Edgar Garza-López

Alejandro Sandoval

Ricardo González-Ramírez

María A Gandini

Arn Van Den Maagdenberg

Michel De Waard

Dr Ricardo Felix
email: rfelix@cell.cinvestav.mx

Familial hemiplegic migraine type 1 mutations

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Introduction

Migraine is a disabling neurovascular disorder that affects ~20% of the general population [START_REF] Goadsby | Migraine -Current understanding and treatment[END_REF]. The disease is characterized by recurrent attacks of severe headache and associated autonomic symptoms, such as nausea and vomiting as well as photo-and phonophobia. In about one-third of the patients, the headache is preceded by transient focal neurological symptoms (migraine aura). Although migraine etiology and genetic influences at the population level are unknown, recent genome-wide association studies have identified the first gene variants for migraine. These findings connect a disturbed neuronal glutamate signaling with the pathophysiology of the disease [START_REF] Anttila | Genome-wide association study of migraine implicates a common susceptibility variant on 8q22.1[END_REF][START_REF] Chasman | Genome-wide association study reveals three susceptibility loci for common migraine in the general population[END_REF].

Until now, the molecular insights on migraine pathophysiology came from studies on familial hemiplegic migraine (FHM), a monogenic subtype of migraine with aura. FHM can be considered a model for common migraine, because attacks in FHM patients are very similar to those in the common types, except for a long-lasting hemiparesis during the aura phase [4,[START_REF] Rajakulendran | Neuronal P/Q-type calcium channel dysfunction in inherited disorders of the CNS[END_REF], and also because the FHM patients may exhibit migraine attacks with or without aura. Likewise, in FHM patients the clinical phenotype can also include epilepsy and/or cerebellar abnormalities ranging from nystagmus to progressive mild ataxia [START_REF] Ducros | The clinical spectrum of familial hemiplegic migraine associated with mutations in a neuronal calcium channel[END_REF][START_REF] Vries | Molecular genetics of migraine[END_REF]. Three genes are known to be associated with FHM. Mutations in CACNA1A and SCN1A, encoding the ion-conducting subunits of the neuronal voltage-gated P/Q-type Ca 2+ (Ca V 2.11 1 ) and Na + (Na V 1.1) channels, are responsible for FHM types 1 and 3 (FHM-1; FHM-3), respectively, whereas mutations in ATP1A2, coding the α2 subunit of the Na + -K + ATPase, are responsible for FHM-2 [START_REF] Rajakulendran | Neuronal P/Q-type calcium channel dysfunction in inherited disorders of the CNS[END_REF][START_REF] Vries | Molecular genetics of migraine[END_REF][START_REF] Felix | Calcium channelopathies[END_REF][START_REF] Pietrobon | Familial hemiplegic migraine[END_REF][START_REF] Uchitel | Ca V 2.1 voltage activated calcium channels and synaptic transmission in familial hemiplegic migraine pathogenesis[END_REF].

The functional consequences of 13 of the 21 FHM-1 mutations in the CACNA1A gene have been tested for their consequences on Ca 2+ channel function using electrophysiology in heterologous expression systems [START_REF] Felix | Calcium channelopathies[END_REF][START_REF] Pietrobon | Familial hemiplegic migraine[END_REF][START_REF] Uchitel | Ca V 2.1 voltage activated calcium channels and synaptic transmission in familial hemiplegic migraine pathogenesis[END_REF][START_REF] Pietrobon | Insights into migraine mechanisms and Ca V 2.1 calcium channel function from mouse models of familial hemiplegic migraine[END_REF]. These studies have shown that the mutations alter different properties of the human Ca V 2.1 channel. For instance, an enhanced channel open probability and increased single channel Ca 2+ influx associated to a shift to lower voltages of channel activation has been reported in HEK-293 cells and in Ca V 2.1α 1 null neurons transfected with FHM-1 mutant Ca V 2.1 channels [START_REF] Hans | Functional of mutations in the human α 1A calcium channel subunit linked to familial hemiplegic migraine[END_REF]13]. Likewise, a decreased density of functional channels and a consequent decreased maximal whole-cell Ca 2+ current density has also been reported for many FHM-1 mutants [START_REF] Hans | Functional of mutations in the human α 1A calcium channel subunit linked to familial hemiplegic migraine[END_REF][13][START_REF] Barrett | Gating deficiency in a familial hemiplegic migraine type 1 mutant P/Q-type calcium channel[END_REF]. Investigation of the functional consequences of FHM-1 gene mutations R192Q and S218L in transgenic knock-in mice [START_REF] Van Den Maagdenberg | A Cacna1a knockin migraine mouse model with increased susceptibility to cortical spreading depression[END_REF][START_REF] Van Den Maagdenberg | High cortical spreading depression susceptibility and migraine-associated symptoms in Ca V 2.1 S218L mice[END_REF], revealed increased whole cell current densities, which are in line with single channel measurements, as well as increased cortical glutamatergic neurotransmitter release [START_REF] Tottene | Enhanced excitatory transmission at cortical synapses as the basis for facilitated spreading depression in Ca V 2.1 knockin migraine mice[END_REF], indicating that FHM-1 mutations more likely exert channel gain-of-function [START_REF] Uchitel | Ca V 2.1 voltage activated calcium channels and synaptic transmission in familial hemiplegic migraine pathogenesis[END_REF][START_REF] Pietrobon | Insights into migraine mechanisms and Ca V 2.1 calcium channel function from mouse models of familial hemiplegic migraine[END_REF].

Much less is known, however, regarding the effects of FHM-1 mutations on the modulation of Ca V 2.1 channels by G proteins. Although no FHM-1 mutation has been found in the channel region involved in G-protein binding, initial studies revealed a reduction of Gprotein-mediated channel inhibition by specific FHM-1 mutations [START_REF] Melliti | The familial hemiplegic migraine mutation R192Q reduces G-protein-mediated inhibition of P/Q-type (Ca V 2.1) calcium channels expressed in human embryonic kidney cells[END_REF][19][START_REF] Serra | The hemiplegic migraine-associated Y1245C mutation in CACNA1A results in a gain of channel function due to its effect on the voltage sensor and G-protein-mediated inhibition[END_REF], an effect that may lead to altered Ca 2+ influx through mutant channels during neuromodulation. Here, we studied the functional consequences of two FHM-1 mutations (W1684R and V1696I) located in the fourth repeat domain of the Ca V 2.1α 1 subunit on G-protein-mediated inhibition. Our results show that both mutants might have compromised G-protein coupling.

Materials and Methods

Cell culture, cDNA clones and transfection

Human embryonic kidney (HEK) 293 cells (ATCC, Manassas, VA) were maintained in Dulbecco's modified essential medium-high glucose supplemented with 10% horse serum, 1% Lglutamine, 110 mg/L sodium pyruvate and antibiotics, at 37°C in a 5% CO 2 -95% air humidified atmosphere. Gene transfer was performed using Lipofectamine Plus reagent (Invitrogen, Carlsbad, CA) as described previously [19]. Briefly, for a 35-mm Petri dish of HEK-293 cells, 2 µg of the plasmid cDNA encoding the WT or the mutant variants of the human Ca V 2.1 (P/Qtype) Ca 2+ channel Ca V 2.1α 1 pore-forming subunit splice isoform 1A-2 (GenBank accession number AF004883) [START_REF] Hans | Structural elements in domain IV that influence and pharmacological properties of human α 1A -containing high-voltageactivated calcium channels[END_REF]; in combination with 2 µg cDNA of the rat brain Ca V β 3 (M88751) [START_REF] Castellano | Cloning and expression of a neuronal calcium channel subunit[END_REF]; and 2 µg cDNA coding the WT rat brain Ca V α 2 δ-1b cDNA (M86621) [START_REF] Kim | Rat brain expresses an alternatively spliced form of the dihydropyridine-sensitive L-type calcium channel α 2 subunit[END_REF] were premixed with 6 µL of Lipofectamine in 100 µL serum-free medium according to the manufacturer's instructions.

The solution was then added to the dish and cells grown at 37°C for 24 h, when medium was changed.

FHM-1 mutations were introduced into the human full-length cDNA encoding the Ca V 2.1α 1 subunit of the neuronal Ca V 2.1 (P/Q-type) Ca 2+ channel as previously described [24].

Mutant PCR products harboring either mutation W1684R or V1696I were subcloned into a mammalian expression vector, and sequences were verified by DNA sequencing. The cDNA coding for the human µ-opioid receptor (hMOR; AY521028) was obtained from the UMR cDNA Resource Center www.cdna.org and used as previously reported [19,[START_REF] Weiss | Rim1 modulates direct G-protein regulation of Ca V 2.2 channels[END_REF].

SDS-PAGE and Western blots

Total extracts from transfected HEK-293 cells as well as from mouse brain (used as control), were prepared as described elsewhere [26,[START_REF] Gandini | Functional coupling of Rab3-interacting molecule 1 (RIM1) and L-type Ca 2+ in insulin release[END_REF]. Briefly, cells were harvested, washed twice with PBS and homogenized during 20 min in cold lysis buffer (50 mM Tris-HCl pH 8.0, 150 mM NaCl, 0.5 mM PMSF, 1% of Triton X-100 and 1X complete -Roche Applied Science).

Homogenized samples were clarified by a 12,000 x g centrifugation step for 2 min. The supernatant was stored at -70°C. Aliquots of 100 µg of protein were mixed with sample buffer (50 mM Tris-HCl, 1.7% SDS, 5% glycerol, 0.002% bromophenol blue) and boiled for 5 min.

Samples were subjected to 10% SDS-PAGE electrophoresis and proteins were transferred to a nitrocellulose membrane (Hybond-N; GE Healthcare, Buckinghamshire, UK). After blocking with non-fat milk (5%) in TBS-T (100 mM Tris-HCl, 0.15 M NaCl, 0.05% Tween 20), membranes were incubated overnight with the primary anti-hMOR antibody (Invitrogen; Cat. # 44-308G) 1:1000 in TBS-T with 5% non-fat milk, washed in TBS-T, incubated with horseradish peroxidase goat anti-rabbit secondary antibody and developed with the Immobilon Western Chemiluminescent HRP Substrate (Millipore) according to the manufacturers' instructions.

Electrophysiological recordings

Ionic currents from HEK-293 cells were recorded 48 h after transfection at room temperature (~22°C) using the whole-cell configuration of the patch-clamp technique [START_REF] Hamill | Improved patch-clamp techniques for high-resolution current recording from cells and cell-free membrane patches[END_REF]. Ba 2+ was used as the charge carrier. The extracellular solution contained (in mM): BaCl 2 , 10; TEA-Cl, 125; HEPES, 10; glucose, 10 [pH 7.3]. The intracellular solution contained (in mM): CsCl, 110; MgCl 2 , 5; EGTA, 10; HEPES, 10; Na-ATP, 4; GTP, 0.1 [pH 7.3]. Recordings were performed using an Axopatch 200B amplifier (Axon Instruments, Foster City, CA). Currents were digitized at a sampling rate of 5.7 kHz and filtered at 2 kHz (four-pole Bessel filter). Linear leak and parasitic capacitance components were subtracted on-line using a P/4 protocol. Membrane capacitance (C m ) was determined as previously described [START_REF] Avila | Intramembrane charge movement associated with endogenous K + channel activity in HEK-293 cells[END_REF] and used to normalize currents.

Data analysis

Current-voltage (I-V) relationships were obtained by step depolarization between -50 mV and +70 mV in 10 mV increments, from a holding potential (V h ) of -80 mV.2 To assess steady-state inactivation properties, a 2-s conditioning pulse to various potentials preceded a test depolarization to +10 mV.2 Inactivation curves were fitted with a Boltzmann function

I Ba =I max /(1+exp[(V m -V 1/2 )/k])
, where the current amplitude (I Ba ) has decreased to a half-amplitude at V 1/2 with an e-fold change over k mV. Current remaining was measured from an average of 3 individual sweeps per recording using the equation: I rem =100*(I end /I peak ),2where I rem is the current remaining at the end of a 140-ms test pulse, I end is the value at the end of the test pulse, and I peak is the maximum current measured during the test pulse.2 Time constant (τ) of inactivation was obtained from single exponential fits of I Ba decaying phase using 140-ms test pulse to +10 mV.

The voltage-dependence of I Ba inhibition by the G-protein Gβγ dimer was examined by applying a family of 25-ms pulses to various voltages (between -50 mV and +70 mV in 10 mV steps) 500 ms after (P1) and 5 ms before (P2) a 50-ms conditioning prepulse to +100 mV, from a V h of -80 mV. Facilitation at different voltages was then determined as the ratio I Ba (P2/P1).

Facilitation decay and development (Gβγ reassociation and dissociation to the Ca V 2.1 channel, respectively) was studied as previously reported [START_REF] Melliti | The familial hemiplegic migraine mutation R192Q reduces G-protein-mediated inhibition of P/Q-type (Ca V 2.1) calcium channels expressed in human embryonic kidney cells[END_REF][START_REF] Serra | The hemiplegic migraine-associated Y1245C mutation in CACNA1A results in a gain of channel function due to its effect on the voltage sensor and G-protein-mediated inhibition[END_REF] applying a three-pulse voltage protocol (Fig. 3A). Facilitation decay was estimated applying two 25-ms test pulses (P1 and P2) to +10 mV separated by a conditioning prepulse to +100 mV (PP), and varying the time between PP and P2 (from 5 to 65 ms). Facilitation development was studied using a similar three-pulse voltage protocol varying the duration of the conditioning prepulse (from 5 to 25 ms). Plots of I Ba (P2/P1) as a function of time were fitted to single exponentials in order to obtain the corresponding time constants (τ).

The time constant of dissociation and re-association (τ off and τ on ) were estimated by fitting the data to monoexponential equations of the form: P2/P1=1+I max [1-exp(-2t/τ off )] or P2/P1=1+I max [exp(-2t/τ on )], respectively, where P1 and P2 are the maximum currents before and after the strong depolarizing prepulse, 1+I max is the maximum ratio of facilitation and ∆t is the interpulse duration or prepulse duration, respectively.

Structural modeling of the segments S4 and S5 of domain IV in the Ca V 2.1α 1 subunit

Homology models of transmembrane2 segments IVS4 and IVS5 as well as the S4-S5 linker domain (residues 1653-1710) in the Ca V 2.1α 1 subunit were generated using the Robetta server (http://robetta.bakerlab.org). The structure of the Shaker potassium K V 1.2 channel model [START_REF] Chen | Structure of the full-length Shaker potassium channel Kv1.2 by normal-mode-based X-ray crystallographic refinement[END_REF] was used as a template. Five models were generated and validated using the Stuctural Analysis and Verification Server (http://nihserver.mbi.ucla.edu/SAVES/Info.php) and the model with the best quality parameters was chosen for analysis. Computational methods for assigning partial charges and determining electrostatic potentials were applied using the Swiss-PdbViewer software (http://www.expasy.org/spdbv/). Electrostatic potentials and free energies were obtained by using a method based on the full nonlinear solution of the Poisson-Boltzmann equation [START_REF] Liang | Computation of molecular electrostatics with boundary element methods[END_REF].

Results

The neuronal Ca V 2.1 Ca 2+ (P/Q-type) channel contains a pore-forming Ca V 2.1α 1 (formerly α 1A ) subunit and several regulatory subunits including Ca V α 2 δ and Ca V β. The Ca V 2.1α 1 subunit consists of four repeated domains (I-IV) each containing six transmembrane regions (S1-S6), voltage sensors in S1-S4 and a pore loop between S5 and S6. The two FHM-1 mutations studied here (W1684R and V1696I) are located in conserved regions of the S4-S5 loop of repeated domain IV4 and S5 segment of domain IV, respectively (Fig. 1A). Though seminal work by Müllner and co-workers (2004) revealed that W1684R and V1696I FHM-1 mutations expressed in Xenopus oocytes alter Ca V 2.1 channel gating and these changes depended on the Ca V 3 subunit associated to the channel complex [24], the authors did not addressed the question of mutant-induced changes in G-protein regulation.

We first characterized the impact of W1684R and V1696I FHM-1 mutations on current density and to this end, we transiently expressed Ca V 2.1α 1 channels in HEK-293 cells along with Ca V β 3 and Ca V α 2 δ-1 auxiliary subunits, and whole-cell Ba 2+ currents (I Ba ) were recorded two days after transfection. The presence of the mutations was verified by DNA sequencing (Suppl. Fig. 1). I Ba densities resulting from expression of mutant W1684R and V1696I FHM-1 mutations were decreased in comparison with current density recorded in WT Ca V 2.1 channels (Fig. 1B).

The potential for half-maximal activation was shifted ~5 mV to hyperpolarized potentials for the W1684R mutant channels, without changing the steepness of the I-V curve or the apparent reversal potential (Fig. 2A; open circles). Likewise, the half-maximal voltage for steady-state inactivation induced by conditioning prepulses ranging -110 to +50 mV was right-shifted ~5 mV in both W1684R and V1696I channels (Fig. 1C). Such an effect was accompanied by a significant slowdown in I Ba decay during a 140-ms test pulses evoked from a V h of -80 mV to AB2 2 +10 mV. To quantify this effect, inactivation time constants (4 inact ) were obtained by fitting a single-exponential function to the decaying phases of Ca V 2.1 currents. W1684R and V1696I mutations increased τ inact 12-fold, and in consequence the current remaining at the end of the depolarizing pulse was also significantly increased (Fig. 1D).

Given that leftward shifts in voltage-dependence of activation and slowed inactivation rate have been reported to facilitate recovery from direct G protein regulation [19], we therefore investigated the effects of the W1684R and V1696I FHM-1 mutations on voltage-dependent Gβγ-mediated inhibition of recombinant Ca V 2.1 channels. To this end, recordings were then performed and current amplitude was examined after co-expressing the µ-opioid receptor (hMOR) using [D-Ala2, N-MePhe4, Gly-ol]-enkephalin (DAMGO), a synthetic opioid peptide with high specificity for hMOR. It is well known that hMORs couple to pertussis toxin (PTX)sensitive G i /G o G-proteins to inhibit Ca 2+ channels [START_REF] Bailey | Opioids: cellular mechanisms of tolerance and physical dependence[END_REF].

I Ba was recorded from HEK-293 cells transiently transfected with either WT or FHM-1 mutant channels together with hMOR. Expression of hMOR was examined by Western blot analysis using a commercially available polyclonal antibody raised against a synthetic peptide derived from an internal region of the receptor (see Materials and Methods). Fig. 2A shows that hMOR immunoreactivity was present both in the mouse brain (used as a positive control) and in hMOR-transfected HEK-293 cells. The identity of the labeled protein band as hMOR was confirmed by the expected size of the protein which migrated at an apparent molecular mass of 150 kDa in 10% SDS-PAGE and the absence of staining when HEK-293 cells were mocktransfected.

Functional studies showed that exposure to 10 µM of DAMGO produced a rapid (within 10 s) voltage-dependent inhibition of the current through WT Ca V 2.1α 1 /Ca V β 3 /α 2 δ-1 channels of AA2 2 about 50% (Fig. 2B). The inhibition was also present at the peak I Ba (0 to +10 mV) in both WT and FHM-1 mutant channel expressing cells (Figs. 2C and2D); though DAMGO reduced I Ba only ~20% in cells expressing W1684R or V1696I mutant channels.2As current amplitudes were measured at their peak, these differences may reflect facilitated recovery from G protein inhibition occurring during membrane depolarization, therefore occurring between the start of the depolarization and the time to peak of the current [19].

One key feature of G protein modulation of Ca V channels is its transient relief by a strong depolarizing prepulse. This phenomenon called facilitation is attributed to the dissociation of Gβγ dimers as channels undergo conformational changes in response to depolarization [START_REF] Melliti | The familial hemiplegic migraine mutation R192Q reduces G-protein-mediated inhibition of P/Q-type (Ca V 2.1) calcium channels expressed in human embryonic kidney cells[END_REF][19][START_REF] Serra | The hemiplegic migraine-associated Y1245C mutation in CACNA1A results in a gain of channel function due to its effect on the voltage sensor and G-protein-mediated inhibition[END_REF]. We took advantage of it to explore whether FHM-1 mutations alter the recovery from G protein mediated channel inhibition. Fig. 3B shows current traces through WT or mutant channels recorded during inhibition by DAMGO and elicited by 25-ms test pulses to the indicated potentials before (P1) and after (P2) the prepulse (PP) to +100 mV (Fig. 3A). Co-expression of Ca V 2.1α 1 WT or the FHM-1 mutations together with Ca V β 3 and Ca V α 2 δ-1 subunits in HEK-293 cells resulted in current facilitation (larger P2 than P1 currents following the PP), reflecting the voltage-dependent relief of Gβγ-mediated channel inhibition.

Notably, in the presence of DAMGO the amplitudes of the currents through WT and FHM-1 mutant channels were facilitated at test potentials ranging from -10 to +20 mV (not shown). However, a clear difference in the magnitude of facilitation was observed. Both WT and mutant channels exhibited maximum facilitation at 0 mV, which was 1.58 ± 0.12 for WT, 1.36 ± 0.06 for W1684R and 1.39 ± 0.07 for V1696I channels. The biggest reduction in facilitation was observed at +10 mV. At this potential, facilitation was significantly reduced from 1.47 ± 0.05 in A12 2

the WT condition to 1.11 ± 0.03 and 1.36 ± 0.03 for W1684R and V1696I channels, respectively (Fig. 3C).

The lower level of DAMGO-mediated inhibition observed for the W1684R and V1696I mutant channels (Fig. 2) associated to a smaller extent of facilitation (Fig. 3), is consistent with changes in the Ca V 2.1α 1 subunit that result in alterations in the Gβγ-mediated inhibitory pathway.

It is worth mentioning that one of the major inhibitory pathways controlling Ca V channel activity at the synaptic level is mediated precisely by G-protein coupled receptor activation. In this context, the FHM-1 mutations may contribute to maintain Ca 2+ influx through Ca V 2.1 channels especially during high synaptic activity by promoting channel de-inhibition.

Combined, the two parameters mentioned above reflect either, i) a lower level of Gβγmediated inhibition on the mutant channels, or ii) a facilitated de-inhibition during the test pulse at higher voltages. Therefore, we sought to determine the mechanism underlying this difference.

To this end, we evaluated the time course for re-inhibition (at -80 mV) following facilitatory depolarization (facilitation decay) and for relief from inhibition (at +100 mV; facilitation onset), reflecting the association and dissociation rates of Gβγ dimers to/from the channel,2respectively.

The time constants for the onset and decay of facilitation can be measured by varying the parameters of the three-pulse voltage protocol. To monitor the onset of facilitation, the ratio of current amplitudes measured before and after the prepulse was plotted as a function of the conditioning pulse duration (Figs. 4A and4B). For each cell, facilitation was fitted by a single exponential to obtain a time constant (τ dissociation; Fig. 4C). As can be seen in Fig. 4D, facilitation developed with an averaged time constant of 4.9 ± 0.5 ms for WT, 2.1 ± 0.5 ms and 3.8 ± 1.1 ms for W1684R and V1696I FHM-1 mutant channels, respectively. These results

A32 2

indicate that both FHM-1 mutations favor G protein dissociation from the channel during membrane depolarization.

The decay of facilitation was monitored by plotting the ratio of current amplitudes measured before and after the prepulse as a function of a variable interval between the conditioning prepulse and the second test pulse (Figs. 5A and5B). For each cell, the decay of facilitation was fitted by a single exponential to obtain a time constant (τ re-association; Fig. 5C).

Facilitation decayed with an averaged time constant of 27.8 ± 2.7 ms for WT, 15.2 ± 3.1 ms and 10.5 ± 1.0 ms for W1684R and V1696I channels, respectively (Fig. 5D).

It is well established that the onset and decay of prepulse facilitation during Gβγ-induced inhibition can be represented by a simple two-state model (Fig. 6A) [START_REF] Melliti | The familial hemiplegic migraine mutation R192Q reduces G-protein-mediated inhibition of P/Q-type (Ca V 2.1) calcium channels expressed in human embryonic kidney cells[END_REF][START_REF] Currie | Comparison of N-and P/Q-type voltage-gated calcium channel current inhibition[END_REF][START_REF] Arnot | Differential modulation of N-type 1B and P/Q-type 1A calcium channels by different G protein subunit isoforms[END_REF][START_REF] Cantí | Dolphin Interaction between G proteins and accessory β subunits in the regulation of α1B in Xenopus oocytes[END_REF], where Ca V 2.1α 1 corresponds to the closed state of the channel, k on is the association kinetic constant and k off is the dissociation kinetic constant, both of them likely to have intrinsic voltage dependencies. During a facilitating depolarization to +100 mV, the Gβγ dimers should dissociate from the channels (Fig. 4). If Gβγ subunits do not also rebind channels during the depolarization, then k off can be approximated by 1/τ off . On repolarization to -80 mV, Gβγ dimers should rebind to channels at a rate equal to k on [Gβγ] + k off . If at resting the inhibition of the channels by the Gβγ dimers is strong, as suggested by the results in Fig. 4, then k off should be small, and k on [Gβγ] can be approximated by 1/τ on [START_REF] Meza | G-Protein-dependent facilitation of neuronal α1A, α1B, and α1E Ca channels[END_REF].

Our results revealed that the time constants for Gβγ dissociation were different for WT and W1684R mutant channels (Fig. 4). Although our measurements reflect only the Gβγ association rate to the closed channel and the dissociation rate from the open channel, and do not allow an analysis at intermediate conformational states, the results clearly show that both mutations accelerates Gβγ dissociation from the channel. Hence, the estimated off-rate [k off (s -1 )] A42 2 in our kinetic analysis was ~204 for the WT Ca V 2.1α 1 subunit and ~261 and ~483 for the W1684R and V1696I mutant subunits, respectively, with a relative increase of ~1.3 and 2.4 fold (Fig. 6B). On the other hand, assuming an intracellular concentration of 50 nM for the Gβγ dimer [START_REF] Cantí | Dolphin Interaction between G proteins and accessory β subunits in the regulation of α1B in Xenopus oocytes[END_REF], as well as that the interaction with the channels2occurs to a stoichiometric ratio of 1:1, the estimated on-rate [k on [Gβγ] (s -1 )] was 0.7, 1.3 and 1.9 x 10 9 (M -1 s -1 ) for the WT, the W1684R and the V1691I subunits, respectively. These alterations in kinetics may help explain the apparent reduced voltage-dependent inhibition by G proteins of the Ca V 2.1 mutant channels.

It is worth noting that there was a difference in the K d of Gβγ binding to the FHM-1 (V1696I < WT < W1684R). Though the reason for the difference in the affinity of the Gβγ dimer for the mutant channels is presently unknown, it is tempting to speculate that differences like this might be related to electrostatic potential changes occurring in the channels due to the presence of the mutations. It is well-known that the electrostatic potential plays an important role in many biological processes including folding, conformational stability, enzyme activity and proteinligand or protein-protein interactions [START_REF] Zakharov | Membrane binding of the colicin E1 channel: activity requires an electrostatic interaction of intermediate magnitude[END_REF][START_REF] Schleifer | Molecular modelling investigation of wild-type and the R528H mutated segment IIS4 of human L-type voltage-gated calcium channels[END_REF][START_REF] Hildebrandt | Electrostatic potentials of proteins in water: a structured continuum approach[END_REF].

Given that hydrophobic interactions and electrostatic complementarity are important for high-affinity interactions, we decided to model the segments 4 and 5 of domain IV as well as the cytoplasmic loop connecting these two transmembrane segments in the Ca V 2.1α 1 subunit (where the studied mutations are located) and determine its electrostatic potential. Our analysis showed that the V1696I mutation did not result any change in the electrostatic potential in the region analyzed. However, the electrostatic potential was drastically affected by the W1684R mutation (Fig. 7) due to the substitution of a nonpolar amino acid (tryptophan) for a polar one (arginine).

Interestingly, patients bearing the W1684R mutation, but not the V1696I mutation, have been shown to exhibit cerebellar ataxia as part of their phenotype [START_REF] Ducros | The clinical spectrum of familial hemiplegic migraine associated with mutations in a neuronal calcium channel[END_REF].

A52 2

Discussion

Ca V 2.1 (P/Q-type) channels are abundant in the mammalian brain where they mediate Ca 2+ influx across presynaptic and somatodendritic membranes, thereby triggering neurotransmitter release and other key neuronal responses [START_REF] Evans | Presynaptic Ca 2+ -integration centers for neuronal signaling pathways[END_REF]. Because of its high expression level in the brain, the pore-forming (α 1A ) subunit of the Ca V 2.1 channel was the first representative of its class to be isolated by cDNA cloning [START_REF] Mori | Primary structure and functional expression from complementary DNA of a brain calcium[END_REF]42]. Its importance also comes from the fact that mutations in the Ca V 2.1α 1 subunit can cause neurological diseases such as FHM-1, episodic ataxia type 2 (EA-2) and spinocerebellar ataxia type 6 (SCA-6) [START_REF] Ophoff | Familial hemiplegic migraine and episodic ataxia type-2 are caused by mutations in the Ca 2+ channel gene CACNL1A4[END_REF][START_REF] Zhuchenko | Autosomal dominant cerebellar ataxia (SCA6) associated with small polyglutamine expansions in the α1A-voltagedependent calcium channel[END_REF].

Inhibition of Ca V 2.1 channels by G protein coupled receptors is widespread and is important for controlling neurotransmitter release. The complexity of this protein signaling mechanism is vast and involves distinct pathways that may converge on these channels. Perhaps the most prominent is the so-called voltage-dependent inhibition mediated by direct binding of the G protein βγ dimer to the Ca V 2.1α 1 subunit of the channel [START_REF] De Waard | Campbell Direct binding of G-protein βγ complex to voltage-dependent calcium channels[END_REF][START_REF] Tedford | Direct G protein modulation of Ca V 2 calcium channels[END_REF].2Characteristic features of this modulation mechanism include a reduction in current amplitude, a slowdown in activation kinetics, and the development of prepulse facilitation during G protein regulation. These characteristics have been incorporated into models in which the Ca V 2.1 channels exhibit two functional gating states, "willing" and "reluctant" [START_REF] Tedford | Direct G protein modulation of Ca V 2 calcium channels[END_REF]. The reluctant channels are bound to Gβγ and display the voltage-dependent shifts in channel gating noted above.

Previous functional studies have investigated the response to G protein modulation of three different FHM-1 mutant channels [START_REF] Melliti | The familial hemiplegic migraine mutation R192Q reduces G-protein-mediated inhibition of P/Q-type (Ca V 2.1) calcium channels expressed in human embryonic kidney cells[END_REF][19][START_REF] Serra | The hemiplegic migraine-associated Y1245C mutation in CACNA1A results in a gain of channel function due to its effect on the voltage sensor and G-protein-mediated inhibition[END_REF]. Using recombinant Ca V 2.1 channels expressed in tsA-201 cells along with the dopamine D2 receptor, initial studies showed that the extent of G protein-mediated inhibition and the prepulse facilitation were reduced by the FHM-1 R192Q mutation. Since this mutation did not alter facilitation onset and decay or slow activation, it was A62 2 suggested that the Gβγ-Ca V channel affinity was not affected and that the consequences of the mutation were restricted to allosteric modifications that occurred after the Gβγ dimer bound to the channel [START_REF] Melliti | The familial hemiplegic migraine mutation R192Q reduces G-protein-mediated inhibition of P/Q-type (Ca V 2.1) calcium channels expressed in human embryonic kidney cells[END_REF]. More recently, we determined the functional consequences of, again, FHM-1 R192Q and mutation S218L mutations on G-protein regulation of Ca V 2.1 channels expressed in HEK-293 cells along with human µ-opioid receptors. Our results show that these mutations did not affect association of the Gβγ dimer onto the channel in the closed state but, in contrast to the results previously reported for R192Q, both mutations facilitated Gβγ dissociation from the activated channel, thereby decreasing the inhibitory G-protein pathway [19].2 Similarly, more recently, it has been reported that also FHM-1 mutation Y1245C reduces G protein channel inhibition by favoring the dissociation of the Gβγ dimer from the channel [START_REF] Serra | The hemiplegic migraine-associated Y1245C mutation in CACNA1A results in a gain of channel function due to its effect on the voltage sensor and G-protein-mediated inhibition[END_REF].

Our data provide the first detailed evidence that W1684R and V1696I mutations cause conformational changes in the Ca V 2.1α 1 subunit which result in alterations in the Gβγ-mediated inhibitory pathway. In particular, the results indicate that both FHM-1 mutations favor G protein dissociation from the channel during membrane depolarization. In a physiological context, this effect on G-protein regulation should contribute to render the neuronal network hyperexcitable, possibly as a consequence of reduced presynaptic inhibition, and help explain some aspects of the pathophysiology of FHM-1.

Likewise, studies in heterologous expression systems have shown that FHM-1 mutations may alter channel properties in a complex way, leading to both gain-and loss-of-function [START_REF] Uchitel | Ca V 2.1 voltage activated calcium channels and synaptic transmission in familial hemiplegic migraine pathogenesis[END_REF][START_REF] Pietrobon | Insights into migraine mechanisms and Ca V 2.1 calcium channel function from mouse models of familial hemiplegic migraine[END_REF][START_REF] Van Den Maagdenberg | Migraine: gene mutations and functional consequences[END_REF]. Our data suggest that the FHM-1 mutations W1684R and V1696I may influence Ca V 2.1 channels by affecting the dissociation of the Gβγ dimer. Although, a reduced channel density was observed in our data that could qualify as a possible mechanism (Fig. 1B), there is general consensus that a reduction of current density is more likely due to the method of A72 2 heterologous expression given that no current reduction is observed when FHM-1 mutations are expressed in more physiological environment, i.e. in knock-in mouse mutants [START_REF] Van Den Maagdenberg | A Cacna1a knockin migraine mouse model with increased susceptibility to cortical spreading depression[END_REF][START_REF] Van Den Maagdenberg | High cortical spreading depression susceptibility and migraine-associated symptoms in Ca V 2.1 S218L mice[END_REF]. Also the evidence that a reduction of mutant Ca V 2.1 expression results in EA-2, not FHM-1, would be in line with this. Last, is not entirely clear how alterations associated with FHM-1 mutations play a role in the pathogenesis of the disease, but a favored hypothesis considers neuronal hyperexcitability in the cerebral cortex as the basis for susceptibility to disease [50]. Although the effects of the W1684R and V1696I mutations on overall neuronal excitability is difficult to predict, an increased postsynaptic excitability might result from this gain-of-function variants of presynaptic channels controlling release of excitatory neurotransmitters. Hence, in addition to altered response to direct G-protein regulation, it is possible that the mutations might interfere also with other molecular signaling important for neurotransmitter vesicle release. Though the two FHM-1 mutations reported here are located in conserved regions of the Cav2.1α 1 subunit (Fig. 1A) where no interaction sites with proteins of the exocytotic machinery has been reported, the possibility exists, that the altered responses of the mutant channels to G-protein regulation could result from inappropriate indirect interactions with such proteins. This is an interesting topic for future studies.

[50] N. Weiss, E. Tournier-Lasserve, M. De Waard, Role of P/Q calcium channel in familial hemiplegic migraine. Med Sci (Paris) 23 (2007) 53-63.

Fig. 1 .

 1 Fig. 1.2FHM-1 mutations W1684R and V1696I may affect recombinant Ca V 2.1 channel activity

Fig. 2 .

 2 Fig. 2. Receptor-mediated G-protein regulation of WT and FHM-1 W1684R and V1696I mutant2

Fig. 3 .

 3 Fig. 3. FHM-1 mutations W1684R and V1696I alter G protein-mediated channel regulation. A:

Fig. 4 Fig. 5 .

 45 Fig. 4.2 FHM-1 mutations W1684R and V1696I accelerate the apparent rate of G protein

Fig. 6 . 2

 62 Fig.6. FHM-1 mutations W1684R and V1696I alter the kinetics of prepulse facilitation. A:

Acknowledgements

We gratefully appreciate the technical expertise of G. Aguilar and M. Urbán. This work was supported in part by grants from Conacyt to R.F. ( 128707) and PAPIIT to A.S. (IN221011). Doctoral and Postdoctoral fellowships from Conacyt to E.G.L., M.A.G. and R.G.R. are gratefully acknowledged. The authors would like to thank the two anonymous reviewers for their helpful comments and suggestions. A92


Jorge Rios-Martinez

Arturo Escobedo

Anne Spalanzani

Christian Laugier

Intention Driven Human Aware Navigation for Assisted Mobility

Keywords: Proxemics, Human aware navigation, User intention, Adapted control

Ensuring proper living conditions for an ever growing number of elderly people is an important challenge for many countries. The difficulty and cost of hiring and training specialized personnel has fostered research in assistive robotics as a viable alternative. In particular, this paper studies the case of a robotic wheelchair, specifically its autonomous navigation and user adapted control. Integration of a technique to interpret user intention using head movements and a human aware motion planner is presented. Test results exhibit emerging behavior showing a robotic wheelchair interpreting gesture commands and taking the user to his desired goal, respecting social conventions during its navigation.

I. INTRODUCTION

Ensuring proper living conditions for an ever growing number of elderly people is a significant challenge for many countries. The difficulty and cost of hiring and training specialized personnel has fostered research in assistive robotics as a viable alternative. In this context, an ideally suited and very relevant application is to transport people with reduced mobility as it can help them to preserve their independence. For such systems, it is crucial to take into account the actual needs and characteristics of both its users and the people around them. This paper studies the case of a robotic wheelchair, specifically its autonomous navigation and user adapted control, whose operation has been designed around the following requirements:

• Usability: People with motor disabilities or aging people often have problems using joysticks and other standard control devices. The system should account for this, for example by favoring the most reasonable actions when presented with an ambiguous command.

• Safety: The system should avoid collisions with both static and dynamic entities. • Sociability: When moving, a robot may considerably disturb people around it, especially when its behavior is perceived as unsocial. Even worse, the wheelchairs passenger may be held responsible for that behavior. It is thus important to produce socially acceptable motion. Social capability of planner chosen is based on the simple idea that, in a human populated environment, when people interact, they often adopt spatial formations implicitly forming "interaction zones". Thus, socially acceptable motion can † {jorge.rios-martinez, jesus.escobedo-cabello, anne.spalanzani, christian.laugier}@inria.fr Jorge Rios-Martinez has been partially funded by CONACYT 250140/308006. be enforced not only by respecting personal space but also by detecting interaction zones and then computing the risk to invade them.

Usability can be improved by adding contextual information in order to ease interaction with the user, for example, the knowledge of interesting or frequently visited locations in a particular environment can be used by the system to infer the user's plan. Once the plan is identified the system can assist the user by executing the low level needed commands. The structure of this paper is as follows:

Section II offers an overview of related works. Section III presents our technique for achieving user adapted control. Section IV describes the RiskRRT method. In section V examples of execution on our real platform are exhibited. Section VI presents conclusions about the work and perspectives.

II. RELATED WORK

A. Semi-Autonomous Navigation

In latest years many efforts have been made to develop robotic wheelchairs that operate in a similar manner to an autonomous robot, where the user gives a final destination and supervises as the smart wheelchair moves (e.g.,NavChair [START_REF] Levine | The NavChair Assistive Wheelchair Navigation System[END_REF], MIT Media Lab wheelchair [START_REF] Kollar | Grounding Verbs of Motion in Natural Language Commands to Robots[END_REF]).

Other smart wheelchairs limit their assistance to collision avoidance and leave the majority of planning and navigation duties to the user. These systems do not normally require prior knowledge of an area or any specific alterations to the environment. They require instead more planning and continuous effort on the part of the user and are only appropriate for users who can effectively plan and execute a path to a destination.

Shared control is presented in situations in which the assisting device combines the control input coming from the robot and the user. This device may be a wheelchair, a teleoperated robot, a robotic travel aid for the visually impaired, or any other device where robot and human cooperate in a task [START_REF] Demeester | Assessing the user's intent using bayes' rule: application to wheelchair control[END_REF].

The estimation of the user's plan is a key point in many shared control tasks because it allows to the automatic controller/robot to adequate its actions to the desire of its user. Inferring the user plan is necessary whenever the interface with the user doesn't allow him to explicitly dictate this to the robot as with many popular electric wheelchair interfaces. Some methods aiming the implicit estimation of the users intention from simple joystick inputs have been proposed in [START_REF] Demeester | Assessing the user's intent using bayes' rule: application to wheelchair control[END_REF], [START_REF] Demeester | Bayesian Estimation of Wheelchair Driver Intents: Modeling Intents as Geometric Paths Tracked by the Driver[END_REF]. They model the users intent as possible trajectories to follow, then a probability distribution is maintained over the set of trajectories and finally the selection of the most probable one is done using the input from the user within a Bayesian framework.

In [START_REF] Taha | POMDP-based long-term user intention prediction for wheelchair navigation[END_REF] a learned Partially Observable Markov Decision Process (POMDP) is used to estimate the intended destination into a predefined map of the environment in a high level topological manner. This means that the user focuses on driving the wheelchair from one spatial location to another without having to worry about all the low level control. Places of interest are selected as spatial locations in the environment where the user spends significantly most of his time.

The method presented in this article to infer the user's intended goal aims to build a model as simple as possible combining the Bayesian network approach of the first mentioned methods and the simple topological goal based representation of the environment used in the second one. A more natural human-machine interface based on a face tracking system is used to command the wheelchair (III-A) while the navigation is performed using a human aware planning algorithm (IV).

B. Human Aware Navigation

Human aware navigation is receiving an increasing attention in robotics community, this area of research appears once that robots navigate in human environments and safety solutions are not enough; now the main concern is related to produce solutions which also have to be understandable and acceptable by human beings. Next is a review of related works. A proposal of human aware navigation was presented in [START_REF] Sisbot | A human aware mobile robot motion planner[END_REF], where a motion planner takes explicitly into account its human partners. The authors introduced the criterion of visibility, which is simply based on the idea that the comfort increases when the robot is in the field of view of a person. Other work, [START_REF] Hansen | Adaptive human aware navigation based on motion pattern analysis[END_REF], introduced an adaptive system which detects whether a person seeks to interact with the robot based on the person's pose and position, that system was presented as a basis for human aware navigation. Their results showed that the system was capable of navigate based in past interaction experiences and to adapt to different behaviors.

In [START_REF] Chung | A mobile robot that understands pedestrian spatial behaviors[END_REF] it was proposed a Spatial Behavior Cognition Model (SBCM) to describe the spatial effects existing between human-human and human-environment. SBCM was used to learn and predict behaviors of pedestrians in a particular environment and to help a service robot to take navigation decisions. Technique in [START_REF] Sehestedt | Robot path planning in a social context[END_REF] proposed an on-line method to learn generally occurring motion patterns in an office environment with a mobile robot. Navigation is realized by using these patterns, in form of sampled HMM, along with a Probabilistic Roadmap based path planning algorithm. Socially acceptable motion is achieved by minimizing social distractions, such as going through someone else's working space.

The work presented in [START_REF] Lam | Human-centered robot navigation, towards a harmoniously human-robot coexisting environment[END_REF] proposed rules that a single robot should obey in order to achieve not only a safe but also a least disturbance motion in a human-robot environment. Rules define sensitive zones for both humans and robots, depending either on their security regions or on psychological feeling of humans.

Personal space, o-space and their relation to comfort were addressed in [START_REF] Rios-Martinez | Understanding human interaction for probabilistic autonomous navigation using Risk-RRT approach[END_REF], where a risk based navigation was extended to include risk due to discomfort. Human's movement is supposed to be known by learning of typical trajectories in a particular environment. Optimization techniques that take into account social factors have been also proposed.

In [START_REF] Kirby | Companion: A constraintoptimizing method for person acceptable navigation[END_REF] a generalized framework for representing social conventions as components of a constrained optimization problem was presented and it was used for path planning, their results exhibited a more social navigation. In [START_REF] Rios-Martinez | Navigating between people: A stochastic optimization approach[END_REF] an stochastic adaptive optimization method was used to minimize discomfort of humans in the environment, while robot navigate to the goal. Results show robot navigation respecting both information process space and personal space of people. Recently, legibility of robot navigation around humans was explored in [START_REF] Kruse | Legible robot navigation in the proximity of moving humans[END_REF]. A context depending cost model was developed to adjust robot behavior to human behavior in crossing scenarios.

III. SEMI AUTONOMOUS CONTROLLER

A. Face Control Subsystem

The user controls the robotic wheelchair by using the movements of his head, this is accomplished by means of a face tracking system that estimates the direction of the sight of the user using data from a Microsoft's Kinect c . The images taken by the 2D RGB camera are used to set up a region of interest over the depth data coming from the infrared sensor.

The face of the user is detected using a typical Haar detector then a set of SWIFT features are selected over the face and 2D tracking is performed using the Lucas-Kanade method as described in [START_REF]Pi face tracker webpage[END_REF]. The identification of the face pose is done by a random forest classifier which takes as input the 3D data from the Kinect sensor and gives the estimated position of the face [START_REF] Fanelli | Real time head pose estimation with random regression forests[END_REF], the results of the face tracking are shown in figure 1.

B. User Intentions Estimation System

The user intentions are modeled as topological poses into a predefined map. Those locations are set by the user's habits (those places where the user spends most of his time are taken into account as probable goals) also interesting points taken from the map of the environment as doors, desks and other facilities are taken into account as probable destinations.

The reasoning method used is based on a Bayesian Network depicted in figure 2 that combines the information taken from the user interface input with the prior knowledge of the environment to infer a posterior probability distribution over the set of possible goals in the environment. This probabilistic model aims to take into account the uncertainty in the estimation of the desired goal and the inherent error over the user command read from the face tracking system.

To estimate the status of the goal variable, the command direction coming from the user-machine interface and the current user's position are applied as evidence. The posterior probability of the current goal given the position of the user and the direction of the command is expressed as P (G i t |C t X t ). The prior probability over each goal in the environment is denoted as P (G i t |X t ). Using Bayes' rule:

P (G i t |C t X t )) = P (C t |X t , G i t )P (G i t |X t ) P (C t |X t (1)
This can be simplified by using the normalizer η.

P (G i t |C t X t )) = ηP (C t |X t , G i t )P (G i t |X t ) (2)
We assume that the direction of the command given by the user C t depends on the current position X t and the intended goal G i t . Therefore this probability should be higher for goals that are in the direction of the current command input as shown in figure 3. P (C t |X t , G i t ) represents the probability of giving a command C t when the user is located at position X t and her goal is at position G i t at current time t. The notation G i t is used to express G t = g i where g i is one of the predefined goals in the environment as appear in Fig. 3.

P ′ (C t |X t , G i t ) = 1 -|a i | π (3)
Where a i term is the angle between both command and goal directions. The we normalize it as:

P (C t |X t , G i t ) = P ′ (C t |X t , G i t ) i P ′ (C t |X t , G i t ) (4)
The prior probability table P (G i t |X t ) was set manually for our current experimental set-up taking into account the user's habits. However, for a real-environment it is mandatory to learn its values autonomously using some machine learning method.

IV. RISKRRT APPROACH

A. Planner main loop

Our planner is based on RiskRRT [START_REF] Fulgenzi | Probabilistic motion planning among moving obstacles following typical motion patterns[END_REF], a partial motion planner which integrates motion predictions to provide safe trajectories. At each loop the algorithm checks if a new goal is available. When a new goal is received, RiskRRT collects information about the static obstacles and humans' position in the environment. Then a prediction of pedestrians trajectories takes place. At this moment RiskRRT has enough information to proceed with the exploration of the environment by means of a Rapidly-Exploring Random Tree which is constantly updated with the new perceived data. New nodes are created by selecting possible compliant controls that conduct the robot towards randomly selected points. The process of exploration has a depth threshold for the nodes and limited time in order to achieve real time performance. A probability of collision is assigned to each node taking into account static obstacles and human predicted trajectories. Finally, a best path is selected by choosing the branch with the lowest probability of collision and with the closest distance to goal. It is important to mention that RiskRRT generated paths include information about space, time and robot dynamics which is very important advantage to navigate in dynamic environments. In the fig. 4 planner execution at two distinct iterations can be observed. Tree shows the portion of the environment already explored. Nodes are represented by colored spheres, their color represents the time at which they would be reached by the robot, same interpretation is done for color in predicted trajectories of humans. Size of nodes represents the estimated risk, therefore a node very close to a predicted pedestrian position of the same color will have a big size.

This method has been extended by including a mechanism to obtain socially acceptable behavior which is explained in next section. One goal (blue arrow) has been passed to the wheelchair (R), while two people (A,B) are walking around. In a) partial path solution was found (red line) avoiding high risk zones identified in the image by the bigger size of nodes. Wheelchair is deliberately not moving then, after some instants, new observations and predictions produce different risk estimation and permits to select a better path.

B. Social conventions in human navigation

When the wheelchair is transporting a human, it will have to move in a populated environment where an "optimal" behavior may be perceived as unsocial. People will become uncomfortable if they are approached at a distance that is deemed to be too close, where the level of discomfort experienced by the person is related to the importance of his or her space. This simple idea was formalized introducing the concept of personal space, first proposed by Hall [START_REF] Hall | The hidden Dimension: Man's Use of Space in Public and Private[END_REF], which characterizes the space around a human being in terms of comfort to social activity.

Another interesting social situation arises when two or more of the persons in the environment are interacting. We model interactions using the concept of o-space which has been developed by sociologists [START_REF] Kendon | Spacing and orientation in co-present interaction[END_REF]. This space can be observed in casual conversations among people where participants' position and orientation are used to establish boundaries of the space. This space is respected by other people and only participants are allowed to access to it, therefore the intrusion of a stranger causes discomfort. In our path planner, human friendly paths are generated by including a module called "Social Filter" which transforms those spaces into corresponding cost functions which lead the robot to avoid them. As a result, the choice of a best path done by RiskRRT is done by considering the probability of not encountering a collision along the path and not entering in a personal space or an o-space. Detailed explanation can be found in [START_REF] Rios-Martinez | Understanding human interaction for probabilistic autonomous navigation using Risk-RRT approach[END_REF].

1) Modeling Personal Space: We have modeled personal space as a composition of two human centered Gaussians, one for the front and one for the back of the space, the front is larger as people is more sensitive to this space. Fig. 5 shows an example of personal space as provided by the Social Filter. 2) Modeling o-Space: When more than two people are in conversation, they tend to make a formation with circular shape. The o-space could be taken as a circle whose center coincides with that of the inner space. For the specific case of two people, some formations, called F-formations, have been identified as being particularly frequent [START_REF] Kendon | Spacing and orientation in co-present interaction[END_REF]. The social filter identifies individual F-formations (Vis-a-vis, L-Shape, C-Shape or V-Shape) and builds the corresponding o-space. in Fig. 6, the calculated o-space for a Vis-a-Vis interaction is shown.

C. Planning under social constraints

This section explains how the social constraints are included in the RiskRRT framework, see [START_REF] Rios-Martinez | Understanding human interaction for probabilistic autonomous navigation using Risk-RRT approach[END_REF], [START_REF] Fulgenzi | Probabilistic motion planning among moving obstacles following typical motion patterns[END_REF] for specific details. First we define P Z i as the probability of disturbing by passing inside the o-space (sec. IV-B.2) of interaction i, and we calculate it as the maximum value of o-space model for that interaction evaluated in the intersection with the robot's path. P Z i can be thought as a collision with a dynamic obstacle:

P cd = 1 - M m=1 [1 -P cd (o m )] r i=1 [1 -P Z i ] (5)
where P cd is the probability of dynamic collision considering the M humans in the environment and P cd (o m ) is the probability of collision with the human o m taking into account the personal space. P ps (o m ) is the risk of disturbing by passing in such personal space and can be approximated as the probability that A, the area swept by the robot's path, intercepts the one represented by the personal space:

P ps (o m ) = A P S(o m (t)) (6)
where P S(o m (t)) is the model of personal space centered in o m (t) at time t as described in IV-B.1. To take into account this last constraint we use:

P cd (o m ) = P dyn (o m ) + P ps (o m )(1 -P dyn (o m )) (7)
where P dyn (o m ) is the probability of dynamic collision between the robot and o m considering only their trajectories. Last, total probability of collision, collP is calculated for each node using:

collP = P cs + (1. -P cs ) * P cd ; (8)
Finally, also for each node we calculate a weight based on probability of collision and distance to goal. In order to compare paths worst node weight is chosen to represent a particular path.

D. Simulation results

In order to test socially acceptable behavior, we conducted several simulation tests. Our first test scenario consisted of two people in the same corridor together with the wheelchair whose task is to navigate towards the goal. We realized one hundred executions of the planner in very similar conditions, as it can be seen in Fig. 7, when the social filter is turned on, all the plans managed to respect both personal space and interaction space without disturbing the involved people. We can observe that because of the random exploration of the environment some executions (almost ten percent) select as best path one that stops before to invade social space. Tests with the social filter off showed that thirty percent of plans passed in the middle of an interaction.

V. INTEGRATION AND EVALUATION

Integration was done by using the semi-autonomous controller presented in sec. III as the source of the goals for the RiskRRT planner. Solution plans are executed in our experimental platform, details follow.

A. Experimental Platform

Our platform, is an automated wheelchair (Fig. 8(a)) equipped with one Sick laser and two Microsoft Kinect, running ROS (Robotic Operating System) for achieving semi-autonomously mobility actions commanded by the wheelchair's user. Laser permits us to build a map of the environment, like shown on Fig. 8(c). Data coming from the upper Kinect allow us to have position and orientation of pedestrians in the scene while data from frontal Kinect collect face features to feed our intention recognizer algorithm.

B. Evaluation in a real scenario

The system was evaluated at scenario shown in Fig. 8(b). User can start the movement at any location of the experi-mental scenario, he is asked to drive the wheelchair by seeing towards his desired destination. In the example, the user is seeing to the left so that it is more probable that he is aiming to go to the coaches located in that direction. The direction of his face is computed as previously explained in section III-A. Typical destinations were defined into the map, they are marked with small arrows in Fig. 8(b).

Whenever a new command is read from the face control, the user estimation module computes the goal with the highest posterior probability, depicted in Fig. 8(c) as the size of the sphere marking each goal, then it is sent to the navigation module to start the movement.

The navigation module receives the map of the environment, the currently computed goal and the list of people present in the field of view of the frontal viewing Kinect to compute the necessary trajectory to the goal as shown in Fig. 8(c). In the example there are two persons in conversation, standing in the middle of the path between the wheelchair and the current estimated goal. Even if the user is pointing to the goal located in the other side of the two persons he does not have to worry about the necessary planning and commands to avoid interrupting the conversation because the autonomous navigation system is in charge of that.

VI. CONCLUSIONS AND FUTURE WORK

The approach presented in this paper has integrated a human aware motion planner and a semi-autonomous controller adapted to the user with the aim to preserve independence of people with reduced mobility. The system was designed to improve both usability by reasoning about user intentions and sociability by including concepts like personal space and o-space in the planning algorithm. Experiments with a real wheelchair show that integration has been successfully achieved. The user intention algorithm has proved to be useful to translate simple input commands into high level orders or goals for our autonomous navigation system. Using the pose of the face as input can be advantageous to assist the elderly because it provides a more natural way of interaction (we usually see where we are going) so they can be more confident when using the wheelchair. In this work we explored the use of head direction to infer the user desired destination in a navigation task. The system is capable of estimating the desired goal among a set of interesting points and to transport the user to it while avoiding humans in a social way. Current work will be extended in two directions. First, by including as interesting points positions where the user should be located when he wants to join a group of people. Second, by adapting autonomously the user intention algorithm to user disability. Moreover other user-machine interfaces, like voice based, will be included to minimize ambiguities like that of the movements of the head that are intended to give a navigation command from those resulting from the natural observation of the environment.

Fig. 1 .

 1 Fig. 1. In the presented approach the user drives the wheelchair by using his face. The face of the user is tracked by processing the RGB image received from a Kinect sensor (left image). The pose of the face is estimated from the depth data as shown in the right.

Fig. 2 .

 2 Fig. 2. The Bayesian network used to estimate the hidden user intention or goal G by knowing the current position X and the user command C.

Fig. 3 .

 3 Fig. 3. The probability distribution for a given command Ct (big arrow) is proportional to the angle a i formed with respect to each goal g i in the environment.

Fig. 4 .

 4 Fig. 4. Example of execution for the RiskRRT at two distinct iterations.One goal (blue arrow) has been passed to the wheelchair (R), while two people (A,B) are walking around. In a) partial path solution was found (red line) avoiding high risk zones identified in the image by the bigger size of nodes. Wheelchair is deliberately not moving then, after some instants, new observations and predictions produce different risk estimation and permits to select a better path.

Fig. 5 .

 5 Fig. 5. Personal space calculated by Social Filter Module. Height of the Gaussian means Risk of disturbance then maximum disturbance is located at human position.

Fig. 6 .

 6 Fig. 6. O-space calculated by Social Filter Module for a Vis-a-Vis Fformation. Maximum risk of disturbance is located at o-space center, in the picture the disturbance is represented by height of Gaussian.

Fig. 7 .

 7 Fig. 7. Socially acceptable navigation in RiskRRT. Each figure shows a sample of generated plans (in red) for one hundred executions of RiskRRT, each execution run for twenty iterations of the algorithm. Goal is the blue arrow. In a) static persons are looking towards walls, therefore there is no social interacting zone, then navigation respects only their personal spaces. In b) both social spaces are respected.

Fig. 8 .

 8 Fig. 8. Experimental scenario, in a) The wheelchair used for testing in b) the INRIA's hall. Possible goals are marked with a circle, the persons present in the scene are tracked by one of the Kinect sensors while the other Kinect is used to track the face of the user. c)Results of the system in a real scenario. The size of the spheres in the environment represent the value of the computed posterior probability for each destination. The computed trajectory and interaction regions are also shown.