Preux Pm

Prof Philippe Couratier

Alteration of nutritional status at diagnosis is a prognostic factor for survival of ALS patients

Keywords: Amyotrophic Lateral Sclerosis, Epidemiology, Cohort Studies, Prognosis, weight loss

Objectives: The aims were to analyze changes in nutritional parameters from diagnosis of ALS to death and to assess their relationships with survival at the time of diagnosis and during follow-up.

Methods: Ninety-two ALS patients were included and clinically assessed every three months (ALS FRS, MMT, forced vital capacity, weight, BMI, percent weight loss). Bioimpedance was performed to evaluate body composition (fat-free mass, fat mass and hydration status) and phase angle. Survival analyses were performed from diagnosis to death or censoring date using a Cox model.

Results:

The evolution of nutritional parameters in ALS patients was marked by significant decreases in weight, BMI, fat-free mass and phase angle, and increased fat mass. We identified an adjusted 30% increased risk of death for a 5% decrease from usual weight at time of diagnosis (Relative Risk (RR): 1.30 95%CI 1.08-1.56). During follow-up, we identified adjusted 34% (95%CI 18-51) and 24% (95%CI 13-36) increased risks of death associated with each 5% decrease in usual weight and each unit decrease in usual BMI, respectively (p<0.0001). Malnutrition during the course was related to shorter survival (p=0.01), and fat mass level was associated with a better outcome (RR 0.90 for each 2.5-kg fat mass increment).

Conclusions: Nutritional parameters of ALS patients worsened during evolution of the disease and worse nutritional status (at time of diagnosis or during the course) was associated with higher mortality. This study offers some justification for studying the use of therapeutic nutritional intervention to modify the survival of ALS patients.

INTRODUCTION

Alteration of nutritional status among patients suffering from amyotrophic lateral sclerosis (ALS) is multifactorial involving: dysphagia, chewing difficulties, difficulty moving the extremities, reduced caloric intake [START_REF] Slowie | Nutritional considerations in the management of patients with amyotrophic lateral sclerosis (ALS)[END_REF] and hypermetabolism [START_REF] Bouteloup | Hypermetabolism in ALS patients: an early and persistent phenomenon[END_REF][START_REF] Desport | Factors correlated with hypermetabolism in patients with amyotrophic lateral sclerosis[END_REF].

Malnutrition is an independent prognostic factor for survival during the course of ALS, with an eight-fold increased risk of death [START_REF] Desport | Nutritional status is a prognostic factor for survival in ALS patients[END_REF]. Body mass index (BMI) has been identified as a prognostic factor for survival at time of gastrostomy placement [START_REF] Desport | Nutritional assessment and survival in ALS patients[END_REF] and indications for noninvasive ventilation [START_REF] Lo Coco | Noninvasive positive-pressure ventilation in ALS: predictors of tolerance and survival[END_REF], and a recent study identified longer survival in ALS patients with a high blood LDL/HDL cholesterol level [START_REF] Dupuis | Dyslipidemia is a protective factor in amyotrophic lateral sclerosis[END_REF].

To date, studies on relationships between nutritional status and survival of ALS patients have considered nutritional status only during the course of the disease. There is a need to obtain further information on the relationships between survival and nutritional status at the time of diagnosis. It would also be of great interest to evaluate this relationship during follow-up, and to describe the evolution of nutritional parameters during the course of the disease. The aims of this study were to collect the following data at the time of diagnosis and during subsequent follow-up, to analyze changes that occur and to assess their relationships with survival: anthropometric nutritional parameters (percentage of weight lost, BMI, triceps skinfold thickness representing fat mass, mid-arm muscular circumference representing fat-free mass) and paraclinical parameters (fat mass, fat-free mass, phase angle, extracellular/intracellular fluid volumes measured by total body impedance analysis (BIA)).

METHODS

Eligibility criteria

This study was performed within the Limoges ALS expert centre. A total of 92 ALS patients diagnosed between 1997 and 2007 according to Airlie House criteria were enrolled. They included patients with a definite, probable or probable laboratory-supported form either at time of diagnosis or during follow-up. Subjects had to be followed at least twice during the course by the nutritional unit of the centre, with the first nutritional evaluation performed at the time of diagnosis.

Data collection

Socio-demographic and neurological data were extracted from the computerized database of the ALS centre, which contains prospectively gathered clinical data on all ALS patients. The database was approved by the CNIL (Commission nationale de l'informatique et des Libertés) and patients gave their informed consent for data collection. End of data collection was March 1 st 2009. Clinical assessments were performed every 3 months.

Neurological and respiratory assessments

These consisted of manual muscular testing (MMT) of all extremities and neck, as defined by the Medical Research Council (maximal value 150) and the ALS Functional Rating Scale (ALS FRS), (maximal value 40). The neurologist specified the date of onset of the first disease symptom, and the site of onset (bulbar or spinal). Diagnosis delay was calculated as the time between the dates of first symptoms and of diagnosis. Forced respiratory vital capacity was measured using a Hans Rudolph pneumotachograph, integrated in a body plethysmography system 1085 (CPF Medical Graphics, St Paul, MN, USA). Results were expressed in relation to a theoretical calculated index value.

Nutritional assessment

Patients were weighed in their underwear in a seated position on an electronic SECA chair scale (Vogel & Halke, Hamburg, Germany) recording to 0.1 kg. Height was obtained standing upright for all the patients at the first evaluation, using a SECA gauge recording to 0.2 cm (Vogel & Halke, Hamburg, Germany). BMI was calculated according to the formula BMI=weight/height 2 . Patients were classified for nutritional status using BMI as follows: (i) [START_REF]Nutrition and food security. Body Mass Index[END_REF][START_REF]Stratégie de prise en charge en cas de dénutrition protéinoénergétique chez la personne âgée[END_REF]. Percentage of weight lost was calculated as compared to usual weight as recorded 6 months before the first symptoms. Units of BMI lost were accordingly calculated using usual weight.

Triceps skinfold thickness (mm) was measured using a Harpenden caliper. Three measurements were performed on each side of the body, and the retained value was the mean of all. Mid-arm muscular circumference (MAMC, cm), was calculated using triceps skinfold thickness (TSF) and the mean mid-arm circumference (MAC, cm) measured on each side of the body, using the equation: MAMC=MAC-0.314xTSF [START_REF] Kasarskis | The use of upper extremity anthropometrics in the clinical assessment of patients with amyotrophic lateral sclerosis[END_REF]. BIA was performed using an Analycor3 instrument with surface electrodes (Spengler, Paris, France) according to standard methods, at 50 kHz, 5 kHz and 100 kHz [START_REF] Desport | Validation of bioelectrical impedance analysis in patients with amyotrophic lateral sclerosis[END_REF], (median number of evaluations: 3, interquartile range (IQR): 2-4). Monofrequency BIA measured phase angle (in degrees) which is directly related to cell membranes (amount and functional status of cells) and whose normal value is considered to be 6° and over in healthy subjects [START_REF] Barbosa-Silva | Bioelectrical impedance analysis: population reference values for phase angle by age and sex[END_REF], fat mass (kg) and fat-free mass (kg), and bifrequency estimated extracellular and intracellular fluid volumes (in liters) and their ratio which gives a picture of the cell membrane status [START_REF] Barbosa-Silva | Bioelectrical impedance analysis: population reference values for phase angle by age and sex[END_REF]. Phase angle (PA) was obtained using the formula: PA=arctan(Xc/R) (in degrees), where Xc is the body reactance (resistive effect due to capacities induced by tissue interfaces and cell membrane in ohms) and R is the bioelectrical resistance (linked to bodily extracellular hydration, in ohms).

Power assessment

When the total number of events is 74, a 0.050 level two-sided log-rank test for equality of survival curves will have 80% power to detect the difference between a group 1 survival probability at time t (24 months, for example) of 0.40, and a group 2 survival probability at time t of 0.62 (constant hazard ratio of 1.92).

Statistical analysis

Quantitative variables were described using median and IQR. Qualitative variables were described using frequency and percentage. Normality for distribution of quantitative variables was assessed using the Shapiro-Wilk test. Paired quantitative variables were compared using the Wilcoxon rank signed test. Quantitative variables were compared between groups using the Kruskal-Wallis test and pairwise comparisons used the Wilcoxon test. Paired proportions were compared using the Mac Nemar Chi-square test. Evolution of nutritional markers was plotted against time, using time until death as baseline. Means (+/-1 standard deviation) are depicted on the graphs. We calculated means (+/-standard deviation) of nutritional markers for all patients at two common time points: time of death and time of diagnosis. At intermediate time points (at least 6 months, 12 months, and 18 months before death) the numbers of patients may be lower than the total due to death over time. Survival was analysed from date of diagnosis until the death of the patient or the censoring date -the date of last neurological consultation. The Kaplan-Meier method was used to estimate survival function and the log rank test was used to compare survival distribution among groups. Univariate and multivariate analyses were performed using the Cox proportional hazard model. To identify the prognostic value of nutritional variables measured at diagnosis, we adjusted our analyses acording to clinical markers measured at diagnosis: ALS FRS (five-unit increment), MMT (five-unit increment), Airlie House Criteria (definite, probable, probable laboratory-supported ALS vs possible ALS), FVC (≥80% of theoretical value vs <80%) and diagnostic delay (1month increment). To identify the prognostic value of nutritional variables measured over the entire follow-up we used time-varying covariates for nutritional variables and for other neurological or respiratory adjustment variables: ALS FRS (five-unit increment), MMT (fiveunit increment), Airlie House criteria (definite ALS vs other categories) and FVC (10% increment) and diagnostic delay (1-month increment). Those adjustment variables were forced in the first multivariable model, which was simplified using a backward stepwise procedure.

Survival analyses for nutritional variables were performed separately. Relevant interactions between variables in each final multivariate model were tested. Respect for hypotheses of loglinearities effects of quantitatives variables were checked graphically and hypotheses for proportional hazard were tested using an interaction term between time and variables. P value<0.05 was considered statistically significant. We complied with STROBE guidelines [START_REF] Von Elm | The Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) statement: guidelines for reporting observational studies[END_REF]. Analyses were performed using SAS ® , Version 9.1.2 (SAS Institute, Cary, NC).

8

RESULTS

Baseline demographic and clinical characteristics

Median age at diagnosis was 65.6 years (IQR 56.5-73.3) and the sex ratio was 1. Bulbar form at onset represented 48% of cases. Supplementary baseline clinical characteristics are depicted in Table e-1 (supplementary file). The median weight variation at diagnosis according to usual weight was -2.32% (IQR -7.76-0.68) and median BMI variation at diagnosis according to usual BMI was -0.55 unit (IQR -1.99-0.15) (Table e-2, supplementary file). The two latter values were significantly different from 0 (p=0.0001). At the time of diagnosis, 8.70% of patients were malnourished according to BMI category.

Supplementary file : Table e-1: Demographic, neurological and respiratory characteristics of ALS patients at time of diagnosis

Characteristics

Evolution of nutritional markers between diagnosis and death

All nutritional markers varied between diagnosis and death (Table 1). Accordingly, weight, BMI, percentage of weight , BMI variation (as regards usual weight) and lean mass showed a .

Prognostic value of nutritional markers over the entire follow-up

While considering nutritional status over the entire follow-up, we identified a 34% increased risk of death for each 5% decrease from usual weight and a 24% increased risk for each unit decrease from usual BMI (Table 3). Rate of weight loss during the course of the disease did not appear to be significantly associated with survival. Malnutrition also appeared significantly associated with survival (p=0.01). As compared to patients in the normal range of BMI, malnourished patients experienced a 2.15 (IC95%

DISCUSSION

We have shown that patients with a weight loss from usual of 5% and over at the time of diagnosis experience a 2-fold increase in the risk of death (median survival time: 20.6 months (95% CI 12.4-29.0)) as compared to patients whose weight remains stable or drops by less than 5% (median survival time: 29.0 months (95% CI 21.2-38.5)). Weight loss at diagnosis was identified as an independent prognostic factor with an adjusted 30% increased risk of death for a 5% decrease from usual weight. We also identified during the course of ALS a decrease in weight, BMI, fat-free mass, and phase angle, and an increase in fat mass. We observed an adjusted 34% increased risk of death associated with each 5% decrease from usual weight during follow-up. Malnutrition during the course was associated with a shorter survival (p=0.01) and fat mass level was associated with a better outcome (RR 0.90 for each

2.5-kg fat mass increment).

This work is, to our knowledge, the first demonstration of the prognostic value for survival of the nutritional status of ALS patients at time of diagnosis. Other authors have reported the prognostic significance of BMI for survival, but only if it is assessed at the time of gastrostomy placement [START_REF] Desport | Nutritional assessment and survival in ALS patients[END_REF], or an indication for non-invasive ventilation, [START_REF] Lo Coco | Noninvasive positive-pressure ventilation in ALS: predictors of tolerance and survival[END_REF] or during the course of the disease [START_REF] Stambler | Prognostic indicators of survival in ALS. ALS CNTF Treatment Study Group[END_REF]. A correlation analysis performed by Kasarskis et al. also found an association between BMI and proximity of death [START_REF] Kasarskis | Nutritional status of patients with amyotrophic lateral sclerosis: relation to the proximity of death[END_REF].

Concerning malnutrition assessed by BMI during the follow-up, our results are in agreement with Desport et al. who, in 1999, (4) showed that malnutrition was an independent prognostic factor for survival. In that study, the mean delay between first symptoms and nutritional assessment (29±25 months) was longer than in our work where assessment was performed at time of diagnosis (median time between first symptoms and diagnosis 7.9 months (IQR 6.0-12.2)) and in subsequent follow-up. The absence of an association between malnutrition at diagnosis and survival here could be due to a lack of power caused by the low initial percentage (8.7%) of malnourished patients.

In a seminal paper, Slowie et al. reported that for a limited number of ALS patients during a large range of times between diagnosis and assessment (6 months to 11 years) 25% of patients lost 10% of their weight [START_REF] Slowie | Nutritional considerations in the management of patients with amyotrophic lateral sclerosis (ALS)[END_REF]. According to our data, at time of diagnosis, the nutritional status of patients is already highly altered: 50% lost more than 2.3% of weight and 25% lost more than 7.8% and 2 units of BMI. It has to be acknowledged that alteration of nutritional status is multifactorial: progressive muscular wasting due to denervation (1), swallowing or salivary disorders and dysphagia present at the time of diagnosis in patients with the bulbar form or appearing during the course are also implicated (4). In addition, anorexia, digestive disorders and upper limb motor difficulties contribute to low intake. Moreover, an increase in energy requirement sufficient to exceed intake has been demonstrated in 50% of patients [START_REF] Bouteloup | Hypermetabolism in ALS patients: an early and persistent phenomenon[END_REF][START_REF] Desport | Factors correlated with hypermetabolism in patients with amyotrophic lateral sclerosis[END_REF]. The reason for this hypermetabolism is not known. Our study was not designed to explore the respective contributions of these factors. A further study looking at that point could also assess the link between mobility and the weight/body composition of ALS patients.

Following the literature, only 9% of patients were malnourished according to BMI at the time of diagnosis, reaching 15% at the last nutritional evaluation [START_REF] Desport | Nutritional status is a prognostic factor for survival in ALS patients[END_REF][START_REF] Desport | Hypermetabolism in ALS: correlations with clinical and paraclinical parameters[END_REF][START_REF] Desport | Phase angle is a prognostic factor for survival in amyotrophic lateral sclerosis[END_REF]. This alteration is also highlighted by the dramatic reduction in phase angle at time of diagnosis and before death.

The early decrease of phase angle during ALS reflects alteration of the body composition, and general health and function. Similar patterns are displayed by the ratio of extracellular fluid volume over intracellular fluid volume.

In common with Nau et al [START_REF] Nau | Individuals with amyotrophic lateral sclerosis are in caloric balance despite losses in mass[END_REF] and other authors [START_REF] Vaisman | Do patients with amyotrophic lateral sclerosis (ALS) have increased energy needs?[END_REF], we identified modifications of body compartments in ALS patients, with a loss of fat-free mass and a gain of fat mass during the course. Our study shows for the first time that a higher fat mass is beneficial for survival of ALS patients. Similar results have already been reported in chronic obstructive pulmonary disease [START_REF] Chailleux | Prognostic value of nutritional depletion in patients with COPD treated by long-term oxygen therapy: data from the ANTADIR observatory[END_REF], cardiac insufficiency [START_REF] Kenchaiah | Body mass index and prognosis in patients with chronic heart failure: insights from the Candesartan in Heart failure: Assessment of Reduction in Mortality and morbidity (CHARM) program[END_REF], and in hemodialysis patients [START_REF] Kalantar-Zadeh | Association of morbid obesity and weight change over time with cardiovascular survival in hemodialysis population[END_REF] suggesting that in several chronic diseases a moderate excess of weight could aid survival. In ALS patients, Dupuis et al. [START_REF] Dupuis | Dyslipidemia is a protective factor in amyotrophic lateral sclerosis[END_REF] have shown that patients with high LDL/HDL cholesterol have longer survival confirming previous results in mice [START_REF] Dupuis | Evidence for defective energy homeostasis in amyotrophic lateral sclerosis: benefit of a high-energy diet in a transgenic mouse model[END_REF]. It is worth considering whether high LDL/HDL may be associated in many cases with either a sustained nutritional status or a weight excess with higher fat storage. In accord with Patel et al. [START_REF] Patel | Nutritional and exercise-based interventions in the treatment of amyotrophic lateral sclerosis[END_REF], our results suggest that enhanced fat storage through an energy enriched diet may improve patient survival. This hypothesis is also supported by animal models showing better outcome for SOD1-G93A transgenic ALS mice fed with a ketogenic diet [START_REF] Zhao | A ketogenic diet as a potential novel therapeutic intervention in amyotrophic lateral sclerosis[END_REF]. This concept is opposed to previous suggestions that modest weight loss may be desirable early in the course of the disease in order to obviate unnecessary accumulation of fat [START_REF] Hardiman | Symptomatic treatment of respiratory and nutritional failure in amyotrophic lateral sclerosis[END_REF].

We have to acknowledge that usual predictions from hospital-based study may have limited validity for population-based patients. Rapidly deteriorating patients may not survive until referral to an academic centre or may be too ill to go there whereas younger patients are more likely to seek a second opinion. Although our study is hospital-based, our ALS centre is the only multidisciplinary care centre in our region and our incidence profile (2.0/100 000 inhabitants for the 1997-2007 period and 4.4/100 000 in the 45-74 age group) is highly consistent with data from American or European registries [START_REF] Marin | Incidence of amyotrophic lateral sclerosis in the Limousin region of France, 1997-2007[END_REF]. It can be convincingly argued that our centre is representative of the ALS population. Moreover, due to the inclusion criteria (follow-up by our nutrition unit), half the patients had a bulbar form at onset. We think our results provide valuable information relevant to the whole ALS population because our study population is probably better followed from a nutritional point of view than the ALS population overall.

This result has three main implications. Finally, in contrast to other recognised prognostic factors at diagnosis, the nutritional status of patients can be modified using oral or enteral procedures. It is interesting to consider that the correction of weight loss at diagnosis could exceed the effect of riluzole on survival [START_REF] Bensimon | A controlled trial of riluzole in amyotrophic lateral sclerosis. ALS/Riluzole Study Group[END_REF].

Consequently, trials to investigate such interventions are needed. Early enteral nutrition could be a challenge because studies showed that percutaneous endoscopic gastrostomy (PEG) is effective in stabilizing body weight/BMI. According to the American guidelines for management of ALS patients, there is level B evidence that PEG should be considered for prolonging survival in patients with ALS, but the optimum time for PEG insertion is still unknown [START_REF] Miller | Practice parameter update: The care of the patient with amyotrophic lateral sclerosis: drug, nutritional, and respiratory therapies (an evidence-based review): report of the Quality Standards Subcommittee of the American Academy of Neurology[END_REF]. There is however growing evidence that PEG placement should be performed before FCV<50% to prevent respiratory deficiency during insertion, and radiological inserted gastrostomy has been shown to be a safe alternative below this threshold [START_REF] Chio | Percutaneous radiological gastrostomy: a safe and effective method of nutritional tube placement in advanced ALS[END_REF]. Although

European guidelines for care of ALS patients state that PEG placement should be envisaged early in the course of the disease (31), patients have difficulty accepting it then. The median delay between diagnosis and gastrostomy placement in our study (10 months) can be considered as early, but is probably late as far as nutritional status and improvement of survival are concerned. Another trial could investigate the effects of nutritional supplementation enriched in energy and lipids close to diagnosis as compared with a diet adapted for caloric needs.

FIGURE LEGEND

No Legend Title :

  significant worsening from diagnosis to death (Figures 1.a, 1.b, 1.c). Before death, median percent weight loss reached 7.05% (IQR 14.36-1.16) and median BMI loss 1.70 (3.62-.25). Fat-free mass also significantly decreased using bioimpedance (Figure 1.d) or mid-arm muscular circumference. Conversely, fat mass and triceps skinfold thickness significantly increased. Phase angle dramatically decreased (median value from 3.37° to 2.29°) and the ratio of extracellular fluid volume over intracellular fluid volume increased (median value from 0.93 to 1.00) (Figure 1.e). During follow up, the proportion of malnourished patients increased to 15.2%, though non-significantly (Mac Nemar Chi-square test p=0.058); the proportions of patients with normal BMI and who were overweight appeared stable (56.5% and 22.8%, respectively) and the proportion with obesity was reduced (5.5%).

  First, our findings provide important support for a reevaluation of daily routine nutritional management and for considering early nutritional intervention to improve survival of ALS patients. The prognostic value of weight loss at the time of diagnosis and quite late nutritional interventions allow us to propose close monitoring of nutritional status following a diagnosis of ALS. Despite the value of BIA in monitoring body composition, our results and their clinical application support weight assessment as the first priority. We propose a weight loss of 5% from usual be considered a threshold for systematic dietary recall, nutritional assessment, and BIA evaluation of fat mass and fat-free mass. For people without such a weight loss, close monitoring every 3 months of weight at least could be appropriate. Our results have other implications for epidemiological and clinical research. Weight loss at the time of diagnosis is an independent prognostic factor for survival of ALS patients, therefore observational studies should adjust their estimations accordingly. Those conducting clinical trials might use percentage weight loss as a stratification criterion because a slight disequilibrium between groups for this strong prognostic factor could mask the modest efficacy of a new treatment.

Figure 1 :Figure 2

 12 Figure 2

  malnutrition: BMI <18.5 if age <70 years and BMI<21 if age ≥70 years; (ii) normal status: 18.5≤BMI<25 if age <70 years and 21≤BMI<27 if age ≥70 years; (iii) overweight: 25≤BMI<30 if age <70 years and 27≤BMI<30 if age ≥70 years; (iv) obesity: BMI≥30

  At time of diagnosis variation statistically different from 0 (p<0.0001). † Less than 92 due to impossible body impedance analysis or missing value

	age ≥70 years; (iii) Overweight: 25≤BMI<30 if age <70 years and 27≤BMI<30 if age ≥70 years;
	(iv) Obese BMI≥30. Medical care and outcome
		Median or
	IQR or % During follow-up, 39.10% of patients underwent non-invasive ventilation and 57.60% were	N
	frequencies 65.64 Median or gastrostomised. All patients were treated with riluzole. The proportion of gastrostomy was Age at diagnosis, years (56.46-73.35) Nutritional variables IQR or % frequencies significantly higher in patients malnourished at the time of diagnosis (75.00%) as compared to	N	92
	Gender Male/female Weight, kg patients with a normal BMI (59.50%), overweight patients (64.50%) and obese patients 46/46 (50.00/50.00) 66.15 (56.95-75.00)	92	92
	Diagnosis delay, months Body mass index (18.20%), (p=0.036). Median time between diagnosis and gastrostomy placement was 10.00 7.93 (6.05-12.22) 24.17 (21.63-26.91)	92	92
	Form at onset Bulbar/Spinal Rate of weight loss from usual weight (% / month) months (IQR 6.10-15.20). During follow-up, 74 patients died (80.40%), median survival time 44/48 (47.83/52.17) -0.32 (-1.04-0.08)	92	92
	Airlie House criteria at diagnosis Rate of BMI loss from usual BMI (unit / month) being 27.80 months, (95% confidence interval (95% CI), 19.50-30.40).	-0.08	(-0.25-0.02)	92	92
	Definite BMI categories*	8		8.70		92
	Probable	Malnourished	53	8	57.61	8.70
	Probable laboratory-supported Normal	3	50	3.26	54.30
	Possible	Overweight	28	23	30.43	25.00
	ALS FRS score at diagnosis /40 Obese	33	11	(30-36)	12.00	92
	MMT score at diagnosis /150 Weight variation from usual weight (%)	135	-2.32*	(125-145) (-7.76-0.68)	92	92
	FVC (percent of theoretical value) BMI variation from usual BMI (unit)	92	-0.55*	(73-108) (-1.99-0.15)	92	92
	Mid-arm muscle circumference, cm		23.89	(21.97-26.57)	92
	Triceps skinfold thickness, mm		12.47	(9.61-16.78)	92
	Phase angle, °		3.38	(2.61-4.34)	83 †
	Extracellular fluid/intracellular fluid volume		0.91	(0.83-1.01)	89 †
	Lean mass, kg		45.11	(36.20-52.74)	86 †
	Fat mass, kg		19.97	(14.83-24.28)	86 †

Legend: IQR: Interquartile range; ALS FRS: Amyotrophic Lateral Sclerosis Functional Rating Score; MMT: manual muscular testing; FVC : forced vital capacity.

Supplementary file :

Table e-2: Nutritional variables at time of diagnosis Legend: IQR: Interquartile range. BMI categorization: (i) Malnutrition: BMI <18.5 if age <70 years and BMI<21 if age ≥70 years; (ii) Normal status 18.5≤BMI<25 if age <70 years and 21≤BMI<27 if *

Table 1 : Nutritional variables at diagnosis and last evaluation for people who died during follow up

 1

	Legend: IQR: Interquartile range.

value of nutritional markers at the time of diagnosis

  At the time of diagnosis, the percentage of weight lost from usual weight was significantly associated with survival. After adjustment for age, gender, bulbar form at onset, ALS FRS, MMT, FVC and diagnostic delay, we identified a 30% increase in the risk of death (95% CI 8-56%) for each 5% decrease in weight (Table2). We identified a significant difference in survival between ALS patients with a weight loss of 5% and over at the time of diagnosis (median survival time : 20.6 months (95% CI 12.4-29.0)) as compared to patients whose weight was stable or dropped by less than 5% (median survival time: 29.0 months (95% CI 21.2-38.5)), Log rank test p=0.01, (Figure2). Patients with a weight loss of 5% or over experienced an adjusted 1.92 Relative Risk (RR) of death (95% CI 1.15-3.18). Each BMI unit lost from the usual BMI was associated with an adjusted 20% increased risk of death (95% CI

6-36%). Rate of weight loss (% per month) and rate of BMI loss (unit per month) between first symptoms and diagnosis were also independently associated with survival. Malnutrition at baseline and other nutritional variables including phase angle and ratio of extracellular fluid volume over intracellular fluid volume were not associated with survival in multivariate analysis.

Table 2 : Relative risks of death associated with nutritional variables measured at diagnosis in univariate and multivariate analysis. Each nutritional variable has been analysed independently from other nutritional variables.

 2 Survival analyses were performed separately for each nutritional variable. † Adjustment on age, gender, bulbar form at onset, ALS FRS at diagnosis, manual muscular testing at diagnosis, forced vital capacity at diagnosis ≥80 vs <80, Airlie House criteria at diagnosis definite, probable or probable laboratory-supported vs possible and diagnostic delay.

		Univariate analysis	Multivariate analysis
	Nutritional variables at diagnosis*
		cHR	95% CI P value aHR † 95% CI	P value
	Weight variationfrom usual weight (for 5% decrease)	1.28	1.06-1.54	0.009 1.31	1.08-1.60	0.006
	BMI variation from usual BMI (for one unit decrease)	1.20	1.06-1.36	0.005 1.23	1.07-1.41	0.003
	Rate of weight loss from usual weight (% / month)	1.09	1.04-1.14 0.0002 1.07	1.02-1.12	0.003
	Rate of BMI loss from usual BMI (unit / month)	1.35	1.16-1.58 0.0001 1.28	1.09-1.50	0.003
	Malnutrition at diagnosis vs other BMI categories	1.67	0.79-3.50	0.18	1.32	0.62-2.80	0.47
	Mid-arm muscle circumference, cm (for one unit increase)	0.96	0.90-1.03	0.23	0.95	0.89-1.01	0.12
	Triceps skinfold thickness, cm (for one unit increase)	0.99	0.96-1.03	0.81	1.00	0.96-1.03	0.78
	Phase angle, ° (for one unit decrease)	1.29	1.02-1.63	0.03	1.15	0.87-1.52	0.33
	Extracellular fluid/intracellular fluid volume (for 0.2 unit increase)	1.40	0.98-2.00	0.06	1.34	0.92-1.97	0.12
	Lean mass, kg (for 2.5 unit increase)	0.97	0.92-1.03	0.33	1.00	0.94-1.07	0.90
	Fat mass, kg (for 2.5 unit increase)	0.99	0.92-1.06	0.81	0.96	0.89-1.03	0.21
	Legend : cHR: crude Hazard Ratio; aHR: adjusted Hazard Ratio.

*

Table 3 : Relative risks of death associated with nutritional variables measured over the entire follow-up in univariate and multivariate analysis. Each nutritional variable has been analysed independently from other nutritional variables.

 3

		Univariate analysis	Multivariate analysis
	During follow-up nutritional variables*
		cHR	95% CI P value aHR † 95% CI	P value
	Weight variation from usual weight (for 5% decrease)	1.40	1.23-1.59 <0.0001 1.34	1.18-1.51	<0.0001
	BMI variation from usual BMI (for one unit decrease)	1.30	1.18-1.42 <0.0001 1.24	1.13-1.36	<0.0001
	Rate of weight loss from usual weight (% / month)	1.11	1.02-1.20	0.01	1.07	0.98-1.17	0.11
	Rate of BMI loss from usual BMI (unit / month)	1.44	1.08-1.93	0.01	1.28	0.94-1.74	0.11
	Malnutrition vs other BMI categories	2.32	1.25-4.29	0.007	2.56	1.33-4.94	0.005
	BMI categories			0.03			0.01
	Malnutrition	2.15	1.14-4.08		2.15	1.09-4.25
	Normality (reference)	1.00			1.00
	Overweight	0.98	0.56-1.72		0.71	0.40-1.28
	Obesity	0.43	0.13-1.40		0.36	0.11-1.19
	Mid-arm muscle circumference, cm (for one unit increase)	0.89	0.82-0.95	0.001	0.93 0.86-1.005	0.07
	Triceps skinfold thickness, cm (for one unit increase)	0.99	0.96-1.03	0.66	0.94	0.90-0.98	0.003

* Survival analyses were performed separately for each nutritional variable. † Adjustment on age, gender, bulbar form at onset, ALS FRS, manual muscular testing, forced vital capacity, Airlie House criteria during followup and diagnostic delay.

* Comparisons between time of diagnosis and before death † At time of diagnosis variation statistically different from 0 (p<0.0001) ‡ Less than 74 due to impossible body impedance analysis or missing values.

AUTHORS AND CONTRIBUTIONS:

All authors significantly contributed to this paper. Philippe Couratier, Jean Claude

COMPETING INTERESTS:

Authors have no conflict of interest to declare.

AKNOWLEDGEMENTS:

Acknowledgement: We thank William Francis for reviewing the manuscript.

FUNDING:

None

LICENCE STATEMENT

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Christian Cibert
email: cibert@lisv.uvsq.fr

Jérémy Toscano

Vincent Pensée

Guy Bonnet

Bending of the "9+2" axoneme analysed by the finite element method

Keywords: axoneme, bending, finite element, flagellum, sliding

), Cell Motil. Cytoskel. 59: 153-68), (ii) the internal tensions of the radial spokes and the tangential links (nexin links, dynein arms), (iii) a theoretical 5 m long proximal segment of the axoneme and (iv) the short proximal segment of the axoneme, we have reevaluated the adjustments of these intervals using a finite element approach. The movements we have calculated within the axonemal cylinder are consistent with the basic hypothesis that found the Geometric Clutch model, excepted that the axonemal side where the dynein arms are active increases the intervals between the two neighbor outer doublet pairs. This result allows us to propose a mechanism of bending reversion of the axoneme, involving the concerted ignition of the molecular engines along the two opposite sides of the axoneme delineated by the bending plane.

INTRODUCTION

Axoneme is the macromolecular scaffold that makes motile the flagella and cilia of the eukaryotic cell [START_REF] Gibbons | Cilia and flagella of eukaryotes[END_REF]. From a physical point of view, it is a cylinder of nine longitudinal beams (the nine Outer Doublet Pairs of microtubules (ODPs)), which surrounds a central apparatus organized by two longitudinal beams (the central pair of microtubules [START_REF] Downing | Structural insights into microtubule doublet interactions in axoneme[END_REF][START_REF] Sui | Molecular architecture of axonemal microtubule doublets revealed by cryo-electron tomography[END_REF]). The coordinated sliding of the ODPs (because of the activity of the periodical dynein arms (DA), the molecular motors (Burgess et al., 1991a;[START_REF] Burgess | Dynein struture and power stroke[END_REF]Burgess et al., 1991b , 2005;[START_REF] Hamasaki | Mechanochemical aspects of axonemal dynein activity studied by in vitro microtubule translocation[END_REF][START_REF] Lindemann | Does axonemal dynein push, pull or oscillate ?[END_REF][START_REF] Mallik | Cytoplasmic dynein functions as a gear in response to load[END_REF][START_REF] Omoto | Cooperativity, in axonemal motion : analysis of a four-state, two-site kinetic model[END_REF][START_REF] Shingyoji | Dynein arms are oscillating force generators[END_REF]) is converted to bending because of the presence of periodic elastic molecular links between each pair of ODPs (the nexin links (NL) and the dynein arms themselves) [START_REF] Brokaw | Direct measurements of sliding between outer doublet microtubules in swimming sperm flagella[END_REF][START_REF] Cibert | Elastic extension and jump of the flagellar nexin links: a theoretical mechanical cycle[END_REF][START_REF] Downing | Structural insights into microtubule doublet interactions in axoneme[END_REF]Lindemann, 1994b;[START_REF] Lindemann | Evidence for axonemal distortion during the flagellar beat of Chlamydomonas[END_REF][START_REF] Lindemann | The counterbend phenomenon in dynein-disabled rat sperm flagella and what it reveals about the interdoublet elasticity[END_REF]), and the periodic radial spokes (RS), which link each ODP to the central apparatus [START_REF] Cibert | Entropy and information in flagellar axoneme cybernetics : a radial spokes integrative function[END_REF][START_REF] Dymek | A conserved CaM-and radial spoke-associated complex mediates regulation of flagellar dynein activity[END_REF][START_REF] Gardner | Components of a "dynein regullatory complex" are located at the junction between the radial spokes and the dynein arms in Chlamydomonas flagella[END_REF][START_REF] Goodenough | Substructure of inner dynein arms, radial spokes, and the central pair/projection complex of cilia and flagella[END_REF][START_REF] Lindemann | The Geometric Clutch as a working hypothesis for future research on cilia and flagella[END_REF][START_REF] Mitchell | ATP Production in Chlamydomonas reinhardtii Flagella by Glycolytic Enzymes[END_REF][START_REF] Mitchell | Bend propagation drives central pair rotation in Chlamydomonas reinhardtii flagella[END_REF][START_REF] Smith | The radial spokes and central apparatus : Mechano-chemical transducers that regulate flagellar motility[END_REF][START_REF] Yang | Localization of calcmodulin and dynein light chain LC8 in flagellar radial spokes[END_REF]. This mechanism induces the propagation of a wave train along the organelles.

Instantaneous regulation of the machinery remains, however, mainly unknown, in spite of the existence of clever biochemical and topological models [START_REF] Brokaw | Effects of viscosity and ATP concentration on the movement of reactivated sea-urchin sperm flagella[END_REF][START_REF] Dymek | A conserved CaM-and radial spoke-associated complex mediates regulation of flagellar dynein activity[END_REF][START_REF] Gertsberg | Intracellular Ca2+ regulates the phosphorylation and the dephosphorylation of ciliary proteins via the NO pathway[END_REF][START_REF] Hayashi | Bending-induced switching of dynein activity in elastase-treated axonemes of sea urchin sperm, roles of Ca2+ and ADP[END_REF][START_REF] Huang | Suppressor mutation in Chlamydomonas reveals a regulatory mechanism of flagellar function[END_REF][START_REF] Inaba | Molecular architecture of the sperm flagella: molecules for motility and signaling[END_REF][START_REF] Li | Torsion of the central pair microtubules in eukaryotic flagella due to bending-driven lateral buckling[END_REF]Lindemann, 1994a;[START_REF] Lindemann | The Geometric Clutch as a working hypothesis for future research on cilia and flagella[END_REF][START_REF] Lindemann | Evidence for axonemal distortion during the flagellar beat of Chlamydomonas[END_REF]Mitchell, 2003a;Mitchell, 2003b;[START_REF] Morita | Microtubule sliding movement in tilapia sperm flagella axoneme is regulated by Ca(2+)/calmodulindependent protein phosphorylation[END_REF][START_REF] Morita | Effects of imposed bending on microtubule sliding in sperm flagella[END_REF][START_REF] Noguchi | Control of ciliary orientation through cAMP-dependent phosphorylation of axonemal proteins in Paramecium caudatum[END_REF][START_REF] Noguchi | Augmented ciliary reorientation response and cAMP-dependent protein phosphorylation induced by glycerol in triton-extracted Paramecium[END_REF][START_REF] Piperno | The Inner Dynein Arms I2 Interact with a "Dynein Regulatory Complex" in Chlamydomonas Flagella[END_REF][START_REF] Rupp | A subunit of the dynein regulatory complex in Chlamydomonas is a homologue of a growth arrest-specific gene product[END_REF][START_REF] Smith | The radial spokes and central apparatus : Mechano-chemical transducers that regulate flagellar motility[END_REF][START_REF] Wilson | Regulation of flagellar assembly by glycogen synthase kinase 3 in Chlamydomonas reinhardtii[END_REF][START_REF] Woolley | Studies on the eel sperm flagellum. I. The structure of the inner dynein arm complex[END_REF].

Among them, the Geometric Clutch (GC) model proposed by Lindemann assumes that the activity of the DAs along the two opposite faces of the axoneme depends on the interdoublet interval that varies during the alternating beating movement: the larger the interval, the lower the canonical propulsive activity of the DAs (which is basically directed toward the minus end of the microtubules (Lindemann, 1994a)); this model promotes the role of the self-organization of the axoneme in the instantaneous regulation of its own machinery [START_REF] Goldstein | Kinetic model for dynein ascillation activity[END_REF][START_REF] Lindemann | Does axonemal dynein push, pull or oscillate ?[END_REF][START_REF] Lindemann | The Geometric Clutch as a working hypothesis for future research on cilia and flagella[END_REF][START_REF] Sakakibara | Diameter oscillation of axonemes in sea-urchin sperm flagella[END_REF]).

In this context, using a finite element approach [START_REF] Cibert | Geometry drives the "deviated-bending" of the bi-tubular structures of the 9 + 2 axoneme in the flagellum[END_REF], we have studied the deformation of the proximal 5 m long segment of a "9+2" axoneme to analyze what might be the topological events occurring at this level, accounting for the synchronous sliding hypothesis [START_REF] Brokaw | Microtubule sliding, bend initiation, and bend propagation parameters of Ciona sperm flagella altered by viscous load[END_REF][START_REF] Goldstein | Form of developing bends in reactivated sperm flagella[END_REF].

MODEL AND CALCULATION

We use the finite element method to calculate the deformed configurations of a theoretical model whose mechanical characteristics were assumed to be equivalent to that of a real axoneme. The calculus is performed using MSC NASTRAN, the "finite element" software used in the industrial field (MSC Software Corporation, USA). All parts of the model are linearly elastic, but nonlinear effects are taken into account: they come from the computation of second order moments induced when the actual configuration after displacement instead of the initial configuration is taken into account for computing internal moments.

Model meshing was done from the knowledge of the axonemal ultrastructure and the basic mechanisms that make it motile.

The first step of the modeling was dedicated to the definition of the bio-mechanical characteristics of the axonemal elements assumed to be essential in the axonemal movement (Figure 1 and Figure 2). We have considered two sorts of elements: beams (which transmit internal moments and longitudinal forces) and rods (which transmit longitudinal forces only). Elements modeled as rods are linked to beams by pin junctions. ODPs, dynein arms and central apparatus are modeled as beams. The other components of the axoneme (i.e. the nexin links, the radial spokes and the actuators) were modeled as rods. Second, because of the longitudinal periodicities of the appendages carried by the ODPs (dynein arms, nexin links and radial spokes) and the cylindrical organization of the axoneme, model is constituted by a series of cylindrical 96 nm long modules, organized by the nine outer doublets associated each to 1 radial spoke, 1 nexin link, 1 outer dynein arm and 1 inner dynein arm, where each of these appendages are considered to be equivalent to the 3 radial spokes, the nexin link, the 4 outer dynein arms and the 3 inner dynein arms constitutively located along the homologous 96 nm long segment of the biological model (Figure 1 and Figure 2). The central apparatus of the axoneme is modeled as a beam along which the heads of the radial spokes are linked by pin junctions.

In the model, the dynein arms do not link directly nodes #3 and 5 of the ODP on which they are permanently bound as observed in the biological situation; they are carried by their actuators only (Figure 1 and Figure 2). This was the sine qua non condition to limit the artifactual bending of the model that we observed using a previous version of the model, considering dynein arms modeled each as a bar. When dynein arms are modeled as bar series along the ODPs, curvature of the model is opposite to that expected. The advantage of the conformation we have chosen is that it reduces the incidence of the forces which are tangential and normal to the axis of the model; in this model the ODPs can move within the axonemal cylinder and be active on the elasticity of both the DAs and the NLs.

The third step is the definition of the modes according to which the actuators of the dynein arms have to move along and around the model (Figure 1). Because of the synchronous sliding and the rigid anchoring of the ODPs at the proximal end of the biological model, the local shear -obtained at a given curvilinear abscissa -depends on the sum of the elementary shear involving each the modules located upstream and at this curvilinear abscissa. Consequently, to promote the bending of the model, we have chosen to move the two actuators associated to each of the dynein arms along the module series according to a linear gradient of amplitude. The activation of the upstream and downstream actuators of each dynein arm were produced using the concept of free deformations (Appendix 1) and according to a gradient along each of the ODPs to obtain a curvature that depends on the cumulative sliding (Appendix 2). Thus, we defined a linear gradient of free deformations along the model that increases and decreases of the same amplitude the length of the two actuators. To limit the skewing and twisting of the model, because of its basic cylindrical architecture, deformations of the actuators depend (at each curvilinear abscissa) on the lengths of the projections of the arms (IDA, ODA) on the bending plane, which has been considered to be constant along the entire length of the model [START_REF] Cibert | Axonemal activity relative to the 2D/3D-waveform conversion of the flagellum[END_REF] (Appendix 3).

It is noteworthy that we have calculated only equilibriums. But, because the curvatures are low under our conditions, the intermediate conformations of the model that would exist between the straight conformation and the curved one could be deduced from the knowledge of these initial and final states.

RESULTS AND DISCUSSION

Internal loading of the axoneme was calculated under two pairs of basic modes (I, II, III and IV) (Figure 3), modifying the lengths of the actuators of the dynein arms as described above (Figure 1). Both of them induce the relative shear of the ODPs (Figure 4).

Under the loading modes I (+z), dynein arms located along the two opposites sides of the axoneme defined by the rank of the outer doublet [#6,7,8,9] and [#1,2,3,4] produce a force directed toward the minus end of the outer doublet on which they walk (their canonic activity) and are inactive, respectively. Along the inactive side of the axoneme, DAs are Under loading modes III (+z) and IV (-z), the DAs located on the two opposites sides of the axoneme pull and push on the neighboring ODPs to promote the bending of the model in the same polarity. These two loading modes are limit cases, because they imply that along one of the opposite sides of the axoneme, the dynein arms produce forces in the "anti canonic" direction (i.e. toward the plus end of the outer doublets on which they walk) a situation which was,observed in vitro, studying reconstructed mammalian models [START_REF] Lindemann | Does axonemal dynein push, pull or oscillate ?[END_REF][START_REF] Lorch | The motor activity of mammalian axonemal dynein studied in situ on doublet microtubules[END_REF]. These four loading modes are defined to induce planar bends (Appendix 2 and Appendix 3). Our calculations neglect the incidence of the swimming medium because only the equilibrium -and not the steady state -of the movement is considered, even if it is clearly demonstrated that the swimming medium has a direct regulatory effect on the axonemal machinery (Brokaw, 1966a;Brokaw, 1966b;[START_REF] Cortez | Simulation of swimming organisms: coupling internal mechanics with external fluid dynamics[END_REF][START_REF] Hilfinger | The chirality of ciliary beats[END_REF].

Figure 6 shows the tangential forces of the RSs and the NLs. These diagrams allowed us to define the length of the segment of interest of the bent models we obtained under the 4 loading modes. Taking into consideration the tangential forces of the RSs, we observed that (i) they increase rapidly, (ii) their maximum range is observed closely to the 21 st module and, (iii) after this abscissa, they converge, tending to 0 at the level of the 41 st module.

Along the 10 last modules, the graphs superpose and are difficult to be analyzed. Thus, we have chosen to consider the segments of interest constituted by the 41 proximal modules along the deformed models.

Figure 7 shows the deformations of the central apparatus that represent the 3D-bending of the model we have obtained under the four loading modes. In spite of the conditions we have chosen, which normally must induce planar bends, loading modes I and II induce clearly the 3D-bending, because projections of the curvature in the xy plane under these two loading modes have the same sign. This means that the effective bending planes we obtain when the model bends in the -z and +z direction form a dihedron. Under loading modes III and IV, curvatures of the model in the xy and the xz planes are roughly proportional, whatever the ranks of the module; the arcs obtained under these two loading modes are coplanar.

The observation of a curvature in the y direction is not expected, because, as stated above, the actuation of the dynein arms was defined in order to induce the bending in the xz plane only. This has to be considered however, more carefully. First, the absolute value of the ratio of the displacements observed in the two perpendicular planes xy and xz at the end of the segment of interest (Figure 7) equals 500/25 ( 20), 500/16 ( 30), 650/25 ( 25) and 650/27 ( 25) under the 4 loading modes, respectively, making the xy component lower than the xz one. Second, when the model is studied in a mathematical linear context (not shown), the projections of the arcs in the xy plane superpose on the x axis. This demonstrates that the nonlinear terms are incident in this calculation, even if they induce a secondary bending of short magnitude.

The movements of the ODPs occurring within the 21 st module under the 4 loading modes are presented in Figure 8 Figure 10 and Figure 11 describe the conformation of 41 st cross section of the segment of interest observed under the 4 loading modes. Along these 20 distal elements, under the loading mode I and II, the intervals between active ODPs are always larger than those of ODPs located on the opposite inactive side of the axoneme, even if the axoneme is involved in a global twisting. Under the loading modes III and IV, the two opposite halves of the axoneme delineated by the bending plane, converge toward the inner side of the curvature, but the intervals between the ODPs located along the two active opposite side are always larger than the others.

Consequently, activity of the dynein arms along the OPDs induces the increase of the intervals of the ODPs, whatever the polarity of the force they produce.

Our calculations show also that, along the active side (whatever the polarity of the force it produces), the outer doublets are pushed baseward; the outer doublets dynein arms of which are inactive are pulled tipward. The outer doublets located outside the curvature are pulled baseward.

From a biological point of view, the moments due to the relative displacements of nodes #1 and 4 -that create mechanical tensions inside the walls of the ODPs -associated to the flexions of the RSs that constrain node #4 as well as the central apparatus, could be involved in the regulation of the axonemal machinery via either the DRC (dynein regulatory complex), which are assumed to be involved in the direct regulation of the dynein arms in the actual biological system [START_REF] Nakano | Central-pair-linked regulation of microtubule sliding by calcium in flagellar axonemes[END_REF][START_REF] Rupp | A subunit of the dynein regulatory complex in Chlamydomonas is a homologue of a growth arrest-specific gene product[END_REF], or the tubulin monomers themselves -associated to the ensemble of the molecules that contribute to the architecture of the ODPs -since the calculations show that the distribution of these moments, their sign and their modules depend on the bending polarity and on the loading mode.

Because the orientations of the ODPs are constant during their rotation around the axonemal cylinder, the apparent lengths of the inner and of the outer dynein arms vary in such a way that those of the outer dynein arms are shortened as compared to those of the inner dynein arms [START_REF] Cibert | Geometry drives the "deviated-bending" of the bi-tubular structures of the 9 + 2 axoneme in the flagellum[END_REF]. This mechanism could be involved in the discrimination of the functions of the inner and outer rows of dynein arms [START_REF] Brokaw | Computer simulation of flagellar movement: VII. Conventional but functionaly different cross-bridge models for inner and outer arm dyneins can explain the effects of outer arm dynein removal[END_REF].

In effect, because of the rotation of the ODPs, the orientation of the bending plane has to change locally, and the activities of the two rows of dynein arms have to be adjusted as functions of these joint rotations.

As stated above the main results of this study is that the intervals of the ODPs whose dynein arms are active increase, while they decrease along the inactive side of the machinery, whatever the polarity of the walk of the dynein arms (Figure 6). They are consistent with the experimental observations that demonstrate the "respiration" of the axoneme [START_REF] Lindemann | Evidence for axonemal distortion during the flagellar beat of Chlamydomonas[END_REF][START_REF] Sakakibara | Diameter oscillation of axonemes in sea-urchin sperm flagella[END_REF], (i.e. the local and cyclic variations of the diameter of the axoneme when it beats). They contradict, however, partly the hypotheses that found the Geometric Clutch model [START_REF] Lindemann | The Geometric Clutch as a working hypothesis for future research on cilia and flagella[END_REF] because of the sign that characterizes the polarity of the relative displacements of the ODPs along the "active" and the "inactive" opposite sides of the axoneme.

Because the finite element method takes into consideration more than the longitudinal tensions (as proposed by the Geometric Clutch model), but the constraints due to the deviated bending of the ODPs and the ones due to the radial spokes and the tangential links in regard to the axonemal cylinder (nexin links and dynein arms), this result is not surprising. The existence of ODP groups within the axonemal cylinder seems to be less significant on its own than the necessary adjustments of the relative intervals between the ODPs in which these groups are involved.

Comparison of the cylindrical deformations we observe under the four loading modes allows us to propose a scheme that could explain the reversion of the bending polarity of the axoneme, this mechanism being equivalent whatever the curvilinear abscissa along the model (Figure 12 and Figure 13). Assuming that: (i) interval between two neighboring ODPs increases when the dynein arms are active, (ii) loading modes I and II are the basic modes allowing the axoneme to bend, (iii) compressed inactive side becomes active during a short period of time inducing the "anti-canonic" polarity of the dynein arms movement, we propose that after the overflowing of internal tension, the activities of the opposite sides of the axoneme revert, and induce the change in the internal tension of the axoneme.

In this scheme, the dynein regulatory complex [START_REF] Piperno | The Inner Dynein Arms I2 Interact with a "Dynein Regulatory Complex" in Chlamydomonas Flagella[END_REF][START_REF] Rupp | A subunit of the dynein regulatory complex in Chlamydomonas is a homologue of a growth arrest-specific gene product[END_REF] could play a crucial function, because it could be sensitive to the moments involving nodes #1 and 4 of each ODP that we have characterized along a 5 m long segment of the axoneme.

We did not observe however, any displacement of the central pair toward the external side of the curvature as described in the case of the flagellum of Chlamydomonas (Mitchell, 2003b). Taking into consideration the assumptions we used, the central apparatus is modeled as a beam whose location within the axonemal cylinder depends on the constraints due to the radial spokes, which have been also modeled as beams.

Consequently, the rigidity of our model could limit the actual displacement of the central apparatus within the axoneme, the more so as, in vivo, these displacements could involve passive and active mechanisms within the complex constituted by the spoke heads and the central apparatus, the last being impossible to conceive in the context of this study.

Topological adjustments are directly involved in the regulation of the axoneme as proposed by the geometric clutch model proposed by Lindemann, the "switch point" that drives the alternating shear of the ODPs [START_REF] Satir | Splitting the ciliary axoneme implications for a 'switchpoint' model of dynein arm activity in ciliary motion[END_REF]) could be considered as those that regulate the small-world networks because of the similitude that exists between the architecture of the axoneme and that of these networks [START_REF] Barabasi | Emergence of scaling in random networks[END_REF][START_REF] Barabasi | Scale-free networks[END_REF][START_REF] Lahtinen | Scaling of random spreading in small world networks[END_REF][START_REF] Newman | The structure and function of complex networks[END_REF][START_REF] Newman | Scaling and percolation in the small-world network model[END_REF][START_REF] Newman | Random graphs with arbitrary degree distributions and their applications[END_REF][START_REF] Newman | Random graph models of social networks[END_REF]. The mechanical characteristics of the rods appendages. Rod elements. All rods have a full discoid cross section. The radius of the radial spokes and the nexin links equals 8 nm and 4 nm, respectively. The nexin links Young's modulus corresponds to a spring constant that equals 1.6 10 -5 pN.nm 2 [START_REF] Lindemann | Structural-functional relationships of the dynein, spokes, and centralpair projections predicted from an analysis of the forces acting within a flagellum[END_REF]. The section of the radial spokes is roughly four times the section of the nexin links, as observed on real sections. The Young's modulus of these elements has been taken as the one of the actuators. The tangential stiffness of the actuators of the dynein arms has been reduced in such way that they do not contribute significantly to the stiffness of the main part of the axoneme. We have checked the incidence of the forces transmitted by the actuators to the dynein arms, and we have verified that they do not induce the artifactual bending of the ODPs -under the construction conditions we have chosen -in spite of the lattice they constitute.

Table 2 The mechanical characteristics of the beams appendages. The beams that represent the ODPs have a full discoid cross section whose radius equals 8 nm.

Their Young modulus and Poisson's ratio are taken from [START_REF] Schoutens | Prediction of elastic properties of sperm flagella[END_REF][START_REF] Tuszynski | Anisotropic elastic properties of microtubules[END_REF]; their flexure inertias are given by Schoutens, 1992 andCibert and[START_REF] Cibert | Geometry drives the "deviated-bending" of the bi-tubular structures of the 9 + 2 axoneme in the flagellum[END_REF] Young's modulus is that calculated by Schoutens, 1992.

The shear coefficients (k y and k z ) are obtained by considering a hollow cylinder.

The area is obtained by considering a substructure of 23 protofilaments whose radius is 2.3 nm [START_REF] Warner | Cross-bridge mechanism in ciliary motility: the sliding-bending conversion[END_REF]). The T-beams are those that link the nodes [1, 2], [1, 3], [1,4] and [4,5] within the periodic plateaus that mimic the cross section of the ODPs (figure 1). The central apparatus is modelled as a pair of beams of discoid cross section (microtubules) made of 13 protofilaments each [START_REF] Warner | Cross-bridge mechanism in ciliary motility: the sliding-bending conversion[END_REF]. Its inertia moments are given by [START_REF] Cibert | Geometry drives the "deviated-bending" of the bi-tubular structures of the 9 + 2 axoneme in the flagellum[END_REF]. Beams modelling ODA and IDA have a full discoid cross section of 8 nm radius, but their moments of inertia have been enhanced by considering a hollow structure; this enforces a better transmission of the flexure moments to the ODP.

Figure 1: The model. A: within each section, each ODP was modeled as a series of 4 edges that link 5 nodes. Node #1 is the centre of inertia of the ODP. Node #2 is the centre of the incomplete microtubule (B), and represents the site towards which converge dynein arms carried by the neighboring ODP; the complete tubule is named A. Nodes #3 and 5 are the sites where the outer dynein arm (ODA) and the inner dynein arms (IDA) are permanently fixed, respectively. Node #4 is the site where the nexin link (NL) and the radial spoke (RS) are carried. Each of these appendages (excepted the NL whose spatial frequency equals 1/96 nm -1 ) represents the series of homologous appendages carried along the 96 nm long segment of each ODP of the actual axoneme deformations, the dynein arm produces a force applied on node #2 of the neighboring ODP. This force moves the ODP of rank N either in the canonical direction (toward the minus end of the ODP of rank N+1), or in the opposite direction (anti-canonical direction). The central apparatus to which converge the radial spokes is represented as a longitudinal beam. Because of the gradient of activity of the actuators of the dynein arms we have created, which respects the geometry of the axoneme [START_REF] Cibert | Axonemal activity relative to the 2D/3D-waveform conversion of the flagellum[END_REF], planar bends as expected, the bending plane including the doublet #1 and the middle of the [5-6] pair. See movie: architecture.

Figure 2: 3D-scheme of the model. A: front view of a module. By convention the first ODP is located on the upper side of the scheme and the ODPs are numbered clockwise from 1 to 9. The broad segments represent the beams that model the cross sections of the ODPs, and the thin lines correspond to the appendages that they carry (Figure 1). The central pair is modeled as a beam on which the radial spokes are embedded. The ranks of the nodes -included in open circles -superpose on the ODP #2. The model is viewed from base to tip. B: 3D view of the model. The basal anchor is located at the left side of the model.

The boundary conditions at basal anchor are such that all nodes are clamped; the other tip is free. See movie: "architecture".

Figure 3: The four loading modes of the model. The axoneme is viewed base to tip. Under the loading mode I and III (the curvature is positive) the dynein arms located along the outer doublets [#6-9] are active according tto heir canonic polarity, it means that they move the outer doublet of which they are appendages (their cargo) toward the minus end of the doublet that they use as a track. Under the loading mode II and IV (the curvature is negative) the situation is inverted. Under the loading mode I and III the dynein arms located along the opposite side are absolutely inactive (free) or active pushing their cargo toward the anticanonic direction (toward the plus end of their track), respectively. Under the loading mode II and IV the situation is inverted.

Figure 4: Deformation and sliding. -Z bending when two opposite sides are active (loading mode IV). Because of the activity of the dynein arms, the sliding of the ODPs is effectively responsible of the bending of the model. Color encoding: central apparatus (black), outer doublets, nexin links and outer dynein arms (and their actuators) (blue), inner dynein arms (and their actuators) (yellow), radial spokes (red).

Figure 5: Method of analysis of the deformation of the bent model. (Left side). As shown in Figure 2, the cross section corresponds to the tipward view of the model, and the numbers included inside the tubule-A indicate the rank of the ODPs. By convention, these numbers are blue and white when the dynein arms are inactive and active, respectively. The white numbers are associated to a sign -or + when the arms move in the "canonic direction" (baseward) and the "anti-canonic direction" (tipward) the ODP on which they are associated permanently (their cargo). The blue background of each of the ODPs defines the cylindrical location and the orientation of each of them within the embedded first cross section of the model. The thin blue and white lines, which are parallel to the orientations of the ODPs, represent the orientations of the ODPs calculated at the level of the basal anchor and within a given cross section, respectively. The angle between these lines defines the twist of the ODPs. In this scheme, the lines that superpose on the outer and inner dynein arms carried by the ODPs are the 2D-Euclidean distances between nodes #3 and #5 and the surfaces of the neighboring ODP; they are homologous to the intervals that can be measured on electron microscope pictures, assumed to be incident in the regulation of the dynein arms as proposed in the GC model. The colors of the arms range within the scale designed by the vertical linear gradient, and characterize the capability of the dynein arms to grasp a -tubulin monomer, assuming that the shortest their length, the highest the activity of the arms (as proposed by Lindemann, 1994), the brightest the arm. The other appendages carried by the ODPs (the nexin links (NL) and the radial spokes (RS)) are schematized using the same color encoding that corresponds here to their 3D-lengths, which are consistent with the tangential forces that subject them; the shortest a link, the brightest the color. The rank of the ODPs that carry the NLs and the RSs are written on the left and the right side of the vertical color scale, respectively. In the upper left corner of the image the expected polarity of bending (+z, -z) is indicated.

(Right side) The longitudinal deformation of the model is characterized by the side view of the cross section designed on the right side of the model. In this scheme, nodes #1 and #4 as well as their links and the radial spokes are represented according to a same color scale as that described above but that corresponds here to their ordinate (y) only (Figure 2). Nodes #1 are the outer ones. By convention, the basal anchor is located on the right side of the scheme. Thus, ODP #8 is the brightest being located in the front plane. The number written at the left side of "basal anchor" in the upper right corner of the image is the magnification coefficient of the longitudinal deformation of the cross section (x axis), which depends on the loading mode; this value was determined -for design reasons only -in such a way that the maximum of the longitudinal displacements of the nodes calculated under the four loading modes equals the half of the diameter of the model.

Figure 6: Tangential forces within the radial spokes and the nexin links. The color encoding of the curves, that corresponds each to a given ODP, is shown within the inset describing the tangential forces within the radial spokes that we obtained under loading mode I. The positive and negative values correspond to the dilation and the compression of the link, respectively. The tangential forces constraining the RSs under the 4 loading modes (as well as the NLs) are represented on the same range. Figure 8: The behavior of the 21 st cross-section under loading modes I and II (see movies loading_mode_I.avi and loading_mode_II.avi). Under loading mode I, ODP #1 remains immotile, the rotation of the other ODPs occurring counterclockwise; the larger displacement is that of ODP #5. Under loading mode II, the same counterclockwise rotation is observed, while the bending polarity is inverted, the outer doublet #6 and #2 being immotile and the most motile, respectively. ODP #5 moves in the clockwise direction. Correlatively to these global movements, the most important observation concerns the variations of the distances between neighboring ODPs, which are dilated and compressed along the active and the inactive opposite sides of the axoneme, respectively. The movements of the ODPs increase the diameter of the Figure 9: The behavior of the 21 st cross-section under loading modes III and IV (see movies loading_mode_III.avi and loading_mode_IV.avi). Under loading mode III, neighboring ODPs #1 and #9 appear to be immotile because they oscillate -with a low amplitude -around their basic position, and the other ODPs could be associated in three groups. ODPs #8, 7 and 6 on one hand, and ODPs #4 and 5 on the other hand, converge toward the outer side of the curvature (i.e. the 5-6 interval); these two groups are involved in a counterclockwise and a clockwise movement, respectively. ODPs #2 and 3 rotate counterclockwise and converge toward the inner side of the curvature. These movements define 4 sectors inside the cross section of the axoneme, delineated each by the expected bending plane (xz) and by the perpendicular direction that includes the neutral surface of the axoneme. Under loading mode IV, ODPs #1, 4 and 8 appear as immotile, and we observe the same movements of convergence of the other ODPs as those occurring under loading mode II in spite of the change of the bending polarity. These convergent rotations correspond to the net increase of the distance of the ODPs involved in both opposite active sides (whatever the polarity of the movement of the dynein arms). These movements enlarge the diameter of the axoneme included into the bending plane and compress the model in the perpendicular direction, as observed under loading modes I and II. As for the deformation of the side view of the model, the observations are the same as those described for the model constrained under loading modes I and II (Figure 8).

Modeling the effect of actuators using free deformations

The forces related to the effect of actuators must be self-equilibrated. This can be achieved by using the concept of free deformations. Consider a beam submitted to an increase in temperature T . Under free conditions (i.e. without external constraints) beam would deform freely, and the equation: * = . T , where * is the free deformation, is the dilation coefficient and T is temperature, describe the dilation effect. When the beam is submitted to a longitudinal constraint, free deformation is limited, and beam is submitted to a complementary elastic deformation due to this constraint ( e ). This leads to the complete deformation given by the equation: = e + * . When the beam is clamped at both ends, the longitudinal deformation equals zero. Consequently, the longitudinal elastic deformation has to be exactly opposite to the free deformation ( e = -* ). It could be demonstrated that free deformations are equivalent to body forces, these body forces being always in equilibrium. In our model, free deformations were chosen to reproduce at best the biological movement of dynein arms, which is mediated by two "free deforming" rods (the actuators). When actuators dilate and contract in a coordinated manner along the entire length of the model, the whole scaffold deforms elastically in order to recover the internal equilibrium and the kinematical conditions at the boundaries.

Coordinated variation in length of the two actuators of each dynein arm

Because the actuators of the dynein arms constitute a lattice associated to each outer doublet and contribute consequently to their inertia parallel to the major axis of their cross section, the mutual deformation of the upstream and downstream actuators which model the stem of the arm was calculated in such a way that the displacement of the nodes where they link the beam -which constitute the stalk/tether of the arm -does not induce on its own any artifactual curvature of the outer doublet.

To respect this condition, this node has to move along the dashed circle whose center is the middle of the 96 nm long segment of the outer doublet. This makes free deformation of the two actuators co-coordinated, avoiding internal tension in the triangle they constitute with the segment of the outer doublet. Practically, variation in length of one of the two actuators was defined as a function of the local free deformation and of the position of the node around the axonemal cylinder; the variation in length of the second actuator was deduced from this calculation using geometry. The same method is used whatever the polarity of the force produced by the arm.

Recent publications demonstrate that the forces produced by the dynein arms seems to be due to a "winch" mechanism that involves the linker domain and the stem/tail of the arms, in place of the tilt of the stalk/tether, even if stalk/tether can tilt to regulate the size of the walking step of the arm, being more rigid than previously reported [START_REF] Burgess | Is the dynein motor a winch?[END_REF][START_REF] Carter | Structure and functional role of dynein's microtubule-binding domain[END_REF][START_REF] Roberts | AAA+ Ring and linker swing mechanism in the dynein motor[END_REF][START_REF] Ueno | Dynein pulls microtubules without rotating its stalk[END_REF]. The stem/tail domain and the linked domain are assumed to play a major function because they are close to the AAA1 ATPase active site of the Walker ensemble. In this mechanism, the orientation of the force produced by the arm is either only parallel to the microtubule, when the AAA domain glides on the surface of the microtubule (as proposed by Ueno et al.), or oblique in regard to the orientation of the microtubules (as proposed by Carter et al.). It is noteworthy that these mechanisms are proposed from the study of either reconstructed systems or isolated arms, and that architecture of the axoneme makes the dynein arms of both the inner and outer rows interacting very closely [START_REF] Bui | Molecular architecture of inner dynein arms in situ in Chlamydomonas reinhardtii flagellum[END_REF][START_REF] Ishikawa | The architecture of outer dynein arms in situ[END_REF]. So the actual mechanism according to which the forces are produced along and around the outer doublet pairs along and around the axoneme remains mainly speculative. We have chosen to construct the inner and outer dynein arms according to the same model described in Figure 1 and Figure 2, assuming that inner and outer of arms are able to produce forces having the same amplitude in the two polarities (i.e. toward the + and the -end of the outer doublets) [START_REF] Badoual | Bidirectional cooperative motion of molecular motors[END_REF][START_REF] Gennerich | Force-induced bidirectional stepping of cytoplasmic dynein[END_REF][START_REF] Lindemann | Does axonemal dynein push, pull or oscillate ?[END_REF][START_REF] Ross | Processive bidirectional motion of dynein-dynactin complexes in vitro[END_REF] 3.5 10 4 3.2 10 3 3.2 10 3 7 10 4

Flexure Inertias { I z (nm 4 ) 5.3 10 4 3.2 10 3 3.2 10 3 23 10 4

Torsion inertia J (nm 4 ) 8.9 10 4 6.4 10 3 6.4 10 3 30 10 4 k y 0.5 0.9 0.9 0.5 Shear coefficients { k z 0.5 0.9 0.9 0.5

  consequently the NLs and the RSs insure the cohesion of the axonemal cylinder and the distribution of the constraints inside the model along this side. Under the loading mode II (-z) the situation is inverted.

  and Figure9. Loading modes I and II induce very symmetrical deformation in regard to both the cylindrical (Figure8left) and longitudinal (Figure8right) deformation of the model, because they generate pendulous movements of the ODPs that remain however, untwisted around their axis of inertia, in spite of their rotation around the axonemal cylinder. The most important observation is that, under these two loading modes dynein arms located along one side of the axoneme are inactive, intervals between the active ODPs increase while those of the inactive ODPs decrease. Loading modes III and IV, in which the two opposite sides are active (in two opposite directions), induce the increase of the intervals of the ODPs on the two opposite sides.

  Figure1: The model. A: within each section, each ODP was modeled as a series of 4 edges that link 5 nodes. Node #1 is the centre of inertia of the ODP. Node #2 is the centre of the incomplete microtubule (B), and represents the site towards which converge dynein arms carried by the neighboring ODP; the complete tubule is named A. Nodes #3 and 5 are the sites where the outer dynein arm (ODA) and the inner dynein arms (IDA) are permanently fixed, respectively. Node #4 is the site where the nexin link (NL) and the radial spoke (RS) are carried. Each of these appendages (excepted the NL whose spatial frequency equals 1/96 nm -1 ) represents the series of homologous appendages carried along the 96 nm long segment of each ODP of the actual axoneme. The actuators (red lines) of the dynein arms (green arrows) are bars submitted to free deformations. B: the lateral view of two parallel N and N+1 ODPs (horizontal large grey bars), whose node #1 associates the rods [1-2] (lower vertical thin grey bar) and[1-[3-5]] (upper vertical thin grey bar); within the brackets the numbers are the ranks of the nodes that delineate each beam. The links of the actuators at both of their two ends are joints. The dynein arm is embedded in node #2 of the neighbor ODP. When the actuators X and X+1 dilate and contract simultaneously because of the local adjustment of their free

Figure 7 :

 7 Figure 7: xy and xz deformations of the segment of interest under the 4 loading modes I, II, III and IV.

  the bending plane, and compress the model in the perpendicular plane. The lateral views of the axoneme at the same abscissa, confirm the symmetrical changes induced by the two loading modes I and II, and show that the longitudinal displacements of nodes #1 and #4 are not equivalent. As expected, because of the bending polarity, nodes #4 of the ODPs located on the inner and the outer sides of the curved segment are pushed tipward and pulled baseward, respectively; nodes #1 resting close to the vertical yz plane. The apparent neutral surface that includes ODPs #4 and 8 delineates the inner and the outer side of the curvature. These displacements create twisting moments inside the ODPs. The axes of these moments are roughly orthogonal to the bending plane.

Figure 10 :

 10 Figure10: The behavior of the 41 st cross-section under loading modes I and II (see movies loading_mode_I.avi and loading_mode_II.avi). Loading mode I and II induce a clockwise rotation of the ensemble of the ODPs and an adjustment of the intervals between neighboring ODPs, which (excepted one), shorten; the intervals between ODPs #1 and 2 (under loading mode I) and #5 and 6 (under loading mode II) increase. The intervals between active ODPs are always larger than those of ODPs located on the opposite inactive side. It is noteworthy that, even if the cylindrical rotation of the ODPs along the distal segment is opposite to that involving the 21 proximal modules, the superposition between the cylindrical location of each ODP and its location at the level of the basal anchor, never occurs. The side views of the model constrained by loading modes I and II show an amplification of the relative displacements of node #1 and 4, and that the active and the inactive sides of the model are respectively pushed tipward and pulled baseward in a symmetrical way. The apparent

Figure 11 :

 11 Figure 11: The behavior of the 41 st cross-section under loading modes III and IV(see movies loading_mode_III.avi and loading_mode_IV.avi). Under these two loading modes the two opposite halves of the axoneme delineated by the bending plane -which are both active and promote the bending of the model in the same direction -converge toward the inner side of the curvature. At the end of the models, since the cylindrical locations of the ODPs are close to those they have within the first embedded cross section, the amplitude of the movement of each ODP is proportional to its displacement observed in the 21 st cross section. This merge is never observed along the 20 modules that constitute the distal portion of the segment of interest, when the model is submitted to loading modes I and II, because the relative displacements of the ODPs within the axonemal cylinder are not synchronized. Intervals measured between the active ODPs located within the neutral surface -the plan orthogonal to the bending plane -are always larger than those of both couples of ODPs #1-2 and #5-6, which are located in the bending plane. As shown by the sides views, the longitudinal displacements of nodes #1 and 4 occurring along the distal part of the segment of interest could be considered as solely amplified as compared to those characterized at the level of the 21 st cross section, excepted that nodes of ODPs #3, 4 and 8 are gently pulled toward the basal anchor.

Figure 12 :

 12 Figure 12: Bending and bending reversion at the 21 st section. The four insets are arranged vertically as a function of the bending amplitude (in the z direction) induced by each of the four loading modes. The color encoding is that described in Figure 5.

Figure 13 :

 13 Figure 13: Bending and bending reversion at the 41 st section (see text and Figure 12).

  in a synchronous manner. Because of the small amplitude of the shear we have calculated, dynein arms are unable to jump and remain linked onto the wall of the doublet N+1. The scaffold we have constructed looks like the model proposed byUeno et al. insofar as stalk/tether of each arm we have constructed is embedded in the wall of the (and does not tilt by default to produce a force), and the ensemble of actuators of each arm pushes and pulls the stalk/tether in a direction parallel to that of the two outer doublets linked by the stalk/tether they move.Projection of the dynein arms one the bending planeBecause of the cylindrical organization of the axoneme, deformation of the dynein arms (IDA and ODA) was a function of their length of their projection on the expected bending plane.From this scheme, the coefficients of correction of the relative activities of the IDA and the ODA were calculated to allow the planar bend of the model. In the following plot, plain and dashed curves represent the coefficients calculated for the IDA and the ODA, respectively.

  Figure 1

Table 1

 1

Table 1

 1

		Nexin	Radial	Actuators
		Links	Spokes	of the dynein arms
	E (pN.nm )	0.016	16	16
	N	0.3	0.3	0.3
	S (nm )	50	200	4
	J (nm 4 )	400	6,400	6,400