Nourdine Chakouri

Cyril Reboul

Doria Boulghobra

Adrien Kleindienst

Stéphane Nottin

Sandrine Gayrard

François Roubille

Stefan Matecki

Alain Lacampagne

PhD Olivier Cazorla
email: olivier.cazorla@inserm.fr

Stress-induced protein S-glutathionylation and phosphorylation crosstalk in cardiac sarcomeric proteins -Impact on heart function

Keywords: myofilament, diastolic dysfunction, exercise, Oxidative stress, beta-adrenergic

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

Introduction

Oxidative stress is common in many cardiac disorders including ischemia/reperfusion, diabetes, and hypertensive heart disease. Oxidative stress leads to impaired cardiac pump function due to changes in the expression or function of proteins that regulate the excitation contraction coupling. There is growing evidence that the cardiodepressant actions of reactive oxygen species (ROS) are not only mediated by myocardial injuries but also are attributable to subtler redox-dependent post-translational modifications of excitation contraction coupling proteins [1]. Each cardiac contraction is triggered by the release of calcium (Ca 2+ ) from the sarcoplasmic reticulum that binds on the troponin-tropomyosin regulatory complex, which activates subsequently the interaction between thick and thin filaments. Oxidative modifications of proteins involved in Ca 2+ handling during excitation contraction coupling are largely described and include inhibitory SERCA2a redox modification [2] and oxidation as well as ROSdependent hyperphosphorylation of the Ryanodine receptor [3]. Although the contractile machinery has been less studied, the sarcomere itself is also the target of oxidative modifications that further contribute to contractile dysfunctions in cardiac disease [4]. In the healthy heart, the role of such modifications to accommodate the difference in hemodynamic loads during rest and cardiac stress remains to be clarified and was the focus of the present study.

The contractile machinery is highly regulated by post-translational modifications of regulatory contractile proteins, such as Myosin Light Chain 2 (MLC2), Troponin I (TnI) and cardiac Myosin Binding Protein-C (cMyBP-C). These sarcomeric proteins are phosphorylated by ROS-sensitive enzymes [5] and can be directly impacted by ROS production [START_REF] Johnston | Ca(2+) signaling in the myocardium by (redox) regulation of PKA/CaMKII[END_REF]. Among redox-sensitive sarcomeric proteins, cMyBP-C is under the scope. Indeed, cMyBP-C is an important regulator of cardiac dynamics, a potential activator of the thin filaments that interacts with myosin [START_REF] Harris | Binding of myosin binding protein-C to myosin subfragment S2 affects contractility independent of a tether mechanism[END_REF] and titin [START_REF] Sadayappan | Cardiac myosin binding protein-C: redefining its structure and function[END_REF] and contributes to the heart β-adrenergic response [START_REF] Gresham | The contributions of cardiac myosin binding protein C and troponin I phosphorylation to beta-adrenergic enhancement of in vivo cardiac function[END_REF][START_REF] Cazorla | Length and protein kinase A modulations of myocytes in cardiac myosin binding protein C-deficient mice[END_REF]. cMyBP-C phosphorylation at Ser273, Ser282, and Ser302 is generally attributed to protein kinase A (PKA) and viewed as a mechanism that modulates the kinetic of thick-thin filament interactions and increases force generation [START_REF] Barefield | Phosphorylation and function of cardiac myosin binding protein-C in health and disease[END_REF]. In the last decade, cMyBP-C was shown to be a preferential target of S-glutathionylation, a reversible post-translational modification between glutathione (GSH) and redox-sensitive cysteines of proteins activated during oxidative stress (see [START_REF] Xiong | S-glutathionylation: from molecular mechanisms to health outcomes[END_REF] for review). S-glutathionylation of cMyBP-C was identified first in a proteomic screen of cardiomyocytes stimulated in vitro with oxidized GSH or diamide a thiol selective oxidant [START_REF] Brennan | The utility of N,Nbiotinyl glutathione disulfide in the study of protein S-glutathiolation[END_REF]. The functional consequences of cMyBP-C S-glutathionylation were demonstrated later in the deoxycorticosterone acetate-salt hypertensive mouse model [START_REF] Lovelock | Ranolazine improves cardiac diastolic dysfunction through modulation of myofilament calcium sensitivity[END_REF]. The level of cMyBP-C Sglutathionylation was correlated with diastolic dysfunction without apparent change in cellular Ca 2+ fluxes [START_REF] Lovelock | Ranolazine improves cardiac diastolic dysfunction through modulation of myofilament calcium sensitivity[END_REF]. The ROS associated with the disease induced S-glutathionylation of cMyBP-C, which slowed cross-bridge kinetics and increased Ca 2+ sensitivity. Several cysteines of cMyBP-C can be Sglutathionylated in vitro and lead to an increase in myofilament Ca 2+-sensitivity [START_REF] Patel | Novel control of cardiac myofilament response to calcium by S-glutathionylation at specific sites of myosin binding protein C[END_REF][START_REF] Stathopoulou | Sglutathiolation impairs phosphoregulation and function of cardiac myosin-binding protein C in human heart failure[END_REF]. Previous experiments have found that every cardiac myofilament protein, except TnT and MLC2 has a cysteine that can be modified by oxidants [START_REF] Brennan | Detection and mapping of widespread intermolecular protein disulfide formation during cardiac oxidative stress using proteomics with diagonal electrophoresis[END_REF][START_REF] Gross | Accessibility of myofilament cysteines and effects on ATPase depend on the activation state during exposure to oxidants[END_REF]. Among them all proteins are not S-glutathionylated. A highmolecular-weight protein, which could be titin has been identified as a likely target of Sglutathionylation following myocardial infarction [START_REF] Avner | Myocardial infarction in mice alters sarcomeric function via post-translational protein modification[END_REF]. Later a study showed clearly in vitro that titin can be S-glutathionylated [START_REF] Kosuri | Sglutathionylation of cryptic cysteines enhances titin elasticity by blocking protein folding[END_REF]. Interestingly, an interaction between phosphorylation and Sglutathionylation of cMyBP-C was explicitly demonstrated in vitro [START_REF] Stathopoulou | Sglutathiolation impairs phosphoregulation and function of cardiac myosin-binding protein C in human heart failure[END_REF]. Reduced site-specific cMyBP-C phosphorylation is accompanied by increased protein S-glutathionylation in ventricular tissue from patients with heart failure. The link between pathways and the functional consequences remains unclear in particular in vivo.

Therefore, the aim of the present study was to focus on the cardiac functional consequences of myofilament protein post-translational modifications induced by ROS or ROS-activated signaling enzymes. We particularly investigated cMyBP-C and cTnI. The β-adrenergic signaling and oxidative stress pathways were differentially activated by modulating in intensity and duration the physiological stress induced by exercise. We observed that depending on the stress duration, the cardiomyocyte contractile machinery is targeted by different post-translational modifications that differentially affect the cardiomyocyte contractile function in vivo.

Materials and Methods

Animal studies. Male Wistar rats (12-week-old, n=78; weight=361±4 g; Janvier, France) were housed with a 12-hour light-dark cycle and free access to water and food. All investigations conformed to the European Parliament Directive 2010/63/EU and were approved by the local ethics committee (Comité d'éthique pour l'expérimentation animale Languedoc-Roussillon, n° CEEA-00322.03). All rats were familiarized with the treadmill by running at 15 m/min for 15min daily for a week. Afterwards, to achieve different degrees of activation of the pathways investigated, some rats performed a bout of exercise at 20m/min (about 65% of the maximal aerobic velocity, MAV) for 35min (Low stress induced by exercise, LSE group) or until exhaustion for about 3 hours (186.7±14.6 min) to induce a high stressinduced by exercise (HSE) [START_REF] Vitiello | beta-Adrenergic receptors desensitization is not involved in exercise-induced cardiac fatigue: NADPH oxidaseinduced oxidative stress as a new trigger[END_REF]. LSE and HSE animals were compared with non-runners (control group).

Animals were regularly given access to water during the exercise protocol to avoid dehydration and hypovolemia. Other rats (n=12) were treated with 50mg/kg N-acetyl cystein (NAC) by i.p. injection 48 hours and 1 hour before HSE (HSE+NAC group). To study the modifications persisting after exercise, all experiments were performed after a recovery of 30min.

In vivo cardiac function analysis. Rats were anesthetized with ketamine and xylazine (75mg/kg and 15mg/kg respectively, i.p.) for echocardiography (MyLab 30 ESAOTE), as previously described [START_REF] Mou | Late exercise training improves non-uniformity of transmural myocardial function in rats with ischaemic heart failure[END_REF]. Isolated perfused hearts. Isolated hearts were retrogradely perfused and LV function evaluated all along the procedure, as described [START_REF] Farah | Exercise-induced cardioprotection: a role for eNOS uncoupling and NO metabolites[END_REF], in presence or not of 80µmol/L 1,3-bis-2chloroethyl-1-nitrourea (BCNU), a glutathione reductase inhibitor, for 5min [START_REF] Sadayappan | Cardiac myosin binding protein-C: redefining its structure and function[END_REF], or with 0.1µM ISO for 5min (n=4).

Force measurements in permeabilized cardiomyocytes. Isometric force was measured in single cardiomyocytes permeabilized with 0.3% Triton X-100 for 5min. [START_REF] Mou | Late exercise training improves non-uniformity of transmural myocardial function in rats with ischaemic heart failure[END_REF] The relationship between Ca 2+activated force and internal Ca 2+ concentration was measured at a SL of 2.3µm and fitted using a modified Hill equation. To mimic β-adrenergic stimulation, some permeabilized cardiomyocytes were incubated before attachment with recombinant PKA catalytic subunit (Sigma Aldrich, France) at room temperature for 50min, as described [START_REF] Cazorla | Length and protein kinase A modulations of myocytes in cardiac myosin binding protein C-deficient mice[END_REF].

Western blot analysis. Myocardial protein expression was studied, as previously described [5]. Briefly, frozen LV tissue was solubilized in non-reducing Laemmli buffer. Proteins were separated using SDS-PAGE electrophoresis and transferred onto nitrocellulose membranes (GE Healthcare). Membranes were blocked with the Odyssey Blocking Buffer in PBS (LI-COR Biosciences) and incubated overnight with primary antibodies (Supplemental TableS1). Bands were revealed and quantified with the Odyssey system (LI-COR Biosciences, Lincoln, Nebraska) after incubation with fluorescent secondary antibodies. Protein content was expressed relative to GAPDH or calsequestrin (CSQ) content.

Determination of glutathione levels and cMyBP-C S-glutathionylation. Levels of oxidized (GSSG)

and reduced glutathione (GSH) in LV were measured using a Glutathione (GSSG/GSH) Detection Kit (ADI-900-160, EnzoLife Sciences, NY, USA), according to the manufacturer's instructions.

Non-reducing SDS-PAGE was used to determine cMyBP-C S-glutathionylation, following a previously described protocol. [START_REF] Patel | Novel control of cardiac myofilament response to calcium by S-glutathionylation at specific sites of myosin binding protein C[END_REF] Malondialdehyde assay. As a marker of myocardial lipid peroxidation, Malondialdehyde (MDA) level was measured in cardiac tissue using the Lipid Peroxidation-MDA Assay Kit (ab118970, Abcam, Cambridge, Mass, United States), according to the manufacturer's instructions.

Determination of protein kinase A activity. PKA activity was determined by a non-radioactive protein kinase assay kit (PKA Kinase Activity Assay Kit, no. ab139435, Abcam, Cambridge, Mass, United States) according to the manufacturer's instructions. Statistical analysis. Statistics were performed using StatView 5.0 (SAS Institute, Cary, NC). Data are presented as the mean±SEM. Differences were assessed with the one-way ANOVA when appropriate. When significant interactions were found, a Bonferroni post hoc test was applied with p< 0.05.

Results

S-glutathionylation affects post-translational modifications of contractile proteins and cardiac function in rats

Isolated control hearts were perfused with or without an inhibitor of glutathione reductase activity (BCNU). Glutathione reductase inhibition decreases the cellular reduced/oxidized glutathione ratio (GSH/GSSG), leading to protein S-glutathionylation [START_REF] Chen | Sglutathionylation uncouples eNOS and regulates its cellular and vascular function[END_REF]. Perfusion of isolated hearts with BCNU reduced markedly the level of free GSH as well as the GSH/GSSG ratio (Fig. S1) without impacting MDA (Fig S1B ), used as a marker of lipid peroxidation. In line with altered GSH/GSSG ratio, BCNU increased the level of S-glutathionylated cMyBP-C (Fig. 1A). Regarding regulatory proteins of sarcomeric function, S-glutathionylation was specific to cMyBP-C and did not affect the other regulatory protein cTnI (Fig. 1B). Interestingly, the phosphorylation levels of cMyBP-C and TnI at PKA sites were decreased in particular for cMyBP-C (Fig. 1C and1D). This was not due to a reduction of PKA activity with BCNU treatment since the level of PKA activity was not altered (Fig. 1E). Those post-translational modifications of cMyBP-C and TnI were associated with changes in the contractile machinery properties investigated in permeabilized cardiomyocytes. The relationship between the Ca 2+activated tension and the amount of Ca 2+ (pCa=-log[Ca 2+ ]) was altered in BCNU-treated myocytes compared with control cells (Fig. 1F). The maximal active tension was decreased by BCNU (Fig. 1F and 1H). The Ca 2+ sensitivity of myofilaments, assessed as the pCa that develops half of the maximal tension (pCa50), was higher in BCNU-treated myocytes than in controls (Fig. 1G and1I). The diastolic stiffness of the myocytes was determined by measuring the level of passive tension developed when stretching the myocyte from the slack length (≈1.8µm) to 2.0 and 2.3µm of SL in absence of Ca 2+ .

Passive tension was not significantly altered by BCNU although a tendency to increase was observed (Fig. 1J). Increasing the amount of oxidized GSH altered the contractile properties of the whole heart evaluated ex vivo using a Langendorff isolated perfused heart model to control cardiac preload, afterload, heart rate and circulating factors. The LV diastolic properties were altered as indicated by the tendency to higher LV diastolic pressure (Fig. 1K) and significant lower relaxation velocity dP/dtmin (Fig. 1N) in BCNU-perfused hearts compared with untreated samples. Systolic function was also altered, as indicated by the lower LV systolic pressure (Fig. 1L) and contraction velocity dP/dtmax (Fig. 1M). In conclusion, high oxidized GSH levels induce negative effects on both diastolic and systolic contractile properties, possibly via protein S-glutathionylation and decreased phosphorylation of regulatory contractile proteins.

Differential balance between β-adrenergic and oxidative pathways mediated by low and high stress-induced by exercise

We explored the physiological relevance of the interaction between protein S-glutathionylation and PKA-dependent phosphorylations in a context of acute physical exercise, known to activate both βadrenergic and oxidative pathways [START_REF] Mason | Muscle redox signalling pathways in exercise. Role of antioxidants[END_REF]. Moderate physiological cardiac stress was achieved in vivo with a single 35min exercise (Low stress induced by exercise, LSE). For high stress induced by exercise (HSE), animals ran until exhaustion. The degree of β-adrenergic signaling pathway activation was determined by measuring the activity of its intracellular effector PKA (Fig. 2A). PKA activity was increased by 15% in LSE hearts and by 30% with HSE to a level reached when isolated control hearts were stimulated ex vivo with isoprenaline (ISO). The phosphorylation levels of cMyBP-C and TnI on PKA sites (Fig. 2B) were both increased with LSE compared with control hearts. The level of TnI phosphorylation after LSE was however lower when compared to hearts directly treated ex vivo with ISO. Interestingly the levels of cMyBP-C and TnI phosphorylation were similar to control hearts after HSE despite the increase in PKA activity (Fig. 2B).

The level of oxidative stress produced by cardiac stress was evaluated by several markers. A marker of lipid peroxidation, MDA, was increased significantly by 66% after LSE and by 240% with HSE compared with controls (Fig. 2C). ISO stimulated hearts had also a higher MDA content of 160%. Both LSE and HSE had no effect on irreversible post-translational modifications such as the protein carbonylation (Fig. S2B). We also measured the level of free GSH as well as the GSH/GSSG ratio (Fig. 2D and2E), which reflect the degree of oxidative stress and altered cellular redox state. Both parameters were unchanged with LSE and significantly decreased with HSE or isoprenaline stimulation. This reflects an increase in oxidized glutathione content and decrease in free glutathione with HSE and isoprenaline stimulation. The level of S-glutathionylated cMyBP-C was increased in all conditions of stress, LSE, HSE and ISO (Fig. 2F). Altogether, the results indicate that these stress protocols provide as expected differential levels of activation of β-adrenergic and oxidative pathways associated with different post-translational modifications of regulatory proteins.

Under these different stresses and modifications, myofilament contractility was unchanged by LSE and altered by HSE (Fig. 3A and3B). The maximal active tension was decreased (Fig. 3A and3C) and the Ca 2+ sensitivity of myofilaments (pCa50) increased in HSE myocytes compared with controls (Fig. 3B and 3D). Finally, the diastolic properties were altered, as indicated by the higher passive tension induced by HSE compared with control myocytes after a stretch to 2.3µm of SL in relaxing solution (Fig. 3E).

LSE had modest impact on the whole heart contractility measured ex vivo in isolated perfused heart model. In such conditions, systolic parameters, such as the developed pressure (Fig. 3F) and dP/dtmax, (Fig. 3G) were similar after LSE to control hearts and only relaxation velocity dP/dtmin, tended to increase (Fig. 3H). Conversely, after HSE all systolic and diastolic parameters were reduced compared to control hearts (Fig. 3F to 3H). Finally, in another set of rats, cardiac contractile function was measured in vivo by echocardiography after a resting period of 30min under anesthesia (Fig. 3E). No difference of heart rate was observed between groups (supplemental Table S2). The left ventricular diastolic end diameter was increased after LSE and reduced after HSE compared with controls. The left systolic ventricular end diameter decreased only after HSE. Systolic function was increased only after LSE as indicated by the higher LV shortening fraction (Fig. 3I, Supplemental Table S2) and LV systolic wall motion velocity (Sm), evaluated by tissue Doppler imaging compared with controls (Supplemental Table S2). The diastolic anterior and posterior wall thicknesses were significantly increased in HSE compared with LSE, synonyms of reduced wall relaxation during diastole in HSE. Other indexes of diastolic function such as the E/A ratios of early diastolic and atrial transmitral inflow velocities (Fig. 3J) as well as the Em/Am ratios obtained by tissue Doppler imaging, were reduced only in HSE compared with controls and LSE (Fig. 3K). Altogether, the in vivo and ex vivo results indicate that in rats, LSE has no major effects on cardiac function and if there is one it is beneficial whereas HSE leads to in vivo intrinsic cardiac dysfunction associated with specific post-translational modifications such as reduced PKA-dependent phosphorylations and increased S-glutathionylated cMyBP-C.

Preventing redox modifications reduces the stress-induced by exercise

N-acetylcysteine (NAC), a cell-permeable cysteine precursor shown to replenish intracellular GSH levels [START_REF] Atkuri | N-Acetylcysteine--a safe antidote for cysteine/glutathione deficiency[END_REF], was administrated to rats to limit the activation of protein S-glutathionylation after HSE.

MDA levels in HSE hearts were normalized to those of control rats (Fig. S2). Moreover the levels of free GSH as well as the GSH/GSSG ratio in HSE-NAC were significantly higher than HSE (Fig. 4A).

NAC also prevented the increased level of S-glutathionylated cMyBP-C after HSE (Fig. 4B). Relative to controls, the levels of PKA-dependent phosphorylations were reduced for cMyBP-C and unchanged for TnI. In isolated hearts, systolic parameters such as the LV developed pressure tended to be higher in hearts from HSE+NAC rats compared with untreated HSE animals (Fig. 4C) and the difference reach significance regarding dP/dtmax, (Fig. 4D). The impaired relaxation (dP/dtmin) after HSE was completely prevented by NAC (Fig. 4E). At the level of the contractile machinery, NAC pre-treatment had no effect on the maximal active tension (Fig. 4F) but prevented the changes induced by HSE on the passive tension and myofilament Ca 2+ sensitivity (Fig. 4, G andH).

Incubation of permeabilized myocytes with the recombinant PKA catalytic subunit led to a reduction in the myofilament Ca 2+ sensitivity (Fig. 4H) in control myocytes, as previously reported [START_REF] Cazorla | Length and protein kinase A modulations of myocytes in cardiac myosin binding protein C-deficient mice[END_REF]. Conversely, myofilaments became insensitive to PKA after HSE. Similar results, as well as impaired relaxation, were previously obtained in transgenic mouse models in which TnI could not be phosphorylated by PKA [START_REF] Konhilas | Troponin I in the murine myocardium: influence on length-dependent activation and interfilament spacing[END_REF] or cMyBP-C was absent [START_REF] Cazorla | Length and protein kinase A modulations of myocytes in cardiac myosin binding protein C-deficient mice[END_REF][START_REF] Tong | Acceleration of crossbridge kinetics by protein kinase A phosphorylation of cardiac myosin binding protein C modulates cardiac function[END_REF]. Interestingly, the myofilament sensitivity to PKA was maintained in the HSE+NAC group, as shown by the reduction in pCa50 upon incubation with recombinant PKA catalytic subunit (Fig. 4H). Altogether, the results indicate that HSE alters the contractile properties through a redox-dependent mechanism.

Discussion

In this study, we investigated the intrinsic contractile defects that persist in the myocardium after physiological cardiac stress induced by different levels of physical activity. We observed that following increased cardiac workload, the contractile machinery is the target of reversible post-translational modifications that affect the cardiac function in vivo. Specifically, moderate exercise induced persistent S-glutathionylation of the regulatory protein cMyBP-C and PKA-dependent phosphorylation of cMyBP-C and TnI that have positive effect on systolic cardiac function. On the other hand, higher cardiac stress induced by prolonged exercise led to cardiac dysfunction with persistent cMyBP-C Sglutathionylation that interfered on the PKA-dependent phosphorylation levels. Our study highlights a crosstalk between S-glutathionylation and phosphorylation of cardiac contractile regulatory proteins resulting in differential cardiac modulations (Fig. S3).

Intrinsic cardiac dysfunction after prolonged exhaustive exercise.

Acute high cardiac stress induced in vivo diastolic dysfunction with preserved systolic contractile function. This is in accordance with previous clinical [START_REF] George | Mitral annular myocardial velocity assessment of segmental left ventricular diastolic function after prolonged exercise in humans[END_REF] and experimental [START_REF] Vitiello | beta-Adrenergic receptors desensitization is not involved in exercise-induced cardiac fatigue: NADPH oxidaseinduced oxidative stress as a new trigger[END_REF] studies showing that HSE induces transient early reduction of LV diastolic function with secondary altered systolic function following longer exercise [START_REF] Oxborough | Exercise-induced cardiac fatigue"--a review of the echocardiographic literature[END_REF]. Cardiac effects of prolonged exhaustive exercise have never been compared to the effects of a shorter exercise bout. We observed that moderate cardiac stress (LSE) increased systolic function. This beneficial effect on cardiac function disappears with prolonged stress (HSE) with the appearance of in vivo diastolic dysfunction and alteration of some systolic parameters function. The mechanisms underlying the decreased LV function after prolonged exhaustive exercise are unclear, but could involve in humans 1) diminution in blood volume due to dehydration that could reduce cardiac preload leading to decreased ventricular performance without direct alteration of cardiac contractility [START_REF] Middleton | Left ventricular function immediately following prolonged exercise: A meta-analysis[END_REF] or 2) intrinsic alterations independent of blood volume changes. Our investigation on isolated perfused hearts normalized loading conditions, heart rate and circulating factors between groups, and detected both systolic and diastolic dysfunctions in HSE. Such intrinsic systolic abnormalities were probably compensated in vivo by high levels of plasma epinephrine and norepinephrine previously reported in similar conditions of HSE [START_REF] Vitiello | beta-Adrenergic receptors desensitization is not involved in exercise-induced cardiac fatigue: NADPH oxidaseinduced oxidative stress as a new trigger[END_REF]. Consistent is the high level of PKA activity measured here in the myocardium after HSE to the same extent as observed with isoprenaline perfusion. In vivo, the heart is clearly under the regulation of the autonomic nervous system during exercise and recovery [START_REF] Porges | Vagal tone: a physiologic marker of stress vulnerability[END_REF].

The complete recovery of the sympathovagal balance after the end of exercise may take up 48 hours [START_REF] Furlan | Early and late effects of exercise and athletic training on neural mechanisms controlling heart rate[END_REF] and is negatively impacted by the duration of exercise [START_REF] Kaikkonen | Can HRV be used to evaluate training load in constant load exercises?[END_REF]. The β-adrenergic pathway plays a key role in the functional and molecular cardiac responses to exercise. However, the β-adrenergic pathway per se does not seem to be necessary to observe HSE-induced biochemical and functional modifications. In LSE (intermediate level of PKA activity) or Isoproterenol perfusion (high level of PKA activity but with short duration), some of the adaptations observed in HSE were present, but without cardiac dysfunction.

Moreover, in conditions of severe adrenergic stress but preserved redox balance with NAC treatment (no oxidative stress and normal oxidized glutathione levels), deleterious effects of HSE were absent.

Finally, pharmacological inhibition of glutathione reductase with BCNU mimicked the HSE-induced biochemical and functional modifications with no impact on PKA activity.

There are several potential mechanisms for diastolic dysfunction. One is increased diastolic Ca 2+ resulting in a slowed ventricular relaxation and diastolic dysfunction. Alternatively, myofilament crossbridge kinetics and response to Ca 2+ are regulated and, if altered, could contribute to diastolic dysfunction ( [START_REF] Flagg | Ca2+independent alterations in diastolic sarcomere length and relaxation kinetics in a mouse model of lipotoxic diabetic cardiomyopathy[END_REF][START_REF] Pohlmann | Cardiac myosin-binding protein C is required for complete relaxation in intact myocytes[END_REF][START_REF] Wolska | CGP-48506 increases contractility of ventricular myocytes and myofilaments by effects on actin-myosin reaction[END_REF]). There is now various evidences that show clearly the link between myofilament S-glutationylation and impaired cardiac function. The group of Solaro has clearly showed in models of hypertension and familial hypertrophic myopathy [START_REF] Lovelock | Ranolazine improves cardiac diastolic dysfunction through modulation of myofilament calcium sensitivity[END_REF][START_REF] Monasky | Tetrahydrobiopterin improves diastolic dysfunction by reversing changes in myofilament properties[END_REF][START_REF] Wilder | N-acetylcysteine reverses diastolic dysfunction and hypertrophy in familial hypertrophic cardiomyopathy[END_REF] that S-glutationylation of cMyBP-C slowed cross-bridge cycling kinetics and increased Ca 2+ sensitivity, which result is diastolic dysfunction.

Those diastolic abnormalities occur with no change in the Ca 2+ transients suggesting that the dysfunction occurs at the level of the sarcomere. Consistent with those previous findings, we evaluated the effect of HSE on cross-bridge cycling kinetics by measuring Ktr after a release-restretch protocol. Ktr was significantly decreased after HSE consistent with a slower cross-bridge cycling kinetic (Fig. S4).

Alternatively, diastolic changes of the heart and cardiomyocytes could be due to the giant elastic protein titin. The relationship between higher cellular stiffness and increased myofilament Ca 2+ sensitivity observed after HSE is consistent with previous reports indicating that the level of titin-based passive tension can influence the myofilament Ca 2+ sensitivity [START_REF] Cazorla | Length modulation of active force in rat cardiac myocytes: is titin the sensor?[END_REF][START_REF] Cazorla | Titin-based modulation of calcium sensitivity of active tension in mouse skinned cardiac myocytes[END_REF][START_REF] Fukuda | Length dependence of tension generation in rat skinned cardiac muscle: role of titin in the Frank-Starling mechanism of the heart[END_REF]. Additionally, S-glutathionylation has been clearly shown in vitro to target titin [START_REF] Kosuri | Sglutathionylation of cryptic cysteines enhances titin elasticity by blocking protein folding[END_REF]. We performed some exploratory experiments showing that S-glutathionylation of titin increases with our cardiac stress conditions LSE, HSE and after BCNU treatment (Fig S5). It is to note that no sign of titin degradation is observed in all conditions. Sglutathionylation of titin may not explain alone the higher passive tension after HSE since previous report showed in vitro a reduction of passive tension with S-glutathionylation of titin [START_REF] Kosuri | Sglutathionylation of cryptic cysteines enhances titin elasticity by blocking protein folding[END_REF]. Changes in titin phosphorylation by PKA, PKC, PKG or CamKII are also expected to affect the level of passive tension [START_REF] Lewinter | Cardiac titin and heart disease[END_REF][START_REF] Linke | Gigantic business: titin properties and function through thick and thin[END_REF]. Muller, et al. reported that a single bout of 15 min exercise in rat increased cellular stiffness and altered PEVK titin phosphorylations probably mediated by PKCα [START_REF] Muller | Acute exercise modifies titin phosphorylation and increases cardiac myofilament stiffness[END_REF]. Moreover, PKG pathway has been shown to be very important in increasing passive tension in heart failure with preserved ejection fraction [START_REF] Lewinter | Cardiac titin and heart disease[END_REF][START_REF] Linke | Gigantic business: titin properties and function through thick and thin[END_REF]. Thus, considering the complex regulation of titin by various redox post-translational modifications and the impact on both passive and active contractile properties, further studies are required to elucidate the exact participation of titin S-glutathionylation and phopshorylations in the contractile changes observed after cardiac stress.

Cardiac stress intensity and function

We propose from our experiments that β-adrenergic signaling pathway activation increased cardiac workload that induced oxidative stress. This consequently activated S-glutathionylation mechanisms that finally affected cardiac function. How to explain the different effects of cardiac stress in our study?

We observed that both moderate and high cardiac stress increased S-glutathionylation of cMyBP-C.

Considering that GSH can prevent damage to important cellular components caused by ROS, it is not surprising that S-glutathionylation is activated early [START_REF] Pompella | The changing faces of glutathione, a cellular protagonist[END_REF]. Importantly, we did not detect any sign of major carbonylation, an irreversible redox modification, of contractile proteins (Fig. S2). This is consistent with previous studies suggesting that direct oxidative modifications of sarcomeric proteins lead to a decrease in force generation, whereas sarcomeric protein phosphorylation by ROS-activated enzymes decrease myofilament Ca 2+ sensitivity, which is not observed here [4]. A main difference between stress conditions was that only moderate stress increased the level of cMyBP-C and TnI phosphorylation. Oxidative stress is a key intermediate in intense exercise-induced myocardium injury [START_REF] Neilan | Myocardial injury and ventricular dysfunction related to training levels among nonelite participants in the Boston marathon[END_REF]. In presence of NAC, HSE induced no persistent oxidative stress (normal MDA level), no Sglutathionylation and no PKA-dependent phosphorylation resulting in normal cardiac function. This is consistent with previous publications showing that restoring redox balance either by relieving NOS uncoupling in the DOCA-salt hypertensive mouse model [START_REF] Monasky | Tetrahydrobiopterin improves diastolic dysfunction by reversing changes in myofilament properties[END_REF] or using NAC in a familial hypertrophic cardiomyopathy mouse model [START_REF] Wilder | N-acetylcysteine reverses diastolic dysfunction and hypertrophy in familial hypertrophic cardiomyopathy[END_REF] restored diastolic function in correlation with a reduction of Sglutathionylation of cMyBP-C. Differences in the stimulus intensity and more importantly duration may explain different effects on the levels of cMyBP-C and TnI post-translational modifications and cardiac function. Firstly, oxidation can affect kinase activities. Hydrogen peroxide can activate type I PKA, which then translocates from the cytosol to the nuclear and myofilament compartments in cardiomyocytes in a cAMP-independent manner [START_REF] Brennan | Oxidantinduced activation of type I protein kinase A is mediated by RI subunit interprotein disulfide bond formation[END_REF]. Similarly, PKA activity is enhanced in mild oxidizing conditions, or after short exposure to oxidants [START_REF] Humphries | Regulation of cAMP-dependent protein kinase activity by glutathionylation[END_REF]. In contrast, longer or higher concentrations of the oxidant diamide inhibit PKA phosphorylation in the same conditions [START_REF] Humphries | Regulation of cAMP-dependent protein kinase activity by glutathionylation[END_REF]. PKA is protected from oxidation in the inactive tetrameric state, but is susceptible to oxidation and S-glutathionylation upon activation [START_REF] Humphries | Regulation of cAMP-dependent protein kinase activity by glutathionylation[END_REF]. The catalytic subunit can be protected against irreversible oxidation-induced inactivation by S-glutathionylation or by disulfide linkage to the regulatory subunit II of PKA. In our study, PKA activity remained increased by 15% with moderate exercise and by 30% with HSE to a level reached when isolated control hearts were stimulated ex-vivo with isoprenaline (Fig. 2). Thus, the reduced phosphorylation levels on PKA sites after HSE cannot be explained by a reduced kinase activity. However, it cannot be excluded that oxidation may modulate PKA phosphorylation via indirect routes by acting on phosphatases [START_REF] Humphries | Regulation of cAMP-dependent protein kinase activity by glutathionylation[END_REF].

Secondly, S-glutathionylation itself could prevent phosphorylations on specific sites. Previous publications showed that several cysteines of cMyBP-C can be S-glutathionylated in vitro [START_REF] Patel | Novel control of cardiac myofilament response to calcium by S-glutathionylation at specific sites of myosin binding protein C[END_REF][START_REF] Stathopoulou | Sglutathiolation impairs phosphoregulation and function of cardiac myosin-binding protein C in human heart failure[END_REF].

Stathopoulou et al [START_REF] Stathopoulou | Sglutathiolation impairs phosphoregulation and function of cardiac myosin-binding protein C in human heart failure[END_REF] showed that in vitro S-glutathionylation of Cys249, localized near the phosphorylation sites, attenuated phosphorylations by protein kinases (PKA and CaMKII). This may explain why after HSE, PKA-mediated phosphorylation of TnI and cMyBP-C was similar in control and HSE hearts despite higher PKA activity (Fig. 2A) and why myofilaments contractile properties were unchanged by recombinant PKA catalytic subunit incubation. Interestingly, similar myofilament insensitivity to PKA was observed previously in transgenic mouse models in which TnI [START_REF] Konhilas | Troponin I in the murine myocardium: influence on length-dependent activation and interfilament spacing[END_REF] or cMyBP-C [START_REF] Cazorla | Length and protein kinase A modulations of myocytes in cardiac myosin binding protein C-deficient mice[END_REF] could not be phosphorylated on PKA sites. The BCNU experiments confirmed the direct link between increased GSSG and cMyBP-C S-glutathionylation amounts, the reduced phosphorylation of regulatory contractile proteins and the cardiac dysfunction with no impact on β-adrenergic signaling pathway (Figure 1E) and oxidative stress (Supplemental Figure 1B). Adaptive responses associated with environmental stressors are critical to cell survival. Under conditions when cellular redox and antioxidant defenses are overwhelmed, the selective oxidation of critical residues within selected protein sensors functions to down-regulate energy metabolism and the further generation of ROS. This may ensure minimal nonspecific cellular damage, allowing for rapid restoration of cellular function through repair of oxidized proteins.

Study limitation:

In our study, we used an antibody approach to detect S-glutathionylation and not an analytical approach.

We thus analyzed only global S-glutathionylation status with the limitations of the detection. In particular, we cannot specifically indify the Cysteines modified and to which extent they are Sglutathionylated as a function of the duration/intensity of exercise/oxidative stress. The relative contribution of S-glutathionylation to reduce cMyBP-C PKA-dependent phosphorylation and to inhibit or prevent PKA activity on the effect of HSE on cardiac function needs to be investigated more precisely.

Only young male rats were tested in this study. Age-and gender-related factors could significantly influence cardiac response to exercise and subsequent cardiac remodeling. Experiments were performed 30 min after exercise and future studies should determine if such reversible changes could become irreversible when the exercise is repeated and lead to potential deleterious heart remodeling, as observed during heart failure.

Taking all these consideration together, our results pave the way: 1/ to further studies to investigate the pathophysiology and for instance propose various modalities of training to reduce these deleterious effects induced by strenuous exercise, and 2/ to pharmacological prevention of such deleterious effect of strenuous exercise. Indeed, activation of the glutathione system is easily available in daily practice (NAC) and above all, innocuity is well-established. Other candidates with anti-oxidative properties could be tested.

Conclusion:

In summary, we demonstrate the importance of both adrenergic and oxidative stress signaling pathways in regulating/dysregulating cardiac function. We show that both pathways work in concert to alter myofilament properties and cardiac function. Depending on the intensity/duration of the stress, we showed that dynamic regulations of the pathways with redox alterations can blunt the adrenergic signaling pathways and lead to cardiac dysfunction. Whether such reversible changes could become irreversible and constitute a key trigger of deleterious heart remodeling, as observed during heart failure remains to be investigated. Expressed as the average delta relative to control conditions of maximal active tension (F) and passive tension (G). *, p<0.05 vs Ctrl, ANOVA followed by Bonferroni's post-hoc tests. (H) Effect of PKA stimulation of myocytes from control (n=16 cells from 4 hearts), HSE (n=16 cells from 4 hearts) and HSE+NAC myocytes (n=12 cells from 4 hearts). *, p<0.05 stress effect vs Ctrl within stimulated and non-stimulated PKA groups, †, p<0.05 PKA within the same group, ANOVA followed by Bonferroni's post-hoc test.

Fig. 1 .

 1 Fig. 1. Effect of S-glutathionylation on cardiac function and post-translational modifications of

Fig. 2 .

 2 Fig. 2. Effect of low (LSE) and high (HSE) stress-induced by exercise on markers of β-adrenergic

Fig. 3 .

 3 Fig. 3. Effect of low (LSE) and high (HSE) stress-induced by exercise on cardiac function. (A) The

Fig. 4 .

 4 Fig. 4. Oxidative stress could be involved in cardiac dysfunction after high stress-induced by exercise. The antioxidant capacities of animals were increased by injecting 50 mg.kg -1 of NAC, a non-

Acknowledgements: Julien Boissiere and Lucas André for their contribution to preliminary experiments. This work was funded by A French National Research Agency grant (COMYOCARD), the French Society of Cardiology (Grant Heart and Sports), and by a PhD grant from Groupe de Réflexion sur la Recherche Cardiovasculaire to N.C. C.R and S.N are associate professor at Avignon University. D.B and A.K are PhD students of Avignon University. S.G is technical assistant form Avignon University. F.R and S.M are full professor at Montpellier University. A.L and O.C are scientists from the Centre National de la Recherche Scientifique. Conception, hypothesis definition, and study design, O.C, C.R, A.L, S.M, S.N, F.R ; data acquisition, analysis, and interpretation N.C, D.B, A.K, S.G, O.C, C.R; article writing, O.C, C.R.

This work was funded by A French National Research Agency grant (COMYOCARD), the French Society of Cardiology (Grant Heart and Sports), and by a PhD grant from Groupe de Réflexion sur la Recherche Cardiovasculaire to N.C

Author Disclosure Statement

No competing financial interest exists. to achieve a LV end diastolic pressure of 5mmHg. The heart was perfused at a constant pressure (80mmHg) and was allowed to stabilize for 30 min. To evaluate specifically the consequence of protein post-translational modifications, some control hearts (n=4) were perfused with 80µmol/L 1,3-bis-2chloroethyl-1-nitrourea (BCNU), a glutathione reductase inhibitor, for 5 min [1], or with 0.1µM ISO for 5 min (n=4). Throughout the procedure, the cardiac function parameters were recorded (MP35, BioPac System Inc) to calculate the developed pressure (DevP), the maximal (dP/dtmax) and minimal (dP/dtmin) first derivative of LV pressure. Finally, at the end of the experimental procedure, LVs were frozen quickly in liquid nitrogen and stored at -80°C for western blot analysis.

Abbreviations Used

Cross-bridge kinetics:

Kinetic of tension redevelopment (ktr) was measured by mechanically disrupting force-generating cross-bridges at either sub-maximal activating solution ([Ca 2+ ]=1.3µM) or at maximal calcium activation ([Ca 2+ ]=32µM). Cross-bridge disruption was induced by rapid release/restretch protocol [2,3]. Briefly, cardiomyocytes were perfused with activating solution, when developed force reached steady state, a rapid (2 ms) release/restretch of 20% original cell length was applied. The cell was shortly kept (20 ms) at the unload shortening prior to 100% restretch. Following the release/restretch step, force will drop to zero indicating that most cross-bridge have detached. After the restretch step, force rises exponentially up to initial maximal force with rate constant ktr. For each cardiomyocyte, at a given SL, the above protocol was repeated 3 times and the average ktr was estimated Western blot analysis. Myocardial protein expression was studied, as previously described [4].

Briefly, LV tissue was quickly frozen in liquid nitrogen and solubilized in non-reducing Laemmli buffer (3% SDS, 50 mM Tris HCL pH 6.8, 8 M urea, 2 M thiourea, 1 mM EGTA, 1 mM EDTA, 10 mM Benzamidine, 0.2 mM Na3VO4, 50 mM NaF, 20 mM β-glycerophosphate). Proteins were separated using SDS-PAGE electrophoresis and were electrically transferred onto nitrocellulose membranes (GE Healthcare). Then, membranes were blocked with the Odyssey Blocking Buffer in PBS (LI-COR Biosciences) at room temperature for 45 min and incubated overnight with primary antibodies (Supplemental TableS1). Bands were revealed and quantified with the Odyssey system (LI-COR Biosciences, Lincoln, Nebraska) after incubation with fluorescent secondary antibodies (1:30,000 dilution, LI-COR Biosciences) at room temperature for 45 min. Protein content was expressed relative to GAPDH or calsequestrin (CSQ) content.

Determination of glutathione levels and cMyBP-C S-glutathionylation (Fig S1).

As an index of myocardial lipid peroxidation, malondialdehyde (MDA) levels were measured in cardiac tissue using the Lipid Peroxidation (MDA) Assay Kit (ab118970, Abcam, Cambridge, Mass, United States), according to the manufacturer's instructions. Briefly, small LV pieces were homogenized in lysis buffer and directly centrifuged at 15,000 g at 4°C for 15 min. The resulting supernatants were used to measure MDA content by spectrofluorimetry.

were incubated in a microplate precoated with substrate. The assay was developed with tetramethylbenzidine substrate and color development was stopped with acid stop solution.

Absorbance measured at 450 nm in a microplate reader was divided by total protein (μg) per sample and the data represented as relative PKA activity.

Supplemental Table S1. Antibody details


Stéphane Perrin
email: stephane.perrin@univ-smb.fr

Eric Benoit
email: eric.benoit@univ-smb.fr

Didier Coquin
email: didier.coquin@univ-smb.fr

Fusion method choice driven by user constraints in a human gesture recognition context

Keywords: gesture recognition, fusion, fuzzy logic, user constraint

Recognition of human gesture leads to a dynamic field that produces many various methods. The main way to improve the recognition process is to perform data fusion based on a qualification of each recognition method. The advance in data fusion gives also several solutions and the choice of a fusion method is a crucial point. The goal of this paper is to present an approach were the choice of the fusion method is driven by the constraints of the final user of data. Such constraints are expressed as bounds on indicators like confidence or accuracy. A practical experimentation illustrating this approach is presented in this paper. From a depth camera sensor, human gesture is interpreted and, fusion method is selected in accordance with the constraints of the final information consumer. This approach is illustrated in a robotic control by human gesture: outputs perform the action to be done by a NAO robot.

I. INTRODUCTION

Human recognition of human gesture leads to a dynamic field that produces many various methods [START_REF] Mitra | Gesture Recognition: A Survey[END_REF]. These methods commonly perform a measurement process in order to convert the physical state of an entity into an information entity. If numerical values are commonly used to represent measurement results, it is now admitted that some applications manipulate symbolic values or linguistic terms better.

In this paper, we concentrate first on recognizing human gesture from upper limb postures detection. The two parts used of upper limb, i.e. arm and forearm, is expressed using linguistic terms. The corresponding symbolic values result from numeric angles measurements of human body. These angles measurements provided by a depth camera sensor, in our case an "xtion pro live" from Asus. We use yet linguistic terms to express a posture from symbolic values of upper limb parts.

Then we focus on decision process performed from symbolic values. Symbolic values are commonly expressed in terms of mass. Fusion methods are particularly effective and used to manipulate mass [START_REF] Dubois | Representation and combination of uncertainty with belief functions and possibility measures[END_REF]. Commonly used in decision system, fusion methods are able to formalized decision criteria from fuzzy information, especially when evidence theory is used. Finally we propose to express the needs of the information consumer which is view as a constraint on the decision process. This allows to choose and to compute the decision, i.e. action to do, in accordance with the consumer's needs and usage.

Gesture recognition done by a human is complex and the decision process can take several criteria in consideration: hesitation between several known gestures, believe in a recognition gesture, etc. Fuzzy logic facilitates the manipulation of these concepts. In the case of automatic and artificial process for the recognition of human gestures, we show that results of fusion methods associated to the evidence theory are a good way to express the consumer criteria. These criteria are finally used to select method fusion. This approach, illustrated into section 5, is used to give orders to a humanoid NAO robot developed by the Aldebaran Company, from human gesture recognition. The system learns a set of gestures. Each known gesture corresponds to an order to be transmitted to the robot. The decision system chooses the order to be transmitted to the robot. For example, the user wants the robot to execute an order if and only if the recognition of the corresponding human gesture is sure, i.e. with low uncertainty or not ambiguous with other possible gestures. Another example: a gesture corresponds to an emergency action. In this case, if this gesture is recognized with enough certainty the corresponding order is chosen even if another gesture is recognized at the same time but with a greater certainty.

In the next section, we detail gesture modeling using fuzzy representation. The gesture recognition process is presented in section 3. In section 4 we introduce a fusion method in order to express the decision criteria using evidence theory. This theory allows defining and formalizing user constraints: recognition quality, threshold of gesture detection. Facilitating threshold determination based on mass transfers inside fuzzy representation of human gesture is discussed in section 5.

User constraints are thrown back to the decision system which is now able to choice robot order to be applied, in accordance to the user expectation.

II. FUZZY LOGIC FOR HUMAN GESTURE MODELING

A. Fuzzy representation : fuzzy nominal scale

This section reminds the concepts of fuzzy nominal scale and metrical scale presented in [START_REF] Benoit | The role of fuzzy scales in measurement theory[END_REF] and that are used to represent gestures. For the sake of simplicity, the notation of any fuzzy subset u will also denote the associated membership function. Then the membership degree of a value x to a fuzzy subset u is denoted u(x). The notation of the membership of a value to a function M(s) is then denoted M(s)(x).

Let X be a set of object states. In order to characterize linguistically any measurement over X, let L be a set of linguistic terms, representative of the physical phenomenon. Let F(L) be the set of fuzzy subsets of L.

The fuzzy scales used in our study are defined by an idsymbolism <X, L, R> where: X is the set of quantity manifestations.

L refers to a set of terms dedicated to the expression of measurement values, it is often known as the universe of discourse.

R, called the representation, is a fuzzy mapping from X to L.

The conversion of a physical state into its linguistic representation is called a fuzzy linguistic description mapping [START_REF] Mauris | Fuzzy symbolic sensors -from concept to applications[END_REF] [START_REF] Benoit | Fuzzy nominal scales[END_REF] or simply a fuzzy description mapping. It transforms an object x of X into a fuzzy subset of linguistic terms D(x) ∈ F(L) called the fuzzy description of x. The fuzzy subsets of linguistic terms are called lexical fuzzy subsets (LFS). A dual mapping, called the fuzzy meaning mapping, associates a fuzzy subset of X to each term l of the lexical set L. This fuzzy subset M(l) is the fuzzy meaning of l (see fig. 1). With fuzzy nominal scales, the fuzzy meanings are chosen to respect some characteristics of fuzzy sensors and they form a strict fuzzy partition of X. Whereas the only relation that can be defined on symbols (or terms) is the equality relation, more interesting relations can be defined on fuzzy subsets of linguistic terms [START_REF] Baets | Metrics and T-equalities[END_REF]. We especially point out the transportation distance operator (denoted d' S ) proposed in [START_REF] Allevard | The transportation distance for fuzzy descriptions of measurement[END_REF] that allows to compute the distance between 2 LFSs. This distance d' S on the space of LFSs has the property to be an extension of a distance d S on the space of linguistic terms. Actually the existence of this distance defines the scale as a fuzzy metrical scale, i.e. a scale that preserves a distance from the measured quantity to its representation: To get the transportation distance d' S between 2 LFSs, a cost of membership transportation is computed. Each transportation of an amount a of membership from a term A to a term B is associated to the cost:

Considering the subset LF(L) of F(L) defined by

A ∈ LF(L) ⇔ Σ l∈L A(l) = 1 (1)
c(a,A,B) = a.d S (A,B) (2)
The transportation distance is then defined as the minimal cost to bring membership amounts.

The distance d S on terms can be experimentally defined by a calibration process, but can also be defined to include some context knowledge. Indeed, the distance between 2 terms considered as quite similar is arbitrary defined as small in order to take this similarity into account.

Another usage of this distance is the definition of a confidence volume playing for the LFSs the same role than the confidence interval for numerical values.

Fuzzy scale gives a tool to represent a gesture with a lexical fuzzy subset (LFS), but gives no semantic to the membership degree of each term to this fuzzy subset. The constraint given by (1) can suggest a Bayesian semantic for these degrees but the building process doesn't involve any Bayesian hypothesis. In this study, we decided to choose a weak semantic by interpretation of fuzzy membership degrees as belief masses as defined in the TBM (Transferable Belief Model) [START_REF] Smets | Data fusion in the transferable belief model[END_REF]. Each LFS is now termed as Bayesian Basic Belief Assignment because the membership degree of a LFS is interpreted as a mass of 1 distributed on the singletons in L.

B. Human gesture representation

In the field of human system interaction, it is big interest in developing natural interfaces using human communication modalities. One of these modalities is communication through gestures. Gestures can be described with words. Fig. 3 illustrates the gesture "come here". In this example, the "come here" configuration is described quite simply as the one with a straight arm, and arm is middle down and fore. This particularity of gestures makes possible to describe them with fuzzy nominal scales. We illustrate our approach with a right upper limb detection gesture. To express the human gesture representation, we decompose the representation into 2 intermediate high level representations corresponding to arm and forearm of measured skeleton.

The angles relative to the arm and the forearm are computed from the joints positions of detected skeleton. From the physical measurement, each body part (i.e. the arm and the forearm) are expressed using word. Lexical sets are chosen to have simple and easily understandable descriptions. Each part (i.e. the arm and the forearm) is characterized by the 2 measured angles issued from joints positions. They are illustrated in fig. 5. We also use lexical fuzzy subsets as illustrated in fig. 1.

1) Arm modeling

For arm angle measurement, we use a-tetha angle and a-psi angle. a-tetha angle corresponds to the angle formed from the vertical to the arm, in the plane of the human body. a-psi is the angle formed from the vertical to the arm when the arm is level up front of the human. Lexical fuzzy subset of a-theta is {down, horizon, up} and the lexical fuzzy subset of a-psi angle is {rear, middle, front}. Fig. 6 illustrates the a-theta angle lexical posture determination from the angle measurements. Then, the arm posture is represented by the combination of these 2 lexical subsets, corresponding of the 2 angles a-tehta and a-psi.

The arm corresponding variable takes its values in the lexical set L arm : L arm = {down, front, up, aside, rear} [START_REF] Benoit | The role of fuzzy scales in measurement theory[END_REF] Table 1 gives the arm position rules from these lexical subsets. 2) Forearm modeling A similar process of arm modeling is done for the forearm part. 2 angles are used: f-tetha which corresponds of angle formed by the forearm axis and arm axis and f-psi which corresponds to the position relative to the horizon. Fuzzification process is the same as arm part and is not detailed in this paper.

The forearm corresponding variable takes its values in the lexical set L forearm : L forearm = {open, vclose, hclose, vmiddle, hmiddle} (4)

3) Right upper limb modeling

The gesture is represented by the combination of an arm posture and a forearm posture. Gesture is also defined by words. Each word represents a human gesture.

The lexical set of gesture is defined by a list of modal gestures L G-modal presented in [START_REF] Benoit | Fuzzy nominal scales[END_REF].

Using rules, each modal gesture made by upper limb posture can be defined in the system. This learning step is based on the sub-gesture entries: the arm and forearm values. Table 3 illustrates rules defining gestures to be detected from lexical subset defined in (3) and (4).

It is noted that the example in table 3 illustrates a 2D dimension case due to the 2 linguistic variables (corresponding to arm and forearm). It is possible to generate the principle to n dimensions. Note that the configuration of arm and forearm postures can be not corresponding to any modal gesture (ND in table 3). For this example, the linguistic set of modal gesture is given in [START_REF] Benoit | Fuzzy nominal scales[END_REF].

L G-modal = {down, front, up, aside, rear, psi, ride, touchEar, shake} [START_REF] Benoit | Fuzzy nominal scales[END_REF] The known gestures presented in this paper are modal gestures. Gestures are expressed into linguistic representation. They are obtained from the measurement of human postures. In order to simplify the approach, we use directly the posture detection to define a static gesture. Dynamic gestures are obtained using the temporal dimension of the sensor measurements. Anyway, as soon as the gesture is computed, further modeling and processing are identical. The next section details the posture recognition process.

III. FUZZY POSTURE RECOGNITION PROCESS

To perform the gesture recognition process, the system has to know which gestures can be detected. Thus, the result of detection process of any gesture can be expressed in terms of mass on known gestures [START_REF] Benoit | Body posture measurement in a context of example-based teaching[END_REF] [START_REF] Allevard | Dynamic gesture recognition using signal processing based on fuzzy nominal scales[END_REF]. The mass criterion is computed from the detected gestures and each known gestures. The linguistic descriptions provided by the gesture recognition process form the linguistic description of this right upper limb posture. Hence, this posture P (considered as a gesture) can be written as:

P = (L G-modal,1 , L G-modal,2 , L G-modal,3 , …, L G-modal,n ) (6)
where n is the number modal gestures contained in L G-modal .

Table 4 illustrates the arbitrary gesture detection case. In this example, the expressed gesture representation is P = (P: 0, Q: 0, R: 0.42, S: 0.28, T:0.18, U: 0.12) [START_REF] Allevard | The transportation distance for fuzzy descriptions of measurement[END_REF] Where P represents the fuzzy representation of the detected posture presented in table 4 and illustrated in fig. 8. From the fuzzy gesture detection (fig. 8) process result (represented by ( 6)), the decision system takes place. Next section presents the decision process.

IV. DECISION SYSTEM UNDER USER CONSTRAINTS

In our application context, the decision process has to choose an action from human gesture detection result. This result is expressed using fuzzy representation. That lets us to express finely the detection: several gestures can be detected from a single human gesture. This fluency of information carried by fuzzy representation is conventionally employed in the case using multi-sensor detection. In this paper, we focus its interests in order to automatize the choice of action to be done from one human gesture detection. The imprecision carries information that represents the possible confusion, hesitation or belief of detected gestures. The output of decision process stems of defuzzification process.

From one single human gesture detection, several modal gestures are detected, as shown in [START_REF] Allevard | The transportation distance for fuzzy descriptions of measurement[END_REF]. We consider that experiment context that each gesture corresponds to an action to be executed by the robot NAO. For each modal gesture L G-modale,i is a corresponding action named A i .

In a first basic approach, the decision is given by the maximum pignistic probability and then the recognized gesture is the modal gesture which has the most important mass. This is the case of the example 1 in of fig. 9.

In a second approach, we consider the uncertainty given by the measurement process. The main source of uncertainty is issued from the camera process detection. The uncertainty estimation is complex is this case and is not presented in this paper. In any case, the epistemic uncertainty, i.e. the uncertainty relative to gesture definition, is more important and taken into account by the consumer. We consider that the consumer accept a confidence volume around each modal gesture on the space of LFSs. This confidence volume plays for the space of LFSs the same role than the confidence interval for numerical spaces. It is defined by the distance between a measured gesture and the modal gesture. The distance between LFSs is the transportation distance as presented in II.A. It is simply computed when one of the LFSs is a modal gesture. Such distance is then equal to the transportation cost of an amount of mass from the modal term to the other terms. And if all the distances between terms are equal to 1, the distance is given by the amount of mass transported from the modal term to the other ones during the distance computation. The recognized modal gesture is a gesture that has the measured gesture inside its confidence volume. Due to the property of the transportation distance, this is equivalent to the definition of a minimum amount of mass to recognize a gesture. In fig. 9, the case 2 defines 0.6 as a minimum of mass for the recognition and no gesture is recognized. This means that the measured gesture is out of the confidence volumes of each modal gesture. In case 3 the minimum amount of mass is defined as 0.4 then the confidence volume around R is large enough to include de measured gesture.

In a third approach, we want to consider that the consumer wants to take into account the possible confusion between 2 possible gestures. The confusion between 2 modal gestures is given by the overlapping of their respective confidence volume. The overlapping depends on the distance between the 2 modal gestures and on the distance that characterizes the confidence volume. So, for a given size of the confidence volume, the overlapping depends only on the distance d' S between the 2 modal gestures themselves represented by singletons. In accordance with the singleton coincidence of d' S with d S , the overlapping depends only on the distance d S between the 2 modal terms that characterize the 2 modal gestures. As the distance between terms is arbitrary defined, it can be done by the consumer in order to express the need to take care about a possible confusion. As for the previous approach, the corresponding decision is expressed as thresholds. In this approach, a relative threshold synthesizes the possible confusion between 2 modal gestures. In fig. 9 case 4, the confusion relative threshold is 0.2 between the terms R and S. With the measured gesture given in example, the difference between R and S is smaller than the confusion relative threshold. So R and S are valid at this decision step. In order to perform the decision, another constraint can be added. The nature of the robot action associated to command gesture is able to influence the decision process. To illustrate this consideration, we consider two classes of actions (each action corresponds to a modal gesture): one class contains the "classical" actions and the second the "emergency" actions, corresponding respectively to a "classical" modal gesture and an "emergency" modal gesture. So when an "emergency" nominal gesture is detected even with a lower mass than a classical detected nominal gesture, the selected decision is the corresponding "emergency" action. If the nominal gesture S is defined as belonging to the "emergency" class, it is chosen in the case 4. In case 5, the confusion relative threshold is not large enough to select S instead of R.

In the last approach, the consumer constraint reduces the set of possible recognized gestures to the emergency related one. This situation is similar to the second approach, but with only one gesture. As only one gesture appears in the decision process, the confidence volume can be larger than in other approaches. The case 6 in fig. 9 illustrates this approach. Fig. 9. Examples of threshold effects on decision from an arbitrary gesture detection result.

V. DISCUSSION

The main problem of this approach is to determine the thresholds levels of mass. This step is critical because its directly impact the decision, i.e. action to be done.

To help the user to fix the threshold levels, one way consist to learn it, during a dedicated period of this stage. After this stage, system will be able to select an action, even if the learning process could be continued to improve the determination of threshold in accordance with the user feedback.

In this section we discuss about facilitating threshold determination based on mass transfers inside fuzzy representation of human gesture.

The symbolic distance between gestures represents their discrimination power. Considering an "emergency" gesture, the distance between the corresponding symbolic gesture to another symbolic gesture, provides information. In the case of a high distance, that means that the cost to switch from a gesture to another one is high. For a low distance, the cost is low. Thus level of transferable mass is higher. This is especially interesting when open word is adopted, i.e. when unknown gesture is admitted in the fusion system. The unknown gesture is considered to be got close from the "emergency" gesture. To implement this way, a small distance is fixed between these two gestures. Thus the "emergency" gesture is favored.

Finally, the distance between fuzzy representations of gesture gives the transferable mass. Mass corresponding to the unknown gesture is transferred to the emergency gesture in accordance to the distance and the determination of threshold principle is thereby facilitated.

VI. CONCLUSION AND PERSPECTIVES

This paper discusses about the importance of human understanding in humans system interaction. An illustrated scenario was implemented in the case of a humanoid NAO robot which is required to make actions by human gesture command. A fuzzy system detection and recognition is constructed to help for gesture recognition more intuitively. In order to automate the decision process, a solution based on the probabilistic and on the evidence theory is presented to take into account the user constraints i.e. rules of decision to be adopted in the case of doubt, hesitancy the priority of actions.

The future scenario of the work will consider several gesture recognition sensors and several kind of sensor. This way illustrates the interest of multi-modal fusion approach which is able to take into consideration conflicting information. In addition, we will consider the way to make a human gesture: the temporal repetition of a gesture or the execution speed of it. That is expressed another kind of user constraints.

Fig. 1 .

 1 Fig. 1. An example of fuzzy nominal scale characterized by a set of fuzzy meanings of lexical terms. On the right the fuzzy description of a value x0 produces a LFS. LF(L) contains any fuzzy description D(x 0 ) of a physical state x 0 as shown in fig. 1.

  d S is a distance defined on terms s of L, d' S is a distance defined on D(X) such that the singleton coincidence with d S is respected: d' S ({a},{b}) = d S (a,b).

Fig. 2 .

 2 Fig.2. The transportation distance between the 2 LFSs is defined as the minimal cost of the transportation of membership degrees between terms in order to get the second LFS from the first one.

Fig. 3 .

 3 Fig. 3. The "come here" gesture can be expressed with word.

Fig. 4

 4 Fig.4illustrates a 2D representation of the body perceived by the depth sensor and of the measured joints. Posture detection is produced from the depth camera sensor (Xtion Pro Live from Asus) using NiTE library. The output is a set of 3D joins positions that we call measured skeleton.

Fig. 4 .

 4 Fig. 4. 2D representation of 3D measurements of joints.

Fig. 5 .

 5 Fig. 5. Used angles from skeleton.

Fig. 6 .

 6 Fig. 6. First sub-lexical for arm posture from a-theta angle value Fig. 7 illustrates the a-psi angle lexical posture.

Fig. 7 .

 7 Fig. 7. Second sub-lexical for arm posture from a-psi angle value.

Fig. 8 .

 8 Fig. 8. Selection of action: a basic approach

TABLE I .

 I

				ARM GESTURE DEFINITION RULES
				a-tetha
			down	horizon	up
		rear	down	rear	up
	a-psi	middle	down	aside	up
		front	down	front	up

Table 2

 2 represents the position rules from lexical subset corresponding to f-theta and f-psi.

TABLE III

 III

			.	MODAL GESTURE DEFINITION RULES
					arm
			down	front	up	aside	rear
		open	down	front	up	aside	rear
	forearm	vclose hclose	ND ND	ND ND	ND ND	Touch Ear ND	ND ND
		vmiddle	shake	ND	ND	psi	ND
		hmiddle	ND	protect	ND	ride	ND
						ND : not defined

TABLE IV

 IV

			.	ARBITRARY GESTURE DETECTION RESULT
						arm
				down	front	up	aside	rear
				0	0	0.6	0.4	0
		open	0	ND	ND	ND	P	P
	forearm	vclose hclose vmiddle	0.7 0.3 0	ND ND ND	Q ND ND	R T ND	S U ND	S ND ND
		hmiddle	0	ND	ND	ND	ND	ND


Robin Ferrari

Elvira Infante

Philippe Chavrier
email: philippe.chavrier@curie.fr

Nucleus-invadopodia duo during cancer invasion

Keywords: Invadopodia, MT1-MMP, microtubule, LINC complex, tumor invasion, centrosome

Matrix proteolysis mediated by MT1-MMP facilitates the invasive migration of tumor cells in dense tissues, which otherwise get trapped in the matrix because of limited nuclear deformability. A digest-on-demand response has been identified, which requires nucleus-microtubule linkage through the LINC complex and triggers MT1-MMP surface-exposure to facilitate nucleus movement.

Text (1449 words) Introduction

During their metastatic journey, tumor cells migrate through dense and complex 3D microenvironments within connective tissues. For carcinoma cells deriving from epithelial tumors, dissemination starts by breaching the 0.1-1 m thick basement membrane (BM) made of laminins, cross-linked type IV collagen and proteoglycans that surround epithelial tissues. BM transmigration signals the transition from in situ to more aggressive infiltrating carcinomatous lesions; then invasive cells can disseminate, mostly in cohorts, through interstitial tissues consisting of bundles of type I collagen-rich fibrils interspaced with discontinuities. A salient feature of tumor cell invasion in confining environments is that it requires extensive nuclear deformation to squeeze the bulky and stiff nucleus through constricting pores within the tissue matrix [START_REF] Wolf | Physical limits of cell migration: control by ECM space and nuclear deformation and tuning by proteolysis and traction force[END_REF]. Recent studies, which are detailed in Box 1, revealed that nuclear deformations during constricted migration can lead to nuclear envelope (NE) rupture with potential consequences for genome stability and tumor progression [START_REF] Harada | Nuclear lamin stiffness is a barrier to 3D migration, but softness can limit survival[END_REF][START_REF] Denais | Nuclear envelope rupture and repair during cancer cell migration[END_REF][START_REF] Raab | ESCRT III repairs nuclear envelope ruptures during cell migration to limit DNA damage and cell death[END_REF][START_REF] Bell | Causes and consequences of nuclear envelope alterations in tumour progression[END_REF]. In addition, it has been shown that when the pore size of the matrix meshwork is below the deformability of nucleus, then cell movement stops [START_REF] Wolf | Physical limits of cell migration: control by ECM space and nuclear deformation and tuning by proteolysis and traction force[END_REF]. It is also established that surface-exposed membrane-type (i.e. trans-membrane) matrix metalloproteinases (MT-MMPs) can enlarge the pores in the matrix [START_REF] Wolf | Physical limits of cell migration: control by ECM space and nuclear deformation and tuning by proteolysis and traction force[END_REF][START_REF] Wolf | Extracellular matrix determinants of proteolytic and non-proteolytic cell migration[END_REF]. All together, these findings have raised important questions as to whether and how the matrix proteolysis machinery of cancer cells can scale with the level of confinement by the matrix and what is the influence of nuclear deformation and mechanosensing to this response and to the invasive potential of tumor cells.

Nucleus pulling and pushing schemes generate nuclear deformation during confined migration

Deformability and mechanical stability of the nucleus depends on nuclear lamina proteins lamin-A and B (LMNA, -B), which form a viscoelastic proteinaceous network underneath the inner nuclear membrane. Nuclear stiffness scales with LMNA levels: LMNA overexpression impedes transmigration by augmenting nuclear rigidity, while reducing LMNA levels increases invasion speed in 3D reconstituted matrix [START_REF] Wolf | Physical limits of cell migration: control by ECM space and nuclear deformation and tuning by proteolysis and traction force[END_REF][START_REF] Harada | Nuclear lamin stiffness is a barrier to 3D migration, but softness can limit survival[END_REF][START_REF] Infante | LINC complex-Lis1 interplay controls MT1-MMP matrix digest-on-demand response for confined tumor cell migration[END_REF].

Thus, nuclear stiffness and limited nuclear deformability have been identified as restrictive factors that impede cell migration in confined environments [START_REF] Wolf | Physical limits of cell migration: control by ECM space and nuclear deformation and tuning by proteolysis and traction force[END_REF][START_REF] Harada | Nuclear lamin stiffness is a barrier to 3D migration, but softness can limit survival[END_REF].

Interestingly, a gradient of LMNA expression decreasing from the core to the invasive front of tumor xenografts has been reported and LMNA-deficient tumors have a growth advantage [START_REF] Harada | Nuclear lamin stiffness is a barrier to 3D migration, but softness can limit survival[END_REF][START_REF] Bell | Causes and consequences of nuclear envelope alterations in tumour progression[END_REF]. The downside is that nuclear resistance to mechanical insults drops with LMNA deficiency and repeated passages across constrictions can lead to cell death as a failure to repair consequent NE rupture and DNA damage [START_REF] Harada | Nuclear lamin stiffness is a barrier to 3D migration, but softness can limit survival[END_REF][START_REF] Denais | Nuclear envelope rupture and repair during cancer cell migration[END_REF][START_REF] Raab | ESCRT III repairs nuclear envelope ruptures during cell migration to limit DNA damage and cell death[END_REF][START_REF] Bell | Causes and consequences of nuclear envelope alterations in tumour progression[END_REF] (see Box 1).

Nuclear deformation reflects the pulling and pushing schemes by tumor cells to move their nucleus across constrictions. As during cell migration in 2D, integrinbased adhesion to surrounding collagen fibers and actomyosin-based contractility produce traction forces that can propel the nucleus forward through constraining spaces ( [START_REF] Petrie | Activating the nuclear piston mechanism of 3D migration in tumor cells[END_REF] and references herein). Additionally, pulling forces can result from dynein and kinesin molecular motors attached to the nuclear surface and moving the nucleus along the microtubule network [START_REF] Bone | Nuclear migration events throughout development[END_REF]. Proteins responsible for nucleocytoskeleton attachment and motor association to the surface of the nucleus belong to the Linker of Nucleoskeleton and Cytoskeleton (LINC) complex. This complex consists in SUN and nesprin proteins, which span the inner and outer nuclear membrane, respectively, and interact through SUN domain and the carboxy-terminal Klarsicht, ANC-1, Syne Homology (KASH) domain of nesprins in the intermembrane space. Nesprin-2 was reported to be required for recruitment of LIS1, a regulatory protein of dynein motor function, to the cytoplasmic face of the nucleus in invasive MDA-MB-231 breast tumor cells [START_REF] Infante | LINC complex-Lis1 interplay controls MT1-MMP matrix digest-on-demand response for confined tumor cell migration[END_REF]. In humans, LIS1 deficiency leads to lissencephaly (smooth brain) due to severe cortical neuron migration and positioning defects caused by impaired dynein-dependent nucleokinesis. It was recently found that LINC complex and LIS1 mediate nucleo-centrosome linkage and centrosome positioning ahead of the nucleus [START_REF] Infante | LINC complex-Lis1 interplay controls MT1-MMP matrix digest-on-demand response for confined tumor cell migration[END_REF]. These observations suggest that Nesprin-2 and LIS1 contribute to pulling forces exerted on the nucleus by dynein moving along microtubules to support nucleus movement through confining environments generating nuclear deformation (Figure 1).

Invadopodia mediate MT1-MMP-based matrix degradation by cancer cells

Membrane-anchored MT1-MMP (aka MMP14) is the sword arm of the collagenolytic program of carcinoma cells. Using the intraductal mammary gland xenograft model, it was reported that silencing of MT1-MMP impairs the ability of ductal carcinoma in situ tumor xenografts to progress into infiltrating lesions, providing validation for the prominence of MT1-MMP for BM transmigration by breast cancer cells in vivo [START_REF] Lodillinsky | p63/MT1-MMP axis is required for in situ to invasive transition in basal-like breast cancer[END_REF].

MT1-MMP has also been implicated in invasive migration of mesenchymal cells through the fibrous interstitial type I collagen network, in the infiltration of vascular and lymphatic compartments and in extravasation during metastasis. Inhibition of MT1-MMP function can evoke protease-independent programs of cancer cells, which can switch to contractility-driven ameboid movement or use the nucleus as a piston to propel the cell ahead [START_REF] Wolf | Extracellular matrix determinants of proteolytic and non-proteolytic cell migration[END_REF][START_REF] Petrie | Activating the nuclear piston mechanism of 3D migration in tumor cells[END_REF]. Moreover, in support of a major role during cancer dissemination, MT1-MMP is linked to malignancy of multiple tumor types including lung, gastric, colon, breast, and cervical carcinomas, gliomas, and melanomas. MT1-MMP is accumulated and spatially restricted to invadopodia that correspond to actinbased plasmalemmal subdomains, which combine membrane protrusive and matrix proteolytic functions to promote cancer cell invasion and metastasis [START_REF] Castro-Castro | Cellular and Molecular Mechanisms of MT1-MMP-Dependent Cancer Cell Invasion[END_REF].

Invadopodia form dynamically in association with constricting matrix fibers and can vary in shape and possibly in composition depending on extracellular matrix topology and components [START_REF] Artym | Dense fibrillar collagen is a potent inducer of invadopodia via a specific signaling network[END_REF].

Nuclear Confinement triggers polarized MT1-MMP/invadopodia-based matrix degradation ahead of the nucleus

Contrasting with gel-like pseudopodial protrusions that can squeeze through narrow pores between matrix fibers, the nucleus has limited deformability (experimentally estimated to be ~10% of original nuclear cross section) [START_REF] Wolf | Physical limits of cell migration: control by ECM space and nuclear deformation and tuning by proteolysis and traction force[END_REF]. When nuclear deformability limit is reached, cell migration physically stops as the nucleus becomes entrapped in the fibrous matrix network [START_REF] Wolf | Physical limits of cell migration: control by ECM space and nuclear deformation and tuning by proteolysis and traction force[END_REF][START_REF] Infante | LINC complex-Lis1 interplay controls MT1-MMP matrix digest-on-demand response for confined tumor cell migration[END_REF]. It is well established that pericellular collagenolysis by matrix metalloproteinases (MMPs) can modulate restricting environmental conditions by widening ECM pores [START_REF] Wolf | Physical limits of cell migration: control by ECM space and nuclear deformation and tuning by proteolysis and traction force[END_REF]. Recent studies demonstrated that MMP inhibition during confined migration of tumor cells in dense collagen environment leads to increased nuclear deformation and mechanical rupture of the NE [START_REF] Wolf | Physical limits of cell migration: control by ECM space and nuclear deformation and tuning by proteolysis and traction force[END_REF][START_REF] Denais | Nuclear envelope rupture and repair during cancer cell migration[END_REF]. However, how mechanical input from the ECM microenvironment triggers the invadopodial response is unknown and of paramount importance in light of data showing that the biomechanical properties of the microenvironment have major impact on cancer progression [START_REF] Kai | Force Matters: Biomechanical Regulation of Cell Invasion and Migration in Disease[END_REF].

Recent work in breast cancer cells revealed that surface exposure of MT1-MMP and pericellular collagenolysis are adaptive responses, which are switched off under low nucleus confinement, while decreased matrix pore size or increased nuclear stiffness trigger the collagenolytic program [START_REF] Infante | LINC complex-Lis1 interplay controls MT1-MMP matrix digest-on-demand response for confined tumor cell migration[END_REF]. MT1-MMP is known to recycle from endolysosomal compartments to invadopodia in metastatic breast cancer cells [START_REF] Castro-Castro | Cellular and Molecular Mechanisms of MT1-MMP-Dependent Cancer Cell Invasion[END_REF]. It was found that MT1-MMP-storage endolysosomal compartments distribute ahead of the nucleus with a centrosome-centered polarization optimal to fuel MT1-MMP delivery to invadopodia forming at the nuclear anterior zone (Figure 1, inset 2) [START_REF] Infante | LINC complex-Lis1 interplay controls MT1-MMP matrix digest-on-demand response for confined tumor cell migration[END_REF].

The polarization of MT1-MMP-secretory compartments and the assembly of functional invadopodia require integrity of nucleo-microtubule linkage depending on the LINC complex and LIS1 functionality (Figure 1, inset 1) [START_REF] Infante | LINC complex-Lis1 interplay controls MT1-MMP matrix digest-on-demand response for confined tumor cell migration[END_REF]. Thus, a working model is that tension generated by dynein motor along the microtubule network through nuclear envelope and cell cortex anchoring, pulls the nucleus forward for movement; extra tension on trapped nucleus through constricting ECM fibrils triggers formation of proteolytically-active invadopodia and dissolution of the confining fibrils to open the way for nucleus migration during confined invasion of tumor cells (Figure 1). This model raises several questions. One question is how migrating cells negotiating changing environments, recognize nucleus-constricting fibers and degrade them, while ECM fibrils involved in integrin-based adhesion and cell movement at the cell front are spared from degradation? One possible mechanism for segregation of specialized degradation and adhesion contact zones is that distinct collagenic receptors selectively trigger assembly of peripheral focal adhesions to mediate traction force generation, and invadopodia, ahead of the nucleus. While beta1 and -3 integrin receptors are classically involved in cell-collagen adhesion, receptors mediating invadopodia formation in association with collagen fibers remain poorly defined and need to be identified. Another conundrum is how mechanical constrains on the nucleus can trigger invadopodia formation and MT1-MMP delivery.

As tumor cells have constantly to adapt to changes in the matrix environment, these responses have to happen on a fast time-scale, too fast for genetic regulation.

Several studies revealed the ability of the nucleus to sense and respond to forces supporting the emerging concept of nuclear mechanotransduction [START_REF] Aureille | Mechanotransduction via the nuclear envelope: a distant reflection of the cell surface[END_REF]. Nuclear mechanosignaling effectors have been recently identified including the nuclear membrane protein emerin, which can contribute to nucleo-centrosome linkage and mediates the response to tensional force applied to the nucleus in relation with LINC complex and LMNA function [START_REF] Aureille | Mechanotransduction via the nuclear envelope: a distant reflection of the cell surface[END_REF]. Therefore, a possible mechanism to be further explored is that nuclear tension and mechanosignaling can control the recycling machinery ensuring MT1-MMP delivery to invadopodia. These observations also highlight the possibility to target the machinery linking nuclear tension with MT1-MMP surface delivery as a new therapeutic road to target cancer metastasis.

BOX 1: Mechanical stress on the nucleus in cancer (200 words max/206 words)

Cells are submitted to compressive forces during physiological and disease conditions. Tumor growth can generate compressive forces due to overgrowth and confinement by the tissue environment. In addition, cancer cells are submitted to elastic deformations of the cell body and bulky nucleus as they invade across interstitial spaces during metastatic spread [START_REF] Wolf | Extracellular matrix determinants of proteolytic and non-proteolytic cell migration[END_REF]. Recent studies reported that extensive nuclear deformation could result in local NE rupture, which can be rapidly repaired [START_REF] Denais | Nuclear envelope rupture and repair during cancer cell migration[END_REF][START_REF] Raab | ESCRT III repairs nuclear envelope ruptures during cell migration to limit DNA damage and cell death[END_REF]. Leakage of nuclear DNA repair factors as well as transient exposure of nuclear DNA to cytoplasmic nucleases such as three-prime repair exonuclease (TREX)1 can lead to DNA damage and double-strand breaks (DSB) as indicated by appearance of foci of DNA damage repair marker γ-H2AX [START_REF] Denais | Nuclear envelope rupture and repair during cancer cell migration[END_REF][START_REF] Raab | ESCRT III repairs nuclear envelope ruptures during cell migration to limit DNA damage and cell death[END_REF][START_REF] Irianto | DNA Damage Follows Repair Factor Depletion and Portends Genome Variation in Cancer Cells after Pore Migration[END_REF]. Sensitivity of tumor cells to mechanical nuclear stress somehow scales with LMNA levels.

Genomic analysis of cancer cell lines following repeated cycles of migration through small microfabricated rigid pores revealed that NE rupture can lead to genomic alterations and chromosomal copy-number changes [START_REF] Irianto | DNA Damage Follows Repair Factor Depletion and Portends Genome Variation in Cancer Cells after Pore Migration[END_REF]. All together, repetitive nuclear rupture could contribute to cancer progression by favoring genomic instability and chromosomal rearrangements, an idea that remains to be experimentally tested.

Acknowledgements

The authors thank Alessia Castagnino and Pedro Monteiro for helpful discussion and Agnieszka Kawska (http://www.IlluScientia.com) for artwork. The authors apologize to all investigators whose work could not be cited due to space constraints. This work was supported by grants from Fondation ARC (PGA1-RF20170205408) and Worldwide Cancer Research (Grant 16-1235) to P.C. and by institutional support from Institut Curie and Centre National pour la Recherche Scientifique (CNRS).

Legend Figure 1: Model of invadopodia-, MT1-MMP-based matrix digest-ondemand response triggered upon nucleus confinement during cancer invasion

Confined migration of tumor cells through dense 3D collagen network results in nucleus confinement by constricting collagen fibrils. Nucleus-microtubule/centrosome linkage and nucleus pulling is mediated by LINC complex interacting with dynein-Lis1 molecular motor (see inset 1). Cortical anchoring of microtubules is required for centrosome and MT1-MMP-positive endosome positioning and for targeted delivery of MT1-MMP to invadopodia. Nucleus movement is facilitated by localized invadopodia-based pericellular proteolysis of confining fibrils ahead of the nucleus (right inset). Left inset, scheme of nucleus-cytoskeletal linkage through LINC complex components nesprin and SUN in association with lamins. Lis1 in complex with dynein associates to the NE depending on Nesprin-2 and is involved in nucleus-microtubule linkage and nucleus pulling (adapted from [START_REF] Infante | LINC complex-Lis1 interplay controls MT1-MMP matrix digest-on-demand response for confined tumor cell migration[END_REF]). Inset 2, model of polarized surfacedelivery of MT1-MMP from recycling endolysosomes (adapted from [START_REF] Castro-Castro | Cellular and Molecular Mechanisms of MT1-MMP-Dependent Cancer Cell Invasion[END_REF]).


Jacques Fontanel

Hypotheses and methodology for the economic analysis of Disarmament

Disarmament and development appear to exert simultaneous relationship, each being at the same time both the cause and the result of the other. Conflicts are not confined to arms production, but also find some expression in economic, political and cultural domination. There are three main forms of disarmament with various economic effects (destruction of military stocks, prohibition of the production of specific weapons, reduction of Military expenditure). Moreover the analysis of the economic determinants of military expenditure is essential in order to understand how to work efficiently with a disarmament process. Finally, what are the main methods for the analysis of the economic effect of a disarmament process (theoretical deductive analysis, mathematical models, simulation, evaluation of structural and reduced forms, Computational General Equilibrium Model, Input-Output analysis, Historical and Case studies)