Voice Reenactment with F0 and timing constraints and adversarial learning of conversions Frederik Bous, Laurent Benaroya, Nicolas Obin, Axel Roebel STMS Lab IRCAM, CNRS, Sorbonne Université Paris, France

Abstract-This paper introduces voice reenactement as the task of voice conversion (VC) in which the expressivity of the source speaker is preserved during conversion while the identity of a target speaker is transferred. To do so, an original neural-VC architecture is proposed based on sequence-to-sequence voice conversion (S2S-VC) in which the speech prosody of the source speaker is preserved during conversion. First, the S2S-VC architecture is modified so as to synchronize the converted speech with the source speech by mean of phonetic duration encoding; second, the decoder is conditioned on the desired sequence of F0values and an explicit F0-loss is formulated between the F0 of the source speaker and the one of the converted speech. Besides, an adversarial learning of conversions is integrated within the S2S-VC architecture so as to exploit both advantages of reconstruction of original speech and converted speech with manipulated attributes during training and then reducing the inconsistency between training and conversion. An experimental evaluation on the VCTK speech database shows that the speech prosody can be efficiently preserved during conversion, and that the proposed adversarial learning consistently improves the conversion and the naturalness of the reenacted speech.

Index Terms-Voice conversion, voice reenactement, prosody preservation

I. INTRODUCTION

A. Context and Related works

Voice conversion (VC) consists of digitally altering the voice of an individual -e.g., its identity, accent, or emotionwhile maintaining its linguistic content unchanged. Primarily applied to identity conversion, VC has considerably gained in popularity and in quality thanks to the advances accomplished with neural VC (see for instance, [START_REF] Toda | The Voice Conversion Challenge 2016[END_REF]- [START_REF] Zhao | Voice Conversion Challenge 2020: Intra-lingual semi-parallel and cross-lingual voice conversion[END_REF]). Neural VC is now widely considered as a standard in VC and has reached a highly-realistic rendering of voice identity conversion from a small amount of data of a target voice. Similarly to face manipulation, voice conversion has a wide range of potential applications, such as voice cloning and deep fake in the fields of entertainment and fraud [START_REF] Lorenzo-Trueba | Can we steal your vocal identity from the Internet?: Initial investigation of cloning Obama's voice using GAN, WaveNet and low-quality found data[END_REF], anonymization of voice identity in the field of security and data privacy [START_REF] Srivastava | Evaluating voice conversion-based privacy protection against informed attackers[END_REF], [START_REF] Ericsson | Adversarial representation learning for private speech generation[END_REF], or digital voice prosthesis of impaired speech in the field of digital healthcare [START_REF] Wang | End-To-End Voice Conversion Via Cross-Modal Knowledge Distillation for Dysarthric Speech Reconstruction[END_REF].

Introduced in the late 2000's, neural VC has gradually moved towards many-to-many and non-parallel datasets allowing the scalability of neural VC to large and multiple speakers datasets with the assumption that the increase of data will induce a substantial increase in terms of quality and naturalness of the VC. In particular, starGAN-VC [START_REF] Kameoka | Stargan-vc: nonparallel many-to-many voice conversion using star generative adversarial networks[END_REF], [START_REF] Kaneko | StarGAN-VC2: Rethinking Conditional Methods for StarGAN-Based Voice Conversion[END_REF] has been proposed to extend the paradigm of cycle-GAN to many-to-many and non-parallel VC by proposing a conditional encoder-decoder architecture. As opposed to the cycleGAN-VC, starGAN-VC is composed of a single encoder-decoder in which the decoder is conditioned on the speaker identity to be converted. In the starGAN-VC, a discriminator is employed to distinguish between real original speech and fake converted speech together with a speaker classifier is employed to determine whether the converted speech has been produced by the target speaker. As in the cycleGAN, a cycle-consistency loss attempts to preserve the linguistic content during conversion. To overcome the issue of linguistic preservation trough conversion, phonetic posterior-grams (PPGs) [START_REF] Sun | Phonetic Posteriorgrams for Many-to-One Voice Conversion without Parallel Data Training[END_REF], [START_REF] Hamidreza | One-Shot Voice Conversion with Disentangled Representations by Leveraging Phonetic Posteriorgrams[END_REF] have been proposed to integrate explicitly linguistic content information by mean of time-aligned phonetic posterior probabilities that are used to condition the conversion.

More recently, neural VC architectures has reformulated the VC problem as a simple auto-encoder [START_REF] Lu | One-Shot Voice Conversion with Global Speaker Embeddings[END_REF]- [START_REF] Zhang | Non-Parallel Sequence-to-Sequence Voice Conversion With Disentangled Linguistic and Speaker Representations[END_REF] (further referred to as AE-VC). The underlying idea is to provide a more structured representation of the information in the process of VC, in particular by explicitly encoding and disentangling linguistic content. VC is then achieved by manipulating the speaker identity by conditioning the decoder on the desired speaker identity. This has been achieved either by carefully tuning a bottleneck to encode only the linguistic content information as in [START_REF] Qian | AutoVC: Zero-Shot Voice Style Transfer with Only Autoencoder Loss[END_REF] or through adversarial learning of linguistic content and speaker identity codes as in [START_REF] Zhang | Non-Parallel Sequence-to-Sequence Voice Conversion With Disentangled Linguistic and Speaker Representations[END_REF]. The advantage of those architectures is that the ground truth is known during training, so that a simple reconstruction loss can be efficiently applied (as opposed to the starGAN-VC). Moreover, linguistic and speaker information are explicitly represented and learned through disentanglement, which should idealistically provide a more accurate control during conversion. Those architectures have opened the possibility of processing VC from a very small number of examples of the target speaker (at the extreme from one-shot [START_REF] Lu | One-Shot Voice Conversion with Global Speaker Embeddings[END_REF] or zero-shot [START_REF] Qian | AutoVC: Zero-Shot Voice Style Transfer with Only Autoencoder Loss[END_REF]). One important assumption of these architectures relies on the fact that though a simple reconstruction is used during training (thus no conversion is actually learned), the manipulation of the speaker identity is still effective during conversion. However, this might seem somehow inconsistent since the actual conversion is not used during training (as opposed to the starGAN-VC).

B. Limitations and Contributions

Though VC systems can now achieve highly-realistic voice identity conversion [START_REF] Lorenzo-Trueba | The voice conversion challenge 2018: Promoting development of parallel and nonparallel methods[END_REF], [START_REF] Zhao | Voice Conversion Challenge 2020: Intra-lingual semi-parallel and cross-lingual voice conversion[END_REF], the only information which is assumed to be preserved from the source speaker through conversion is the actual linguistic content of the spoken utterance (i.e., the text transcript). This constitutes an important limitation of current VC systems since one could desire to preserve some aspects of the source speaker through conversion, e.g. the prosody and the expressivity of the source speaker. By direct analogy with the image domain, face reenactement is defined by preserving the expression of the source face while converting the identity to the one of a target face [START_REF] Thies | Face2Face: Real-Time Face Capture and Reenactment of RGB Videos[END_REF]. This provides a more flexible and controllable transformation as it is commonly known as deep fakes, in which the source face provides the desired pose and expression to be rendered with the target identity.

The same definition can be applied in voice conversion, which will be further referred to as voice reenactement. Voice reenactement aims at preserving some aspects of the prosody of the source speaker during conversion, namely its timing -by means of phoneme durations -and its fundamental frequency (F0) both being commonly considered as the most important aspects of speech prosody. Though timing is ineherently preserved in some VC architectures such as cycleGAN-VC or starGAN-VC, this is not the case for all architectures including some of the aforementioned VC architectures based on autoencoders. Besides, the only research to date to the knowledge of the authors on the F0-preservation of the source speaker in VC has been proposed by [START_REF] Kaizhi Qian | F0-Consistent Many-To-Many Non-Parallel Voice Conversion Via Conditional Autoencoder[END_REF], which is solely obtained by conditioning the decoder of Auto-VC on the desired sequence of F0-values. Moreover, AE-based VC suffers from the fact that the conversion is actually not learned during training while the GAN-based VC suffers from the fact that no ground truth is available to learn the conversion (and instead applying the adversarial loss). However, research on face manipulation including the original starGAN [START_REF] Choi | StarGAN: Unified Generative Adversarial Networks for Multi-domain Image-to-Image Translation[END_REF] have presented strategies that can make both advantage of reconstruction of the original real data and adversarial learning of the manipulated data [START_REF] He | AttGAN: Facial Attribute Editing by Only Changing What You Want[END_REF]. The main contributions of this paper can be listed as follows:

1) The task of voice reenactement is introduced with the objective of preserving the expressivity of the source speaker during conversion while transferring the identity of the target speaker; 2) An original solution to this task is presented by preserving the timing and the F0 of the source speaker during conversion within a S2S AE-VC architecture [START_REF] Zhang | Non-Parallel Sequence-to-Sequence Voice Conversion With Disentangled Linguistic and Speaker Representations[END_REF]. In particular, a F0-loss is explicitly formulated and exploited during training; 3) Inspired by the original formulation of the starGAN, an adversarial learning of identity conversion is integrated within the AE-VC architecture so as to both take advantage of reconstruction and conversion during training and reducing the inconsistency between training and conversion.

II. PROPOSED METHOD

A. Original S2S Neural VC

The VC framework used in this paper is rooted on a sequenceto-sequence (S2S) auto-encoder as proposed in [START_REF] Zhang | Non-Parallel Sequence-to-Sequence Voice Conversion With Disentangled Linguistic and Speaker Representations[END_REF], in which disentangled linguistic and speaker representation are encoded through dedicated encoders as illustrated in Figure 1. The inputs of the system are the speech signal matrix A represented by the Mel-spectrogram computed on T time frames, and the sequence of T phonemes p corresponding to the phonetic transcription of the input text aligned to the corresponding speech signal.

Dual encoders E c and E s are employed to encode linguistic content and speaker information. The speaker encoder E s converts the speech signal A into a time-independent vector h s , since it is assumed that the identity of a speaker does not vary within an utterance. A speaker classification loss L SE is defined between the speaker identity predicted from h s and the true speaker identity s. The linguistic encoder E c converts either the phoneme sequence p or the speech signal A into a shared linguistic embedding H c through a contrastive loss. Contrary to [START_REF] Zhang | Non-Parallel Sequence-to-Sequence Voice Conversion With Disentangled Linguistic and Speaker Representations[END_REF], the linguistic embedding has the same length T as the aligned phoneme sequence (and the Mel-spectrogram), so that the time information is preserved during encoding. A S2S decoder G a conditioned on the content embedding H c and the speaker embedding h s is employed to reconstruct an approximation A of the original speech signal A. A reconstruction loss L RC is defined between the reconstructed speech signal A and the original speech signal A.

During training, the S2S-VC neural network is pre-trained on a multiple-speakers dataset, and then fine-tuned with respect to a given pair of source and target speakers. During conversion, the recognition encoder E c computes the content embedding H c src corresponding to one utterance A src of the source speaker; and the speaker encoder E s computes the speaker embedding h s tgt corresponding the one utterance A tgt of the target speaker. Then, decoder G a is conditioned on the linguistic embedding H c src and the speaker embedding h s tgt to generate the utterance B tgt with the identity of the target speaker. Without explicit notification, the architecture and parameters of the S2S-VC are the same as those described in [START_REF] Zhang | Non-Parallel Sequence-to-Sequence Voice Conversion With Disentangled Linguistic and Speaker Representations[END_REF].

B. Pre-processing and Post-Net

The S2S-VC operates on a Mel-spectrogram representation of the speech signal. For the signal analysis we follow the parameterization proposed in [START_REF] Liu | WaveNet Vocoder with Limited Training Data for Voice Conversion[END_REF], that is the input signal is down-sampled to 16kHz, converted into an STFT using an Hanning window of 50ms with hop size of 12.5ms and an FFT size of 2048. We then use 80 Mel bins covering the frequency band from 0 to 8Khz and convert the result into log amplitude domain. A standardization of the log Mel-spectrogram is applied at the input of the VC system, i.e. on each Mel bin, removing the mean and diving by the standard deviation, which are pre-computed on the entire training dataset. For rendering the speech signal from a generated Mel-spectrogram, a multispeaker waveglow neural decoder following loosely [START_REF] Prenger | WaveGlow: A Flow-based Generative Network for Speech Synthesis[END_REF] was employed. This decoder was trained over 900, 000 iterations

A src G a  tgt target speech B tgt E s E F0 h src F0 F0 encoder
Fig. 1. Architecture of the proposed S2S-VC system. On left: The original VC comprises linguistic and speaker encoder E c and E s , and a decoder G a which reconstructs the speech signal A conditioned on content embedding H c and speaker embedding h s . A F0 encoder E F 0 is added to encode the sequence of F0 values from the original Mel-spectrogram, and a F0 loss is computed between the F0 of the reconstructed speech signal and the one of the original speech signal. On right: During conversion, content embedding H c src and F0 h F 0 src is extracted from speech signal of the source speaker and the speaker embedding h s tgt of the target speaker.

using all samples of the VCTK database with batch size 50, and segment length 375ms using the Adam optimizer with learning rate 1e -4 .

C. Proposed S2S Neural Voice Reenactemen 1) Contribution 1: S2S-VC with time-synchronization and F0-conditioning: S2S-VC architecture does not ensure timesynchronicity between the original speech and the converted speech, by definition of the sequence-to-sequence architecture. The S2S-VS is basically composed on a speech-to-text encoding time-compression and a text-to-speech decoding timedecompression with a similar architecture as the Tacotron ( [START_REF] Wang | Tacotron: Towards End-to-End Speech Synthesis[END_REF], [START_REF] Shen | Natural TTS Synthesis by Conditioning Wavenet on MEL Spectrogram Predictions[END_REF]). In order to preserve time-synchronization between the original and the reconstructed speech signals, the time dimension of length T is preserved all through the network, from the original speech signal A to the linguistic embedding H t , and to the reconstructed speech signal A. To do so, the auto-regressive S2S part of the recognition encoder E t and the decoder G a are modified accordingly by employing simple recurrent architectures. The recognition encoder E t is composed of two bidirectional LSTM layers of dimension 128 followed by a fully connected layer (FC) of dimension 128, resulting in a linguistic embedding of dimension (128×T ). The decoder G a is using two bidirectional LSTMs of dimension 128 each and a Fully Connected layer of dimension 80 which outputs an approximated Mel-spectrogram with the same dimensions as the input Mel spectrogram, i.e., (80 × T ). These simplifications enable time-synchronous conversions and a consequent saving in computational time: approximately 33% of the computational time for training on our server with a single GPU. In order to preserve the F0 of the original speech signal during conversion, a F0 encoder E F0 is added and a F0-loss is explicitly formulated (as opposed to [START_REF] Kaizhi Qian | F0-Consistent Many-To-Many Non-Parallel Voice Conversion Via Conditional Autoencoder[END_REF]). The F0 encoder converts the input Mel-spectrogram into a corresponding sequence of F0 values. This value corresponds to the estimated F 0 value for voiced frames and to 0 for unvoiced frames. This encoding is passed to condition the decoder G a in addition to the linguistic and speaker embeddings to create the Mel-spectrogram. A F0 loss is defined as the mean square error between the F0 values of the generated speech and the F0 values of the original speech, as

L F0 (h F 0 , h F 0 ) = 1 T T t=1 (h F 0 (t) -h F 0 (t)) 2 (1)
The F0 encoder E F0 is described in [START_REF] Ardaillon | Fully-Convolutional Network for Pitch Estimation of Speech Signals[END_REF], pre-trained on the training set of the VCTK speech database, and then fixed during VC training, i.e. is only used to compute the F0 loss L F0 . Contrary to [START_REF] Kaizhi Qian | F0-Consistent Many-To-Many Non-Parallel Voice Conversion Via Conditional Autoencoder[END_REF] this loss explicitly constrains the F 0 to the desired F 0 by defining a dedicated loss. This ensures that the F 0 of the converted speech to be effectively preserved during conversion. This loss is added to the reconstruction loss with a weight λ F 0 varying linearly from 10e -6 to 10e -2 with the effect of increasing gradually the importance of the F0 preservation versus the reconstruction loss during training. During conversion, the F 0 can be transferred from an utterance of a source speaker or fixed arbitrarily (e.g., by applying transposition or setting any arbitrary values). In this paper, the F 0 used for conditioning was adapted to the range of the target speaker in order to prevent unnatural converted speech that would be caused by some important difference between the respective ranges of the source and target speakers (typically when converting a male to a female or conversely). This was accomplished by normalizing the F 0 values corresponding to the sentence of the source speaker with respect to the log(F0) mean and standard deviation of the target speaker.

2) Contribution 2: Adversarial Training of S2S-VC: S2S-VC basically relies on an auto-encoder optimizing a reconstruction loss between the original speech signal and the reconstructed one. This is somehow inconsistent with the conversion in which the identity of the speaker is manipulated during conversion (eventually, the F0 and timing) . In the case of a conversion, one does not have access to the ground truth speech signal and thus one cannot apply the reconstruction loss of the auto-encoder.

To overcome this limitation and construct a VC system whose training is more consistent with conversion, we propose to split the training process into two modes, as inspired by the original starGAN [START_REF] Choi | StarGAN: Unified Generative Adversarial Networks for Multi-domain Image-to-Image Translation[END_REF]: a reconstruction loss corresponding to the classical auto-encoder in which the reconstruction loss can be computed; an adversarial loss, in which we assume that the true speech signal may not be available. This is typically the case in which least one of the codes conditioning the decoder is manipulated. For this mode, we introduce an adversarial module which is similar to the one used in a GAN.

A discriminator D adv is optimized to distinguish between the real speech samples and the converted ones, while the decoder G a is optimized to fool the discriminator. During training, each samples contained in a batch is both passed to the decoder in the reconstruction mode with original unchanged codes and in the conversion mode with unchanged or manipulated codes. In this paper, only the speaker identity is manipulated so that the reconstruction has the right identity and the conversion mode a randomly picked identity. The total loss L GEN including reconstruction and conversion losses can then be expressed as,

L GEN = L RC + λ adv L ADV (2)
For clarity, the F0 loss is not specified in the above loss but is still used as previously described. In this paper, the discriminator D adv is composed of 4 convolution layers with 128 filters of size (3 × 3) with a stride of (2 × 2) and λ adv = 1 was found to provide a good trade-off between the effect of the reconstruction and the conversion on the decoder G a .

III. EXPERIMENTS

A. Speech dataset

The English multi-speaker corpus VCTK [START_REF] Yamagishi | CSTR VCTK Corpus: English Multi-speaker Corpus for CSTR Voice Cloning Toolkit (version 0.92)[END_REF] is used for training and testing. The VCTK dataset contains speech data uttered by 110 speakers and the corresponding text transcripts. Each speaker read about 400 sentences selected from English newspaper, which represents a total of about 44 hours of speech. Four speakers All speakers are included into the training and validation sets. For each speaker, we split the database in a training set with 90% of the sentences and a validation set with 10% of them. The total duration of the database is around 27 hours after removing silences at the beginning and at the end of each sentence.

B. Subjective Experiment Setup

The experiment consisted into the judgment by listeners of: the similarity of the converted speech to the target speaker and the naturalness of the converted speech, using 5-degree MOS scale as commonly used for the experimental evaluation of VC algorithms. Each participant had to judge 15 speech samples which were randomly selected among the total number of speech samples produced for the subjective experiments. The experiment was conducted on-line. Participants were encourage to perform the experiment in a quiet environment and with a headphone. Four speakers were used for the experiment: two males (p232 and p274) and two females (p253 and p300) with eight randomly chosen sentences per speaker in the validation set. Conversion were computed between male speakers and between females speakers, resulting in two male and two female conversion setups. Four configurations were compared: 1) the original audio signal and the converted speech with : 2) timesynchronous and F0-preserved VC system (referred to as F0 cond.); 3) time-synchronous and F0-preserved VC system with discriminator trained only with the true speaker identity (same identity as the source speech utterance) , referred to as F0 cond. w/adv same id; 4) time-synchronous and F0-preserved VC system with discriminator trained only with varying speaker identities (different identities from the one of the source speech utterance), referred to as F0 cond. w/adv diff id1 .

C. Results and Discussion

Table I presents the root mean squared error of the F0 of the converted speech with the proposed configurations for the 4 speakers used in the experiment. The error is around 5 Hz. in average which is not audible in most cases. This shows the efficiency of the proposed F0 preservation strategy, even in combination with the adversarial loss. Table II presents the mean MOS scores of the compared system configurations obtained with 25 participants. On the one hand, the baseline VC system using time-synchronization and F0 preservation presents fair to good similarity to the target speaker (MOS=3.92 for similarity), even though the timing and the F0 contours is inherited from the source speaker. Also, the naturalness is also rated to the fair range (MOS=3.09). One can observe that the naturalness is degraded with the female speakers (MOS=2.85) as compared to the male speakers (MOS=3.38). These results are consistent with the ones obtained in the literature about S2S-VC, as in [START_REF] Zhang | Non-Parallel Sequence-to-Sequence Voice Conversion With Disentangled Linguistic and Speaker Representations[END_REF]. This indicates that the application of a timing and a F0 contour from a different speaker does not degrade consistently neither the similarity nor the naturalness of the converted speech. On the other hand, the proposed VC system with time and F0 preservation together with adversarial loss on varying speaker identities improves the scores in almost all cases compared to the baseline. The overall similarity to the target speaker is good (MOS=4.06) and the naturalness of the conversion is fair (3.18). The improvement in similarity is particularly substantial for the female speakers (MOS=4.23) while in the same time the difference in naturalness between the male and female conversions is much less pronounced (MOS=3.16 for male speakers and MOS=3. [START_REF] Wang | Tacotron: Towards End-to-End Speech Synthesis[END_REF] speakers). This indicates that the add of the discriminator not only helps to improve the naturalness of the converted speech (by suppressing perceptible artifacts) but also increases the similarity to the target speaker. Also, the use of varying speaker identities with the adversarial loss improves the scores in all cases compared to using only the true identity of the speaker. This is probably mainly due to the fact that the discriminator is being more efficient when subject to a larger variety of sentence and speaker identities.

IV. CONCLUSION This paper presented a S2S-VC algorithm which allows to preserve the timing and the F0 of the source speaker during conversion. Moreover, an adversarial module is added so that the S2S-VC can learn both from real speech samples as well as manipulated ones. Experimental evaluation on the VCTK speech database shown that the F0 is effectively preserved during conversion and that the adversarial module clearly helps to reduce the audible artifacts of the conversion as well as improve the perceived identity of the converted speech. Further research will investigate the manipulation of timing and F0 during training, in addition to the speaker identity.

TABLE I ROOT

 I MEAN SQUARE ERROR OF THE RECONSTRUCTED F0 (IN HZ.).

	VC system	M-to-M F-to-F	M-to-F F-to-M
	F0 cond w/ adv. same id	2.712	5.686	2.970	5.090
	F0 cond w/ adv. diff id	2.574	6.246	4.171	5.252

Converted speech samples are available at: http://recherche.ircam.fr/anasyn/ obin/VC EUSIPCO22.html

V. ACKNOWLEDGEMENTS

The research in this paper has been funded by the ANR project TheVoice : ANR-17-CE23-0025.


domain: spi sde

text: Rheological properties of stabilizers at low temperatures in concentrated sucrose solutions


Hélène D Moreau
email: helene.moreau@curie.fr

Matthieu Piel

Raphaël Voituriez

Ana-Maria Lennon-Duménil

Affiliations

Integrating physical and molecular insights of immune cell migration

Keywords: Cell migration, cytoskeleton, microenvironment, biophysics

The function of most immune cells depends on their ability to migrate through complex microenvironments, either randomly to patrol for the presence of antigens, or directionally to reach their next site of action. The actin cytoskeleton and its partners are key conductors of immune cell migration as they control the intrinsic migratory properties of leukocytes as well as their capacity to respond to cues present in their environment. In this review, we will focus on the latest discoveries regarding the role of the actomyosin cytoskeleton in optimizing immune cell migration in complex environments, with a special focus on recent insights provided by physical modeling.

TRENDS

-Immune cells in vivo mostly use non-adherent confined migration. This type of migration relies on Myosin II-dependent actin retrograde flow, which generates forward propulsion forces by friction with the environment, rather than through specific receptor-ligand interactions.

-An alternation of fast and slow migration conducted by distinct actin subcellular pools is observed in many immune cells. Such intermittent migration mode can optimize space exploration by immune cells.

-Immune cell migration is guided by a combination of chemical and physical environmental cues. The actin cytoskeleton contributes to detection and response to these cues, allowing immune cells to integrate them and navigate in complex environments.

Effective immune responses rely on optimized cell migration

In mammals, the adaptive immune response results from the collective effort of distinct cell populations that circulate between tissues and/or lymphoid organs. While detection of danger often occurs in peripheral tissues, i.e. in the sites that are more often exposed to external threats such as the skin and mucosa, initiation of the adaptive immune response primarily takes place in lymphoid organs. Multiple immune players are at work: leukocytes such as neutrophils and monocytes directly migrate to the site of infection or damage to provide a rapid defense, while tissue-resident dendritic cells (DCs) that detect danger at the periphery transport the information to lymph-nodes for presentation to T lymphocytes, which in turn interact with B lymphocytes for full adaptive immunity activation. It therefore appears that the success of the immune response relies on the ability of these various cell populations to be at the right place at the right time to efficiently perform their immune function. How is their migration optimized to ensure immune efficacy? We will focus our review on this question and present recent evidence highlighting how the actomyosin cytoskeleton helps leukocytes adapt their migration mode to their functional requirement in time and space, as well as to the tremendous physical complexity of the tissues they navigate through. We will further emphasize how physical modeling has helped immunologists move forward in the unraveling of the basic ingredients that account for leukocyte locomotion.

THE ACTIN CYTOSKELETON IN FORCE GENERATION AND CELL

MIGRATION

Basics of actin-dependent cell migration: forces and adhesion/ friction.

Beyond the case of immune cells, defining the basic mechanisms of eukaryotic cell migration in general has been a major challenge. Besides the indisputable progress made by cell biology and biochemistry to identify the molecular players involved, the contribution of physical modeling to the field has become very important over the last decade [START_REF] Danuser | Mathematical modeling of eukaryotic cell migration: insights beyond experiments[END_REF][START_REF] Juelicher | Active behavior of the cytoskeleton[END_REF][START_REF] Prost | Active gel physics[END_REF]. Basic physical laws show that motion at the scale of the cell can occur only under two main requirements:

(1) force generation and (2) momentum transfer to the environment, which implies a contact interaction with the cell, for example through adhesion or friction (Figure 1). At the molecular scale, mechanical forces involved in cell migration are in most of cases produced by the actomyosin system, which is extremely conserved in the eukaryotic world. We refer to this system as an "active system" because it converts the energy of ATP hydrolysis into mechanical work. Conversion occurs through two main mechanisms. First, the polymerization of actin filaments, which generates forces by pushing against the cell membrane, for example in cell protrusions such as lamellipodia or filopodia. Second, the active crosslinking of actin filaments by molecular motors, in particular myosin II, which exerts contractile stresses on the actin network. Regarding momentum transfer, it has been classically attributed to adhesion complexes such as focal adhesions in fibroblasts or podosomes in immune cells, which involve transmembrane proteins from the integrin family. In this picture, a migrating cell is characterized by an adherent protrusive actin network at the cell front, which pushes the leading edge forward, and a contractile actomyosin network at the back that drags the cell rear. If these elementary molecular mechanisms are now fairly well characterized, their global integration and coordination at the cell scale is however not fully understood, and motile phenotypes can vary significantly between types of cells and microenvironments.

Figure 1: Actin, forces and non-adherent migration under confinement. Myosin II accumulation at the back of the cell maintains the actin retrograde flow, which generates unspecific friction between the cortex and the environment allowing momentum transfer. This results in effective non-adherent migration, even in environments preventing any adhesion as long as confinement can provide some level of friction.

Immune cells in confinement undergo actin-dependent non-adhesive cell migration

Traditionally, cells relying on strong adhesion complexes and pronounced protrusion activity at their leading edge are classified as belonging to the mesenchymal migration mode, while less adherent cells with a roundish phenotype and higher contractile capacity belong to the amoeboid mode [START_REF] Sanz-Moreno | Rac activation and inactivation control plasticity of tumor cell movement[END_REF]. Following this classification, immune cells such as DCs, which lack focal adhesions and migrate in a myosin II dependent manner, display an amoeboid phenotype.

However, this standard classification of migration modes, which tends to assign to each cell type a specific migration mechanism has been challenged over the recent years by different studies that showed that the physical properties of the cell environmentgeometric confinement and adhesion -could significantly change the motile phenotypes of a given cell type [START_REF] Callan-Jones | Actin flows in cell migration: from locomotion and polarity to trajectories[END_REF][START_REF] Paluch | Focal Adhesion-Independent Cell Migration[END_REF]. In particular, it was already observed in vitro by Malawista & de Boisfleury [START_REF] Malawista | Random locomotion and chemotaxis of human blood polymorphonuclear leukocytes (PMN) in the presence of EDTA: PMN in close quarters require neither leukocyte integrins nor external divalent cations[END_REF] that leukocytes with impaired adherence could migrate only if confined between two flat surfaces (i.e. a 2D slab geometry, see Figure 1). More recently, it was demonstrated that activated DCs migrate in peripheral and lymphoid tissues, or in vitro in collagen gels, independently of integrins, while in vitro migration on flat 2D substrates remains adhesiondependent [START_REF] Lammermann | Rapid leukocyte migration by integrin-independent flowing and squeezing[END_REF][START_REF] Renkawitz | Adaptive force transmission in amoeboid cell migration[END_REF]. These results pointed to an important role of the local geometry of the cellular environment. In fact, geometric confinement was shown to be crucial to allow nonadhesive migration in experiments using 1D channels or 2D slabs, where geometric confinement was controlled by microfabrication techniques and adhesion varied by chemical treatment of surfaces [START_REF] Liu | Confinement and low adhesion induce fast amoeboid migration of slow mesenchymal cells[END_REF][START_REF] Bergert | Force transmission during adhesion-independent migration[END_REF]. These experiments showed that even after a non-specific chemical suppression of adhesion (for example by PEG coating), which prevented most specific cell substrate interaction on flat 2D surfaces, motile behaviors could be observed in confinement. Interestingly, these findings were shown to go beyond immune cells and a similar non-adhesive migration mode in confinement was observed in various cell types, including those classically labelled as mesenchymal in classical 2D adhesive migration assays [START_REF] Liu | Confinement and low adhesion induce fast amoeboid migration of slow mesenchymal cells[END_REF][START_REF] Ruprecht | Cortical contractility triggers a stochastic switch to fast amoeboid cell motility[END_REF]. Overall these results indicate that non-adhesive migration in confinement is a very robust migration mode, which is especially relevant to immune cells such as DCs, whose function in vivo is to patrol in the complex and intrinsically confined geometry of interstitial tissues. This does not rule out adhesion-based locomotion for immune cells, which can be required for certain steps such as transmigration, as well as in looser tissues [START_REF] Overstreet | Inflammation-induced interstitial migration of effector CD4(+) T cells is dependent on integrin alphaV[END_REF]. It rather suggests that immune cells that have to navigate through potentially very diverse tissue geometries could benefit from migration mode plasticity.

The analysis of non-adhesive motile immune cells in confinement revealed a very conserved phenotype, which displays the prototypical shape of migrating neutrophils with a pronounced uropod and a smooth, rounded front. Importantly, it is characterized by a cell-scale retrograde flow of cortical actin, which is critically driven by the contractile rear [START_REF] Renkawitz | Adaptive force transmission in amoeboid cell migration[END_REF][START_REF] Liu | Confinement and low adhesion induce fast amoeboid migration of slow mesenchymal cells[END_REF][START_REF] Bergert | Force transmission during adhesion-independent migration[END_REF][START_REF] Ruprecht | Cortical contractility triggers a stochastic switch to fast amoeboid cell motility[END_REF]. This retrograde actin flow, driven by a gradient of contractile stress in the actin network, is at the core of adhesion-independent migration: force transmission to the substrate is then mediated by a non-specific effective friction that results from the indirect interaction (involving either transmembrane proteins or lipids) of flowing actin filaments and extracellular matrix (ECM) molecules, and does not require specific adhesion complexes. Indeed, unspecific friction can be generated by leukocyte surface molecules, which may contain low affinity binding sites for extracellular proteoglycans, collagens or laminins. They may vary in composition and therefore in the "molecular" friction they impose on the motile leukocyte. Friction forces may also result from the microvilli or veiled structures present at the surface of some leukocytes such as neutrophils, DCs or T cells [START_REF] Von Andrian | A central role for microvillous receptor presentation in leukocyte adhesion under flow[END_REF], which provide what we could call "geometrical" or "structural" friction. Importantly, such non-specific friction is drastically increased in confinement due to a higher pressure, which can yield sufficient propulsion forces even on slippery surfaces such as PEGylated surfaces [START_REF] Liu | Confinement and low adhesion induce fast amoeboid migration of slow mesenchymal cells[END_REF][START_REF] Bergert | Force transmission during adhesion-independent migration[END_REF][START_REF] Hawkins | Pushing off the walls: a mechanism of cell motility in confinement[END_REF]. This mechanism was originally called chimneying [START_REF] Malawista | Random locomotion and chemotaxis of human blood polymorphonuclear leukocytes (PMN) in the presence of EDTA: PMN in close quarters require neither leukocyte integrins nor external divalent cations[END_REF][START_REF] Friedl | CD4+ T lymphocytes migrating in three-dimensional collagen lattices lack focal adhesions and utilize beta1 integrin-independent strategies for polarization, interaction with collagen fibers and locomotion[END_REF]. Interestingly, it was shown [START_REF] Renkawitz | Adaptive force transmission in amoeboid cell migration[END_REF] that in DCs, the actin flow speed is significantly increased in non-adherent conditions to compensate the lack of adhesion and overall maintain the cell speed. These main features are recapitulated by minimal physical models based on active gel theory [START_REF] Prost | Active gel physics[END_REF][START_REF] Bergert | Force transmission during adhesion-independent migration[END_REF][START_REF] Maiuri | Actin flows mediate a universal coupling between cell speed and cell persistence[END_REF][START_REF] Hawkins | Spontaneous contractility-mediated cortical flow generates cell migration in three-dimensional environments[END_REF][START_REF] Callan-Jones | Active Gel Model of Amoeboid Cell Motility[END_REF], and even seem reproducible in reconstituted systems [START_REF] Shah | Symmetry breaking in reconstituted actin cortices[END_REF], which pleads for the robustness of non-adherent confined migration in immune cells and beyond. At larger scales, it was argued that cell scale actin flows observed in nonadherent migration stabilized cell polarity, thus leading to more persistent cell trajectories and potentially a more efficient exploration of space [START_REF] Maiuri | Actin flows mediate a universal coupling between cell speed and cell persistence[END_REF].

ACTIN DYNAMICS OPTIMIZE IMMUNE CELL TRAJECTORIES AND FUNCTION

From the first part of this review, we learned that the actin cytoskeleton controls both the generation of forces and the transfer of momentum to serve the motility of immune cells. In this second part, we will discuss how actin dynamics in migrating leukocytes determine the type of trajectory they display when evolving in complex environments and accordingly, influence their immune function.

Actin dynamics determine the migratory pattern of immune cells

Through regulation of actin nucleation

Analysis of actin dynamics in migrating DCs and T lymphocytes has revealed that their migratory behavior is often adapted to their immune function. Such adaptation is particularly evident when analyzing the migration modes of immature and mature DCs. While immature DCs, whose main function is tissue patrolling, alternate phases of slow and fast migration, mature DCs, which are in charge of transporting antigens to lymph nodes to initiate the immune response, migrate at a rather constant high speed and with a higher persistence [START_REF] Vargas | Innate control of actin nucleation determines two distinct migration behaviours in dendritic cells[END_REF].

By investigating actin dynamics in these cells, two separate actin pools were identified as accounting for these different migratory patterns. At the cell rear, actin cables nucleated by the formin mDia1 downstream of the RhoA small GTPase are responsible for fast and persistent migration, both in immature and mature DCs. The second actin pool identified is located at the front of immature DCs, mostly in ruffles and around macropinosomes, and depends on nucleation of branched actin by the Arp2/3 complex downstream of the small GTPase Cdc42. It contributes to antigen capture but reduces cell velocity in immature DCs.

The Cdc42-Arp2/3 axis is inactivated upon DC maturation, leading to the loss of actin at the cell front, which has two consequences: (1) it down-regulates antigen capture and (2), together with CCR7 upregulation, it allows DCs to migrate in a faster and more directional manner towards lymphatic vessels and lymph nodes. Consistent with these findings, it was shown that the deletion of the Hem1 subunit of WAVE, the Nucleating Promoting Factor (NPF) that activates Arp2/3 at the leading edge, leads to a loss of lamellipodia in immature DCs [START_REF] Leithner | Diversified actin protrusions promote environmental exploration but are dispensable for locomotion of leukocytes[END_REF]. They then adopt a needle-like shape that depends on F-actin nucleation by formins.

The effect of WAVE deletion is strikingly different on mature DCs, which present a rounded cell body but numerous dynamic filopodia that extends in multiple directions. These results point toward a differential regulation of actin nucleation by Arp2/3 and formins, depending on the state of the cell and leading to distinct intrinsic migratory properties. Interestingly, similar observations have been made in neutrophils [START_REF] Wilson | Mechanisms of leading edge protrusion in interstitial migration[END_REF] as well as in T lymphocytes, in which mDia1 is required for migration [START_REF] Eisenmann | T cell responses in mammalian diaphanous-related formin mDia1 knock-out mice[END_REF][START_REF] Tanizaki | Rho-mDia1 pathway is required for adhesion, migration, and Tcell stimulation in dendritic cells[END_REF] while Arp2/3 is not [START_REF] Moreau | Signal strength regulates antigen-mediated T-cell deceleration by distinct mechanisms to promote local exploration or arrest[END_REF]. In agreement with these findings, Arp2/3 activity is mainly required for Integrin-dependent cellular functions of macrophages in vivo, this complex being dispensable for the locomotion of these cells in 3-dimensional environments [START_REF] Rotty | Arp2/3 Complex Is Required for Macrophage Integrin Functions but Is Dispensable for FcR Phagocytosis and In Vivo Motility[END_REF]. It therefore appears that most leukocytes do not rely on branched actin nucleation for migration in confinement, consistent with their migration being independent of adhesion in such complex environment.

Through regulation of actin-based molecular motors

Actin-based molecular motors, which regulate the dynamics of the actin cytoskeleton, further play a key role in determining the migration mode of leukocytes. This particularly applies to DCs: the arrest phases observed when Arp2/3 nucleates actin at the front of immature DCs are associated to the cell front recruitment of myosin II, which results in its depletion from the cell rear [START_REF] Chabaud | Cell migration and antigen capture are antagonistic processes coupled by myosin II in dendritic cells[END_REF]. Strikingly, myosin II local inhibition at the front of these cells is sufficient to increase their speed. These transient enrichments of myosin II at the front of immature DCs not only decrease their speed but further help the formation and maturation of macropinosomes, i.e. the arrival of their content to lysosomes, where they are processed for presentation onto MHC molecules. Consistent with these findings, periodic recruitment of myosin II at the cell front is mediated by its interaction with the MHC class II-associated Invariant Chain (Ii or CD74) [START_REF] Faure-Andre | Regulation of dendritic cell migration by CD74, the MHC class II-associated invariant chain[END_REF]. We proposed that diversion of myosin II by Ii from the migratory apparatus at the rear of immature DCs to their front allows the coordination of antigen capture and cell migration. Accordingly, mature DCs, which neither nucleate actin nor recruit myosin II at their front migrate in a fast and continuous manner, similarly to Iideficient immature DCs [START_REF] Vargas | Innate control of actin nucleation determines two distinct migration behaviours in dendritic cells[END_REF][START_REF] Faure-Andre | Regulation of dendritic cell migration by CD74, the MHC class II-associated invariant chain[END_REF]. Consistent with the idea that migration of cells under confinement relies on an actin retrograde flow induced by an increased contractility at the rear of the cell (See first part), the recruitment of myosin II at the front of the cell would perturb the gradient of contractility and as a result would decrease actin flow and thus cell speed [START_REF] Hawkins | Pushing off the walls: a mechanism of cell motility in confinement[END_REF].

Figure 2: Actomyosin control of migratory patterns of immune cells. In dendritic cells, formin-mediated cabled actin polymerization at the rear of the cell results in fast directional migration. This is reinforced by myosin accumulation at the back by Invariant chain leading to higher contractility at the rear. On the contrary, Arp2/3-mediated branched actin together with Myosin II and Ii at the front of the cell is associated with slow migration and environment sampling by macropinocytosis. Alternance of these two types of migration (whether it is cell intrinsic or environment driven) optimizes search strategy of the environment. Interestingly similar cytoskeleton and migration behaviors have been reported for other immune cells such as T cells of NK cells.

Physical modeling of the competition for myosin II of the cell rear and the cell front indicates that it generates a dynamic instability whereby cells switch from unidirectional persistent migration to self-oscillation [START_REF] Lavi | Deterministic patterns in cell motility[END_REF], suggesting that this will apply to any cell wherein there is competition for limited resources involved in locomotion. Of note, B and T lymphocytes also use myosin II to migrate in confinement [START_REF] Faure-Andre | Regulation of dendritic cell migration by CD74, the MHC class II-associated invariant chain[END_REF][START_REF] Jacobelli | Confinement-optimized three-dimensional T cell amoeboid motility is modulated via myosin IIA-regulated adhesions[END_REF]. Interestingly, arrest phases upon TCR activation require the down-regulation of myosin II activity [START_REF] Friedman | Surface-bound chemokines capture and prime T cells for synapse formation[END_REF]. Similarly, in activated natural killer (NK) cells, myosin II is needed for granule transport towards the target cell [START_REF] Andzelm | Myosin IIA is required for cytolytic granule exocytosis in human NK cells[END_REF].

Altogether, these results suggest that a similar scenario might be operating in these cells:

myosin II enrichment at their rear promotes their migration and its diversion to the front in response to antigen receptor stimulation helps these cells reducing their speed while forming an immune synapse with their antigen presenting (B and T lymphocytes) or target (NK cells) cell [START_REF] Jacobelli | Myosin-IIA and ICAM-1 regulate the interchange between two distinct modes of T cell migration[END_REF][START_REF] Vascotto | The actin-based motor protein myosin II regulates MHC class II trafficking and BCR-driven antigen presentation[END_REF]. In vivo imaging of myosin II at the single cell level should further substantiate this paradigm, according to which diversion of myosin II from the front to the back and viceversa would be central in coordinating immune cell migration to other immune cell functions.

Another interesting actin-based motor protein that has been shown to modify the migration modes of T lymphocytes is the myosin IG [START_REF] Gerard | Detection of rare antigen-presenting cells through T cell-intrinsic meandering motility, mediated by Myo1g[END_REF]. This is a non-classical calcium-responsive myosin that binds to membrane-associated lipids such as PI(4,5)P 2 through their tail and to actin through their head. By linking the actin cytoskeleton to the plasma membranes, class I myosins have been shown to be major regulators of lymphocyte membrane tension [START_REF] Gerard | Detection of rare antigen-presenting cells through T cell-intrinsic meandering motility, mediated by Myo1g[END_REF][START_REF] Santos-Argumedo | Class I myosins in B-cell physiology: functions in spreading, immune synapses, motility, and vesicular traffic[END_REF].

Noticeably, myosin IG-deficient T cells migrate faster and change direction less often that their wild-type counterpart, suggesting that phases of arrest are facilitated by this motor protein and might thus require a tight regulation of surface tension. Whether myosins I also control the locomotion modes of immature and mature DCs remain to be investigated.

Intermittent migration: an internal clock?

The function of many immune cells first depends on their capacity to find a needle in the haystack of the tissue environment. For example, immature DCs need to efficiently patrol tissues to detect rare danger-associated antigens, while naïve T cells need to sample many APCs before potentially finding the one presenting its cognate antigen in a lymph node. Here, we will present recent experimental and theoretical evidence suggesting that by imposing specific migration modes to leukocytes, the actin cytoskeleton contributes to the optimization of their trajectories and immune function.

As mentioned above, immature DCs alternate fast and slow motility phases depending on the subcellular localization of their actomyosin cytoskeleton: when myosin II contracts actin at the DC rear, it triggers forward movement, whereas it reduces migration but allows antigen capture when it contracts actin at the cell front. Interestingly, alternating fast migration with limited environment sampling and slow migration with high antigen uptake can optimize the search for hard to find targets in a large space, and is referred to as an "intermittent random walk" (See Textbox). The duration of the migration periods in immature DCs lies close to the optimal values determined by theoretical modeling [START_REF] Chabaud | Cell migration and antigen capture are antagonistic processes coupled by myosin II in dendritic cells[END_REF], suggesting that the internal clock defined by the regulation of the actomyosin cytoskeleton has evolved to optimize the sampling of the environment by these cells. The use of an intermittent migration mode might thus help immature DCs finding rare target antigens (separated by more than 800 μm), explaining how they efficiently perform their immune function despite their low concentration in peripheral tissues.

In vivo, T cells were also found to alternate phases of high and low motility [START_REF] Miller | Autonomous T cell trafficking examined in vivo with intravital two-photon microscopy[END_REF]. However, given the complex environment of tissues, these observations cannot assess whether this stop and go behavior is an intrinsic property of T cells or whether it is environmentally driven.

Modeling the "stop and go" behavior of T cells has resulted in distinct interpretations. It could be a consequence of an internal clock that would make T cells adopt a Levy-walk search strategy (See Textbox) as was described for migration in the infected brain [START_REF] Harris | Generalized Levy walks and the role of chemokines in migration of effector CD8+ T cells[END_REF].

Alternatively, it can be explained by the encounter of obstacles in the lymph node during random constant migration [START_REF] Beltman | Lymph node topology dictates T cell migration behavior[END_REF] and/or by opposite chemotactic go signals and TCRdependent stop signals that T cells integrate while migrating [START_REF] Dustin | Stop and go traffic to tune T cell responses[END_REF]. Interestingly, in microchannels, contrary to immature DCs, naïve T cells do not exhibit intrinsic alternate phases of stop and go [START_REF] Moreau | Signal strength regulates antigen-mediated T-cell deceleration by distinct mechanisms to promote local exploration or arrest[END_REF][START_REF] Jacobelli | Confinement-optimized three-dimensional T cell amoeboid motility is modulated via myosin IIA-regulated adhesions[END_REF], suggesting that stop phases observed in vivo might rather result from constrains imposed by their environment. Nonetheless, the observation that Myosin IGdeficient T lymphocytes turn less frequently indicates that an actin-dependent intrinsic component might also be at work [START_REF] Gerard | Detection of rare antigen-presenting cells through T cell-intrinsic meandering motility, mediated by Myo1g[END_REF]. More recently, comparative modeling of T cell trajectories in lymph nodes has uncovered the heterogeneity of T cell behaviors in terms of speed, pauses and turns, while evolving in the same microenvironment [START_REF] Banigan | Heterogeneous CD8+ T cell migration in the lymph node in the absence of inflammation revealed by quantitative migration analysis[END_REF][START_REF] Read | Leukocyte Motility Models Assessed through Simulation and Multi-objective Optimization-Based Model Selection[END_REF], suggesting that T cells in slightly different states may have different intrinsic migratory properties giving rise to distinct search strategies. Interestingly, neutrophil migration in response to laserinduced tissue damage can also be modeled by a Levy walk [START_REF] Read | Leukocyte Motility Models Assessed through Simulation and Multi-objective Optimization-Based Model Selection[END_REF]. Beyond the specific choice of random walk model, neutrophils, just like DCs, display a stop and go behavior, which might optimize their chances to find and eliminate the microbes in tissues.

In summary, recent data advocate that leukocytes have rather optimized search strategies in vivo that are adapted to the density of targets and the tissue they navigate in. However, the contribution of stochastic cell-autonomous processes (such as an acto-myosin internal clock) and deterministic environmentally driven biases (such as neighboring cells or extracellular matrix) remains to be clarified for the different immune cell types.

TEXT BOX: Which strategy is the best for immune cells looking for a target? Intermittent search strategy versus Levy walks models. Different theoretical models have been used to characterize immune cell trajectories and to estimate their efficiency at finding a target. These studies emphasize the difficulty of identifying the mode of leukocyte migration that gives the best trade-offs over the numerous parameters characterizing migration, but also highlight the power of modeling for formulation of new hypotheses on intrinsic versus extrinsic migratory properties of immune cells.

Regarding target finding, the two main models used are "intermittent search strategy", which alternates fast migration with limited environment sampling and slow migration with sampling, and "Levy walks", which consists of a succession of randomly oriented persistent runs, whose lengths are broadly distributed. Both have been shown theoretically to efficiently explore space. In practice, Levy walks share a similar stop and go behavior with intermittent random walks, and their experimental identification is often disputed. The main difference relies on the hypothesis that target detection (e.g. antigen uptake in the case of DCs) is more efficient during pauses in intermittent random walks, whereas it is assumed independent of cell speed in Levy walks.

ACTIN HELPS IMMUNE CELLS TO NAVIGATE IN A COMPLEX

ENVIRONMENT

As highlighted in the introduction of this review, immune cells migrate in complex environments, which they can patrol randomly. Nonetheless, in some cases, they need some guidance to find their path: for example, when DCs become activated, they must reach lymphatic vessels to leave the tissues and migrate to lymph nodes in order to meet T lymphocytes. While chemokines have been thought for long to guide immune cells, it is only recently that the existence and the role of chemokine gradients have been formally demonstrated in vivo [START_REF] Weber | Interstitial dendritic cell guidance by haptotactic chemokine gradients[END_REF][START_REF] Sarris | Inflammatory chemokines direct and restrict leukocyte migration within live tissues as glycan-bound gradients[END_REF]. Similarly, although the concept of physical guidance of immune cells is well admitted [START_REF] Charras | Physical influences of the extracellular environment on cell migration[END_REF], the individual contribution of the physical cues (confinement, stiffness, topology…) that guide them in vivo and the underlying mechanisms are far from being understood. Being guided requires two processes: the first one is to detect the guidance signal and the direction it indicates, and the second is to follow this direction by steering the migration path. Here, we will address the contribution of the actomyosin machinery to the guidance of immune cells following either chemical or physical guidance cues. We focus here on interstitial migration, but one should not forget that leukocyte crossing of mechanical barriers imposed by endothelial cells implicates specific mechanisms (during transmigration and diapedesis, via paracellular or transcellular routes [START_REF] Carman | T Lymphocyte-Endothelial Interactions: Emerging Understanding of Trafficking and Antigen-Specific Immunity[END_REF][START_REF] Filippi | Mechanism of Diapedesis: Importance of the Transcellular Route[END_REF]).

The actomyosin cytoskeleton in chemical guidance of leukocytes

Different mechanisms of chemotaxis have been proposed for leukocytes. While approaching the chemokine source they can increase: (1) their migration speed, a process referred to as orthotaxis, (2) their persistence, or (3) both parameters. Orthotaxis has recently been observed when analyzing the migration of neutrophils in zebrafish [START_REF] Sarris | Inflammatory chemokines direct and restrict leukocyte migration within live tissues as glycan-bound gradients[END_REF], as well as in mature DCs migrating in immobilized chemokine gradients in collagen gels or in the mouse skin [START_REF] Vargas | Innate control of actin nucleation determines two distinct migration behaviours in dendritic cells[END_REF][START_REF] Weber | Interstitial dendritic cell guidance by haptotactic chemokine gradients[END_REF].

Interestingly, in the latter case, guidance is not controlled by Arp2/3, but rather by the formin mDia1, which is also needed for T lymphocyte chemotaxis [START_REF] Eisenmann | T cell responses in mammalian diaphanous-related formin mDia1 knock-out mice[END_REF][START_REF] Sakata | Impaired T lymphocyte trafficking in mice deficient in an actinnucleating protein, mDia1[END_REF]. Although the mechanisms by which mDia1 controls the chemotactic response of DCs and T cells are not fully understood, the results obtained in both cell types are compatible with F-actin nucleation in response to chemokine stimulation being impaired. Formins might also play a role in the recently described "short-term directional memory of migrating HL-60 neutrophil-like cells" [START_REF] Prentice-Mott | Biased migration of confined neutrophil-like cells in asymmetric hydraulic environments[END_REF]. In this scenario, the presence of a chemokine gradient imposes the initial cell polarization and direction of migration, but migration persistence mostly results from directional memory. This would help leukocytes navigating in noisy environments. It might further provide an explanation for experiments showing that persistence of migration might be opposite to chemokine gradient when chemokines are released in waves. When the wave arrives to the front of the cell, it imposes cell polarization and the migration directionality.

When the wave passes the cell, inverting the chemokine gradient along the cell axis, directional memory remains and keeps the cell moving forward. Nevertheless, prolonged exposure to a strong opposite gradient of chemokine can overcome this directional memory and force a cell to change direction.

Although, as discussed above, Arp2/3 activity is dispensable for the motility of immune cells in confinement, a recent study has highlighted the important role of the WAVE complex, which promotes Arp2/3-dependent actin nucleation at the cell front, in the chemotactic response of DCs [START_REF] Leithner | Diversified actin protrusions promote environmental exploration but are dispensable for locomotion of leukocytes[END_REF]. On one hand, deletion of the WAVE gene renders immature DCs more persistent and faster, consistent with the results obtained with Arp2/3-deficient cells [START_REF] Vargas | Innate control of actin nucleation determines two distinct migration behaviours in dendritic cells[END_REF].

However, WAVE-deficient immature DCs have troubles turning in response to a chemokine gradient, even though their chemokinetic response (increase in speed in response to chemokine) remains unaltered. How WAVE contributes to such direction changes in immature DCs remains to be determined. On the other hand, in mature DCs, knocking out the WAVE gene results in the loss of the lamellipodium and appearance of filopodia. This compromises their ability to choose a direction as well as to find the pores for entering into lymphatic vessels, resulting in impaired migration of mature DCs to lymph nodes. These observations suggest that WAVE (and the resulting actin structures) might help sensing the environment and choosing an appropriate path. Whether the phenotype of WAVE-deficient DCs can be fully attributed to impaired Arp2/3 activation has not been shown. Interestingly, recent results obtained on Arp2/3-deficient macrophages suggest that it is only required for these cells to follow immobilized gradient of chemokines, an integrin-dependent process referred to as haptotaxis [START_REF] Rotty | Arp2/3 Complex Is Required for Macrophage Integrin Functions but Is Dispensable for FcR Phagocytosis and In Vivo Motility[END_REF].

The actomyosin cytoskeleton in leukocyte physical guidance

While a lot of work has been focused on how cells interpret and follow chemokine gradients, it is only recently that efforts have been developed to evaluate the impact of physical cues on cell migration and guidance. This is particularly relevant for immune cells as, being highly migratory, they often have to cross tissues that exhibit different physical properties including rigidity, local topology, hydraulic resistance, etc…How do they adapt to the specific physical cues of the tissues they migrate through to be able to reach their final destination?

Stiffness

One physical property that varies greatly between different tissues and that can be sensed by cells, in general, is rigidity or stiffness [START_REF] Discher | Tissue cells feel and respond to the stiffness of their substrate[END_REF]. Mechanosensing of global and local stiffness of the substrate during migration implicates the actomyosin contraction as well as integrindependent adhesion [START_REF] Pasapera | Rac1-dependent phosphorylation and focal adhesion recruitment of myosin IIA regulates migration and mechanosensing[END_REF]. Generally, cells tend to migrate towards stiffer environments, a phenomenon referred to as durotaxis, which is associated to increased actomyosin contractility [START_REF] Trichet | Evidence of a large-scale mechanosensing mechanism for cellular adaptation to substrate stiffness[END_REF]. As in vivo interstitial migration of immune cells occurs independently of integrins [START_REF] Lammermann | Rapid leukocyte migration by integrin-independent flowing and squeezing[END_REF], it is not clear whether these cells do sense the rigidity of their environment while evolving within tissues. Rigidity sensing through integrins might nonetheless play a role in situations where these molecules are involved, for example in migration along haptotactic chemokine gradients (see above), or in extravasation from vessels into tissues or lymphoid organs. In this context, it would be interesting to assess whether there are chemical or physical cues that are dominant over the other. For example, what does happen if a leukocyte simultaneously meets a soft-to-stiff and a chemokine gradient? Of note, it is also possible that immune cells have evolved to be insensitive to changes in the rigidity of their environment so that they can equally patrol tissues whether they are soft or stiff.

Constrictions

Another highly variable parameter within and between different tissues is porosity. Indeed, the organization of the ECM and the intercellular space of organs and membranes is such that immune cells often end up migrating in narrow spaces such as pores or confined channels. In vivo or in collagen gels, some immune cells can increase the porosity and dig their way through thanks to leukocyte proteases that degrade the ECM (such as neutrophil elastase, DC matrix-metalloproteases, cytotoxic T lymphocyte granzyme B). Yet, immune cells still encounter geometries exhibiting very small holes, experimentally in channels but also physiologically such as in the ear dermis [START_REF] Raab | ESCRT III repairs nuclear envelope ruptures during cell migration to limit DNA damage and cell death[END_REF]. In such geometries, the nucleus, as the stiffer organelle within the cell (due to the viscosity of chromatin and the presence of lamins), has been shown to be the main factor limiting cell locomotion [START_REF] Lammermann | Rapid leukocyte migration by integrin-independent flowing and squeezing[END_REF][START_REF] Wolf | Physical limits of cell migration: control by ECM space and nuclear deformation and tuning by proteolysis and traction force[END_REF][START_REF] Harada | Nuclear lamin stiffness is a barrier to 3D migration, but softness can limit survival[END_REF][START_REF] Davidson | Design of a microfluidic device to quantify dynamic intranuclear deformation during cell migration through confining environments[END_REF]. This effect can be used to design in vitro cell guiding assays [START_REF] Caballero | Ratchetaxis: Long-Range Directed Cell Migration by Local Cues[END_REF][START_REF] Le Berre | Geometric Friction Directs Cell Migration[END_REF]. Interestingly, the nuclei of different immune cell types do not exhibit the same size or the same deformability. This could enable or preclude different cell types from moving in tissues presenting small pores. The most striking example is neutrophils, which display multi-lobulated highly deformable nuclei and can therefore migrate in smaller holes than the majority of cells [START_REF] Wolf | Physical limits of cell migration: control by ECM space and nuclear deformation and tuning by proteolysis and traction force[END_REF]. Interestingly, softness of neutrophil nuclei was shown to be more important than lobularity to squeeze through small constrictions [START_REF] Rowat | Nuclear envelope composition determines the ability of neutrophil-type cells to passage through micron-scale constrictions[END_REF]. How does the nucleus deform while cells migrate in confined spaces? Is nuclear deformation a passive consequence of pushing the nucleus through a small hole? Or is there a specific mechanism involved? We recently showed that when immature DCs migrate through constrictions (of 2 µm width or below), a WAVE and Arp2/3-dependent cage of Factin assembles around their nucleus [START_REF] Thiam | Perinuclear Arp2/3-driven actin polymerization enables nuclear deformation to facilitate cell migration through complex environments[END_REF]. This actin cage induces nuclear lamin A breakage, making it more deformable, and enabling its passage through the constriction. This "confinement-induced actin network" might merely result from the response of the actin cortex to physical load [START_REF] Bieling | Force Feedback Controls Motor Activity and Mechanical Properties of Self-Assembling Branched Actin Networks[END_REF], as it is also observed around stiff beads that have been engulfed by DCs and remain stuck within the constriction. Interestingly, HL60 neutrophil-like cells, which express low levels of lamin A and display a softer nucleus, can pass through small constrictions without Arp2/3 and with no detectable accumulation of actin. Consistent with these observations, DCs depleted of Lamin A/C do not need Arp2/3 anymore to pass the constrictions. Notably, the requirement of an actin cage for the nucleus to migrate in confined spaces has also been described for cancer cells [START_REF] Jayo | Fascin Regulates Nuclear Movement and Deformation in Migrating Cells[END_REF] although in this case actin nucleation was dependent on Fascin interacting with the nuclear envelope protein Nesprin-2. These findings demonstrate the contribution of actin to the deformation of the nucleus and passage of a small constriction, but do not explain how the nucleus is pushed (or pulled?) through a narrow gap.

Different studies, both in mature DCs [START_REF] Lammermann | Rapid leukocyte migration by integrin-independent flowing and squeezing[END_REF] and in T cells [START_REF] Soriano | In vivo analysis of uropod function during physiological T cell trafficking[END_REF][START_REF] Jacobelli | Activated T cell trans-endothelial migration relies on myosin-IIA contractility for squeezing the cell nucleus through endothelial cell barriers[END_REF], highlighted the role of Myosin II in pushing the nucleus when a cell has to migrate through a constriction, either in collagen gels or in models of trans-endothelial migration. Surprisingly, neither immature DCs nor neutrophils need myosin II to migrate through channels with small constrictions, except in very small constrictions (1 µm in width) for neutrophils, in which case the chromatin (which is viscous) could be the limiting element, requiring more force to pass through.

Topography

Each structure encountered by immune cells while migrating in tissues can present different nanoscale topographical organization, that could define some migration paths or on the contrary prevent migration in some places. The impact of topography on immune cell migration has been studied with T cells migrating on surfaces presenting nano-grooves, ridges or angles [START_REF] Song | Sinusoidal wavy surfaces for curvature-guided migration of T lymphocytes[END_REF][START_REF] Kwon | Nanotopography-guided migration of T cells[END_REF][START_REF] Kwon | Migration of T cells on surfaces containing complex nanotopography[END_REF]. Different parameters influence T cell guidance by ridges, including the wavelength of the surface, as well as the value of angles between ridges, but also the level of confinement. The mechanisms contributing to T cell guidance by nanotopography have not been fully elucidated even though actin polymerization by Arp2/3, lamellipodium formation, and actomyosin contractility have been implicated in this process. It is also likely that microvilli or veiled structures present at the surface of leukocytes influence the guidance by nanotopographical structures, as the friction they generate will depend on the surface of the substrate. Altogether, these observations suggest that the impact of nanotopography can be very different depending on the confinement provided by the microenvironement, for example during interstitial migration versus extravasation. The precise nanotopographical structures that contribute to cell guidance in vivo have not been characterized so far.

Hydraulic resistance

Recently, hydraulic resistance has also emerged as a potential guiding clue for immune cells, leading to the concept of barotaxis [START_REF] Prentice-Mott | Biased migration of confined neutrophil-like cells in asymmetric hydraulic environments[END_REF]. When facing a bifurcation presenting two paths of distinct hydraulic resistance, neutrophils tend to choose the lower resistance path. They first extend arms in both directions, "testing" for resistance, resulting at some point in an asymmetry between the two extending arms, followed by the retraction of the shorter arm.

The mechanism by which hydraulic resistance imposes cell directionality remains unknown.

Notably, the physical cue provided by hydraulic resistance can overcome the chemical cue given by uncaging of a chemokine in front of the arm extending in high hydraulic resistance path. In this case, "chemical" polarization of the cell (as assessed by PH-Akt distribution) is reversed compared to chemotaxis, suggesting that distinct mechanisms control direction decision in cells depending on the nature of the guidance cue.

In summary, the pivotal role of actin and myosin II contractility in deciphering guidance cues and directing cell migration could help immune cells to prioritize the different cues and choose the best path so that they can efficiently navigate from one tissue to another.

Concluding Remarks and Future Perspectives

Here, we have presented multiple lines of evidence highlighting the essential role of the actomyosin cytoskeleton in the cell-intrinsic migratory properties of immune cells, as well as in their ability to respond to the chemical and physical cues present in the environment. It appears that different actin pools, which are generated by distinct actin nucleators and detected at distinct subcellular locations, exist in immune cells. Remarkably, these various actin pools are responsible for distinct cellular activities associated to cell migration. In DCs, T cells and neutrophils, the cortical actin pool localized towards the cell rear is nucleated by the formin mDia1 and responsible for forward movement in confinement. In contrast, the actin pool localized at their front is nucleated by Arp2/3, does not impact on migration but rather promotes cellular activities related to the individual functions of these cells: macropinocytosis in immature DCs, phagocytosis in neutrophils and immune synapse formation in T cells. Interestingly, this pool of actin imposes to leukocytes an intermittent migration mode that might be optimal for environment sampling. A third actin pool assembles around the nucleus of immature DCs and T cells as a result of confinement. This actin cage is also nucleated by Arp2/3 and helps deforming the nucleus for these cells to migrate through narrow pores. It is dispensable in neutrophils as they lack the Lamin A/C proteins and thus have a softer nucleus as compared to DCs. Altogether, these findings suggest that compartmentalization of actin nucleating factors might play an essential role in leukocyte locomotion and guidance by physical external cues. How are actin dynamics regulated in space and time while immune cells migrate in their natural environment? How are environmental cues and thus leukocyte actin dynamics modified in pathology? Specifically, modifications of the extracellular matrix and interstitial fluid volume have been reported in inflammatory conditions [START_REF] Kai | Force Matters: Biomechanical Regulation of Cell Invasion and Migration in Disease[END_REF]. The organization of the extracellular matrix directly influences porosity, rigidity or nanotopography of tissues, while the amount of interstitial fluid is likely to modify hydraulic resistance. Therefore, both of these parameters are expected to influence physical migration cues, and to reinforce or counteract chemical ones. Future experiments combining mouse intra-vital live imaging, tissue engineering and physical modeling should help addressing these questions in a quantitative manner (See Outstanding Questions).

OUTSTANDING QUESTIONS BOX

-What is the respective contribution of cell intrinsic properties and environment constraints in migration patterns exhibited by immune cells in vivo? -How do cells integrate distinct environmental cues? Which cues (chemical or physical) are dominant on others? -How is the environment modified in pathological situations? Are actin cytoskeleton properties still contributing to optimized immune cell function in these situations?

Figure 3 :

 3 Figure 3: Actomyosin cytoskeleton in leukocyte guidance. Immune cells are guided by a combination of chemical and physical extracellular cues. Actin is highly implicated in detection and response to these guidance cues. Having actin as a central player can enable cells to integrate the different cues and choose their global direction of migration in complex environments.

Acknowledgements

This work was supported by grants from the Association pour la Recherche contre le Cancer (ARC-PDF20140601095 to HDM) and the DCBIOL Labex (ANR-10-IDEX-0001-02-PSL and ANR-11-LABX-0043) to A.M.L.-D., as well as the ANR (PhyMax), the Fondation pour la recherché Médicale and the Institut National du Cancer to A.-M.L.-D., M.P. and R.V.

Conflict of interest statement:

The authors declare no conflict of interest.