PhD Jérôme Montnach

PhD Isabelle Baró

PhD Flavien Charpentier

PhD Michel De Waard

PhD Gildas Loussouarn
email: gildas.loussouarn@inserm.fr

Modeling sudden cardiac death risks factors in COVID-19 patients -the hydroxychloroquine and azithromycin case

Keywords: COVID-19, QT duration, arrhythmia, predictive model, asymptomatic

Aims. Coronavirus disease of 2019 has rapidly become a worldwide pandemic.

Many clinical trials have been initiated to fight the disease. Among those, hydroxychloroquine and azithromycin had initially been suggested to improve clinical outcomes. Despite any demonstrated beneficial effects, they are still in use in some countries but have been reported to prolong the QT interval and induce life-threatening arrhythmia. Since a significant proportion of the world population may be treated with such COVID-19 therapies, evaluation of the arrhythmogenic risk of any candidate drug is needed.

Methods

Using the O'Hara-Rudy computer model of human ventricular wedge, we evaluate the arrhythmogenic potential of clinical factors that can further alter repolarization in COVID-19 patients in addition to HCQ and AZM such as tachycardia, hypokalemia, and subclinical to mild long QT syndrome.

Results. HCQ and AZM drugs have little impact on QT duration and do not induce any substrate prone to arrhythmia in COVID-19 patients with normal cardiac repolarization reserve. Nevertheless, in every tested condition in which this reserve is reduced, the model predicts larger ECG impairments, as with dofetilide. In subclinical conditions, the model suggests that mexiletine limits the deleterious effects of AZM and HCQ.

Conclusion.

By studying the HCQ and AZM co-administration case, we show that the easyto-use ORd model can be applied to assess the QT-prolongation potential of off-label drugs, beyond HCQ and AZM, in different conditions representative of COVID-19 patients and to evaluate the potential impact of additional drug used to limit the arrhythmogenic risk.

Introduction

The coronavirus disease of 2019 (COVID-19) caused by the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2), and first identified in Wuhan, China, in December 2019, has rapidly become a global pandemic, with more than 69.5 million confirmed cases and over 1,580,000 deaths on December 12, 2020 (WHO COVID-19 Dashboard). The high transmission rate of the virus and the lack of collective immunization and therapy have made it a threat to public health, despite its low morbidity in a large part of the population [START_REF] Chan | A familial cluster of pneumonia associated with the 2019 novel coronavirus indicating person-to-person transmission: a study of a family cluster[END_REF]. Preexisting cardiovascular disease, including cardiac arrhythmias, is associated with a prognosis worsening [START_REF] Hulot | COVID-19 in patients with cardiovascular diseases[END_REF][START_REF] Wang | Clinical Characteristics of 138 Hospitalized Patients With 2019 Novel Coronavirus-Infected Pneumonia in Wuhan, China[END_REF][START_REF] Mehra | Cardiovascular Disease, Drug Therapy, and Mortality in Covid-19[END_REF][START_REF] Izcovich | Prognostic factors for severity and mortality in patients infected with COVID-19: A systematic review[END_REF]. Arrhythmias were reported in 17% of patients affected by COVID-19 and this percentage reaches 44% for patients in intensive care unit (ICU) [START_REF] Hulot | COVID-19 in patients with cardiovascular diseases[END_REF][START_REF] Wang | Clinical Characteristics of 138 Hospitalized Patients With 2019 Novel Coronavirus-Infected Pneumonia in Wuhan, China[END_REF][START_REF] Mehra | Cardiovascular Disease, Drug Therapy, and Mortality in Covid-19[END_REF]. In absence of approved drugs to prevent or treat COVID-19, many clinical trials have been initiated to test the efficiency of drugs already approved for other diseases on this new pathology. Among those, more than 260 focused on hydroxychloroquine (HCQ) (clinicaltrials.gov), a chloroquine (CQ) derivative historically used to treat malaria and autoimmune diseases [START_REF] Ben-Zvi | Hydroxychloroquine: from malaria to autoimmunity[END_REF]. HCQ has shown potent in vitro activity against both SARS-CoV-1 and SARS-CoV-2 [START_REF] Wang | Remdesivir and chloroquine effectively inhibit the recently emerged novel coronavirus (2019-nCoV) in vitro[END_REF][START_REF] Biot | Design and synthesis of hydroxyferroquine derivatives with antimalarial and antiviral activities[END_REF][START_REF] Yao | In Vitro Antiviral Activity and Projection of Optimized Dosing Design of Hydroxychloroquine for the Treatment of Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2)[END_REF]. Two small, non-randomized, open-label clinical trials in France, suggested that the combination of HCQ and azithromycin (AZM) drugs may reduce the viral load of infected patients and improve clinical outcomes [START_REF] Gautret | Hydroxychloroquine and azithromycin as a treatment of COVID-19: results of an open-label non-randomized clinical trial[END_REF][START_REF] Gautret | Clinical and microbiological effect of a combination of hydroxychloroquine and azithromycin in 80 COVID-19 patients with at least a six-day follow up: A pilot observational study[END_REF]. Despite accumulation of studies questioning the clinical efficacy of HCQ, the topic remains highly debated [START_REF] Uzunova | Insights into antiviral mechanisms of remdesivir, lopinavir/ritonavir and chloroquine/hydroxychloroquine affecting the new SARS-CoV-2[END_REF][START_REF] Prodromos | Hydroxychloroquine is protective to the heart, not Harmful: A systematic review. New microbes and new infections[END_REF][START_REF] Ong | Effects of Antimalarial Drugs on Neuroinflammation-Potential Use for Treatment of COVID-19-Related Neurologic Complications[END_REF][START_REF] Oldenburg | Azithromycin for severe COVID-19[END_REF][START_REF] Albani | Impact of Azithromycin and/or Hydroxychloroquine on Hospital Mortality in COVID-19[END_REF][START_REF] Peng | Systematic Review and Pharmacological Considerations for Chloroquine and Its Analogs in the Treatment for COVID-19[END_REF].

HCQ has been occasionally reported to prolong the QT interval on surface ECG and provoke torsades de pointes (TdP), a life-threatening arrhythmia [START_REF] O'laughlin | Life Threatening Severe QTc Prolongation in Patient with Systemic Lupus Erythematosus due to Hydroxychloroquine[END_REF][START_REF] Morgan | Suspected hydroxychloroquine-associated QTinterval prolongation in a patient with systemic lupus erythematosus[END_REF][START_REF] De Olano | Toxicokinetics of hydroxychloroquine following a massive overdose[END_REF][START_REF] Chen | Chronic hydroxychloroquine use associated with QT prolongation and refractory ventricular arrhythmia[END_REF][START_REF] Oscanoa | Frequency of Long QT in Patients with SARS-CoV-2 Infection Treated with Hydroxychloroquine: A Meta-analysis[END_REF]. AZM has been developed for the treatment of respiratory tract infections [START_REF] Owens | Antimicrobial-associated QT interval prolongation: pointes of interest[END_REF][START_REF] Kowey | Discarding the baby with the bathwater[END_REF][START_REF] Huang | Azithromycin-induced torsade de pointes. Pacing and clinical electrophysiology[END_REF] because the related macrolide, erythromycin, induced prolonged QT intervals and TdP. Nevertheless, AZM has been occasionally reported as a triggering factor of QT prolongation [START_REF] Sears | Incidence of Sustained Ventricular Tachycardia in Patients with Prolonged QTc After the Administration of Azithromycin: A Retrospective Study[END_REF][START_REF] Yang | Azithromycin Causes a Novel Proarrhythmic Syndrome[END_REF], arrhythmias [START_REF] Huang | Azithromycin-induced torsade de pointes. Pacing and clinical electrophysiology[END_REF][START_REF] Tilelli | Life-threatening bradyarrhythmia after massive azithromycin overdose[END_REF][START_REF] Kezerashvili | Azithromycin as a cause of QT-interval prolongation and torsade de pointes in the absence of other known precipitating factors[END_REF] and increased risk for sudden death [START_REF] Huang | Azithromycin-induced torsade de pointes. Pacing and clinical electrophysiology[END_REF][START_REF] Ray | Azithromycin and the risk of cardiovascular death[END_REF][START_REF] Mosholder | Cardiovascular risks with azithromycin and other antibacterial drugs[END_REF]. Both HCQ and AZM are categorized as being at 'torsades de pointes' risk (crediblemeds.org) and their administration is not recommended to patients presenting with congenital long QT syndrome (LQTS) [START_REF] Naksuk | Cardiac safety of off-label COVID-19 drug therapy: a review and proposed monitoring protocol[END_REF].

On the other hand, large population studies indicate that AZM use was not associated with an increased risk of death from cardiovascular causes in a general population of young and middle-aged adults [START_REF] Svanstrom | Use of azithromycin and death from cardiovascular causes[END_REF], and 85 out-patients treated with HCQ for connective tissue diseases for a minimum of 1 year did not show QTc interval and heart rate different from those in a population of healthy young adults [START_REF] Costedoat-Chalumeau | Heart conduction disorders related to antimalarials toxicity: an analysis of electrocardiograms in 85 patients treated with hydroxychloroquine for connective tissue diseases[END_REF]. Last, in two recent studies investigating HCQ and AZM treatment of COVID-19 patients, subsets of 9.2% (11/119 patients) and 16% (40/251) of the treated patients presented severely prolonged QTc to values >500 ms, a known marker of high risk of malignant arrhythmia and sudden cardiac death [START_REF] Saleh | The Effect of Chloroquine, Hydroxychloroquine and Azithromycin on the Corrected QT Interval in Patients with SARS-CoV-2 Infection[END_REF][START_REF] Chorin | QT Interval Prolongation and Torsade De Pointes in Patients with COVID-19 treated with Hydroxychloroquine/Azithromycin[END_REF]. A more recent meta-analysis reported major QTc prolongation above 60 ms in about 13% of the COVID-19 patients treated with both drugs, with an overall considerable heterogeneity, though [START_REF] Mega | The Outcome of Hydroxychloroquine in Patients Treated for COVID-19: Systematic Review and Meta-Analysis[END_REF].

In face of this variability, we exploited a computer model of human ventricular wedge to test the arrhythmogenic potential of a combination of several factors: (i) HCQ and/or AZM treatments, (ii) events occurring in COVID-19 patients that can contribute to alter repolarization: hypokalemia, tachycardia, and (iii) subclinical LQTS phenotypes. We chose the O'Hara and Rudy pseudo-ECG computer model, based on non-diseased human ventricular data [START_REF] O'hara | Simulation of the undiseased human cardiac ventricular action potential: model formulation and experimental validation[END_REF]. This model has been previously used and thoroughly validated by many laboratories, including ours, to study cardiac pathophysiological mechanisms in multiple diseases such as inherited and acquired long QT, short QT and Brugada syndrome [START_REF] Yang | In silico Prediction of Sex-Based Differences in Human Susceptibility to Cardiac Ventricular Tachyarrhythmias[END_REF][START_REF] Whittaker | Computational Analysis of the Mode of Action of Disopyramide and Quinidine on hERG-Linked Short QT Syndrome in Human Ventricles[END_REF][START_REF] Tyan | Long QT syndrome caveolin-3 mutations differentially modulate Kv 4 and Cav 1.2 channels to contribute to action potential prolongation[END_REF][START_REF] Tomek | Modulation of Cardiac Alternans by Altered Sarcoplasmic Reticulum Calcium Release: A Simulation Study[END_REF][START_REF] Portero | Dysfunction of the Voltage-Gated K+ Channel beta2 Subunit in a Familial Case of Brugada Syndrome[END_REF][START_REF] Lee | Pro-arrhythmogenic Effects of the V141M KCNQ1 Mutation in Short QT Syndrome and Its Potential Therapeutic Targets: Insights from Modeling[END_REF][START_REF] Romero | In silico screening of the impact of hERG channel kinetic abnormalities on channel block and susceptibility to acquired long QT syndrome[END_REF][START_REF] Li | Improving the In Silico Assessment of Proarrhythmia Risk by Combining hERG (Human Ether-a-go-go-Related Gene) Channel-Drug Binding Kinetics and Multichannel Pharmacology[END_REF]. The model was adapted to incorporate off-target effects of HCQ and AZM on cardiac ion currents [START_REF] Yang | Azithromycin Causes a Novel Proarrhythmic Syndrome[END_REF][START_REF] Capel | Hydroxychloroquine reduces heart rate by modulating the hyperpolarization-activated current If: Novel electrophysiological insights and therapeutic potential[END_REF].

Methods

Transmural wedge simulations

We computed the pseudo-ECG using a 1-dimensional model of a transmural wedge consisting in 165 human ventricular myocytes (ORd model) [START_REF] O'hara | Simulation of the undiseased human cardiac ventricular action potential: model formulation and experimental validation[END_REF]. Cells 1-60 were subendocardium type, 61-105 were mid-myocardium type, and 106-165 were sub-epicardium type (Supplemental figure 1). The spatially weighted sum of the voltage gradient was determined at a point 2 cm from the sub-epicardium end of a heterogeneous multicellular fiber, along the fiber axis. The number of computed beats needed to reach convergence in ECG and action potential (AP) mathematical parameters, was determined by following at each beat, computed single cardiomyocyte AP and Ca 2+ transient evolution at 1000-ms cycle length, starting from the model initial default conditions. Of note, the number of iterations needed to reach steady-state cannot be used to predict the number of action potentials necessary to reach biological steady-state. At first, AP duration decreased and Ca 2+ transient amplitude increased to reach a constant value at the 250 th beat (Supplemental figure 2; https://models.cellml.org/e/71). A value of 300 beats was chosen for all the tested conditions as it reflected stability of the modelling conditions. The healthy condition was modeled at 1000-ms cycle length, and tachycardia was modeled at 700-ms cycle length, that is commonly observed in COVID-19 patients (3) and at 500-ms cycle length.

To model cardiac response of COVID-19 patients with moderate hypokalemia, external K + concentration has been decreased from 5.4 to 3.4 mM. We reasoned that LQTS patients with major alterations in repolarization would not be prescribed QT lengthening compounds. Thus, we operated moderate modifications of the implicated currents to model long QT syndromes. For type 1 LQTS, we reduced the conductance of the slow component of the delayed rectifier K + current (I Ks ) to 50% of the wild-type condition to mimic moderate loss-of-function of mutated KCNQ1-encoded channels, without any dominant negative effect usually associated with severe LQT [START_REF] Vanoye | High-Throughput Functional Evaluation of KCNQ1 Decrypts Variants of Unknown Significance[END_REF][START_REF] Chouabe | Properties of KvLQT1 K+ channel mutations in Romano-Ward and Jervell and Lange-Nielsen inherited cardiac arrhythmias[END_REF].

Similarly, for type 2 LQTS (LQT2), we reduced the conductance of the rapid component of the delayed rectifier K + current (I Kr ) to 50% of the wild-type condition to mimic moderate lossof-function [START_REF] Ng | High-throughput phenotyping of heteromeric human ether-a-go-go-related gene potassium channel variants can discriminate pathogenic from rare benign variants[END_REF]. For type 3 LQTS (LQT3), we reproduced the consequences of the QKP1507-1509 mutant on SCN5A-encoded channel, Na v 1.5, with 4-fold increase in the conductance of the late component of the Na + current [START_REF] Shi | The cardiac sodium channel mutation delQKP 1507-1509 is associated with the expanding phenotypic spectrum of LQT3, conduction disorder, dilated cardiomyopathy, and high incidence of youth sudden death. Europace : European pacing, arrhythmias, and cardiac electrophysiology : journal of the working groups on cardiac pacing, arrhythmias, and cardiac cellular electrophysiology of the[END_REF][START_REF] Montnach | Arrhythmias precede cardiomyopathy and remodeling of Ca(2+) handling proteins in a novel model of long QT syndrome[END_REF].

Effects of 3 µM HCQ have been chosen based on the serum concentration measured in COVID-19 patients treated with 600 mg/day [START_REF] Gautret | Hydroxychloroquine and azithromycin as a treatment of COVID-19: results of an open-label non-randomized clinical trial[END_REF]. HCQ effects on ion channels have been modeled as follows: 35% decrease of I Kr conductance and 12% decrease of the conductance of the L-type Ca 2+ current, I Ca,L [START_REF] Capel | Hydroxychloroquine reduces heart rate by modulating the hyperpolarization-activated current If: Novel electrophysiological insights and therapeutic potential[END_REF]. For AZM, data on serum concentrations from SARS-Cov2 patients are not available so far. Peak plasma AZM concentrations during oral dosing range from ≈0.4 to 1.1 μmol/L. However, plasma concentrations are misleading, as the drug accumulates within cells, achieving concentrations approaching 900 μmol/L in leukocytes and pulmonary tissue [START_REF] Yang | Azithromycin Causes a Novel Proarrhythmic Syndrome[END_REF]. A previous study by the pharmaceutical sponsor, Pfizer Inc., reported similar accumulation of the drug in cardiac cells for mice receiving oral AZM (200 mg•kg -1 •d -1 for 10 days), with ≈200-fold increase in concentration compared with plasma at day 10 (53). Based on that, Yang et al. used an in vitro concentration of 50 µM, which seems reasonable to estimate the effect on cardiac currents [START_REF] Yang | Azithromycin Causes a Novel Proarrhythmic Syndrome[END_REF]. Of Note, AZM has different effects with regard to acute (instantaneous) or "chronic" 24-hour exposure, regarding the Na + current. Acute exposure to AZM was shown to decrease both the peak sodium current and peak L-type calcium current. It also decreases the inward rectifier potassium current I K1 , and the delayed potassium currents I Kr and I Ks . In contrast, 24-hour exposure increases the peak and late sodium currents. Unfortunately, the effects of 24-hour exposure AZM on I K1 , I Kr , I Ks and the L-type calcium current were not tested in this earlier report [START_REF] Yang | Azithromycin Causes a Novel Proarrhythmic Syndrome[END_REF]. Interestingly, even in the case of acute exposure, Yang et al. showed an enlargement of QTc duration in mice (see figure 2 of their publication), suggesting that the decrease in L-type calcium current is counterbalanced or even exceeded by the decrease in I K1 (I Kr and I Ks being absent in adult mice). Because AZM is administered for several days in the COVID-19 context, we considered only reported 24-hour effects of this compound on ion channels, as follows: 1.8-fold increase in sodium peak current conductance and 2.5-fold increase in late sodium current conductance. Of note, adding the other current alterations, based on their studied acute effects (65% reduction in L-type calcium current, 30% reduction in I Kr and I Ks , 66% reduction in I K1 ) further increased QT duration (supplemental figure 3).

Since the equivalence between acute and 24-hour effects is hypothetical, we chose to keep the condition with the minimal effect (only clearly established 24-hour effect of AZM on sodium channel). This point stresses out the importance of the characterization of longer application (at least 24-hour) of a given molecule on the currents.

State-dependent effects of mexiletine (MEX) were modeled at therapeutic concentration (0.8-2 µg/mL) (54) by a 40% decrease in only the late sodium current conductance [START_REF] Crumb | An evaluation of 30 clinical drugs against the comprehensive in vitro proarrhythmia assay (CiPA) proposed ion channel panel[END_REF].

Two antiarrhythmic drugs, that prolong QT interval and have been reported to induce torsades de pointes, were also tested as positive controls. Dofetilide is mostly active on I Kr and I to at about 2 nM corresponding to the free plasma C max concentration (factors applied: 0.45, 0.98, 0.98, 0.85, 0.98, and 0.95 to I Kr , I Ca,L , I Na fast , I to , I Ks and I K1 conductances, respectively) [START_REF] Crumb | An evaluation of 30 clinical drugs against the comprehensive in vitro proarrhythmia assay (CiPA) proposed ion channel panel[END_REF]. Quinidine has a larger spectrum and was tested at its free plasma C max concentration of about 850 nM (factors applied: 0.3, 0.9, 0.98, 0.85, 0.9, and 0.95 to I Kr , I Ca,L , I Na fast , I to , I Ks and I K1 conductances, respectively) [START_REF] Crumb | An evaluation of 30 clinical drugs against the comprehensive in vitro proarrhythmia assay (CiPA) proposed ion channel panel[END_REF].

Combined effects (such as LQT mutation+AZM+HCQ+MEX) were obtained by applying each factor respective of each drug or condition to the appropriate conductance(s). Models were processed with C++ code.

Electrophysiological determinations

Pseudo-ECG time parameters were determined as previously described [START_REF] Ledezma | A modeling and machine learning approach to ECG feature engineering for the detection of ischemia using pseudo-ECG[END_REF]. As expected, this model adapts to frequency by decreasing QT duration when frequency increases [START_REF] O'hara | Simulation of the undiseased human cardiac ventricular action potential: model formulation and experimental validation[END_REF].

As presented above, pseudo-ECG models are obtained from 1-dimensional strand of 165 cells reporting left ventricle transmural activity. For example, apex-to-base and right ventricle-to-left ventricle gradients are absent in this model. Therefore, generated pseudo-ECG time parameters are lower than human ECG values. QRS and QT durations are 46 and 312 ms, respectively, in this model compared to 90-100 and 370-440 ms in patients (i.e.

-60 ms), suggesting that difference in QT between the model and patients is mainly due to the difference in QRS, not ST duration. For the sake of comparison, we arbitrarily added the empirical value of 60 ms to the model QT duration to obtain 'clinical-like' QT values (in figure 7). QRS widening induced by HCQ may occur in COVID-19 patients. It is a slight median increase of 4 ms of borderline significance [START_REF] Mazzanti | Association of Hydroxychloroquine With QTc Interval in Patients With COVID-19[END_REF]. However, we kept this 60-ms value constant in every tested condition. Arrhythmogenic risks were assessed by the repolarization time from APD 30 to APD 90 (APD 90- 30 ) measured from the beginning of AP upstroke until 30% and 90% of repolarization as previously described [START_REF] Hondeghem | Instability and triangulation of the action potential predict serious proarrhythmia, but action potential duration prolongation is antiarrhythmic[END_REF] and by QT duration [START_REF] Elming | The prognostic value of the QT interval and QT interval dispersion in all-cause and cardiac mortality and morbidity in a population of Danish citizens[END_REF]. The breaks in the repolarization slope in early phase 3 of the computed APs were considered as early afterdepolarizations (EADs) by analogy with the EAD originally defined as a depolarizing afterpotential that begins prior to the completion of repolarization and causes (or constitutes) an interruption or retardation of normal repolarization, in the princeps publication by Cranefield [START_REF] Cranefield | Action potentials, afterpotentials, and arrhythmias[END_REF]. Data were analyzed using R3.6.2 and GraphPad8.

Results

We started with the most general case of COVID-19 patients, presenting no arrhythmia risk factor that reduces the repolarization reserve. Thus, we first investigated the effects of HCQ or AZM alone and their combined effects on the ventricular repolarization on simulated 'normal' ECG. At a cycle length of 1,000 ms, we observed that AZM alone induced a shortening of the QRS complex (-24%) and an increase in QT duration (+7%) due to the increased contribution of the peak and late sodium currents, respectively (Figure 1A-B and Table 1). HCQ alone induced a larger increase in QT duration (+21% vs. baseline) without affecting the QRS duration (Figure 1A-B). The combined AZM and HCQ synergistically prolonged the QT interval (30%; figure 1A-B). These drugs target two different types of ion channels. HCQ reduces a repolarizing current (I Kr ), while AZM increases a depolarizing current (late I Na ). Their effects are thus more than additive on the action potential duration as described by previous studies [START_REF] Virag | Self-augmentation of the lengthening of repolarization is related to the shape of the cardiac action potential: implications for reverse rate dependency[END_REF]. Looking at specific cell levels, modeled action potentials from sub-endocardium (cell #19), mid-myocardium (cell #84) and sub-epicardium (cell #144) underwent major modifications when the effects of HCQ alone or combined with AZM were simulated (Figure 1C).

Because COVID-19 patients admitted in ICU are frequently tachycardic, we investigated the effects of the treatment at a faster rate (cycle length, CL = 700 ms). The resulting effects of the three treatments on pseudo-ECG and APs parameters were in the same range as at 1,000-ms CL (Figure 2A-B and Table 1). When higher heart rate was tested (CL = 500 ms), similar results were observed (Supplemental figure 4).

Because hypokalemia can precipitate acquired LQTS (62), we investigated AZM and HCQ effects when a moderate hypokalemia (3.4 mM of extracellular K + ) commonly observed in COVID-19 patients [START_REF] Chen D | Hypokalemia and Clinical Implications in Patients with Coronavirus Disease[END_REF] was implemented in the model in addition to tachycardia. As shown in Figure 2C, hypokalemia induced a QT prolongation (+5% compared to baseline at 700-ms CL) and exacerbated the effects of the AZM+HCQ combination (+33% of increase in QT compared to +25% of increase in normokalemia at 700-ms CL; figure 2C). Hypokalemia also hyperpolarized the diastolic membrane potential of each cardiomyocyte layer (-99.2 mV in hypokalemia vs. -86.9 mV in normokalemia) leading to increased sodium channel availability. This increased availability caused QRS shortening. The combination of both drugs induced a triangulation of the AP shape as assessed by the prolongation of the repolarization time from APD 30 to APD 90 (APD 90-30 ; 195 ms vs. 110 ms with no treatment, in the sub-endocardium; figure 2D), which is known to favor early afterdepolarizations [START_REF] Guo | L-type calcium current reactivation contributes to arrhythmogenesis associated with action potential triangulation[END_REF][START_REF] Grant | Action potential and QT prolongation not sufficient to cause Torsade de Pointes: role of action potential triangulation[END_REF].

In summary, the model suggests that COVID-19 patients with tachycardia and hypokalemia, even 'sub-clinical', have to be closely monitored due to the potentiation of HCQ and AZM arrhythmogenic effects.

QT and AP duration lengthening were also observed when the reference drugs dofetilide and quinidine were applied (Supplemental figures 5 and 6). The deleterious effects of wellknown arrhythmogenic drugs can be clearly identified. It appears that AZM+HCQ have similar effects as dofetilide, a high risk torsadogenic drug. In summary, our results confirm the AZM+HCQ-induced QT prolongation observed in patients and validate the use of the model to investigate the arrhythmogenic consequences of drugs to treat COVID-19.

In order to validate the use of this model to predict arrhythmogenic susceptibility of patients with moderate long QT syndrome, we first tested AZM and HCQ effects in a LQT2 model replicating hERG haplo-insufficiency in normokalemia. As expected, a 33% prolongation of the QT was obtained. AZM+HCQ combined effects further prolonged it by 21% vs.

'untreated' LQT2 condition (Figure 3A). In LQT2 conditions, AP repolarization relies mostly on I Ks . As expected, the AZM-HCQ combined effects were major in the mid-myocardium where I Ks is of small amplitude. Mid-myocardium APD 90-30 , already prolonged by I Kr decrease, was severely prolonged from 145 to 203 ms by AZM+HCQ treatment and associated with the occurrence of a subthreshold early afterdepolarization (Figure 3B).

Again, AZM+HCQ treatment had effects in the same range as those observed with dofetilide (Supplemental figures 5 and 6). In the same conditions, quinidine application led to more pronounced QT prolongation and EADs particularly at the mid-myocardium level. These sets of data show that the ORd model replicated the impact of proarrhythmic drugs on LQT2 AP and ECG. These results confirm the absolute proscription of the use of such proarrhythmic drugs in COVID-19 patients with baseline long QT [START_REF] Giudicessi | Urgent Guidance for Navigating and Circumventing the QTc-Prolonging and Torsadogenic Potential of Possible Pharmacotherapies for Coronavirus Disease 19 (COVID-19)[END_REF][START_REF] Roden | Considerations for Drug Interactions on QTc in Exploratory COVID-19 (Coronavirus Disease 2019) Treatment[END_REF][START_REF] Wu | SARS-CoV-2, COVID-19 and inherited arrhythmia syndromes[END_REF].

Then, we used the model to predict the effects of AZM and HCQ in the context of a subclinical QT prolongation as seen in parents of patients with autosomal recessive Jervell and Lange-Nielsen LQTS, for instance [START_REF] Schulze-Bahr | Autosomal recessive long-QT syndrome (Jervell Lange-Nielsen syndrome) is genetically heterogeneous[END_REF]. Despite a 50% reduction in I Ks amplitude, a minimal 3% prolongation of the QT duration was observed (Figure 4A). However, the combination of AZM and HCQ induced a 26% increase in QT duration (vs. 'untreated' LQT1 condition) as well as APD 90 prolongation (Figure 4). This approach suggests that COVID-19 patients with primary moderate hypokalemia or asymptomatic LQT1 have a slightly higher risk to develop drug-induced arrhythmias when treated with AZM and HCQ than patients without these comorbidities (+11% and +4% QT prolongation in hypokalemia and LQT1, respectively, compared to QT values of 'treated' 'normal' ECG at the same heart rhythm). These patients have to be followed closely and additional preventive anti-arrhythmic therapy might be proposed in this case.

As AZM increases the late component of the sodium current, we also investigated the effects of the combined therapy in a model in which the late component of the Na + current was already increased i.e. in the model replicating LQT3. A 13% QT prolongation was obtained, to a lesser extent than in the LQT2 condition, though. However, a dramatic QT prolongation of 44% was induced by AZM+HCQ treatment (Figure 5A). At the 'cellular level', combining both drugs effects favored AP triangulation (APD 90-30 duration increased from 102 to 195 ms) and occurrence of early afterdepolarizations in mid-myocardium, close to what was obtained with the LQT2 model (Figure 5B).

Since it appears that the ORd model confirmed the observed and expected results regarding HCQ and AZM effects on ECG, we used the model to predict the effect of mexiletine treatment. Mexiletine, a well-known anti-arrhythmic drug used in LQTS patients was proposed to be associated with HCQ and AZM treatment of COVID-19 patients to limit excessive QT prolongation [START_REF] Giudicessi | Genetic susceptibility for COVID-19-associated sudden cardiac death in African Americans[END_REF][START_REF] Carpenter | COVID-19 Management and Arrhythmia: Risks and Challenges for Clinicians Treating Patients Affected by SARS-CoV-2[END_REF]. As shown in Figure 6, mexiletine reversed AZM+HCQinduced QT prolongation in all tested conditions (+19% vs. +25% in tachycardia, +22% vs.+33% in hypokalemia, +16% vs.+21% in LQT2, +20% vs.+26% in LQT1, and +28% vs.+45% in LQT3 model). In hypokalemia, LQT2 and LQT3 models, mexiletine reduced the AZM+HCQ-induced early afterdepolarization susceptibility in mid-myocardium (APD 90-30 of 131 ms vs.148 ms, 186 ms vs. 203 ms and 159 vs.195 ms for in hypokalemia, LQT2, and LQT3 models, respectively). Of note, the model predicts that mexiletine supplementation to shorten the prolonged QT has a mild but not negligible effect. Moreover, the model may be robust enough to evaluate the combined effects of new additional drugs (with known effects on ion channels) to limit AZM+HCQ arrhythmogenic consequences. milliseconds (right Y-axis). A QTc cut-off of 500 ms is clinically considered as pathological [START_REF] Giudicessi | Urgent Guidance for Navigating and Circumventing the QTc-Prolonging and Torsadogenic Potential of Possible Pharmacotherapies for Coronavirus Disease 19 (COVID-19)[END_REF][START_REF] Roden | Considerations for Drug Interactions on QTc in Exploratory COVID-19 (Coronavirus Disease 2019) Treatment[END_REF][START_REF] Wu | SARS-CoV-2, COVID-19 and inherited arrhythmia syndromes[END_REF]. At 700 ms of cycle length, the corresponding absolute QT duration according to Bazett's formula is 418 ms.

Discussion

Our study confirms that treating COVID-19 patients with HCQ and AZM drugs has, in most patients, little impact on QT duration [START_REF] Mercuro | Risk of QT Interval Prolongation Associated With Use of Hydroxychloroquine With or Without Concomitant Azithromycin Among Hospitalized Patients Testing Positive for Coronavirus Disease 2019 (COVID-19)[END_REF] and does not induce any substrate prone to arrhythmia. However, in clinical conditions in which the repolarization reserve is reduced, the model predicts larger ECG impairments including QT > 418 ms at 700 ms of cycle length, corresponding to QTc > 500 ms (figure 7). Such dramatic QT prolongations are potentially enabling the occurrence of life-threatening events, such as ventricular fibrillation. In addition, the model allows the dissection of the relative contribution of each drug to the establishment of pro-arrhythmic conditions, as well as their synergic effects to the mechanisms involved.

We also show that, mexiletine can limit only partly the dramatic increase in QT duration for patients with tachycardia, hypokalemia or reduced conduction reserve, but can bring it back to manageable duration for the mildest phenotypes. These results are in agreement with observations reported by Badri et al. after mexiletine treatment on acquired-LQT syndrome patients [START_REF] Badri | Mexiletine Prevents Recurrent Torsades de Pointes in Acquired Long QT Syndrome Refractory to Conventional Measures[END_REF]. The use of lidocaine, another class I antiarrhythmic drug has shown some benefits in a COVID-19 patient treated with AZM and HCQ [START_REF] Mitra | An algorithm for managing QT prolongation in coronavirus disease 2019 (COVID-19) patients treated with either chloroquine or hydroxychloroquine in conjunction with azithromycin: Possible benefits of intravenous lidocaine[END_REF]. Therefore, the ORd model may be used to evaluate the potential impact of additional drug, with known effects on ion channels, to limit the arrhythmogenic risks.

There is currently an explosion of proposed therapies for treating the virus but none of them have clearly demonstrated their efficacy [START_REF] Kupferschmidt | Race to find COVID-19 treatments accelerates[END_REF]. Among these therapies, hydroxychloroquine combined with azithromycin is still being used based on in vitro studies indicating their ability to inhibit virus-cell fusion (7-9) and despite accumulation of studies questioning their clinical efficacy, the topic is still debated [START_REF] Uzunova | Insights into antiviral mechanisms of remdesivir, lopinavir/ritonavir and chloroquine/hydroxychloroquine affecting the new SARS-CoV-2[END_REF][START_REF] Prodromos | Hydroxychloroquine is protective to the heart, not Harmful: A systematic review. New microbes and new infections[END_REF][START_REF] Ong | Effects of Antimalarial Drugs on Neuroinflammation-Potential Use for Treatment of COVID-19-Related Neurologic Complications[END_REF][START_REF] Oldenburg | Azithromycin for severe COVID-19[END_REF][START_REF] Albani | Impact of Azithromycin and/or Hydroxychloroquine on Hospital Mortality in COVID-19[END_REF]. A major concern of this therapy has been the risk of QT prolongation and TdP. The proarrhythmic mechanism of HCQ is thought to be due to its ability to inhibit hERG potassium channel and L-type calcium channel, which can result in early afterdepolarization triggered activity [START_REF] Capel | Hydroxychloroquine reduces heart rate by modulating the hyperpolarization-activated current If: Novel electrophysiological insights and therapeutic potential[END_REF]. Association of well-timed early afterdepolarization and QT prolongation results in TdP. The proarrhythmic mechanism of AZM is thought to be due to its ability to increase cardiac sodium current and promote intracellular sodium loading [START_REF] Yang | Azithromycin Causes a Novel Proarrhythmic Syndrome[END_REF]. Obviously, clinical decision cannot rely on the results obtained with this ECG model, but, by comparing the effects obtained with AZM+HCQ, and two proarrhythmic drugs, it can be suspected that the treatment has deleterious effects in vivo. Indeed, based on the proposed mechanisms we confirmed, using this in silico model, recent reports indicating QT prolongation [START_REF] Mercuro | Risk of QT Interval Prolongation Associated With Use of Hydroxychloroquine With or Without Concomitant Azithromycin Among Hospitalized Patients Testing Positive for Coronavirus Disease 2019 (COVID-19)[END_REF][START_REF] Chorin | The QT interval in patients with COVID-19 treated with hydroxychloroquine and azithromycin[END_REF] and high risk of TdP [START_REF] Szekely | Chloroquine-induced torsade de pointes in a COVID-19 patient[END_REF] in COVID-19 patients treated with HCQ and/or AZM. The discrepancy between occasional reports of QT prolongation and life-threatening arrhythmias triggered by HCQ and AZM and the absence of QT prolongation effects in large population studies (especially with AZM (33)), is probably due to the necessity, for triggering arrhythmia, of the combination of factors such as tachycardia, hypokalemia, and subclinical LQTS as substrate.

More than 280 drugs have been reported to induce QTc prolongation [START_REF] Woosley | CredibleMeds.org: What does it offer?[END_REF]. Among them several are antiarrhythmic drugs, but also non-cardiovascular drugs, that are widely used in ICU [START_REF] Etchegoyen | Drug-induced QT Interval Prolongation in the Intensive Care Unit[END_REF]. Clear recommendations have been established to avoid their administration to patients with symptomatic and well-established congenital long QT syndrome. In addition, I Kr , I Ks , I Ca,L , I Na late and more generally Ca 2+ homeostasis, are differentially impaired in various cardiopathies and cardiomyopathies frequently associated with aging, and also in hypoxia, much more frequent conditions in hospitalized COVID-19 patients. This is of concern, especially since I Na late increase, most frequently associated with these acquired diseases, appears to lead to severe ECG changes (LQT3).

Regardless of genetic aspects or pre-existing chronic pathologies, clinical case series have also identified risk factors for drug-induced LQTS including hypokalemia as commonly observed in COVID-19 patients [START_REF] Roden | Predicting drug-induced QT prolongation and torsades de pointes[END_REF]. Hypokalemia prolongs QT and is a risk factor for drug-induced LQTS. In addition to direct consequences on I Kr current [START_REF] Yang | Extracellular potassium modulation of drug block of IKr. Implications for torsade de pointes and reverse use-dependence[END_REF][START_REF] Yang | Rapid inactivation determines the rectification and [K+]o dependence of the rapid component of the delayed rectifier K+ current in cardiac cells[END_REF], hypokalemia may activate CaMKII leading to an increase in late sodium current and further prolongation of ventricular repolarization [START_REF] Pezhouman | Molecular Basis of Hypokalemia-Induced Ventricular Fibrillation[END_REF]. Moderate to severe hypokalemia has been reported in COVID-19 patients [START_REF] Chen D | Hypokalemia and Clinical Implications in Patients with Coronavirus Disease[END_REF]. SARS-CoV-2 virus invades cells through binding to angiotensin I converting enzyme 2 (ACE2) that enhances ACE2 degradation. The final effect of this degradation is a continuous renal K + loss that makes it difficult to correct hypokalemia [START_REF] Chen D | Hypokalemia and Clinical Implications in Patients with Coronavirus Disease[END_REF].

Noteworthy, low levels of potassium have been correlated with QTc > 500 ms occurrence in COVID-19 patients under HCQ and AZM medication [START_REF] Chorin | QT Interval Prolongation and Torsade De Pointes in Patients with COVID-19 treated with Hydroxychloroquine/Azithromycin[END_REF]. Consistent with these observations, this model emphasizes the fact that kalemia of COVID-19 patients has to be followed very carefully, particularly in case of medication with drugs such as HCQ or AZM.

More generally, this model could be used to evaluate in a pre-clinical approach, the risk of drug-induced QT prolongation in this context. In addition to electrolyte imbalance, there is also a greater prevalence of risks factors among COVID-19 patients in ICU, including older age, presence of underlying heart disease, and co-treatment with other QT prolonging medications.

With the possibility that a significant proportion of the world population may receive SARS-CoV-2 drugs with torsadogenic potential, the risk to treat patients with asymptomatic and undiagnosed long QT syndrome is increasing. These patients have a QTc duration in the limit of the general population variability and are not identified as such. Indeed, in a recent study, patients with extreme QTc prolongation when treated with HCQ and AZM, presented a baseline QTc around 431 ms only, within the normal QTc range [START_REF] Chorin | QT Interval Prolongation and Torsade De Pointes in Patients with COVID-19 treated with Hydroxychloroquine/Azithromycin[END_REF]. As modeled in the present study, cardiomyocytes harboring mutations leading to haplo-insufficiency in KCNQ1 may present very minimal action potential prolongation because of a normal I Kr [START_REF] Roden | Genetics of acquired long QT syndrome[END_REF], but I Kr blockers such as HCQ, can lead to marked action potential prolongation in limited repolarization reserve. All guidelines for QT management in COVID-19 context [START_REF] Giudicessi | Urgent Guidance for Navigating and Circumventing the QTc-Prolonging and Torsadogenic Potential of Possible Pharmacotherapies for Coronavirus Disease 19 (COVID-19)[END_REF][START_REF] Roden | Considerations for Drug Interactions on QTc in Exploratory COVID-19 (Coronavirus Disease 2019) Treatment[END_REF][START_REF] Wu | SARS-CoV-2, COVID-19 and inherited arrhythmia syndromes[END_REF] recommend to avoid QT prolonging drugs in individuals with a QTc > 500 ms due to a twofold to three-fold increase in risk for TdP [START_REF] Schwartz | Predicting the Unpredictable: Drug-Induced QT Prolongation and Torsades de Pointes[END_REF]. Nevertheless, those asymptomatic patients might receive these drugs based on this criterion. As modeled in this study, despite the absence of QT prolongation in baseline conditions because of a normal I Kr [START_REF] Roden | Genetics of acquired long QT syndrome[END_REF] and regardless of the origin of low repolarization reserve, these patients are at high risk of TdP when I Kr blockers such as HCQ are used. However, the model shows that, in a borderline condition such as moderate LQT1, mexiletine can limit to some extent the deleterious effects of AZM and HCQ. Therefore, we propose that the ORd model can be used to evaluate the potential impact of other additional drugs, with known effects on ion channels, that may be used in the future to limit arrhythmogenic risk of COVID-19 therapies.

In summary, the ORd model appears to be an easy-to-use tool to assess off-label drug arrhythmia potential in different conditions representative of COVID-19 patients at risk for arrhythmia and life-threatening torsades de pointes.

Limitations

We used the original ORd model based on its more realistic conductance values compared to others. This model may underestimate I Ks amplitude even if obtained from human cardiomyocytes [START_REF] Virag | The slow component of the delayed rectifier potassium current in undiseased human ventricular myocytes[END_REF]. In some rare cases (heterozygous non-dominant-negative LQT1 mutations) a minimal reduction (less than 50%) of the channel activity leads to severe QTc prolongation (very minor cases, cf. for instance [START_REF] Biliczki | Trafficking-deficient long QT syndrome mutation KCNQ1-T587M confers severe clinical phenotype by impairment of KCNH2 membrane localization: evidence for clinically significant IKr-IKs alpha-subunit interaction[END_REF]). The model we use is simple, robust, and incorporates pseudo ECGs but not inter-individual variability, to remain affordable in time and resources. Since the model does not include the population variability (e.g., due to genetic background), it cannot reproduce the LQTS phenotype heterogeneity. Other studies focusing on single cell AP, adjusted I Ks amplitude to compensate for this insufficiency leading to more severe LQT1 phenotype [START_REF] Mann | Convergence of models of human ventricular myocyte electrophysiology after global optimization to recapitulate clinical long QT phenotypes[END_REF]. It would be interesting to try optimizing pseudo-ECG models using the same strategy.

One-dimension strip of 165 cardiomyocytes simulates only the transmural gradient. Apex-tobase and right-to-left gradients are absent in this model. There are 3D models but (i) they are highly computationally demanding thus requiring simpler alternative approaches to model single cell action potential [START_REF] Lopez-Perez | Three-dimensional cardiac computational modelling: methods, features and applications[END_REF] and (ii) they are less realistically adaptive because each current is not individually modelled. Therefore, we preferred to use a 1D-model in which precise biophysical equations representing the biological currents can be finely tuned to model the drug effects at the AP then ECG levels. Thus, the resulting caveat is the lower QT duration values. In order to allow translational approach, we suggest adding an empirically estimated value of 60 ms. The calculated QT values can then be roughly compared to clinical ECG values. In addition, T wave shape results more from regional heterogeneity than from transmural gradients [START_REF] Janse | Counterpoint: M cells do not have a functional role in the ventricular myocardium of the intact heart[END_REF]. As another limit of the 1D-model, it cannot simulate changes in T wave amplitude.

In this study, we investigated potential effects of drugs prescribed to patients with COVID-19 on AP with reduced repolarization reserve, in order to detect any arrhythmogenic substrate.

To do so, we used well-defined conditions with "pure" repolarization reserve decrease such as LQT syndrome with various genetic origins. Cardiopathies and cardiomyopathies frequently associated with aging, and in hypoxia, are much more frequent conditions in hospitalized COVID-19 patients. However, instead of adding another condition, generic for these pathologies, which is difficult to establish since conductance decreases are not the same for all the pathologies (91), conditions with "pure" repolarization-reserve decrease as LQT syndromes were preferred. Similarly, the complex modifications induced by systemic inflammation and oxidative stress observed in COVID-19 patients have not been introduced at the level of the ion currents in the modeling. Such complex alterations of expression and/or activity of ion channels are hardly quantifiable and cannot be mimicked. In any case, it can be suspected that the addition of pre-existing pathologic conditions and COVID-19related modifications would exacerbate the arrhythmia susceptibility.

The effects of adrenergic stimulation were not evaluated for the following reason. An observational study of 138 patients affected by COVID-19 reported moderate tachycardia with a median heart rate of 88 bpm (3) indicating that the adrenergic tone is not high in those patients. Thus, in this study, we evaluated, during moderate tachycardia, the theoretical effect of the drugs on AP with reduced repolarization reserve, in order to detect any arrhythmogenic substrate. Interestingly, a very recent work, complementary to ours, used a modified version of the ORd model to study the β-adrenergic receptor stimulation on the cellular proarrhythmic effects of chloroquine and azithromycin, at the single AP level [START_REF] Sutanto | Beta-Adrenergic Receptor Stimulation Modulates the Cellular Proarrhythmic Effects of Chloroquine and Azithromycin[END_REF]. In this paper, Sutanto and Heijman suggest that sympathetic stimulation limits drug-induced APD prolongation. Therefore, at least for CQ and AZM, the unstimulated situation that we studied may represent the most critical situation.

It has to be mentioned that the ECG ORd model is conservative. Arrhythmogenic mechanisms such as triggered activities are hardly induced. Indeed, significant impairment of the Ca 2+ current window was needed to induce repolarization failure in the recent study of Sutanto and Heijman [START_REF] Sutanto | Beta-Adrenergic Receptor Stimulation Modulates the Cellular Proarrhythmic Effects of Chloroquine and Azithromycin[END_REF]. However, the deleterious effects of arrhythmogenic drugs can be clearly identified with the ECG model, namely EADs and QT lengthening.

Gender differences, resulting from multiple intersecting processes implying complex regulations of ion channels, cannot be easily modeled and was not investigated in this study. This would be indeed another improvement of the model.

Figure 7

 7 Figure 7 summarizes the QT duration values obtained at 700-ms cycle length. The ORd transmural wedge model values are arbitrarily transposed to clinical-like values by adding 60

Figure 1 :

 1 Figure 1: Hydroxychloroquine/azithromycin-induced prolongation of ventricular repolarization in a healthy heart (wedge in silico model). A. Computed pseudo-ECG in control (black), azithromycin (AZM, blue), hydroxychloroquine (HCQ, orange) and AZM+HCQ (red) condition at 1000-ms of cycle length (CL). B. QT interval measured in each condition. C. Left: Simulation of ventricular action potential from sub-endocardium (top), midmyocardium (middle) and sub-epicardium (bottom) in control, AZM, HCQ and AZM+HCQ condition. Right: Quantification of action potential duration at 30% (APD 30 ), 50% (APD 50 ), 70% (APD 70 ) and 90% (APD 90 ) of repolarization in each condition.

Figure 2 :

 2 Figure 2: Hydroxychloroquine/azithromycin combination effects in COVID-19 patient model with tachycardia and hypokalemia. A. Tachycardia, (a) computed pseudo-ECG in control (black), azithromycin (AZM, blue), hydroxychloroquine (HCQ, orange) and AZM+HCQ (red) condition at 700-ms of cycle length. (b) QT interval measured in each condition. B. (a) Simulation of ventricular action potential from sub-endocardium (left), midmyocardium (middle) and sub-epicardium (right) in control, AZM, HCQ and AZM+HCQ condition. (b) Quantification of action potential duration at 30% (APD 30 ), 50% (APD 50 ), 70% (APD 70 ) and 90% (APD 90 ) of repolarization in each condition. C. Hypokalemia, (a) computed pseudo-ECG in control (dashed black line), hypokalemia (3.4 mM extracellular K + , solid black line) and hypokalemia with AZM+HCQ (red) condition at 700 ms of cycle length. (b) QT interval measured in each condition. D. (a) Simulation of ventricular action potential from sub-endocardium (left), mid-myocardium (middle) and sub-epicardium (right) in control, hypokalemia and hypokalemia with AZM+HCQ condition. (b) Quantification of action potential duration as in B(b), in each condition.

Figure 3 :

 3 Figure 3: Arrhythmogenic effects of AZM+HCQ combination in long QT type 2 model. A. (a) Computed pseudo-ECG in control (dashed black line), long QT type 2 (LQT2) modeled as a KCNH2 haploinsufficiency (solid black line) and LQT2 with AZM+HCQ (red) condition at 700-ms of cycle length. (b) QT interval measured in each condition. B. (a) Simulation of ventricular action potential from sub-endocardium (left), mid-myocardium (middle) and sub-epicardium (right) in control, LQT2, and LQT2 with AZM+HCQ condition. *: subthreshold early afterdepolarization. (b) Quantification of action potential duration at 30% (APD 30 ), 50% (APD 50 ), 70% (APD 70 ) and 90% (APD 90 ) of repolarization in each condition.

Figure 4 :

 4 Figure 4: Hydroxychloroquine/azithromycin combination reveals arrhythmia susceptibility in asymptomatic long QT type 1 model. A. (a) Computed pseudo-ECG in control (dashed black line), long QT type 1 (LQT1) modeled as a KCNQ1 haploinsufficiency (solid black line) and LQT1 with AZM+HCQ (red) condition at 700-ms of cycle length. (b) QT

Figure 5 :

 5 Figure 5: Arrhythmogenic effects of AZM+HCQ combination in long QT type 3 model. A. (a) Computed pseudo-ECG in control (dashed black line), long QT type 3 (LQT3) modeled as a 4-fold increase in persistent sodium current (solid black line) and LQT3 with AZM+HCQ (red) condition at 700-ms of cycle length. (b) QT interval measured in each condition. B. (a) Simulation of ventricular action potential from sub-endocardium (left), midmyocardium (middle) and sub-epicardium (right) in control, LQT3 and LQT3 with AZM+HCQ condition. *: subthreshold early-afterdepolarization. (b) Quantification of action potential duration at 30% (APD 30 ), 50% (APD 50 ), 70% (APD 70 ) and 90% (APD 90 ) of repolarization in each condition.

Figure 6 :

 6 Figure 6: Mexiletine partially limits AZM+HCQ-induced QT prolongation. Combination of mexiletine with AZM+HCQ (purple) limits increase in QT interval in pseudo ECG (a) and simulated ventricular action potential (b) prolongation in tachycardia (A), hypokalemia (B), LQT1 (C), LQT2 (D) and LQT3 (E) conditions compared to the same condition without mexiletine (red).

Figure 7 :

 7 Figure 7: ORd model QT transposed to clinical human QT. In all conditions, converted AZM+HCQ QT values exceed (right Y-axis) the 418 ms cut-off (dashed line) and the use of mexiletine allows a partial reversion close to the cut-off value in tachycardia alone or combined with hypokalemia or LQT1 condition.

  Figure1

Table 1 . Drugs effects on pseudo-ECG parameters QRS (ms) QT (ms)

 1

		Basal +AZM +HCQ	+AZM + HCQ	+AZM + HCQ + MEX	+Dof. +Quinidine Basal +AZM +HCQ	+AZM + HCQ	+AZM + MEX + HCQ	+Dof. +Quinidine
	Control	46	35	46	35	35	n.d.	n.d.	312	333	378	407	382	n.d.	n.d.
	Tachycardia	47	35	47	35	35	50	48	297	310	352	372	353	410	470
	HypoK	40	n.d.	n.d.	32	32	40	40	311	n.d.	n.d.	414	378	395	461
	LQT1	46	n.d.	n.d.	35	35	50	48	307	n.d.	n.d.	388	368	433	506
	LQT2	46	n.d.	n.d.	35	35	50	48	394	n.d.	n.d.	478	457	512	587
	LQT3	46	n.d.	n.d.	35	35	50	48	337	n.d.	n.d.	487	433	466	538

AZM: azithromycin ; HCQ: hydroxychloroquine ; MEX: mexiletine ; HypoK: hypokalemia; Dof. : dofetilide ; Control at 1000 ms cycle length and other conditions at 700 ms cycle length.

Acknowledgments

None Sources of Funding M. De Waard and G. Loussouarn thank the Agence Nationale de la Recherche for its financial support to the Région Pays de la Loire (ANR FLASH Covid-19 -CoV2-E-TARGET) and the laboratory of excellence "Ion Channels, Science and Therapeutics" (grant N° ANR-11-LABX-0015). The fellowship of J. Montnach is provided by a National Research Agency Grant to M. De Waard entitled OptChemCom (grant N° ANR-18-CE19-0024-01). Genavie foundation supported J. Montnach and G. Loussouarn.

Disclosures


Mahamane L Abdoulaye
email: mlabdoulaye@gmail.com

Particle ga/ka: Purposive, infinitive, and auxiliary verb constructions in Zarma Chiine 1

Keywords: Songhay, Zarma Chiine, grammaticalization, infinitive, auxiliary 1 Songhay, zarma, grammaticalisation, infinitif, auxiliaire

This chapter uses grammaticalization theory to describe the relation between various uses of the particle ga/ka in Zarma Chiine (Songhay). Although ga functions most frequently as an infinitive marker, it very likely derives from a purposive marker ga, following a pattern of change found cross-linguistically. The particle however also marks more grammatical functions marking auxiliary verb constructions, and serial-like resultative constructions. The paper shows that in the less grammaticalized purposive and infinitive constructions, the particle appears in syntactically flexible ga + VP structure, whereas in the more grammaticalized auxiliary and resultative constructions the particle appears in a more syntactically rigid V + ga + V structure.

Introduction

Zarma Chiine (henceforth, ZC) has a remarkable -although areally not isolated -verb combination constructions where two (or more) verbs are linked with an element ga (or the variant ka, which is optional in Niamey city but more prevalent in other Zarma towns). This construction, like similar constructions in other West African languages (cf. N. [START_REF] Nikièma | Les constructions à verbes sériels en moore[END_REF], does not straightforwardly conform to canonical definitions of a serial verb construction (SVC), an auxiliary verb construction (AVC), or a verb complement construction. Nonetheless, ZC V + ga + V seems to fulfill functions typical of these and other constructions and hence appears in a variety of contexts and forms. The construction is illustrated with three of its functions in the following examples (see L. Sibomana, 2001, p. 222, 230):

(1) a. Ng mò kàa g â noo ng`kaynè sè. 3s then come GA 3s give 3s younger.sister to 'She then came to give it to her sister.' b. Irkòy n`taas-oo bar g`tee dòonu bònyan. God SEP sand-df change GA make millet balls 'God transformed the sand into millet balls.' c. À dìi g`hen day à nê... 3s catch GA cry indeed 3s say 'She started crying indeed and said...'

In example (1a) particle ga is clearly a subordinating conjunction introducing a full complement clause (in this case a purposive or sequential clause), which has the same subject at the main clause. In this context, there is very little interaction between the verbs' syntactic frames or even their meaning. In (1b), ga introduces a verb phrase (VP) and the verbs are closer semantically in the sense that there is essentially one action described by the two verbs, as seen in the English translation, although each verbs has an independent lexical meaning. Finally in (1c), there is one main action as described by V2, while V1 can be taken to be an auxiliary expressing a grammatical meaning (aspectual, modal, and temporal, as we will see in due course). By their function, these constructions are naturally limited to the few verbs suited for expressing aspectual or modal meanings. Most descriptions of ZC focus only on the construction illustrated in (1c), which is usually taken to be an auxiliary construction (A. Hamani, 1980, R. Nicolaï, 1983, B. Oumarou Yaro, 1993). For Koyra Chini, a Songhay language spoken in Djene and Timbuktu, J. [START_REF] Heath | A Grammar of Koyraboro (Koroboro) Senni: The Songhay of Gao[END_REF] describes at length and near exhaustively the structures akin to those in (1b-c) and claimed that structures such as (1a) do not exist in this language.

The aim of this paper is first to explore the relationships between the three constructions in (1) and other constructions involving particle ga. In order to establish this relationship clearly, one case study will be presented showing the various uses of the verb yêe 'return' from a motion verb to an auxiliary verb.

The paper is cast in the grammaticalization framework (see P. Hopper and E. C. Traugott, 2003, amongst others) and takes into account typological studies of complex verb constructions (for example G. [START_REF] Anderson Gregory | Auxiliary verb constructions in the languages of Africa[END_REF], B. Heine, 1993). The data comes mostly from L. [START_REF] Sibomana | Trois contes zarma[END_REF] who presents three texts recorded with Niamey informants. This source is supplemented with my own data collected with informants and students from Niamey and other areas.

The paper is organized as follows. Section 1 presents the previous studies. Section 2 explores the purposive and some related functions of ga. Section 3 describes the uses of ga/ka as linker in auxiliary constructions (with copulas or verbs that contribute an aspectual meaning). Section 4 discusses the use of ga in semantically resultative constructions.

Previous studies

There are two notable descriptions of the V + ga + V constructions. A. Hamani (1981, p. 8) focused on the more grammatical functions of the construction where V1 expresses an auxiliary meaning. He distinguishes the following eight such "aspectual" auxiliary meanings (each with its most frequent base verb): Ingressive (sintìn 'start'), iterative (dòona 'have the habit of'), potential (hin 'be able' < hìna 'be able, know how'), unreal (hoo 'fail'), obligative (hìmà 'must, resemble'), "successive" (i.e. durative; gày 'to have done for a long time'), "volitive" (i.e, desiderative; baa 'want', waasu 'hurry'), and "resultative" (this in fact refers to a volitional/ intentional meaning; haw 'do on purpose'). It should be noted that Hamani only gives the semantic specifications and does not characterize the syntax of these auxiliary constructions nor their relationships with other constructions implicating the particle ga/ka.

J. [START_REF] Heath | A Grammar of Koyraboro (Koroboro) Senni: The Songhay of Gao[END_REF] is probably the most detailed description of the construction, but his study concerns Koyra Chiini (Western Songhay). J. Heath (1998, p. 304-322) proposes five regular types of constructions involving infinitive ka verbs, as seen next:

(2) a. As one can see, all these patterns correspond to the patterns illustrated for ZC in (1b-c) only. Indeed, according to J. Heath (1998, p. 304), the ka + verb construction is not used in purposive clauses, or in complements of desiderative, allowing and preventing verbs. The label "serial" verb for type (2b-c) is problematic, since Heath claims that a serial verb is "[...] a verb that is specialized to occur in combination with a fuller VP, which we will call the "substantive VP"". And further he says "The full VP represents the core scenario ('boy kill dog'), while the attached serial verb adds a grammatical category (aspect, mood), motion, or a higher predicate (e.g. 'try')" (J. Heath, 1998, p. 304). This characterization does not correspond to the standard definitions of serial verb constructions (see Section 6 below) and indeed all verbs of the type (2b) correspond to auxiliary verbs construction in ZC (see Section 4 below), while those of the type (2c) correspond to resultative constructions (see Section 5). The situation in Koyraboro Senni (cf. J. Heath, 1999, p. 333) is very similar to that in Koyra Chiini, except that in Koyraboro Senni, the construction has somehow retained the purposive function.

In the next sections, I review the various functions of ga in ZC.

Ga in purposive, sequential, infinitive, and related constructions

Although it is rather neglected in descriptive studies (cf. Y. Bernard and M. White-Kaba, 1994, etc.) or even lack altogether in the grammar of some varieties (cf. J. Heath, 1998, p. 304 for Koyra Chiini and J. Heath, 1999 for Koyraboro Senni), the purposive marking function of ga is very frequent in ZC. Some typical usages are given next (see L. Sibomna, 2001, p. 220, 222, 224, 236, 238):

(3) a. Màt kân ng gà tee g bay? how that 3s IPF do GA know 'How would he know?' Lit. 'How does he do in order to know?' b. Ng mò kàa g â noo ng`kaynè banda wanaa sè. 3s PRT come GA 3s give 3s junior behind POSS to 'Then she came to give it to her little sister.' c. Ni m`ày sambu g kondà ay… 2S SBJ 1s take GA take 1s 'You may take me [on horse] and carry me away…' d. Son bòràa kûl g`koy isà nô g`nyumày. now person all FUT go river FOC GA bath 'Now, may everybody go to the river and take a bath.' Lit.: 'It is going to the river that everybody will do, to take a bath.' e. Ni g`koy g

[ngay kwàaràa muusù bèeròo kân goo 2s FUT go GA 3p town lion that be saagyòo raa] wii. bush in kill 'You will go and kill the lion lurking their town, that is in the bush.' L. Guererro (2009, p. 92), citing S. Christofaro (2003, p. 157), defines a purposive clause as a clause coding an event the future realization of which is the goal of a performed event coded in another (the main) clause. All the examples above express two events that are in an enabling-enabled relation. Formally, the main clause and the purposive clause are loosely associated and it is no surprise that in ZC, the syntactic contexts in which the purposive construction appears are varied. In (3a) we have simple V + ga + V structure. In (3b) the particle introduces a tensed clause. In (3c) a direct object with the same referent is specified for each verb. In (3d) the clause containing the V1 is focalized and separated from the ga phrase by the focus copula nôo. Finally, in (3e), the preverbal direct object of V2 following ga is a very complex noun phrase (given in brackets). All these examples show that the purposive construction is very flexible and may represent the earliest function of the particle ga.

Besides the purposive meaning, ga also has related usages that can be construed as further elaborations/grammaticalization of the purposive sense, chiefly the sequential and infinitive use. M. [START_REF] Haspelmath Martin | From purposive to infinitive: A universal path of grammaticization[END_REF] has discussed how in a number of languages (for example, English and German, but also languages all over the world), allative constructions grammaticalize into (motion, then non-motion) purposive clauses and finally into infinitive clauses (cf. go to Mary's place/ go to take a picture/ buy a camera to take a picture/ to take it is easy). I will subscribe to this general scheme, though in ZC the origin of particle ga is obscure. The sequential and the infinitive functions are illustrated next (data (4a) from L. Sibomana, 2001, p. 224 and (4b) In sentences (4a-b), the second verbs clearly express a sequential rather than purposive actions. In particular in (4a) the event of the second verb is more of an unintended consequence. In (4c), the V2 probably describes not a sequential but a concomitant event with the event of V1. This maybe an example of the infinitive use of "ga + VP". Further cases where ga is a pure grammatical linker are given in the next examples (data (5a-b) from L. Sibomana 2001, p. 220, 228 and (5d) from H. Saydu Hanfiiyu, 2004):

(5) a. Zàa ir bàabà dìrà g kàa sohòn... since our father go GA come now 'From the time of our father's departure up to now...' b. Wàndoo g`kurnyòo zukù g nê: "Fìlaanà..." woman IPF husband incite GA say "Hey you…" 'The wife was inciting the husband, saying: "Hey you…"' c. Ì fatta ga nêe dùngây gǒo nòo. 3p go.out GA say heat be there 'They went out because it is hot.' d. Han kulu daa zàyey kà ga nêe ngèy mà zaj… day all when thieves come GA say 3p SBJ steal 'Whenever the thieves come in order to rob (him)...' In all these examples, though one may in some cases interpret a meaning for ga, in reality it is a simple linker. In (5a) the construction ga kàa (literally 'to come') is frozen and functions as a complex preposition meaning 'up to' and can be complemented with a time or locative expression (cf. ga kàa Maradi '(from somewhere) up to Maradi'). Example (5b) presents a situation where the second verb ('say') seems to specify the generic action expressed by the first verb ('incite'). However, the expression has a more frequent use where there is no actual speaking and ga nêe 'to say' simply functions as a causal subordinating conjunction, as seen in (5c-d). Finally, there is at least one example where the ga marker seems superfluous, as seen next (see L. Sibomana, 2001, p. 230, 222):

(6) a. À gòo g dìi g`hen g dìi g`hen… 3s be GA start GA cry GA start GA cry 'She was crying, kept crying, kept crying…' b. À dìi g bòori à dìi g bòori. 3s start GA beautiful 3s start GA beautiful 'She kept becoming beautiful.'

In (6a), the third instance of ga (in boldface) is superfluous between two repeated instances of the same proposition. Example (6b) presents the normal structure where the repeated propositions are simply juxtaposed.

In most examples presented in this section, one has two separate events that may even occur at different times. The next section considers the auxiliary constructions where V1 does not refer to a distinct event. It is very likely that the infinitive and linking functions of ga allowed it to become a marker in auxiliary constructions where it is a simple grammatical linker between two verbs without a semantic contribution. Indeed in some such cases, the linker can be omitted (and in fact systematically so in some dialects).

Ga as a linker in auxiliary verb constructions

An auxiliary construction is generally defined as a construction with a sequence of two predicates where one expresses a grammatical meaning and the other the lexical meaning (see G. Anderson, 2006, p. 7 and references cited there). In this sense, an AVC refers only to a single event, in contrast to a purposive construction, as seen in the previous section. Formally, it is also frequent in languages for the two (or more) predicates in an AVC to be syntactically closeknit, since they form one clause, although we will see that in ZC the construction has some flexibility.

There are essentially two types of AVCs in ZC. The first type involves the auxiliarized copulas gǒo 'be (at)', and its negative sii, combined with the ga particle to express the progressive aspect. the second type involves otherwise regular verbs that have been auxiliarized to express phasal aspect and modality, among others.

Ga as linker in the progressive aspect construction

Besides a general imperfective marked ga/gà (and its negative si), ZC has a progressive construction that only refers to actions in progress (contrary to the general imperfective, which can also refer to future punctual events; see Y. Bernard and M. Kaba, 1994). The progressive construction is based on the copula gǒo 'be (at)' and sii 'not be (at)' (for general studies on the changes from a copula to an auxiliary see C. Lehmann, 2015, p. 35, amongst others). There are at least three variants of the progressive construction, as illustrated next:2 (7) a. Zànk The construction in (7a) and ( 8a) is a periphrastic construction involving the auxiliarized locative copulas gǒo or negative sii, the adverb nôo 'there' and the particle ga introducing the lexical verb, with a progressive meaning only. In examples (7b) and (8b) the constructions are more integrated where the adverb nôo is dropped. In (7c) and (8c), where both the adverb nôo and the particle ga are dropped, there is a remarkable variation in the grammaticality judgments. Some speakers would reject the sentences outright (for example speakers of extreme northern varieties). B. Oumarou Yaro (1993, p. 133) however reports similar sentences but posits some complex tonal adjustment whereby the high tone of the particle is retained (floating), causing a modulation on the gǒo/ sii. Some speakers yet accept sentences (7c) or (8c) but only with a general imperfective meaning, not a progressive meaning, as indicated. 3 The parallel form/ meaning development from (7a) to (7c) is a general process characterizing many languages, including neighboring Hausa (cf. ya-nàa nan gà shâ-n giyàa 'he is now drinking beer', lit. 'he-is there at drinking-of beer' > ya-nàa gà shâ-n giyàa 'he is now drinking beer' > ya-nàa shâ-n giyàa 'he is drinking beer/ he is a beer drinker/ he will drink beer'). It may be noted that all speakers accept a version of (8c) with the general negative imperfective marker si (with a short vowel). Copula gǒo can also express the progressive with a nominalized clause with some variations, as illustrated next (see L. Sibomana, 2001, p. 234):

3 According to Y. Bernard and M. White-Kaba (1994), the constructions in (7-8) are possible only with verbs koy 'go ' and kà 'come'. But B. Oumarou Yaro (1993, p. 133) seems more inclusive ("certain verbs") but nonetheless illustrates only theses two verbs. What is certain is that the verb fatta 'go out' is frequently used without ga (cf. îr gǒo fatta Ƙwànni 'we are exiting Konni town', overheard once in a traveling bus).

(9) a. Bàr kân g â nyumày gòo nyumàyyan ga. person that IPF 3s bath be bathing on 'Those whose job was to bath her were at it.' b. Bàr kân g â tuusu gòo tuusuyan. person that IPF 3s clean be cleaning 'Those whose job was to clean her were at it.'

In (9a), the locative copula has a (figurative) locative complement the gerund nyumàyyan 'bathing' that is marked with the locative postposition ga (presumably unrelated to the purposive particle ga). The construction in (9b) does not retain the postposition. Both constructions reflect the structure of basic locative predications (cf. Abdù gǒo fuwòo ra 'Abdu is inside the house'; Abdù gǒo taray 'Abdu is outside'). This progressive construction, which may be more frequent cross-linguistically (cf. English and Hausa), is less frequent than the ones in (7-8) above and in fact was so far unreported (L. [START_REF] Sibomana | Trois contes zarma[END_REF], the source of data (9), does not comment on the constructions).

Ga as linker in aspectual or modal AVCs

The function of ga as linker in AVCs is its most prominent and most studied function. In AVCs, a lexical verb, mostly the V1, undergoes changes whereby it loses part of its lexical meaning and acquires a grammatical (mostly aspectual or modal) meaning. These processes have sufficiently been described in grammaticalization studies (notably G. [START_REF] Anderson Gregory | Auxiliary verb constructions[END_REF], B. Heine, 1993, P. Hopper and E. C. Traugott, 2003, C. Lehmann 2015, pp. 29-34). There are many paths whereby a verb can become an auxiliary but in all cases, in appropriate contexts, an ambiguity can arise between an original meaning and a new meaning taken by the verb. This is illustrated in the following with the range of functions of the verb yêe 'return', one of the verbs auxiliarizing to a phasal aspectual meaning:

(10) a. Hiimù yêe fuwòo ra ga sìgaarì haŋ. Himu return house in GA cigarette smoke 'Himu returned in the house to smoke a cigarette.' b. Hiimù yêe ga sìgaarì haŋ. Himu return GA cigarette smoke 'Himu returned (here/ somewhere) to smoke a cigarette.' 'Himu resumed (went back to his habit of) smoking.' 'Himu smoked a cigarette again.' c. Hiimù yêe ga miilà ndà Faatì. Himu return GA think with Fati 'Himu thought about Fati again.' Example (10a) shows the verb yêe 'return' with an obligatory motion meaning, given the specified locative complement before the purposive clause. Sentence (10b), without the locative complement, but with the ga-marked purposive clause, is ambiguous between a motion sense and an auxiliary resumptive or iterative meaning. Finally in (10c), with a verb that renders irrelevant a motion sense, only the iterative auxiliary meaning is available. While the examples in (10) illustrate a change from an intransitive verb followed by a purposive clause to an AVC, in other cases, the change is from a main verb taking an infinitive or sequential clause to a structure where the main verb becomes an auxiliary, as we will see below.

Given the semantic grammaticalization change in (10), one may expect ZC AVCs to show some syntactic rigidity and indeed sentences (10b-c) are more syntactically integrated than sentence (10a) (for example, various tests show that insertion of locative and adverbs between yêe and ga or the displacement of the ga-phrase are not possible in sentences (10b-c)). This rigid syntax is even more evident in AVCs deriving from original transitive complement-taking verbs. Indeed, the data show indications of lack of syntactic flexibility, such as a non-canonical word order where the direct object is shifted away from the lexical verb, which in some cases results in a V + ga + V structure. This is illustrated in the following (see L. Sibomana, 2001, p. 226, 228, 238) In (11a), the direct object of the lexical verb (wòybòr fo 'some woman') is shifted to the right of the verb, although this verb, hiijì 'marry', is normally an S-Aux-O-V-X order verb (i.e., with the direct object placed immediately before the verb). In (11b), the pronominal direct object of the lexical verb kay 'bother' is shifted to the left of the auxiliary zàa 'continue' (cf. the expected woodìn nôo gà zàa ga à kay, where the object pronoun à '3s' appears before the verb kay 'bother'). Finally in (11c), muusò 'lion' is the direct object of wi 'kill', a strong OV verb, but is shifted to the left of ga away from its verb. Despite these examples, ZC AVCs also seem to have some syntactic flexibility and can appear under many syntactic configurations, as illustrated in the following (see L. Sibomana, 2001, p. 222, 240 andA. Hamani, 1981, p. 374):

(12) a. …ir m`dùu g ir bàry-òo hañ-andì. 1p SBJ obtain GA 2p horse-DF water-CAU '…so that we can water our horse.' b. Ì yê g zàa g dàk â ga. 3p return GA continue GA press 3s on 'They again closed on following her.' c. Ay hoo ga yêe ga kâa. 1s fail GA return GA come 'I almost came back.' d. …ng m`dùu g dùu wurà daràizè. 3s SBJ obtain GA obtain gold coin '…so that she gets to get the gold coin.' In (12a), V2 hañandì 'give water' is a causative verb, which is a class of verbs that rarely accepts a post-verbal direct object (basic transitive verbs with a primary OV order can optionally have a VO order, see M. L. Abdoulaye, 2008). Maybe for this reason, the direct object of the verb (ir bàryòo 'our horse') stays in position, inserted between ga and the lexical verb. This shows that ZC AVCs, beside the rigid V + ga + V constructions, can also have a V + ga + VP structure, just like the purposive constructions. Sentences (12b-c) have a double nested AVC in a [Aux [AUX [V]]] structure. Sentence (12d) shows the same verb can be auxiliary and main verb.

Semantically, any syntactic flexibility notwithstanding, the AVC still refers to a single event and the auxiliary and the lexical verb obligatorily share certain operators like tense/aspect or negation. Sharing of tense/aspect is illustrated next (data from a Niamey speaker):

(13) Musa gay ga dìra wind-ǒo raa. musa last GA walk/go house-DF in 'Musa left the house long time ago.' (Lit. 'Musa lasted to walk in house')

In sentence (13), the perfective is zero-marked (normally, overt tense/ aspect markers appear before the V + ga + V constructions). As one can see in the translation, the perfective sense in fact applies to the lexical verb (i.e., Musa stayed away from home for a long time, not that he stayed home for a long time before going).

As discussed in the literature, verbs taking clausal complements are the ones most prone to auxiliarization. In the next set of data I list some auxiliary verbs (and their lexical source) culled from the three tales in L. [START_REF] Sibomana | Trois contes zarma[END_REF] (16) a. Han fo wòybòr-aa kàa g`tee gundè. day one woman-DF come GA do belly 'One day, as it happened, the woman became pregnant.' b. Irkoy kàa g`tee wòybòr-aa hin ng`kurnyò.

God come GA do woman-DF can 3s husband 'By God's will, the woman won control of her husband.' c. à kàa ga gar bor gǒo nèe… it come GA find one be there 'It happened someone was there.'

In many examples in L. [START_REF] Sibomana | Trois contes zarma[END_REF]'s texts, kâa appears naturally as V1 with the motion meaning 'come' in purposive constructions, as illustrated in (1a) above. In examples ( 16), the verb kâa has no motion meaning component and it simply codes the happening of some event, especially in narrative contexts. For example the difference between (16a) and its version without kàa ga (cf. wòybòraa tee gundè 'the woman became pregnant') is that (16a) is woven into a story where the pregnancy is highlighted and important in the story as a consequence or as a new departure. In (16b) a motion meaning is irrelevant with the subject (God), while in (16c) the 3 rd person singular pronoun subject à '3S' has an impersonal 'it' use.

Generally, the auxiliary is the first verb (V1), but it seems that verbs meaning 'finish' can also appear as auxiliary in V2 position, as illustrated next (data (17a) from L. Sibomana, 2002, p. 232, (17b) In (17a), ginger 'pray', the V1, is the main verb, while ban 'finish', the V2, is the auxiliary, contributing a perfective meaning. In (17b), too, it is the V2 daabandì 'close, finish' that contributes the perfective semantics. Apparently, it is a property of 'finish' verbs to appear as auxiliary verbs in V2 position (J. Heath, 1999, p. 337 also describes the same issue with ben 'finish' in Koyraboro Senni). Indeed, the verb ban 'finish', which besides its basic lexical use (cf. goyǒo ban 'finish the work'), can also appear as auxiliary in V1 or V2 position, as illustrated in ( 18). The two sentences may seem very close in meaning, but as V1 auxiliary, ban contributes a phasal aspectual semantics in (18a), but a perfective semantics in (18b), where it is the process of eating itself that is seen in its completion. Sentence (18a) says nothing about whether the process of eating itself has been completed through and through. It may be noted that J. [START_REF] Heath | A grammar of Koyra Chiini: The Songhay of Timbuktu[END_REF], trying to differentiate the meaning in the two orders, says that there is an iconicity ('eat' then 'finish') in sentences like (18b), but this does not seem to be a sufficient characterization of the two sentences.

In conclusion, AVCs in ZC seem to show features of both flexible and rigid constructions (for example, with a shifting of the direct object for a more closeknit V + ga + V structure). Nonetheless, they can be considered to be distinct form the original purposive and infinitive source constructions, which display only normal verb phrase syntax. The next section examines resultative constructions.

Ga as a linker in resultative constructions

ZC and related varieties are not serializing languages anywhere near typical examples like Yoruba or More (cf. N. Nikièma, 2003, p. 191). Nonetheless, as seen in Section 2, J. [START_REF] Heath | A Grammar of Koyraboro (Koroboro) Senni: The Songhay of Gao[END_REF] characterizes the Koira Chiini equivalents of the auxiliary constructions described in data (17-18) as being serial verb constructions. However, when one considers a stricter definition of serial verb constructions, then the conclusion is clear that ZC has no such constructions. The examples that come closest to a serialized structure in ZC are presented in the following (adapted (19a-d) from L. Sibomana, 2001, p. 228, 230, 232, (19ef) (1992, p.191) says that a resultative construction semantically involves a dynamic action and a resulting state, both typically expressed by the same verb form. In all these sentences, the two verbs describe essentially a single event in a way reminiscent of serial verbs. However, one would face a few problems analyzing these examples as serial constructions. First, ZC would be atypical in having a linker between the two serialized verbs. Indeed, one of A. Aikhenvald (2006. p. 20)'s criteria for serialization requires that no verb in the serial construction carry a mark of subordination or dependency (see also M. Haspelmath 2016, p. 296). Secondly, the resultative construction is very rare in ZC and these are the only three examples culled from L. Sibomana (2001)'s texts. In this case, it would be difficult to say that ZC is a serializing language. Finally, semantically the two verbs do not create a new meaning different from the meaning of any one of the verbs, as is typical in serial constructions (cf. A. Aikhenvald. 2006, p. 4). In fact there is no new meaning so much so that in all sentences, the first verbs can be dispensed with, while essentially keeping the same meaning, as can be seen in the translations. This is why I analyze these sentences as containing resultative constructions where the dynamic action is expressed by the first (and dispensable) verb and the result by the second verb. For example, in (19a) the husband raises ('strikes') his voice over that of the wife, with the result that the wife's speech is cut off. It may be noted that examples (17-18) may in fact derive from resultative constructions, which would then fall in line with M. Haspelmath's (1992) hypothesis that resultative forms can end up expressing the perfect and related aspectual values.

Conclusion

This paper has distinguished and described at least four main uses of the particle ga. First, ga introduces a purposive clause, following the main verb.

Secondly, ga can function as a sequential or infinitive marker that has a purely grammatical function and appearing sometimes for no obvious reason. All these constructions are bi-clausal with a main and a subordinating verb. A third major function of ga is to bind two verbs in an auxiliary constructions where the auxiliary, generally the V1, contributes phasal aspect semantics. Finally, the particle can also bind two verbs in a resultative construction where V1 describes the transformative change that results in the situations described by the second verb. The paper has shown that the auxiliary and resultative constructions are more grammaticalized, with one clause, and are syntactically more rigid than the purposive or infinitive constructions.

  and from Y. Bernard and M.[START_REF] Mary | Esquisse de grammaire zarma[END_REF].

	(14)Some auxiliaries expressing phasal or other aspecto-temporal semantics:
	a. sintin 'start'
	b. yêe 'resume, do again' (< motion 'return')
	c. too 'attain' (< motion 'reach, arrive at')
	d. ban 'finish'
	e. dìi 'start' (< 'seize, grab')
	f. gine 'have already done' (< 'precede')
	g. gay 'take a long time'
	h. waasu 'hurry'
	i. ban 'to have already (done)' (< 'finish')
	(15)Auxiliaries expressing a modal meaning:
	a. hìma 'ought to' (< 'resemble')
	b. hin 'be able'
	c. baa 'be about to, incline' (< 'want')
	d. duu 'succeed' (< 'win, obtain')
	e. koy 'risk' (< motion 'go')
	All these verbs express an aspectual semantics (inchoative, durative,
	completive, etc.) or a modal semantics (obligation, possibility, ability, intention,
	etc.). One of the most frequent auxiliary verbs in L. Sibomana (2001)'s texts is
	the verb kâa 'come' with the auxiliarized meaning 'happen to (verb)'. It appears
	no less than eight times. Some examples are given in the following (data (16a-
	b) from L. Sibomana, 2001, p. 224, 228):

  from Y. Bernard and M. White-Kaba, 1994):

	b. Irkòy n`taasoo bar	g`tee	dòonu bònyan. (=1b)
	God SEP sand-DF change GA make millet balls
	'God transformed the sand into millet balls.'
	c. Zaa	à dii woybòr-àa, à tun g`kay à n â sê…
	soon.as 3s see woman-DF 3s rise GA stand 3s say 3s to
	'As soon as he saw the woman, he stood up and said to her…'
	d. Bòrèy kar g	sày.
	people hit GA disperse
	'The people scattered.'
	e. Kàydiyà	tee ka bìsa.
	rainy.season do GA pass
	'The rainy season is now done/ over.'
	f. À tee ka si.
	3S do GA not,exist
	'He is dead.'
	(19) a. Kurnyè m`à sannoo kar g	kàa	maayòo ra.
	husband SBJ 3s talk	hit GA take.out mouth	in
	'[Whenever she speaks ill of his sister] the husband would
	interrupt her.'

I will analyze the sentences in (19) as resultative constructions. Haspelmath

It may be noted that B. OumarouYaro (1993, p. 132f) identifies the "ga" in (7-8) as the imperfective marker ga/gà, with a low or a high tone, which is different from the high tone only linker ga/ka (see alsoB. Oumarou Yaro, 1993, p. 113). While our investigations have not entirely cleared this issue, there are many speakers who would not allow a low-toned gà in these sentences. Y. Bernard and M.White-Kaba (1994, p. 124) also only cite a high-tone ga for the progressive construction. Complicating the matter further, L.Sibomana (2008, p. 64) claims that in the sequence "gǒo + ga + Verb", the verb conditions a polar tone on ga, which in turn conditions a polar tone on gǒo. However, his own illustrations do not support his claim.