Natan Monvoisin

Elizabeth Hemsley

Lucas Laplanche

Guilhem Almuneau

Stéphane Calvez
email: scalvez@laas.fr

Antoine Monmayrant

Improved oxide VCSEL aperture inspection using hyperspectral imaging

Oxide-aperture Vertical-cavity Surface-Emitting Lasers (VCSELs) are the prime light sources used in data centres, and are becoming increasingly embedded in optical sensors such as for LIght Detection And Ranging (LIDAR) or 3D (facial) recognition [START_REF] Dallesasse | III-V Oxidation: Discoveries and Applications in Vertical-Cavity Surface-Emitting Lasers[END_REF]. Central to their fabrication and to their electrical and optical characteristics is the tight control over the oxide aperture, the latter being created by the selective lateral thermal oxidation of a thin layer of semiconducting AlGaAs buried in the middle of the VCSEL vertical stack into an insulating oxide (AlOx) material [START_REF] Dallesasse | Oxidation of Al-bearing III-V materials: A review of key progress[END_REF]. If real-time in-situ monitoring systems using either a white-light or a single narrowband illumination and a near infrared camera [START_REF] Feld | In situ optical monitoring of AlAs wet oxidation using a novel lowtemperature low-pressure steam furnace design[END_REF], [START_REF] Almuneau | Real-time in situ monitoring of wet thermal oxidation for precise confinement in VCSELs[END_REF] have been implemented to address this issue, there are still particular combinations of VCSEL stacks and process conditions that make the oxide aperture detection difficult.

In this submission, we report the improvement in the oxide aperture measurement brought by using hyperspectral imaging techniques. Practically, we have built an illumination source, based on a supercontinuum laser source and a digital micromirror device (DMD), whose spectrum can be shaped at will. Top-view images of the aperture of an already-oxidized VCSEL sample were acquired under static in-situ inspection conditions at room temperature (see Fig. 1a) and subsequently compared. Three types of illuminations were used, respectively, panchromatic lighting, which corresponds to the white-light broadband case, monochromatic illumination for which the spectrum is restricted to the narrow (~5 nm) spectral band giving maximum contrast between the AlOx and AlGaAs areas, and the shaped illumination, where the spectrum is proportional to the positive intensity contrast distribution between these two regions (see Fig. 1b). The most precise oxide aperture edge-detection was achieved using shaped spectrum illumination. Indeed, this illumination enables to make the most between the high-contrast but speckle-altered images of monochromatically-lit scenes and the high-fluence (hence highspeed) recordings usually obtained using panchromatic illumination. The accuracy of the VCSEL oxide aperture measurement was confirmed by Scanning Electron Microscopy (SEM) imaging enabled by a destructive Focus Ion Beam Etching (FIBE) of the top half of the VCSEL stack (Fig. 1c). Future work will be devoted to moving away from the above-described improvement in the static inspection of lateral oxidation to report an adjusted system enabling real-time monitoring.

Fig. 1

 1 Fig. 1 (a) Schematic of the oxidation furnace and in-situ optical monitoring system. (b) The three illumination shapes generated with the spectrally-shaped source used for the VCSEL oxide aperture imaging. (c) Composite image with the overlap of the optical in-situ inspection view obtained with shaped spectrum illumination (upper part), the zoomed FIBE SEM image (bottom center), and a wider-view FIBE SEM image (bottom part).


Coline Marché
email: marche@lma.cnrs-mrs.fr.

Sabine Meunier

Olivier Macherey

Olivier Macherey Pure Tone

may come   PURE TONE INTENSITY DISCRIMINATION AND DYNAMIC RANGE ADAPTATION

Keywords: psychoacoustics, dynamic range, intensity discrimination

Electrophysiological animal studies have shown that in response to a noise fluctuating in level, neurons adapt their dynamic range according to the level distribution. This Dynamic Range Adaptation (DRA) shifts the neurons' input-output growth function towards the most probable levels. The present study investigates the effect of context on intensity discrimination, in search of a perceptual correlate of DRA. Nine normal-hearing participants took part. Intensity difference limens (DLs) were measured for 2-kHz, 50-ms pure tones at 55-and 75-dB SPL, embedded in sequences of 50-ms narrowband non-simultaneous noise with a Gaussian level distribution centered around 55-or 75-dB SPL. The hypothesis was that DRA should yield lower DLs for matched tone and context levels than for unmatched levels. The results showed a significant interaction between tone level and context level but not consistent with DRA: DLs remained larger for the loud than for the soft context for both tone levels. Possible explanations include (i) the use of different stimuli compared to the animal studies, (ii) the presence of off-frequency listening which may lower DLs when the tone level is higher than the context level, and (iii) differences in absolute thresholds between context levels, which may affect DLs more than DRA.

INTRODUCTION

The response function of individual neurons is known to depend on stimulus statistics and, in particular, on the recent stimulus history [START_REF] Costalupes | Effects of continuous noise backgrounds on rate response of auditory nerve fibers in cat[END_REF]. Several studies [START_REF] Dean | Neural population coding of sound level adapts to stimulus statistics[END_REF][START_REF] Dean | Rapid neural adaptation to sound level statistics[END_REF][START_REF] Wen | Dynamic range adaptation to sound level statistics in the auditory nerve[END_REF][START_REF] Wen | Time course of dynamic range adaptation in the auditory nerve[END_REF][START_REF] Watkins | Specialized neuronal adaptation for preserving input sensitivity[END_REF] performed measurements with a continuous noise called context, and showed a shift of the dynamic range of neurons dependent on the context mean level. The context level changed every 50 ms, following a distribution consisting of a highprobability region (HPR), a 10-12 dB range with a high presentation probability, and a low-probability region with all the remaining tested levels. Depending on the HPR's mean level, the horizontal shift of the rate-level function (RLF) places its steepest part near the most probable levels, leading to an increased difference between the spike rates obtained for two nearly probable levels, and thus to the improvement of the coding of HPR levels. This phenomenon is called dynamic range adaptation (DRA). It was observed in small mammals : first in the inferior colliculus of guinea pigs [START_REF] Dean | Neural population coding of sound level adapts to stimulus statistics[END_REF][START_REF] Dean | Rapid neural adaptation to sound level statistics[END_REF], then in the auditory nerve of cats [START_REF] Wen | Dynamic range adaptation to sound level statistics in the auditory nerve[END_REF][START_REF] Wen | Time course of dynamic range adaptation in the auditory nerve[END_REF] and in the auditory cortex of marmosets [START_REF] Watkins | Specialized neuronal adaptation for preserving input sensitivity[END_REF]. The effects observed were smaller in the auditory nerve than in the inferior colliculus [START_REF] Wen | Dynamic range adaptation to sound level statistics in the auditory nerve[END_REF], so it appears that DRA may be enhanced throughout the auditory pathways. Wen et al [START_REF] Wen | Time course of dynamic range adaptation in the auditory nerve[END_REF] focused on the time course of DRA at the level of the auditory nerve. For an increase in HPR, the mean time needed for the shift caused by DRA to happen was of 211 ms, and for a decrease, 262 ms. In general, the range of time constants were comprised between 100 and 400 ms. Several psychophysical tasks have used similar stimulus paradigms to study the effects of the level distribution on loudness discrimination or amplitude modulation detection. However, their results have not been consistent with DRA. For example, Herrmann et al [START_REF] Herrmann | Neural responses and perceptual sensitivity to sound depend on sound-level statistics[END_REF] investigated the effect of experimental context on cortical responses, and on modulation detection in a group of human subjects. They concluded from electroencephalography recordings that some DRA is observable in the human auditory cortex, but for the modulation detection task, performance was better for levels that had a low probability of presentation than for levels in the high probability region. However in this study, the stimuli were separated by silences longer than the time constant of DRA observed by Dean et al [START_REF] Dean | Neural population coding of sound level adapts to stimulus statistics[END_REF] and Wen et al [START_REF] Wen | Dynamic range adaptation to sound level statistics in the auditory nerve[END_REF] (100-ms signals every 500 ms). No perceptual correlate of DRA has thus been observed in humans yet. Here we hypothesize that a consequence of DRA on intensity discrimination tasks should be a lower discrimination threshold when test tones have a similar level as the context compared to when they have different levels. The goal of this experiment is to study the differences in intensity discrimination performance for different level configurations, using a narrowband context with a fluctuating level and pure tone standards.

INTENSITY DISCRIMINATION IN A NARROWBAND CONTEXT

Material and methods

The main experiment was an intensity discrimination task of short pure tones presented in different contexts, using matched and mismatched levels for context and test tones. Only subjects with a threshold at least 10 dB lower than the lower standard level were selected. This ensures that all standards were presented at least at 10 dB SL in the loud context. The hypothesis formulated based on the physiological data from the literature was as follows : discrimination thresholds for test tones and context matched in levels are expected to be lower than for mismatched levels. The mean level of the context being close to the steepest part of the neurons' response function, the representation of small intensity differences should be enhanced in the matched level condition, so discrimination thresholds should be lower.

Results

Intensity discrimination thresholds are presented for each standard level as a function of context type (figures 1 and 2). The data were analyzed in a two-ways repeatedmeasures (rm) ANOVA with factors context level and standard level. Both effects are significant (respectively : F 1,8 = 272.309, p<1e-6 ; F 2,16 = 89.604, p<1e-8), as well as their interaction (F 2,16 = 56.551, p<1e-7). Additional one-way rmANOVA were performed for each standard level, as well as Bonferroni pairwise comparisons.

For the soft standard (figure 1), the results and pairwise comparisons are consistent with the hypothesis : thresholds are significantly higher when the context level is different from the standard level (p<1e-5), and higher in the loud context than in silence (p<1e-4). However for the loud standard (figure 2) there is no difference between context conditions, even though there is a significant effect of context level (one-way rmANOVA on context level for the 75-dB SPL standard, F 2,16 = 5.80, p = 0.013).

DISCUSSION

Our results are only partially consistent with an effect of dynamic range adaptation. Although we did find an interaction between context and standard levels, there was no significant difference in discrimination thresholds between context levels for the loud standard level. There may be several possible explanations for that : 1. Intensity discrimination may rely on other cues than the slope of the rate-level function, so this task may not be adequate to reveal a perceptual correlate of DRA. signals, we used narrowband signals meaning that the levels at the output of auditory filters are much higher in our case. Maybe DRA is not as efficient at these high levels. One solution would be to perform a similar task using broadband signals. Consequences of DRA on perception might be easier to observe when stimulating larger neural populations.

Contrary to animal experiments which used broadband

3. Maybe DRA has an effect in our task but additional processes mask its effect for the loud standard. For example, it is possible that for the low context level, there is some off-frequency listening : as the loud standard is presented at a significantly higher level than the soft context, its excitation pattern is probably broader than that of the context. That may make discrimination thresholds lower than they would really be if subjects were listening only to a restricted frequency range where the context is effective (i.e. around 2000Hz). One solution to test this is to add a notched noise to suppress any clues arising from the spread of excitation. 4. A last possibility is that performance is worse than expected in the loud context-loud standard condition. Ab- solute thresholds increase with context level (tested in preliminary experiments, results not shown), and studies [START_REF] Jesteadt | Intensity discrimination as a function of frequency and sensation level[END_REF][START_REF] Florentine | Intensity discrimination as a function of level and frequency and its relation to high-frequency hearing[END_REF] have shown that discrimination thresholds in dB SL follow the near-miss to Weber's law. As a consequence, an increase in context level can be expected to result in an increase in thresholds : the task with context would be equivalent to a quiet condition but with a softer standard level, yielding higher discrimination thresholds. It is what we observe in figure 1 for the soft standard. However for the loud standard, in figure 2, it is not the case : the lower SL in the loud context does not significantly increase the thresholds, even though a small tendency is observable. It is possible that the higher standard level is simply less affected by the context since it is played at a higher SL than the soft standard in all conditions.

  Discrimination thresholds were obtained with an interleaved 2I-2AFC, 2-down, 1-up adaptive protocol in six conditions. There were two standard levels (55-and 75-dB SPL, respectively labeled soft and loud), which were tested in silence, and in two different mean context levels (55-and 75-dB SPL). The context was a continuous narrowband noise (1880-2120 Hz) played continuously throughout the procedure, except it stopped during the test signals' presentation. The context was divided in 50-ms "epochs", with 5-ms onset and offset half-Hanning windows for smoothing. The context level changed every 50 ms (every epoch), following a Gaussian distribution centered around its mean level, with a standard deviation of 3 dB. The distribution was truncated so the levels were bounded to ± 10 dB around the mean level. The test signals (standards) were 2-kHz pure tones, of duration 50 ms, with 5-ms onset and offset half-Hanning windows for smoothing. The same 500 ms of context were played before both test intervals. Nine normal-hearing participants took part (thresholds below 20 dB HL between 125 and 8000 Hz). All subjects completed a preliminary experiment testing their detec-tion thresholds in the loud context (results not shown).

Figure 1 .

 1 Figure 1. Discrimination thresholds for the soft 55-dB SPL standard, plotted against context type (including silence). The median is presented as a red bar, with the first and third quartile limiting the blue box around it. Whiskers are including all non-outlier values (more than 3 times the interquartile value away from the first or third quartile) that do not fall into the box. The loud (75-dB SPL) context produces significantly higher thresholds than the soft (55-dB SPL) one and the silence.

Figure 2 .

 2 Figure 2. Discrimination thresholds for the loud 75-dB SPL standard, as in figure 1. No significant difference appears between conditions.


Samuel Willingham
email: samuel.willingham@inria.fr

Mårten Sjöström

Christine Guillemot

Prior for Multi-Task Inverse Problems in Image Reconstruction Using Deep Equilibrium Models

Keywords: Inverse Problems, Computer Vision, Image Reconstruction, Deep Equilibrium Models

Inverse problems in imaging consider the reconstruction of clean images from degraded observations, like deblurring or inpainting. These inverse problems are generally ill-posed. Solving them therefore requires regularization, which exists in multiple approaches: plug-and-play (pnp) methods are designed to generically solve any inverse problem by replacing a regularizing proximal operator with a denoiser. Unrolled methods perform a fixed number of iterations and train a network endto-end for a specific degradation, but necessitate re-training for each specific degradation. Deep equilibrium models (DEQs), on the other hand, iterate an unrolled method until convergence and thereby enable end-to-end training on the reconstruction error with simplified back-propagation. We have investigated to what extent a solution for several inverse problems can be found by employing a multi-task DEQ (MTDEQ). This MTDEQ is used to train a prior on the actual estimation error, in contrast to a theoretical noise model used for pnp methods. This has the advantage that the resulting prior is trained for a range of degradations beyond pure Gaussian denoising. The investigation also demonstrates that different search methods can be used in training (forward-backward) and in testing (alternating direction method of multipliers).

I. INTRODUCTION

Inverse problems refer to a broad class of problems which appear in a plethora of image processing and computer vision applications. In imaging, inverse problems refer to the problem of recovering images from a set of degraded or incomplete observations, for instance inpainting, super-resolution, and deblurring. We consider an observed image y = Ax + ε to be the ground truth image x ∈ R d degraded by a degradationoperator A : R d → R d ′ with Additive White Gaussian Noise (AWGN) ε ∈ R d ′ , and d, d ′ ∈ N. This problem is generally ill-posed and can be solved by minimizing

min x 1 2 ∥Ax -y∥ 2 2 + R(x), (1)
where the first term is called the data-term, ∥•∥ 2 is the 2-norm and R : R d → R is a regularization term that is intended to impose prior knowledge on the estimated image. To solve this minimization, the combination of optimization methods and This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 956770. trainable, complex image priors have recently emerged as a powerful tool for image reconstruction.

Plug-and-play (pnp) methods are one approach to combine optimization and trainable priors: a pre-trained, network-based prior is plugged into an iterative optimization algorithm, such as the alternating direction method of multipliers (ADMM) [START_REF] Chan | Plug-and-play admm for image restoration: Fixed-point convergence and applications[END_REF], or the forward backward algorithm (FB) [START_REF] Pesquet | Learning maximally monotone operators for image recovery[END_REF]. These algorithms use a proximal operator to implicitly represent the prior. A proximal operator is defined as

prox σ 2 R (z) := argmin x 1 2 ∥x -z∥ 2 2 + σ 2 R(x). (2)
In the Gaussian case, this proximal operator for regularization solves a Gaussian denoising problem, so [START_REF] Venkatakrishnan | Plug-and-play priors for model based reconstruction[END_REF] explains that the proximal operator can be replaced with a denoiser, because the proximal operator does not have to be exact and it is sufficient for it to decrease the underlying objective function. This approach has led to successful, general imagereconstruction methods [START_REF] Chan | Plug-and-play admm for image restoration: Fixed-point convergence and applications[END_REF]- [START_REF] Zhang | Plugand-play image restoration with deep denoiser prior[END_REF], but it is worth considering that the regularizing proximal operator can be quite different from a Gaussian denoiser when its input is not Gaussian -as is the case for pixel-wise completion with no AWGN. Priors can take several other forms, such as approximations of a projection operator on a learned image subspace as in [START_REF] Chang | One network to solve them all-solving linear inverse problems using deep projection models[END_REF]. Another well known approach is called regularization by denoising (RED) [START_REF] Romano | The little engine that could: Regularization by denoising (red)[END_REF]. This approach uses a Laplacian regularizer that represents the cross-correlation between an estimated image and its denoising residual produced by some pre-trained denoiser. Finally, there are other ways to leverage pre-trained priors for regularization, e.g. Regularizing Gradient (pnp-ReG) [START_REF] Fermanian | Learned gradient of a regularizer for plug-and-play gradient descent[END_REF], which trains the gradient of a Maximum A Posteriori regularizer jointly with its corresponding denoiser to be used in a gradient-based iterative algorithm. Pre-trained priors have the advantage of being generic in the sense that they can be used for any inverse problem without re-training. However, being trained independently of the task at hand, pnp methods may not result in optimal performance.

Unrolled optimization methods are less general in application, but by coupling optimization algorithms with end-toend trained regularization, they recently emerged as powerful solutions to inverse problems [START_REF] Diamond | Unrolled optimization with deep priors[END_REF]- [START_REF] Sun | Deep admm-net for compressive sensing mri[END_REF]. Similar to pnp methods, the neural network (NN) is used to regularize the inverse problem. However, training such unrolled NNs end-to-end can come with a large memory footprint and unrolled methods do not generally train the underlying prior, because they have a fixed number of iterations and do not generally converge [START_REF] Gilton | Deep equilibrium architectures for inverse problems in imaging[END_REF].

In the context of image reconstruction, deep equilibrium (DEQ) models [START_REF] Gilton | Deep equilibrium architectures for inverse problems in imaging[END_REF]- [START_REF] Ling | Global convergence of over-parameterized deep equilibrium models[END_REF] can be seen as an extension of unrolled methods to with a theoretically infinite amount of iterations -a mathematical description is found in [START_REF] Bai | Deep equilibrium models[END_REF]. DEQ models leverage fixed-point properties (convergence for overparametrized structures is shown in [START_REF] Ling | Global convergence of over-parameterized deep equilibrium models[END_REF]), allowing for simpler back-propagation, which can even be done in a Jacobian-free manner [START_REF] Fung | Fixed point networks: Implicit depth models with jacobian-free backprop[END_REF], visualized in Fig. 1.

DEQ models allow the training of an iterative method on the resulting reconstruction-error [START_REF] Gilton | Deep equilibrium architectures for inverse problems in imaging[END_REF], while still training the full iterative method instead of limiting the amount of iterations. While the Gaussian assumption made for pnp does provide good results [START_REF] Chan | Plug-and-play admm for image restoration: Fixed-point convergence and applications[END_REF]- [START_REF] Zhang | Plugand-play image restoration with deep denoiser prior[END_REF], it is worth exploring how one could improve the training of a plug-and-play prior, as the noise generated by a data-step in ADMM or FB is generally not Gaussian in nature. DEQ models allow for this by allowing end-to-end training the full iterative scheme on the reconstruction error. The contributions of this paper are:

• An MTDEQ model is used to train a network for multi-task proximal regularization on the resulting reconstruction-error, resulting in competitive performance.

• We demonstrate that the resulting MTDEQ-prior outperforms a Gaussian denoiser when used in pnp-ADMM, especially when the input to the regularization is very different from an image that is perturbed by AWGN. • Using hyper-parameters that were set up for the pnp-ADMM with a Gaussian denoiser to test the MTDEQprior shows that it is flexible with respect to hyperparameters.

• Training a prior with the FB algorithm and testing it in a pnp-ADMM algorithm shows the trained regularization is not constrained to the scheme it was trained in.

II. METHODS

We propose the MTDEQ model as a method of training a multi-task prior that can be used for different problems and different noise-levels. Since DEQ models can train a regularization for an inverse problem on the resulting reconstructionerror, we train a multi-task regularizer by exposing the NN to different degradations and noise-levels in training.

To solve the inverse problem for multiple tasks, we use the FB algorithm in conjuction with the DEQ model on a range of noise-levels and degradations, resulting in our MTDEQ model.

We chose the FB algorithm for training, because it does not rely on a proximal operator for the minimization of the dataterm.

Algorithm 1 MTDEQ

Require: Training Data D ⊂ R d , d ∈ N >0 Set of problems A ⊂ {A : R d → R d | d ∈ N >0 } Set of noise-levels Σ ⊂ R
Jacobian-free back-propagation procedure Optim Resizing procedure P : R d → R d for a number of epochs do for x ∈ D do for i = 1, ..., N do

(A i , σ i ) picked from A × Σ AWGN ε i ∈ R d with standard deviation σ i y i ← A i (x) + ε i ▷ Generate degraded images z i ← P (y i ) while 1 d ∥z i -f i,θ (z i )∥ 2 2 ≥ 10 -7 do z i ← f i,θ (z i ) ▷ Find equilibrium point end while L i ← 1 d ∥f i,θ (z i ) -x∥ 2 2 end for L ← 1 N N i=1 L i ▷ Sum losses for all problems θ ← Optim(θ, L)
▷ Update NN-parameters end for end for

The MTDEQ that trains the prior is described in algorithm 1. For each ground truth image x, we pick N degradations and noise-levels at random, leading to N degraded and noisy observations. This in turn leads to N estimates produced by the iterative procedure used. We use the FB algorithm in this training of the prior:

f i,θ (z) := Q θ,σi z -η δ 1 2 ∥A i z -y i ∥ 2 2 δ z , (3)
where Q θ,σ represents regularization in form of a DRUNet (as in [START_REF] Pendu | Preconditioned plug-and-play admm with locally adjustable denoiser for image restoration[END_REF] and [START_REF] Zhang | Plugand-play image restoration with deep denoiser prior[END_REF]) with parameters θ used on noise-level σ i ; η ∈ R is a step size. The iteration in the while-loop results in an equilibrium point z ∞ i ∈ R d , which is the estimated reconstructed image. The loss L i for each of the N estimates is averaged and then used for Jacobian-free back-propagation, which finds a direction of descent p that minimizes the loss for the N degradation problems considered:

p = 1 N N i=1 ∂l(z, x) ∂z z=z ∞ i ∂f i,θ (z ∞ i ) ∂θ , (4)
where

l(z, x) = 1 d ∥z -x∥ 2 2 .
The NN is exposed to different degradations in training, and is so guided to represent a regularizer, as the data-fidelity step (i.e. the gradient descent on the data-term) takes care of degradation-dependent operations. Because a DEQ model iterates until convergence, the resulting NN represents a prior for the problem at hand that is not limited to the specific architecture used. This means that if the regularizer is end-toend trained while being exposed to different degradations and noise-levels, we can strive to train a more general prior that contains information on what proper clean images look likebeyond the assumption that a proximal regularization behaves like a Gaussian denoiser.

III. EXPERIMENTS

A. Step-sizes and degradations

We chose a step-size of η = 0.49 in the FB algorithm for the MTDEQ model. The noise-standard-deviations considered in training are taken from Σ noise = {0.005 • s | s = 0, 1..., 49} (pixel-values are normalized to be in [0, 1]). The degradations used for training are:

• super-resolution by using bicubic down-sampling with factor f downscale ∈ {1, 2, 3, 4}, where the iterations are initialized using bilinear resizing to the original size • blurring with a Gaussian kernel with standard-deviation σ blur picked from Σ blur = {0.

B. Dataset, architecture and optimizer

The dataset used in training is a collection of BSD500 (300 images [START_REF] Arbelaez | Contour detection and hierarchical image segmentation[END_REF]), flick2k (2650 images [START_REF] Lim | Enhanced deep residual networks for single image super-resolution[END_REF]), the Waterloo exploration database (4744 images [START_REF] Ma | Waterloo exploration database: New challenges for image quality assessment models[END_REF]) and DIV2k (900 images [START_REF] Agustsson | Ntire 2017 challenge on single image super-resolution: Dataset and study[END_REF]), similar to the one used in [START_REF] Pendu | Preconditioned plug-and-play admm with locally adjustable denoiser for image restoration[END_REF], [START_REF] Zhang | Plugand-play image restoration with deep denoiser prior[END_REF], [START_REF] Fermanian | Learned gradient of a regularizer for plug-and-play gradient descent[END_REF]. When an image is drawn from the dataset, it is cropped to be 128 times 128 pixels in size (the location of this cropping is random at each iteration).

The NN used is a DRUNet that uses the noise-level-map as additional input as in [START_REF] Zhang | Plugand-play image restoration with deep denoiser prior[END_REF]; it is pre-trained as a Gaussian denoiser, using the NN obtained in [START_REF] Zhang | Plugand-play image restoration with deep denoiser prior[END_REF]. The noise-standarddeviation given as input in each regularization step of the FB algorithm is σ denoise = ησ noise , where σ noise ∈ Σ noise is the noise-level considered. Back-propagation is done in a Jacobian-free manner [START_REF] Fung | Fixed point networks: Implicit depth models with jacobian-free backprop[END_REF].

The algorithm is considered to have converged after the mean square error (MSE) of the difference between iterates is less than 10 -7 and we capped the amount of iterations at 350. Further, we terminate iteration if any coordinate of the estimate has an absolute value larger than 10 10 . In training, the procedure properly converges before 350 iterations and without any coordinate exceeding 10 10 in more than 99% of cases.

The weights of the NNs are updated using the adam optimizer [START_REF] Kingma | Adam: A method for stochastic optimization[END_REF] with a batch-size of 16, using 250 epochs, starting with a learning-rate of 10 -5 and scaling it by a factor of 0.25 every 25 epochs.

C. Comparing to plug-and-play

We compare our prior to RED, pnp-ADMM with a Gaussian denoiser and pnp-ReG by plugging the prior resulting from the MTDEQ into the ADMM algorithm as described and used for testing in [START_REF] Fermanian | Learned gradient of a regularizer for plug-and-play gradient descent[END_REF]. The number of iterations, minimal denoising standard-deviation σ 0 and maximal denoising standarddeviation σ m used in the ADMM are the ones that produced the best results for the pnp-ADMM reference method based on a Gaussian denoiser and are listed in [START_REF] Fermanian | Learned gradient of a regularizer for plug-and-play gradient descent[END_REF]. This means that the hyperparameters were not fine-tuned for the MTDEQ-prior. The degradations that the MTDEQ model was trained on are Gaussian deblurring, dropped pixels and super-resolution on an image that was down-sampled using a bi-cubic kernel; this is significant because one of the degradations tested is super- resolution on a image that is degraded using a Gaussian kernel (with σ blur = 0.5). The results can be seen in Tables I and II and the visual results can be observed in Fig. 2. The pnp-ADMM is the closest comparison to our MTDEQ-prior, since it uses the same algorithm in testing, only with a Gaussian denoiser as prior.

ST Comp and ST SR are single-task DEQ priors trained using the MTDEQ with the following parameters: Both have N=1 and ST Comp is trained for A only containing pixelwise completion with probability p drop = 0.9 and no AWGN (i.e. Σ noise = {0.00}). ST SR is trained for A containing only bicubic down-sampling with factor f downscale = 2 and AWGN of Σ noise = {0.01}. In testing, both single-task priors were plugged into the pnp-ADMM scheme from [START_REF] Fermanian | Learned gradient of a regularizer for plug-and-play gradient descent[END_REF] with the same parameters as the Gaussian denoiser and our MTDEQ-prior.

The following section will discuss the results found from the above experiments and talk about the advantages and disadvantages of our MTDEQ-prior when compared to other methods.

IV. RESULTS AND DISCUSSION

Using the MTDEQ model to train on different degradations and noise-levels leads to a multi-task prior usable for iterative methods, like the pnp-ADMM algorithm we use for testing. Different from pnp training, the prior trained with MTDEQ is exposed to a larger range of qualitatively different inputs (i.e. images that are not purely perturbed by AWGN).

The results were obtained using a different iterative algorithm from the one used to train the MTDEQ-prior. This means that the NN represents a regularization that is not closely linked to the exact structure of the iterative algorithm used and can be said to represent an image prior for the problems at hand.

As discussed in III-A, the MTDEQ-prior is trained for a single step size and still performs well when used in the fine-tuned setting of the pnp-ADMM algorithm [START_REF] Fermanian | Learned gradient of a regularizer for plug-and-play gradient descent[END_REF], where different step-sizes and denoising-levels are used for different degradations. This suggests that the method could be further improved, if one could find a correspondence between different degradations and step-sizes to be used for the MTDEQ.

The proposed MTDEQ-prior performs well on multi-task image reconstruction and this is obvious on problems with no AWGN added to the input, where the degradation itself is responsible for the entire difference between observation and ground truth. This is quite reasonable, because the best denoiser for a zero-noise-problem is the identity, which provides no regularization at all. Pnp methods usually remedy this by using a low denoising-level instead of zero, so the denoiser still provides some regularization. A trick of this sort is not necessary for a regularizer that was trained on the reconstruction error, as it can learn to add meaningful regularization, even when the "noise-level-map" is set to zero. Also, the closer the inverse problem is to a Gaussian denoising problem, the more appropriate a Gaussian denoiser is for the purpose of regularization. Thus, it can be seen that the use of a Gaussian denoiser for proximal pnp methods can be further improved using DEQ, especially when the inverse problems considered differ significantly from pure Gaussian denoising problems.

Single-task DEQ models do not perform especially well when compared in a pnp-ADMM algorithm, but we have seen that a single-task DEQ model clearly outperforms the MTDEQ on the problem and noise-level it was trained on, when used in FB. While the comparisons in Tables I and II are unfair to single-task DEQ models because they are only trained for a single noise-level and pnp-ADMM uses scaling denoisinglevels, the comparisons showcase that the MTDEQ model adds significant performance when used on a range of noise-levels and degradations. Thus, the multi-task training-structure does add performance besides the performance single-task DEQ models bring to the table.

We consider the pnp-ADMM using a Gaussian denoiser for proximal regularization to be the closest comparison to our prior, as the only difference is the used regularization. When comparing the reconstruction results for the pnp-ADMM which uses a Gaussian denoiser and our MTDEQ-prior, it is clear that the MTDEQ-prior produces better performance across all the degradations and noise-levels tested, meaning that using an MTDEQ model to fine-tune a prior beyond a Gaussian denoiser does indeed increase performance.

As the DEQ requires iterating until convergence before allowing updates to the weights, it is significantly slower in training when compared to a denoiser, which only has one forward-operation. Combining the training objectives of a denoiser with the loss function used by a MTDEQ model approach may allow for a speed up in training while further improving performance.

V. CONCLUSION Among the different ways of solving inverse problems, DEQ models permit end-to-end training of a regularization and are well-suited to solve multi-task inverse problems, bridging the gap between end-to-end trained methods like unrolled models or single-task DEQ models and pnp methods: An MTDEQ model can be used to train a multi-task prior that outperforms a Gaussian denoiser in a pnp-ADMM scheme.

Fig. 1 .

 1 Fig.1. Traditional back-propagation and Jacobian-free back-propagation[START_REF] Fung | Fixed point networks: Implicit depth models with jacobian-free backprop[END_REF] (only back-propagates through one step using the fixed-point x∞ as input).

  (a) Example for completion with 90 percent of pixels dropped and σ noise = 0. (b) Example of Gaussian deblurring with σ blur = 1.6 and σ noise = 0.01. (c) Example for bicubic super-resolution with factor two and σ noise = 0.01.

Fig. 2 .

 2 Fig.2. Image-comparisons with RED[START_REF] Romano | The little engine that could: Regularization by denoising (red)[END_REF], pnp-ADMM with the Gaussian denoiser from[START_REF] Zhang | Plugand-play image restoration with deep denoiser prior[END_REF] (Gauss), pnp-ReG[START_REF] Fermanian | Learned gradient of a regularizer for plug-and-play gradient descent[END_REF], and pnp-ADMM with the prior obtained via MTDEQ; results are reported in PSNR.

  4, 0.8, 1.2, 1.6, 2.0, 2.4} • pixel-wise completion with each pixel having a chance of p drop ∈ {0.2, 0.4, 0.5, 0.6, 0.8, 0.9} of being droppedeach selection of p drop corresponds to a different degradation Each image is degraded by 5 degradations and the resulting losses are averaged for back-propagation, meaning one ground-truth image is degraded five ways.

TABLE I COMPARING

 I OUR MTDEQ-BASED PRIOR USED IN PNP-ADMM ON THE SET5 DATASET[START_REF] Bevilacqua | Lowcomplexity single-image super-resolution based on nonnegative neighbor embedding[END_REF] FOR COMPLETION WITH σNOISE = 0 AND 80 AND 90 PERCENT OF PIXELS DROPPED, RESPECTIVELY AS WELL AS AND GAUSSIAN DEBLURRING WITH DIFFERENT DEGREES OF BLURRING AND σNOISE = 0.01. ST COMP AND ST SR ARE SINGLE-TASK DEQ PRIORS TESTED IN PNP-ADMM (SEE III-C). THE RESULTS FOR EGULARIZATION BY DENOISING (RED)[START_REF] Romano | The little engine that could: Regularization by denoising (red)[END_REF], PNP-ADMM WITH THE GAUSSIAN DENOISER (GAUSS) FROM[START_REF] Zhang | Plugand-play image restoration with deep denoiser prior[END_REF] AND PNP-REG[START_REF] Fermanian | Learned gradient of a regularizer for plug-and-play gradient descent[END_REF] ARE TAKEN FROM[START_REF] Fermanian | Learned gradient of a regularizer for plug-and-play gradient descent[END_REF]. ALL RESULTS ARE REPORTED IN PEAK-SIGNAL-TO-NOISE-RATIO (PSNR) AND DB. THE HIGHEST PSNR PER TASK IS WRITTEN BOLD AND THE SECOND-BEST IS UNDERLINED.

	Methods		Completion	Deblurring
			80%	90%	σ blur = 1.6 σ blur = 2.0
	RED		27.17	22.75	31.76	30.62
	ST Comp	30.24	26.71	31.92	30.68
	ST SR		29.48	24.96	32.38	31.43
	Gauss		30.20	26.20	32.06	30.88
	pnp-ReG		30.36	26.94	32.51	31.19
	Proposed		30.72	27.09	32.82	31.83
	Proposed vs. Gauss +0.52 +0.89	+0.76	+0.95
				TABLE II
	THIS TABLE SHOWS THE RESULTS FOR SUPER-RESOLUTION ON AN IMAGE
	THAT WAS DOWN-SAMPLED USING A GAUSSIAN KERNEL WITH
	σBLUR = 0.5 AND THE RESULTS FOR SUPER-RESOLUTION ON A
	BICUBICALLY DOWN-SAMPLED IMAGE. THESE DEGRADATIONS WERE
	TESTED ON TWO NOISE-LEVELS AND WITH SUPER-RESOLUTION FACTORS
		TWO AND THREE, RESPECTIVELY.
				Bicubic	Gaussian
		Methods		w/ σ noise	w/ σ noise
				0.00	0.01	0.00	0.01
		RED		35.05	33.78	34.99	32.84
	2x SR	ST Comp ST SR Gauss		34.07 35.71 35.20	33.55 34.29 33.80	33.42 35.57 35.14	32.46 33.23 32.74
		pnp-ReG		35.34	34.29	35.30	33.41
		Proposed		35.61	34.43	35.42	33.45
		Proposed vs. Gauss +0.41 +0.63 +0.28 +0.71
		RED		31.47	30.78	31.44	30.05
	3x SR	ST Comp ST SR Gauss		30.69 32.08 31.49	30.09 30.97 30.39	30.28 31.97 31.45	28.80 30.02 29.17
		pnp-ReG		31.75	31.13	31.60	30.39
		Proposed		32.10	31.15	31.94	30.17
		Proposed vs. Gauss +0.61 +0.76 +0.49 +1.00


John James

Artem I Fokin

Dmitry Y Guschin

Hong Wang

Anna Polesskaya

Svetlana N Rubtsova

Christophe Le Clainche

Pascal Silberzan

Alexis M Gautreau
email: alexis.gautreau@polytechnique.edu

Stéphane Romero
email: srstephane.romero@polytechnique.edu

Vinculin Antagonizes Branched Actin in Controlling Membrane Protrusion, Cell Migration and Cell Cycle Progression

Keywords: Vinculin, Arp2/3, lamellipodium, cell cycle progression, adherens junctions, Ecadherin

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INTRODUCTION

Actin dynamics control cell shape, adhesion and migration [START_REF] Pollard | Actin, a central player in cell shape and movement[END_REF].

Actin filaments form linear and branched arrays [START_REF] Le Clainche | Regulation of actin assembly associated with protrusion and adhesion in cell migration[END_REF]. Whereas branched actin arrays generate pushing forces through the Arp2/3 complex, linear arrays can generate pulling forces through myosin-mediated contractility [START_REF] Pollard | Actin and Actin-Binding Proteins[END_REF][START_REF] Garrido-Casado | Nonmuscle Myosin II Regulation Directs Its Multiple Roles in Cell Migration and Division[END_REF]. Indeed, cell migration requires a combination of forces to drive protrusion of the plasma membrane and to pull on the substratum [START_REF] Blanchoin | Actin Dynamics, Architecture, and Mechanics in Cell Motility[END_REF].

The RAC1-WAVE-Arp2/3 pathway drives membrane protrusions [START_REF] Papalazarou | The cell pushes back: The Arp2/3 complex is a key orchestrator of cellular responses to environmental forces[END_REF][START_REF] Bieling | From WRC to Arp2/3: Collective molecular mechanisms of branched actin network assembly[END_REF]. This pathway is embedded in positive feedback loops that sustain the membrane protrusion at the front edge of a migrating cell and increases the persistence of migration [START_REF] Krause | Steering cell migration: lamellipodium dynamics and the regulation of directional persistence[END_REF]. Signaling from branched actin at the cell cortex is also critical for cells to progress into the cell cycle by impinging on tumor suppressor genes controlling the G1/S transition [START_REF] Molinie | Cortical branched actin determines cell cycle progression[END_REF]. Various Arp2/3 complexes coexist in the same cells through the combinatorial assembly of paralogous subunits [START_REF] Pizarro-Cerdá | The Diverse Family of Arp2/3 Complexes[END_REF]. For example, ARPC1B-containing Arp2/3 complexes are more efficient at nucleating branched actin and at forming stable branched junctions than ARPC1Acontaining Arp2/3 complexes [START_REF] Abella | Isoform diversity in the Arp2/3 complex determines actin filament dynamics[END_REF]. ARPC1B-containing Arp2/3 complexes, but not the ones containing ARPC1A, generate cortical branched actin that drives persistent migration and delivers a signal for cell cycle progression [START_REF] Molinie | Cortical branched actin determines cell cycle progression[END_REF].

Vinculin is recruited by mechanosensitive proteins that sense forces exerted in cell adhesions and responds to these forces by reinforcing the linear arrays of actin filaments attached to cell adhesions [START_REF] Bays | Vinculin in cell-cell and cell-matrix adhesions[END_REF]. Vinculin is composed of a head that interacts with adhesion proteins and a tail that binds to actin filaments [START_REF] Humphries | Vinculin controls focal adhesion formation by direct interactions with talin and actin[END_REF][START_REF] Le Clainche | Vinculin Is a Dually Regulated Actin Filament Barbed End-capping and Side-binding Protein[END_REF]. This ability of vinculin to link actin filaments to adhesion sites is inhibited by an intra-molecular interaction masking relevant binding sites of the head and the tail [START_REF] Atherton | Mechanosensitive components of integrin adhesions: Role of vinculin[END_REF]. In adhesions to the extracellular matrix (ECM), vinculin head is recruited to cryptic binding sites in talin that are exposed upon stretching due to myosinmediated contractility [START_REF] Del Rio | Stretching single talin rod molecules activates vinculin binding[END_REF][START_REF] Ciobanasu | Actomyosin-dependent formation of the mechanosensitive talin-vinculin complex reinforces actin anchoring[END_REF]Yao et al., 2014a). Vinculin head is similarly recruited to a cryptic binding site of a-catenin at cell-cell adhesions upon myosin-mediated contractility of actin filaments (Yao et al., 2014b;[START_REF] Seddiki | Force-dependent binding of vinculin to α-catenin regulates cell-cell contact stability and collective cell behavior[END_REF][START_REF] Vigouroux | Talin dissociates from RIAM and associates to vinculin sequentially in response to the actomyosin force[END_REF]. Force-dependent recruitment of vinculin results in its activation allowing vinculin tail to link additional actin filament and thereby reinforce the cytoskeletal attachment of cell adhesions. In the process, vinculin mechanotransduces signals, since vinculin-depleted cells exhibit enhanced proliferation, survival and anchorage-independent growth [START_REF] Fernández | Suppression of vinculin expression by antisense transfection confers changes in cell morphology, motility, and anchorage-dependent growth of 3T3 cells[END_REF][START_REF] Subauste | Vinculin modulation of paxillin-FAK interactions regulates ERK to control survival and motility[END_REF][START_REF] Dewane | Vinculin Y822 is an important determinant of ligand binding[END_REF].

The cytoskeleton reinforcement function of vinculin is in line with the fact that cell adhesions mature over time. Adhesions to the ECM mature from Nascent Adhesions at the edge of membrane protrusions into focal adhesions (FAs) as the leading edge moves forward and myosin motors exert contractility on newly formed adhesions [START_REF] Depasquale | Accumulation of talin in nodes at the edge of the lamellipodium and separate incorporation into adhesion plaques at focal contacts in fibroblasts[END_REF][START_REF] Alexandrova | Comparative dynamics of retrograde actin flow and focal adhesions: formation of nascent adhesions triggers transition from fast to slow flow[END_REF][START_REF] Thievessen | Vinculin-actin interaction couples actin retrograde flow to focal adhesions, but is dispensable for focal adhesion growth[END_REF]. Similarly, E-Cadherin based adherens junctions (AJs) form initial interdigitations that mature into straight cell-cell adhesions, as contractility develops [START_REF] Kovacs | Cadherin-directed actin assembly: E-cadherin physically associates with the Arp2/3 complex to direct actin assembly in nascent adhesive contacts[END_REF][START_REF] Leerberg | Tension-Sensitive Actin Assembly Supports Contractility at the Epithelial Zonula Adherens[END_REF][START_REF] Li | Actin protrusions push at apical junctions to maintain E-cadherin adhesion[END_REF][START_REF] Li | Cadherin puncta are interdigitated dynamic actin protrusions necessary for stable cadherin adhesion[END_REF]. Vinculin was shown in vitro to remodel branched actin networks into bundles [START_REF] Boujemaa-Paterski | Talin-activated vinculin interacts with branched actin networks to initiate bundles[END_REF]. In this context, the reported interaction of vinculin with Arp2/3, the major player in protrusion formation, is particularly intriguing.

Vinculin binds to the Arp2/3 complex through the linker that connects its head to its tail [START_REF] Demali | Recruitment of the Arp2/3 complex to vinculin: coupling membrane protrusion to matrix adhesion[END_REF]. This linker is not masked by the head-to-tail intramolecular interaction [START_REF] Borgon | Crystal Structure of Human Vinculin[END_REF], suggesting that the interaction should be independent from vinculin activation. Subsequently, 'vinculin-Arp2/3 hybrid complexes' were purified from chicken smooth muscles [START_REF] Chorev | Regulation of focal adhesion formation by a vinculin-Arp2/3 hybrid complex[END_REF]. These hybrid complexes lack subunits of the canonical Arp2/3, namely ARPC1, ARPC4 and ARPC5 subunits. These observations suggest the existence of constitutive vinculin-Arp2/3 complexes. However, the interaction of vinculin with Arp2/3 is regulated by EGF stimulation, RAC1 activity and Src-dependent phosphorylations of vinculin on tyrosine residues that are located far away from the Arp2/3 binding site, but which contribute to vinculin activation [START_REF] Demali | Recruitment of the Arp2/3 complex to vinculin: coupling membrane protrusion to matrix adhesion[END_REF][START_REF] Zhang | The Phosphorylation of Vinculin on Tyrosine Residues 100 and 1065, Mediated by Src Kinases, Affects Cell Spreading[END_REF][START_REF] Moese | The Helicobacter pylori CagA protein disrupts matrix adhesion of gastric epithelial cells by dephosphorylation of vinculin[END_REF][START_REF] Auernheimer | Vinculin phosphorylation at residues Y100 and Y1065 is required for cellular force transmission[END_REF]. The point mutation P878A in vinculin was shown to impair its interaction with Arp2/3 and a re-expression of this mutant in vinculin-null mouse embryonic fibroblasts (MEFs) does not rescue defective protrusions and spreading of these cells, unlike wild type vinculin [START_REF] Demali | Recruitment of the Arp2/3 complex to vinculin: coupling membrane protrusion to matrix adhesion[END_REF]. Together these data suggest that vinculin was required to activate the Arp2/3 and form membrane protrusions.

Here we used epithelial cells to investigate the role of the vinculin-Arp2/3 interaction.

We were able to distinguish the specific subset of functions that the vinculin-Arp2/3 interaction endows, compared with the more general role of vinculin in the cytoskeletal reinforcement of cell adhesions. We found that vinculin antagonizes Arp2/3-dependent branched actin in the control of membrane protrusion, cell migration, cell cycle progression, and that this interaction regulates the stability of cell-cell junctions.

RESULTS

The Vinculin Linker Enhances Membrane Protrusion and Migration Persistence through

Arp2/3 Binding

We first examined the interaction of vinculin with the Arp2/3 complex in the MCF10A cell line, where we have characterized the role of the Arp2/3 complex in cell migration [START_REF] Molinie | Cortical branched actin determines cell cycle progression[END_REF][START_REF] Simanov | Arpin Regulates Migration Persistence by Interacting with Both Tankyrases and the Arp2/3 Complex[END_REF]. MCF10A cells are human mammary epithelial cells, which are immortalized but not transformed [START_REF] Soule | Isolation and characterization of a spontaneously immortalized human breast epithelial cell line, MCF-10[END_REF]. Importantly this cell line is diploid for the most part of its genome [START_REF] Worsham | High-resolution mapping of molecular events associated with immortalization, transformation, and progression to breast cancer in the MCF10 model[END_REF][START_REF] Kadota | Delineating Genetic Alterations for Tumor Progression in the MCF10A Series of Breast Cancer Cell Lines[END_REF]. We found that antibiotic-selected MCF10A cells down-regulated the exogenous expression of tagged full length vinculin in an increasing number of cells over time, but not when the construct was limited to the vinculin linker that connects the head to the tail and which contains the Arp2/3 binding site. We obtained stable MCF10A cell lines expressing the GFP tagged linker of vinculin (amino acids 811-881) or its derivative containing the point mutation P878A that impairs Arp2/3 binding [START_REF] Demali | Recruitment of the Arp2/3 complex to vinculin: coupling membrane protrusion to matrix adhesion[END_REF]. When mutated, the linker indeed bound much less efficiently to the Arp2/3 complex despite an expression level similar to the wild type linker (Fig. 1a). Interestingly, the immunoprecipitate of the vinculin linker contained the Arp2/3 subunit ARPC1B, which is not present in the vinculin-Arp2/3 hybrid complexes that were purified from tissues [START_REF] Chorev | Regulation of focal adhesion formation by a vinculin-Arp2/3 hybrid complex[END_REF], suggesting that in our cell system, vinculin binds to the canonical Arp2/3 complex.

MCF10A cells expressing the wild type linker, but not its P878A derivative, exhibited extensive membrane protrusions at their periphery (Fig. 1b, Supplementary Movie 1). Cells expressing the vinculin linker were significantly more spread (Fig. 1c) and migrated more persistently than parental cells (Fig. 1d,e), two read-outs of cortical polymerization of branched actin. Decreased cell speed and mean square displacement (MSD) were associated with this increased persistence of cell migration (Supplementary Fig. 1). Decreased speed and MSD are often associated with increased cortical branched actin in MCF10A cells, for example when RAC1 is activated by mutation or when the Arp2/3 inhibitory protein Arpin is down-regulated, but not quantitatively correlated [START_REF] Molinie | Cortical branched actin determines cell cycle progression[END_REF]. In contrast, cell migration persistence systematically correlates with increased polymerization of cortical branched actin [START_REF] Dang | Inhibitory signalling to the Arp2/3 complex steers cell migration[END_REF][START_REF] Molinie | Cortical branched actin determines cell cycle progression[END_REF][START_REF] Simanov | Arpin Regulates Migration Persistence by Interacting with Both Tankyrases and the Arp2/3 Complex[END_REF].

We then examined membrane protrusions that power cell migration. Following mCherry-actin expression, we were able to measure speed as well as length of the protrusions, defined as the distance between the protrusion edge and the first transverse arc at the base of protrusions (Fig. 1f). Protrusions were longer and protruded 1.7-fold faster when cells expressed the wild type vinculin linker, but not the P878A derivative (Fig. 1g,h,i). Fluorescent actin also allowed us to image the rearward flow of the cytoskeleton using Total Internal Reflection Fluorescence -Structured Illumination Microscopy (TIRF-SIM, Supplementary Movie 2). We found that the rearward flow, relative to the substratum, was also significantly increased in cells expressing the vinculin linker (Fig. 1h,j) and that translated into a 2-fold faster actin assembly rate, relative to the leading edge (Fig. 1k). In the different cell lines, protrusion efficiency, calculated as the ratio of protrusion speed to actin assembly rate, was similar, indicating that protrusion speed scaled with actin assembly rate (Fig. 1l). These results suggest either that vinculin activates the Arp2/3 complex through the linker domain, or that vinculin inhibits Arp2/3 and the linker behaves as a dominant-negative fragment. Therefore, we produced and purified the vinculin linker in its wild type and P878A forms. In vitro, these proteins did not modify the kinetics of spontaneous actin polymerization, nor the Arp2/3-mediated branched nucleation (Supplementary Figure 2), indicating that the observed effects of the vinculin linker in cells described above results from a dominant negative effect, or requires additional factors or post-translational modifications that are only present in cells in order to regulate Arp2/3.

A Knock-In of the Point Mutation that Impairs Arp2/3-Vinvulin Interaction Phenocopies Vinculin Knock-Out

The two above-mentioned alternative hypotheses prompted us to generate knock-outs of the VCL gene that encodes vinculin. To this end, we transfected MCF10A cells with purified Cas9 and a guide RNA (gRNA) that targets the beginning of the Open Reading Frame (ORF) in the first exon of the VCL gene. Cas9-mediated double strand breaks (DSBs) are frequently repaired by the error-prone non-homologous end joining (NHEJ) mechanism [START_REF] Jasin | The democratization of gene editing: Insights from sitespecific cleavage and double-strand break repair[END_REF]. This method using purified Cas9 and gRNA was sufficiently efficient to identify KO clones without selection by a Western blot-based screen (Fig. 2a). We selected two KO clones with different frameshifts within the two alleles of VCL (Fig. 2b), for further characterization.

As expected, focal adhesions (FAs) of these two clones were not stained by vinculin antibodies (Fig. 2c,d). Paxillin-stained FAs were significantly more elongated, by 60 % on average, in vinculin KO compared with parental cells (Fig. 2e).

To specifically examine the role of the Arp2/3 interaction, we designed a strategy based on homology-directed recombination (HDR) to introduce the P878A point mutation in the endogenous VCL gene of MCF10A cells. We transfected MCF10A cells with 3 plasmids and a long repair oligonucleotide that provides the P878A mutation together with a PvuII restriction site. One of the plasmids provided Cas9, the second plasmid encoded a gRNA that allows Cas9 to cut the VCL gene close to the P878 codon and the third one encoded a gRNA that targets the ATP1A1 gene. ATP1A1 encodes the ubiquitous and essential sodium-potassium ion pump, which is the target of the drug ouabain. The gRNA targets the ATP1A1 region that is directly recognized by ouabain. Upon ouabain treatment, only cells that have repaired the ATP1A1 DSB by NHEJ so as to introduce an in-frame indel, produce an ion pump that is both functional and insensitive to ouabain [START_REF] Agudelo | Marker-free coselection for CRISPR-driven genome editing in human cells[END_REF]. The ouabain selection is more efficient than more classical antibiotic selection of transfected plasmids, because it ensures that Cas9-mediated DSBs are efficiently produced in the selected cells, and not only that the selected plasmid is present. The DSBs in VCL are often repaired by NHEJ, but can also be repaired by HDR using the provided oligonucleotide as a template. After extensive screening of clones by PvuII restriction of the PCR amplified genomic region, we managed to isolate the desired knock-in (KI) clone, where the P878A mutation was introduced in both alleles of VCL (Fig. 2f,g). P878A

vinculin properly localized to FAs (Fig. 2h,i) and did not impact elongation of FAs (Fig. 2j), suggesting that it is functional and that Arp2/3 binding is not required for the FA-related functions of vinculin.

We then evaluated KO and KI clones for their ability to migrate and produce membrane protrusions. Like the MCF10A clone that expressed the vinculin linker, KO clones exhibited more persistent trajectories than parental cells (Fig. 3a,b, Supplementary Movie 3). They were also 20 % more spread than parental cells (Fig. 3e). The KI clone that expresses the vinculin protein containing the P878A substitution displayed a similar, but even more pronounced phenotype of increased persistence and spreading than the KO clones that expressed no vinculin (Fig. 3c-f). This suggests that the vinculin-Arp2/3 interaction is critical for these functions. We then examined membrane protrusions by transiently transfecting our KO and KI clones with mCherry-actin. The length of membrane protrusions was increased in both KO and KI clones compared with parental cells (Fig. 3g,h). The increase was, however, significantly higher in KO than in KI cells for this parameter. When protrusion speed was examined, both KO and KI cells behaved similarly. They displayed 1.6-fold increased protrusion speed compared with parental cells (Fig. 3i,j, Supplementary Movie 4). KO and KI cells also displayed 1.5 and 1.3-fold increased actin rearward flow, respectively, compared with parental cells (Fig. 3i,k). This translated into increased actin assembly rate in both KO and KI cells, compared with parental cells (Fig. 3l). Protrusion efficiency was not significantly different in KO compared with parental cells, but was slightly increased in KI cells (Fig. 3m).

The phenotype induced by the expression of the vinculin linker is similar to the one of vinculin KO. Therefore, we conclude that the vinculin linker is a dominant negative of vinculin.

The interaction of vinculin with Arp2/3 appears critical for the negative regulation that vinculin exerts on membrane protrusion and migration persistence.

Vinculin Controls Stability of Cell-Cell Junctions and Efficiency of Collective Migration

Since vinculin plays a key role in stabilizing cell-cell junctions [START_REF] Bays | Vinculin in cell-cell and cell-matrix adhesions[END_REF], we used our cell system to examine the potential role of vinculin-Arp2/3 interaction in junction stability. We verified that KO cells displayed no vinculin staining at cell-cell junctions (Fig. 4a,b). P878A vinculin of KI cells was recruited as efficiently as the wild type protein in parental cells at a-catenin positive junctions (Fig. 4c,d). Because on 2D substrates such as Petri dishes or glass coverslips, cell-cell interactions were not obviously affected in KO cells, we decided to embed cells into collagen gels to examine cell-cell interactions. In this 3D setting, behaviors of KO cells and parental cells were markedly different. Parental cells rarely dissociated when they met and formed multicellular slugs (Fig. 4e, Supplementary Movie 5). In contrast, interactions between KO cells appeared not to engage them in a multicellular behavior (Fig. 4e). KI cells did not present the asocial behavior of KO cells and formed multicellular "slugs" like parental cells (Fig. 4f, Supplementary Movie 6). From movies, we were able to count the number of events, where a cell disengaged from cell-cell interactions after having met another cell or dissociating from slugs, per unit of time. The counts were then converted into frequencies expressed in s -1 or Hertz. In this 3D setting, the frequency of junction disassembly was about 10-fold higher in KO than parental cells (Fig. 4g). We verified that E-Cadherin expression was not down-regulated in KO cells and that E-Cadherin was properly recruited at cell-cell junctions in KO cells (Supplementary Fig. 3). Vinculin thus regulates the stability of junctions, but not E-Cadherin-dependent cell-cell adhesion. In contrast, in KI cells, the quantification revealed that cell-cell junctions were significantly more stable than those of parental cells, dissociating 2.6-fold less (Fig. 4g).

We then analyzed collective migration of MCF10A, KO and KI cells in a wound healing assay obtained by lifting an insert that initially constrained the monolayer, also referred as "barrier assay" [START_REF] Poujade | Collective migration of an epithelial monolayer in response to a model wound[END_REF]. The front edge of the monolayer of KO cells progressed significantly faster than parental cells and therefore covered the cell-free area more rapidly (Fig. 5a, b, Supplementary Movie 7). KI cells, although slower than KO cells, were also significantly faster than parental cells. Images were then analyzed by Particle Image Velocimetry (PIV) to associate a displacement vector to different (x,y) positions over time [START_REF] Petitjean | Velocity Fields in a Collectively Migrating Epithelium[END_REF]. Cell speed was increased in KO and KI cells, and this increase was transmitted further backwards, away from the edge, when compared with parental cells (Fig. 5c).

The local order parameter, which reflects the local alignment of displacement vectors, was also transmitted further backwards in KO and KI cells when compared with parental cells (Fig. 5d).

In agreement with the fast progression of the front edge of the KO monolayer, the increase in cell speed and local order parameter was transmitted further backwards in the monolayer of KO cells, compared to KI cells. Thus, collective migration was for the most part depending on the mechanical linker function of vinculin, unlike single cell migration.

Vinculin Recruits Arp2/3 at Adherens Junctions and Restricts Cell Cycle Progression through Arp2/3 Binding

We then analyzed Arp2/3 recruitment by immunofluorescence at E-Cadherin positive AJs of KO and KI cells. In parental MCF10A cells, Arp2/3 was enriched at AJs, 6 h after plating, the amount of junctional Arp2/3 reached a maximum 1 day after plating and declined to residual amount after 3 days (Fig. 6a). Vinculin was present at AJs throughout junction maturation, even if it peaked 1 day after plating like Arp2/3 (Supplementary Fig. 4). KO cells displayed reduced Arp2/3 staining at AJs compared with parental cells (Fig. 6b). This was especially striking one day after cell plating, when no junctional Arp2/3 was detected. 6 h after plating, a low amount of Arp2/3 was detected at AJs of KO cells, but KO cells still recruited significantly less Arp2/3 than parental cells (Fig. 6b). In KI cells, Arp2/3 recruitment at AJs was increased 6 h after plating compared with parental cells, and even more so compared with KO cells (Fig. 6c,b). Yet, 1 day after plating, Arp2/3 recruitment at AJs of KI cells was dramatically reduced compared with parental cells, as in KO cells. 3 days after plating, Arp2/3 at AJs is minimum in all 3 types of cells. This kinetic analysis thus reveals two distinct phases of Arp2/3 recruitment at AJs. The early recruitment, at 6 h, only partially depends on the presence of vinculin and on its ability to interact with the Arp2/3. Later recruitment, after one day, fully depends on the presence of vinculin and on its ability to interact with the Arp2/3. Therefore, vinculin appears to retain Arp2/3 at AJs after an initial recruitment of Arp2/3 that does not depend on its interaction with vinculin. Stable MCF10A cell lines expressing GFP fusions with Arp2/3 subunits that are not part of the vinculin-Arp2/3 hybrid complexes revealed a GFP signal enriched at cell-cell junctions, 1 day after cell plating (Supplementary Fig. 5), thus confirming that vinculin interacts with the canonical Arp2/3 complex in MCF10A cells.

Untransformed cells stop proliferating when confluent. This phenomenon commonly called "contact inhibition of proliferation", can be more precisely referred to as density dependence of cell cycle progression, since cells do not stop proliferating as soon as they touch each other, but rather enter less and less frequently into a new cell cycle, as the cell culture becomes denser. We observed that KO and KI cells reached a ~30 % higher saturation density than parental MCF10A cells (Fig. 7a, Supplementary Fig. 6). We then measured the number of cycling cells by estimating the % of cells incorporating EdU, an analog of thymidine incorporated in DNA during S phase. The % of cycling cells steadily decreased as a function of the cell density. KO cells behaved like parental cells, with a high cycling rate at low density and a low cycling rate at high density. However, at an intermediate density, KO cells were significantly more prone to enter into a new cell cycle than parental cells (Fig. 7b). A similar behavior was observed for KI cells (Fig. 7c), suggesting that the mere presence of vinculin was not sufficient to control contact inhibition, vinculin should also be able to interact with the Arp2/3. To confirm this point, we analyzed the density dependence of cell cycle progression MCF10A cells expressing the vinculin linker. Cells expressing the dominant-negative construct exhibited significantly increased cycling even at high cell density (Fig. 7d). In contrast, the P878A mutation in the linker abolished this increased cycling, thus reinforcing the idea that vinculin controls cell cycle progression through its ability to interact with the Arp2/3 complex.

When parental cells were treated with the Arp2/3 inhibitory compound CK-666, cell cycle progression was inhibited in a dose-dependent manner (Fig. 7e). KO and KI cells, as well as MCF10A cells expressing the dominant-negative vinculin linker also displayed a dosedependent inhibition of cell cycle progression, but required more CK-666 to achieve the same level of inhibition (Fig. 7e,f). Cell cycle progression thus appears to be inhibited by vinculin through its effect on Arp2/3 activity, in a manner similar to what occurs for membrane protrusion and persistence of single cell migration.

DISCUSSION

The vinculin-Arp2/3 interaction was first assumed to be a transient regulated interaction that involved the canonical Arp2/3 complex [START_REF] Demali | Recruitment of the Arp2/3 complex to vinculin: coupling membrane protrusion to matrix adhesion[END_REF]. However, alternative assemblies of so-called vinculin-Arp2/3 hybrid complexes have then been discovered [START_REF] Chorev | Regulation of focal adhesion formation by a vinculin-Arp2/3 hybrid complex[END_REF]. Since Arp2/3 subunits analyzed in vinculin immunoprecipitates by DeMali belonged to both canonical and hybrid complexes, it was not known whether the two modes of binding existed or if the vinculin-Arp2/3 interaction only involved assembly of hybrid complexes. In the present study, we unambiguously detected subunits that belong to the canonical Arp2/3 complex, but not to hybrid complexes, in vinculin immunoprecipitates or at cell-cell junctions at a time when vinculin is solely responsible for Arp2/3 recruitment.

Therefore, even if these experiments do not rule out the presence of vinculin-Arp2/3 hybrid complexes in MCF10A cells, they show that the interaction of vinculin with the canonical Arp2/3 complex does exist, as suggested by the original reference. We also favor the interpretation that the roles of the vinculin-Arp2/3 interaction we report here are due to an interaction of vinculin with the canonical Arp2/3 complexes, because these functions in membrane protrusion, migration persistence and cell cycle progression were all previously ascribed to the canonical Arp2/3 complex [START_REF] Wu | Arp2/3 is critical for lamellipodia and response to extracellular matrix cues but is dispensable for chemotaxis[END_REF][START_REF] Suraneni | The Arp2/3 complex is required for lamellipodia extension and directional fibroblast cell migration[END_REF][START_REF] Molinie | Cortical branched actin determines cell cycle progression[END_REF].

Our strategy to compare the phenotypes of KO and KI cells allowed us to distinguish the cytoskeletal linker function of vinculin that only depends on the presence of vinculin, from the vinculin functions that required both vinculin and its interaction with Arp2/3 (Fig. 8). Among the Arp2/3-dependent functions of vinculin in MCF10A cells, we found an inhibition of membrane protrusion and cell spreading. It was reported in the original article mapping the Arp2/3 binding site on vinculin that vinculin KO mouse embryonic fibroblasts (MEFs) had impaired lamellipodia and cell spreading [START_REF] Demali | Recruitment of the Arp2/3 complex to vinculin: coupling membrane protrusion to matrix adhesion[END_REF]. These two phenotypes were rescued by the expression of WT vinculin, but not by the P878A derivative. Our two studies thus implicate the same functions, but with cellular effects in opposite directions.

Similarly, the increased migration persistence we observed in vinculin KO MCF10A cells is in contrast to the decreased persistence observed upon vinculin depletion in MEF KO cells or siRNA-treated mammary carcinoma MDA-MB-231 cells, using different assays [START_REF] Thievessen | Vinculin is required for cell polarization, migration, and extracellular matrix remodeling in 3D collagen[END_REF][START_REF] Rahman | Vinculin regulates directionality and cell polarity in two-and three-dimensional matrix and three-dimensional microtrack migration[END_REF][START_REF] Lee | Vinculin and metavinculin exhibit distinct effects on focal adhesion properties, cell migration, and mechanotransduction[END_REF]. Even if the migration phenotypes of vinculin depleted cells strongly depend on cell types and precise assay conditions, in particular 2D vs. 3D conditions [START_REF] Fernández | Suppression of vinculin expression by antisense transfection confers changes in cell morphology, motility, and anchorage-dependent growth of 3T3 cells[END_REF][START_REF] Mierke | Vinculin Facilitates Cell Invasion into Three-dimensional Collagen Matrices[END_REF][START_REF] Thievessen | Vinculin is required for cell polarization, migration, and extracellular matrix remodeling in 3D collagen[END_REF], it is clear that untransformed epithelial cells MCF10A cells behave in a significantly different manner than the previously examined cell types. Another surprising observation came from the examination of the molecular clutch that connects actin polymerization at the leading edge to cell adhesions to the substratum. In fibroblasts, vinculin has been implicated in mediating the molecular clutch that connects the retrograde flow of actin to cell adhesions to the substratum [START_REF] Thievessen | Vinculin-actin interaction couples actin retrograde flow to focal adhesions, but is dispensable for focal adhesion growth[END_REF][START_REF] Hirata | Force-dependent vinculin binding to talin in live cells: a crucial step in anchoring the actin cytoskeleton to focal adhesions[END_REF]. In our vinculin KO MCF10A cells, however, the increased actin assembly rate at the protrusion edge translates into effective protrusions, with no additional slippage, suggesting that the molecular clutch is mediated by other proteins than vinculin in these epithelial cells. Our epithelial cell system allowed us to examine the role of vinculin at cell-cell adhesions.

We found that vinculin KO MCF10A cells had dramatically decreased stability of AJs when cells were embedded into soft 3D collagen gels, highlighting the interplay between adhesions to the substratum and to the neighboring cells. Vinculin belongs to both cell adhesions, the specific incorporation into cell-cell adhesions being determined by Abl-mediated phosphorylation of Y822 [START_REF] Bays | Vinculin phosphorylation differentially regulates mechanotransduction at cell-cell and cell-matrix adhesions[END_REF]. Decreased cell-cell adhesion upon vinculin KO was recently observed in mouse 4T1 breast cancer line [START_REF] Dewane | Vinculin Y822 is an important determinant of ligand binding[END_REF] and is in line with the aberrant AJs between cardiac myocytes reported in heart-specific KO of vinculin in mice [START_REF] Zemljic-Harpf | Cardiac-Myocyte-Specific Excision of the Vinculin Gene Disrupts Cellular Junctions, Causing Sudden Death or Dilated Cardiomyopathy[END_REF]. Vinculin is an essential component of cell-cell junctions that allows myosin-dependent tensile forces to develop mature junctions [START_REF] Twiss | Vinculin-dependent Cadherin mechanosensing regulates efficient epithelial barrier formation[END_REF]. KI cells do not exhibit unstable AJs and even exhibit more stable AJs than parental cells. Disabling Arp2/3 binding thus appear to increase the function of vinculin in reinforcing AJs. Increased branched actin at early cell-cell junctions can account for the increased junction stability of KI cells, if we assume that branched actin is remodeled in linear arrays for myosin-mediated contractility. Indeed, branched actin is a poor substrate for myosin motors [START_REF] Muresan | F-actin architecture determines constraints on myosin thick filament motion[END_REF], but GMF and coronin proteins were shown to debranch actin networks of lamellipodia [START_REF] Cai | Coronin 1B Antagonizes Cortactin and Remodels Arp2/3-Containing Actin Branches in Lamellipodia[END_REF][START_REF] Haynes | GMF controls branched actin content and lamellipodial retraction in fibroblasts[END_REF] and might play a similar role at cell-cell junctions.

In 2D wound healing assay of MCF10A cells, vinculin KO cells were more efficient at closing the wound than parental cells, as previously reported using 4T1 cells [START_REF] Dewane | Vinculin Y822 is an important determinant of ligand binding[END_REF]. KO MCF10A cells exhibited fast and directional migration towards the wound and transmitted the signal further back in the monolayer, indicating that the mechanotransduction of E-Cadherin dependent cell adhesions that vinculin provides (Le [START_REF] Duc | Vinculin potentiates E-cadherin mechanosensing and is recruited to actin-anchored sites within adherens junctions in a myosin II-dependent manner[END_REF] is not essential to this transmission, and even rather inhibitory. These phenotypes are less prominent when vinculin is present, but with an impaired interaction with Arp2/3, indicating that the vinculin-Arp2/3 interaction is less critical for collective migration than for single cell migration.

Cadherins at AJs were found to be associated with branched actin, which pushes membranes from neighboring cells against one another to initiate cell-cell adhesion or repair unzipped membranes due to excessive tension [START_REF] Efimova | Branched actin networks push against each other at adherens junctions to maintain cell-cell adhesion[END_REF][START_REF] Li | Actin protrusions push at apical junctions to maintain E-cadherin adhesion[END_REF][START_REF] Li | Cadherin puncta are interdigitated dynamic actin protrusions necessary for stable cadherin adhesion[END_REF][START_REF] Senju | Actin-rich lamellipodia-like protrusions contribute to the integrity of epithelial cell-cell junctions[END_REF]. We found that vinculin was essential to recruit the Arp2/3 complex at AJs, but not at an early time point, 6 h after cell plating, where not only Arp2/3 recruitment did not depend on vinculin, but also Arp2/3 recruitment increased in KI cells. These results

show that vinculin plays an essential role in Arp2/3 recruitment at AJs, but that there are also other ways to recruit it. The a-catenin molecule, which recruits vinculin at AJs, also binds to the Arp2/3 and inhibits it, but this involves a free form of a-catenin that is not bound to Ecadherin and b-catenin [START_REF] Drees | Alpha-catenin is a molecular switch that binds E-cadherin-beta-catenin and regulates actin-filament assembly[END_REF][START_REF] Benjamin | αE-catenin regulates actin dynamics independently of cadherin-mediated cell-cell adhesion[END_REF]. The nucleation promoting factors, WAVE and N-WASP, recruit Arp2/3 and induce polymerization of branched actin at AJs [START_REF] Kovacs | Cadherin-directed actin assembly: E-cadherin physically associates with the Arp2/3 complex to direct actin assembly in nascent adhesive contacts[END_REF][START_REF] Verma | A WAVE2-Arp2/3 actin nucleator apparatus supports junctional tension at the epithelial zonula adherens[END_REF][START_REF] Rajput | Neural Wiskott-Aldrich Syndrome Protein (N-WASP)mediated p120-Catenin Interaction with Arp2-Actin Complex Stabilizes Endothelial Adherens Junctions* ♦[END_REF]. Cortactin, which is now recognized as an Arp2/3 stabilizer of the branched junction of actin filaments [START_REF] Gautreau | Nucleation, stabilization, and disassembly of branched actin networks[END_REF], is also critical for Arp2/3 localization at AJs [START_REF] Helwani | Cortactin is necessary for E-cadherin-mediated contact formation and actin reorganization[END_REF][START_REF] Han | Cortactin Scaffolds Arp2/3 and WAVE2 at the Epithelial Zonula Adherens[END_REF].

These proteins are obvious candidates for the early vinculin-independent recruitment of Arp2/3 at AJs we observed here. However, their implication is difficult to test, since they also have a critical role in the formation and maintenance of AJs, the very structure where one would like to assess Arp2/3 recruitment.

Vinculin was found to regulate cell cycle progression as a function of cell density and the saturating cell density. This increased proliferation was observed in both KO and KI cells, indicating that this vinculin function strictly depends on its ability to interact with the Arp2/3. We previously established that cell cycle progression in untransformed cells depends on cortical branched actin [START_REF] Molinie | Cortical branched actin determines cell cycle progression[END_REF]. In fact, the Arp2/3-dependent functions of vinculin uncovered here, membrane protrusions, persistence of single cell migration and cell cycle progression, were previously shown to depend on the RAC1-WAVE-Arp2/3 pathway [START_REF] Dang | Inhibitory signalling to the Arp2/3 complex steers cell migration[END_REF][START_REF] Molinie | Cortical branched actin determines cell cycle progression[END_REF][START_REF] Simanov | Arpin Regulates Migration Persistence by Interacting with Both Tankyrases and the Arp2/3 Complex[END_REF]. Increased protrusions, increased persistence and increased cycling observed in KO and KI MCF10A cells are phenotypes, which are all associated with increased branched actin, showing that the vinculin-Arp2/3 interaction should antagonize the formation of branched actin. Nevertheless, we were unable to show that the vinculin linker that binds the Arp2/3 in the cell was inhibiting the Arp2/3 complex in vitro, in the pyrene-actin assay, suggesting that additional factors or post-translational modifications are probably involved in the cell. Future work should be aimed at deciphering the precise molecular mechanisms by which vinculin antagonizes the nucleation of branched actin networks by the Arp2/3 complex.

METHODS

Cell Culture and Drugs

MCF10A cells were grown in DMEM/F12 medium supplemented with 5% horse serum, 20 ng/mL epidermal growth factor, 10µg/mL insulin, 100 ng/mL cholera toxin, 500 ng/mL hydrocortisone and 100U/mL penicillin. Medium and supplements were from Life Technologies and Sigma. Cells were incubated at 37°C in 5% CO2. Cells were trypsinised (12605010, Gibco) and sub-cultured every 3 days. CK-666 (182515, Sigma) was used for Arp2/3 inhibition as stated.

Plasmids, Transfection and Isolation of Stable Cell Lines

GFP tagged proteins were expressed from a home-made vector, MXS AAVS1L SA2A Puro bGHpA EF1Flag GFP Blue SV40pA AAVS1R that was previously described [START_REF] Molinie | Cortical branched actin determines cell cycle progression[END_REF]. Vinculin linker WT, P878A, ARPC1A, ARPC1B, ARPC5, ARPC5 were inserted into this plasmid in place of the Blue cassette using Fse1 and Asc1 restriction sites. The P878A mutation was generated from the WT plasmid using the Quikchange Lightning mutagenesis kit (Agilent) and primers (CCTAGGCCTCCACCAGCAGAGGAAAAGGATG, GTAGGAAAAGGAGACGACCACCTCCGGATCC).

Transfections of MCF10A cells were performed using Lipofectamine 3000 (Invitrogen). To obtain stable cell lines, MXS AAVS1 vectors were co-transfected with two TALEN constructs (Addgene #59025 and 59026) inducing a double strand break at the AAVS1 locus [START_REF] González | An iCRISPR platform for rapid, multiplexable, and inducible genome editing in human pluripotent stem cells[END_REF]. Cells were selected with 1 µg/mL puromycin (ant-pr-1, Invivogen) and pooled if the expression was homogeneous or cloned otherwise.

Genome Editing

To generate vinculin KO lines, MCF10A cells were transfected with a sgRNA (ATCGTGCGCGTATGAAACAC) targeting nucleotides 7 to 26 of the VCL coding sequence, corresponding to amino acids 3 to 9 of the vinculin protein, along with the purified Cas9 protein using the Lipofectamine CrisprMax kit (#CMAX00001, ThermoFisher). Cells were then diluted and seeded in 96-well plate at 1 cell/well. Wells containing two or more clones were not analyzed. 130 clones were screened by dot blot using anti-vinculin antibodies at 1:1000 dilution. Cells with minimal signal on dot blots were further screened using Western blot, immunostaining and sequencing to derive characterized KO clones.

To characterize the VCL mutations on the vinculin gene, base pairs 14-494 were amplified by PCR using DreamTaq (EP0702, ThermoFisher) for 32 cycles with annealing temperature 58°C and the (TCTGTCTCTTCGCCGGTTC, AGCCTTTTTCATGACTGCTCC) primers. The PCR product was sequenced. When several sequences overlapped, PCR products were cloned into a blunt vector using the Zero Blunt PCR cloning kit (#K270040, ThermoFisher) to sequence the two alleles independently.

To obtain the vinculin KI line, MCF10A cells were cotransfected by electroporation with a Cas9 expressing plasmid (CMV hSpCas9 bGH pA), a plasmid expressing the ATP1A1 sgRNA [START_REF] Agudelo | Marker-free coselection for CRISPR-driven genome editing in human cells[END_REF], a pRG2(-GG) plasmid expressing the VCL sgRNA (GCCTCCACCACCAGAGGAAA) and a single-stranded 87 bp repair oligonucleotide (base pairs 110878-110964 in the VCL gene). Colonies resistant to ouabain (0.5 µM, Sigma 03125)

were cloned using dilution and screened by PCR using DreamTaq (EP0702, ThermoFisher) for 32 cycles with annealing temperature 52°C and the (GGTGACGATCGAAAAAC, TATTGGCAACACAGGAACC) primers, followed by PvuII restriction.

Antibodies

Antibodies used for immunostaining and western blots were anti-vinculin (#V9131, Sigma), anti-α-catenin (#C2081, Sigma), anti-E-cadherin (#MABT26, Merck), anti-Paxillin (#GTX125891, GeneTex), anti-ARPC2 (#07-227-I, Millipore), anti-ARPC1B (#HPA004832, Sigma), anti-ARPC3 (#HPA006550, Sigma). For immunostaining, secondary antibodies for anti-mouse-647 (#A21236, Life technologies) and anti-rabbit-405(#A34556, Life technologies)

were used along with Acti-Stain 555 (Cytoskeleton).

Immunoprecipitation and Western Blot

Two 15-cm dishes of MCF10A cells were lysed 1 day after seeding and scraped off in (50mM HEPES pH7.7, 10mM EDTA, 50mM KCl, 1mM MgCl2 and 1%NP-40) supplemented with a protease inhibitor cocktail (Roche, 1:10000). Cell lysates were centrifuged at 10,000xg for 10 min. The supernatant was incubated at 4°C for 1 h with GFP-Trap Agarose beads (Chromotek)

and washed 4 times. Lysates and immunoprecipitates were analyzed by Western blot.

Immunofluorescence and Image Analysis

To image cells, 15,000 cells (to obtain individual cells) or 1.5x10 6 cells (to obtain a monolayer)

were plated on 22x22 mm coverslips that were coated with fibronectin (10 µg/mL, F1141, Sigma) and fixed after 1 day (unless otherwise stated) with 4% PFA for 15 min. Cells were permeabilized in 0.2% Triton X-100 and blocked in 10% FBS in PBS. Cells were stained in a 1:200 dilution of first primary and then secondary antibodies along with Acti-stain 555.

Coverslips were mounted in Dako mounting medium and imaged using an SP8 laser-scanning confocal microscope (Leica). Images were analyzed using FIJI. To measure cell spreading, cell area was quantified on images by thresholding (Triangle algorithm) in Fiji.

To quantify vinculin recruitment at AJs and FAs, the thresholded α-catenin or paxillin staining, respectively was used to generate a mask in which fluorescence intensity of vinculin was quantified. Lengths of focal adhesions were manually measured using paxillin staining. To quantify Arp2/3 and vinculin enrichment at AJs, a line was manually drawn along the junction labeled with anti-E-cadherin. Width of the line was then increased iteratively to measure total fluorescence intensity at increasing distances from the junction. Intensity at a distance n from the junction corresponded to (total intensity of line widthn) -(total intensity of line widthn-1).

Values were finally normalized to the average fluorescence intensity at a line ≈ 12 µm from the junction, corresponding to intensity in the cytoplasm. Enrichment of E-cadherin at AJs was measured similarly using phalloidin staining as a reference for cell-cell contacts.

Live Cell Imaging

For 2D cell migration assays, 15,000 cells were seeded 1 day prior to imaging on microslides (#80826, Ibidi) coated with fibronectin. For 3D migration of cells embedded in a collagen matrix, 15,000 cells were plated into microchambers (#80826, Ibidi) on a 3.5 mg/ml Collagen Type1 (#354236, Corning) matrix in DMEM:F12 supplemented with FBS (10%). After cells attached, another layer of collagen was added on top and cells were incubated in culture medium for 1 day before imaging. Cells were imaged on an AxioObserver Z1 microscope (Zeiss)

equipped with an Orca-R2 CCD camera (Hamamatsu) and controlled by the AxioVision software (Zeiss). Images were acquired at 5 min (2D migration) or 10 min intervals (migration in 3D collagen matrix) for 24h. Cell-cell junction disassembly events were counted manually at each time point. Analysis of migration persistence was performed as previously described [START_REF] Gorelik | Quantitative and unbiased analysis of directional persistence in cell migration[END_REF].

For TIRF-SIM imaging, 100,000 mCherry-actin transfected cells were plated 1 day prior to imaging on glass-bottom dishes (P35G-0.170-14-C, MatTek Corp) coated with fibronectin. To image actin flows in lamellipodia, images were acquired at 2 s intervals for 2 min using 3 phase shifted angles, each with 3 fringe patterns, on the Deltavision OMX SR (GE Healthcare) microscope. High resolution images were reconstructed and 2-color images were aligned using softWoRx (AppliedPrecision). Kymographs were generated in FIJI using manually drawn lines Spurious vectors were filtered-out by their amplitude and were replaced by interpolated velocities from neighboring vectors. The local order parameter was calculated using a previously published code [START_REF] Deforet | Automated velocity mapping of migrating cell populations (AVeMap)[END_REF].

Cell Cycle and Proliferation

To quantify saturation density, 2x10 6 cells were plated on fibronectin coated cover slips in 6well plates. Cells were fixed 4 days after seeding and nuclei were stained with DAPI. To perform the EdU incorporation assay, cells were seeded on fibronectin-coated coverslips (12 mm) for 1 day. Cells were incubated with 10 µM EdU for 1 h prior to fixation in 4% PFA for 15 min and permeabilized in 1% Triton X-100 for 5 min. EdU was labeled with the Alexa Fluor 488 Click-iT EdU Imaging Kit (#C10337, Thermo Fisher Scientific) according to the manufacturer instructions and nuclei were labeled with DAPI (Thermo Fisher Scientific).

Images were acquired on an inverted microscope (Olympus IX83) using a 20x objective (NA 0.5) equipped with an Orca-Flash4.0 V3 camera (Hamamatsu), controlled by Micro-Manager 2.0 and analyzed using a custom script in FIJI to count DAPI-or EdU-positive cells. The percentage of cells in S-phase was scored as the ratio of EdU-positive nuclei/DAPI-stained nuclei in segmented images. For each condition, at least 5000 cells were counted.

Statistical Analysis

For all t-tests, populations were first tested for Gaussian distribution using a Shapiro-Wilk Test with a α-value of 0.05. If both populations were Gaussian, difference between means was tested using Welch's T-test and if one or both of the populations were non-Gaussian, the difference between means was tested using a Mann-Whitney U test. focal adhesion size, protrusion speed and frequency of cell junction disassembly were tested with a one-tailed distribution as the lower limit of measurement was close to a lower bound of 0. All other t-tests assumed a twotailed distribution. Analysis of migration persistence was performed as previously described [START_REF] Gorelik | Quantitative and unbiased analysis of directional persistence in cell migration[END_REF]. Exponential decay and plateau fit (! = (1 -&) * ) ! ! " + &) were performed for all individual cells. Coefficients were then compared using one-way ANOVA.

Statistical analysis was performed in R using linear mixed-effect models to take into account the resampling of the same statistical unit as previously described [START_REF] Polesskaya | Restrained activation of CYFIP2-containing WAVE complexes controls membrane protrusions and cell migration[END_REF].

  that followed the direction of actin retrograde flow and the Multi Kymograph tool. Protrusion speed and rearward flow are given by the tan of the angle made with the time axis in kymographs. Protrusion speeds and rearward flow values have opposite signs, but absolute values are given for clarity. The actin assembly rate is the sum of protrusion speed and rearward flow.Analysis of wound healing experiments80,000 cells were plated on microslides (#80826, Ibidi) coated with fibronectin within inserts (#80209, Ibidi) one day before the experiment. Inserts were removed, and timelapse acquisitions were performed at 10 min intervals during 24h on an AxioObserver Z1 microscope (Zeiss) equipped with a 10x objective, an Orca-Flash4 v3 camera (Hamamatsu) and controlled by the MicroManager 2.0 software. Fields focused on only one edge of the wound were acquired, and average leading-edge positions perpendicular to the axis of the wound gave leading edge progression. The velocity field was obtained by PIV[START_REF] Petitjean | Velocity Fields in a Collectively Migrating Epithelium[END_REF] using the PIVlab software package[START_REF] Thielicke | Particle Image Velocimetry for MATLAB: Accuracy and enhanced algorithms in PIVlab[END_REF] for Matlab (MathWorks). The window size was set to 32 pixels, i.e. 23.75 µm with a 0.75 overlap between windows. A time sliding window averaging velocity fields over 40 minutes (equal to 4 frames) was used.

Figure 1 .

 1 Figure 1. Expression of the vinculin linker that binds to the Arp2/3 complex increases actin polymerization and membrane protrusion. a The Arp2/3 complex co-immunoprecipitates with the vinculin linker (amino acids 811-881). MCF10A cells stably expressing GFP, the GFP tagged linker in a WT or P878A form were lysed and subjected to GFP immunoprecipitation and Western blot analysis. N=3, 1 representative experiment shown. b Phase contrast images of the same cell lines. Scale bar = 5 µm. c Cell area of the cell lines stained for actin. Mean ± SD, n=25, t-test. N=3, 1 representative experiment shown. d, e Single cell migration. Cell trajectories (d) and migration persistence (e). Mean ± SD, n=10, linear mixed effect model. N=3, 1 representative experiment shown. f, g Membrane protrusions of the stable MCF10A cell lines expressing the vinculin linker

Figure 2 .Figure 3 .

 23 Figure 2. Characterization of VCL knock-out and knock-in cell lines. a Parental MCF10A, and isolated clones transfected with VCL targeting gRNA or a non-targeting gRNA were analyzed by Western blot. b Sequences of the two alleles in each KO cell line. All mutations induce a frameshift and thus a premature stop codon in the ORF. c Staining of vinculin and paxillin in parental and KO cells. Scale bar = 5 µm. d Quantification of vinculin staining in focal adhesions (FAs) and normalization by the intensity of parental cells. BG refers to the background in the non-FA cytoplasm.Mean ± SD, n=45, t-test. N=3 with similar results, pooled measurements from the 3 independent repeats are plotted. e Quantification of length of FAs. Mean ± SD, n=45, t-test. N=3 with similar results, pooled measurements from the 3 independent repeats are plotted. f Genome analysis of the

Figure 4 .Figure 5 .

 45 Figure 4. Vinculin stabilizes cell-cell junctions. a-d Presence of vinculin at cell-cell junctions in KO and KI cells. Staining of vinculin and a-catenin (a, c) and quantification of intensity at cell-cell

Figure 6 .

 6 Figure 6. Vinculin retains Arp2/3 at cell-cell junctions. a Staining of vinculin, ARPC2 and Ecadherin 6 h, 1 day or 3 days after plating. Scale bar 5 µm. Max z-projection from confocal microscopy. b,c Quantification of ARPC2 enrichment at adherens junctions in KO (b) and KI (c) cells. Mean ± SD, n=10, t-test. N=3, 1 representative experiment shown.

Figure 7 .Figure 8 .

 78 Figure 7. Vinculin controls cell cycle progression through its interaction with the Arp2/3 complex. a Saturation density of KO and KI cells. Mean ± SD, n=10, t-test. N=3, 1 representative experiment shown. b-d Cell cycle progression of KO (b), KI (c) and linker expressing MCF10A cells (d). Percentage of cells incorporating EdU is represented as a function of cell density. e,f Cell cycle progression of KO and KI cells (e), or linker expressing MCF10A cells (f) plated at a density of 5.10 4 cells and treated with increasing doses of the Arp2/3 inhibitory compound CK-666. Mean ± SD, n=8 fields of views with more than 5000 cells in total, t-test. N=3, 1 representative experiment shown. pvalues are shown only when both KOs or KI cells are different from both controls in b,c,e and when the linker is significantly different from parental MCF10A in d,f

Acknowledgments

This work was supported by grants from Agence Nationale de la Recherche (ANR-20-CE13-0016, ANR-22-CE44-0006 and ANR-22-CE13-0041) and from Fondation ARC pour la Recherche sur le Cancer (ARC PJA 2021 060003815).

Competing interests

The authors declare no competing interests.