domain: sdv phys

text:
Émilie Su
email: emilie.su@u-paris.fr

Catherine Villard

Jean-Baptiste Manneville
email: jean-baptiste.manneville@u-paris.fr

Mitochondria: at the crossroads between mechanobiology and cell metabolism

Keywords: Mitochondrial morphodynamics, mechanotransduction, oxidative phosphorylation, glycolysis, membrane tension, cytoskeleton, cancer

published or not. The documents may come

Introduction

Cells sense and process signals from their external environment to coordinate structural and functional processes such as growth, proliferation, homeostasis and regeneration. Both chemical and mechanical cues are known to be regulators of cell fate and behavior. Cells integrate information from their physical environment through the process of mechanotransduction, during which mechanical cues are translated into biochemical signals which further induce adaptive changes in cell functions. Extracellular mechanical stimuli such as compressive, tensile or shear stresses are transmitted into the cell through the coordinated activity of mechanosensors along mechanosignaling pathways. Previous studies have investigated and reviewed the role of the plasma membrane, mechano-activated ion channels, focal adhesion proteins, cytoskeletal filaments (actin, microtubule and intermediate filaments)

and the nucleus in sensing and transducing mechanical stresses [Ingber, 2006;[START_REF] Orr | Mechanisms of mechanotransduction[END_REF][START_REF] Jaalouk | Mechanotransduction gone awry[END_REF]Schwartz, 2010;[START_REF] Isermann | Nuclear mechanics and mechanotransduction in health and disease[END_REF][START_REF] Douguet | Mammalian mechanoelectrical transduction: structure and function of force-gated ion channels[END_REF][START_REF] Kechagia | Integrins as biomechanical sensors of the microenvironment[END_REF][START_REF] Uray | Mechanotransduction at the plasma membrane-cytoskeleton interface[END_REF], but the molecular mechanisms of mechanotransduction are still incompletely understood, in particular when intracellular compartments such as the endomembrane system are involved [START_REF] Phuyal | Endomembranes: Unsung heroes of mechanobiology[END_REF][START_REF] Phuyal | Mechanobiology of organelles: illuminating their roles in mechanosensing and mechanotransduction[END_REF]. With the spurring growth of intracellular rheology, the mechanical properties of the cytoplasm, intracellular organelles and the cytoskeleton emerge as key players in both mechanosensing and mechanotransduction [START_REF] Mathieu | Intracellular mechanics: connecting rheology and mechanotransduction[END_REF].

Cellular metabolism, comprising the biochemical processes that produce or consume energy in a cell, underpins virtually every cellular process through catabolism and anabolism [START_REF] Ferreira | Intermediary metabolism: An intricate network at the crossroads of cell fate and function[END_REF]. In catabolism, cells break down complex molecules, such as polysaccharides, lipids, proteins and nucleic acids, in smaller units, like monosaccharides, fatty acids, amino acids and nucleotides. These small molecules are then oxidized to release energy or supply other chemical reactions. Cells can also synthesize new macromolecules via anabolic pathways.

There is mounting evidence of a reciprocal regulation between cell mechanics and metabolism. Mechanical forces rewire the metabolism of cells to adapt to their mechanically constrained environment. In return, metabolic changes modulate mechanosensing and mechanotransduction. From an evolutionary standpoint, the hypothesis that cytoskeletal proteins derive from metabolic enzymes provides an intrinsic link between metabolism and mechanics [START_REF] Evers | Reciprocal regulation of cellular mechanics and metabolism[END_REF]. External cues activate downstream signaling pathways. As reviewed in [START_REF] Evers | Reciprocal regulation of cellular mechanics and metabolism[END_REF][START_REF] Romani | Crosstalk between mechanotransduction and metabolism[END_REF][START_REF] Torrino | Metabo-reciprocity in cell mechanics: feeling the demands/feeding the demand[END_REF], all aspects of the subsequent cell response, including cytoskeletal remodeling, actomyosin contraction and transcriptional changes, are energy-consuming and can rewire metabolism. Resulting metabolic changes may in turn induce a reorganization of cellular components and processes impacting the mechanical properties of the cell.

Commonly referred to as the energy powerhouse of the cell, mitochondria are essential regulators of cell metabolism [START_REF] Ernster | Mitochondria: a historical review[END_REF][START_REF] Spinelli | The multifaceted contributions of mitochondria to cellular metabolism[END_REF]. From the oxidative degradation of carbohydrates, amino acids and fatty acids, they supply cells with energy in the form of adenosine triphosphate (ATP) through the citric acid cycle and oxidative phosphorylation (OXPHOS). Mitochondria also generate metabolic precursors for macromolecules, including lipids, proteins, DNA and RNA. They ensure calcium buffering and are the major intracellular sources of reactive oxygen species (ROS), which are a byproduct of cellular oxidative metabolism [START_REF] Sena | Physiological roles of mitochondrial reactive oxygen species[END_REF][START_REF] Hernansanz-Agustín | Generation of reactive oxygen species by mitochondria[END_REF]. Although ROS were mostly considered for their damaging oxidative effects and their contribution to mitochondrial dysfunction and cell death [START_REF] Ott | Mitochondria, oxidative stress and cell death[END_REF], there is now mounting evidence that they are important regulators of cell homeostasis. ROS are signaling molecules which not only regulate a wide range of physiological processes, but fluctuations of their levels also activate adaptive mechanisms, also termed mito-hormesis [START_REF] Sena | Physiological roles of mitochondrial reactive oxygen species[END_REF][START_REF] Yun | Mitohormesis[END_REF][START_REF] Pizzino | Oxidative stress: harms and benefits for human health[END_REF]. In addition to these metabolic functions, mitochondria also regulate cell signaling and apoptosis [START_REF] Mcbride | Mitochondria: more than just a powerhouse[END_REF].

The morphology of mitochondria is well characterized (Figure 1). The endosymbiotic theory of mitochondrial origin stating that mitochondria are ancient proteobacteria which developed a symbiotic relationship with archae more than 1.5 billion years ago, is now well confirmed [START_REF] Roger | The origin and diversification of mitochondria[END_REF][START_REF] Boguszewska | The similarities between human mitochondria and bacteria in the context of structure, genome, and base excision repair system[END_REF]. However, the exact lineage is still debated [START_REF] Martijn | Deep mitochondrial origin outside the sampled alphaproteobacteria[END_REF]. As a result, mitochondria possess their own DNA (mtDNA) and are limited by an inner membrane and an outer membrane. The outer mitochondrial membrane acts both as a protective physical barrier and an exchange interface by allowing the selective diffusion of preproteins, small hydrophilic metabolites and ions. The presence of specific transporters in the outer mitochondrial membrane ensures metabolite exchange between the intermembrane space and the cytosol [START_REF] Becker | Mitochondrial outer membrane channels: emerging diversity in transport processes[END_REF]. The outer mitochondrial membrane also contains large quantities of porins, integral membrane proteins allowing the diffusion of small molecules. In contrast, the inner mitochondrial membrane, which encloses a space containing mtDNA, ribosomes and various soluble compounds (e.g. enzymes, small organic molecules...) named the matrix, is highly impermeable, even to small metabolites. It is densely packed with the complexes of the OXPHOS machinery. Perhaps the most striking characteristic of mitochondria is their exceptional morphological plasticity. Indeed, the prokaryotic mitochondrial ancestor developed structural and functional mechanisms to adapt to the intracellular environment of its eukaryotic host. Across different tissues and within the same cell types, a large spectrum of mitochondrial morphologies has been observed, ranging from hyperfused or tubular to short tubes and fragmented shapes [START_REF] Wai | Mitochondrial dynamics and metabolic regulation[END_REF]. The cristae, which are folds of the inner mitochondrial membrane, display a wide range of morphologies, from simple tubular structures to large, flat lamella and vacuolated intercristal spaces [START_REF] Mannella | The internal compartmentation of rat-liver mitochondria: tomographic study using the high-voltage transmission electron microscope[END_REF].

ATP is the main source of high-energy phosphate bonds involved in essentially all cellular processes, including intracellular signaling, DNA synthesis and active transport [START_REF] Dunn | Physiology, adenosine triphosphate[END_REF]. Most intracellular ATP is synthesized from two different processes: mitochondrial OXPHOS and cytosolic glycolysis. OXPHOS is carried out by the mitochondrial electron transport chain, a group of five enzyme complexes (I to V) bound to the inner mitochondrial membrane. This process has been thoroughly described at the molecular level [START_REF] Ernster | Mitochondria: a historical review[END_REF]Saraste, 1999]. In a nutshell, the citric acid cycle or Krebs cycle, which takes place in the mitochondrial matrix, is a set of redox reactions of substrates derived from glucose, fatty acids and amino acids through different pathways. The Krebs cycle feeds the electron transport chain with reduced cofactors (NADH and FADH2). The latter donate electrons to complexes I and II and the liberated energy is used by complexes I, III and IV to pump protons to the intermembrane space. This proton motive force is finally used by complex V (ATP synthase) to synthesize ATP from ADP and inorganic phosphate. Cytosolic glycolysis, the other ATP-generating process, is a metabolic pathway that can occur under both aerobic and anaerobic conditions [START_REF] Chaudhry | Biochemistry, glycolysis[END_REF]. This process yields two pyruvate molecules per glucose molecule and ultimately 32 ATP molecules in aerobic conditions where pyruvate enters mitochondria and is degraded through OXPHOS. In anaerobic conditions, pyruvate stays in the cytosol and is converted to lactate, producing in fine only 2 ATP molecules per glucose molecule (Figure 1). Mitochondria are organized in an extensive network in the cell. Their morphology, motility and distribution across the cytosol, which we refer to here as mitochondrial morphodynamics, are largely determined by cytoskeletal filaments [START_REF] Korobova | An actindependent step in mitochondrial fission mediated by the ER-associated formin INF2[END_REF][START_REF] Miragoli | Microtubule-dependent mitochondria alignment regulates calcium release in response to nanomechanical stimulus in heart myocytes[END_REF][START_REF] Pernas | Mito-morphosis: mitochondrial fusion, fission, and cristae remodeling as key mediators of cellular function[END_REF][START_REF] Bartolák-Suki | Regulation of mitochondrial structure and dynamics by the cytoskeleton and mechanical factors[END_REF][START_REF] Casafuz | Morphological fluctuations of individual mitochondria in living cells[END_REF]Fatima and Ananthanarayan, 2023]. Besides, mitochondria are involved in interorganellar contact sites such as the endoplasmic reticulum (ER), lipid droplets and the Golgi apparatus, which can regulate their morphodynamics and functions [START_REF] Murley | The emerging network of mitochondria-organelle contacts[END_REF]Lackner et al., 2019;[START_REF] Tábara | The complex dance of organelles during mitochondrial division[END_REF]. The actin cytoskeleton is required for short-distance movements of mitochondria and for their immobilization at sites of high ATP demand, as reported in neurons [START_REF] Boldogh | Interactions of mitochondria with the actin cytoskeleton[END_REF]. As reviewed in [START_REF] Schwarz | Intermediate filaments as organizers of cellular space: how they affect mitochondrial structure and function[END_REF], the distribution, anchorage and function of mitochondria at regions of high-energy demand are mostly ensured by intermediate filaments, such as neurofilaments in neuronal cells [Wagner et al., 2003], keratin in epithelial cells [START_REF] Duan | The Pirh2-keratin 8/18 interaction modulates the cellular distribution of mitochondria and uv-induced apoptosis[END_REF], vimentin in fibroblasts [Nekrasova et al., 2011] or desmin in muscle cells [START_REF] Capetanaki | Muscle inter-mediate filaments and their links to membranes and membranous organelles[END_REF]. The contribution of microtubules to mitochondrial directional transport is also well documented [START_REF] Summerhayes | Effect of microtubules and intermediate filaments on mitochondrial distribution[END_REF][START_REF] Morris | Axonal transport of mitochondria along microtubules and f-actin in living vertebrate neurons[END_REF][START_REF] Boldogh | Mitochondria on the move[END_REF][START_REF] Saxton | The axonal transport of mitochondria[END_REF].

Mitochondria undergo anterograde and retrograde transport along microtubules, powered by kinesin and dynein motor proteins respectively [START_REF] Casafuz | Intracellular motor-driven transport of rodlike smooth organelles along microtubules[END_REF]. Actin controls the positioning and redistribution of mitochondria during mitosis [START_REF] Moore | Actin cables and comet tails organize mitochondrial networks in mitosis[END_REF].

Translocation of mitochondria along cytoskeletal tracks also requires adaptor proteins to couple the three types of motor proteins -myosins for actin filaments and kinesins and dyneins for microtubules, with mitochondria. Miro GTPases are tail-anchored in the outer mitochondrial membrane and interact with both the mitochondrial intermembrane space bridging (MIB) complex and TRAK proteins to form the Miro-TRAK adaptor complex that recruits kinesin or dynein-dynactin motors [START_REF] Kruppa | Motor proteins at the mitochondriacytoskeleton interface[END_REF]Zinsmaier, 2021].

The variety of mitochondrial lengths and shapes observed in different cell types and under different conditions stems from changes in fusion and fission rates [START_REF] Griparic | The many shapes of mitochondrial mem-branes[END_REF]Youle and Van Der Bliek, 2012]. The processes of cristae remodeling, fission and fusion allow the mitochondria to constantly support and regulate their bioenergetic and biosynthetic functions. To preserve cellular homeostasis, eukaryotic cells activate autophagy in order to degrade unnecessary energy-consuming organelles and recycle their components [START_REF] Reggiori | Autophagy in the eukaryotic cell[END_REF]. Mitophagy, defined as the selective autophagy of mitochondria, requires the fragmentation of mitochondria to complete their engulfment in autophagosomes of a restricted size [START_REF] Rambold | Tubular network formation protects mitochondria from autophagosomal degradation during nutrient starvation[END_REF][START_REF] Zorov | Lessons from the discovery of mitochondrial fragmentation (fission): a review and update[END_REF]. Morphodynamic mechanisms underlying mitochondrial quality control regulation and mitophagy are reviewed in [START_REF] Ni | Mitochondrial dynamics and mitochondrial quality control[END_REF][START_REF] Song | Mitochondrial quality control in the maintenance of cardiovascular homeostasis: the roles and interregulation of UPS, mitochondrial dynamics and mitophagy[END_REF][START_REF] Tang | Mitochondrial quality control in kidney injury and repair[END_REF].

A number of molecular complexes involved in mammalian mitochondrial cristae remodeling, fission and fusion have been identified. The detailed mechanisms of mitochondrial fission and fusion have been extensively reviewed previously [Chan, 2006;[START_REF] Pernas | Mito-morphosis: mitochondrial fusion, fission, and cristae remodeling as key mediators of cellular function[END_REF][START_REF] Wai | Mitochondrial dynamics and metabolic regulation[END_REF][START_REF] Jones | Simple to Complex: The Role of Actin and Microtubules in Mitochondrial Dynamics in Amoeba, Yeast, and Mammalian Cells[END_REF]. High molecular weight guanosine triphosphatases (GTPases) are key regulators of mitochondrial morphodynamics. In mammalian cells, the canonical fission machinery involves the dynamin-related protein 1 (DRP1). ER tubules wrap around the mitochondrion [START_REF] Friedman | The er in 3d: a multifunctional dynamic membrane network[END_REF], initiating a pre-constriction which facilitates the recruitment of cytosolic DRP1 [START_REF] Otera | Mff is an essential factor for mitochondrial recruitment of Drp1 during mitochondrial fission in mammalian cells[END_REF]. DRP1 colocalizes with mitochondrial constrictions and multimerizes into a spiral to further constrict the outer mitochondrial membrane with the use of the free energy of GTP hydrolysis [START_REF] Labrousse | C. elegans dynamin-related protein drp-1 controls severing of the mitochondrial outer membrane[END_REF][START_REF] Smirnova | Dynamin-related protein drp1 is required for mitochondrial division in mammalian cells[END_REF][START_REF] Francy | The mechanoenzymatic core of dynamin-related protein 1 comprises the minimal machinery required for membrane constriction[END_REF]. Translocation of DRP1 is coordinated by a number of outer mitochondrial membrane proteins, such as fission protein 1 (FIS1), mitochondrial fission factor (MFF) and mitochondrial dynamics proteins of 49 and 51 kDa (MID49 and MID51) [START_REF] Losón | Fis1, Mff, MiD49, and MiD51 mediate Drp1 recruitment in mitochondrial fission[END_REF]. In ER-mediated fission, actin polymerization at contact sites between the ER and the mitochondrion involves both the ER-localized inverted formin 2 (INF2) and the actin-nucleating spire protein Spire1C and provides the mechanical force needed to sever the mitochondrion [START_REF] Korobova | An actindependent step in mitochondrial fission mediated by the ER-associated formin INF2[END_REF][START_REF] Li | Transient assembly of f-actin on the outer mitochondrial membrane contributes to mitochondrial fission[END_REF][START_REF] Manor | A mitochondria-anchored isoform of the actin-nucleating spire protein regulates mitochondrial division[END_REF].

Recent studies shed light on alternative fission pathways which do not necessarily rely on the canonical fission machinery. Mitochondrial fission can be actin, DRP1 or ER-dependent or independent. Inhibitors of the electron transport chain, ATP synthase or permeability transition pore induce reversible mitochondrial fission which is dependent on both DRP1 and the actin cytoskeleton [De Vos et al., 2005]. Similarly, the fusion/fission balance of the mitochondrial network is regulated by actin cyclic polymerization and depolymerization at the level of mitochondrial subpopulations. In HeLa cells, actin transiently cycles onto all mitochondrial subsets, but preferentially assembles and disassembles on the outer membrane of elongated mitochondria, thereby promoting DRP-1 dependent fission [START_REF] Moore | Dynamic actin cycling through mitochondrial subpopulations locally regulates the fissionfusion balance within mitochondrial networks[END_REF].

However, force-induced mitochondrial fission might be DRP1-dependent but actinindependent [START_REF] Helle | Mechanical force induces mitochondrial fission[END_REF]. Conversely, an actin-dependent but DRP1-independent fission process can be mediated by the stress-responsive protein GJA1-20k, which localizes to the outer mitochondrial membrane and inhibits actin depolymerization [START_REF] Shimura | Protective mitochondrial fission induced by stress-responsive protein GJA1-20k[END_REF]. A recent study also showed that different components are involved depending on the positioning of the fission sitein the so-called midzone or in the peripheral regionsin relation with the fate of the mitochondria. Although both types of fission events require DRP1, in contrast with peripheral division which is followed by mitophagy, midzone fission recruits ER, actin and MFF [START_REF] Kleele | Distinct fission signatures predict mitochondrial degradation or biogenesis[END_REF]. The requirement for DRP1 and actin regulators, such as Arp2/3, INF2 or Spire1C, thus seems to depend on the context of mitochondrial fission. For instance, the stiffness of the extracellular matrix (ECM) was recently shown to regulate actin perimitochondrial assembly and fission [START_REF] Romani | Mitochondrial fission links ECM mechanotransduction to metabolic redox homeostasis and metastatic chemotherapy resistance[END_REF].

Another family of proteins involved in mitochondrial dynamics are mitofusins.

Mitofusins 1 and 2 (MFN1 and MFN2) are key proteins required for fusion of two outer mitochondrial membranes, while Optic Atrophy 1 (OPA1) ensures cristae remodeling via the fusion of the inner mitochondrial membranes [START_REF] Chen | Mitofusins Mfn1 and Mfn2 coordinately regulate mitochondrial fusion and are essential for embryonic development[END_REF]. Their mRNA or protein expression levels are different among tissues [START_REF] Eura | Two mitofusin proteins, mammalian homologues of FZO, with distinct functions are both required for mitochondrial fusion[END_REF]].

Here we review the emerging relations between mechanics, metabolism and mitochondrial morphodynamics. We show that reciprocal links exist between these three elements (Figure 2). We examine these links in pairs, starting with the coupling between morphodynamics and metabolism (section 2), the links between mitochondrial morphodynamics and mechanics (section 3) and then the links between mechanics and metabolism at the level of mitochondria (section 4). While some of these links are well established, others are still poorly documented and open new fields of research. Finally, we identify the working hypotheses that may guide future experimental investigations on the emerging topic of mitochondrial mechanometabolism (section 5). Mitochondria display not only a substantial heterogeneity across tissues in terms of density and shapes, but also an intra-tissue heterogeneity, reflecting the coupling between their structure and their function.

Each tissue or organ presents specific energetic needs which correlate with their physiological functions. Mitochondrial morphodynamics thus reflects the tissue physiology and more specifically its bioenergetic efficiency and adaptation to nutrient availability [Kunz, 2003;[START_REF] Liesa | Mitochondrial dynamics in the regulation of nutrient utilization and energy expenditure[END_REF][START_REF] Wai | Mitochondrial dynamics and metabolic regulation[END_REF]. In terms of spatial distribution and network organization, mitochondria can be uniformly or non-uniformly distributed in the cell, depending on the cell type [START_REF] Collins | Mitochondria are morphologically and functionally heterogeneous within cells[END_REF][START_REF] Kuznetsov | The cell-type specificity of mitochondrial dynamics[END_REF][START_REF] Faitg | 3D neuronal mitochondrial morphology in axons, dendrites, and somata of the aging mouse hippocampus[END_REF]. The cell-type specificity of mitochondrial morphology and intracellular distribution is reviewed in [START_REF] Kuznetsov | The cell-type specificity of mitochondrial dynamics[END_REF]. For instance, in differentiated podocytes, which have a complex structure of interdigitating foot processes, mitochondria are clustered around the nucleus and absent in the foot processes [START_REF] Ozawa | Glycolysis, but not Mitochondria, responsible for intracellular ATP distribution in cortical area of podocytes[END_REF]. This heterogeneous distribution correlates with the spatial differences of energy metabolism: while both glycolysis and mitochondrial respiration support ATP production in the central area, glycolysis is predominant in the cortical area and notably regulates cell motility and lamellipodia formation. A sub-cellular regional specificity is also observed in neurons: axonal mitochondria display much simpler morphologies and a volume of about half that of their dendritic counterparts, a feature associated with the need of highly mobile mitochondria in axons [START_REF] Faitg | 3D neuronal mitochondrial morphology in axons, dendrites, and somata of the aging mouse hippocampus[END_REF].

Individual mitochondria can display very different shapes -elongated, rod-like and ovoid [START_REF] Kuznetsov | The cell-type specificity of mitochondrial dynamics[END_REF] which have been characterized by a complexity index [START_REF] Vincent | Quantitative 3D mapping of the human skeletal muscle mitochondrial network[END_REF]. Because different tissues are subjected to distinct microenvironments which may affect the distribution and shape of mitochondria, studies have been performed both in situ and in vitro [START_REF] Kuznetsov | Analysis of mitochondrial function, structure, and intracellular organization in situ in cardiomyocytes and skeletal muscles[END_REF]. A peculiar instance is the liver, which plays a pivotal role in essentially all metabolic processes by ensuring the homeostasis of carbohydrates, lipids and proteins. Hepatocyte mitochondria constantly regulate the flux of metabolites in response to changes in in energy demand and nutrient supply, through liver-specific metabolic pathways such as glycogenolysis, gluconeogenesis or ketogenesis [Rui, 2014]. In cultured mammalian cells, hepatocyte mitochondria are ovoid and evenly distributed in the cytosol [Kuznetsov et al., 2009]. In terms of mitochondrial morphology, cultured fibroblasts are an opposite instance to hepatocytes, since they are predominantly elongated and form interconnected networks (Figure 3B) [START_REF] Kuznetsov | The cell-type specificity of mitochondrial dynamics[END_REF].

Intra-tissue heterogeneity is particularly emphasized in the two types of striated muscles, the skeletal and cardiac muscles, which both display a highly specialized structure: cardiomyocytes and skeletal muscle cells are surrounded by a sarcolemma and comprise myofibril bundles. Cells of both tissues display similar mitochondrial network patterns: spheroid interfibrillar mitochondria are evenly aligned in longitudinal rows, subsarcolemmal mitochondria are irregularly spread under the sarcolemma and perinuclear mitochondria are found clustered around the nucleus [START_REF] Li | Mitochondrial dynamics in adult cardiomyocytes and heart diseases[END_REF]. Furthermore, skeletal muscle fibers differentiate into specific fiber types with distinct metabolic properties whether they rely on OXPHOS or on glycolysis [Bourdeau Julien et al., 2018]. Oxidative muscle fibers, characterized by slow contraction rates and high OXPHOS activity, are associated with a higher density and more elongated morphology of mitochondria, compared to the fragmented mitochondria in glycolytic fibers which perform rapid contractions [Mishra et al., 2015].

Interestingly, such morphological differences seem to stem from the fiber metabolic profile. Indeed, while genetically enhancing the expression of mitofusins to promote higher fusion rates in glycolytic fibers does not switch them into oxidative fibers, increasing the respiratory capacity of the mice through endurance exercise induces a substantial switching of glycolytic fibers to oxidative ones and elongation of their mitochondria [Mishra et al., 2015].

Besides their spatial and morphological heterogeneity in mature tissues, mitochondria are subjected to changes during tissue differentiation and maturation [START_REF] Porter | Bioenergetics, mitochondria, and cardiac myocyte differentiation[END_REF][START_REF] Kere | Ultrastructural characterization of porcine growing and in vitro matured oocytes[END_REF], as reviewed in [START_REF] Ding | Mitochondrial biogenesis, mitochondrial dynamics, and mitophagy in the maturation of cardiomyocytes[END_REF]Garben and Lee, 2021] for pluripotent stem cellderived cardiomyocytes. Although cardiomyocyte mitochondria are fragmented and clustered around the nucleus at early embryonic stage, they then become long and rod-shaped after 13.5 weeks. In adult cardiomyocytes, elongated rod-shaped mitochondria are replaced by spheroid mitochondria which densely align along the myofibrils [START_REF] Porter | Bioenergetics, mitochondria, and cardiac myocyte differentiation[END_REF]. Mitochondrial structural and morphological remodeling notably coincides with the bioenergetic changes occurring during heart development, from anaerobic glycolysis at early stages of development to aerobic fatty acid oxidation after placenta maturation and blood circulation development [START_REF] Porter | Bioenergetics, mitochondria, and cardiac myocyte differentiation[END_REF].

Metabolism induces mitochondrial morphodynamic changes

To adapt to energetic demand and supply and sustain metabolic homeostasis, mitochondria undergo remodeling which further modifies their function (Figure 4). Both fast and longer-term mechanisms can regulate the mitochondrial networks in response to changes in nutrient scarcity or oversupply, as reviewed in [START_REF] Babbar | Metabolic stress and disorders related to alterations in mitochondrial fission or fusion[END_REF][START_REF] Liesa | Mitochondrial dynamics in the regulation of nutrient utilization and energy expenditure[END_REF][START_REF] Gao | Mitochondrial response to nutrient availability and its role in metabolic disease[END_REF].

As a protective response to nutrient or oxygen deprivation, mitochondria elongate to be spared from mitophagy and maintain sufficient ATP levels during starvation. Induction of autophagy by starvation in various cell types triggers mitochondrial elongation, resulting in tubular and interconnected networks [START_REF] Gomes | During autophagy mitochondria elongate, are spared from degradation and sustain cell viability[END_REF][START_REF] Zemirli | Mitochondrial dynamics in basal and stressful conditions[END_REF]. Interestingly, in mouse embryonic fibroblasts, starvation conditions can differentially affect mitochondrial morphodynamics: glucose reduction does not induce mitochondrial tubulation, whereas deprivation of either glutamine or amino acids, thus of a nitrogen source, is followed by an increase in mitochondrial tubulation after six hours of starvation [START_REF] Rambold | Tubular network formation protects mitochondria from autophagosomal degradation during nutrient starvation[END_REF].

Nutrient replenishment after starvation decreases tubulation and interconnection in the mitochondrial network, showing that starvation-induced elongation of mitochondria is a reversible mechanism [START_REF] Rambold | Tubular network formation protects mitochondria from autophagosomal degradation during nutrient starvation[END_REF]. Mitochondria elongation also correlates with an increased cristae surface area. Cristae remodeling is crucial in modulating mitochondrial function as the proliferation of cristae folds under high energy demands may provide more surface area for OXPHOS processes [START_REF] Pernas | Mito-morphosis: mitochondrial fusion, fission, and cristae remodeling as key mediators of cellular function[END_REF][START_REF] Nielsen | Plasticity in mitochondrial cristae density allows metabolic capacity modulation in human skeletal muscle[END_REF] and an optimal assembly of the respiratory chain supercomplexes [START_REF] Cogliati | Mitochondrial cristae shape determines respiratory chain supercomplexes assembly and respiratory efficiency[END_REF], which both increase the mitochondrial respiratory efficiency. Electron cryo-tomography showed that elongated mitochondria have higher levels of the dimeric form of ATPase, associated with increased efficiency in ATP production [START_REF] Strauss | Dimer ribbons of ATP synthase shape the inner mitochondrial membrane[END_REF]. Different post-translational mechanisms induce mitochondrial elongation upon nutrient starvation. Nutrient starvation increases the intracellular levels of cyclic adenosine monophosphate (cAMP), thereby activating protein kinase A (PKA) [Beebe, 1994]. Mitochondrial elongation can then be promoted by increased PKA-mediated phosphorylation and inactivation of DRP1, which impairs mitochondrial fission [START_REF] Gomes | During autophagy mitochondria elongate, are spared from degradation and sustain cell viability[END_REF], Rambold et al., 2011].

Besides this starvation-induced mitochondrial elongation, nutrient oversupply correlates with mitochondrial network fragmentation in different cell types [START_REF] Leinninger | Mitochondria in DRG neurons undergo hyperglycemic mediated injury through Bim, Bax and the fission protein Drp1[END_REF][START_REF] Molina | Mitochondrial networking protects β-cells from nutrient-induced apoptosis[END_REF][START_REF] Wang | Mitochondrial fission triggered by hyperglycemia is mediated by ROCK1 activation in podocytes and endothelial cells[END_REF][START_REF] Kobayashi | Mitochondrial fission and mitophagy coordinately restrict high glucose toxicity in cardiomyocytes[END_REF][START_REF] Audzeyenka | Hyperglycemia alters mitochondrial respiration efficiency and mitophagy in human podocytes[END_REF].

In dorsal root ganglia neurons exposed to high glucose, upregulation of DRP1 entails mitochondrial network fragmentation, which increases the number of mitochondria to support glucose excess [START_REF] Leinninger | Mitochondria in DRG neurons undergo hyperglycemic mediated injury through Bim, Bax and the fission protein Drp1[END_REF]. Similarly, in differentiated mouse podocytes, a fiveday period of high glucose exposure also triggers mitochondrial fragmentation, consistent with a downregulation of MFN1 and MFN2 and an upregulation of DRP1 [START_REF] Audzeyenka | Hyperglycemia alters mitochondrial respiration efficiency and mitophagy in human podocytes[END_REF].

Hyperglycemia is proposed to induce Rho-associated coiled coil-containing protein kinase 1 ROCK1-mediated mitochondrial fission by promoting DRP1 recruitment in podocytes and endothelial cells [START_REF] Wang | Mitochondrial fission triggered by hyperglycemia is mediated by ROCK1 activation in podocytes and endothelial cells[END_REF]. Exposing primary β-cells within mouse islets to a nutrientrich environment combining high levels of glucose and palmitate for 48 hours decreases their fusion rates and induces a fragmentation of their mitochondrial networks [START_REF] Molina | Mitochondrial networking protects β-cells from nutrient-induced apoptosis[END_REF].

However, high levels of glucose alone without palmitate do not significantly affect the mitochondrial network connectivity [START_REF] Molina | Mitochondrial networking protects β-cells from nutrient-induced apoptosis[END_REF], which echoes the glucolipotoxicity hypothesis in pancreatic β-cells [START_REF] Lytrivi | Recent insights into mechanisms of β-cell lipo-and glucolipotoxicity in type 2 diabetes[END_REF]. It was proposed that mitochondrial fragmentation in β-cells within islets and INS-1 cells is partially due to increased nutrientinduced ROS production [START_REF] Molina | Mitochondrial networking protects β-cells from nutrient-induced apoptosis[END_REF]. In various cell types at different developmental stages (primary neonatal and adult rodent cardiomyocytes and liver, myoblast and aortic cell lines), acute or sustained exposure to high levels of glucose trigger mitochondrial fragmentation [START_REF] Yu | Increased production of reactive oxygen species in hyperglycemic conditions requires dynamic change of mitochondrial morphology[END_REF][START_REF] Yu | Mitochondrial fission mediates high glucose-induced cell death through elevated production of reactive oxygen species[END_REF][START_REF] Yu | High-glucose stimulation increases reactive oxygen species production through the calcium and mitogen-activated protein kinasemediated activation of mitochondrial fission[END_REF][START_REF] Kobayashi | Mitochondrial fission and mitophagy coordinately restrict high glucose toxicity in cardiomyocytes[END_REF]. In neonatal rat ventricular cardiomyocytes, mitochondrial fragmentation is associated with decreased MFN1 expression and no change in DRP1 expression [START_REF] Kobayashi | Mitochondrial fission and mitophagy coordinately restrict high glucose toxicity in cardiomyocytes[END_REF]. Conflicting data have nevertheless been reported on the role of mitochondrial fission in response to hyperglycemia in cardiomyocytes. Following former studies [START_REF] Yu | Increased production of reactive oxygen species in hyperglycemic conditions requires dynamic change of mitochondrial morphology[END_REF][START_REF] Yu | Mitochondrial fission mediates high glucose-induced cell death through elevated production of reactive oxygen species[END_REF], inhibiting DRP1mediated fission by overexpression of a dominant-negative mutant form of DRP1, limits hyperglycemia-induced cardiomyocyte death. Contrasting results show that mitochondrial fragmentation may rather be a protective mechanism to cope with high glucose toxicity [START_REF] Kobayashi | Mitochondrial fission and mitophagy coordinately restrict high glucose toxicity in cardiomyocytes[END_REF].

ROS levels may have implications in mitochondrial morphodynamics. Various methods have been employed to modulate ROS levels, including hyperglycemia [START_REF] Yu | High-glucose stimulation increases reactive oxygen species production through the calcium and mitogen-activated protein kinasemediated activation of mitochondrial fission[END_REF], acute exposure to hydrogen peroxide (H2O2) [START_REF] Jendrach | Short-and long-term alterations of mitochondrial morphology, dynamics and mtDNA after transient oxidative stress[END_REF][START_REF] Fan | H2O2-induced mitochondrial fragmentation in C2C12 myocytes[END_REF][START_REF] Iqbal | Oxidative stress-induced mitochondrial fragmentation and movement in skeletal muscle myoblasts[END_REF] or photoexcitation [START_REF] Wu | Mitochondrial oxidative stress causes mitochondrial fragmentation via differential modulation of mitochondrial fission-fusion proteins[END_REF]. All led to a fragmentation of the mitochondrial networks, which appears reversible upon stopping the applied stress. The reversible nature of mitochondrial fragmentation after an acute, dose-dependent and non-cytotoxic ROS exposure is reminiscent of a transient upregulation of mitophagy to limit ROS levels. Oxidative stress may be better mitigated in some cells such as myocytes, since contracting skeletal muscle fibers physiologically releases ROS [START_REF] Fan | H2O2-induced mitochondrial fragmentation in C2C12 myocytes[END_REF]. Although mitochondrial morphological changes may occur on the order of hours, Fan et al. reported no major transcriptional changes in the regulation of the main proteins of the fission and fusion machineries. Since a decrease of both the inner mitochondrial membrane potential and the maximum respiratory state have been reported to precede mitochondrial network fragmentation, the molecular mechanism could involve H2O2 inhibition of some proteins of the Krebs cycle [START_REF] Fan | H2O2-induced mitochondrial fragmentation in C2C12 myocytes[END_REF]. DRP1 phosphorylation rather than transcriptional changes in this protein synthesis seem to partially mediate the morphological response of mitochondria in skeletal muscle myoblasts [START_REF] Iqbal | Oxidative stress-induced mitochondrial fragmentation and movement in skeletal muscle myoblasts[END_REF]. A recent study reporting mitochondrial fragmentation in primary neuronal cultures induced by ROS-induced down-expression of Mortalin, a chaperone protein involved in quality control of proteins imported into the mitochondrial matrix, supports such a view [START_REF] Ferré | HSPA9/Mortalin mediates axo-protection and modulates mitochondrial dynamics in neurons[END_REF]. In hyperglycemic conditions, intracellular Ca 2+ acts as an upstream signaling factor for mitochondrial fragmentation. Increase of intracellular Ca 2+ relies on Ca 2+ entry across the plasma membrane, but it remains unclear why high-glucose stimulation activates this influx [START_REF] Yu | High-glucose stimulation increases reactive oxygen species production through the calcium and mitogen-activated protein kinasemediated activation of mitochondrial fission[END_REF]. Photoexcitation of an endogenous photoacceptor by high-fluence low-power laser irradiation in the electron transport chain triggers oxidative stress in ASTC-a-1 cells and COS-7 cells, followed by mitochondrial fragmentation through inhibition of fusion and enhanced fission [START_REF] Wu | Mitochondrial oxidative stress causes mitochondrial fragmentation via differential modulation of mitochondrial fission-fusion proteins[END_REF].

Metabolic needs impact mitochondria morphodynamics during cell adhesion and cell spreading

Cell adhesion and spreading are energy-consuming processes. The uptake of glucose required to generate ATP for cytoskeleton remodeling and cell adhesion-mediated contractility depends on substrate stiffness. On stiffer substrates (Young modulus E = 20 kPa) compared to soft substrates (E = 1 kPa), cell spreading induces an initial drop in intracellular ATP, which is associated with the formation of focal adhesions and the reorganization of the actin cytoskeleton [START_REF] Xie | Energy expenditure during cell spreading regulates the stem cells responses to matrix stiffness[END_REF]. AMP-activated protein kinase (AMPK) is subsequently activated by the drop in ATP concentration. AMPK is known to be activated by different types of metabolic stresses that deplete cellular energy levels, including nutrient starvation and hypoxia [START_REF] Hardie | AMPK: a nutrient and energy sensor that maintains energy homeostasis[END_REF][START_REF] Kim | AMPK activators: mechanisms of action and physiological activities[END_REF]. Inhibition of AMPK correlates with significantly reduced glucose uptake even on stiff substrates, suggesting that substrate stiffness is only an exogenous mean to enhance glucose uptake by activating AMPK [START_REF] Xie | Energy expenditure during cell spreading regulates the stem cells responses to matrix stiffness[END_REF]. Surprisingly, AMPK activation following the drop in intracellular ATP during cell spreading on stiff substrates induces fragmentation of the mitochondrial network due to increased fission rates compared to cell spreading on soft substrates.

Overall, the nature, the intensity and the duration of the metabolic signal all have an impact on mitochondrial morphodynamics (Figure 4). Enhanced fission or fusion events can be part of a cytoprotective mechanism to allow cellular adaptation. However, too high levels of metabolic stress may lead to abnormal mitochondrial morphodynamics and cell damage.

Mitochondrial morphodynamics induces metabolic changes

While structural and functional remodeling of the mitochondrial network has been observed in response to metabolic inputs, conversely there is also mounting evidence that mitochondrial morphodynamics has dramatic effects on cell metabolism. Fission and fusion are coordinated processes controlling the mitochondrial network. Alterations of these mechanisms can spark metabolic dysfunction. Mitochondrial quality control by fission and fusion is all the more central in post-mitotic tissues such as skeletal muscles, which cannot mitigate impaired mitochondria through cellular division. For example, disruption of mitochondrial morphodynamics was found to disturb signaling pathways regulating muscle mass and performance [START_REF] Romanello | The connection between the dynamic remodeling of the mitochondrial network and the regulation of muscle mass[END_REF].

The predominance of either elongated or fragmented mitochondria in pathologies suggests that an imbalance between fission and fusion rates can lead to metabolic dysfunction.

Loss-or gain-of-function studies targeting proteins associated with mitochondrial morphodynamics, as well as the use of cells harboring mutations leading to identified pathologies (such as the Charcot-Marie-Tooth disease), allowed to decipher how these proteins affect metabolism. For a comprehensive overview of how dysregulated activity of fusion-or fission-related proteins can impact cell metabolism, the reader is referred to [START_REF] Babbar | Metabolic stress and disorders related to alterations in mitochondrial fission or fusion[END_REF][START_REF] Schrepfer | Mitofusins, from mitochondria to metabolism[END_REF][START_REF] Zemirli | Mitochondrial dynamics in basal and stressful conditions[END_REF][START_REF] Eisner | Mitochondrial dynamics in adaptive and maladaptive cellular stress responses[END_REF]Filadi et al., 2018;[START_REF] Dai | Dysregulated mitochondrial dynamics and metabolism in obesity, diabetes, and cancer[END_REF]. We summarize below some key instances related to MFN1, MFN2 and DRP1 mutations.

MFN1 and MFN2

Implication of MFN1 and MFN2 in the regulation of metabolism has been demonstrated in different physiological and pathological cell models [START_REF] Bach | Mitofusin-2 determines mitochondrial network architecture and mitochondrial metabolism: a novel regulatory mechanism altered in obesity[END_REF][START_REF] Bach | Expression of Mfn2, the Charcot-Marie-Tooth neuropathy type 2A gene, in human skeletal muscle: effects of type 2 diabetes, obesity, weight loss, and the regulatory role of tumor necrosis factor α and interleukin-6[END_REF][START_REF] Chen | Disruption of fusion results in mitochondrial heterogeneity and dysfunction[END_REF][START_REF] Pich | The Charcot-Marie-Tooth type 2A gene product, Mfn2, upregulates fuel oxidation through expression of OXPHOS system[END_REF][START_REF] Loiseau | Mitochondrial coupling defect in Charcot-Marie-Tooth type 2A disease[END_REF][START_REF] Kulkarni | Mfn1 deficiency in the liver protects against diet-induced insulin resistance and enhances the hypoglycemic effect of metformin[END_REF]. Although these GTPases cooperatively regulate mitochondrial outer membrane fusion, MFN1 plays a more prominent role in membrane tethering than MFN2 [START_REF] Ishihara | Mitofusin 1 and 2 play distinct roles in mitochondrial fusion reactions via GTPase activity[END_REF]. The latter is rather more strongly involved in mitochondrial metabolism, as it notably governs mitochondrial membrane potential, glucose, fatty acid and amino acid oxidation and OXPHOS, as reviewed in [START_REF] Schrepfer | Mitofusins, from mitochondria to metabolism[END_REF]. Differently from MFN1, a small fraction of MFN2 has been observed to be located in ER membranes juxtaposed to outer mitochondrial membranes. MFN2 deletion is reported to induce an ER stress, through a mechanism still under debate [START_REF] Yang | Mitochondria-associated endoplasmic reticulum membrane: Overview and inextricable link with cancer[END_REF], which can lead to a deterioration of cellular functions [START_REF] Filadi | Mitofusin 2: from functions to disease[END_REF].

MFN2 is downregulated in some metabolic diseases such as type 2 diabetes and obesity, leading to a fragmented mitochondrial network [START_REF] Schrepfer | Mitofusins, from mitochondria to metabolism[END_REF][START_REF] Vezza | The role of mitochondrial dynamic dysfunction in age-associated type 2 diabetes[END_REF]. For instance, in primary fibroblasts derived from Charcot-Marie-Tooth disease type 2 patients who display MFN2 mutations, mitochondrial metabolism is greatly affected, with a reduction of both mitochondrial membrane potential and OXPHOS efficacy [START_REF] Loiseau | Mitochondrial coupling defect in Charcot-Marie-Tooth type 2A disease[END_REF]. In vitro studies show that MFN2 knockdown or knockout models are associated with alterations of both mitochondrial and non-mitochondrial functions. MFN2 downregulation in either L6E9 skeletal myotubes or 10T1/2 mouse embryonic fibroblasts (mediated by an adenoviral vector encoding a mouse MFN2 antisense sequence) induces fragmentation of the mitochondrial network into independent clusters, along with a reduction of glucose oxidation and mitochondrial membrane potential and the inhibition of both pyruvate and palmitate oxidation [START_REF] Bach | Mitofusin-2 determines mitochondrial network architecture and mitochondrial metabolism: a novel regulatory mechanism altered in obesity[END_REF]. These changes are mediated by a reduced expression of subunits of the complexes I, II, III and V of the OXPHOS system, as observed in MFN2-deficient obese rats [START_REF] Pich | The Charcot-Marie-Tooth type 2A gene product, Mfn2, upregulates fuel oxidation through expression of OXPHOS system[END_REF]. More recent in vivo studies on mouse brown adipose tissues show that MFN2 knockout is associated with the disruption of brown adipose tissue thermogenic function [START_REF] Boutant | Mfn2 is critical for brown adipose tissue thermogenic function[END_REF][START_REF] Mahdaviani | Mfn2 deletion in brown adipose tissue protects from insulin resistance and impairs thermogenesis[END_REF]. More precisely, this impairment correlates with a reduced lipolytic capacity and fatty acid oxidation, which are controlled by mitochondrial uncoupling protein 1. Conversely, MFN2 upregulation in HeLa cells by transient transfection of a truncated form of human MFN2 results in the increase of glucose oxidation and mitochondrial membrane potential [START_REF] Pich | The Charcot-Marie-Tooth type 2A gene product, Mfn2, upregulates fuel oxidation through expression of OXPHOS system[END_REF].

While MFN2 knockout consistently reduces mitochondrial membrane potential, glucose oxidation and OXPHOS, MFN1 knockout impacts differentially the metabolism depending on the tissues. Liver-specific deletion of the MFN1 gene in mice increases the dependence of hepatocytes on lipids as an oxidative energy source through fatty acid oxidation [START_REF] Kulkarni | Mfn1 deficiency in the liver protects against diet-induced insulin resistance and enhances the hypoglycemic effect of metformin[END_REF]. Fed mice lacking MFN1 in proopiomelanocortin neurons display increased respiratory capacity through mitochondrial complex I and II, along with enhanced ROS production upon glucose stimulation [START_REF] Ramírez | Mitochondrial dynamics mediated by mitofusin 1 is required for POMC neuron glucose-sensing and insulin release control[END_REF]. Conversely, MFN1 knockout specific to brown adipose tissue does not alone alter mitochondrial bioenergetics [Boutant et al., 2017].

DRP1

In muscle cells, loss of DRP1 remodels the mitochondrial network inducing larger but fewer mitochondria. Functionally, reduction of mitochondrial respiration is observed, consistent with a downregulation of respiratory chain complexes subunits and alteration of calcium homeostasis [START_REF] Favaro | Drp1mediated mitochondrial shape controls calcium homeostasis and muscle mass[END_REF]. Silencing DRP1 in HeLa cells induces abnormal branching and excessive budding of the mitochondrial network accompanied by an increase in mitochondrial membrane fluidity, which downregulates the expression of the molecular machinery required for ATP synthesis [START_REF] Benard | Mitochondrial bioenergetics and structural network organization[END_REF]. Of note, an increase in membrane fluidity from another origin (i.e. mediated by an intracellular amyloid beta-peptide (Aβ) accumulation) leads also to a decrease in the efficiency of mitochondrial ATP production [START_REF] Aleardi | Gradual alteration of mitochondrial structure and function by β-amyloids: importance of membrane viscosity changes, energy deprivation, reactive oxygen species production, and cytochrome c release[END_REF]. In DRP1 knockdown pancreatic MIN6 cells which express 50 % less DRP1 mRNA and 80 % less protein than control MIN6 cells, coupled mitochondrial respiration is reduced upon glucose stimulation, demonstrating an enhanced mitochondrial proton leak by DRP1 depletion [START_REF] Kabra | Direct Substrate Delivery Into Mitochondrial Fission-Deficient Pancreatic Islets Rescues Insulin Secretion[END_REF]. Conversely, overexpression of DRP1 in skeletal muscle of a transgenic mouse line does not significantly affect mitochondrial bioenergetics. While the rates of oxygen consumption in control and transgenic mice are similar, there is a slight but not significant increase of ATP levels produced by OXPHOS in transgenic mice [START_REF] Touvier | Muscle-specific Drp1 overexpression impairs skeletal muscle growth via translational attenuation[END_REF].

Mechanical cues and alterations in mitochondrial mechanical properties re-shape and reorganize the mitochondrial network

Changes in the mechanical properties of mitochondria in response to signaling cues should contribute to reshape and reorganize the mitochondrial network. It is indeed becoming increasingly clear that mitochondrial mechanics regulates their morphodynamics. In stark contrast, to our knowledge, evidence for the reciprocal link has not been demonstrated until now.

External forces reshape the mitochondrial network

External forces applied to the cell can modify cell functions in the process known as mechanotransduction. Several modules that transduce forces into intracellular signals have been identified at the plasma membrane, including cell-substrate and cell-cell adhesions or stretchactivated ion channels [START_REF] Mathieu | Intracellular mechanics: connecting rheology and mechanotransduction[END_REF]. From a physical point of view, forces applied to membranes often change their tension. In the case of the plasma membrane, changes in osmotic pressure [START_REF] Roffay | Passive coupling of membrane tension and cell volume during active response of cells to osmosis[END_REF], stresses applied by the underlying actomyosin cortex during cell motility [START_REF] Sitarska | Pay attention to membrane tension: Mechanobiology of the cell surface[END_REF] or stresses stemming from cell spreading on substrates [START_REF] Raucher | Cell spreading and lamellipodial extension rate is regulated by membrane tension[END_REF]] modify membrane tension. Similarly, for mitochondrial membranes, forces applied inside (internal) or outside (external) the cell may affect membrane tension and, consequently, mitochondrial morphodynamics. However, how external forces are transmitted from the plasma membrane to mitochondria is still largely unexplored. As for other endomembranes [START_REF] Phuyal | Endomembranes: Unsung heroes of mechanobiology[END_REF] and for the nucleus, the cytoskeleton is probably a major actor. Several studies have shown that external mechanical stimulation of either intracellular or isolated mitochondria increase fission or fusion events [START_REF] Phuyal | Mechanobiology of organelles: illuminating their roles in mechanosensing and mechanotransduction[END_REF]. A variety of mechanical stimuli -encounter with motile intracellular pathogens, external pressure applied by an atomic force microscope or cell migration across uneven microsurfaces -have been shown to induce mitochondrial fission [START_REF] Helle | Mechanical force induces mitochondrial fission[END_REF].

Cell stretching

The mitochondrial response to mechanical cues has been particularly studied in cells which integrate mechanical stimuli, such as stretches, as part of their physiological functions. For instance, stretching lung fibroblasts induces an elongation of mitochondria at membrane area strains of 7-14 % and mitochondrial fission for strains above 30 % [START_REF] Imsirovic | Design of a novel equi-biaxial stretcher for live cellular and subcellular imaging[END_REF].

Similar strains also result in local stretching of the mitochondria of pulmonary endothelial cells [START_REF] Chapman | Cyclic mechanical strain increases reactive oxygen species production in pulmonary epithelial cells[END_REF]. Although the actomyosin cortex [START_REF] Duda | Polarization of myosin II refines tissue material properties to buffer mechanical stress[END_REF] and/or membrane reservoirs [START_REF] Sinha | Cells respond to mechanical stress by rapid disassembly of caveolae[END_REF] are likely to buffer a large fraction of the applied force on the whole cell, stretching or fission of mitochondria may occur due to their attachment to the cytoskeleton [ [START_REF] Bartolák-Suki | Regulation of mitochondrial structure and dynamics by the cytoskeleton and mechanical factors[END_REF].

Moreover, the organization of the mitochondrial networks can be differently altered depending on the temporal pattern of the applied forces. To mimic irregular mechanical fluctuations, such as those arising from changes in blood pressure, Bartolák-Suki et al. have shown in bovine aortic cells the spectacular effects of variable cyclic stretches that incorporate physiological levels of cycle-by-cycle variability in stretch amplitude, compared to monotonous stretch cycles of constant amplitudes [START_REF] Bartolák-Suki | Fluctuation-driven mechanotransduction regulates mitochondrial-network structure and function[END_REF]. The authors found that the average mitochondrial cluster area per cell increases from the unstretched control significantly more during variable stretch than monotonous stretch. The space-filling capacity of the network increases solely in variable stretch. Importantly, variable stretch enhances ATP production by increasing the expression of the catalytic domain of ATP synthase, the expression of cytochrome c oxidase and its tyrosine phosphorylation, and the expression of mitofusins and PGC-1α. The precise mechanism leading to these results is still unknown, although actin and microtubule networks seem to respond differentially to monotonous stretch and variable stretch stimulations [START_REF] Bartolák-Suki | Fluctuation-driven mechanotransduction regulates mitochondrial-network structure and function[END_REF].

Plasma membrane disruption

The nature and the magnitude of external forces applied on cells can indirectly affect mitochondrial morphodynamics. A slowly increasing compression applied on primary bovine aortic endothelial cells using a spherical microindentor, without membrane rupture, is not sufficient to induce generalized mitochondrial fission [START_REF] Gonzalez-Rodriguez | Elastocapillary instability in mitochondrial fission[END_REF]. In that case, fission is observed only for dynamic mitochondria and the threshold strain required for fission has not been measured yet. However, local deformation and rupture of the cell plasma membrane using a glass micropipette induce mitochondrial fission in primary bovine aortic endothelial cells [START_REF] Gonzalez-Rodriguez | Elastocapillary instability in mitochondrial fission[END_REF]. The inner mitochondrial membrane potential decreases after plasma membrane disruption, which demonstrates a partial permeabilization of the inner mitochondrial membrane. The application of cytoskeleton disrupting agents, such as cytochalasin D or nocodazole, does not significantly modify these observations, suggesting that actin and microtubule filaments might only play a role in mitochondrial fission when the plasma membrane integrity is not compromised. However, the question arises whether mitochondrial fission is induced here by an apoptotic process following plasma membrane rupture, which triggers fast, Ca 2+ signaling pathways. Previous studies have shown that fragmentation of mitochondria and loss of membrane potential are observed during apoptosis through Ca 2+ signaling, involving permeabilization of the outer mitochondrial membrane and cytochrome c release from the intermembrane space of the mitochondria into the cytosol [START_REF] Karbowski | Dynamics of mitochondrial morphology in healthy cells and during apoptosis[END_REF][START_REF] Gottlieb | Mitochondrial membrane potential regulates matrix configuration and cytochrome c release during apoptosis[END_REF]. A more recent study on local disruption of plasma membrane by laser injury in primary mouse embryonic fibroblasts also reports extracellular calcium influx and DRP1-mediated mitochondrial fragmentation at the injury site a few seconds after plasma membrane disruption [START_REF] Horn | Mitochondrial fragmentation enables localized signaling required for cell repair[END_REF]. Injury-proximal mitochondrial fragmentation has a twofold function: it does not only preserve mitochondria from calcium overload and apoptosis, but also enables polarized mROS signaling to mediate plasma membrane repair.

Effect of pressure and osmotic shocks

Elevated hydrostatic pressure can affect mitochondrial structure and network morphology. In differentiated retinal ganglion cells, incubation for three days at elevated hydrostatic pressure (4000 Pa) results in mitochondrial fragmentation and cristae depletion [START_REF] Ju | Elevated hydrostatic pressure triggers mitochondrial fission and decreases cellular ATP in differentiated RGC-5 cells[END_REF][START_REF] Ju | Elevated hydrostatic pressure triggers release of OPA1 and cytochrome C, and induces apoptotic cell death in differentiated RGC-5 cells[END_REF]. These changes are associated with higher DRP1 translocation from the cytosol to mitochondria [START_REF] Ju | Elevated hydrostatic pressure triggers mitochondrial fission and decreases cellular ATP in differentiated RGC-5 cells[END_REF], increased cytosolic OPA1 and cytochrome c fractions [START_REF] Ju | Elevated hydrostatic pressure triggers release of OPA1 and cytochrome C, and induces apoptotic cell death in differentiated RGC-5 cells[END_REF]. Cytochrome c release might be triggered by either an OPA1 or DRP1-mediated mechanism after pressure treatment [START_REF] Ju | Elevated hydrostatic pressure triggers release of OPA1 and cytochrome C, and induces apoptotic cell death in differentiated RGC-5 cells[END_REF]. Similar results are observed in the optic nerve of glaucomatous mice, which spontaneously develop high intraocular pressure [START_REF] Ju | Intraocular pressure elevation induces mitochondrial fission and triggers OPA1 release in glaucomatous optic nerve[END_REF]. Conversely, in human umbilical vein endothelial cells cultured for 24 hours at a much higher hydrostatic pressure (40 kPa), mitochondria are more elongated than in control conditions, consistent with a decreased expression level of DRP1 and increased expression level of OPA1 [START_REF] Xu | A facile cell culture device for studying nuclear and mitochondrial response of endothelial cells to hydrostatic pressure[END_REF].

Although sometimes difficult to interpret when not combined with other experimental techniques, osmotic shocks may also generate mechanical forces that impact on mitochondrial morphodynamics and mechanics. In monkey kidney epithelial cells, hypertonic conditions induced by high concentration of NaCl result in a reversible mitochondrial network fragmentation, which occurs from the very first five minutes and further develops within an hour [START_REF] Copp | Hypertonic shock inhibits growth factor receptor signaling, induces caspase-3 activation, and causes reversible fragmentation of the mitochondrial network[END_REF]. This fragmentation is secondary to mitochondrial membrane potential dissipation. In the same study involving plasma membrane rupture by a glass micropipette in aortic endothelial cells [START_REF] Gonzalez-Rodriguez | Elastocapillary instability in mitochondrial fission[END_REF], in hypertonic conditions, mitochondria are less fragmented after plasma membrane mechanical disruption than in isotonic conditions. Such a hypertonic shock prior to plasma membrane rupture may result in a shrinking of the mitochondria, associated with a reduction of their membrane tension [START_REF] Gonzalez-Rodriguez | Elastocapillary instability in mitochondrial fission[END_REF].

Substrate stiffness

The in vitro response of mitochondrial morphodynamics to substrate stiffness is a matter of debate and the molecular signaling pathways involved in the regulation of mitochondrial morphology are still under investigation. While some studies report mitochondrial fragmentation on stiff substrates [START_REF] Tharp | Adhesion-mediated mechanosignaling forces mitohormesis[END_REF][START_REF] Xie | Energy expenditure during cell spreading regulates the stem cells responses to matrix stiffness[END_REF][START_REF] Guo | Mitochondrial fission and bioenergetics mediate human lung fibroblast durotaxis[END_REF], stiffnessinduced mitochondrial elongation has been evidenced in [START_REF] Papalazarou | The creatine-phosphagen system is mechanoresponsive in pancreatic adenocarcinoma and fuels invasion and metastasis[END_REF], Chen et al., 2021, Romani et al., 2022, Li et al., 2023]. Such conflicting results could result from the different experimental conditions and cell types used in these studies.

In human mammary epithelial cells, it is proposed that solute carrier family 9 member A1-dependent ion exchange SLC9A1 mediates mitochondrial fission in stiffer conditions [START_REF] Tharp | Adhesion-mediated mechanosignaling forces mitohormesis[END_REF]. In primary human lung fibroblasts, which perform durotactic migration, DRP1 and MFF-mediated mitochondrial fission is also enhanced on stiffer substrates mimicking the pulmonary fibrotic environment, although the mechanotransduction pathways are not clear yet [START_REF] Guo | Mitochondrial fission and bioenergetics mediate human lung fibroblast durotaxis[END_REF].

Conversely, in human and mouse pancreatic cancer cells, elongated mitochondrial shapes are also observed on stiff substrates and even on glass [START_REF] Papalazarou | The creatine-phosphagen system is mechanoresponsive in pancreatic adenocarcinoma and fuels invasion and metastasis[END_REF]. Along the same line, in human breast epithelial cells, a soft ECM induces DRP1-mediated mitochondrial fission [START_REF] Romani | Mitochondrial fission links ECM mechanotransduction to metabolic redox homeostasis and metastatic chemotherapy resistance[END_REF]. Increased fission events follow the formation of peri-mitochondrial F-actin driven by Spire1C and Arp2/3 [START_REF] Romani | Mitochondrial fission links ECM mechanotransduction to metabolic redox homeostasis and metastatic chemotherapy resistance[END_REF][START_REF] Phuyal | Mechanobiology of organelles: illuminating their roles in mechanosensing and mechanotransduction[END_REF]. In mesenchymal stem cells, lung adenocarcinoma A549 cells and fibrosarcoma HT1080 cells, ECM stiffening induces mitochondrial elongation by both promoting fission and inhibiting fission [START_REF] Chen | Extracellular matrix stiffness regulates mitochondrial dynamics through PINCH-1-and kindlin-2mediated signalling[END_REF]. Two integrin-dependent signaling pathways are involved, namely kindlin-2-dependent upregulation of fusion and PINCH-1-dependent suppression of DRP1 expression and inhibition of fission [START_REF] Chen | Extracellular matrix stiffness regulates mitochondrial dynamics through PINCH-1-and kindlin-2mediated signalling[END_REF].

Internal forces reshape the mitochondrial network

Mitochondria are mechanically stimulated by forces generated within the cell. Because they are involved in inter-organellar and cytoskeletal contacts, mitochondria are continually subjected to tensile and compressive stresses [START_REF] Feng | Mechanical forces on cellular organelles[END_REF]. There is mounting evidence that mitochondrial fission correlates with these intracellular mechanical cues.

Internal forces are produced by actin and microtubule-associated motor proteins that anchor mitochondria to the cytoskeleton [START_REF] Boldogh | Mitochondria on the move[END_REF]. In particular, the microtubule-based motor proteins dynein and kinesin move mitochondria along microtubule tracks and deliver piconewton forces which induce tension on mitochondrial membranes [Howard, 2002;[START_REF] Xie | Cytoskeleton force exertion in bulk cytoplasm[END_REF]. Moreover, recruiting molecular motors to the outer mitochondrial membrane via an optogenetic approach induces membrane deformation and pulls membrane tubules which systematically undergo DRP1-dependent and ER-dependent fission [START_REF] Liu | Mechanical force induces DRP1-dependent asymmetrical mitochondrial fission for quality control[END_REF][START_REF] Song | Light-inducible deformation of mitochondria in live cells[END_REF]. The mechanisms underlying the preferential fission at the protruding tubules are not yet clear. On one hand, there is a higher probability that long mitochondrial tubules reach the ER and form contact sites [START_REF] Liu | Mechanical force induces DRP1-dependent asymmetrical mitochondrial fission for quality control[END_REF]. On the other hand, mitochondrial tubules, which are thinner than the mitochondrial body diameter, have a higher local membrane curvature and may provide preferential fission sites by recruiting the fission machinery. This observation is echoing a previous in vitro study on curvature-dependent dynamin polymerization on tubules pulled from giant unilamellar vesicles as model membrane systems [START_REF] Roux | Membrane curvature controls dynamin polymerization[END_REF]. In order to deform the membrane into tubules, the force generated by dynamin polymerization has to overcome membrane tension. Taken together, these results further suggest that force-induced mitochondrial fission may involve the spontaneous or physically-mediated recruitment of the fission machinery. However, recent experiments performed with synthetic actin-based biomolecular devices on short (i.e. minute) time scales suggest that fission can also occur in the absence of DRP1 independently of the endogenous mitochondrial fission machinery [START_REF] Nakamura | ActuAtor, a molecular tool for generating force in living cells: Controlled deformation of intracellular structures[END_REF][START_REF] Miyamoto | Rapid manipulation of mitochondrial morphology in a living cell with iCMM[END_REF].

Physico-chemical cues regulate mitochondrial morphodynamics

Physico-chemical stimuli can affect the mechanical properties of mitochondria and change their morphodynamics. The role of cardiolipin (CL), a unique negatively charged phospholipid found only in membranes of both bacteria and mitochondria, in mitochondrial function and dynamics has been thoroughly reviewed in [START_REF] Paradies | Role of cardiolipin in mitochondrial function and dynamics in health and disease: molecular and pharmacological aspects[END_REF][START_REF] Yang | Mitochondrial membrane remodeling[END_REF]. Besides the regulation of proteins and enzymes involved in mitochondrial metabolic functions, CL is substantial in both fission and fusion dynamics. In particular, it emerges as a key player of the inner mitochondrial membrane plasticity by contributing to cristae structure and physicochemical properties [START_REF] Joubert | Mitochondrial cristae architecture and functions: Lessons from minimal model systems[END_REF], and by interacting with fission and fusion proteins such as DRP1 [START_REF] Stepanyants | Cardiolipin's propensity for phase transition and its reorganization by dynamin-related protein 1 form a basis for mitochondrial membrane fission[END_REF] and OPA1 [START_REF] Liu | OPA1 and cardiolipin team up for mitochondrial fusion[END_REF][START_REF] Ban | Relationship between OPA1 and cardiolipin in mitochondrial inner-membrane fusion[END_REF][START_REF] Ge | Absence of cardiolipin from the outer leaflet of a mitochondrial inner membrane mimic restricts Opa1-mediated fusion[END_REF]. For instance, CL is required for mediating heterotypic mitochondrial inner membrane fusion through its interaction with the long form of OPA1. The morphology of mitochondria can be drastically altered by changes in cardiolipin concentration. Low levels of cardiolipin are associated with enlargement and swelling of mitochondria, along with disorganization of the cristae structure which may be linked to a decrease in membrane fluidity [START_REF] Nichols-Smith | Thermodynamic and mechanical properties of model mitochondrial membranes[END_REF].

pH levels can also affect the deformability of mitochondria and their fission and fusion rates by perturbing the organization of the mitochondrial membranes [START_REF] Wang | Membrane deformability and membrane tension of single isolated mitochondria[END_REF][START_REF] Gonzalez-Rodriguez | Elastocapillary instability in mitochondrial fission[END_REF][START_REF] Yoneda | Effects of proton pumping on the structural rigidity of cristae in mitochondria[END_REF]. A non-physiological pH stiffens isolated mitochondria, as deduced from the deformation of these organelles using the micropipette aspiration technique [START_REF] Wang | Membrane deformability and membrane tension of single isolated mitochondria[END_REF]. Acidification of the outer surface of the inner membrane is associated with a decrease in cristae rigidity, its unfolding and subsequent mitochondrial inner membrane swelling [START_REF] Yoneda | Effects of proton pumping on the structural rigidity of cristae in mitochondria[END_REF]. Since the inner mitochondrial membrane contains a large concentration of proteins, including proteins of the cristae junction complexes [START_REF] Yang | Mitochondrial membrane remodeling[END_REF], such softening as the pH decreases may be due to a higher flexibility of these proteins and/or changes in lipid composition and charge. In giant unilamellar vesicles containing cardiolipin, a local modulation of the pH across the membrane creates or represses the formation of cristae-like invaginations [START_REF] Khalifat | Membrane deformation under local ph gradient: mimicking mitochondrial cristae dynamics[END_REF].

Is mitochondrial membrane tension essential for mitochondrial fission?

The lipid double-membrane of mitochondria participates both in mitochondrial mechanics and morphodynamics. The inner and outer mitochondrial membranes play specific functional roles and understanding how they respond to mechanical stimulation has been of recent interest.

The role of mitochondrial membrane tension in mitochondrial morphodynamics has recently drawn attention, with a recent work shedding light on the correlation between this physical parameter and fission events [START_REF] Mahecic | Mitochondrial membrane tension governs fission[END_REF]. In this work, the authors followed Nocodazole may be an indirect consequence of cytoskeletal-dependent changes. As reviewed in [Fatima and Ananthanarayan, 2023], results in [START_REF] Mahecic | Mitochondrial membrane tension governs fission[END_REF] contrast with those in [START_REF] Mehta | Association of mitochondria with microtubules inhibits mitochondrial fission by precluding assembly of the fission protein Dnm1[END_REF], as depolymerization of microtubules in budding yeast upon deletion of kinesin-like proteins is correlated with a higher mitochondrial fission frequency. Furthermore, although in a different context, a decrease in plasma membrane tension was shown to favor abscission during cell division [START_REF] Lafaurie-Janvore | ESCRT-III assembly and cytokinetic abscission are induced by tension release in the intercellular bridge[END_REF]. Overall, there are many pending questions to be answered: is an increase in mitochondrial membrane tension sufficient to induce fission? Is this membrane tension-induced fission DRP1-dependent, ER-dependent and actindependent? Are mitochondrial membrane tension changes rather a consequence of the recruitment of the canonical or non-canonical fission machinery?

In summary, mechanical forces, whether applied externally (by stretching the cell, applying pressure or modulating substrate stiffness) and transmitted to mitochondria, or applied internally directly on mitochondria (by the cytoskeleton or the fission machinery), can alter mitochondrial morphodynamics. During these mechanotransduction events, while signaling events involving not only proteins but also lipids play critical roles, physical parameters such as membrane curvature and membrane tension also emerge as key regulators.

Mitochondrial mechanics and metabolism are reciprocally regulated

How cellular mechanics and metabolism are connected at multiple scales, from molecular mechanosensors to the cytoskeletal networks and the organelles, is a topic of growing interest [START_REF] Evers | Reciprocal regulation of cellular mechanics and metabolism[END_REF]. We focus here on the interplay between mechanics and metabolism at the level of mitochondria. The links between mechanical cues, mitochondrial mechanics and their metabolic functions are still poorly understood. While it is clear that the physical integrity of the mitochondrial membrane is crucial for OXPHOS, the mechanical properties of mitochondria and/or physical cues could also influence mitochondrial metabolic processes including ATP or ROS production (Figure 6).

Mechanical cues and mechanosensitive pathways regulate metabolism at the level of mitochondria

Physical cues regulate cell metabolism

OXPHOS is sensitive to physical variations of the mitochondrial environment. Two early studies investigated the effects of osmotic pressure on the respiration of rat liver mitochondria [START_REF] Sitaramam | Differential effects of osmotic pressure on mitochondrial respiratory chain and indices of oxidative phosphorylation[END_REF][START_REF] Sitaramam | Oxidative phosphorylation in rat liver mitochondria: Influence of physical[END_REF]. Based on the generation and use of the proton electrochemical gradient in the respiratory chain, the activity of the complexes of the OXPHOS system in mitochondrial membranes was assessed by the well-established polarographic technique [START_REF] Chance | A simple and rapid assay of oxidative phosphorylation[END_REF][START_REF] Wenchich | Polarographic evaluation of mitochondrial enzymes activity in isolated mitochondria and in permeabilized human muscle cells with inherited mitochondrial defects[END_REF][START_REF] Li | Measurement of mitochondrial oxygen consumption using a clark electrode[END_REF]. Mitochondria subjected to hyperosmotic pressure undergo structural shrinking and inhibition of respiration. Additionally, the mitochondrial respiratory chain complexes display a differential osmotic sensitivity [START_REF] Sitaramam | Differential effects of osmotic pressure on mitochondrial respiratory chain and indices of oxidative phosphorylation[END_REF].

Applied forces change cell metabolism

Mitochondrial metabolic responses strongly depend on the nature of the applied forces. This is particularly true for primary bovine aortic smooth muscle cells subjected to sinusoidal stretches with either a constant or a variable amplitude, compared to unstretched conditions [START_REF] Bartolák-Suki | Fluctuation-driven mechanotransduction regulates mitochondrial-network structure and function[END_REF]. Stretching cells induces a reorganization of the mitochondrial network, but the bioenergetic responses depend on the stretch pattern. A variable amplitude enhances ATP production compared to a constant amplitude, as a consequence of the increase in the expression of the ATP synthase catalytic domain and of cytochrome c oxidase [START_REF] Bartolák-Suki | Fluctuation-driven mechanotransduction regulates mitochondrial-network structure and function[END_REF].

These results indicate that the temporal pattern of stretching is sensed by mitochondria and promotes ATP production through OXPHOS.

Flow-generated mechanical forces play a critical role in cellular metabolism. In particular, the luminal surface of the endothelium is constantly exposed to shear stress induced by the blood circulation. Endothelial cells need a constant supply of energy to perform various processes such as the trafficking of blood-borne cells, nutrients and hormones, angiogenesis and the maintenance of blood fluidity. The shear stress magnitude and the flow pattern can significantly vary. For instance, during exercise, the shear stress can increase from 1.5 Pa to 3

Pa in human arteries [START_REF] Tang | Abdominal aortic hemodynamics in young healthy adults at rest and during lower limb exercise: quantification using image-based computer modeling[END_REF]. Changes in the magnitude and the pattern of hemodynamic flow induce mitochondrial remodeling and metabolic reprogramming. As reviewed in [START_REF] Hong | Mitochondrial and metabolic adaptations to exercise-induced fluid shear stress in endothelial cells[END_REF], several studies have focused on metabolic reprogramming within endothelial cells subjected to laminar shear stress or oscillatory shear stress. Laminar shear stress is associated with an increase in mitochondrial respiration, a decrease in glycolysis and an upregulation of lipid metabolism [START_REF] Kim | Exercise-mediated wall shear stress increases mitochondrial biogenesis in vascular endothelium[END_REF][START_REF] Doddaballapur | Laminar shear stress inhibits endothelial cell metabolism via KLF2-mediated repression of PFKFB3[END_REF]Feng et al., 2017;[START_REF] Wu | HIF-1 is required for disturbed flow-induced metabolic reprogramming in human and porcine vascular endothelium[END_REF][START_REF] Venturini | Integrated proteomics and metabolomics analysis reveals differential lipid metabolism in human umbilical vein endothelial cells under high and low shear stress[END_REF]. High laminar shear stress induces activation of the anti-inflammatory transcription factor, Kruppel-like factor Klf2 [START_REF] Coon | A mitochondrial contribution to anti-inflammatory shear stress signaling in vascular endothelial cells[END_REF],

which downregulates gene expression of glycolytic enzymes [START_REF] Doddaballapur | Laminar shear stress inhibits endothelial cell metabolism via KLF2-mediated repression of PFKFB3[END_REF].

Interestingly, either mitophagy or an antioxidant response can activate Klf2, which shows that the MEKK2/3-MEK5-ERK5-Klf2 signaling pathway is an instance of mito-hormesis. Hypoxia inducible factor-1 (HIF-1) and protein kinase AMP-activated/AMP-activated protein kinases (PRKA/AMPK) are the major transcriptional regulators activated by oscillatory shear stress and increase the expression of glycolytic enzymes [START_REF] Wu | HIF-1 is required for disturbed flow-induced metabolic reprogramming in human and porcine vascular endothelium[END_REF][START_REF] Yang | PRKAA1/AMPKα1-driven glycolysis in endothelial cells exposed to disturbed flow protects against atherosclerosis[END_REF].

Enhanced glycolysis under oscillatory shear stress may be a protective metabolic adaptation providing endothelial cells sufficient energy to counteract the disturbed flow. Interestingly, upregulation of aerobic glycolysis in endothelial cells of atheroprone arteries promotes endothelial proliferation which is essential for repair [START_REF] Doddaballapur | Laminar shear stress inhibits endothelial cell metabolism via KLF2-mediated repression of PFKFB3[END_REF]. Flowgenerated mechanical forces also affect the mitochondrial metabolic response in metastatic cancer cells [START_REF] Park | Fluid shear stress enhances proliferation of breast cancer cells via downregulation of the c-subunit of the F1Fo ATP synthase[END_REF]. Two breast cancer cell lines with different levels of aggressiveness (MDA-MB-231 and MCF-7 cells) display distinct ATP production pathways when exposed to shear stress. Although shear stress increases oxygen consumption in both cell lines, the more invasive MDA-MB-231 cells rely more on aerobic glycolysis than on OXPHOS, characterized by higher lactate production, when compared to MCF-7 cells [START_REF] Park | Fluid shear stress enhances proliferation of breast cancer cells via downregulation of the c-subunit of the F1Fo ATP synthase[END_REF].

Overall, shear stress enhances oxygen consumption and a non-monotonous fluid flow induces a switch towards a more glycolytic behavior. However, how fluid shear stress affects the mechanical properties of mitochondria remains to be understood.

Mechanical stimulation also impacts ROS production. Cyclic mechanical strain of 25 % on human umbilical vein endothelial cells significantly increases mitochondrial ROS production compared to unstretched conditions, suggesting that endothelial cells detect cyclic strain and transmit mechanical stimuli via the actin-cytoskeleton to the mitochondria, thus triggering ROS production [START_REF] Ali | Mitochondrial requirement for endothelial responses to cyclic strain: implications for mechanotransduction[END_REF]. Similarly, cyclic mechanical strain increases ROS production in pulmonary endothelial cells [START_REF] Chapman | Cyclic mechanical strain increases reactive oxygen species production in pulmonary epithelial cells[END_REF]. Strains above a threshold value of 15 % trigger an increase in ROS production. This threshold level is of the same order of magnitude as physiological strain levels experienced by lungs in vivo during breathing [START_REF] Birukov | Magnitude-dependent regulation of pulmonary endothelial cell barrier function by cyclic stretch[END_REF]. The mechanisms linking ROS production and the magnitude of stretching still have to be clarified.

Mechanotransduction regulates metabolic changes

Modulation of the physical and mechanical properties of the microenvironment and notably of the ECM induces metabolic changes through adhesion-mediated mechanosignaling [START_REF] Papalazarou | The creatine-phosphagen system is mechanoresponsive in pancreatic adenocarcinoma and fuels invasion and metastasis[END_REF][START_REF] Park | Mechanical regulation of glycolysis via cytoskeleton architecture[END_REF][START_REF] Romani | Crosstalk between mechanotransduction and metabolism[END_REF][START_REF] Tharp | Adhesion-mediated mechanosignaling forces mitohormesis[END_REF]Romani et al., 2022]. ECM stiffness sensing by integrin-and cadherin-mediated adhesions triggers intracellular signaling cascades and subsequent rearrangements of the cytoskeleton and focal adhesions. Both the expression and activity of metabolic enzymes can be affected by mechanosignaling-induced cytoskeleton remodeling. Recent findings related to the links between ECM architecture and mitochondrial functions have been reviewed in [START_REF] Yanes | The interplay between cell-extracellular matrix interaction and mitochondria dynamics in cancer[END_REF].

Using Seahorse extracellular flux analysis and different ECM hydrogels, the influence of the ECM stiffness on OXPHOS and glycolysis can be assessed in a high-throughput fashion [START_REF] Bertero | Vascular stiffness mechanoactivates YAP/TAZ-dependent glutaminolysis to drive pulmonary hypertension[END_REF][START_REF] Chakraborty | Mechanical stiffness controls dendritic cell metabolism and function[END_REF][START_REF] Romani | Mitochondrial fission links ECM mechanotransduction to metabolic redox homeostasis and metastatic chemotherapy resistance[END_REF]. While an overall increase in glycolysis and decrease in OXPHOS have been observed in stiff conditions, differences in in the basal or maximal levels of glycolysis and OXPHOS have been observed in stiff conditions [START_REF] Bertero | Vascular stiffness mechanoactivates YAP/TAZ-dependent glutaminolysis to drive pulmonary hypertension[END_REF][START_REF] Romani | Mitochondrial fission links ECM mechanotransduction to metabolic redox homeostasis and metastatic chemotherapy resistance[END_REF]. In pulmonary arterial endothelial cells and smooth muscle cells, basal glycolysis increases on a stiff matrix (Young modulus E = 50 kPa) compared to a soft matrix (E = 1 kPa), while the rates of basal oxygen consumption, ATPdependent oxygen consumption and maximal oxygen consumption decrease [START_REF] Bertero | Vascular stiffness mechanoactivates YAP/TAZ-dependent glutaminolysis to drive pulmonary hypertension[END_REF]. The results by [START_REF] Romani | Mitochondrial fission links ECM mechanotransduction to metabolic redox homeostasis and metastatic chemotherapy resistance[END_REF] report a significant increase in the maximal respiratory capacity in human mammary epithelial cells in stiff conditions. In dendritic cells, changes in substrate stiffness also induce a similar metabolic reprogramming, reflected by an upregulation of glucose uptake, glycolysis gene expression and maximal glycolytic and respiratory capacity on stiff hydrogels (E = 50 kPa) [START_REF] Chakraborty | Mechanical stiffness controls dendritic cell metabolism and function[END_REF]. Since this switch from OXPHOS to glycolysis with increased stiffness is not sufficient to sustain the growing energetic needs during proliferation, the two main anaplerotic pathways, glutaminolysis and carboxylation of pyruvate to oxaloacetate, are also concomitantly activated to replenish carbon intermediates [START_REF] Bertero | Vascular stiffness mechanoactivates YAP/TAZ-dependent glutaminolysis to drive pulmonary hypertension[END_REF]. In human mammary epithelial cells, mitochondrial oxygen consumption is impaired on a stiff ECM (E = 60 kPa) compared to a soft ECM (E = 400 Pa), due to the downregulation of some electron transport chain subunits [START_REF] Tharp | Adhesion-mediated mechanosignaling forces mitohormesis[END_REF].

Together with this reduction of mitochondrial oxygen consumption, these cells display higher levels of lactate and lower levels of metabolites involved in two cytosolic metabolic processes, namely the upstream glycolysis and pentose-phosphate pathway. Mechanistically, in all these different cell types, remodeling of the cell bioenergetics in response to increased ECM stiffness requires the mechanoactivation of downstream Hippo-signaling pathway transcriptional coactivators Yes-Associated Protein 1 (YAP) and TAZ [START_REF] Dupont | Role of YAP/TAZ in mechanotransduction[END_REF][START_REF] Bertero | Vascular stiffness mechanoactivates YAP/TAZ-dependent glutaminolysis to drive pulmonary hypertension[END_REF][START_REF] Chakraborty | Mechanical stiffness controls dendritic cell metabolism and function[END_REF][START_REF] Romani | Mitochondrial fission links ECM mechanotransduction to metabolic redox homeostasis and metastatic chemotherapy resistance[END_REF].

Understanding how cancer cells fine-tune their energy production and consumption in response to the heterogeneous mechanical properties of the microenvironment is of relevance to further identify the mechanisms regulating proliferation and migration. Indeed, during the metastatic cascade, they are subjected to changes in stiffness, from the stiff environment of primary tumors to often softer sites of secondary metastases. In MDA-MB-231 metastatic breast cancer cells, both the collagen matrix density and fiber orientation influence the intracellular ATP:ADP ratio [START_REF] Zanotelli | Regulation of ATP utilization during metastatic cell migration by collagen architecture[END_REF]. In denser collagen matrices where cell migration is impaired, the ATP:ADP ratio is higher than in less dense gels. Moreover, in aligned collagen matrices, a facilitated cell migration goes hand in hand with a decrease of the ATP:ADP ratio. These results show that impaired motility in more challenging environments induces an increase in ATP consumption and production to compensate for higher energetic needs related to cytoskeleton and focal adhesion remodeling. In mouse KPC and human PANC-1 pancreatic cancer cells, ECM stiffening induces a metabolic shift that could support both cell invasion and migration [START_REF] Papalazarou | The creatine-phosphagen system is mechanoresponsive in pancreatic adenocarcinoma and fuels invasion and metastasis[END_REF]. While a softer matrix favours aerobic glycolysis, a stiffer substrate engages sustained ATP production through the TCA-cycle and OXPHOS, which correlates with higher levels of ROS. Inhibition of the mitochondrial ATP synthase and OXPHOS by oligomycin A reduces cancer cell invasion, which points to a substantial role of mitochondrial respiration in driving cell motility [START_REF] Papalazarou | The creatine-phosphagen system is mechanoresponsive in pancreatic adenocarcinoma and fuels invasion and metastasis[END_REF].

On a soft ECM, MCF10AneoT human mammary epithelial cells treated with ROCK and myosin light chain kinase (MLCK) inhibitors and D2.OR mouse metastatic breast cancer cells both show an increase in cytoplasmic, mitochondrial and membrane lipid ROS, predominantly of mitochondrial origin [START_REF] Romani | Mitochondrial fission links ECM mechanotransduction to metabolic redox homeostasis and metastatic chemotherapy resistance[END_REF]. Increased levels of ROS upregulate the transcriptional factor nuclear factor erythroid 2-related factor (NRF2) which exerts a feedback control on ROS. Activation of DRP1 on soft ECM regulates ROS levels and subsequently enables cells to overcome oxidative stress [START_REF] Romani | Mitochondrial fission links ECM mechanotransduction to metabolic redox homeostasis and metastatic chemotherapy resistance[END_REF]. Using the recently synthesized

Peroxymycin probe [Chung et al., 2018], Tharp et al. observed an increase in intracellular ROS on stiffer substrates, which could regulate the expression of heat shock factor 1 (HSF1) target genes [START_REF] Tharp | Adhesion-mediated mechanosignaling forces mitohormesis[END_REF]. They suggested that HSF1 in turn represses ROS-induced oxidative stress by limiting oxygen consumption. Alternatively, there is evidence that the YAP/TAZ pathway is involved in the regulation of the HSF1 target genes [START_REF] Luo | Heat stress activates YAP/TAZ to induce the heat shock transcriptome[END_REF]. However, the increase in ROS on stiff substrates observed in [START_REF] Tharp | Adhesion-mediated mechanosignaling forces mitohormesis[END_REF] using Peroxymycin is conflicting with the results from the same study using the more common probe DCFDA and with other studies using DCFDA, MitoSOX and Cystine-FITC [START_REF] Romani | Mitochondrial fission links ECM mechanotransduction to metabolic redox homeostasis and metastatic chemotherapy resistance[END_REF] or

CellRoxOrange [START_REF] Yang | Materials stiffness-dependent redox metabolic reprogramming of mesenchymal stem cells for secretome-based therapeutic angiogenesis[END_REF]. These results suggest that a stiff ECM induces a decrease, rather than an increase, in ROS production. Future studies should help clarify this issue.

Metabolic activity controls mitochondrial mechanics

Although crucial for our understanding of the mechano-metabolic feedback control of mitochondria, very little is known about the mechanical adaptation of mitochondria in response to metabolic cues. A theoretical approach has shown that mechanical parameters of the inner mitochondrial membrane, such as its surface tension, bending rigidity and elastic modulus of Gaussian curvature, are affected by metabolic-driven changes of the proton-motive force, such as proton leakage and mitochondrial membrane potential [Chvanov, 2006]. How different metabolic cues alter the electrochemical fluxes and thus the mechanical properties of mitochondria still remain to be explored.

In a recent optomechanical study, the mechanical properties of mitochondria isolated from rat glial cells were measured using real-time fluorescence and deformability cytometry [START_REF] Komaragiri | Mechanical characterization of isolated mitochondria under conditions of oxidative stress[END_REF]. Results show that mitochondrial mechanics correlates with intracellular superoxide levels. Exposing cells to H2O2 reduces the size of mitochondria and significantly increases their deformation in the microfluidic channel. Mitochondrial stiffness is reduced with increasing H2O2 concentrations. This elegant study provides a first step towards elucidating how mitochondrial mechanics depends on metabolic cues. Tharp et al., 2021, [6] [START_REF] Bartolák-Suki | Fluctuation-driven mechanotransduction regulates mitochondrial-network structure and function[END_REF], [7] Kim et al., 2014, [8] Doddaballapur et al., 2015, [9] Feng et al., 2017, [10] Wu et al., 2017, [11] Yang et al., 2018, [12] Venturini et al., 2019, [13] Coon et al., 2022, [14] Park et al., 2022.

Discussion and perspectives

Bidirectional links exist between mitochondrial

morphodynamics, mechanics and metabolism

In the past decade, there has been a rising interest in organellar mechanosensing and mechanotransduction. The role of mitochondria in the cross-talk between mechanotransduction and cell metabolism has just begun to receive some attention. It is becoming clear that mitochondria can be described as dynamic systems which constantly adjust their response to mechanical and chemical cues. Recent studies have cast light on one or several aspects of the tripartite interactions between mitochondrial morphodynamics, mechanics and metabolism.

Grasping such complex correlations not only allows to understand the physiological contribution of mitochondria as key organelles but is also relevant in pathological conditions.

Despite the intercellular and intracellular heterogeneity of mitochondrial morphodynamics, which goes hand in hand with the physiological functions of cells and tissues, it is possible to identify similar effects induced by mechanical and physico-chemical stimuli.

When cells are exposed to stress, whether in the form of intracellular variations in metabolite fluxes or in the form of forces exerted by the environment, mitochondria change their morphology, their dynamics and their organization. These changes at the level of the mitochondria have important implications for their functions and for cell metabolism.

Mechanistically however, it is not yet clear how different internal or external stimuli can trigger similar morphological and metabolic changes.

Going beyond correlation between mitochondrial morphodynamics, mechanics and metabolism

Given the numerous pathways which contribute to mitochondrial morphodynamics and which may be interconnected and redundant, it is challenging to interpret the reciprocal effects of mechanics and metabolism and to go beyond simple correlation. Determining whether alterations in mitochondrial shapes and dynamics are a cause or a consequence of an impairment of their mechanical properties and/or metabolic functions, requires to precisely identify and monitor sequential mechanosensitive signaling pathways. A systematic exploration of the direct bidirectional links between mitochondrial morphodynamics, mechanics and metabolism is still lacking. For instance, whether mitochondrial morphological changes impact their mechanical or mechanosensing properties is not demonstrated yet, even if disrupting mitochondrial morphodynamics is known to have dramatic effects on cell metabolism which could in turn regulate mitochondrial mechanics.

Another limitation of the studies performed so far is the variability of the results depending on the cell type or the technique. A large spectrum of cell types (e.g. endothelial cells, muscle cells, endocrine cells, cells from connective tissues) has been investigated

separately. It would be interesting to compare the response of mitochondria to a given mechanical or metabolic cue in different cell types with the same technique. In addition to the nature and the magnitude of the environmental stress, the metabolic and mechanical phenotypes of the cell have to be taken into account. The relative contributions of OXPHOS and cytosolic glycolysis and the mechanical properties of the cell, such as its visco-elasticity, may modulate the response of the cell to both mechanical and physico-chemical cues.

Studying mechanotransduction and metabolism at mitochondria is technically challenging

Mitochondria are extremely dynamic organelles in both physiological and pathological conditions. They undergo fission and fusion in response to mechanical and metabolic cues.

Studying the mechanobiology of mitochondria is technically challenging as it requires intracellular micro-manipulation hence to develop new techniques or to adapt existing methods [START_REF] Fuller | Advances in the analysis of single mitochondria[END_REF].

One key issue is whether mitochondria should be studied individually and/or collectively to fully characterize their mechanobiology. In cells, the three cytoskeletal networks not only support the reorganization of mitochondrial networks and the directional transport of mitochondria within the cell, but can also transmit internal and external forces to these organelles [START_REF] Bartolák-Suki | Regulation of mitochondrial structure and dynamics by the cytoskeleton and mechanical factors[END_REF][START_REF] Phuyal | Mechanobiology of organelles: illuminating their roles in mechanosensing and mechanotransduction[END_REF]. Therefore, since they are tethered to cytoskeletal components, mitochondria are constantly under tension in cells [START_REF] Feng | A toolbox for organelle mechanobiology research-current needs and challenges[END_REF]. In contrast, mitochondria are rounder when isolated in vitro [START_REF] Gonzalez-Rodriguez | Elastocapillary instability in mitochondrial fission[END_REF]. In cells, they also form interconnected networks and contact other organelles such as the ER [START_REF] Rizzuto | Close contacts with the endoplasmic reticulum as determinants of mitochondrial Ca2+ responses[END_REF][START_REF] Rowland | Endoplasmic reticulum-mitochondria contacts: function of the junction[END_REF][START_REF] Csordás | Endoplasmic reticulum-mitochondrial contactology: structure and signaling functions[END_REF]. Studying isolated mitochondria can thus provide clues for understanding their mechanobiology, as mechanical parameters such as the viscosity of the mitochondrial matrix impacts on the organization of the mitochondrial network [START_REF] Yang | A self-calibrating bipartite viscosity sensor for mitochondria[END_REF] and correlates with higher H2O2 levels in multiple cell types from various organisms [START_REF] Fan | A mitochondria-specific orange/near-infrared-emissive fluorescent probe for dual-imaging of viscosity and H2O2 in inflammation and tumor models[END_REF][START_REF] Li | A mitochondria-targeted two-photon fluorogenic probe for the dual-imaging of viscosity and H2O2 levels in Parkinson's disease models[END_REF]. However, it is certainly not sufficient to fully characterize their properties in a cellular environment. Besides the traditional differential centrifugation methods to isolate mitochondria [START_REF] Bustamante | A highyield preparative method for isolation of rat liver mitochondria[END_REF][START_REF] Wieckowski | Isolation of mitochondria-associated membranes and mitochondria from animal tissues and cells[END_REF][START_REF] Djafarzadeh | Isolation of intact mitochondria from skeletal muscle by differential centrifugation for high-resolution respirometry measurements[END_REF], microfluidics allows efficient and damage-free isolation of mitochondria. A recent study introduced a curved 3D-microfluidic device which exploits the balance between the inertial lift force and the Dean drag force in a size-dependent fashion to separate mitochondria from cellular debris [START_REF] Lee | A three-dimensional printed inertial microfluidic platform for isolation of minute quantities of vital mitochondria[END_REF].

Whether isolated in vitro or in live cells, studying the molecular mechanisms that govern the responses of mitochondria to mechanical and metabolic signals remains a technical challenge. The development of non-invasive and possibly high-throughput intracellular mechano-stimulators and probes is required to address this question in live cells. Microfluidics has been used to examine the mechano-response of mitochondria to large and global stresses.

For instance, microchannels with constrictions that are less than 1 µm wide, which is the typical diameter of an ovoidal mitochondrion, were designed to study the mitochondrial response to cell squeezing [START_REF] Feng | A toolbox for organelle mechanobiology research-current needs and challenges[END_REF]. Real-time fluorescence and deformability cytometry is another high-throughput microfluidic technique that allows to measure mitochondrial size, deformation and Young's modulus using a hydrodynamic flow field [START_REF] Komaragiri | Mechanical characterization of isolated mitochondria under conditions of oxidative stress[END_REF].

Mechano-stimulation can also be performed in a highly targeted manner by exerting local forces on mitochondria with magnetic, optical or acoustic tweezers, although with a lower throughput than microfluidics [START_REF] Norregaard | Manipulation and motion of organelles and single molecules in living cells[END_REF].

As emphasized in section 3, membrane tension seems to be a key mechanical property underpinning mitochondrial morphodynamics. Probing mitochondria is difficult because of their inner membrane and negative membrane potential. They are impermeable to most molecules targeting intracellular compartments [START_REF] Ma | Mitochondrial targeting of probes and therapeutics to the power-house of the cell[END_REF]. Molecules with lipophilic and cationic moieties are thus commonly used to target the mitochondria. Flipper probes can indirectly report membrane tension or lipid order through their fluorescence lifetime [Colom et al., 2018;[START_REF] Goujon | Mechanosensitive fluorescent probes to image membrane tension in mitochondria, endoplasmic reticulum, and lysosomes[END_REF][START_REF] Roffay | Technical insights into fluorescence lifetime microscopy of mechanosensitive flipper probes[END_REF]. These fluorogenic mechanophores spontaneously insert between lipid hydrophobic tails. They measure changes in lipid bilayer organization through their conformational changes and the associated variations in their fluorescence properties. Flipper probes that selectively label mitochondria have been designed [START_REF] Colom | A fluorescent membrane tension probe[END_REF][START_REF] Goujon | Mechanosensitive fluorescent probes to image membrane tension in mitochondria, endoplasmic reticulum, and lysosomes[END_REF] and have already been shown to be extremely pertinent tools to report mitochondrial mechanics in live cells [START_REF] Mahecic | Mitochondrial membrane tension governs fission[END_REF].

Deciphering the cross-talk between mechanics and metabolism requires the combination of mechanical and metabolic measurements. Techniques for bulk metabolic analysis performed on a large number of cells [START_REF] Teslaa | Techniques to monitor glycolysis[END_REF] should be made compatible with high-throughput mechanical measurements. To compare glucose uptake and lactate production for glycolytic flux quantification, chromatography combined with mass spectrometry is widely used, allowing labeled glucose-derived carbon tracing in glycolytic intermediates [START_REF] Luo | Simultaneous determination of multiple intracellular metabolites in glycolysis, pentose phosphate pathway and tricarboxylic acid cycle by liquid chromatography-mass spectrometry[END_REF]. To evaluate OXPHOS through oxygen consumption rate, Clark-type micro-oxygen electrodes are commonly used [START_REF] Li | Measurement of mitochondrial oxygen consumption using a clark electrode[END_REF]. However, these techniques do not allow the simultaneous measurement of glycolysis and OXPHOS in cells. Alternatively, it is possible to measure both the oxygen consumption rate and the extracellular acidification rate using Seahorse flux analyzer [START_REF] Little | High-content fluorescence imaging with the metabolic flux assay reveals insights into mitochondrial properties and functions[END_REF][START_REF] Gu | Measurement of mitochondrial respiration in adherent cells by Seahorse XF96 Cell Mito Stress Test[END_REF].

This technique provides data on the energetic demand of cells under basal conditions, the maximal capacity of the electron respiratory chain, the glycolytic capacity of cells and their ability to adapt to changes in energy demand. Combining such techniques with mechanical measurements and/or mechanical stimuli as in previous studies on the role of substrate stiffness [START_REF] Bertero | Vascular stiffness mechanoactivates YAP/TAZ-dependent glutaminolysis to drive pulmonary hypertension[END_REF][START_REF] Chakraborty | Mechanical stiffness controls dendritic cell metabolism and function[END_REF][START_REF] Romani | Mitochondrial fission links ECM mechanotransduction to metabolic redox homeostasis and metastatic chemotherapy resistance[END_REF] should be instrumental for a better understanding of the links between cell mechanics and cell metabolism at the mitochondrial level.

Is the mechano-morpho-metabolic signature of mitochondria a potential diagnostic tool in pathologies?

Mutations in mitochondrial DNA or in nuclear genes encoding mitochondrial proteins can cause so-called primary mitochondrial diseases. Such genetic alterations notably impair the electron transport chain machinery and subsequently OXPHOS [Wallace, 2010, Niyazov et al., 2016]. In contrast to these primary mitochondrial diseases, secondary mitochondrial dysfunctions rather stem from multifactorial disorders, such as diabetes, neurodegenerative disorders or cancers [START_REF] Pich | The Charcot-Marie-Tooth type 2A gene product, Mfn2, upregulates fuel oxidation through expression of OXPHOS system[END_REF][START_REF] Loiseau | Mitochondrial coupling defect in Charcot-Marie-Tooth type 2A disease[END_REF][START_REF] Camara | Potential therapeutic benefits of strategies directed to mitochondria[END_REF]Zambrano et al., 2022]. The importance of investigating the mechanometabolic signature of mitochondria in pathologies is twofold. First, although many diseases do not necessarily stem from a mitochondrial dysfunction, the latter may contribute to their progression. Second, disruption of mitochondrial function was shown to contribute to the etiology of distinct pathologies through common pathways, such as mitochondrial fission and fusion dynamics [START_REF] Murphy | Mitochondria as a therapeutic target for common pathologies[END_REF]. Given the reciprocal regulation between cell metabolism and mitochondrial mechanics, targeting the latter aspect in therapeutic approaches can possibly improve the outcome of multiple diseases.

Characterizing the morphological and mechanical properties of mitochondria, in addition to their metabolic functions, emerges as a tool for cancer detection, prognosis and possibly therapy. One striking historical example suggesting a causative relationship between metabolic disruption and tumorigenesis is the in vitro induction of malignancy in rat heart fibroblasts subjected to intermittent anaerobiosis [START_REF] Goldblatt | Induced malignancy in cells from rat myocardium subjected to intermittent anaerobiosis during long propagation in vitro[END_REF]. The focus on mitochondria in cancer was initiated by Warburg's discovery that most cancer cells undergo aerobic glycolysis as their main ATP production pathway, while decreasing their dependence on mitochondrial OXPHOS [Warburg, 1956;[START_REF] Gatenby | Why do cancers have high aerobic glycolysis?[END_REF]. Biochemical processes within mitochondria of cancer cells were later shown to be critical for both tumorigenesis and metastasis [START_REF] Vyas | Mitochondria and cancer[END_REF][START_REF] Zong | Mitochondria and cancer[END_REF][START_REF] Scheid | Roles of mitochondria in the hallmarks of metastasis[END_REF]. How cancer cells adapt their bioenergetics in response to fluctuating metabolic needs during migration and invasion, processes which combine protrusive and contractile forces through e.g. actin dynamics and actomyosin contractility, is well reviewed in [START_REF] Zanotelli | Mechanoresponsive metabolism in cancer cell migration and metastasis[END_REF]. Along this line, Garde et al. reported very recently that ATP bursts are produced by enhanced mitochondria recruitment at the front of anchor cells crossing the uterine and vulval basal membranes to sustain a local increase in glucose import, showing that energy import, processing and generation are interlinked with the invasive machinery [START_REF] Garde | Localized glucose import, glycolytic processing, and mitochondria generate a focused ATP burst to power basement-membrane invasion[END_REF].

There is also mounting evidence that cancer is coupled with an alteration of mitochondrial dynamics. In particular, an imbalance of mitochondrial fission and fusion dynamics, yielding a fragmented mitochondrial network, is often observed in cancer cells [START_REF] Senft | Regulators of mitochondrial dynamics in cancer[END_REF].

In lung cancer, fragmentation of mitochondria is triggered by high expression or enhanced activation of DRP1 and/or downregulation of MFN2 [START_REF] Rehman | Inhibition of mitochondrial fission prevents cell cycle progression in lung cancer[END_REF]. Hypoxia promotes the migratory activity of glioblastoma U251 cells through upregulation of DRP1 [START_REF] Wan | Involvement of Drp1 in hypoxia-induced migration of human glioblastoma U251 cells[END_REF]. Similarly, in breast cancer cells, increased mitochondrial fission through an upregulation of DRP1 may be correlated to cell motility and invasion by promoting lamellipodia formation at the leading edge of the cell [START_REF] Zhao | Mitochondrial dynamics regulates migration and invasion of breast cancer cells[END_REF]. Conversely, downregulation of DRP1 results in mitochondria elongation and enhanced apoptosis in HCT116 and SW480 human colon cancer cells [START_REF] Inoue-Yamauchi | Depletion of mitochondrial fission factor DRP1 causes increased apoptosis in human colon cancer cells[END_REF]. Besides the metabolic and morphodynamic changes occurring during tumorigenesis and metastasis, cancer cells are subjected to a myriad of well identified mechanical cues from their microenvironment, including solid stresses, interstitial fluid pressure, tissue material properties and shear stress in the vasculature [Nia et al., 2020;[START_REF] Colin | Biomechanics: a driving force behind metastatic progression[END_REF]. However, how the physical interactions between cancer cells and their environment tune the morphodynamics, metabolic functions and mechanics of mitochondria remains to be elucidated.

These observations raise many questions. Is mitochondrial fission necessary for migration in all cancer cells? Can increased mitochondrial fragmentation be considered as a diagnostic biomarker for metastasis? Because mitochondrial morphodynamics depends on the mechanical properties of mitochondria, is it possible to identify a common mechanophenotype for mitochondria from cancer cells of the same grade or similar aggressiveness? Technical and conceptual advances are clearly required to convert mitochondrial mechanobiology into an efficient diagnostic and prognostic method. Associating different techniques at multiple scales to probe the morphological, metabolic and mechanical properties of mitochondria should provide clues for a better understanding of tumor progression and other pathologies.

Figure 1 :

 1 Figure 1: Schematic representation of the internal structure of a mitochondrion and the two main ATP synthesis processes in a eukaryotic cell: oxidative phosphorylation (OXPHOS) and cytosolic glycolysis. OXPHOS relies on the citric acid cycle or Krebs cycle, which is a set of redox reactions of substrates derived from glucose (through cytosolic glycolysis), fatty acid or amino acid oxidation.

Figure 2 :

 2 Figure 2: Established (solid arrows) or potential (dashed arrows) bidirectional links between metabolism, mitochondrial morphodynamics, mechanics and mechanical cues. The influence of metabolism on mechanics is supported by few data, while the impact of changes in mitochondrial morphodynamics on their mechanics is not yet highlighted in the literature.

Figure 3 :

 3 Figure 3: Links between mitochondria morphodynamics and metabolism. (A) Mitochondria exhibit a wide variety of shapes depending on the balance between fission and fusion rates. (B)

Figure 4 :

 4 Figure 4: Mitochondrial responses to metabolic cues, depending on the nature, the intensity and the duration of the metabolic signal. Metabolic cues either induce protective mechanisms in mitochondrial dynamics to support cellular homeostasis or impairs cellular signaling and triggers apoptosis.

  the fluorescence lifetime of the mechanosensitive MitoFlipper probe as an indirect sensor of the mitochondrial membrane tension in COS-7 cells. In COS-7 cells, constriction sites enriched in DRP1 and/or overlapping with ER tubules do not always lead to fission. Moreover, these reversible constriction events ('reversals') do not result from differences in the recruitment of DRP1, Dyn2 and the colocalization between ER tubules and DRP1-enriched constriction sites.By comparing the occurrence of fission events with MitoFlipper fluorescence lifetimes and analytical membrane tension values, Mahecic et al. show that a higher membrane tension coincides with a greater probability of fission events. Mitochondrial constrictions under higher membrane tension (typically 6 µN/m) are more likely to undergo fission than constrictions under low tension (typically 4 µN/m). This study also suggests that fluctuations in membrane tension could play a critical role in mitochondrial fission by stochastically increasing the local membrane elastic energy and lowering the energy barrier for fission. The mechanisms underlying changes in mitochondrial membrane tension are however not clear (Figure5). The observed reduction in mitochondrial membrane tension and fission upon inhibition of nonmuscle myosin II using ML-7 or Blebbistatin, or depolymerization of microtubules using

Figure 5 :

 5 Figure 5: Schematic representation of the actin-dependent and DRP1-dependent mitochondrial fission process and the variety of fission-inducing stimuli contributing to the increase in mitochondrial membrane tension. A hypothetical membrane tension gradient is represented in the boxed region of the constriction site, with the maximum value localized at the level of the DRP1 helical structure. The recruitment of DRP1 at a pre-constricted fission site, the association with the endoplasmic reticulum (ER) and the coordinated activity of actin filaments

Figure 6 :

 6 Figure 6: Mitochondrial metabolic adaptation to mechanical cues. The contribution of OXPHOS and glycolysis in ATP production is regulated by the nature and the magnitude of mechanical forces exerted on the cell. References indicated on the figure are : [1] Bertero et al., 2016, [2] Chakraborty et al., 2021, [3] Romani et al., 2022, [4]Papalazarou et al., 2020, [5]

Figure 1

 1 Figure 1 Schematic representation of the internal structure of a mitochondrion and the two main ATP synthesis processes in a eukaryotic cell: oxidative phosphorylation (OXPHOS) and cytosolic glycolysis. OXPHOS relies on the citric acid cycle or Krebs cycle, which is a set of redox reactions of substrates derived from glucose (through cytosolic glycolysis), fatty acid or amino acid oxidation.

Figure 2

 2 Figure2Established (solid arrows) or potential (dashed arrows) bidirectional links between metabolism, mitochondrial morphodynamics, mechanics and mechanical cues. The influence of metabolism on mechanics is supported by few data, while the impact of changes in mitochondrial morphodynamics on their mechanics is not yet highlighted in the literature.

Figure 3

 3 Figure 3 Links between mitochondria morphodynamics and metabolism. (A) Mitochondria exhibit a wide variety of shapes depending on the balance between fission and fusion rates.(B) Mitochondria display not only a substantial heterogeneity across tissues in terms of density and shapes, but also an intra-tissue heterogeneity, reflecting the coupling between their structure and their function.

Figure 4

 4 Figure 4 Mitochondrial responses to metabolic cues, depending on the nature, the intensity and the duration of the metabolic signal. Metabolic cues either induce protective mechanisms in mitochondrial dynamics to support cellular homeostasis or impairs cellular signaling and triggers apoptosis.

Figure 5

 5 Figure 5 Schematic representation of the actin-dependent and DRP1-dependent mitochondrial fission process and the variety of fission-inducing stimuli contributing to the increase in mitochondrial membrane tension. A hypothetical membrane tension gradient is represented in

Figure 6

 6 Figure 6 Mitochondrial metabolic adaptation to mechanical cues. The contribution of OXPHOS and glycolysis in ATP production is regulated by the nature and the magnitude of mechanical forces exerted on the cell. References indicated on the figure are : [1] Bertero et al., 2016, [2] Chakraborty et al., 2021, [3] Romani et al., 2022, [4] Papalazarou et al., 2020, [5]Tharp et al., 2021, [6] Bartolák-Suki et al., 2015, [7] Kim et al., 2014, [8] [START_REF] Doddaballapur | Laminar shear stress inhibits endothelial cell metabolism via KLF2-mediated repression of PFKFB3[END_REF], [9] Feng et al., 2017, [10] Wu et al., 2017, [11] Yang et al., 2018, [12] [START_REF] Venturini | Integrated proteomics and metabolomics analysis reveals differential lipid metabolism in human umbilical vein endothelial cells under high and low shear stress[END_REF], [13] Coon et al., 2022, [14] [START_REF] Park | Fluid shear stress enhances proliferation of breast cancer cells via downregulation of the c-subunit of the F1Fo ATP synthase[END_REF]

Acknowledgments E.S. acknowledges the support provided by the French Ministry of Higher Education, Research and Innovation ('Physique en Île-de-France' PhD grant). Work in the MSC laboratory was supported by the Labex 'Who am I?' (IDEX) through the 'BioMechanOE' transverse project.

We thank the reviewers for their constructive comments on the manuscript.

Conflict of interest statement

The authors have declared no conflict of interest.