This is the case of BLASSO (Beurling LASSO [START_REF] Vincent | Exact Support Recovery for Sparse Spikes Deconvolution[END_REF]), in which Θ equals X . In BLASSO, the solution belongs to the space of measures MpΘq and is numerically approximated by a weighted sum of Dirac measures:

m " K ÿ k"1 α k δ θ k , (2)
involving the weights α k P R and θ k P Θ elements of the parameter space where the measure is not zero. The optimization problem is given by: minimize

mPMpΘq }z ´Φpmq} 2 2 `λ|m|pΘq, (3)
where |m|pΘq is the total variation of the measure m, [20, Section 6.1], λ ą 0, and the operator Φ is defined as:

Φ : MpΘq ÝÑ L 2 pΘq m Þ ÝÑ ż Θ φp¨; θqdmpθq " K ÿ k"1 α k φp¨; θ k q.
The last equality holds when m is written as in [START_REF] Azaïs | Spike detection from inaccurate samplings[END_REF]. With some hypothesis on the regularity of the kernel φ, theoretical recovery guarantees have been established for BLASSO [START_REF] Vincent | Exact Support Recovery for Sparse Spikes Deconvolution[END_REF][START_REF] Duval | Support Recovery for Sparse Deconvolution of Positive Measures[END_REF][START_REF] Candès | Super-Resolution from Noisy Data[END_REF]. In the specific case of convolution kernels, numerically solving BLASSO can be performed efficiently using different methods [START_REF] Azaïs | Spike detection from inaccurate samplings[END_REF][START_REF] Chizat | Sparse Optimization on Measures with Over-parameterized Gradient Descent[END_REF][START_REF] Peyré Q. Denoyelle | The sliding Frank-Wolfe algorithm and its application to super-resolution microscopy[END_REF]. For example, the Sliding Frank-Wolfe method [START_REF] Blanc-Féraud | Off-The-Grid Variational Sparse Spike Recovery: Methods and Algorithms[END_REF][START_REF] Peyré Q. Denoyelle | The sliding Frank-Wolfe algorithm and its application to super-resolution microscopy[END_REF], based on the Frank-Wolfe method [START_REF] Levitin | Constrained minimization methods[END_REF], transforms the non-constrained optimization problem (3) in a compact constrained problem where it is possible to apply the Frank-Wolfe algorithm. Sliding Frank-Wolfe method benefits from flexibility with respect to the space X , and theoretical guarantees [START_REF] Peyré Q. Denoyelle | The sliding Frank-Wolfe algorithm and its application to super-resolution microscopy[END_REF]. Contributions: We investigate BLASSO in the case of a space-scale transformation. In this context, we propose a new optimization method that combines continuous and discrete optimization allowing to reach spatial accuracy and good performance on scale recovery, without being sensitive to numerical instabilities. We also show that theoretical recovery guarantees of Sliding Frank-Wolfe algorithm are not affected in the hybrid model. The proposed algorithm is applied in the context of single molecule DNA replication studies [START_REF] Theulot | Genome-wide mapping of individual replication fork velocities using nanopore sequencing[END_REF]. Numerical tests show the adequacy and relevance of the hybrid method in estimating position (space) and speed (scale) with high precision.

Outline: In Section 2, we study the consequences of a space-scale dictionary in the original Sliding Frank-Wolfe algorithm. In Section 3, we present our hybrid algorithm, continuous in space and discrete in scale, highlighting the main theoretical differences between the proposed algorithm and original Sliding Frank-Wolfe. Finally, Section 4 presents a case study in the context of DNA replication with numerical experiments to support the relevance of the method.

2 Sliding Frank-Wolfe algorithm for space-scale parametrization Space-scale setting -For a set S Ă R, we focus on a parameter space Θ " X ˆS. The dictionary set D is

D " ! φp¨; px, sqq " csψ ´¨´x s ¯, px, sq P Θ ) ( 4
)
where the continuous function ψ : R Ñ R is a reference atom and c s , the normalizing constant, is such that }φp¨, px, sqq} 2 " 1, for every θ " px, sq P Θ. When handling the discrete signal z, the variable p¨q is replaced by a discretization space tu i u N i"1 of the signal z. We consider the operator Φ : MpΘq Ñ L 2 pX q such that Φ : m "

K ÿ k"1 α k δ px k ,s k q Þ ÝÑ K ÿ k"1 α k φp¨; px k , s k qq.
In this context, the Sliding Frank-Wolfe algorithm (Section SIV), proposed on [15, Algorithm 2], provides a sequence with an accumulation point that minimizes problem (3). This accumulation point is approximated by tα k , s k , x k u 1ďkďK that defines the sum of Dirac measures m

˚" ř N k"1 α k δ px k ,s k q .
For the iteration ℓ, let tα rℓs , θ rℓs u define the set of amplitudes and spikes (space ˆscale), and K rℓs " |θ rℓs | be the number of spikes. The algorithm loops on three steps until it reaches the stopping criterion: [Step 1] Estimate an additional spike θ by maximizing

η SFW pθq " ˇˇˇˇˇ1 2λ xzp¨q ´Φ ¨Krℓs ÿ k"1 α rℓs k δ θ rℓs k ', φp¨, θqy ˇˇˇˇˇ, (5)
and add θ to the spike set, composed now by K rℓs `1 spikes.

[

Step 2] Adjust the amplitudes with the new set of spikes and obtain

! α rℓ`1 2 s , θ rℓ`1 2 s
)

, where ˇˇθ rℓ`1 2 s ˇˇ"

K rℓs `1.

[Step 3] Solve the non-convex optimization problem (3) when restricted to a sum Dirac measures with K rℓs `1 components. The initialization is made with the previous estimates. This step results on the refined parameters ␣ α rℓ`1s , θ rℓ`1s ( , where K rℓ`1s " ˇˇθ rℓ`1s ˇˇ. Scale dictionary specificities -The optimization problem involved in Step 1 relies on the gradient of η SFW with respect to θ " px, sq, which may lead to numerical instabilities in the computation of ∇ x η SFW . These instabilities are due to oscillations in the gradient ∇ x ψpx " r

x, sq, for a fixed r x, when using a relatively large grid step ν " u i`1 ´ui . A specific analysis is provided in the supplementary material. On the other hand, for s fixed, ∇ x η SFW px, s " sq is well-behaved, motivating the hybrid scheme proposed in Section 3.

Hybrid continuous-discrete method

To solve the numerical instabilities that arise when the scale s is considered as a continuous parameter, we propose to reformulate problem (3) treating the scale parameter set as discrete. We consider r Θ " X ˆr S, where r S " ts 1 , ..., s M u denotes the discretization of S and for every i P t1, . . . , M u, we consider m i P MpX q. The new formulation is given by: minimize m"pm1,...,m M q

M ÿ i"1 Φ i pm i q ´z 2 2 `λ M ÿ i"1 |m i |pX q. ( 6
)
where m i " ř k α i,k δ x i,k , for x i,k P X and the operator Φ i : MpX q Ñ L 2 pX q is defined as:

m i " Ki ÿ k"1 α i,k δ x i,k Þ Ñ Ki ÿ k"1 α i,k c si ψ ˆ¨´x i,k s i ˙. (7)
This lead us to the hybrid discrete-continuous Algorithm 1.

The objective is to estimate the components tα i,k , x i,k u, for i P t1, ..., M u of m i , forming the solution m ˚" pm 1 , ..., m M q. The index i incorporates the scale information. This algorithm loops on three steps: [Step 1] choose both the scale s i and a first approximation of the translation component x i,k by maximizing η HSFW [Step 2] adjust the amplitudes α i,k based on the previously estimated x i,k , for all i and k, and [Step 3] solve the non-convex optimization problem (3) with the operators Φ i , i P t1, ..., M u defined by [START_REF] Chizat | Sparse Optimization on Measures with Over-parameterized Gradient Descent[END_REF] to refine the parameters tα i,k , x i,k u starting from the previous estimates.

When atoms are not overlapping, steps ( 2)-( 3) can focus only on the scale i chosen by Step 1. The algorithm employed on Steps 1 and 3 is L-BFGS-B. In Step 1, the problem is solved separately for each discrete scale variable. Step 2 is solved by FISTA [START_REF] Zhu | Algorithm 778: L-BFGS-B: Fortran Subroutines for Large-Scale Bound-Constrained Optimization[END_REF][START_REF] Beck | A fast Iterative Shrinkage-Thresholding Algorithm with application to wavelet-based image deblurring[END_REF]. The stopping criterion of Algorithm 1 is specified line 3 of the algorithm.

The following theorem formalizes the fact that Algorithm 1 is the Frank-Wolfe algorithm applied to the hybrid formulation [START_REF] Candès | Super-Resolution from Noisy Data[END_REF]. With this result, Algorithm 1 benefits from the same convergence results than Frank-Wolfe method.

Theorem 1. The Hybrid Sliding Frank-Wolfe (Algorithm 1) is the Frank-Wolfe Algorithm [START_REF] Levitin | Constrained minimization methods[END_REF][START_REF] Peyré Q. Denoyelle | The sliding Frank-Wolfe algorithm and its application to super-resolution microscopy[END_REF] applied to problem (6) when ϕ i are defined by [START_REF] Chizat | Sparse Optimization on Measures with Over-parameterized Gradient Descent[END_REF]. In addition, if ψ P KER p2q , as defined in [START_REF] Peyré Q. Denoyelle | The sliding Frank-Wolfe algorithm and its application to super-resolution microscopy[END_REF]Definition 4], any accumulation point (for the weak ˚-topology) of the sequence pm ˚,rℓs q ℓPN obtained from the Algorithm 1 is in the set of minimizers of problem [START_REF] Candès | Super-Resolution from Noisy Data[END_REF].

The proof is provided in Annex (Section 5).

Application to single molecule DNA replication data

Data description -One of the current goals in DNA replication studies is to characterize the location and the speed of the molecular motors responsible for DNA synthesis along the chromosomes. This can be achieved using DNA sequencing data [START_REF] Theulot | Genome-wide mapping of individual replication fork velocities using nanopore sequencing[END_REF] that captures the passage of the molecular motors by measuring the variation of the concentration of a chemical (BrdU, a modified nucleotide that incorporates in replacement of thymidines) as a function of the 1D coordinate along the chromosomes (Figure 1A). The molecular motors incorporate BrdU following its time-dependent intracellular level ψptq. ψptq has been determined experimentally and follows an asymetrical wave pattern [1, Section Methods] defined in the supplementary material. The passage of the motors of constant speed s and passing position x at time 0 results in a 1D spatial pattern ψ `¨´x s ˘in the measured BrdU profile (Figure 1A). Hence, the faster the local replication speed, the longer the observed BrdU spatial wave (Figure 1B).

We note that ψ is not differentiable at the start of the wave and at the point of maximal BrdU concentration. This difficulty was overcome using directional derivatives that proved to be numerically well behaved when executing the Algorithm 1. In our discrete case, the normalization constant is approximated by c s "

1 ? s}ψ}2 .
Experimentally, the BrdU concentration is determined with a spatial sampling period of 100 bp (base Algorithm 1 Hybrid Sliding Frank-Wolfe (HSFW) Initialization: Let λ ą 0, p@iq K r0s i " 0 and x r0s i " H. 1: For ℓ " 0, 1, . . .

2:

Step 1: Estimate an additional spike:

$ ' ' ' ' ' & ' ' ' ' ' % x rℓ`1 2 s ī " x rℓs ī Y txu, x rℓ`1 2 s i " x rℓs i for all i ‰ ī, K rℓ`1 2 s ī " K rℓs ī `1, K rℓ`1 2 s i " K rℓs i
for all i ‰ ī.

3:

If η HSFW px, sīqď1 STOP.

4:

Step 2: Estimate the amplitudes using the elements of the spike-sets:

α rℓ`1 2 s " arg min α › › › › › › › › z´M ÿ i"1 K rℓ`1 2 s i ÿ k"1 α i,k cs i ψ ¨¨´x rℓ`1 2 s i,k si '› › › › › › › › 2 `γ}α}1 5:
Step 3: Determine a solution m ˚,rℓ`1s of the non-convex problem (6) restricted to Dirac measures

m i with K rℓ`1 2 s i spikes. The initialization is set to mi " ř K rℓ`1 2 s i k"1 α rℓ`1{2s i,k δ x rℓ`1{2s i,k
where K rℓ`1 2 s i denotes the number of spikes for scale s i .

6:

Step 4: Update for all i : K rℓ`1s i " |m ˚,rℓ`1s i |, x rℓ`1s " x ˚,rℓ`1s and α rℓ`1s " α ˚,rℓ`1s pairs). This distance establishes the grid tu i u N i"1 for the signal z (Section 2). In principle, the maximal spatial precision for x is 1 bp. Our goal is thus, considering the proposed off-the-grid method, to overcome the 100 bp sampling limit. Experimental setting -We evaluate the performance of the proposed Hybrid Sliding Frank-Wolfe algorithm (Algorithm 1) with M -scales and compare them to a dictionary discretized both in time (position) and scale, thus with r K " M ˆN in (1). In our experiments we consider Matching Pursuit (MP) rather than LASSO as reference fully discrete method as it appears to be more efficient in this applicative context of very sparse representation. The experiments are run for P " 200 noisy signals and 200 noiseless signals z ppq P R N . For each atom, position and speed are chosen according to a uniform distribution on [0,300] (kbp) and r´3, ´0.5s Y r0.5, 3s (kbp/min) respectively. The stochastic degradation is assumed to follow a Poisson distribution with intensity parameter β " 700 to mimic the non-Gaussian experimental noise [START_REF] Theulot | Genome-wide mapping of individual replication fork velocities using nanopore sequencing[END_REF]. A fidelity term adapted to Poisson noise was tested in this context [START_REF]Codage espace-échelle parcimonieux en présence de bruit non-gaussien. Application à l'analyse de la réplication de l'ADN en molécule unique[END_REF] and was not advantageous compared to the Euclidian norm, which explains our choice of distance. In experimental data, most signals have 1 or 2 atoms. Based on that, in our simulated data, signals have a maximum of 2 atoms.

For both approaches (hybrid and fully discrete), we compare the precision of position and velocity estimation by computing the mean absolute error compared to the ground truth. The choice of the parameter λ " 0.001 in Algorithm 1 is made in order to detect all the replication patterns. Results -Figure 2 illustrates the performance of both hybrid (proposed HSFW) and discrete strategy (MP) when M " 40 for signal with one replication pattern. Both methods have a good behavior. A more accurate estimation of the position and amplitude of the atom is obtained with the HSFW as illustrated by the zoom. The MP solution is the constrained by grid step of 100 bp = 0.1 kb, while the hybrid solution is able to place the position between two grid elements.

In Figure 3, we compare the mean absolute error for discrete and hybrid methods with noisy and noiseless samples. As expected, increasing speed detection accuracy (increasing M ) decreases position error. Note that the proposed HSFW systematically reduces the error from 20% up to 40% compared to MP for configurations with or without noise. We observe that for M " 40, MP achieves the optimal performance that can be obtained for a discrete method (black solid line) while the hybrid method overcomes this limit.

In Fig. 4 we display the scattered plot of the reconstruction error (i.e. }z ´p y ' } 2 2 ) w.r.t the absolute position error for samples without noise and M " 40. The colors gradient represents the speed error. With HSFW (red), we observe that samples with low reconstruction error are those that have low position and speed error, allowing to easily select small absolute position/speed errors from the reconstruction error. With MP (blue), error in position are compensate by errors in speed resulting in a low reconstruction error but relatively high errors in the parameter estimations. The noisy samples exhibits a similar but less accurate behavior (results not shown). řĂ K k"1 p a k p φ k (in blue) and p yHSFW " ř K k"1 p α k φp¨; p θ k q (in red). When zooming we can observe that the hybrid method is able to improve the resolution of position detection.

5 Annex : proof of Theorem 1.

The convergence proof is divided in four parts: (i) rewrite problem [START_REF] Candès | Super-Resolution from Noisy Data[END_REF] with the aim of achieving a convex objective function with a different feasible set; (ii) prove the compactness of the feasible set; (iii) prove that the linear optimization (Step 1 of Frank-Wolfe method [START_REF] Peyré Q. Denoyelle | The sliding Frank-Wolfe algorithm and its application to super-resolution microscopy[END_REF]) can be written as Step 1 of Algorithm 1; (iv) conclude that the sequence generated by Algorithm 1 has a convergent sub-sequence.

Following [START_REF] Peyré Q. Denoyelle | The sliding Frank-Wolfe algorithm and its application to super-resolution microscopy[END_REF]Lemma 4], (6) can be reformulated as the convex optimization problem with an epigraphic constraint: min pm,tqP r C r T λ pm, tq :"

ÿ i Φ i pm i q ´z 2 2 `λt (8)
where r C " # pm1, ..., mM , tq :

ÿ i |mi|pX q ď t ď ζ and ζ " }z} 2 λ + .
The upper bound ζ of r C is obtained applying m i " 0 to [START_REF] Candès | Super-Resolution from Noisy Data[END_REF]. One of the key points for applying Frank-Wolfe to problem ( 8) is to note that r C is a compact set in the weak ˚-topology. As mentioned for the Sliding Frank-Wolfe convergence [15, Remark 2], the ball in MpX q with the total variation metric is compact. We observe that r C is a closed set contained in the product of balls: Π iPt1,..,M u tm i : |m i |pX q ď ζu ˆtt : 0 ď t ď ζu which is compact by the Tychonoff's theorem, [21, Section 9.6, Theorem 1]), hence r C is compact. The Frank-Wolfe algorithm consists in successive linear optimization problems in a convex and compact set. In our case, at iteration ℓ, the minimization is reformulated as follows:

max pm,tqP r C ÿ i ż X η i pxqdm i `λt (9)
where η i pxq " 1 2λ xz ´Φi pm rℓs i q, φ si p¨, xqy. Following [START_REF] Peyré Q. Denoyelle | The sliding Frank-Wolfe algorithm and its application to super-resolution microscopy[END_REF]Remark 4], we shall compute the extremal points of the set C with the purpose of simplifying this minimization step. In our case, the extremal set of C can be easily computed as:

Ep Cq " tpm 1 , ..., m M , ζq, m i " 0, for i ‰ i 0 and m i0 " ζδ x , for some x P X and i 0 P t1, ..., M uu.

Therefore, by [START_REF] Dragoni | Spike sorting for massive neurophysiological datasets : sliding window working set strategy for the estimation of convolutional models in high dimension[END_REF], the sum of integrals becomes the value of η i pxq, for some x P X , and for some i P t1, ..., M u leading to: arg max txPX, iPt1,2,..,M uu |η i pxq|.

In addition, we observe that in Sliding Frank-Wolfe [15, Algorithm 2], the search step (see [15, Algorithm 1]) is replaced by any procedure able to decrease the value of the objective function. Therefore, we conclude that Algorithm 1 is the Frank-Wolfe algorithm applied to problem (6) and we can benefit from all convergence results of the later.

Following the steps of [15, Proposition 5], with the assumption that ψ P KER p2q , we conclude that the sequence m ˚,rℓs is a bounded minimizing sequence. In addition, we observe that the objective function in (6) is l.s.c and convex to obtain that any accumulation point of m rℓs is a solution to (6).

Conlusion

We propose a study of the Sliding Frank-Wolfe method for space ˆscale dictionaries. Numerical instabilities arise from the interaction of discretized signals with continuous optimization, specifically in the scale dependency of the dictionary. To address this limitation, we propose a hybrid algorithm dealing with space as a continuous variable and scale as a discrete variable. Compared to the MP algorithm, where the whole parameter space is discretized, our hybrid approach proves its efficiency and promising solution for DNA replication analysis.

This work was supported by the Agence Nationale de la Recherche (ANR-18-CE45-0002 and ANR-19-CE12-0028). We thank R. Gribonval for insightful discussions. value r " 0 is found in humans cells, while yeast presents higher values of r. The value of t 0 represents the duration of the BrdU pulse. Parameters τ 1 and τ 2 are related to the rate of import/export of BrdU by the cell. c controls the maximum level of BrdU. Since here r " 0 the function ψ decreases to zero for large values of t.

Gradient instability:

In Section II, we discuss the numerical instabilities on the first step of Sliding Frank-Wolfe (Algorithm 2), when considering scale dictionaries. This observation is illustrated when ψ has the form [START_REF] Levitin | Constrained minimization methods[END_REF]. In Figure 5, we observe the derivative ∇ x ηpx " r

x, sq and ∇ x ηpx, s " r sq for different values of the sampling period ν. They present oscillating behavior if s is not fixed. This problem is not specific to the function ψ in equation [START_REF] Levitin | Constrained minimization methods[END_REF], and can also appear with other space-scale dictionaries described by (4).

10 Sliding Frank-Wolfe algorithm:

Algorithm 2 Sliding Frank-Wolfe 1: Initialization: Let λ ą 0, K r0s " 0, θ r0s " H 2: For ℓ " 0, 1, . . .

3:

Step 1: Estimate an additional spike: θ " arg max and define θ rℓ`1 2 s " θ rℓs Y t θu and K rℓ`1 2 s " K rℓs `1

4:

If ηpθqď1 STOP.

5:

Step 2 Estimate the amplitudes by solving α rℓ`1 2 s " arg min

α › › › › › › › z ´Φ ¨Krℓ`1 2 s ÿ k"1 α k δ θ rℓ`1 2 s k ‹ ' › › › › › › › 2 2 `λ}α}1
where θ Ð θ rl`1 2 s .

6:

Step 3: Estimate a solution m ˚of (3) restricted to Dirac measures with K rℓ`1 2 s spikes. The initialization is set to m "

K rℓ`1 2 s ř k"1 α rℓ`1 2 s k δ θ rℓ`1 2 s k .
Update: K rℓ`1s " |θ rl`1s |, θ rl`1s " θ ˚and α " α ˚.

η

  HSFW px,s i q and define

Figure 1 :

 1 Figure 1: (A) Example of BrdU concentration signal along the chromossome with two divergent replication patterns. (B) 3 atoms of the dictionary. (C) Spikes of position and amplitude associated to the forks of signal (A).

Figure 2 :

 2 Figure 2: Example of a single replication fork fit, represented as in Figure 1 A,C. (First row) Reconstructed signals p yMP "řĂ K k"1 p a k p φ k (in blue) and p yHSFW " ř K k"1 p α k φp¨; p θ k q (in red). When zooming we can observe that the hybrid method is able to improve the resolution of position detection.

Figure 3 :

 3 Figure 3: Mean absolute position error for MP/HSFW for noiseless/noisy regimes (β " 700). Black line: optimal mean position error for discrete methods with a grid step of 100 bp.

Figure 4 :

 4 Figure 4: Scatter plot of the reconstruction error vs. position error for discrete (left) and continuous (right) methods when estimated without noise for M " 40. The color intensity of dots is given according to the absolute speed error.

Supplementary material 7 Convolution kernel

In this work, we consider the sparse coding optimization problem for a parameter set Θ " X ˆS, where X represents a translation component: φp¨; θq " φp¨; px, sqq " ψ s p¨´xq.

(

When Θ is a discrete set, Θ " tx 1 , ..., x N u ˆts 1 , ..., s M u, it is possible to write the problem in the convolutive form:

where φ si P R N , and the sparse vectors b i P R N encodes the discretized location and coefficients related to i-th atom.

Figure 5: λ∇xη for DNA replication atoms for the first iteration of Sliding Frank-Wolfe Algorithm S1. We consider z " φp¨, θq, with θ " px, sq " p100 kbp, 1 kbp/minq, and grids tu i u N i"1 with different step sizes ν " u i`1 ´ui . (A,B,C) λ∇xηpx " x, ¨q as a function of s. (D,E,F) λ∇xηp¨, s " sq as a function of x.

Dictionary form:

The dictionary defined in (4) relies on a reference atom ψ. In the DNA replication application this function was determined experimentally [START_REF] Tibshirani | Regression Shrinkage and Selection via the Lasso[END_REF] as:

where the parameters τ 1 , τ 2 , a and c are assumed constant, with τ 1 " 0.8 min, τ 2 " 1.4 min, c " 0.4, t 0 " 2 min and r " 0. The parameter r represents the residual level of intracellular BrdU in the cell. The


Barbara Dupret

Pamela Völkel

Constance Vennin

Robert-Alain Toillon

Xuefen Le Bourhis

Pierre-Olivier Angrand
email: pierre-olivier.angrand@univ-lille1.fr

The histone

Keywords: Zebrafish -TALEN -Polycomb repression -Ezh2 -GSK126 base pair, dpf: days post fertilization, dpa: days post amputation, ezh2 paired-like homeobox 2bb, PRC: Polycomb Repressive Complex, rnf2: ring finger protein 2, TALEN

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INTRODUCTION

Polycomb-group (PcG) proteins are epigenetic repressors of transcriptional programs involved in the maintenance of cellular identity during development and differentiation [START_REF] Croce | Transcriptional regulation by Polycomb group proteins[END_REF][START_REF] Schuettengruber | Recruitment of polycomb group complexes and their role in the dynamic regulation of cell fate choice[END_REF][START_REF] Surface | Polycomb group proteins set the stage for early lineage commitment[END_REF]. PcG proteins assemble into at least two well-characterized and biochemically distinct chromatinmodifying protein complexes that are termed Polycomb Repressive Complex 1 and 2 (PRC1 and PRC2). In the canonical pathway, PRC2 composed of the core proteins EZH2, EED and SUZ12 together with RBAP46/48 and other accessory subunits, initiates gene silencing by catalyzing di-and trimethylation of lysine 27 of histone H3 (H3K27me2/3) [START_REF] Cao | Role of histone H3 lysine 27 methylation in Polycomb-group silencing[END_REF][START_REF] Czermin | Drosophila enhancer of Zeste/ESC complexes have a histone H3 methyltransferase activity that marks chromosomal Polycomb sites[END_REF][START_REF] Kuzmichev | Histone methyltransferase activity associated with a human multiprotein complex containing the Enhancer of Zeste protein[END_REF][START_REF] Margueron | The Polycomb complex PRC2 and its mark in life[END_REF][START_REF] Müller | Histone methyltransferase activity of a Drosophila Polycomb group repressor complex[END_REF]. PRC1 is then recruited to the target regions by binding to H3K27me3 marks through the CBX component of PRC1 [START_REF] Boyer | Polycomb complexes repress developmental regulators in murine embryonic stem cells[END_REF], and subsequently catalyzes the monoubiquitinylation of H2AK119 (H2AK119ub1) to maintain gene silencing [START_REF] Francis | Chromatin compaction by a polycomb group protein complex[END_REF][START_REF] Müller | Biochemical mechanisms of gene regulation by polycomb group protein complexes[END_REF][START_REF] Wang | Role of histone H2A ubiquitination in Polycomb silencing[END_REF].

Within the PCR2, EZH2 is a SET domain-containing protein harboring the histone methyltranferase activity, whereas EED and SUZ12 are involved in PRC2 stability and are necessary for EZH2 catalytic activity [START_REF] Cao | SUZ12 is required for both the histone methyltransferase activity and the silencing function of the EED-EZH2 complex[END_REF][START_REF] Pasini | Suz12 is essential for mouse development and for EZH2 histone methyltransferase activity[END_REF][START_REF] Tie | The N terminus of Drosophila ESC binds directly to histone H3 and is required for E(Z)-dependent trimethylation of H3 lysine 27[END_REF]. Genome-wide studies in mouse and human embryonic stem cells revealed that PRC2 and H3K27me3 marks are deposited at the promoters of numerous genes involved in cell differentiation, lineage specification and development, leading to the idea that EZH2 may be involved in the maintenance of the pluripotency of stem cells by keeping developmental genes repressed [START_REF] Boyer | Polycomb complexes repress developmental regulators in murine embryonic stem cells[END_REF][START_REF] Azuara | Chromatin signatures of pluripotent cell lines[END_REF][START_REF] Bernstein | A bivalent chromatin structure marks key developmental genes in embryonic stem cells[END_REF][START_REF] Bracken | Genome-wide mapping of Polycomb target genes unravels their roles in cell fate transitions[END_REF][START_REF] Lee | Control of developmental regulators by Polycomb in human embryonic stem cells[END_REF][START_REF] Mikkelsen | Genome-wide maps of chromatin state in pluripotent and lineage-committed cells[END_REF][START_REF] Pan | Wholegenome analysis of histone H3 lysine 4 and lysine 27 methylation in human embryonic stem cells[END_REF][START_REF] Zhao | Whole-genome mapping of histone H3 Lys4 and 27 trimethylations reveals distinct genomic compartments in human embryonic stem cells[END_REF].

Differentiation would then be associated with a relocation of PRC2, in turn responsible for the repression of the stem cell genes and enabling activation of gene expression programs specific to given developmental lineages. Indeed, the PRC2 components are essential for early mouse development and knock-out mutants for Ezh2, Eed and Suz12 initiate but fail to complete gastrulation and die at around embryonic days 7 to 9 [START_REF] Pasini | Suz12 is essential for mouse development and for EZH2 histone methyltransferase activity[END_REF][START_REF] Faust | The eed mutation disrupts anterior mesoderm production in mice[END_REF][START_REF] O'carroll | The polycomb-group gene Ezh2 is required for early mouse development[END_REF]. This death correlates with the alteration of lineage-specifying gene expression, a decrease in cell proliferation and an increase of apoptosis [START_REF] Pasini | Suz12 is essential for mouse development and for EZH2 histone methyltransferase activity[END_REF].

In human, recent cancer genome sequencing and expression studies reported that several genes encoding PRC2 subunits are mutated or have their expression altered in different cancer types [START_REF] Völkel | Diverse involvement of EZH2 in cancer epigenetics[END_REF][START_REF] Wassef | The multiple facets of PRC2 alterations in cancers[END_REF]. Furthermore, mutations in EZH2 were shown to cause the Weaver syndrome (OMIM:277590), a syndrome characterized by skeletal overgrowth, tall stature, a dysmorphic craniofacial appearance and variable intellectual disability [START_REF] Gibson | Mutations in EZH2 cause Weaver syndrome[END_REF][START_REF] Tatton-Brown | Germline mutations in the oncogene EZH2 cause Weaver syndrome and increased human height[END_REF][START_REF] Tatton-Brown | Weaver syndrome and EZH2 mutations: Clarifying the clinical phenotype[END_REF][START_REF] Cohen | Weaver Syndrome-Associated EZH2 Protein Variants Show Impaired Histone Methyltransferase Function In Vitro[END_REF].

The zebrafish model provides a unique tool to investigate gene function during development.

The zebrafish (Danio rerio) is a widely used vertebrate model for studying development and morphogenesis. Owing to external fertilization and optical transparency of the embryos, early development of zebrafish can be easily monitored. Furthermore, the recent emergence of powerful genome-editing technologies, such as the Transcription Activator-Like Effector Nuclease (TALEN) and Clustered Regularly Interspaced Short Palindromic Repeats / CRISPRassociated System (CRISPR/Cas9) applied to zebrafish allows rapid gene function studies in this organism [START_REF] Dahlem | Simple methods for generating and detecting locus-specific mutations induced with TALENs in the zebrafish genome[END_REF][START_REF] Bedell | In vivo genome editing using a high-efficiency TALEN system[END_REF][START_REF] Moore | Improved somatic mutagenesis in zebrafish using transcription activator-like effector nucleases (TALENs)[END_REF][START_REF] Chang | Genome editing with RNA-guided Cas9 nuclease in zebrafish embryos[END_REF][START_REF] Hwang | Efficient genome editing in zebrafish using a CRISPR-Cas system[END_REF][START_REF] Xiao | Chromosomal deletions and inversions mediated by TALENs and CRISPR/Cas in zebrafish[END_REF]. Using the TALEN technology, we generated here a heterozygous zebrafish line harboring an ezh2 loss-of-function allele to investigate its role in development.

We show that in contrast to what is observed in mice, ezh2 zygotic expression is not required for gastrulation and tissue specification in zebrafish. However, homozygous mutants die at about 12 dpf with defects in the intestine wall, suggesting that zygotic ezh2 expression is necessary for the maintenance of the integrity of the intestine at later developmental time points. Furthermore, we show that the ability of spinal cord regeneration at the caudal fin is also affected in homozygous mutant larvae.

MATERIALS AND METHODS

Zebrafish maintenance, embryo preparation and treatment.

Zebrafish (TU strain) were maintained at 27.5°C in a 14/10h light/dark cycle. The evening before spawning, males and females were separated into individual tanks. Spontaneous spawning occurred when the light turned on and embryos or larvae were collected and staged according to Kimmel et al. [START_REF] Kimmel | Stages of embryonic development of the zebrafish[END_REF].

The feeding of zebrafish larvae starts at 6 dpf for all experiments. The chorions were removed from embryos by the action of 1% pronase (Sigma) for 1 min. Zebrafish embryos or larvae were fixed overnight in 4% paraformaldehyde in PBS (phosphate-buffered saline, Invitrogen), dehydrated gradually to 100% methanol and kept at -20°C.

For caudal fin amputation, 6-month-old adult zebrafish were anesthetized with MS-222 (tricaine, ethyl 3-aminobenzoate methanesulphonate, 250 mg/L; Sigma-Aldrich) and approximately two-thirds of the fin was cut with a blade. After amputation, fish were placed in the aquarium at 27.5°C for fin regeneration. The blastemal starts to form at approximately 24 hours post amputation (hpa) and the amputated fins have been fully restored at around 20 days post amputation (dpa). Larval caudal fin transections were performed at 3 dpf within the pigment gap distal to the circulating blood after anesthesia, as described by Wilkinson et al. [START_REF] Wilkinson | A method for high-throughput PCRbased genotyping of larval zebrafish tail biopsies[END_REF].

To inhibit Ezh2 activity, dechorionated embryos were exposed to 1 µM GSK126 (A11757, Adooq Bioscience) dissolved in DMSO or to an equivalent concentration of DMSO (0.01%, control) at the 1-2 cell stage, at 3 hpf or after larval caudal fin amputation.

Animal ethics statement.

The zebrafish experiments described in this study were conducted according to the French and European Union guidelines for the handling of laboratory animals (Directive 2010/63/EU of the European Parliament and of the Council of 22 September 2010 on the protection of animals used for scientific purposes). The experimental procedures carried out on zebrafish were reviewed and approved by the local Ethics Committee of the Animal Care Facility of the University of Lille. At the end of the experiment, fish older than 8 dpf were humanely euthanized by immersion in an overdose of tricaine methane sulfonate (MS-222, 300 mg/L) for at least 10 minutes, whereas younger fish were immobilized by submersion in ice water (5 parts ice/1 part water, 0-4°C) for at least 1 hour to ensure death by hypoxia.

TALEN design and assembly. The ezh2

TALEN target site was selected using the online TAL Effector-Nucleotide Targeter tool (https://tale-nt.cac.cornell.edu/; [START_REF] Doyle | TAL Effector-Nucleotide Targeter (TALE-NT) 2.0: tools for TAL effector design and target prediction[END_REF]) in exon 2 with the following parameters: (i) spacer length of 14-17 bp, (ii) repeat array length of 16-18 bp, (iii) each binding site was anchored by a preceding T base in position ''0'' as has been shown to be optimal for naturally occurring TAL proteins [START_REF] Moscou | A simple cipher governs DNA recognition by TAL effectors[END_REF][START_REF] Boch | Breaking the code of DNA binding specificity of TAL-type III effectors[END_REF], (iv) presence of a restriction site (DdeI) within the spacer sequence for screening and genotyping purposes.

Ezh2-specific TALEN constructs were engineered using the TALEN Golden Gate assembly system described by Cermak et al., [START_REF] Cermak | Efficient design and assembly of custom TALEN and other TAL effector-based constructs for DNA targeting[END_REF]. The TALEN expression backbones, pCS2TAL3DD and pCS2TAL3RR [START_REF] Dahlem | Simple methods for generating and detecting locus-specific mutations induced with TALENs in the zebrafish genome[END_REF], and the plasmids providing repeat variable diresidues (RVD) [START_REF] Cermak | Efficient design and assembly of custom TALEN and other TAL effector-based constructs for DNA targeting[END_REF] for Golden Gate Cloning were obtained from Addgene.

mRNA injection into zebrafish embryos.

Capped mRNAs were synthetized using the SP6 mMESSAGE mMACHINE kit (Ambion) from linearized plasmid templates. mRNAs (50-100 pg) were injected into 1-cell zebrafish embryos using a FemtoJet microinjector (Eppendorf).

Genotype analyses.

Three-days-old embryos or pieces of caudal fin were incubated in 20 µL PCR extraction buffer (10 mM Tris-HCl pH8.0, 2 mM EDTA, 0.2% Triton X-100, 100 µg/mL Proteinase K) and placed at 50°C for 4 hours prior proteinase K inactivation at 95°C for 5 min.

Genotype analysis was performed by PCR on 2.5 µL of samples using the primer set TAL_ezh2_5'_S21Ac (GGTATGGTTGTTGCAGTTCACAGAC) and TAL_ezh2_3'_S21Ac (AACACCAAACTCTACACAAGCAGCA) followed by PCR product digestion with the DdeI restriction enzyme. Sequence determination (GATC-Biotech, Germany) was performed after cloning of the PCR products into pCR-XL-TOPO (Invitrogen) according to the manufacturer's instructions.

To achieve genotyping on paraformaldehyde-fixed embryos and larvae, DNA was extracted using sodium hydroxide and Tris [START_REF] Meeker | Method for isolation of PCR-ready genomic DNA from zebrafish tissues[END_REF]. Briefly, single embryos were placed into microcentrifuge tubes containing 20 µL 50 mM NaOH and heated 20 min at 95°C. The tubes were then cooled to 4°C and 2 µL of 1 M Tris-HCl, pH7.4 was added to neutralize the basic solution. Genotype analysis was performed on 2.5 µL of samples by PCR-DdeI digestion, as described above.

Alcian blue staining.

Alcian blue staining was performed as previously described [START_REF] Dupret | The Polycomb Group Protein Pcgf1 is dispensable in zebrafish but involved in early growth and aging[END_REF].

Zebrafish larvae were fixed 2 hours at room temperature in 4% paraformaldehyde and dehydrated 10 min in 50% ethanol. Cartilages were stained in 0.02% Alcian blue (Sigma Aldrich), 60 mM MgCl2, 70% ethanol, overnight at room temperature. Pigments were bleached by a 2-hours incubation in water containing 1% KOH, 3% H2O2. Larvae were then digested with 0.05% trypsin (Sigma Aldrich) until tissue disappeared (around 4 hours) before storage in 70% glycerol. After imaging with a Leica MZ125 stereomicroscope equipped with a Leica DFC295 digital camera, DNA was extracted using sodium hydroxide and Tris for genotyping purposes.

Whole-mount immunohistochemistry.

Zebrafish embryos were fixed 2 hours at room temperature in 4% paraformaldehyde, followed by dehydration and storage overnight in methanol at -20°C. Embryos were then permeabilized in PBS containing 0.1% Tween20, 10 µg/mL proteinase K and blocked in PBS containing 0.1% Tween20 and 2% sheep serum.

For muscle development studies, the primary antibody used was a mouse anti-MF20 (1:20;

Developmental Studies Hybridoma Bank, developed under the auspices of the NICHD and maintained by The University of Iowa, Department of Biology, Iowa City, IA 52242) and the secondary antibody was a peroxidase conjugated AffiniPure goat anti-mouse (1:500; 115-035-003, Jackson ImmunoResearch). The embryos were imaged using a Leica MZ125 stereomicroscope equipped with a Leica DFC295 digital camera. For H3K27me3 analyses, the primary antibody used was a rabbit anti-H3K27me3 (1:750; 07-449, Millipore) and the secondary antibody was an Alexafluor 546 conjugated goat anti-rabbit antibody (1:5,000; A11035, Invitrogen). The embryos were then imaged using a Leica MZ10F stereomicroscope equipped with a Leica DFC3000G digital camera. After imaging, DNA was extracted using sodium hydroxide and Tris and embryos were genotyped. probes, whereas ins and gcga cDNA containing vectors were a gift from Dr Julien Bricambert and Pr Amar Abderrahmani (CNRS UMR 8099, EGID). try and phox2bb probes were generated using RT-PCR from total mRNA extracted from zebrafish larvae at 5 dpf using the RNeasy Mini Kit (Qiagen), following the manufacturer's protocol. After Reverse Transcription (Superscript III, Invitrogen), cDNAs were amplified by PCR using the probe specific primers, coupled to the T7 sequence for forward primers and the SP6 sequence for reverse primers. DIG labelled Antisense-RNA probes have been synthetized using the DIG RNA Labeling Kit (SP6) (Roche), following the manufacturer's instructions.

Oil red

The primers used for probe generation were:

ISH_try_F: TAATACGACTCACTATAGGGTGCTCACTGCTACAAGTCCCGT ISH_try_R: GATTTAGGTGACACTATAGCCCGAGCTTAGTTGGAGTTCATGGT ISH_phox2bb_F: TAATACGACTCACTATAGGGGGGCCTAACCCGAACCCTACCTC

ISH_phox2bb_R: GATTTAGGTGACACTATAGGAGCGCACATCGCAGTCTATCGG

In situ hybridization was performed as described by Thisse and Thisse [START_REF] Thisse | High-resolution in situ hybridization to whole-mount zebrafish embryos[END_REF]. Briefly, the fixed embryos were rehydrated and permeabilized with 10 µg/mL proteinase K for 30 sec (1 to 2cell embryos), 10 min (24 hpf embryos) or 30 min (48 to 120 hpf embryos) at room temperature. Ten to 50 embryos from each time point were hybridized with digoxigeninlabeled antisense RNA probes at 70°C. After extensive washing, the probes were detected with anti-digoxigenin-AP Fab fragment (Roche Diagnostics, 1093274, diluted at 1:10,000), followed by staining with BCIP/NBT (5-bromo-4-chloro-3-indolyl-phosphate/nitro blue tetrazolium) alkaline phosphate substrate. The embryos were imaged using a Leica MZ125 stereomicroscope equipped with a Leica DFC295 digital camera.

Regenerating fins from adult fish or fin amputated larvae were fixed in 4% paraformaldehyde overnight, then rehydrated and permeabilized with 10 µg/mL proteinase K for 10 min (5 dpf larvae) or 40 min (adult fish) before whole-mount in situ hybridization and imaging.

To visualize ezh2 mRNA signals in the eye, the digoxigenin-labeled and hybridized antisense RNA probes were detected using tyramide signal amplification (TSA)-Cy5 reagent (Roche) according to Brend and Holley [START_REF] Brend | Zebrafish whole mount high-resolution double fluorescent in situ hybridization[END_REF]. Larvae were then embedded in paraffin, cut into 5-µmthick sections and the eye sections were imaged using a Nikon Eclipse Ti microscope equipped with a Nikon DXM1200C digital camera.

Histone extraction and western blot analysis.

Histone extracts were prepared by lysis of 5 to 10 embryos per tube in PBS containing 0.5% Triton X-100, 2mM phenyl-methylsulfonyl fluorid (PMSF), 0.02% NaN3, 10 min on ice. After centrifugation, the pellet was resuspended in 0.2 N HCl and core histones extracted overnight at 4°C while rocking. Samples were centrifuged and the supernatant containing the histones was stored at -20°C.

For Western blotting, protein samples in SDS loading buffer were electrophoresed on 4-12% Bis-Tris gels (NuPAGE, Invitrogen) and transferred to nitrocellulose membranes using the iBlot® Dry Blotting System (Invitrogen). Efficiency of the transfer is verified by immersing the blotted membrane into a Ponceau S staining Solution (0.1% Ponceau S in 5% acetic acid, Sigma). The membranes were then destained and blocked in 5% milk powder in PBS-T (1x PBS with 0.1% Tween20) for 1 hour at room temperature, incubated for the same time with the primary antibody in PBS-T, and washed three times 10 min in PBS-T. The membranes were then incubated with the peroxidase-conjugated secondary antibody in PBS-T for 1 hour and afterward washed three times 10 min in PBS-T. The signal was detected using a chemiluminescence substrate (Western Lightning Ultra, PerkinElmer) with a Luminescent Image Analyzer (LAS-4000, Fujifilm).

Primary antibodies used were mouse anti-H3K27me3 (1:1,000; ab6002, Abcam) and rabbit anti-H3 (1:5,000; ab1791, Abcam). The secondary antibodies were peroxidase conjugated anti-mouse antibody (1:10,000; 115-035-003, Jackson ImmunoResearch) and peroxidase conjugated anti-rabbit antibody (1:10,000; 711-035-152, Jackson ImmunoResearch).

RNA extraction and RT-PCR.

Total RNA was isolated from 2 hpf, 3 dpf, 5 dpf and 9 dpf wild-type and mutant embryos or larvae using Trizol. cDNA was synthesized using Superscript III (18080-044, Invitrogen). To recover ezh2 transcripts, a forward primer in Exon 1

(GAGGTGAAAGGACCCTCTACC) and a reverse primer in Exon 3

(CTCAGTTTCCATTCCTGATTTAAG) were used, whereas -actin primers were already published (b-actinF: CGTGACATCAAGGAGAAGCT and b-actinR: ATCCACATCTGCTGGAAGGT) [START_REF] Verri | Molecular and functional characterisation of the zebrafish (Danio rerio) PEPT1-type peptide transporter[END_REF].

RESULTS

TALEN-mediated ezh2 inactivation in zebrafish. To gain insights into the function of ezh2

in zebrafish development, we generated ezh2 loss-of-function mutants using the transcription activator-like effector (TALE) nuclease (TALEN)-based technology. TALENs consist in the fusion of the endonuclease domain of the restriction enzyme FokI to engineered sequence-specific DNA-binding domains from TALEs in order to target the nuclease activity to chosen genomic sequences. Once activated through dimerization, the FokI catalytic domain introduces a double strand DNA break which is repaired through the non-homologous end joining (NHEJ) pathway. This repairing process is error prone and may introduce insertion and/or deletion (indel) mutations. Among the resulting mutations, several will lead to shifts in the open reading frame, impairing the resulting protein sequence. TALENs were designed to target a region within the second exon of ezh2 in order to introduce a frame shift upstream of all known Ezh2 conserved domains, including two SANT domains and the catalytic SET domain.

In addition, the targeted region was chosen to contain a DdeI restriction site that could be used to screen for mutations and for genotyping purposes (Figure 1A). TALENs were assembled using the Golden Gate Cloning methodology [START_REF] Cermak | Efficient design and assembly of custom TALEN and other TAL effector-based constructs for DNA targeting[END_REF] and in vitro transcribed mRNAs encoding each TALEN pair were injected into one-cell stage embryos. Genomic DNA was extracted from single embryos collected at 3 days after TALEN mRNA injection. PCR amplification of the targeted region, followed by DdeI digestion revealed the efficacy of the designed TALENs and the convenience of the diagnostic restriction site as a genotyping strategy (Figure 1B).

When analyzed by restriction of genomic DNA at 3 days after TALEN mRNA injection, the mutation rate at the ezh2 locus was about 94% (17 of 18 injected embryos tested). Then, we raised TALENs-injected embryos to establish an adult F0 founder population. To evaluate the efficiency of germ line transmission of the mutations, individual F0 fish carrying mutations were crossed to wild-type TU partners to obtain F1 offspring. Genomic DNA was isolated from individual F1 embryos from each F0 fish and analyzed by DdeI restriction. Embryos from 3 of 14 individual F0 fish were heterozygous mutants, demonstrating successful germ line transmission of the mutations. One mutation causes a 22 bp net insertion (insertion of 27 nucleotides together with a deletion of 5 bp) leading to a frame shifting of the coding sequence and appearance of a premature stop codon (Figure 1C). This ezh2 + allele codes for a predicted protein of 60 amino acids, lacking all conserved protein domains (Figure 1D, Supplementary Figure S1) and was selected to raise the mutant ezh2 +/-zebrafish line used for further phenotypic studies after outcross to wild-type TU fish. Heterozygous ezh2 +/-fish are viable, fertile and do not show any phenotype. Surprisingly, among siblings from heterozygous ezh2 +/-crosses, homozygous ezh2 -/-fish were identified till 12 dpf indicating that ezh2 zygotic function is not required for zebrafish early development. Furthermore ezh2 -/-mutant fish do not present gross morphological alterations (Figure 2A) and show a normal craniofacial cartilage and muscle development (Figure 2B-C). However, we could not identify ezh2 -/-fish after 12 dpf suggesting that zygotic ezh2 function is required for zebrafish development at this time point.

Ezh2 expression during zebrafish development.

In order to study ezh2 mRNA expression, embryos from heterozygous ezh2 +/-crosses were subjected to whole-mount in situ hybridization (Figure 3). At the 2-cell stage, maternal ezh2 mRNAs are detected in the embryo (Figure 3A). To investigate whether the maternally provided transcripts correspond to wild type and/or mutant products, RNAs were extracted, amplified by RT-PCR and the PCR products were subjected to DdeI digestion. Figure 3B shows that these maternal transcripts are mainly derived from the wild-type allele, but not from the mutant allele, suggesting that mutant ezh2 transcripts are subjected to nonsense-mediated decay (NMD) in the zebrafish female germline. In situ hybridization experiments revealed that ezh2 is ubiquitously expressed in the anterior part of wild-type embryos at 24 hpf, but its expression becomes restricted to specific regions such as the pectoral fin buds, the optic tectum, the mid-hindbrain region, the branchial arches, the eyes and the intestine, at later developmental stages (Figure 3C-D, Supplementary Figure S2A). This restricted ezh2 expression correlates with a decrease of total ezh2 mRNA abundance assessed by RT-PCR (Supplementary Figure S2B).

In mutant embryos, only a weak hybridization signal could be detected by in situ hybridization (Figure 3C-D). This residual ezh2 expression is found in the same restricted regions as found in wild-type embryos, suggesting that these transcripts do not derive from maternally deposited products. Indeed, studies of ezh2 mRNAs found in mutant embryos by RT-PCR, followed by DdeI cleavage and sequencing, show that these transcripts contain the +22 nt net insertion and consequently arise from the transcription of the mutant allele (Supplementary Figure S2C-D). This also indicates that mutant ezh2 mRNAs escape, at least in part, to NMD regulation in ezh2 -/-embryos. Altogether, our results demonstrate that maternal wild-type transcripts are present at very early developmental stages, but are not maintained at later stages. Furthermore, ezh2 zygotic expression is ubiquitous and relatively high at 24 hpf, but becomes restricted to a limited number of tissues at later developmental stages.

Ezh2 mutant fish die at around 12 dpf with intestine defects.

To investigate in more details why ezh2 -/-embryos die at 12 dpf, zebrafish larvae from ezh2 +/-crosses were stained with the neutral lipid dye oil red-O in order to better visualize the digestive organs. At 9 dpf, this lipid staining reveals marked differences between ezh2 -/-and their ezh2 +/+ counterparts (Figure 4A). In particular, the liver shows a stronger coloration in mutant fish, suggesting that the lipid composition might change in absence of ezh2 function. More strikingly, oil red-O staining points out differences in the structure of the intestine. In mutant ezh2 -/-fish, the intestine epithelium looks finer than in wild-type fish. This observation was confirmed by the analysis of histological sections of larvae at 9 dpf (Figure 4B). The intestine wall of ezh2 -/- mutants is strongly reduced and lacks folds in the intestine bulb. In contrast, the architecture of more proximal and distal parts of the digestive tract does not present such defects in the mutants at 9 dpf and 11 dpf (Supplementary Figure S3A). Interestingly, at 5 dpf, when the digestive tract achieves its formation and compartmentalization [START_REF] Ng | Formation of the digestive system in zebrafish: III. Intestinal epithelium morphogenesis[END_REF], the structure of the intestine wall in all regions is similar in both ezh2 -/-and ezh2 +/+ siblings (Figure 4B, Supplementary Figure S3B). This indicates that the development of the intestine is normal, but its structure cannot be maintained in ezh2 -/-mutant fish, then leading to their death at 12 dpf. To determine whether the absence of maintenance of the intestine structure results from an enhanced cell death, we performed a terminal deoxynucleotidyl transferase-mediated dUTP nick end labeling (TUNEL) assay for detecting DNA fragmentation generated during apoptosis, on intestine sections at 9 dpf. As shown on Figure 4C, the altered intestine structures in ezh2 -/-mutant are strongly stained by the TUNEL assay, indicating that the absence of maintenance of the intestine integrity is due to a massive increase in apoptosis.

Ectopic expression of phox2bb in ezh2 mutants.

Since the development of the enteric nervous system is critical for normal functioning of the digestive system, we performed in situ hybridizations to detect phox2bb expression. Phox2bb is a transcription factor required for the specification of enteric neural crest fate [START_REF] Elworthy | Phox2b function in the enteric nervous system is conserved in zebrafish and is sox10-dependent[END_REF] and its expression is used to monitor the localization of the enteric progenitors. Our study reveals that the organization of the enteric neural crest cells along the rostral-caudal axis of the gut tube is similar in wild-type and ezh2 mutant fish at 5 dpf (Figure 5A). However, we could detect striking differences in phox2bb expression in the eyes (Figure 5B-C). Phox2bb expression is not detected by in situ hybridization in the eyes of wild-type larvae whereas ezh2 positive cells can be visualized in the retina. In contrast, ezh2 -/-siblings which do not express the ezh2 transcripts, ectopically express phox2bb in the eye. This observation suggests that Ezh2 may negatively control phox2bb expression in the eye.

To further investigate the expression of ezh2 in the eye, in situ hybridization experiments on wild-type larvae at 9 dpf using digoxygenin-labeled ezh2 riboprobes and tyramide signal amplification (TSA)-Cy5 reagent [START_REF] Jülich | Screen Consortium. beamter/deltaC and the role of Notch ligands in the zebrafish somite segmentation, hindbrain neurogenesis and hypochord differentiation[END_REF] were performed prior sections of the eyes. This approach revealed that ezh2 is expressed in the cornea and in all the layers of the retina, but not in the inner plexiform, the outer plexiform, and the retinal pigmented epithelium (Figure 5D).

However, in spite of the loss of the Ezh2 product and ectopic expression of phox2bb, observed at 5 dpf, we could not identify histological alteration in the eyes of ezh2 -/-fish, later at 9 dpf, when compared to wild-type siblings (Figure 5E).

Loss of ezh2 function affects the development of the exocrine pancreas. Because ezh2 -/-

mutants show defects in digestive organs including the intestine and the liver, we investigated the development of the pancreas (Figure 6). In situ hybridization experiments at 5 dpf with probes for the markers of the endocrine pancreas ins and gcga, revealing -and α-cells respectively, do not highlight differences between ezh2 -/-and ezh2 +/+ siblings. In contrast, in situ hybridization for try, a terminal differentiation marker for the exocrine pancreas, revealed that this organ is less developed in the ezh2 -/-mutant fish (Figure 6A, Supplementary Figure S4).

To determine whether the reduced size of the exocrine pancreas is an early or late event, we assayed for try expression at 3 dpf. Figure 6B shows that at this stage, the exocrine pancreas development is similar in ezh2 -/-and ezh2 +/+ siblings. This indicates that, as for the intestine development, the development of the exocrine pancreas in fish lacking embryonic ezh2 expression is normally formed at early stages but its proper maintenance is affected at later developmental stages.

Impaired H3K27me3 methylation in ezh2 mutant zebrafish. Since Ezh2 trimethylates

lysine 27 of histone H3 (H3K27), we evaluated the trimethylation status of histone H3 at lysine 27 in ezh2 -/-mutant fish. Total histones were extracted from mutant and wild-type siblings at 9 and 12 dpf and trimethylation of lysine 27 of histone H3 was analyzed by western blot using a specific anti-H3K27me3 antibody. Figure 7A shows that global levels of trimethylated lysine 27 of histone H3 are severely decreased but not abolished, in ezh2 -/-mutants at both developmental time points. Interestingly, heterozygous ezh2 +/-fish show intermediated levels of global H3K27me3 methylation (Figure 7B), indicating that ezh2 haploinsufficiency is responsible for a decrease in H3K27me3 methylation without affecting the phenotype, whereas homozygous loss of ezh2 does not fully abolish H3K27me3 levels but leads to cell death and loss of maintenance of the intestine structures. Whole-mount in situ immunodetection of H3K27me3 at 24 hpf does not show staining differences between ezh2 +/+ and ezh2 -/-siblings suggesting that Ezh2 maternal products and/or Ezh1 are the main factors involved in H3K27me3 methylation at this stage (Figure 7C). In contrast, in situ immunostaining for H3K27me3 at 4 dpf reveals a reduction of global levels of this epigenetic mark in ezh2 -/-mutants. Moreover, this decrease affects all tissues of the organism, rather than specific tissues (Figure 7C).

Pharmacological inhibition of Ezh2 alters zebrafish development. Maternal ezh2

transcripts are detected at the embryonic 1-2 cell stage. In order to investigate the role of maternally deposited Ezh2 products in early zebrafish development, we used a pharmacological approach to inhibit Ezh2 activity at early developmental stages.

Dechorionated embryos were exposed to the EZH2 specific inhibitor GSK126 [START_REF] Mccabe | EZH2 inhibition as a therapeutic strategy for lymphoma with EZH2-activating mutations[END_REF] at 3 hpf. The GSK126 was chosen to inhibit Ezh2 activity because this drug acts in vivo and is 150-fold selective for EZH2 over EZH1 and more than 1,000-fold selective for EZH2 over a range of other methyltransferases [START_REF] Xu | Targeting EZH2 and PRC2 dependence as novel anticancer therapy[END_REF]. Since zebrafish embryo and larvae rapidly absorb low molecular weight compounds, diluted in the surrounding media, through skin and gills the treatment concentrations used were the same as described for applications in cells in culture [START_REF] Mccabe | EZH2 inhibition as a therapeutic strategy for lymphoma with EZH2-activating mutations[END_REF].

Morphological abnormalities were first detected at 24 hpf with 1 µM GSK126 (Figure 8A-B).

At 96 hpf, phenotypic aberrations include cardiac edemas, absence of pectoral fins (Figure 8B), as well as a decrease in eye size (Figure 8C). Further investigations revealed that the loss of pectoral fins, as well as the reduced size of the eyes of the treated embryos reflects a developmental delay rather than a developmental alteration, since pectoral fins appear later.

None of these phenotypes, such as the appearance of cardiac edemas and developmental delays, were observed in ezh2 -/-mutants indicating that the inhibition of Ezh2 activity at 3hpf more severely affects zebrafish development. To determine whether GSK126 exposure affected total H3K27me3 methylation levels, dechorionated embryos cultured from 3 hpf to 96 hpf in presence of 1 µM GSK126, were analyzed by Western blotting using a specific anti-H3K27me3 antibody. We show that H3K27me3 relative levels were decreased by about 60% in treated embryos (Figure 8D). The whole-mount in situ immunodetection of H3K27me3 methylation shows that the decrease in H3K27me3 levels is rather global than limited to specific organs (Figure 8E). The remaining H3K27me3 levels are probably due to the fact that GSK126 blocks de novo Ezh2-mediated methylation, but do not affect H3K27me3 marks implemented before the drug exposure at 3 hpf. A similar experiment was conducted by applying 1 µM GSK126 on embryos at the 1-2 cell stage. In these conditions, gastrulation and the establishment of the body plan is seemingly normal, but the GSK126 treatment also induces cardiac edemas and developmental delays (Supplementary Figure S5A), as observed when the treatment is applied at 3 hpf, but not found in ezh2 -/-mutants. H3K27me3 relative levels were deceased by about 35% in treated embryos (Supplementary Figure S5B).

Although the loss of H3K27me3 is not complete, inhibiting Ezh2 activity at the 1-2 cell stage or at 3 hpf elicits stronger developmental defects than the loss of zygotic Ezh2 activity underlying a role of the maternal Ezh2 products at early developmental stages. However, loss of maternal Ezh2 activity does not dramatically affect the establishment of the zebrafish body plan.

Ezh2 function is involved in caudal fin regeneration.

Upon amputation, the zebrafish caudal fin fully regenerates in about 20 days. This regeneration process involves various cellular events such as wound closure, dedifferentiation, mesenchymal proliferation, blastema formation and outgrowth, actinotrichia formation, apical blastema maintenance, progressive redifferentiation and morphogenesis [START_REF] Pfefferli | The art of fin regeneration in zebrafish[END_REF]. Moreover, a role of H3K27 methylation in caudal fin regeneration has been demonstrated [START_REF] Stewart | A histone demethylase is necessary for regeneration in zebrafish[END_REF]. In situ hybridization revealed that ezh2 is expressed in the growing blastema of regenerating fins at 4 days post-amputation in adult zebrafish whereas the sense probe lacked any discernable signal (Supplementary Figure S6).

Since caudal fins of larvae also regenerate after amputation by a mechanism highly similar to that used by adult fish [START_REF] Kawakami | Early fin primordia of zebrafish larvae regenerate by a similar growth control mechanism with adult regeneration[END_REF][START_REF] Yoshinari | Gene expression and functional analysis of zebrafish larval fin fold regeneration[END_REF], and because ezh2 -/-adult fish are not viable preventing the study of the role of ezh2 in caudal fin regeneration at this stage, we focused our attention on larval caudal fin regeneration. The tip of the caudal fin was transected at 3 dpf within the pigment gap distal to the circulating blood. This fin clip procedure induces blastema formation at the site of amputation followed by caudal fin regeneration and normal development of the embryo ( [START_REF] Wilkinson | A method for high-throughput PCRbased genotyping of larval zebrafish tail biopsies[END_REF]; Figure 9). Using in situ hybridization, we showed that ezh2 expression is detected in larval caudal fin after amputation (Figure 9A). To investigate whether Ezh2 function is required for caudal spinal cord regeneration, larvae were subjected to caudal fin amputation at 3 dpf and the regeneration process was studied in presence of the Ezh2-specific inhibitor GSK126 (Figure 9B). In presence of 1 µM GSK126, regeneration of the fin fold and of the spinal cord is severely impaired, compared to control DMSO treated embryos. Similarly, the spinal cord of ezh2 -/-larvae also fails to regenerate properly after transection, when compared to wild-type siblings (Figure 9C). Altogether, our results indicate that ezh2 is expressed in the regenerating caudal fin after amputation and suggest that Ezh2 function is required for larval caudal spinal cord regeneration.

DISCUSSION

In the past decade, an increasing amount of data underlined the fundamental role of epigenetic modifications in controlling the activity of regulatory genes involved in development, lineage specification, differentiation and tissue renewal. In the present study, we examine the role of Ezh2 in zebrafish development. Ezh2 catalyzes the trimethylation of lysine 27 of histone H3 (H3K27me3), a post-translational modification that has been widely implicated in epigenetic suppression of gene expression.

To address the question of the function of Ezh2, we generated an ezh2 loss-of-function allele in zebrafish using the TALEN technology. A zebrafish line harboring a 22 bp net insertion (insertion of 27 nucleotides associated with a deletion of 5 bp) within the ezh2 gene, leading to a frame shift in the coding sequence and encoding a predicted protein of 60 amino acids, lacking all of the essential conserved protein domains, has been generated. The heterozygous ezh2 +/-fish are viable, fertile, and do not show any obvious phenotype.

Surprisingly, and in total contrast to what was observed in mice where Ezh2 loss-of-function results in lethality at gastrulation [START_REF] O'carroll | The polycomb-group gene Ezh2 is required for early mouse development[END_REF], homozygous ezh2 -/-zebrafish mutants gastrulate properly and develop normally. However, at 9 dpf, the ezh2 -/-mutant presents a striking alteration of the intestine wall, presumably responsible for the death of the ezh2 -/-fish.

Interestingly, at 5 dpf the intestine of ezh2 -/-mutants is normal, indicating that this organ develops properly in absence of zygotic Ezh2 function, but that the maintenance of its structure requires Ezh2 action. The defects in the maintenance of the integrity of the intestine are due to enhanced cell death rather than to an arrest of development, as a TUNEL assay shows a massive increase of apoptosis in ezh2 loss-of-function mutants. Remarkably, the structure of the intestine bulb is severely impaired in ezh2 mutants at 9 dpf whereas the wall of the mid-intestine of ezh2 -/-and wild-type siblings remains similar. Since the cell proliferation rate is higher in the intestine bulb than in the mid-intestine [START_REF] Wallace | Intestinal growth and differentiation in zebrafish[END_REF], our data also establish a link between Ezh2 function and intestinal cell renewal.

Zebrafish ezh2 -/-mutants present alterations of the intestine and this phenotype differs to what has been found in mice. Indeed, using a Cre-mediated conditional knock-out approach, Koppens et al. [START_REF] Koppens | Deletion of Polycomb Repressive Complex 2 From Mouse Intestine Causes Loss of Stem Cells[END_REF] generated mice lacking Ezh2 activity in the intestine. These mutants present a reduction of H3K27me3 marks in the intestine but this does not result in an overt adverse phenotype, since the intestines lacking Ezh2 function are morphologically similar to controls and cell proliferation and differentiation are not affected. Moreover, no difference can be observed between mice lacking Ezh2 function in the intestines and control mice [START_REF] Koppens | Deletion of Polycomb Repressive Complex 2 From Mouse Intestine Causes Loss of Stem Cells[END_REF].

This may suggest that Ezh2 contributes differently to the maintenance of the structure of the intestine in mice and in zebrafish.

Different mutations, including sst m311 (straight shot), nor m264 (no relief), pie m497 (piebold) or polr3b m74 (polr3b, slim jim), have been reported to be responsible for the intestine degeneration in zebrafish [START_REF] Pack | Mutations affecting development of zebrafish digestive organs[END_REF]. Moreover, it has also been shown that these mutations are responsible for alterations in the exocrine pancreas development [START_REF] Pack | Mutations affecting development of zebrafish digestive organs[END_REF]. Similarly, ezh2 -/- mutants present defects in the development of the exocrine pancreas in addition to a striking intestinal phenotype. Indeed, the development of the exocrine pancreas, as judged by the expression of the terminal differentiation marker try, is impaired in ezh2 deficient fish at 5 dpf.

However, as for the intestine, the development of the exocrine pancreas in ezh2 -/-mutants is normally formed at early stages (3 dpf). This indicates that zygotic ezh2 expression is not required for exocrine pancreas implementation whereas Ezh2 in necessary to properly maintain the development of this organ at later stages.

The analyses of mRNA expression profile of ezh2 in zebrafish showed that maternal transcripts are detected in the embryo at the 2-cell stage. At 24 hpf, the ezh2 mRNA is ubiquitously expressed, whereas its expression becomes restricted to defined regions such as the pectoral fin buds, the optic tectum, the mid-hindbrain region, the branchial arches, the eyes and the intestine during later development, as recently shown by San et al. [START_REF] San | Normal formation of a vertebrate body plan and loss of tissue maintenance in the absence of ezh2[END_REF]. This observation parallels the experiments performed in mouse showing that murine Ezh2 is ubiquitously expressed throughout early embryogenesis, while in later embryonic development, Ezh2 expression tends to be restricted to specific sites within the central and peripheral nervous system and to the major sites of fetal hematopoiesis, as well as in the intestine, the testis, the placenta and the muscles [START_REF] Hobert | Isolation and developmental expression analysis of Enx-1, a novel mouse Polycomb group gene[END_REF][START_REF] Ningxia | The expression pattern of polycomb group protein Ezh2 during mouse embryogenesis[END_REF].

The presence of ezh2 mRNAs in the early zebrafish embryo suggests that maternally deposited ezh2 products may be involved in early development. Since maternal contribution takes place till the 2-cell stage in mice whereas in zebrafish maternal contribution could be maintained until at least the 1,000-cell stage (3 hpf) [START_REF] Mathavan | Transcriptome analysis of zebrafish embryogenesis using microarrays[END_REF][START_REF] Tadros | The maternal-to-zygotic transition: a play in two acts[END_REF], this difference could explain in part, why ezh2-deficient zebrafish mutants develop normally. To investigate the potential contribution of ezh2 from maternal origin in early development, we used a pharmacological approach to inhibit Ezh2 activity before zygotic genome activation. In our approach, dechorionated embryos were exposed at the 1-2 cell stage or at 3 hpf to GSK126, a specific inhibitor of EZH2 [START_REF] Mccabe | EZH2 inhibition as a therapeutic strategy for lymphoma with EZH2-activating mutations[END_REF]. In both cases, GSK126-mediated inhibition of maternal Ezh2 activity elicits developmental aberrations, including appearance of cardiac edemas as well as a developmental delay. Because these phenotypes were not observed in the ezh2-deficient zygotic mutants, we speculate that maternal Ezh2 activity contributes to zebrafish Zebrafish embryos treated with DZNep at the 1-2 cell stage present defects in somites, notochord and tail, resulting in abnormal body shape, as well as observed cardiac edema.

Head development is also severely affected and insufficient brain segmentation, brain underdevelopment and edema are observed together with severe defects in the ear, the eye and/or in the jaw [START_REF] Ostrup | The specific alteration of histone methylation profiles by DZNep during early zebrafish development[END_REF]. The stronger effect of DZNep, when compared to GSK126 action is probably due to the fact that DZNep may be responsible for the inhibition of other Sadenosylmethionine-dependent methyltransferases in addition to Ezh2 [START_REF] Miranda | DZNep is a global histone methylation inhibitor that reactivates developmental genes not silenced by DNA methylation[END_REF]. However, as

DZNep treated and non-treated embryos develop with comparable survival rates, even upon gastrulation, this study reinforces the idea that maternal Ezh2 is not required for early development and global implementation of the body plan. Both, the role of ezh2 in zebrafish tissue maintenance and the absence of ezh2 requirement in the establishment of the body plan have also been demonstrated in the recent work from San et al. [START_REF] San | Normal formation of a vertebrate body plan and loss of tissue maintenance in the absence of ezh2[END_REF]. This study describes the generation of maternal zygotic (MZ) ezh2 mutant embryos through germ cell transplantation. MZezh2 mutant embryos gastrulate and form a normal body organization, but die at around 2 dpf with defects including the loss of myocardial integrity and the alteration of liver and pancreas terminal differentiation. Altogether, these data indicate that maternal ezh2 function contributes to zebrafish development, but the loss of its activity does not block gastrulation and body plan formation.

After fertilization, the zebrafish embryonic genome is inactive till transcription is initiated during the maternal-zygotic transition, which starts around the mid-blastula transition (3.3 hpf) [START_REF] Tadros | The maternal-to-zygotic transition: a play in two acts[END_REF]. This transition is accompanied by the formation of pluripotent cells, the degradation of maternal transcripts and changes in epigenetic marks. In particular, H3K27me3 methylation levels, which were low before the maternal-zygotic transition, gradually increase and numerous genes appear to be marked with H3K27me3 after this time point [START_REF] Vastenhouw | Chromatin signature of embryonic pluripotency is established during genome activation[END_REF][START_REF] Lindeman | Prepatterning of developmental gene expression by modified histones before zygotic genome activation[END_REF][START_REF] Andersen | Epigenetic marking of the zebrafish developmental program[END_REF][START_REF] Andersen | Epigenetic complexity during the zebrafish mid-blastula transition[END_REF]. This indicates that the deposition of H3K27me3 epigenetic marks may be important after the zygotic genome activation for embryonic development. In this regard, we observed a reduction, but not the abolition of H3K27me3 methylation both in ezh2 -/-mutants and in GSK126 treated embryos. This raises the possibility that Ezh1 may be able to compensate for loss of Ezh2 function, since Ezh1 also trimethylates H3K27 [START_REF] Shen | EZH1 mediates methylation on histone H3 lysine 27 and complements EZH2 in maintaining stem cell identity and executing pluripotency[END_REF][START_REF] Margueron | Ezh1 and Ezh2 maintain repressive chromatin through different mechanisms[END_REF]. The remaining H3K27me3 marks in ezh2 -/-larvae may allow the recruitment and the action of the PRC1 complex and may explain why PRC1-deficient fish present a phenotype with more severe alterations. Indeed, rnf2 mutant zebrafish embryos lacking PRC1 function, die at around 4-5 dpf with a normal body plan, but displaying craniofacial alterations and defects in pectoral fin development [START_REF] Van Der Velden | The Polycomb group protein Ring1b is essential for pectoral fin development[END_REF][START_REF] Van Der Velden | The polycomb group protein ring1b/rnf2 is specifically required for craniofacial development[END_REF].

During the course of our experiments, we observed the ectopic expression of phox2bb in the eyes of ezh2 -/-mutants. Phox2bb is a homeobox-containing transcription factor often used to monitor the localization of enteric progenitors. At 5 dpf, phox2bb is mainly expressed in the enteric nervous system and in the hindbrain of wild-type larvae. However, additional phox2bb positive cells are also observed in the eyes of ezh2 -/-siblings. The fact that phox2bb is ectopically expressed in ezh2-deficient larvae suggests that this gene is repressed directly or indirectly, by Ezh2. This control of phox2bb expression by Ezh2 appears to be also cell-specific because phox2bb is not ectopically expressed in all the cells and regions lacking ezh2 expression in the mutant fish. The role of ezh2 in phox2bb regulation in the eye remains unclear since ezh2 -/-mutants losing the expression of ezh2 and ectopically expressing phox2bb

do not present histological defects in the eye. However, it is interesting to notice that this phox2bb ectopic expression affects limited areas in the eye, indicating that Ezh2 is not the only element controlling the expression of phox2bb. Furthermore, the restricted ectopic expression explains why phox2bb was not identified as an Ezh2 target in large scale gene expression analyses using microarrays on MZezh2 mutants [START_REF] San | Normal formation of a vertebrate body plan and loss of tissue maintenance in the absence of ezh2[END_REF].

The capacities of zebrafish to regenerate some of its organs and in particular its caudal fin rely on the zebrafish ability to maintain access to a number of developmental programs and may correlate with a certain plasticity of the epigenome. In this context, it has been shown that DNA demethylation correlates with the early phase of zebrafish fin regeneration [START_REF] Hirose | Transient reduction of 5-methylcytosine and 5hydroxymethylcytosine is associated with active DNA demethylation during regeneration of zebrafish fin[END_REF]. Several epigenetic factors, including components of nucleosome remodeling and deacetylase (NuRD) complex such as hdac1, mta2, rbb4 and chd4a, are also upregulated in the proliferative compartment of the blastema and required for the redifferentiation of skeletal precursors and for actinotricha formation [START_REF] Pfefferli | Specific NuRD components are required for fin regeneration in zebrafish[END_REF]. Similarly, Stewart et al. [START_REF] Stewart | A histone demethylase is necessary for regeneration in zebrafish[END_REF] demonstrated that H3K27me3 demethylation at specific loci might be crucial to reactivate the regeneration gene expression programs and to initiate the regeneration process in response to caudal fin amputation. Here, we show that ezh2 is expressed in regenerating caudal fin tissues after amputation both in adult and larval zebrafish. Furthermore, ezh2-deficient as well as wild-type larvae treated with the Ezh2 specific inhibitor GSK126, fail to properly regenerate their caudal spinal cord after transection. These results suggest that Ezh2 and H3K27me3 methylation might also be involved in processes of regeneration in zebrafish.

CONCLUSIONS.

In this work, we generated a zebrafish ezh2 mutant allele using the TALEN technology.

Heterozygous mutant fish are viable, fertile and do not show any obvious phenotype. In contrast to what was found in mice, homozygous ezh2 -/-mutant zebrafish gastrulate properly, present a normal body plan but die at 12 dpf with defects of the intestine wall. Analysis of the intestine revealed that at 5 dpf its development is normal, but its integrity is not maintained at later developmental stages, due to enhanced cell death in ezh2 loss-of-function mutants.

Similarly, terminal differentiation of the exocrine pancreas is determined but not fully maintained in absence of zygotic ezh2 expression. Studies of ezh2 expression showed that maternal ezh2 transcripts are loaded in the embryo. At 24 hpf ezh2 is ubiquitously expressed, whereas its expression becomes restricted to defined regions at later stages. Treatment of zebrafish embryos with the EZH2-specific inhibitor GSK126 revealed that maternal ezh2 products contribute to early development but are not required for normal body plan formation. Our results parallel and supplement those of San et al. [START_REF] San | Normal formation of a vertebrate body plan and loss of tissue maintenance in the absence of ezh2[END_REF] using maternal-zygotic MZeh2 mutants. But in addition, we show that ezh2 might play a role in the regeneration processes. Indeed, a GSK126 treatment, as well as the ezh2 loss-of-function mutation, alters the regeneration of the chord after transection. Altogether, our work sheds light on the complex role of Ezh2 in cell fate decisions and demonstrates that zebrafish provides a remarkable model system to study Ezh2 function and H3K27me3 methylation in tissue maintenance.

Figure 4. Ezh2 is required for maintenance of the intestine integrity in zebrafish. (A)

Representative images of lateral views of ezh2 +/+ and ezh2 -/-larvae as indicated, stained with oil Red-O at 9 dpf. On the enlarged picture, the liver is indicated by an asterisk. The intestine wall appears well defined and finer in ezh2 -/-mutants (arrow). Scale bar is 500 μm, or 200 µm on the enlargement panels. (B) Intestinal sections from ezh2 +/+ and ezh2 -/-larvae immunostained for actin and counterstained with hematoxylin, at 5 dpf (left) and 9 dpf (right).

Scale bar is 100 μm. (C) TUNEL assay on sections from the intestinal bulb of ezh2 +/+ (left) and ezh2 -/-(right) larvae at 9 dpf, showing an increase of apoptosis levels in the intestine and the pancreas (asterisk) in ezh2 -/-mutants. Scale bar is 100 μm.

  development and at least in the proper development of the heart. However, embryos exposed to GSK126 at the 1-2 cell stage gastrulate and show a normal body organization, indicating that maternal Ezh2 contributes to development but is not required for the set up of the body plan. In another study, Ostrup et al. [65] used 3-deazaneplanocin A (DZNep), an inhibitor of the S-adenosyl homocysteine hydrolase to impair Ezh2 function and H3K27me3 methylation.

Figure 1 .

 1 Figure 1. Generation of ezh2 mutant zebrafish using the TALEN technology. (A) Schematic representation of the genomic structure of the ezh2 gene, with coding and untranslated exons depicted as solid and open boxes, respectively. The exonic regions coding for the conserved SANT and SET domains are shown in red and brown, respectively. The location of the ezh2 TALEN in exon 2 is indicated. The ezh2 TALEN target sequence with Left and TALEN binding sites in red is shown. The DdeI restriction site is indicated in green. (B) Identification of mutant embryos using a diagnostic restriction. Genomic DNA was prepared from an uninjected (Control) and an ezh2 TALEN injected (TAL-ezh2) embryo. The TALEN targeted DNA region is amplified by PCR and subjected to DdeI digestion. The TAL-ezh2 injected embryo contains undigested material (arrow at 466 bp), indicating that the DdeI diagnostic restriction site has been disrupted. (C) Sequence of the mutant allele compared to its wild-type counterpart. Small letters indicate inserted nucleotides. The mutated ezh2 allele (Mut) contains a 22 bp net insertion resulting from a deletion of 5 nucleotides (underlined in the wild-type sequence) and an insertion of 27 nucleotides (small letters). (D) Schematic representation of the wild-type (Ezh2 wt ) and mutant (Ezh2 mut ) proteins. The gray line in the predicted mutant protein indicates residues read out of frame prior to encountering a premature stop codon, whereas the red and brown motifs in the wild-type protein correspond to SANT (SMART: SM00717) and SET (SMART: SM00317) domains, respectively. Size of the predicted proteins is indicated.

Figure 2 .

 2 Figure 2. Loss of Ezh2 function does not affect early zebrafish development. (A) At 5 dpf, ezh2 - /-mutants from ezh2 +/-crosses are phenotypically indistinguishable from heterozygous and wild-type siblings. (B) Alcian blue stained head cartilages of ezh2 +/+ (up) and ezh2 -/-(down)

Figure 3 .

 3 Figure 3. ezh2 expression in ezh2 +/+ and ezh2 -/-siblings at different developmental time points. (A) In situ hybridization at the 1-and 2-cell stages showing that ezh2 mRNA is maternally provided in zebrafish embryos. (B) The analysis of ezh2 transcripts by RT-PCR at 2 hpf shows that wild-type, but not mutant transcripts are delivered into the embryos from ezh2 +/-crosses (♂x♀ ezh2 +/-). Ezh2 transcripts from ezh2 +/+ crosses are shown on the left part (WT). By RT-PCR, wild-type ezh2 mRNA is expected to give a band at 328 bp, whereas the size of the mutant transcript should be at 350 bp. After DdeI digestion, the predicted restriction fragments from the wild-type cDNA will be at 171, 122, 31 and 4 bp, while those from the mutant will be at 315, 31 and 4 bp. Relative mRNA abundance is shown by RT-PCR amplification of the -actin mRNAs (act) (C) In situ hybridization to detect ezh2 transcripts in ezh2 +/+ (left) and ezh2 -/-(right) siblings from ezh2 +/-crosses at the indicated time points. (D) Lateral view of 96 hpf ezh2 +/+ (left) and ezh2 -/-(right) siblings showing ezh2 expression detected by in situ hybridization in the intestine of wild-type larvae (arrow). Scale bar is 500 μm.

Figure 5 .

 5 Figure 5. Ectopic expression of phox2bb in the eyes of ezh2 mutants. (A) In situ hybridization showing that the localization of phox2bb expressing neural crest cells along the gut (arrow) is not altered by loss of Ezh2 function at 5 dpf. (B) Expression of ezh2 (up) and phox2bb (down) in the anterior region of ezh2 +/+ (left) and ezh2 -/-(right) siblings at 5dpf, as shown by in situ

Figure 6 .

 6 Figure 6. The exocrine pancreas development is affected in ezh2 -/-mutants. (A) In situ hybridization for different markers of the pancreas in ezh2 +/+ (left) and ezh2 -/-(right) siblings from ezh2 +/-crosses, performed at 5 dpf. No difference is found for markers of the endocrine pancreas (ins and gcga, arrow), whereas try, a marker for terminal differentiation of the exocrine pancreas reveals a reduced signal area in ezh2 -/-larvae. Representative fish of each genotype are shown. Scale bar is 500 μm. (B) In situ hybridization at 3 dpf showing that the try signal is similar in ezh2 +/+ (left) and ezh2 -/-(right) siblings. Scale bar is 500 μm.

Figure 7 .

 7 Figure 7. Global trimethylation of lysine 27 of histone H3 is reduced in ezh2-/-mutants. After genotyping of the caudal region of the larvae, total histones from pools of 5 larvae of ezh2 +/+ and ezh2 -/-genotypes at 9 and 12 dpf (A) or from ezh2 +/+ , ezh2 +/-and ezh2 -/-genotypes at 9 dpf (B) as indicated, were extracted and analyzed by western blotting using a specific anti-H3K27me3 antibody and an anti-H3 antibody as a control. (C) Immunostaining for H3K27me3 in wildtype and ezh2 -/-embryos as indicated at 24 hpf (left) and 4 dpf (right). Scale bars are 500 µm and 1 mm for 24 hpf embryos and 4 dpf larvae, respectively.

Figure 8 .

 8 Figure 8. GSK126 elicits developmental aberrations in zebrafish. (A) Scoring of abnormal and dead embryos at 24 and 96 hpf. Embryos were exposed to 1 µM GSK126 (n=397) or to 0.01% DMSO (n=114) at 3 hpf. (B) Representative phenotype of embryos and larvae without treatment (DMSO 0.01%) or treated with 1 µM GSK126 at the indicated time points. Notice cardiac edemas (arrows) and absence of pectoral fins at 96 hpf. Scale bar is 500 μm. (C)

Figure 9 .

 9 Figure 9. Ezh2 and larval caudal fin regeneration. (A) In situ hybridization to visualize ezh2 expression on a representative control untransected zebrafish larvae at 5 dpf (top) and on a representative larval fin at 5 dpf, 2 days post-amputation (bottom). Ezh2 expression is detected in regenerating tissues (arrow head). (B) The Ezh2 specific inhibitor GSK126 affects larval caudal fin regeneration. At 3 dpf (a, a'), the tip of the caudal fin of wild-type larvae is sectioned within the pigment gap distal to the circulating blood (b, b') and embryos were subsequently treated with 1 µM GSK126 or with 0.01 % DMSO (control). At 2 days postamputation the spinal cord regeneration is inhibited in the treated larvae (c'), but not in the controls (c). The dotted line indicates the transection site. (C) Ezh2 function is required for spinal cord regeneration. At 3 dpf (a, a'), the tip of the caudal fin of wild-type (ezh2 +/+ ) or Ezh2deficient (ezh2 -/-) siblings is sectioned within the pigment gap distal to the circulating blood (b, b'). Two days after the transection, spinal cord regeneration is reduced in mutant larvae (c') compared to wild-type (c). The dotted line indicates the transection site.

2.11. Whole-mount in situ hybridization. For

	digital camera. After imaging, DNA was extracted using sodium hydroxide and Tris for
	genotyping analyses.
	2.9. Histological analyses. For histological analyses, tail biopsies were used for genotyping
	before paraformaldehyde fixation of the larvae. Larvae were embedded in paraffin and cut
	into 5 μm-thick sections. These were mounted on sylanated glass slides, deparaffinated,
	rehydrated and stained with hematoxylin and eosin for histological analysis.
	Immunostainings on zebrafish sections were done to visualize actin using a rabbit anti-actin
	primary antibody (1:50; A2066, Sigma) and a horseradish peroxidase conjugated anti-rabbit
	IgG secondary antibody (1:500; 711-035-152, Jackson ImmunoResearch) and counterstained
	with hematoxylin (RAL Diagnostic) for nuclear staining. F-actin was visualized by Alexa fluor
	594 conjugated phalloidin (1:100; A12381, Thermofisher) staining and nuclear counterstaining
	done with 1 mM Hoechst 33258 (861405, Sigma). Image acquisition was performed using a
	Nikon Eclipse Ti microscope equipped with a Nikon DXM1200C digital camera.
	2.10. TUNEL assay. TUNEL assays were performed using the In Situ Cell Death Detection Kit
	(Roche, 11 684 817 910), according to the manufacturer's instructions. Briefly, larvae were
	embedded in paraffin and cut into 5 μm-thick sections. These were mounted on sylanated
	glass slides, deparaffinated, rehydrated and digested 10 min at room temperature with 3
	U/mL DNase I in 50 mM Tris-HCl pH7.5, 10 mM MgCl2, 1 mg/mL BSA. The TUNEL Reaction
	Mixture was added to slides, incubated 1 hour at 37°C, rinsed 3 times with PBS before addition
	of the Converter-POD for 30 min at 37°C. Samples were rinsed 3 times with PBS, incubated 45
	min at room temperature in presence of the DAB substrate, washed 3 times with PBS,
	dehydrated and mounted under glass coverslips. The images were acquired using a Nikon
	Eclipse Ti microscope equipped with a Nikon DXM1200C digital camera.
	-O staining. Zebrafish larvae were fixed in 4 % paraformaldehyde overnight at 4°C ezh2, ins and gcga, antisense RNA probes were
	and their pigments bleached by 2-hours incubation in a solution containing 1% KOH and 3% synthesized with the DIG RNA Labeling Kit (SP6/T7) (Roche, 11175025910), following the
	H2O2. Larvae were washed five times in PBS and stained with oil red-O (Hamiya Biomedical manufacturer's instructions from 1 µg of linearized plasmid DNA. The cDNA clone
	Company) for 15 min. Stained larvae were washed with PBS, stored in 70% glycerol and MGC:152758 IMAGE:2639510 purchased at imaGenes GmbH (Berlin) was used for ezh2
	imaged on a bright-field dissecting microscope (Leica MZ125) equipped with a Leica DFC295

Ezh2 in Zebrafish

ACKNOWLEDGEMENTS.

We are grateful to Dr Julien Bricambert and Pr Amar Abderrahmani (CNRS UMR 8099, EGID) for providing the ins and gcga plasmids and for helpful discussions.

We thank Pauline Follet for technical assistance and excellent animal care. FUNDING. This work was supported by the Inserm, the University of Lille, the SIRIC ONCOLille, and grants from le Comité du Nord de la Ligue Contre le Cancer and l'ITMO Biologie Cellulaire, Développement et Evolution (BCDE). BD is supported by a fellowship from the Région Hauts de France Nord-Pas de Calais-Picardie and the University of Lille.

AVAILABILITY OF DATA AND METERIAL. All data generated and analyzed in this study are included in this published article and its supplementary information files.

embryos from ezh2 +/-crosses correspond to zygotic transcripts, rather than to maternally deposited mRNAs. By RT-PCR using the primers designed in exons 1 and 3, wild-type ezh2 transcripts are expected to give a band at 328 bp, whereas the size of the mutant transcript should be at 350 bp. After DdeI digestion, the predicted restriction fragments derived from the mutant cDNAs will be at 315, 31 and 4 bp. The mRNAs used in the RT-PCR experiment were extracted from 3 dpf old ezh2 +/+ (WT) and ezh2 -/-siblings coming from ezh2 +/-in-crosses.

Supplementary Figure S6. Expression of ezh2 in regenerating caudal fin. Whole-mount in situ

hybridization of regenerating caudal fins at 4 days post-amputation (dpa) using an anti-sense (up) or a sense (down) ezh2 probe performed on 6 months old wild-type (TU) fish.

Dupret et al. -Additional


Jules Bernard-Espina

Mathieu Beraneck

Marc Maier

Michele Tagliabue

Proprioceptive deficits and visual compensation in stroke patients: a theoretical approach to reinterpret upper-limb sensory assessments

This novel classi cation of post-stroke sensory de cits may lead to innovative approaches to stroke assessment and rehabilitation. Targeted training of proprioception and/or cross-reference transformations, depending on the patient's speci c sensory de cit, may be key to improved recovery. Furthermore, correlations between lesion site and size with behavioral performance in various tasks could bring new insights to identify neural networks that are speci c to proprioception or cross-reference processing.

Perspectives

5

STG

SMG

IPS SPL S1 M1

Reinterpreting the relation between cerebral structures [5,6] and proprioceptive functions in the light of our theoretical approach provides a novel rationale for an improved strati cation of stroke patients [3]. ''Pure'' proprioceptive processing (W-AP tasks) appears to involve mainly S1, whereas tasks requiring cross-reference processing involve the regions within the superior temporal and posterior parietal cortex: -Superior Temporal Gyrus (STG) -Supramarginal Gyrus (SMG) -Superior Parietal Lobule (SPL) -Intraparietal Sulcus (IPS) This categorization of clinical tests, together with optimal sensory integration modeling, can reconcile the apparently contradictory results of a large number of clinical studies and can explain why di erent tests lead, in the same patients, to di erent outcomes.

Insights from lesion and fMRI studies

Based on the literature, we identi ed 3 categories of post-stroke sensory de cits:

-Purely proprioceptive (P) -Purely cross-reference (C) -Mixed (P+C)

A. Proprioceptive tasks:

We predicted the variability of the behavioral performance of stroke patients in the 4 categories of tasks depending on the sensory de cit (P, C or P+C).

B. Visuo-proprioceptive tasks:

This theoretical approach can also predict the ability or inability [4] of patients to compensate for the proprioceptive de cits using vision.

Results

Within-arm (W-AP) Between-arms symmetric (sB-AP) Cross-modal (C-MP) Between-arms asymmetric (aB-AP)

(e.g. position matching task) (e.g. mirror matching task) (e.g. thumb localizing task) (e.g. reaching task eyes closed)

categories of clinical tests were identi ed:

Proprioceptive de cits are very common in post-stroke patients, and contribute to the motor de cits.

We postulated that some clinical assessments might confound proprioceptive and cross-reference functions.

The latter can add variability in the movement to be performed during the assessment task, and could be, misleadingly, interpreted as a proprioceptive de cit [3]. When reaching an object, experimental evidence suggests that object-related and hand-related visual and proprioceptive signals, such as object-and hand-position, are compared in multiple, parallel reference frames [1], i.e. in retinal (ΔR) and joint (ΔJ) reference frames respectively.

Post

If hand and object positions cannot be compared within the same frame of reference, the brain can encode the position of the hand, originally encoded in the joint space, in the visual space (and vice versa) [1].

This process is referred to as cross-reference transformations.

Even in the absence of vision, proprioceptive signals can be re-encoded in visual space, or relative to another reference frame (gravity, trunk...) [2]. Proprioceptive de cits and visual compensation in stroke patients:

a theoretical approach to reinterpret upper-limb sensory assessments.

: reinterpretation of experimental observations 3

 3 Direct

Multisensory processing: theoretical framework 1 CNRS

 1 UMR 8002 -INCC, Université Paris Cité J Bernard-Espina, MA Maier, M Beraneck, M Tagliabue