Pietro Mesirca

Daria Mamaeva

Isabelle Bidaud

Romain Davaze

Mattia L Difrancesco

Violeta Mitutsova

Angelo G Torrente

Nikola Arsic

Joël Nargeot

Jörg Striessnig

Amy Lee

Ned J Lamb

Matteo E Mangoni

Anne Fernandez

Bradycardic mice undergo

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Stem cells with the capacity to self-renew and differentiate into several lineages can be isolated from most adult tissues and organs. However, as the largest vascularised and innervated organ in the body, and one with the life-long ability to undergo atrophy and regeneration, skeletal muscle is particularly rich in multipotent stem cells (reviewed by Peault et al., 1 and by Tamaki et al 2,[START_REF] Tamaki | Plasticity and physiological role of stem cells derived from skeletal muscle interstitium: contribution to muscle fiber hyperplasia and therapeutic use[END_REF] ). Various populations of stem cells were isolated from muscle, the best studied being satellite cells. Named from their tight association to muscle fibres, satellite cells account for muscle fibre regeneration and are an heterogeneous population (reviewed by Yin et al. [START_REF] Yin | Satellite cells and the muscle stem cell niche[END_REF] ). In addition skeletal muscle contains connective tissue-, vascularisation-, and innervation-derived progenitor and stem cells, which cooperate with satellite cells in tissue repair (reviewed by Peault et al. 1 , Tamaki et al. [START_REF] Tamaki | Plasticity and physiological role of stem cells derived from skeletal muscle interstitium: contribution to muscle fiber hyperplasia and therapeutic use[END_REF] and Ten Broek et al. [START_REF] Broek | Regulatory factors and cell populations involved in skeletal muscle regeneration[END_REF] ). Consistent with the neuro-muscular identity of skeletal muscle, differentiation of muscle-derived stem cells into different meso-ectodermal cell lineages was reported in several studies including from human muscle [START_REF] Romero-Ramos | Neuronal differentiation of stem cells isolated from adult muscle[END_REF][START_REF] Alessandri | Isolation and culture of human muscle-derived stem cells able to differentiate into myogenic and neurogenic cell lineages[END_REF][START_REF] Uezumi | Functional heterogeneity of side population cells in skeletal muscle[END_REF] and after clonal growth of muscle stem cells [START_REF] Tamaki | Clonal multipotency of skeletal muscle-derived stem cells between mesodermal and ectodermal lineage[END_REF] .

We previously reported that a population of muscle-derived stem cells (MDSCs) [START_REF] Arsic | Muscle-derived stem cells isolated as non-adherent population give rise to cardiac, skeletal muscle and neural lineages[END_REF] isolated from adult mouse muscle on the basis of their low adherence by sequential preplating [START_REF] Qu-Petersen | Identification of a novel population of muscle stem cells in mice: potential for muscle regeneration[END_REF][START_REF] Gharaibeh | Isolation of a slowly adhering cell fraction containing stem cells from murine skeletal muscle by the preplate technique[END_REF] is multipotent [START_REF] Arsic | Muscle-derived stem cells isolated as non-adherent population give rise to cardiac, skeletal muscle and neural lineages[END_REF] . In particular this population spontaneously differentiated into autonomously beating cardiomyocyte-like cells [START_REF] Arsic | Muscle-derived stem cells isolated as non-adherent population give rise to cardiac, skeletal muscle and neural lineages[END_REF] . This autonomous phenotype questioned whether beating cardiomyocytes derived from MDSC may be identical to pacemaker myocytes, a small population of highly specialized cells in the right atrium of adult hearts located in the Sino-Atrial (SAN) and Atrio-Ventricular Node (AVN) [START_REF] Mangoni | Genesis and regulation of the heart automaticity[END_REF] . Pacemaker cells are endowed with automatic electrical activity, and this enables them to generate the cardiac impulse that is conducted through the atrial tissue and the AVN, to the Purkinje fibre network from which it depolarizes the ventricular myocardium [START_REF] Mangoni | Genesis and regulation of the heart automaticity[END_REF] . In vertebrates, automaticity is one of the first features of cardiogenesis, with all cardiac cells of the early embryo capable of autonomous beating. During late development of the chambers and conduction system, the SAN emerges from a morphologically distinct area that develops within the sinus venosus, at the site where the right atrium enters the intercaval region, due to up-regulation of the Tbx18 and Tbx3 transcription factors and their repression of cardiogenic Nkx2.5 [START_REF] Christoffels | Development of the pacemaker tissues of the heart[END_REF][START_REF] Wiese | Formation of the sinus node head and differentiation of sinus node myocardium are independently regulated by Tbx18 and Tbx3[END_REF] . The generation and conduction of the pacemaker impulse within the SAN differs from that in working atrial myocytes in that membrane depolarisation is spontaneous and intercellular electrical resistance is high [START_REF] Verheijck | Atrio-sinus interaction demonstrated by blockade of the rapid delayed rectifier current[END_REF][START_REF] Watanabe | Modulation of pacemaker activity of sinoatrial node cells by electrical load imposed by an atrial cell model[END_REF] . To fulfil this requirement, pacemaker myocytes uniquely express a particular set of ion channels: the hyperpolarisation-activated cAMP-gated cation channel 4, HCN4; voltagegated Cav1.3 channels; and a specific subset of connexins, including connexin45 (Cx45) and Cx30.2 (but not the high-conductance gap junction proteins Cx40 and Cx43 which are typically expressed in working cardiomyocytes) [START_REF] Verheule | Connexin diversity in the heart: insights from transgenic mouse models[END_REF][START_REF] Mesirca | Functional role of voltage gated Ca(2+) channels in heart automaticity[END_REF] . Pacemaker myocytes thus represent a specialized cardiac myocyte type that is essential for proper heart function and whose properties and defining markers are distinct from those of working cardiomyocytes.

In humans, SAN dysfunction (SND) results in reduced life expectancy and necessitates the implantation of >450,000 pacemakers/year in Europe and the U.S., a number predicted to double over the next half century [START_REF] Jensen | Incidence of and risk factors for sick sinus syndrome in the general population[END_REF] . Whereas pacemaker implantation remains the primary therapy for SAN dysfunction and bradycardia-associated arrhythmias [START_REF] Mond | The 11th world survey of cardiac pacing and implantable cardioverter-defibrillators: calendar year 2009--a World Society of Arrhythmia's project[END_REF] , this approach is costly, requiring lifelong management including regular technical inspections. These limitations and complexity in the use of an electronic device are even greater in pediatric and young patients [START_REF] Rosen | The road to biological pacing[END_REF] . Considering the global impact of SAN dysfunction, it is generally agreed that new therapeutic strategies are needed.

The development of a cell-therapy approach to repair the damaged SAN and restore pacemaker activity is paramount to achieving stable, life-long improved heart function and to restoring patient quality of life [START_REF] Rosen | The road to biological pacing[END_REF] . Toward this goal it will be necessary to identify suitable sources of transplantable stem cells that are capable of differentiating, in vivo, into functional pacemaker myocytes.

In the current study, we tested the ability of MDSCs to differentiate, both in vitro and in vivo in mutant mice, into pacemaker myocytes. We report that MDSC can migrate and home to the SAN where they differentiate into pacemaker-like cardiomyocytes, and that this homing and differentiation of MDSCs ameliorates heart rhythm in congenitally bradycardic mutant mice.

Results

In vitro analysis: MDSCs spontaneously differentiate into autonomously beating cardiomyocytes with the characteristics of pacemaker cells.

MDSCs were isolated from mouse hind-limb muscle via sequential preplating of non-adherent cells, as shown in Fig. 1a and described previously [START_REF] Arsic | Muscle-derived stem cells isolated as non-adherent population give rise to cardiac, skeletal muscle and neural lineages[END_REF] . Non-adherent stem cells were replated in fresh proliferation medium every 24 hours to avoid their premature differentiation and to stimulate their proliferation. The rationale for daily replating and centrifugation is two-fold: the replating prevents loss of the less adherent stem cells, which would otherwise attach to counterparts that adhere and proliferate more rapidly (e.g., fibroblasts, myofibroblasts and pre-adipocytes); and the centrifugation depletes the cultures of muscle fibre-derived microsomes and other muscle-specific non-cellular components that may contribute to the myogenic commitment of muscle stem cells. A comparative analysis of the transcriptomes of muscle cells extracted 24 hours after activation of proliferation (corresponding to PP1) and MDSCs isolated after 7 days of pre-plating (corresponding to PP8) revealed a 12-fold increase in cyclinA2 expression (Fig. 1b), indicating a high level of cell proliferation. The same analysis revealed a 10-fold increase in the expression of Islet-1, a LIMhomeodomain transcription factor expressed in heart and pancreatic progenitor/stem cells, and a >30-fold increase in expression of Peg3/PW1, which is expressed in stem cells isolated from muscle and several adult tissues [START_REF] Besson | PW1 gene/paternally expressed gene 3 (PW1/Peg3) identifies multiple adult stem and progenitor cell populations[END_REF] . Of note, the stemness factor Nestin, whose expression is high even in PP1 cells, was increased >2-fold in PP8 MDSCs (Fig. 1b). These data confirm that 7 days of preplating non-adherent cells from mouse skeletal muscle is an effective means of isolating a proliferating stem cell population.

We previously reported that non-adherent MDSCs in PP8 cultures provided with an attachment matrix such as laminin, fibronectin, or a fibroblast layer (but not collagen) became adherent and underwent multi-lineage differentiation [START_REF] Arsic | Muscle-derived stem cells isolated as non-adherent population give rise to cardiac, skeletal muscle and neural lineages[END_REF] . Amongst the different phenotypes observed, cells with the ability to beat autonomously were observed within 3 to 5 days and these cells exhibited persistent contractile activity for over 2 months in culture (Fig. 1c and Supplementary video 1). Single beating cells or clusters of cells with coordinated beating rhythms were observed (Supplementary videos 2 and 3), and the morphology of these beating myocytes was reminiscent of that of native SAN pacemaker cells (Supplementary Fig. 1). Henceforth, we refer to these in vitro differentiated, spontaneously beating cells as MDSC-derived pacemaker-like cells (MDSC-PMs). To investigate whether these cells exhibit properties of SAN cardiomyocytes, we first analyzed a number of molecular markers of pacemaker development and activity. SAN development is initiated in a small area of the septum venosus that co-expresses Tbx18 and Islet1 transcription factors, after which expression of the Shox2 and Tbx3 transcription factors is initiated and that of Nkx2.5 is down-regulated [START_REF] Christoffels | Development of the pacemaker tissues of the heart[END_REF][START_REF] Hoogaars | Tbx3 controls the sinoatrial node gene program and imposes pacemaker function on the atria[END_REF][START_REF] Ye | A common Shox2-Nkx2-5 antagonistic mechanism primes the pacemaker cell fate in the pulmonary vein myocardium and sinoatrial node[END_REF] . RT-PCR analysis of non-differentiated MDSCs (Fig. 2a, Supplementary Table 1) revealed that Tbx18, Islet1, Shox2 and Tbx3 were expressed, whereas Nkx2.5 was not. Notably, Shox2 is a core component of the myogenic program resulting in development of the venous pole and pacemaker [START_REF] Ye | A common Shox2-Nkx2-5 antagonistic mechanism primes the pacemaker cell fate in the pulmonary vein myocardium and sinoatrial node[END_REF] , and also of the pacemaker program in embryoid bodies [START_REF] Hashem | Shox2 regulates the pacemaker gene program in embryoid bodies[END_REF] . Pacemaker-like differentiated MDSC-PMs likewise expressed Tbx18, Tbx3 and Islet1 no longer expressed Shox2 and showed little or no expression of Nkx2.5. This specific expression pattern is consistent with the identification of beating myocytes differentiated in vitro from MDSCs as mature cardiac pacemaker myocytes and not fetal-derived immature cardiomyocytes. Indeed, pacemaker cells in the adult heart differ from atrial and ventricular cardiomyocytes in that they do not express Nkx2.5, which acts as a repressor of the pacemaker gene expression program [START_REF] Christoffels | Development of the pacemaker tissues of the heart[END_REF][START_REF] Ye | A common Shox2-Nkx2-5 antagonistic mechanism primes the pacemaker cell fate in the pulmonary vein myocardium and sinoatrial node[END_REF] . In addition, pacemaker myocytes are unique in retaining Islet1 expression in adult heart [START_REF] Weinberger | Localization of Islet-1-positive cells in the healthy and infarcted adult murine heart[END_REF] .

A hallmark of cardiac pacemaker cells is their expression of the channel HCN4 [START_REF] Ludwig | A family of hyperpolarizationactivated mammalian cation channels[END_REF] , which is responsible for generating the "funny" current (If) [START_REF] Brown | How does adrenaline accelerate the heart?[END_REF] . RT-PCR analysis of pacemaker-like MDSC-PMs (Fig. 2b, Table S1) showed that they express the pore-forming subunits of HCN4 and Cav1.3 channels, both of which are required for normal cardiac pacemaker activity in mice [START_REF] Mangoni | Functional role of L-type Cav1.3 Ca2+ channels in cardiac pacemaker activity[END_REF][START_REF] Alig | Control of heart rate by cAMP sensitivity of HCN channels[END_REF][START_REF] Baruscotti | Deep bradycardia and heart block caused by inducible cardiac-specific knockout of the pacemaker channel gene Hcn4[END_REF][START_REF] Mesirca | Cardiac arrhythmia induced by genetic silencing of 'funny' (f) channels is rescued by GIRK4 inactivation[END_REF][START_REF] Torrente | L-type Cav1.3 channels regulate ryanodine receptor-dependent Ca2+ release during sino-atrial node pacemaker activity[END_REF] and humans [START_REF] Milanesi | Familial sinus bradycardia associated with a mutation in the cardiac pacemaker channel[END_REF][START_REF] Baig | Loss of Ca(v)1.3 (CACNA1D) function in a human channelopathy with bradycardia and congenital deafness[END_REF] . MDSC-PMs also express the pacemaker-specific gap junction protein Cx45 [START_REF] Christoffels | Development of the pacemaker tissues of the heart[END_REF][START_REF] Verheijck | Electrophysiological features of the mouse sinoatrial node in relation to connexin distribution[END_REF] and the cardiac contractile proteins -actinin and Troponin I (Fig. 2b). The co-expression of these proteins in beating pacemaker-like cells was tested by double-immunofluorescence of cultured, differentiated MDSCs, with cells undergoing sustained beating filmed before fixation. Fig. 2c shows immunostaining of MDSC-PMs for HCN4 and Cav1.3. Given that HCN proteins, Cav1.3, and Cx45 are also markers of neural cells, co-staining for cytoskeletal markers of striated muscle cells (cardiac Troponin I or sarcomeric -actinin) was necessary to confirm the cardiac phenotype (Fig. 2c). Of note, in the panels showing co-staining for -actinin and Cx45, a typical neural cell on the right expressed Cx45 but not -actinin. Fig. 2d displays cells co-stained for Cav1.3 and Islet1 (nuclei indicated by arrows including a phase-contrast field showing that both markers are expressed in beating cells (see Supplementary video 4).

Importantly, in vitro differentiation of muscle-derived stem cells into MDSC-PMs was not a peculiarity of mouse muscle stem cells. It was also observed in muscle stem cells isolated from adult Sprague Dawley rat muscle (Supplementary Fig. 2 and Supplementary video 5), and both the kinetics and co-expression of pacemaker markers (shown in Fig. S2 are HCN4 and -Actinin) were similar to that in mice.

We next tested MDSC-PMs for the functional properties of native sino-atrial pacemaker using current-clamp recordings (Fig. 3). Readings from isolated beating pacemaker-like myocytes revealed spontaneous repetitive action potentials at rates comparable to those produced by native SAN pacemaker myocytes (170 bpm in pacemaker-like myocytes, Fig. 3a, versus 190 bpm in native SAN myocytes [START_REF] Mesirca | Cardiac arrhythmia induced by genetic silencing of 'funny' (f) channels is rescued by GIRK4 inactivation[END_REF] ). Consistent with HCN4-positive staining (Fig. 2), MDSC-PM myocytes displayed the If current (Fig. 3b), which is involved in the pacemaker activity of native SAN myocytes [START_REF] Brown | How does adrenaline accelerate the heart?[END_REF][START_REF] Difrancesco | The role of the funny current in pacemaker activity[END_REF] . We then recorded the spontaneous contraction frequency of beating cells by using a cell edge detection device (see methods). The selective If inhibitor ivabradine (IVA) [START_REF] Bois | Mode of action of bradycardic agent, S 16257, on ionic currents of rabbit sinoatrial node cells[END_REF] reduced the frequency of spontaneous cell contraction by more than 75%, demonstrating that the If is a key determinant of the spontaneous activity of pacemaker-like myocytes (Fig. 3c).

Whether contracting myocytes generate spontaneous intracellular Ca 2+ ( Ca 2+ i) transients similar to those produced by native mouse sino-atrial pacemaker myocytes was tested by loading MSDC-PMs with Fluo-4-AM. Line-scan images (Fig. 3d) revealed spontaneous Ca 2+ i transients with upstroke and recovery phases similar in form and timing to those of native mouse pacemaker myocytes [START_REF] Torrente | L-type Cav1.3 channels regulate ryanodine receptor-dependent Ca2+ release during sino-atrial node pacemaker activity[END_REF][START_REF] Sah | Ion channel-kinase TRPM7 is required for maintaining cardiac automaticity[END_REF][START_REF] Chen | Local control of Ca2+induced Ca2+ release in mouse sinoatrial node cells[END_REF] . Line-scan images were recorded before and after the cultures were perfused with epinephrine or acetylcholine, to determine whether the frequency of spontaneous Ca 2+ i transients was regulated in opposite directions by the activation of -adrenergic [START_REF] Torrente | L-type Cav1.3 channels regulate ryanodine receptor-dependent Ca2+ release during sino-atrial node pacemaker activity[END_REF] and muscarinic [START_REF] Mesirca | G protein-gated IKACh channels as therapeutic targets for treatment of sick sinus syndrome and heart block[END_REF] receptors. Indeed, epinephrine (2 nM, Fig. 3d) accelerated, whereas acetylcholine (50 nM, Fig. 3d) reduced, the frequency of spontaneous Ca 2+ i transients. Ryanodine receptors (RyRs) are also involved in sino-atrial pacemaker activity (reviewed in ref. [START_REF] Lakatta | A coupled SYSTEM of intracellular Ca2+ clocks and surface membrane voltage clocks controls the timekeeping mechanism of the heart's pacemaker[END_REF] ) and perfusion of MSDC-PMs with ryanodine (3 M, Fig. 3d) led to a near-complete arrest of spontaneous Ca 2+ i transients. Thus, RyRs appear to play a major role in the automaticity of MDSC-PMs, similar to that in native SAN pacemakers [START_REF] Lakatta | A coupled SYSTEM of intracellular Ca2+ clocks and surface membrane voltage clocks controls the timekeeping mechanism of the heart's pacemaker[END_REF] .

We previously showed that loss of Cav1.3 channels slows automaticity and leads to arrhythmia in native SAN myocytes [START_REF] Mangoni | Functional role of L-type Cav1.3 Ca2+ channels in cardiac pacemaker activity[END_REF][START_REF] Torrente | L-type Cav1.3 channels regulate ryanodine receptor-dependent Ca2+ release during sino-atrial node pacemaker activity[END_REF] . To test whether MDSC-PMs differentiated from Cav1.3 knockout (Cav1.3 -/-) mice reproduced the phenotype of native Cav1.3 -/-SAN myocytes, we compared their beating frequency to that of MDSC-PMs derived from wild-type MDSCs. As shown Fig. 3e, the rate of spontaneous Ca 2+ i transients in MDSC-PMs differentiated from Cav1.3 -/- MDSCs was significantly slower and their frequency less regular than those in MDSC-PMs from wild type MDSCs, consistent with findings from our previous work on native SAN myocytes from Cav1.3 -/-mice [START_REF] Torrente | L-type Cav1.3 channels regulate ryanodine receptor-dependent Ca2+ release during sino-atrial node pacemaker activity[END_REF][START_REF] Mesirca | G protein-gated IKACh channels as therapeutic targets for treatment of sick sinus syndrome and heart block[END_REF] .

Together, these data show that MDSCs are capable of differentiating, in vitro, into beating pacemaker-like myocytes with all the specific markers and electrophysiological properties of native cardiac pacemaker cells. Furthermore, in vitro differentiation of MDSCs derived from the muscle of bradycardic SND Cav1.3 -/-mutant reproduced the slower beating phenotype of bradycardic SND Cav1.3 -/-mutant hearts. These results also demonstrate that Cav1.3 channels play a key role in the pacemaker activity of MDSC-PMs, consistent with in vivo data from Cav1.3 -/-mice [START_REF] Mesirca | G protein-gated IKACh channels as therapeutic targets for treatment of sick sinus syndrome and heart block[END_REF][START_REF] Platzer | Congenital deafness and sinoatrial node dysfunction in mice lacking class D L-type Ca2+ channels[END_REF][START_REF] Zhang | Functional Roles of Ca(v)1.3 (alpha(1D)) calcium channel in sinoatrial nodes: insight gained using gene-targeted null mutant mice[END_REF] and from humans carrying congenital loss-of-function of Cav1.3 channels [START_REF] Baig | Loss of Ca(v)1.3 (CACNA1D) function in a human channelopathy with bradycardia and congenital deafness[END_REF] .

In vivo analysis: MDSCs injected into mice lacking Cav1.3 and Cav3.1 channels migrate and home to the SAN where they differentiate resulting in improved heart rate

To test the ability of MDSCs to differentiate in vivo into pacemaker cells and their potential therapeutic effects, we employed the Cav1.3 -/-deficient mouse, a well-characterized model of human SAN dysfunction [START_REF] Baig | Loss of Ca(v)1.3 (CACNA1D) function in a human channelopathy with bradycardia and congenital deafness[END_REF][START_REF] Mesirca | G protein-gated IKACh channels as therapeutic targets for treatment of sick sinus syndrome and heart block[END_REF] , as recipients in stem cell transplantation experiments. Both embryonic stem cells (ESCs) and induced pluripotent stem cells (iPSC) can be differentiated into SAN-like cardiomyocytes in vitro and have been shown to provide promising short-term "biological" pacemaker activity in the ventricle [START_REF] Laflamme | Heart regeneration[END_REF][START_REF] Kleger | Modulation of calcium-activated potassium channels induces cardiogenesis of pluripotent stem cells and enrichment of pacemaker-like cells[END_REF][START_REF] Chauveau | Induced Pluripotent Stem Cell-Derived Cardiomyocytes Provide In Vivo Biological Pacemaker Function[END_REF][START_REF] Protze | Sinoatrial node cardiomyocytes derived from human pluripotent cells function as a biological pacemaker[END_REF] . However, the high proliferation rate and associated tumorigenicity of these cell types preclude their direct use as stem cells for in vivo cell therapy in the absence of previous differentiation. In contrast, we found no evidence for a long-term teratogenic or tumorigenic potential of MDSCs (Supplementary Fig. 3a). Whereas mouse ESCs grafted subcutaneously onto 8-week-old immunodeficient SCID mice (n=2) induced tumour outgrowth at the site of the graft, requiring euthanasia after 3 weeks, no tumours formed in mice (n=4) engrafted with MDSCs, and the animals remained tumour-free for over 4 months after either sub-cutaneous (Supplementary Fig. 3a) or intraperitoneal transplantation (data not shown, n=6). In addition, RT-PCR analysis (n=4) revealed that MDSCs express 3 of 4 pluripotency transcription factors (Sox2, Nanog, Lin28) but not the major one, Pou5F1/Oct4 (Supplementary Fig. 3b) a result confirmed by RNAseq analysis on triplicate MDSC samples. The lack of teratoma formation after MDSC injection supports the direct use of these stem cells in vivo, without the need for prior differentiation.

At 24 and 72 hours after I.V. injection, DiI membrane-labelled MDSCs were found to be similarly distributed to major filtration organs (e.g., liver and kidney) and lymph organs (spleen and lymph nodes) in wild-type and mutant recipient mice (Davaze, Mitutsova et al. manuscript in preparation). Similar analyses of I.P.-injected, labelled-MDSCs showed enhanced MDSC homing to organs with targeted injury, such as streptozotocin-damaged pancreatic islets [START_REF] Mitutsova | Adult muscle-derived stem cells engraft and differentiate into insulinexpressing cells in pancreatic islets of diabetic mice[END_REF] . Thus, MDSCs used directly as stem cells in vivo without prior differentiation have the ability to migrate and home to a variety of organs. This property was exploited to test the capacity of MDSCs to migrate to the SAN tissue, differentiate in vivo, and restore compromised heart automaticity in our mouse models with SAN-dysfunction, as represented in Fig. 4a. MDSCs labelled with the membrane-binding cell tracker DiI-CM were transplanted, by I.V. or I.P. injection, into Cav1.3 -/-mutant mice with severe defects in SAN impulse generation and atrioventricular conduction as well as into age-matched wild-type counterparts. At 48 hours after injection, a significant number of labelled stem cells were found implanted in the SAN tissue of recipient Cav1.3 -/-mice (Fig. 4c), whereas only few were present in the SAN of wild-type mice (Fig. 4b); this finding was reproduced in 4 wild-type and 4

Cav1.3 -/-mutant mice using the same MDSC preparation. These results show that in the Cav1.3 -/- mutant mouse, effective migration of stem cells into the bloodstream after I.P. injection occurred and engraftment to the SAN tissue was enhanced compared to that in wild type SAN tissue. Such increased homing of MDSCs in mutant SAN tissue may be related to the SDF-1-CXCR4 chemotactic axis, a major pathway in the regulation of stem-cell migration and homing [START_REF] Miller | CXCR4 signaling in the regulation of stem cell migration and development[END_REF][START_REF] Stumm | CXC chemokine receptor 4 regulates neuronal migration and axonal pathfinding in the developing nervous system: implications for neuronal regeneration in the adult brain[END_REF] . Indeed, comparison of the expression of SDF1 and CXCR4 levels in SAN tissue isolated from the two groups of mice showed that SAN tissue from Cav1.3 -/-mice expressed higher levels of both SDF1 and CXCR4 than did SAN tissue from wild-type counterparts (RT-PCR analysis in Supplementary Fig. 4).

To determine whether SAN engraftment of injected wild type MDSC was followed by their differentiation into cardiac myocytes, we isolated intact SAN tissue from the hearts of Cav1.3 -/- mice 30 to 40 days after MDSC injection and performed whole-mount immunostaining for cells expressing the Cav1.3 pore-forming 1 subunit, which is absent from SAN tissue originating from the recipient mutant mouse [START_REF] Platzer | Congenital deafness and sinoatrial node dysfunction in mice lacking class D L-type Ca2+ channels[END_REF][START_REF] Christel | Distinct localization and modulation of Cav1.2 and Cav1.3 L-type Ca2+ channels in mouse sinoatrial node[END_REF] . As shown Fig. 5, the SAN of transplanted Cav1.3 -/-mice was positive for Cav1.3 staining. Notably, arrays of cells (zoomed panels 5a and 5c with 49 and 54 Cav1.3 -expressing cells, respectively) showed membrane and striated patterns of staining for Cav1.3 similar to those for native mouse SAN pacemaker cells [START_REF] Christel | Distinct localization and modulation of Cav1.2 and Cav1.3 L-type Ca2+ channels in mouse sinoatrial node[END_REF] , including increased staining at junctions between cells with typical pacemaker morphology (arrow in Fig. 5b).

The effectiveness of the differentiation of MDSCs into Cav1.3-expressing myocytes and their long-term colonisation was further confirmed by clear detection of Cav1.3-stained cells in the SAN of Cav1.3 -/-/Cav3.1 -/-double-mutant mice 5 months after IV injection of wild-type MDSCs (Supplementary Fig. 5). Staining for Cav1.3 was specific because it was absent in the SAN of control mock-transplanted Cav1.3 -/-mice (n=5, Supplementary Fig. 6).

Whether colonization of the SAN by MDSCs and their differentiation in bradycardic mutant mice was accompanied by an improvement in heart rhythm was determined by analyzing heart rate during the resting (daylight) period. To this end, telemetric ECG recordings were made in freely moving Cav1.3 -/-mice, before and at different times after the injection of undifferentiated wild-type MDSCs (Fig. 6a). Consistent with a previous study [START_REF] Platzer | Congenital deafness and sinoatrial node dysfunction in mice lacking class D L-type Ca2+ channels[END_REF] , Cav1.3 -/-mice experienced SAN dysfunction and atrioventricular blocks before injection, (Fig. 6a and Table 1). However, by 40 days after systemic transplantation of muscle-derived stem cells, the MDSC-injected mice had a significantly higher (32%, Fig. 6b) heart rate than before the procedure (Fig. 6b and Table 1), indicating that the SAN pacemaker activity had improved. Heart rate elevation in Cav1.3 -/-mice was due to improvement of SAN rate (PP interval). No significant differences were observed in heart rate and the other ECG parameters in wild-type mice. Similarly, no significant changes in heart rate were observed following implantation of only a ECG transmitter (no MDSCs; Supplementary Fig. 7a) or when control wild-type mice were injected with MDSCs (Table 1). All control animals were kept under identical conditions as MDSC-injected Cav1.3 -/-mice. Measurement of QT, rate-corrected QT (QTc) and QRS ECG intervals showed that MDSC injection did not affect ventricular repolarization, and no episodes of ventricular arrhythmia or sudden death were observed in MDSCinjected Cav1.3 -/-and wild-type mice (Table 1). We then tested whether injection of MDSC could improve the heart rate in mice lacking both Cav1.3 and Cav3.1 channels (Cav1.3 -/-/Cav3.1 -/-) [START_REF] Marger | Functional roles of Ca(v)1.3, Ca(v)3.1 and HCN channels in automaticity of mouse atrioventricular cells: insights into the atrioventricular pacemaker mechanism[END_REF] . This mouse model presents with strong SND hallmarks and highly variable SAN rate. If MDSC injection ameliorated the heart rate of Cav1.3 -/-/Cav3.1 -/-mice, this would have been reflected as an increase in SAN rate and in a reduction in the inter beat variability. Indeed, upon injection of wild-type MDSCs, the heart rates of Cav1.3 -/-/Cav3.1 -/-mice were clearly improved within 30 days (as measured during the active night-time period: +20%) (Fig. 6c-d, Table 2). Heart rate of double-mutant Cav1.3 - /-/Cav3.1 -/-and wild-type mice was also recorded under anesthesia 10 to 20 days after injection of MDSCs. This recording of sedated mice revealed a significant increase in heart rate in the doublemutant mice by 10 days (+28%, Supplementary Fig. 7b) and a decrease in the inter beat standard deviation after 20 days (Supplementary Fig. 7c), whereas similar injection of MDSCs into wild-type mice did not result in significant changes in either heart rate or inter beat standard deviation (Supplementary Fig. 7b-c). The number of SAN pauses or AV blocks after MDSC injection into either single Cav1.3 -/-or double Cav1.3 -/-/Cav3.1 -/-mutants did not change significantly (Table 1 and2). Together these data show that systemic injection of wild-type MDSCs into bradycardic mutant mice resulted in a significant improvement in the heart rate of mutant mice whereas it did not affect the heart rate of wild-type mice.

Discussion

Our data reveal that skeletal muscle harbours a population of non-tumorigenic stem cells, MDSC, that can be directly transplanted by systemic injection and are capable of differentiating into functional pacemaker-like myocytes. Given the limitations of other sources that have been considered, MDSCs represent an attractive and easily available source of stem cells with a high potential for use in cell therapy for the treatment of disorders of human heart automaticity.

In the last decade, human myoblasts (derived from satellite cells) have been on early clinical trial as a source of stem cells for myocardial autologous cell therapy raising hope of bringing functional benefit (reviewed by Menasché [START_REF] Menasche | Stem cell therapy for chronic heart failure: lessons from a 15-year experience[END_REF] ). However, it is now clearly recognized that myoblasts do not differentiate into cardiomyocytes after injection into the heart, but instead may fuse into multinucleated myotubes. Such differentiation may cause conduction blocks eventually leading to ventricular arrhythmia. This disappointing outcome essentially put a brake on considering skeletal muscle as a source of stem cells in cardiac cell therapy. Although most of the regenerative capacity of skeletal muscle throughout life is accounted for by satellite cells, it has become clear that the muscle niche is remodelled in dynamic balance with other stem cells derived from peri-vascular and peri-neural muscle compartment that represent an alternative source of MDSCs 2,9,10 .

Taking into account this alternative, our study opens a new avenue of research on the use of skeletal muscle as a source of stem cells in therapies for diseases of heart automaticity. Indeed, our data show that the systematic injection of undifferentiated MDSCs produced functional improvements in heart rhythm (and reduced arrhythmia) in recipient mutant mice, with the stem cells migrating and homing to the SAN region and differentiating into pacemaker-like cells expressing the Cav1.3 channel. Whereas alternative approaches towards effective biological pacing have been reported, with some using ion channel gene transfer in the ventricular conduction system [START_REF] Rosen | The road to biological pacing[END_REF][START_REF] Boink | HCN2/SkM1 gene transfer into canine left bundle branch induces stable, autonomically responsive biological pacing at physiological heart rates[END_REF] and others in situ reprogramming of ventricular cardiomyocytes [START_REF] Kapoor | Direct conversion of quiescent cardiomyocytes to pacemaker cells by expression of Tbx18[END_REF] , the current study is the first to demonstrate direct repair of the SAN through the in situ differentiation of transplanted stem cells.

Although transplantation of a similar population of MDSCs has been reported to improve recovery of the heart from ischemic injury, the effect in that case was attributed to the secretion of paracrine factors without significant retrieval or differentiation of donor stem cells [START_REF] Okada | Human skeletal muscle cells with a slow adhesion rate after isolation and an enhanced stress resistance improve function of ischemic hearts[END_REF] . ESCs and iPSCs can differentiate into beating, pacemaker-like cells in vitro [START_REF] Laflamme | Heart regeneration[END_REF][START_REF] Kleger | Modulation of calcium-activated potassium channels induces cardiogenesis of pluripotent stem cells and enrichment of pacemaker-like cells[END_REF] . These differentiated cells were recently shown to be able to engraft in the ventricle and support pacemaker activity [START_REF] Chauveau | Induced Pluripotent Stem Cell-Derived Cardiomyocytes Provide In Vivo Biological Pacemaker Function[END_REF][START_REF] Protze | Sinoatrial node cardiomyocytes derived from human pluripotent cells function as a biological pacemaker[END_REF] . However, their transforming and teratoma-forming potential precludes their direct use for cell therapy and requires prior cueing toward cardiac differentiation, with a potential loss of plasticity, migration and survival ability [START_REF] Laflamme | Heart regeneration[END_REF][START_REF] Mohsin | Empowering adult stem cells for myocardial regeneration[END_REF] . In contrast, MDSCs, which are non-tumorigenic, were directly transplanted into the bloodstream or peritoneal space of mutant recipient mice, where they not only homed to the SAN and differentiated into beating, pacemaker-like cells, but also reduced defects in heart automaticity that are associated with the knock-out of the Cav1.3 Ca 2+ channel [START_REF] Platzer | Congenital deafness and sinoatrial node dysfunction in mice lacking class D L-type Ca2+ channels[END_REF] . Importantly, we also show here that MDSCs can differentiate in vitro into spontaneously active MDSC-PMs, displaying features of mature SAN pacemaker cells. This also make MDSCs a convenient source of stem cells to recapitulate defects in heart automaticity ex vivo and assay potential therapeutic drugs.

In SAN cells, heart automaticity is generated by an association between the activity of ion channels such as Cav1.3 [START_REF] Mangoni | Functional role of L-type Cav1.3 Ca2+ channels in cardiac pacemaker activity[END_REF] , HCN4 [START_REF] Difrancesco | The role of the funny current in pacemaker activity[END_REF] and that of RyR-dependent Ca 2+ release from the sarcoplasmic reticulum [START_REF] Lakatta | A coupled SYSTEM of intracellular Ca2+ clocks and surface membrane voltage clocks controls the timekeeping mechanism of the heart's pacemaker[END_REF] . Genetic ablation (from muscle-donor mouse) or pharmacologic inhibition of these channel activities in spontaneously active MDSC-PMs reproduced slowing of pacemaker activity, as reported in the current literature on native SAN-resident pacemaker cells. Our results thus indicate that the pacemaker mechanism underlying spontaneous activity of MDSC-PMs is similar to that of native SAN, and support the notion that MDSCs differentiated in vitro from mutant mice can reproduce and model heart-rhythm dysfunctions. This hypothesis is in line with the capability of MDSCs to improve the heart rate of mutant mice following their colonization of the SAN and differentiation at this site.

Although the mechanism underlying the spontaneous ability of MDSCs to migrate and home to the SAN tissue of mutant mice is not fully understood, it likely involves chemotaxis via the SDF1-CXCR4 pathway, as supported by data shown in Supplementary Fig. 4. Furthermore, in light of reports on heart regeneration by exercise-activated cardiac stem cells [START_REF] Ellison | Adult c-kit(pos) cardiac stem cells are necessary and sufficient for functional cardiac regeneration and repair[END_REF] , on the activation of muscle stem cells by exercise (review by Macaluso & Myburgh [START_REF] Macaluso | Current evidence that exercise can increase the number of adult stem cells[END_REF] ), and on the presence of stem cells from recipient patients in transplanted human hearts (i.e., "chimeric transplanted hearts") [START_REF] Quaini | Chimerism of the transplanted heart[END_REF][START_REF] Laflamme | Evidence for cardiomyocyte repopulation by extracardiac progenitors in transplanted human hearts[END_REF] , it is tempting to speculate that some stem cells that have been classified as "resident cardiac" may have originated from exercise-activated circulating MDSCs. It is known that denervation, like exercise, results in long-lasting activation and proliferation of resident muscle stem cells but that 90% of these cells are subsequently lost from the muscle (and not fused to the denervated-reinnervated muscle) [START_REF] Murray | Cell proliferation in denervated muscle: time course, distribution and relation to disuse[END_REF] . In this regard, it will be important to compare profiles of circulating stem cells retrieved after exercise or muscle denervation to those in the resting state.

We recently showed that the MDSCs studied here migrate and home to streptozotocindamaged pancreatic islets 48 hours after I.P. injection and that within 10 days they differentiate into cells expressing insulin [START_REF] Mitutsova | Adult muscle-derived stem cells engraft and differentiate into insulinexpressing cells in pancreatic islets of diabetic mice[END_REF] . Further, we found that MDSCs are recruited to site(s) of injury, be it chemically induced [START_REF] Mitutsova | Adult muscle-derived stem cells engraft and differentiate into insulinexpressing cells in pancreatic islets of diabetic mice[END_REF] or mechanically induced (such as glycerol injection in one of the two tibialis muscles) (Davaze, Mitutsova et al., manuscript in preparation). Thus, the capability of MDSCs to migrate and home to damaged tissues could be exploited for therapeutic purposes.

SAN dysfunction is a multi-factorial disease that often begins with a moderate reduction in heart rate that is otherwise asymptomatic, and that this subsequently degenerates into bradycardia associated with invalidating symptoms and syncope [START_REF] Semelka | Sick sinus syndrome: a review[END_REF] . Early therapy of SAN dysfunction could potentially avoid or delay the need to implant an electronic pacemaker [START_REF] Jensen | Incidence of and risk factors for sick sinus syndrome in the general population[END_REF] . In this regard, restoring damaged or degenerated SAN tissue by direct transplantation of MDSCs, in particular from the own muscle of the patient, constitutes an attractive possibility. We found that amelioration of heart rate in bradycardic mice occurs about 3 weeks following cell transplantation. This delay presumably reflects the time required for MDSCs to differentiate into MDSC-PMs. However, we recently also showed that the inhibition of G-protein gated K + channels (IKACh) (by either genetic deletion or a pharmacologic agent) may rescue the SAN dysfunction and heart block normally observed in Cav1.3 -/-mice [START_REF] Mesirca | G protein-gated IKACh channels as therapeutic targets for treatment of sick sinus syndrome and heart block[END_REF] . It is thus possible that future therapies for SAN dysfunction may combine a pharmacologic strategy such as IKACh inhibtion to improve heart rate in the short term, followed by a long-term cell therapy-based approach employing MDSCs.

Materials and Methods

Mouse strains

Six to ten week-old wild-type C57Bl/6 mice or transgenic C57Bl/6 "green mice" expressing eGFP under beta-actin promoter [START_REF] Okabe | Green mice' as a source of ubiquitous green cells[END_REF] were used to prepare MDSC as donor mice for transplantation experiments. Recipient wild-type, Cav1.3 -/-and Cav1.3 -/-/Cav3.1 -/-mice used for transplantation experiments were all of C57Bl/6 genetic background [START_REF] Marger | Functional roles of Ca(v)1.3, Ca(v)3.1 and HCN channels in automaticity of mouse atrioventricular cells: insights into the atrioventricular pacemaker mechanism[END_REF] . All procedures were performed in accordance with the animal care guidelines of the European Union, French laws and the Ethical committee of the University of Montpellier (N°: 2017010310594939).

Cell culture

MDSC were prepared using the preplate procedure originally described by Qu-Petersen et al. [START_REF] Qu-Petersen | Identification of a novel population of muscle stem cells in mice: potential for muscle regeneration[END_REF] as modified in Arsic et al. [START_REF] Arsic | Muscle-derived stem cells isolated as non-adherent population give rise to cardiac, skeletal muscle and neural lineages[END_REF] Briefly, mouse hind-limb muscles were removed, minced and enzymatically dissociated at 37°C for 45 min in 0.2% collagenase A (Roche) and 1 mg/ml dispase (GibcoBRL). After digestion, muscle cells were passed through 100 µm then 40 µm nylon cell strainers (BD Falcon) and centrifuged at 360 g for 10 min. Pelleted cells were washed twice in phosphate buffer saline (PBS), suspended in growth medium GM [DMEM/F12 (SIGMA, Les Ulis, France), 16% fetal bovine serum (PAA), 1% Ultroser G (Pall Life Sciences, Washington, USA), 100uM Beta-mercapto-ethanol, antibioticantimycotic mix (Gibco, Invitrogen Inc. Saint Quentin Fallavier, France) and plated on uncoated dishes (NUNC). After an initial 40 min pre-plating, non-adherent cells were collected and transferred to a new dish. The same operation was repeated every 24 h for 7 days with the addition of a centrifugation step at 360g, followed by resuspending the pelleted non-adherent cells in fresh GM.

MDSC used for RNA extraction, I.V. and I.P. transplantation and sub-cutaneous grafting experiments were non-adherent cells obtained after 6-7 days sequential pre-plating of stem cells extracted from hind limb skeletal muscle of adult mice.

Mouse adult fibroblast (MAF) were obtained from ATCC (Ltk-11) and grown as recommended by the supplier. Mouse ESCs were grown and harvested as described [START_REF] Ganier | Synergic reprogramming mammalian cells by combined exposure to mitotic Xenopus egg extracts and transcription factors[END_REF] .

Immunofluorescence analysis

Immunofluorescence analysis was performed on 2-6 week-cultured differentiated MDSC obtained from serial preplates as described [START_REF] Arsic | Muscle-derived stem cells isolated as non-adherent population give rise to cardiac, skeletal muscle and neural lineages[END_REF] . Cells were fixed with 3.7% formaldehyde for 5 min, snap permeabilized for 30 sec in -20°C acetone, preincubated 30 min with 0.5% BSA in PBS. Cells were then incubated for 1h at 37°C with primary antibodies against HCN4, (1:100, Alomone), sarcomeric -actinin, clone EA-53 (1:100, Sigma-Aldrich), connexin45 (1:100, H-85, Santa Cruz Biotechnology), Cav1.3 polyclonal antibody [START_REF] Christel | Distinct localization and modulation of Cav1.2 and Cav1.3 L-type Ca2+ channels in mouse sinoatrial node[END_REF] , cardiac troponin I (1:100, Millipore), Islet1 monoclonal antibody 39.3f7 (developed by Thomas M. Jessell and Susan Brenner-Morton and obtained from the Developmental Studies Hybridoma Bank, created by the NICHD of the NIH and maintained at The University of Iowa, Department of Biology, Iowa City, IA 52242). Specific staining was revealed using anti-mouse or anti-rabbit Alexa Fluor 488 and Alexa Fluor 555conjugated secondary antibodies (InVitrogen) with Hoechst33358 nuclear stain (0.1 µg/ml) for 30 min at 37°C.

RNA isolation and reverse transcription polymerase chain reaction

Total RNA was extracted from sino-atrial node tissue, ventricular tissue, ESCs, mouse adult fibroblasts, MDSC and in vitro cultured differentiated MDSC using RNeasy kit (Qiagen) and then treated with RQ1 DNase treatement (Promega) according to the manufacturer's recommendations.

Ventricular and sino-atrial node tissues were obtained from 7-week-old C57Bl/6 adult male mice. Total RNA was used to synthesize cDNA using the Superscript III reverse transcriptase kit (Invitrogen) with random primers or with gene-specific primer in the case of Hcn4. The gene specific primers for Hcn4, were designed from alignment of four sequences (Hcn1, Hcn2, Hcn3 and Hcn4) and chosen on the basis of a specific N-terminal Hcn4 fragment. PCR was performed with GoTaq DNA polymerase (Promega); primer sequences are shown in supplemental Table S1. The cDNA was amplified using 35 cycles of PCR with an annealing temperature of 60°C to 62°C. PCR products were separated on 2% agarose gel (Invitrogen), stained with ethidium bromide; visualized and photographed on a UV transluminator (Fischer Scientific). For comparative RNA expression in whole muscle cells from first preplate: PP1 (at 24h) versus the 8th preplate: PP8-MDSC shown

Cell transplantation experiments

Intravenous (I.V.) and intraperitoneal (I.P.) transplantation experiments were performed using wild-type, Cav1.3 -/-or Cav1.3 -/-/Cav3.1 -/-mice as recipients. MDSC were extracted from wildtype C57Bl/6 or transgenic C57Bl/6 mice expressing eGFP under the control of a beta-actin promoter [START_REF] Okabe | Green mice' as a source of ubiquitous green cells[END_REF] . Approximately 5x10 5 cells per recipient mouse were resuspended in 0.9% sodium chloride solution and injected into the tail vein. Mock-transplanted Cav1.3 -/-mice were injected with sodium chloride solution alone. Transplanted mice were sacrificed 2, 10, 20, 30 and 41 days after injection followed by sino-atrial node dissection. For cell tracking experiments in the SAN tissue, MDSC were labelled before injection for 30 min with the lipophilic membrane-bound cell tracker DiI-CM (C7000 at 1µg/ml, ThermoFisher Scientific) according to the manufacturer's instruction.

Immunohistochemistry

Sino-atrial node tissue was dissected and fixed in 4% formaldehyde for 20 min before washing in PBS. After permeabilization in -20°C acetone, the whole SAN tissue was rehydrated with PBS. Non-specific binding of antibodies was blocked by incubation for 1h at room temperature with blocking solution (10% goat serum (Abcam), 0.1% Triton X-100 in PBS) followed by incubation with Mouse Ig Blocking Reagent (Vector Laboratories) for 30 min.

Permeabilized and blocked sino-atrial tissue was then incubated overnight at 4°C with primary polyclonal anti-Cav1.3-1 subunit antibodies (prepared as described in ref. [START_REF] Christel | Distinct localization and modulation of Cav1.2 and Cav1.3 L-type Ca2+ channels in mouse sinoatrial node[END_REF] ,1:500) diluted in 1% goat serum in PBS. Alexa488 or 555 fluorochrome goat anti-rabbit secondary antibodies (1:100, InVitrogen) in 1% goat serum were applied for 30 min at 37°C with Hoechst33358 nuclear stain (0.1 g/ml) for 40 min at 37°C. Autofluorescence was quenched by incubating in 1% Sudan Black B (Sigma-Aldrich) in 70% ethanol for 10 min before washing in 70% ethanol for 5 min at room temperature. Tissues were mounted with AirVol mounting medium before photomicroscopy as described in Arsic et al. [START_REF] Arsic | Muscle-derived stem cells isolated as non-adherent population give rise to cardiac, skeletal muscle and neural lineages[END_REF] . The specificity of Cav1.3 staining was confirmed by its absence in sinoatrial tissue prepared from non-injected Cav1.3 -/-mice.

Measurements of contraction frequency

Cellular contraction of differentiated MDSC-PM was measured by an edge-detection IonOptix system device (LLC, 309 Hillside Street, Milton, MA 02186, USA). Cells were grown in 35 mm dishes in complete medium and analysed on an Olympus IX71 inverted microscope. MDSC-PM were imaged at 120 Hz using an IonOptix™ Myocam-S CCD camera. Digitized images were displayed within the IonWizard™ acquisition software (IonOptix™). To measure changes in cell length, two cursors were placed at opposing edges of the cell defined as difference in optical density (maximum: dark; minimum: light). The relative movement of cursors assessed cell shortening. Experiments were performed at 36 °C.

Electrophysiological recordings of beating MDSC-PM, differentiated from MDSC in vitro

For electrophysiological recordings, aliquots of cell suspension were harvested in custom made recording chambers (working volume 500 µL) allowing controlled unidirectional solution flow and mounted on the stage of an Olympus, X71 inverted microscope, and continuously perfused with normal Tyrode solution. The recording temperature was set to 36°C. The whole-cell variation of the patch-clamp technique [START_REF] Hamill | Improved patch-clamp techniques for high-resolution current recording from cells and cell-free membrane patches[END_REF] was used to record cellular ionic currents, employing an Axopatch 200A (Axon Instruments Inc., Foster USA) patch-clamp amplifier, grounded by an agar bridge filled with 150 mM KCl. Cellular automaticity was recorded by the perforated patch technique with escin (50 M). Recording electrodes were pulled from borosilicate glass, using a Flaming-Brown microelectrode puller (Sutter, Novato CA, USA). For recording cell automaticity, as well as If we used an intracellular solution containing (mM/L): K + -aspartate, 130; NaCl, 10; ATP-Na + salt, 2; creatine phosphate, 6.6; GTP-Mg 2+ , 0.1; CaCl2, 0.04 (pCa=7); Hepes-KOH, 10;

(adjusted to pH=7.2 with KOH). Electrodes had a resistance of about 5 M . Seal resistances were in the range of 2-5 G . The extracellular solution contained (in mM/L): NaCl, 140; KCl, 5.4; CaCl2, 1.8; MgCl2, 1; Hepes-NaOH, 5; and D-glucose, 5.5; (adjusted to pH=7.4 with NaOH). If was routinely recorded in Tyrode solution containing 5 mM BaCl2 to block IK1. Data was acquired with pClamp software (ver. 9, Axon Instruments Inc.).

Confocal imaging of Ca 2+ i transients and measurements of contraction.

Intracellular Ca 2+ ( Ca 2+ i) transients were imaged by loading in vitro differentiated MDSC-PM with the Ca 2+ indicator Fluo-4 AM 15 M (from a stock solution in a mixture of DMSO/Pluronic F-127) in the medium for 45 min at 37°C. Spontaneous [Ca 2+ ]i transients were recorded in differentiated pulsing MDSC-PM loaded with Fluo-4 AM under control conditions (culture medium), or medium containing either epinephrine, acetylcholine (ACh) or ryanodine.

Recordings were performed at 36°C. Differentiated MDSC-PM were distinguished from other cell types (i.e. fibroblasts and adipocytes cells) by their morphology (spindle and elongated shape), size

Microscope and video imaging system

Digital images were collected using Leica DM LB microscope and Canon EOS300D digital camera as described before [START_REF] Arsic | Muscle-derived stem cells isolated as non-adherent population give rise to cardiac, skeletal muscle and neural lineages[END_REF] . Videos of contracting cells were recorded using a NIKON D90 camera coupled to a Zeiss Axiovert 35M. A Nanozoomer Hamamatsu blade scanner was used for 2D reconstruction of whole mount SAN tissue (in Fig. S5 and Fig. S6).

Tumour formation assay 1x10 [START_REF] Romero-Ramos | Neuronal differentiation of stem cells isolated from adult muscle[END_REF] MDSC resuspended in 0.2 ml of 1/2X matrigel in HBSS were injected subcutaneously into the back of n=4 8-week-old SCID/beige mice (Charles River). Follow up observation was carried out for up to 4 months.

ESCs derived tumours were obtained by similar subcutaneous injection of 1x10 6 mouse ESCs into the back of 8-week-old SCID/beige mice (n=2). Tumours developed in all ES-grafted mice within 2 weeks. The mice were euthanized after 4 weeks when tumour size reached more than 2 cm.

ECG recordings and analysis in sedated mice

One-lead surface ECG measurements were recorded from wild-type and Cav1.3 -/-/Cav3.1 -/- mice sedated with 1.5% isofluorane. Body temperature was continuously maintained at 36° -37°C using a heated pad connected to a controller that received feedback from a temperature sensor attached to the mouse. Ag/AgCl gel-coated ECG electrodes (Unomedical) were attached to the superior right and both inferior limbs of mice. The electrodes were connected to a standard one-lead ECG amplifier module (EMKA Technologies, Paris, France), which included high-and low-pass filters (set to 0.05 Hz and 500 Hz, respectively) and a gain selection device (set to 1,000-fold).

Signals were digitized continuously at 2 kHz and recorded using an IOX data acquisition system (EMKA Technologies, France). The recordings were carried out for a 45-min period before (day 0) and at different days after transplantation (day 10 and day 20). The software ecgAuto (EMKA Technologies, France) was used to perform offline analysis of the data recorded. For each mouse the mean heart rate value and the Standard Deviation (SD) were calculated. Beat-to-beat analysis of heart rate was carried out on a 30-min interval taken 10 min after the beginning of each 45-min recording.

Telemetric recordings of ECG and analysis

For telemetric recording, adult wild-type and Cav1.3 -/-male mice were anesthetized with 2% isofluorane. A midline incision was made on the back along the spine to insert a telemetric transmitter (TA10EA-F20, Data Sciences International) into a subcutaneous pocket with paired wire electrodes placed over the thorax (chest bipolar ECG lead). Local anaesthesia was obtained with lidocaine (1%) injected subcutaneously at the sites of electrodes and transmitter implantation.

To manage possible post-surgery pain, Advil (paracetamol and ibuprofene, 7 mL/l) was added to the drinking water for four days after implantation. Mice were housed in individual cages with free access to food and water and were exposed to 24-hour light/dark cycles (light, 8:30 AM to 8:30 AM) in a thermostatically controlled room. Heart rates were averaged over a 24-hour recording period or over two 12-hour periods corresponding to "day-time" (light, 8:30 AM to 8.30 PM) or "night-time" (dark, 8.30 PM to 8.30 AM). Recordings were initiated at least 8 days after recovery from surgical implantation. ECG signals were recorded using a telemetry receiver and an analog-todigital conversion data acquisition system for display and analysis by DataquestTM A.R.T.TM software (Data Sciences International). ECG parameters were measured using ecgAuto 1.5.7 software. RR, PR, QRS, QT and QTc intervals were first calculated automatically by ecgAuto based on a large (>250) ECG sample library and then verified by visual inspection. Heart rates (in bpm) were then determined from RR intervals. PP intervals were measured manually over shorter recording windows.

Statistical analysis

The statistical significance of measured differences in heart rates or cellular rates of contraction was evaluated through paired or unpaired Student's t test. Statistical significance was set at p<0.05. Data analysis was performed with GraphPad Prism 6.0

Author Contributions

Fig. 1b :

 1b Fig.1b: data shown are from pseudo-counts-RLE obtained after RNAseq analysis of triplicate samples from RNA banks made with the TruSeq Stranded mRNA sample preparation kit (Illumina) and sequencing with a HiSeq2500 Illumina sequencer (MGX Montpellier GenomiX: http://www.mgx.cnrs.fr)

(

  ~10 m diameter) and pulsing activity. Extended Datavideos S1-S3 show examples of differentiated MDSC-PM with typical morphology. Ca 2+ i transient images were obtained by confocal microscopy (Meta Zeiss LSM 510 and Zeiss LSM 780) scanning cells with an Argon laser in line scan configuration (1.54 ms line rate); fluorescence was excited at 488 nm and emissions collected at >505 nm. A 63x water immersion objective (n.a. 1.2), a 63x oil immersion objective (n.a. 1.32) and a 40x objective (n,a. 1.2) were used for recordings in differentiated pulsing MDSC-PM. Image analyses were performed using ImageJ software. Images were corrected for background fluorescence and the fluorescence values (F) normalized to basal fluorescence (F0) in order to obtain the fluorescence ratio (F/F0). Light intensity intervals were analyzed by pClamp software (ver. 9, Axon Instruments Inc.).

A

  .F. and M.E.M. designed and analysed the experiments. P.M., D.M., I.B. performed the experiments with additional input from A.G.T., V.M., R.D., M.L.D.F., N.A., J.N., A.L. and N.J.C.; D.M. performed muscle stem cell culture and differentiation, RT-PCR analysis with advice from N.A. and immunocyto-and histochemistry with supervision from A.F. and N.J.L.; P.M. performed whole-cell patch clamp, Ca 2+ imaging and ECG telemetric recordings with supervision from M.E.M.; J.S. provided research tools; A.F. and M.E.M wrote the manuscript with comments and approval from all co-authors.

Fig 1 .

 1 Fig 1. Muscle stem cell isolation, expression of stemness factors, and differentiation of pacemaker-like cells in vitro. a: Schematic overview of the protocol for isolating non-adherent muscle-derived stem cells (MDSCs) from mouse hind-limb muscle. b: Levels of RNA expression for CyclinA2, Islet-1, Peg3/PW1, and Nestin in PP1 muscle cells cultured for 24 hours versus MDSC PP8 cells, as determined by RNAseq profiling of independent replicates. Shown are the fold increase in PP8 MDSCs vs. PP1 cells (levels in PP1 cells normalized as 1x). *p<0.05. c: Phasecontrast image of MDSCs differentiated into muscle stem cell-derived pacemaker myocytes (MDSC-PMs) after 3 weeks on laminin. The field is the same as that shown in Supplementary video 1.

Fig 2 .

 2 Fig 2. Expression of sino-atrial markers in MDSCs and in MDSC-PMs differentiated in vitro from MDSCs. a. RT-PCR-based analysis of expression of transcription factors involved in sinoatrial node (SAN) development (Tbx18, Islet1, Tbx3, Shox2 and Nkx2.5). SAN: mouse sino-atrial node; MDSCs: muscle-derived stem cell; MDSC-PMs: MDSCs differentiated in vitro into pacemaker-like beating cells. GAPDH was used as loading control. b. RT-PCR-based analysis of expression of cardiac pacemaker-specific markers in mouse. HCN4; Islet-1; CaV1.3; Cx45 (Connexin45); Tnni: (cardiac Troponin I); Actc: (cardiac -actinin). SAN, heart ventricles (HrV); mouse adult fibroblasts (MAF). Control without cDNA are indicated as Cont. Results for (a) and (b) are representative of analysis of n=3 independent MDSC and MDSC-PM RNA preparations. c. Coimmunostaining of MDSC-PMs for HCN4 and cardiac TroponinI (cTnI); sarcomeric -actinin and CaV1.3; and sarcomeric -actinin and Connexin45 (Cx45). d. Co-immunostaining for Islet1 and CaV1.3, and phase-contrast image of 2 beating MDSC-PMs (indicated by arrows) that are also shown in Supplementary video S4. Immunostaining is representative of n=20 independent cultures of MDSC-PMs from wild-type mouse muscle. Scale bars, 10 m.

Fig. 3 .

 3 Fig. 3. Electrophysiology and Ca 2+ signaling in pacemaker-like MDSC-PMs differentiated in vitro. a. Representative traces of action potentials recorded from in vitro-differentiated beating MDSC-PMs. b. Voltage protocol, sample current traces (left panel) and averaged current-to-voltage relationship of If (right panel) recorded in differentiated MDSC-PMs (peak If density at -135 mV: 2.5 ± 0.2 pA/pF, n=11). If was evoked by applying hyperpolarizing voltage steps from a holding potential of -30 mV. c. Spontaneous contraction rates (right panel) and corresponding edgedetection recording samples (left panel) of in vitro-differentiated MDSC-PMs under control conditions, without ivabradine (0 IVA) and during perfusion with ivabradine (IVA 3 M, n=15). d. Chronotropic response of Fluo-4-loaded MDSC-PMs, measured as the change in frequency of spontaneous Ca 2+ i transients pre-(top line) and post-(bottom line) perfusion with the following agonists: epinephrine, 2 nM (left panel: n=12); acetylcholine (Ach) 50 nM (middle panel: n=11); and ryanodine, 3 μM (right panel: n=5). Corresponding representative confocal line-scan images of Ca 2+ transients in MDSC-PMs. Light intensity integrals (red traces) are shown underneath each scan. e. Spontaneous Ca 2+ transients in MDSC-PMs (left panel) derived from wild-type (WT, top line) and Cav1.3 -/-(bottom line) mice, compared to spontaneous Ca 2+ transients measured in isolated native SAN cells (right panel) from wild-type (top line) and Cav1.3 -/-(bottom line) mice. Light intensity integrals (red traces) are shown underneath each scan. Note that the rate of spontaneous Ca 2+ i transients in MDSC-PMs differentiated from Cav1.3 -/-mice are slower than those in their wild-type counterparts. Means are given ± S.E.M. *p<0.05; **p<0.01; ***p<0.001; ****p<0.0001

Fig. 4

 4 Fig. 4 Summary of in vivo experiments with bradycardic mutant mice and early engraftment to the SAN by MDSCs. a. Schematic representation of assays testing the reparative potential of MDSCs in vivo. b-c. Assays of MDSC migration and engraftment to SAN tissue, in age-and sexmatched wild-type and Cav1.3 -/-mice 48 hours after I.P. injection with 3x10 5 MDSCs pre-labelled with the membrane marker DiI for. b. SAN tissue from a male wild-type mouse injected with DiI-MDSCs. c. SAN tissue from a male Cav1.3 -/-mouse injected with DiI-MDSCs. Shown are representative bright-field images at 60x and close-ups (areas shown by frames) of red fluorescence (DiI). RA: right atrium; CT: crista terminalis; SAN: sino-atrial node area. Bar = 200 microns.

Fig. 5 .

 5 Fig. 5. Engraftment and differentiation of wild-type MDSCs in the SAN tissue of Cav1.3 -/- mutant mice. SAN tissue of Cav1.3 -/-mutant mice injected (I.V.) with MDSCs, shown at 40 days post-injection. Immunofluorescence labelling for Cav1.3 (green) was carried out on whole-mount SAN tissue together with Hoechst DNA staining as described in Methods. Shown are bright-field images of the whole SAN region, with the right atrium (RA, cut before final mounting), superior and inferior vena cava (SVC and IVC) and inter-atrial septum (SEP) marked. Higher-magnification immunofluorescence images of areas marked 1-4 in the bright-field image show arrays of individual Cav1.3-positive cells with typical patchy membrane staining. Further magnification of areas a, b, and c show membrane-associated and striated patterns, with enhanced staining at cell junctions (arrow in b). Similar results were obtained from 5 independent MDSC injection experiments into Cav1.3 -/-mice.

Fig. 6 .

 6 Fig. 6. In vivo recordings of heart rate in Cav1.3 -/-single-mutant and Cav1.3 -/-/Cav3.1 -/-doublemutant mice before and after transplantation of MDSCs from wild-type muscle. a. Samples of in vivo telemetric ECG recordings from a freely moving Cav1.3 -/-mouse before and after systemic transplantation (I.V. injection) of MDSCs. b. Quantitation of 24-hour telemetric recordings of heart rate in n=6 Cav1.3 -/-mice (see Table 1), before and up to 40 days after systemic transplantation of MDSCs. Data are presented as mean ± S.E.M. *p<0.05; **p<0.01; c. Quantitation of in vivo telemetric heart rate recordings in Cav1.3 -/-/Cav3.1 -/-double mutant mice before and after systemic transplantation of MDSCs (I.P. injection). d. Quantitation of heart rate recorded in Cav1.3 -/-/Cav3.1 - /-mice before (day 0) and on day 30 after I.P. transplantation of MDSCs from wild-type mice.

  Fig. 6. In vivo recordings of heart rate in Cav1.3 -/-single-mutant and Cav1.3 -/-/Cav3.1 -/-doublemutant mice before and after transplantation of MDSCs from wild-type muscle. a. Samples of in vivo telemetric ECG recordings from a freely moving Cav1.3 -/-mouse before and after systemic transplantation (I.V. injection) of MDSCs. b. Quantitation of 24-hour telemetric recordings of heart rate in n=6 Cav1.3 -/-mice (see Table 1), before and up to 40 days after systemic transplantation of MDSCs. Data are presented as mean ± S.E.M. *p<0.05; **p<0.01; c. Quantitation of in vivo telemetric heart rate recordings in Cav1.3 -/-/Cav3.1 -/-double mutant mice before and after systemic transplantation of MDSCs (I.P. injection). d. Quantitation of heart rate recorded in Cav1.3 -/-/Cav3.1 - /-mice before (day 0) and on day 30 after I.P. transplantation of MDSCs from wild-type mice.

Table 1 . Telemetric ECG intervals for transplanted Cav1.3 -/-and wild-type mice during 12 hours resting (day) time.

 1 Shown are the values of the ECG parameters and the presence of sinus (SAN) pauses and 2 nd -degree atrioventricular blocks (AVBII), (mean ± S.E.M.).

		Cav1.3 -/-before injection	Cav1.3 -/-40 days post-injection	n	p value Ca v1.3 -/-	Wild-type before injection	Wild-type 40 days post-injection	n	p value WT
	Heart rate (bpm)	310 ± 15	410 ± 19	6	0.012	568 ± 6	548 ± 2	4	ns
	PP (ms)	215 ± 6	169 ± 6	6	0.006	115 ± 6	112 ± 1	4	ns
	PR (ms)	55 ± 2	51 ± 1	6	ns	34 ± 1	35 ± 1	4	ns
	QRS (ms)	17 ± 1	16 ± 1	6	ns	10 ± 1	10 ± 1	4	ns
	QT (ms)	71 ± 5	66 ± 3	6	ns	43 ± 1	41 ± 1	4	ns
	QTc (ms)	50 ± 3	52 ± 2	6	ns	41 ± 1	39 ± 1	4	ns
	SAN pauses/60s	0.9 ± 0.5	0.3 ± 0.1	6	ns	0	0	4	ns
	AVBII/60s	0.5 ± 0.2	0.3 ± 0.1	6	ns	0	0	4	ns

Table 2 . Telemetric ECG intervals for transplanted Cav1.3 -

 2 Summary of ECG parameters recorded in n=6 Cav1.3 -/-/Cav3.1 -/-double mutant mice before (day 0) and after (day 30) 30 days following I.P. transplantation of wild-type MDSCs. Shown are the values of the ECG parameters and the presence of sinus (SAN) pauses and 2 nddegree atrioventricular blocks (AVBII), (mean ± S.E.M.).

		Day 0	Day 30	n	p value
	PP (ms)	169 ± 8	135 ± 8	6	0.011
	PR (ms)	54 ± 2	52 ± 1	6	ns
	QRS (ms)	15 ± 1	15 ± 1	6	ns
	QT (ms)	64 ± 3	62 ± 6	6	ns
	QTc (ms)	50 ± 2	53 ± 4	6	ns
	SAN pauses/60s	6 ± 2	2 ± 1	6	ns
	AVBII/60s	6 ± 1	4 ± 2	6	ns

/-/Cav3.1 -/-mice during 6 hours active (night) time.

Acknowledgements

We thank Chantal Jacquet (IGMM, Montpellier) for initial help with MDSC I.V. injection, MRI and RHEM from Biocampus Montpellier facilities, Dr. Olivier Ganier (IGH) for mouse embryonic stem cells and Dr. G Enikolopov (Cold Spring Harbor Laboratory, NY, USA) for the transgenic mouse line Nestin-eGFP described in Mignone et al. 2004. The hybridoma monoclonal antibodies Nestin (Rat-401) developed by S. Hockfield, and Islet1 39.3f7 developed by Thomas M. Jessell and Susan Brenner-Morton were obtained from the Developmental Studies Hybridoma Bank, created by the NICHD of the NIH and maintained at The University of Iowa, Department of Biology, Iowa City, IA 52242.


D Magliacano

M Ouisse

S De Rosa

F Franco

A Khelif

INVESTIGATIONS ABOUT THE MODELLING OF ACOUSTIC PROPERTIES OF PERIODIC POROUS MATERIALS WITH THE SHIFT CELL APPROACH

Keywords: vibroacoustics, periodic structure, shift cell, foam, inclusion

The main advantage of designing sound packages with periodic arrangements is that they can provide a combination of absorption effects, resonance effects and wave interferences effects. This offers different applications in transportation (aeronautics, space, automotive, railway), energy and civil engineering sectors, where both weight and space, as well as vibroacoustic quality of performance and comfort, still remain as critical issues. The application of shift cell technique is presented and discussed for periodic porous media described with equivalent fluid models: it consists in a reformulation of classical Floquet-Bloch (F-B) conditions, whose major advantage stands in allowing the introduction of any frequency dependence of porous material behavior, through the resolution a quadratic eigenvalue problem, providing an efficient way to compute the dispersion curves of a porous material modelled as an equivalent fluid. The central part of this work shows the results, in terms of absorption coefficient and transmission loss curves, obtained through a numerical test campaign involving different melamine and polyurethane foams. The 48 test cases involve a cubic unit cell of porous material with a cylindrical inclusion. Furthermore, some absorption coefficient and transmission loss comparisons are shown, between a homogeneous unit cell and a unit cell with a perfectly rigid inclusion; the comparisons are carried out at fixed dimensions, then at fixed mass and then at fixed performance in the periodicity peak range. The results clearly point out the advantage of designing foam layer with periodic inclusion patterns in order to improve the performances in a specific range of frequencies, allowing a save both in terms of thickness and, most of all, mass, respect to a classical homogeneous foam layer.

INTRODUCTION

The inclusion of vibroacoustic treatments at early stage of product development, through the use of porous media with periodic inclusions, is a powerful strategy for the achievement of lightweight sound packages and represents a convenient solution for manufacturing aspects.

Indeed, although porous materials are commonly used for vibroacoustic applications, they suffer from a lack of absorption at low frequencies compared to their efficiency at higher ones; this difficulty is usually overcome by multi-layering [START_REF] Allard | Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials[END_REF]. However, while reducing the impedance mismatch at the air-material interface, the efficiency of such devices relies on the allowable thickness [START_REF] Weisser | Acoustic behavior of a rigidly backed poroelastic layer with periodic resonant inclusions by a multiple scattering approach[END_REF].

A more efficient way to enhance the low frequency performances of sound packages consists in embedding periodic inclusions in a porous layer [START_REF] Groby | Acoustic response of a rigid-frame porous medium plate with a periodic set of inclusions[END_REF] in order to create wave interferences or resonance effects that may play a positive role in the dynamics of the system.

The classical approach, known as Floquet-Bloch (F-B) theory, provides a strategy to analyze the behavior of systems with a periodic structure.

In layered systems, due to the heterogeneity of the relevant elastic properties or to particular geometric features, or to both, only certain wave modes can physically propagate inside the structure. Each of these modes can be identified by a determined (generally nonlinear) function relating the time frequency and the spatial frequency (or wave number). These relationships are called dispersion curves and they summarize all the dynamic behavior of the system [START_REF] Floquet | Sur les équations différentielles linéaires à coefficients périodiques[END_REF]. Therefore, dispersion curves offer a better perspective to explain the wave field behavior inside bodies.

For instance, the Helmholtz equation is a known example of equation describing the spatial behavior: there, the physical periodic structure of the studied object translates into spatial periodicity of its coefficients. Therefore, the F-B theory can be applied to obtain the dispersive properties of different mechanical periodic systems, reducing the problem to the calculations performed in the so-called unit cell under to certain specific boundary conditions derived from the F-B theory itself [START_REF] García | Floquet-Bloch Theory and Its Application to the Dispersion Curves of Nonperiodic Layered Systems[END_REF].

In order to develop efficient numerical techniques to handle the problem, the shift cell operator technique is presented. It allows the description of the propagation of all existing waves from the description of the unit cell through the resolution of a quadratic eigenvalue problem, in which the phase shift of the boundary conditions related to wave propagation is integrated into the partial derivative operator; consequently, the periodicity is included in the overall behavior of the structure, while continuity conditions are imposed at the edges of the unit cell. This is done through a 𝑘(𝜔) (wave number as a function of the angular frequency) method, which allows computing dispersion curves for frequency-dependent problems; instead of using the classical 𝜔(𝑘) (angular frequency as a function of wave number) that leads to nonlinear eigenvalue problems.

Similar techniques, which use a modified F-B approach in order to handle a 𝑘(𝜔) problem, can be found in literature ([6]- [START_REF] Wang | Wave propagation in two-dimensional viscoelastic metamaterials[END_REF]). The main reason why the shift cell method differs from them is that it consists in a reformulation of classical F-B conditions, in which the phase shift of the boundary conditions related to wave propagation is integrated into the partial derivative operator; consequently, the periodicity is included in the overall behavior of the structure, while continuity conditions are imposed at the edges of the unit cell. This technique has been successfully applied for describing the mechanical behavior of periodic structures embedding visco-elastic materials ( [START_REF] Collet | Floquet-Bloch decomposition for the computation of dispersion of two-dimensional periodic, damped mechanical systems[END_REF], [START_REF] Billon | Design and experimental validation of a temperature-driven adaptive phononic crystal slab[END_REF]) or piezoelectric materials [START_REF] Collet | Adaptive metacomposites for vibroacoustic control applications[END_REF]. Here it is proposed an extension to equivalent fluid models: this makes possible to overcome the limits of existing approaches by a more specific design of the system, through a process of optimization and testing of different inclusions, in order to obtain a device whose frequency efficiency outperforms existing designs.

The behavior of the porous materials is described by Johnson-Champoux-Allard (JCA) model ( [START_REF] Johnson | Theory of dynamic permeability and tortuosity in fluid-saturated porous media[END_REF], [START_REF] Champoux | Dynamic tortuosity and bulk modulus in air-saturated porous media[END_REF]) in the following sections, but one can identically use any other equivalent fluid model ([14]- [START_REF] Lafarge | Dynamic compressibility of air in porous structures at audible frequencies[END_REF]).

SHIFT CELL OPERATOR TECHNIQUE

In this paper, a periodic arrangement of porous materials is considered. For a more detailed discussion, one can refer to [START_REF] Magliacano | Computation of dispersion diagrams for periodic porous materials modeled as equivalent fluids[END_REF]. The behavior of each material is described by an equivalent fluid model in the frequency domain, i.e.:

𝜌 𝜔 2 𝐾 𝑝 + ∆𝑝 = 0, (1)
where 𝑝 = 𝑝(𝒙, 𝜔) is the acoustic pressure, 𝒙 = (𝑥, 𝑦, 𝑧) is the coordinate vector, 𝜔 is the angular frequency, 𝜌 = 𝜌(𝒙, 𝜔) is the equivalent fluid density and 𝐾 = 𝐾(𝒙, 𝜔) is the bulk modulus [START_REF] Bensoussan | Asymptotic Analysis of Periodic Structures[END_REF]. The periodicity is described by 𝜌(𝒙 + 𝒓𝒏) = 𝜌(𝒙) and 𝐾(𝒙 + 𝒓𝒏) = 𝐾(𝒙), ∀𝒙 ∈ 𝛺, where 𝒏 is a vector of integers normal to the face considered, 𝒓 = (𝒓 𝟏 , 𝒓 𝟐 , 𝒓 𝟑 ) is a matrix containing the three vectors defining the cell periodicity directions and lengths, and 𝛺 is the domain of interest.

For the purpose of the shift cell technique development, considering Eq. 1 and applying the Bloch theorem such as 𝑝(𝒙, 𝜔) = 𝑝(𝒙)𝑒 𝑗𝒌𝒙 , where 𝒌, for a 3D application, is

𝒌 = 𝑘 ( 𝑐𝑜𝑠𝜃𝑐𝑜𝑠𝜙 𝑐𝑜𝑠𝜃𝑠𝑖𝑛𝜙 𝑠𝑖𝑛𝜃 ) (2)
one can obtain

𝝆 𝝎 𝟐 𝑲 𝒑 + (𝜵 + 𝒋𝒌) 𝑻 (𝜵 + 𝒋𝒌)𝒑 = 𝟎. (3)
𝑝(𝑥) being periodic, the Dirichlet boundary conditions imply 𝑝(𝐿) = 𝑝(0).

Weak formulation

The aim of this section is the development of the weak formulation of the problem, in order to obtain a matrix equation that fully describes what happens inside a periodic unit cell of equivalent fluid. A weak formulation of Eq. ( 3) consists in finding 𝑝 such that ∀𝑝 ̃, which obeys to the periodic boundary conditions, one has:

𝝎 𝟐 ∫ 𝟏 𝑲 𝒑 ̃𝒑 Ω 𝒅Ω + ∫ 𝟏 𝝆 𝒑 ̃𝜵𝑻 𝜵𝒑 Ω 𝒅Ω + 𝒋𝒌 ∫ 𝟏 𝝆 𝒑 ̃𝜵𝑻 𝒑 Ω 𝒅Ω + +𝒋𝒌 𝑻 ∫ 𝟏 𝝆 𝒑 ̃𝜵𝒑 Ω 𝒅Ω -𝒌 𝑻 𝒌 ∫ 𝟏 𝝆 𝒑 ̃𝒑 Ω 𝒅Ω = 𝟎. (4)
After several passages, considering that 𝝋 is the eigenvector, the equation can be written in its matrix form

(𝑲 + 𝒋𝒌𝑳 + 𝒌 𝟐 𝑯 -𝝎 𝟐 𝑴)𝝋 = 𝟎 (5)
with the following matrices:

 𝑲 ∝ ∫ 1 𝜌 ∇𝑝 ̃∇𝑝 𝛺 𝑑𝛺;  𝑳 ∝ ∫ 1 𝜌 (∇𝑝 ̃𝑝 -𝑝 ̃∇𝑝) 𝛺 𝑑𝛺;  𝑯 ∝ ∫ 1 𝜌 𝑝 ̃𝑝 𝛺 𝑑𝛺;  𝑴 ∝ ∫ 1 𝐾 𝑝 ̃𝑝 𝛺 𝑑𝛺.
Here, 𝑴 and 𝑲 are respectively the standard symmetric definite mass and symmetric semidefinite stiffness matrices, 𝑳 is a skew-symmetric matrix and 𝑯 is a symmetric semi-definite positive matrix. In this formulation, all matrices are frequency dependent.

NON-RIGID INCLUSIONS NUMERICAL TEST CAMPAIGN

Herein, all results are related to a 3D unit cell constituted by a cube with side equal to 2 cm (homogeneous case) and with a 0.5 cm radius cylindrical inclusion (cases with inclusion).

The analyses are carried out in the frequency range 0-17000 Hz. It is well known that the parameters of the equivalent fluid models can have a strong impact on the performances of the acoustic device [START_REF] Ouisse | On the sensitivity analysis of porous material models[END_REF], hence they should be determined in a confident way.

In the current case, the characteristics of the materials called "Melamine" and "Black PU" are experimentally determined, while those of the materials called "P1" and "M10" are taken from the work performed by Doutres et al. [START_REF] Doutres | Impact of the irregular microgeometry of polyurethane foam on the macroscopic acoustic behavior predicted by a unit-cell model[END_REF] and those related to "Melamine 173" and "P60" from a paper by Deckers et al. [START_REF] Deckers | Modelling Techniques for Vibro-Acoustic Dynamics of Poroelastic Materials[END_REF]. Except for the "Melamine" and "Melamine 173" materials, all the others are polyurethane foams. While dispersion curves are computed for an infinite repetition of unit cells, absorption coefficient and transmission loss are calculated for a finite repetition of five unit cells, using the same domain and boundary conditions of the infinite periodic system. This, in a first approximation, allows comparing the dispersion relations and the acoustical characteristics of the equivalent finite medium. Indeed, it has been noted that a further increasing in the number of repeated cells would lead to a change in the mean value of absorption coefficient and transmission loss respectively below 2% and 20% compared to the usage of a repetition of five unit cells.

The general definition of the sound absorption coefficient is the fraction of incident energy propagating into a sample material versus the energy propagating out. A part of the incident energy will be absorbed into the sample material, or rather dissipated inside it. The absorption coefficient 𝛼 can be computed starting from the reflection coefficient 𝑅 as

𝛼 = 1 -|𝑅| 2 , ( 16
)
where 𝑅 depends on the surface impedance 𝑍 𝑠 . The surface impedance of the material is often presented in real and imaginary terms respectively; the real part describes the energy losses whereas the imaginary part describes the phase changes caused by the material [START_REF] Wolkesson | Evaluation of impedance tube methods -A two microphone in-situ method for road surfaces and the three microphone transfer function method for porous materials[END_REF]:

𝑍 𝑠 = 𝑝(𝐿) 𝑉(𝐿) = 𝑍 0 1+𝑅 1-𝑅 . ( 6
)
This technique is only valid for plane waves impinging upon homogeneous media, and just at low frequencies for non-homogeneous ones. In a more general way, that is always correct, the absorption coefficient can be computed as [START_REF] Sgard | Use of a hybrid adaptive finite element/modal approach to assess the sound absorption of porous materials with meso-heterogeneities[END_REF] 𝛼 = 𝛱 𝑑𝑖𝑠𝑠𝑖𝑝𝑎𝑡𝑒𝑑 𝛱 𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡 [START_REF] Krushynska | Visco-elastic effects on wave dispersion in three-phase acoustic metamaterials[END_REF] where

𝛱 𝑑𝑖𝑠𝑠𝑖𝑝𝑎𝑡𝑒𝑑 = 𝛱 𝑡ℎ𝑒𝑟𝑚𝑎𝑙 + 𝛱 𝑣𝑖𝑠𝑐𝑜𝑢𝑠 (8)
The terms can be expressed as [START_REF] Sgard | Use of a hybrid adaptive finite element/modal approach to assess the sound absorption of porous materials with meso-heterogeneities[END_REF] 𝛱

𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡 = 𝑆|𝑝 𝑖𝑛𝑐 | 2 2𝜌 0 𝑐 0 , ( 9
)
𝛱 𝑡ℎ𝑒𝑟𝑚𝑎𝑙 = 1 2 ℑ (-𝜔 ∫ 𝜙 2 𝐾 𝑝𝑝 * 𝑑𝛺 𝛺 𝑝 ), (10)
𝛱 𝑣𝑖𝑠𝑐𝑜𝑢𝑠 = 1 2 ℑ (∫ 𝜙 2 𝜔𝜌 ̃22 𝛻𝑝. 𝛻𝑝 * 𝑑𝛺 𝛺 𝑝 ), (11)
where


where 𝛱 𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡 and 𝛱 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑒𝑑 represent the incident and transmitted power, respectively. These values are obtained using an implementation of the plane wave forced response of the periodic cell accounting for fluid loading [START_REF] Atalla | NOVAFEM User's guide[END_REF]. For a plane wave configuration, the value computed through Eq. ( 12) for homogeneous flat configurations is equivalent to the one obtained with the Transfer Matrix Method [START_REF] Allard | Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials[END_REF]:

𝑇𝐿 = 10

Results

The JCA-modeled 3D unit cell that is described in the previous sections can be tested with some perfectly rigid and non-rigid inclusions. In particular, 48 setups are discussed here (Table 2), whose fundamental parameters are reported in Table 1. In Figures 234567, some comparative absorption coefficient and transmission loss plots are shown for each of the 48 cases of study: in particular, each of the six foams is tested using eight different inclusions, according to the combinations reported in Table 2.

It can be noticed that, for what concerns the transmission loss, the effect of the inclusion is not particularly advantageous in these situations: in the case of the air, indeed, there is a drop of performances at all frequencies while, in the case of a foam inclusion, only a slight change of the values can be seen, as well as a very small effect of the periodicity when this is equal to half of the wavelength (around 7000 Hz).

Anyway, some different cases, that may be more interesting from the practical point of view, can be studied by modelling the foam unit cell through the use of the Biot model [START_REF] Biot | Mechanics of Deformation[END_REF], instead that as an equivalent fluid; doing so, indeed, allows to take into account the elasticity of the skeleton and the entire problem formulation depends not anymore only on the pressure, but on the skeleton displacements too: this means that it should possible to properly write the coupling conditions between the foam and an eventual (non-perfectly rigid) solid inclusion.

COMPARISON OF ACOUSTIC PERFORMANCES BETWEEN A HOMOGENEOUS UNIT CELL AND AN UNIT CELL WITH INCLUSION WITH FIXED MASS

In the previous sections, all the comparisons between homogeneous cases and cases with inclusions are made considering unit cells with the same dimensions; in other words, it means that the performances of a layer with periodic inclusions are estimated assuming that is has the same thickness of the related homogeneous one.

One may want also to compare absorption coefficient and transmission loss plots for the case in which the unit cell with inclusion has the same mass (and therefore different dimensions) respect to the homogeneous one. For example, considering an unit cell made of Melamine and with a perfectly rigid inclusion (Configuration 2 of Table 2), when comparing it to the homogeneous case with fixed dimensions, it obviously has a slower mass (75.56% of the homogeneous unit cell value); therefore, in order to perform a comparison with fixed mass respect to the homogeneous case, one should increase each dimension of the unit cell with inclusion of a certain quantity that, for the specific case, is equal to the 7.56%.

At this point, making some considerations based on the results shown in Figures 8 and9, one may notice that the curve with fixed mass, respect to the one with fixed dimensions, has a performance peak caused by periodicity effect that is shifted at lower frequencies (this is due to the different dimensions between the two cases with inclusion) and also of different amplitude (due to the different mass of the compared unit cells).

Furthermore, in order to obtain the same transmission loss performances in the periodicity peak range (between 6000 and 8000 Hz, for the specific cases considered) by the use of a simple homogeneous layer made of the same foam, one should use a thickness that is around twice the one required for the cases with inclusion, therefore leading to an increment of the mass of about 100%. This clearly point out the advantage of designing foam layer with periodic inclusion patterns in order to improve the performances in a specific range of frequencies, allowing a save both in terms of thickness and, most of all, mass, respect to a classical homogeneous foam layer. Comparison of transmission loss curves between the homogeneous case, the case with inclusion with fixed dimensions, the case with inclusion with fixed mass and the homogeneous case with fixed performance in the 6000-8000 Hz frequency range.

CONCLUSIONS

The shift cell technique has been presented, providing details on its numerical formulation. Numerical results have been shown, in terms of absorption coefficient and transmission loss curves obtained through a test campaign involving 48 different JCA-modelled melamine and polyurethane foam unit cell configurations.

Furthermore, it has been shown the comparison between absorption coefficient and transmission loss plots for the case in which the unit cell with inclusion has the same mass (and therefore different dimensions) respect to the homogeneous one.

Further developments of the work will include the implementation of the shift cell technique using Biot model, for both 2D and 3D geometries, as well as the design and experimental tests of a specific unit cell configuration, chosen accordingly to an optimization process that will involve geometry, foam and inclusion material.

Figure 1 :

 1 Figure 1: Reciprocal lattice vector in a 3D unitary cell.

  𝑆 = surface interested by incident pressure;  𝑝 𝑖𝑛𝑐 = amplitude of the excitation mode (incident pressure);  𝜌 0 = density of the interstitial fluid (air);  𝑐 0 = sound speed in the interstitial fluid (air);  𝛺 = poro-elastic volume;  𝑝 * = 𝑐𝑜𝑛𝑗(𝑝);  𝛻 𝑜𝑝𝑒𝑟𝑎𝑡𝑜𝑟 = gradient. The transmission loss is numerically computed as

Figure 2 :

 2 Figure 2: Comparison between absorption coefficient (on the left) and TL (on the right) curves for cases 1-8.

Figure 3 :

 3 Figure 3: Comparison between absorption coefficient (on the left) and TL (on the right) curves for cases 9-16.

Figure 4 :

 4 Figure 4: Comparison between absorption coefficient (on the left) and TL (on the right) curves for cases 17-24.

Figure 5 :

 5 Figure 5: Comparison between absorption coefficient (on the left) and TL (on the right) curves for cases 25-32.

Figure 6 :

 6 Figure 6: Comparison between absorption coefficient (on the left) and TL (on the right) curves for cases 33-40.

Figure 7 :

 7 Figure 7: Comparison between absorption coefficient (on the left) and TL (on the right) curves for cases 41-48.

Figure 8 :

 8 Figure 8: Comparison of absorption coefficient curves between the homogeneous case, the case with inclusion with fixed dimensions and the case with inclusion with fixed mass.

Figure 9 :

 9 Figure9: Comparison of transmission loss curves between the homogeneous case, the case with inclusion with fixed dimensions, the case with inclusion with fixed mass and the homogeneous case with fixed performance in the 6000-8000 Hz frequency range.

Table 1 :

 1 Non-acoustic parameters of the foams used for the numerical test campaign.

		Porosity Tortuosity	Resistivity [Pa*s/m^2]	Viscous characteristic length [mm]	Thermal characteristic length [mm]
	Melamine	0.99	1.02	8430	0.138	0.154
	P1	0.956	1.06	3490	0.187	0.250
	Black PU	0.96	1.075	5815	0.102	0.269
	M10	0.982	1.25	3670	0.240	0.310
	Mel. 173	0.98	1.01	9500	0.166	0.249
	P60	0.98	1.17	3750	0.110	0.742

Table 2 :

 2 Combinations of foams and inclusions used for the numerical test campaign.

	Configuration Foam	Inclusion Configuration	Foam	Inclusion
	1		none	25		none
	2		rigid	26		rigid
	3		air	27		air
	4 5	Melamine	PU 1 PU black	28 29	M10	PU 1 Melamine
	6		M10	30		PU black
	7		Mel. 173	31		Mel. 173
	8		PU 60	32		PU 60
	9		none	33		none
	10		rigid	34		rigid
	11		air	35		air
	12 13	P1	Melamine PU black	36 37	Melamine 173	PU 1 Melamine
	14		M10	38		PU black
	15		Mel. 173	39		M10
	16		PU 60	40		PU 60
	17		none	41		none
	18		rigid	42		rigid
	19		air	43		air
	20 21	PU black	PU 1 Melamine	44 45	P60	PU 1 Melamine
	22		M10	46		PU black
	23		Mel. 173	47		M10
	24		PU 60	48		Mel. 173

ACKNOLEDGEMENTS

This project has received funding from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No. 675441.