Frédéric Coppin

Laureline Février

Arnaud Martin-Garin

An Operational Method to Easily Determine the Available Fraction of a Contaminant in Soil and Associated Soil-Solution Distribution Coefficient

Keywords: contaminant environmentally available fraction, successive batch extractions, soil, predictive modeling, radionuclide, trace element, pollutant

Well understanding the solid/solution partitioning of a contaminant is of first importance to determine its residence time in the environment, environmental availability, or bioavailability.

Currently, parameters of contaminant transfer models are derived from two conceptually different approaches: one considering that the totality of the contaminant is in equilibrium between the solid and the solution and the other one considering that only a part of the contaminant can be transferred from the solid to the solution without considering equilibrium. Our work offers to reconcile these two approaches by assuming that the contaminant associated with the solid is present under two fractions: one available at equilibrium with the solution, and a second one not available and nontransferable to the solution. We propose to use simple operational batch methods (successive desorption batch experiments, or batch desorption conducted at different volume of solution/mass of solid (V/M) ratios) to check this assumption and to determine the real available contaminant fraction (i.e., the contaminant in the solid which can be at equilibrium with the solution) and its associated solid/solution distribution coefficient. The robustness of the proposed method was tested on simulated conditions, on experiments performed to validate the approach, and on the reinterpretation of literature data. Finally, the use of the available contaminant fraction and its associated solid/solution distribution coefficient in transfer models can improve the predictive modeling of contaminant transfer in the soil/solution/plant system.

Introduction

Soil is a major compartment at the biosphere/geosphere interface and understanding contaminant behavior in soils is needed to predict its potential dissemination in terrestrial ecosystems. The mechanisms leading to the retention of contaminants in soils (adsorption under outer or inner-sphere complexes, (co)precipitation, bioretention...) as well as carrier phases (minerals organic matter, (micro)organisms...), which partly control their solid/solution distribution, are numerous. Therefore, in the article, the terms sorption and desorption are used as generic terms to qualify any retention of contaminants in soil and any transfer of contaminants from solid to soil_solution, respectively, independent of the chemical process behind this retention or transfer. Well understanding the solid/solution partitioning of contaminants such as trace elements [START_REF] Rodrigues | Evaluation of an approach for the characterization of reactive and available pools of 20 potentially toxic elements in soils: Part II -Solid-solution partition relationships and ion activity in soil solutions[END_REF] or radionuclides [START_REF] Vidal | Two Approaches to the Study of Radiocaesium Partitioning and Mobility in Agricultural Soils from the Chernobyl Area[END_REF] is of first importance to determine their residence time in soils [3] , environmental availability [START_REF] Divincenzo | Slow sorption kinetics of pentachlorophenol on soil: Concentration effects[END_REF] or bioavailability [START_REF] Kennedy | Use of single and sequential chemical extractants to assess radionuclide and heavy metal availability from soils for root uptake[END_REF] . To estimate the contaminant transfer from soil to solution two different concepts are usually considered. The first one considers that all the contaminant sorbed onto the solid is available for solution, whereas the second one considers that only a fraction of the contaminant is available and can be transferred to the solution. Within both concepts, the distribution between the available fraction of the contaminant retained on the solid and the soil-solution is assumed to be controlled by reactions at equilibrium. For both concepts, experiments are conducted to obtain the target parameters which are used for predictive modeling. Concerning the first concept, the main target parameter is the soil/solution distribution coefficient (KD) which can be derived from the concentration ratio between soil and solution (RD) from sorption [START_REF] Cipullo | Assessing bioavailability of complex chemical mixtures in contaminated soils: Progress made and research needs[END_REF] or desorption [START_REF] Février | Variation of the distribution coefficient (Kd) of selenium in soils under various microbial states[END_REF] batch experiments or from in situ measurements [START_REF] Almahayni | Effects of incubation time and filtration method on Kd of indigenous selenium and iodine in temperate soils[END_REF] . For the second concept, the target parameter is the percentage of the environmentally available fraction of contaminants (i.e. the fraction transferring from solid to solution from where it can be taken up by organisms) [START_REF] Sanchez | Predictions of in situ solid/liquid distribution of radiocaesium in soils[END_REF] . Usually, this fraction is estimated from batch extraction experiments conducted with chemical extractants such as water, acetate or others reagents [START_REF] Divincenzo | Slow sorption kinetics of pentachlorophenol on soil: Concentration effects[END_REF] and expressed as a percentage of the total contaminant in soil [START_REF] Rodrigues | Evaluation of an approach for the characterization of reactive and available pools of 20 potentially toxic elements in soils: Part II -Solid-solution partition relationships and ion activity in soil solutions[END_REF] [START_REF] Kim | Bioavailability of heavy metals in soils: definitions and practical implementation-a critical review[END_REF] . However, for both concepts, the initial main hypotheses (i.e., all the contaminant, or only a part, is available) are rarely checked during the experiments. Both approaches have sometimes been used for the same soil to describe soil/solution contaminant transfer depending on whether sorption or desorption was considered. Sorption experiments are most often interpreted with an equilibrium-based approach and used to derive KD, whereas desorption experiments are used to derive a finite extraction yield [START_REF] Roig | Estimating the radionuclide available fraction in m i n e r a l s o i l s u s i n g a n e x t r a c t i o n t e c hn i q u e[END_REF] [START_REF] Rigol | Effect of the ionic status and drying on radiocesium adsorption and desorption in organic soils[END_REF] . In addition, results showing that KD or % of the available fraction depends on the volume of solution/mass of solid ratios (V/M) used in batch extraction [START_REF] Sastre | Use of sorption and extraction tests to predict the dynamics of the interaction of trace elements in agricultural soils contaminated by a mine tailing accident[END_REF]- [START_REF] Parajuli | Variation in available cesium concentration with parameters during temperature induced extraction of cesium from soil[END_REF] may also be a consequence of the wrong use of the initial assumptions. Indeed, if all the contaminant retained on the solid is available and at equilibrium with the solution, KD has to be independent of V/M.

In the same way, if only a % of contaminant retained in the solid is available, this percentage should relate to the intrinsic soil composition only and has to be independent of the experimental protocol used to determine it. A single-step batch extraction often fails to determine it, since it is not sufficient to recover the whole available fraction of the contaminant from the solid. Finally, the main drawback of interpreting experiments without having checked this main hypothesis is to provide transfer parameters that could be uncertain; this is particularly true for KD. Moreover, experiments conducted to provide only the percentage of contaminant that could be extracted from soil depend on the experimental protocol (e.g., the nature of the extracting solution, V/M ratio...) and do not provide information on the dynamics of solution resupply (i.e., resupply of solution in case of water flux throughout the soil). Thereby, using only the extracted percentage for predictive modeling could be difficult.

Based on the hypothesis that the contaminant associated with the solid is present under two fractions: one available at equilibrium with the solution, and a second one not available and non-transferable to the solution, the objective of this study is to propose simple operational batch methods to check this hypothesis and to determine the real available contaminant fraction (i.e., contaminant in the solid which can be at equilibrium with the solution) and its associated solid/solution distribution coefficient. Even if a lot of physicochemical properties of soil or solution are known to influence the retention parameters of contaminants in soil (nature of soil and mineralogy, chemistry of the solution, grain size...), the objective of this paper is not to discuss their influence on the targeted parameters. We will demonstrate that two experimental approaches already used for specific conditions in very few studies could provide the same results and be generalizable to determine the available contaminant fraction and its associated distribution coefficient for radionuclides and trace elements. The two selected approaches are batch experiments conducted at different V/M ratio for characterization of Ni retention on clay [START_REF] Zheng | Release of contaminant U(VI) from soils[END_REF] and successive batch extractions used to describe organic compounds retention onto soils [START_REF] Wauters | Availability of radiocaesium in soils: a new methodology[END_REF] .. The determination of the available contaminant fraction and its associated contaminant distribution coefficient with these two approaches is first explained from a theoretical point of view. Then, the effectiveness of the two experimental approaches is demonstrated by applying them to various data: either simulated, acquired with different radionuclides or trace elements (Se, Cs, and U), or from literature.

Theoretical Approach

The proposed method is based on the analysis of the mass balance of the contaminant between soil and solution during batch experiments to determine the available fraction of contaminant sorbed onto the solid and its distribution coefficient. Two types of batch experiments can be realized. The first types are batch experiments conducted at different V/M as already done recently for Ni retention on clay [START_REF] Zheng | Release of contaminant U(VI) from soils[END_REF] . Basically, solid contaminated material is introduced in a batch and put in contact with a solution. After shaking for a given time, the batch is centrifuged to separate the supernatant from the solid. The supernatant is sampled and analyzed for concentration. The second types are in line with the infinite bath technique which consists in introducing a resin to decrease the element concentration in solution [START_REF] Montavon | Nickel Retention on Callovo-Oxfordian Clay: Applicability of Existing Adsorption Models for Dilute Systems to Real Compact Rock Environmental Science and Technology[END_REF] , and successive batch extractions. Such extractions, which have already been used to quantify the release of retained contaminants from soils [13][18] , require a lot of successive steps to recover the totality of the available fraction [START_REF] Roig | Estimating the radionuclide available fraction in m i n e r a l s o i l s u s i n g a n e x t r a c t i o n t e c hn i q u e[END_REF] . Within successive batch extractions, the first step is similar to the classical batch extraction described above, but the supernatant is renewed after centrifugation and the pellet is resuspended. Then the batch is shaken again. This sequence can be performed several times. For both types of batch experiments, the solid/liquid equilibrium (pH, ion composition...) must be identical between the batches considered in the experiment.

Based on the hypothesis that a fraction of the contaminant sorbed on the solid is available and resupplies the solution while the other fraction remains fixed (nonavailable according to the procedure used) to the solid and never participates in the process of solution resupply, two parameters may be obtained by using successive extractions, or extractions conducted at different V/M ratios: the percentage of the available fraction (%available) and the distribution coefficient between the contaminant available fraction on the solid and the solution (k'D). In the successive batch extraction technique, the mass balance of the contaminant in the batch is conserved at each step of the successive extractions and the concentration in the solid can be expressed by the following equations.

𝐶 𝑠𝑜𝑙𝑖𝑑_𝑡𝑜𝑡𝑎𝑙_𝑖𝑛𝑖𝑡𝑖𝑎𝑙 = 𝐶 𝑠𝑜𝑙𝑖𝑑_𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 _𝑖𝑛𝑖𝑡𝑖𝑎𝑙 + 𝐶 𝑠𝑜𝑙𝑖𝑑_𝑓𝑖𝑥𝑒𝑑_𝑖𝑛𝑖𝑡𝑖𝑎𝑙

(1)

𝐶 𝑠𝑜𝑙𝑖𝑑_𝑡𝑜𝑡𝑎𝑙_𝑓𝑖𝑛𝑎𝑙 = 𝐶 𝑠𝑜𝑙𝑖𝑑_𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒_𝑓𝑖𝑛𝑎𝑙 + 𝐶 𝑠𝑜𝑙𝑖𝑑_𝑓𝑖𝑥𝑒𝑑_𝑖𝑛𝑖𝑡𝑖𝑎𝑙 (2)
where Csolid_total_initial, Csolid_available_initial and Csolid_total_final, Csolid_available_final are the total and the available concentrations of the contaminant on the solid at the beginning and at the end of thecontaminant concentration on the solid at the beginning of the experiment (in Bq kg -1 , mol kg -1 , mg kg -1 ...) and it is assumed to be constant throughout the extraction steps.

Equilibrium is assumed between C solid _available and C solution so that,

𝐶 𝑠𝑜𝑙𝑖𝑑_𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒_𝑓𝑖𝑛𝑎𝑙 = 𝑘 𝐷 ′ × 𝐶 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛_𝑓𝑖𝑛𝑎𝑙 ( 3
)
Where Csolution_final is the concentration of the target element in the solution at the end of each extraction step (in Bq L -1 , mol L -1 , mg L -1 ...), and k ′ D is the distribution coefficient between the solid available fraction and the solution (L kg -1 ). This coefficient is assumed to be constant.

Merging equation ( 2) and (3), yields

𝐶 𝑠𝑜𝑙𝑖𝑑_𝑡𝑜𝑡𝑎𝑙_𝑓𝑖𝑛𝑎𝑙 = 𝑘 𝐷 ′ × 𝐶 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛_𝑓𝑖𝑛𝑎𝑙 + 𝐶 𝑠𝑜𝑙𝑖𝑑_𝑓𝑖𝑥𝑒𝑑_𝑖𝑛𝑖𝑡𝑖𝑎𝑙 (4)
This equation is verified at each step of the extraction. So, by plotting 𝐶 𝑠𝑜𝑙𝑖𝑑_𝑡𝑜𝑡𝑎𝑙_𝑓𝑖𝑛𝑎𝑙 against 𝐶 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛_𝑓𝑖𝑛𝑎𝑙 at each extraction step, we can deduce 𝑘 𝐷 ′ (slope of the straight line) and 𝐶 𝑠𝑜𝑙𝑖𝑑_𝑓𝑖𝑥𝑒𝑑_𝑖𝑛𝑖𝑡𝑖𝑎𝑙 (y-intercept).

For single-step extractions conducted at different V/M ratios, equation ( 4) can be applied. Plotting when all contaminant is available (i.e., 𝐶 𝑠𝑜𝑙𝑖𝑑_𝑓𝑖𝑥𝑒𝑑_𝑖𝑛𝑖𝑡𝑖𝑎𝑙 = 0), R D is equal to k' D , which is equivalent to the classical K D .

For all the equations, 𝐶 𝑠𝑜𝑙𝑖𝑑_𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒_𝑖𝑛𝑖𝑡𝑖𝑎𝑙 can be calculated with equation (1) knowing 𝐶 𝑠𝑜𝑙𝑖𝑑_𝑓𝑖𝑥𝑒𝑑_𝑖𝑛𝑖𝑡𝑖𝑎𝑙 and 𝐶 𝑠𝑜𝑙𝑖𝑑_𝑡𝑜𝑡𝑎𝑙_𝑖𝑛𝑖𝑡𝑖𝑎𝑙 .

Simulated conditions

To have an overview of the power of the method, Eq(1) to (4) were applied to simulated conditions summarized in Table 1. For these simulations, the initial concentration of the contaminant is arbitrarily chosen to be 100 Bq g -1 . The 𝑘 𝐷 ′ , % 𝑠𝑜𝑙𝑖𝑑_𝑓𝑖𝑥𝑒𝑑_𝑖𝑛𝑖𝑡𝑖𝑎𝑙 and V/M ratio ranged from 1 to 1 000 L kg -1 , 0 to 99%, and 0.1 to 500, respectively, leading to the simulation of 224 different combinations. The number of extraction steps has been fixed to four, which seems reasonable to obtain a straight line in real conditions. The obtained results for all simulations are available in the supporting information Excel file (Table S1).

Experiments performed to validate the approach

The successive extraction method was tested on different couples of radionuclides and solids and for both in situ contaminated materials and fresh laboratory contaminated ones (either classical batch or dialysis bag experiments). The soil contamination procedure used for spike conditions is available in previous publications [19][20] . The main details of the experimental conditions are given in Table 2, whereas additional details are provided in table S2. Se was chosen because its isotope 79 is of first importance in the study of nuclear waste management impact, whereas 137 Cs is the major radionuclide present in the environment for a long term after nuclear accidents like Fukushima [19][20].

Batch

In Situ Silty soil

(0-10 cm) C 2 H 7 NO 2, 1M 12 4 (6)
UHQ Water : Ultra high quality water (>18.2MΩ•cm).

In Brief, classical batch experiments consisted in mixing contaminated solid materials with a solution containing the selected extractant in centrifuge tubes (first, the solid is introduced into the tube, followed by the solution). The tubes used were 50 mL polycarbonates tubes (1a, 1b and 2a experiments) or 50 mL polypropylene tubes (experiments 3, 4, 5 and 6). The tubes were shaken (300 RPM, orbital agitator) for a given time (Table 2), and then centrifuged (10 000 g for 20'). The supernatant was removed, filtered (PolyterSulfone syringe filters 0.8/0.2 µm) and renewed in each tube. The pellet was again fully dispersed, and the same procedure was reproduced. For dialysis bag experiments [START_REF] Teramage | The impact of radiocesium input forms on its extractability in Fukushima forest soils[END_REF] , the solid was introduced into a dialysis bag (cellulose dialysis membrane, Visking dialysis tubing MWCO 12-14 kDa), then the extractant was added, and the bag was closed. The filled dialysis bag was introduced into a batch (50 mL polycarbonate tubes) containing the same extractant and shaken. After a given time (Table 2), the external extractant was renewed. In order to calculate 𝐶 𝑠𝑜𝑙𝑖𝑑_𝑡𝑜𝑡𝑎𝑙_𝑓𝑖𝑛𝑎𝑙 at the end of each extraction step it is necessary to take into account the residual solution closely associated with the solid material or that remaining inside the dialysis bag. The 𝐶 𝑠𝑜𝑙𝑖𝑑_𝑡𝑜𝑡𝑎𝑙_𝑓𝑖𝑛𝑎𝑙 is obtained using the following equation:

𝐶 𝑠𝑜𝑙𝑖𝑑_𝑡𝑜𝑡𝑎𝑙_𝑓𝑖𝑛𝑎𝑙 = 𝐶 𝑠𝑜𝑙𝑖𝑑_𝑡𝑜𝑡𝑎𝑙_𝑖𝑛𝑖𝑡𝑖𝑎𝑙 - 𝐶 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 𝑓𝑖𝑛𝑎𝑙 ×𝑉 𝑓𝑖𝑛𝑎𝑙 -𝐶 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 𝑎𝑑𝑑𝑒𝑑 ×𝑉 𝑎𝑑𝑑𝑒𝑑 -𝐶 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙 ×𝑉 𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙 𝑀 𝑠𝑜𝑙𝑖𝑑
where V final , V added and V residual (mL) are the volume at the end of the extraction step, the added volume and the residual one respectively, M solid (g) is the solid mass, C solution_added (Bq mL -1 ) and C solutionjesidual (Bq mL -1 ) are the concentrations of the target element in the added solution and in the residual solution linked to the solid phase after the previous step, respectively. C solid_total_final and C solid_total_initial are the solid concentration (Bq g -1 ) at the end and at the beginning of each extraction step, respectively.

During these experiments, no unexpected or unusually high safety hazards were encountered.

Data from the literature

In order to demonstrate the benefits of this method to the scientific community, works in which enough information was available to be reinterpreted or, for which authors provided complementary information, have been selected. The works conducted by Zheng and Wan (7) (2005) [15] , Elias et al. (2003) [22] , Nagao et al. (2020) [START_REF] Elias | A procedure for quantitation of total oxidized uranium for bioremediation studies[END_REF] and Rigol et al. (1999) [START_REF] Roig | Estimating the radionuclide available fraction in m i n e r a l s o i l s u s i n g a n e x t r a c t i o n t e c hn i q u e[END_REF] have been reinterpreted using our proposed method. The experimental protocols used by the authors to acquire their data are described here.

Zheng and Wan (2005) [START_REF] Parajuli | Variation in available cesium concentration with parameters during temperature induced extraction of cesium from soil[END_REF] evaluated the impact of V/M ratios on the release of U(VI) from contaminated soils. U(VI) released concentrations are then compared to the solubilities of U(VI)containing phases of the soil. The extractions have been conducted with NaNO3 0.01 M (pH 7.5) and with V/M ratios ranging from 2/1 to 100/1 (L kg -1 ) for three contact times of 4, 30, and 120 days.

Elias et al. ( 2003) [START_REF] Valcke | The behaviour dynamics of radiocesium and radiostrontium in soils rich in organic matter[END_REF] tested the impact of the V/M ratio and efficiency of a single versus repeated extraction steps on the extraction yield of uranium for U-contaminated sand and clay sediments. One part of this work was focused on the determination of the optimal V/M ratio to reach this objective.

The extractions were realized using a 222 mM NaHCO3 solution (pH 8.3) with V/M ratios ranging from 1/1 to 10/1 (L kg -1 ). Each extraction was repeated three times. Four sediments were used: fine and coarse sands, clays mixed with weathered Mancos shales from the uranium contaminated Shiprock, NM site and a clay sample from the uraniumcontaminated Oak Ridge TN site. Nagao et al. (2020) [START_REF] Elias | A procedure for quantitation of total oxidized uranium for bioremediation studies[END_REF] realized successive batch desorption experiments using seawater to extract 137 Cs from four beach sand cores sampled at a distance of 32 km from the Fukushima Daichi Nuclear power plant at four different depths. The objective of this study was to determine the amount of 137 Cs which could be transferred with time from sand to seawater. The last example used to test the method on literature data is Rigol et al.'s (1999) work [START_REF] Roig | Estimating the radionuclide available fraction in m i n e r a l s o i l s u s i n g a n e x t r a c t i o n t e c hn i q u e[END_REF] . The objective of their study was to determine the impact of soil ionic status and drying on the interaction of radiocesium with organic soils. After checking the impact of solution composition on KD of 134 Cs for sorption experiments on four organic soils , they realized up to 60 successive desorptions to estimate the desorption yield using 1M CH3COONH4 or CaCl2 solutions. CaCl2 was used to extract 134 Cs sorbed at the outer surface of clays and humic compounds, whereas CH3COONH4 can additionally extract 134 Cs located in the inter lattice positions at the edges of the clay particles. 134 Cs sorption experiments were conducted after temperature (D) or kept in moist conditions (M). These led to three conditions (H2O-M, PCaKD, and PCaK-M) for which successive desorption experiments were performed.

Results and Discussion 1.

Simulated conditions

The conclusions obtained for the 224 simulations presented in the supporting information (Table S1) are the same whatever the chosen combination of % 𝑠𝑜𝑙𝑖𝑑 _𝑓𝑖𝑥𝑒𝑑_𝑖𝑛𝑖𝑡𝑖𝑎𝑙 , 𝑘 𝑑 ′ and V/M. As example, some results obtained for the condition with % 𝑠𝑜𝑙𝑖𝑑_𝑓𝑖𝑥𝑒𝑑_𝑖𝑛𝑖𝑡𝑖𝑎𝑙 equal to 30%, 𝑘 𝑑 ′ =10 L kg -1 and for the 8

V/M ratios are presented in figure 1 and figure 2. Figure 1 shows the plotting of the 𝐶 𝑠𝑜𝑙𝑖𝑑_𝑡𝑜𝑡𝑎𝑙_𝑓𝑖𝑛𝑎𝑙 against 𝐶 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛_𝑓𝑖𝑛𝑎𝑙 for the four extractions and the eight V/M ratios. As expected, based on theoretical hypotheses, for all V/M ratios the same linear regression was obtained with a slope equal to 10 and an intercept equal to 30 which correspond to the theoretical 𝑘 𝐷 ′ and % 𝑠𝑜𝑙𝑖𝑑 _𝑓𝑖𝑥𝑒𝑑_𝑖𝑛𝑖𝑡𝑖𝑎𝑙 respectively for all the experiments. This result implies that whatever the V/M ratio chosen for the successive extractions the same available fraction (calculated from the yintercept value and eq (1)) was obtained independent of the V/M ratio contrary to the extracted fraction (i.e, the amount extracted at a given step for a given experimental setup) as shown in the calculations presented in Table S1. For high V/M ratios, the total concentration in the solid after the first steps of extraction approaches the "true" nonavailable concentration in the solid (given by the y-intercept). This confirms that extraction with a high V/M ratio better targets the available contaminant fraction [14][15] . However, in these conditions, all extraction steps lead to very close Csolid_total_final/Csolution_final values, which make the determination of k' D difficult . Therefore, intermediate V/M ratios can be a better choice to simultaneously obtain the available fraction and k'D. Figure 1 also confirms that the available fraction and k'D may be obtained from the results of single extraction performed at different V/M ratios, but only for the same soil weight, by use of the same plot.

The difference in the recovery of the available fraction between a single-step extraction versus the four steps extraction is given in Figure 2, for the same theoretical condition (% 𝑠𝑜𝑙𝑖𝑑_𝑓𝑖𝑥𝑒𝑑_𝑖𝑛𝑖𝑡𝑖𝑎𝑙 equal to 30% and the 𝑘 𝐷 ′ =10 L kg -1 ). For the readability of the figure, the two highest V/M ratios are not presented in Figure 2, with results being available in supporting information Table S1. The quantity of the contaminant recovered by a single extraction is in any case lower than that recovered by four extraction steps, and lower than the total available quantity (in grey). For the 50, 10 and 1 V/M ratios, the amounts of the recovered contaminant after four steps of extraction represented 99.9, 93.8, and 31.7% of the theoretical available fraction, respectively. For a single extraction, these amounts dropped to 83.3, 50 and 9.1 % respectively. These results showed that for a given contaminated system if the available fraction was estimated by the extracted fraction at the end of the extraction and not the y-intercept the estimation of the available fraction depends on the experimental setup used (number of extractions, V/M ratio) and does not reflect the real value of the available fraction.

For example, only 1% of the contaminant is extracted after one step and 3.9% after four steps for a V/M ratio of 0.1 (representative of an in situ soil water content of 10%) (Figure 2), well below the theoretical available fraction of 70%. This observation showed that: (i) the extracted fraction underestimates the available fraction and (ii) four steps of extraction were not sufficient to deplete the soil available fraction (in this case, after four steps, only 3.9% of available contaminant was extracted, meaning that 66.1 % of the contaminant in the solid is still available). In fact, 700 extraction steps would be necessary to recover 99.9% of the available fraction (results not shown). The results obtained for this combination of parameters are also valid for all tested conditions (Table S1). This result questioned previous estimations of the contaminant available/extractable fraction using only a single extraction step and its transposition from a batch experiment to an in situ situation, for which the real available fraction is certainly underestimated [START_REF] Nagao | Desorption behavior of Fukushima-derived Radiocesium in sand collected from Yotsukura beach in Fukushima prefecture[END_REF][25] [START_REF] Makino | Remediation of cadmium contamination in paddy soils by washing with chemicals: Selection of washing chemicals[END_REF][27][28] [START_REF] Ure | Single extraction schemes for soil analysis and related applications[END_REF] as already also underlined.

A second interesting point, presented in Figure 2 ), is reported in Figure 2 for the different V/M ratios and the first and fourth extraction steps. Like the extracted fraction, the RD value depends also on the experimental protocol used. For the scenarios illustrated in Figure 2, the RD values varied over 3 orders of magnitude depending both on whether they were calculated after one or four steps of extraction or at different V/M ratios. This range would even have been higher with more extraction steps (results not shown). For V/M ratios of 50 and 0.1, the R D values were 36 and 14 (L kg -1 ), respectively, for the first step of extraction, whereas they were 5 565 and 14 (L kg -1 ) for the fourth step of extraction. The difference in RD values is due to the fact that in our proposed approach only the solid available fraction is at equilibrium with the solution, whereas in the classical KD calculation, the total solid concentration of contaminant is considered to be at equilibrium with the solution.

Thus, in our approach, when the solid available fraction decreases, involving a contaminant decrease in solution, the RD increases due to the 𝐶𝑠𝑜𝑙𝑖𝑑 _𝑓𝑖𝑥𝑒𝑑_𝑖𝑛𝑖𝑡𝑖𝑎𝑙 fraction which remains constant. This result can explain the higher RD measurements obtained from in situ measurements compared to the RD measurements made in the laboratory from a single batch extraction step, [START_REF] Sastre | Use of sorption and extraction tests to predict the dynamics of the interaction of trace elements in agricultural soils contaminated by a mine tailing accident[END_REF] in line with the difference in V/M ratios. Therefore, assimilating a RD to a KD to predict contaminant transfer could generate important bias in the prediction, in the case where only a part of the contaminant sorbed on the solid is available and in equilibrium with the solution (i.e., y-intercept statistically ≠ 0). RD values depend on the experimental protocol and/or field conditions (sampling made after rain, after a dry period, and time after contamination...).

Experiments performed to validate the approach

The results presented in this paragraph are not intended to be discussed in detail but are used to highlight the applicability of the method, using different extractants, contaminants or solid materials.

Figure 3 presents the results obtained for different batch or dialysis bag experiments, for two radionuclides ( 75 Se, and 137 Cs) and one stable element ( 133 Cs). The experimental protocols are presented in Table 2, and k'D and available fraction calculated from linear regression analyses are presented in Table 3. In addition to the two above parameters, the % of recovery after the first and the last steps of extraction compared to the available fraction estimated by the y-intercept is also presented in Table 3. The results showed that, in line with the theoretical approach, a linear regression was obtained for all conditions allowing us to calculate k'D and the available fraction. The recoveries of the available fraction after a single extraction ranged from 27 to 83 %, confirming that a single extraction step was not enough to determine the real available fraction. 3(a) presents the results obtained for batch extraction (V/M = 5/1) of a 75 Se(IV)-contaminated silty clay soil for two different contact times [START_REF] Toro | A particle interaction model of reversible organic chemical sorption[END_REF] . No evolution of k'D and % of available 75 Se was observed between the two contact times, suggesting that a steady state was reached faster than 48h. A small percentage of Se(IV) was available for water migration (2.7%) in line with literature data for similar silty clay soils with the same pH [START_REF] Vázquez | Assessment of metal bioavailability in the vineyard soil-grapevine system using different extraction methods[END_REF] . Adding information on the k'D (5 L kg -1 ) of the available fraction will permit the improvement of predictive transfer models by integrating a dynamic approach coupled to water flux compared to just information on the % of available 75 Se. Water extraction of a 137 Cs-contaminated andosol [START_REF] Coppin | Methodological approach to assess the effect of soil ageing on selenium behaviour: First results concerning mobility and solid fractionation of selenium[END_REF] by classical batch experiments or dialysis experiments is presented in Figure 3 Both experiments gave the same results for k'D and % of available 137 Cs (Table 3, experiments 2a and 2b), confirming that these parameters do not depend on the V/M used [START_REF] Zheng | Release of contaminant U(VI) from soils[END_REF] , although the recovery of the available fraction after the fourth extraction step is clearly different for the two experimental setups (70% and 95% for batch and dialysis bag experiments, respectively). to the sampling campaign schedule, only three successive extractions were realized. As expected, [20][31][32] the acetate available fraction was higher than the water available fraction for both Cs isotopes ranging from 12% (for 133 Cs in soil) to 53 % ( 133 Cs in humus).

This paragraph illustrates that the proposed method could be used to macroscopically describe the mobility of different radionuclides and stable elements in soils, whatever the chemical processes that have led to their retention in soils (adsorption, reduction, precipitation...). For all experiments, the obtained straight line permits to determine k'D and % of the available contaminant. By comparison to the estimated available fraction, the % of recovery after the first extraction step (Table 3) confirmed that using a single extraction protocol could underestimate the real available fraction, from 19 to 72% in the presented examples, even with ammonium acetate (1 M) which is classically used to obtain the exchangeable fraction of a contaminant using a single extraction.

3. New light on some literature data the work of Zheng and Wan (2005) [START_REF] Parajuli | Variation in available cesium concentration with parameters during temperature induced extraction of cesium from soil[END_REF] on U(VI) release from soils showed that Rd and aqueousschoepite dissolution could be the controlling factor for U release. This assumption was based on the comparison of the observed aqueous U(VI) concentrations with simulated aqueous U(VI) concentrations in equilibrium with schoepite at pH 7.5 for the different V/M ratios. However, the simulation was not entirely satisfactory with a slight underestimation of simulated aqueous U(VI) for the lowest V/M ratio and an overestimation increasing with V/M ratios for the other ones.

As their simulation relied only on schoepite dissolution/precipitation, the authors attributed their unperfect simulations to the involvement of potential other mechanisms in U(VI) release that could be dependent on the V/M ratio (ion exchange, dissolution, desorption...). By analyzing their results with our proposed methodology, we will demonstrate that another explanation can be proposed.

Because the obtained results showed that the steady state was not reached at 4 and 30 days and only Rd and aqueous U(VI) concentration data were reported, equation ( 6) was used for the reinterpretation of data obtained for 120 days of contact time. The results presented in Figure 4(a)

show a linear correlation between R D and the inverse of U(VI) concentration in solution for the different V/M. Using the proposed method, we can estimate that 62 ± 3 % of U(VI) is available (calculated from equation (1) knowing the slope (𝑖. 𝑒. 𝐶 𝑠𝑜𝑙𝑖𝑑_𝑓𝑖𝑥𝑒𝑑_𝑖𝑛𝑖𝑡𝑖𝑎𝑙 ) and the total initial concentration of U: 206 mg.kg -1 ) with a k' D of 11 ± 7 L kg -1 whatever the V/M considered. As shown in the previous parts of this work, the observed dependence of R D with the V/M ratio by Zheng and Wan [START_REF] Parajuli | Variation in available cesium concentration with parameters during temperature induced extraction of cesium from soil[END_REF] can thus easily be explained by the fact that only a part of U(VI) retained on soil is available and at equilibrium with the solution. The percentage of available U(VI) estimated with our proposed method is close to the sum of U(VI) in the water-soluble form, exchangeable form, carbonate-associated or bound to the organic (55 ± 7 %) determined by the authors with a sequential extraction procedure. This observation can suggest that these forms may constitute the reservoir of U available forms in their soil. Interestingly, a single distribution coefficient (k' D of 11 ± 7 L kg [START_REF] Rodrigues | Evaluation of an approach for the characterization of reactive and available pools of 20 potentially toxic elements in soils: Part II -Solid-solution partition relationships and ion activity in soil solutions[END_REF] could thus be used to model the uranium transfer to solution in this sediment even if the available fraction of U is constituted by different U forms. 6) applied to Zheng and Wan (2005) [START_REF] Parajuli | Variation in available cesium concentration with parameters during temperature induced extraction of cesium from soil[END_REF] data (a) and to Elias et al. ( 2003) [START_REF] Valcke | The behaviour dynamics of radiocesium and radiostrontium in soils rich in organic matter[END_REF] (b).

In the same way, Elias et al. ( 2003) [START_REF] Valcke | The behaviour dynamics of radiocesium and radiostrontium in soils rich in organic matter[END_REF] tried to determine the optimal V/M to quantify the sorbed U(VI) pool in their contaminated sediments with a 222 mM acetate solution. They observed that the optimal V/M depended on the sediments. For the fine sand sediment, the amount of extracted U increased from V/M 1/1 to 10/1, whereas for the three other sediments no increase was observed for V/M ratios higher than 6/1 or 8/1. Based on this result no real conclusion was provided by the authors on the choice of the optimal V/M to use to estimate the complexed U(VI) pool in sediments. The use of our proposed method demonstrates that the complexed U(VI) pool estimation could be obtained based on the combination of V/M ratios or successive extractions for a given V/M realized by the authors. Finally, no estimation of optimal V/M was necessary. Their data were re-interpreted using equation (6). As the authors did not conduct their experiments to estimate the proportion of U available fraction but only to estimate the amount of complexed U(VI) extracted from sediments, the total U in the sediments was not analyzed in raw samples (personal communication from authors).

So, we had to use an estimated U total concentration to use equation (6). Of course, the R D value and 𝐶 𝑠𝑜𝑙𝑖𝑑_𝑓𝑖𝑥𝑒𝑑_𝑖𝑛𝑖𝑡𝑖𝑎𝑙 depend on the total initial chosen concentration (range tested from 5 times the maximum of extracted U to 100 times). However, the available fraction (calculated from equation (1) knowing the slope (𝑖. 𝑒. 𝐶 𝑠𝑜𝑙𝑖𝑑_𝑓𝑖𝑥𝑒𝑑_𝑖𝑛𝑖𝑡𝑖𝑎𝑙 ) and the total initial concentration) and k'D given by equation ( 6) are independent of the initial chosen concentration (same results for all total U concentration tested, results not shown). The results obtained for the four sediments, the 6 V/M ratios, a 𝐶 𝑠𝑜𝑙𝑖𝑑_𝑖𝑛𝑖𝑡𝑖𝑎𝑙 corresponding to 5 times the maximum amount of extracted U by the authors and the three extractions steps are reported in Figure 4b. The figure shows that for a given sediment all the points are on the same line, permitting the calculation of the U(VI) extractable by a 222 mM acetate solution and its k'D. Considering uncertainties, k'D is very close for all sediments (ranging from 3.4 ± 1.4 to 6.1 ± 1.5). Concerning the available fraction (calculations are provided in Table S3), it ranges from 13 ± 1 to 47 ± 1 µg g -1 (coarse sand 13 ± 1, fine sand 15 ± 1, Mancos Shale 26 ± 1 and clay 47 ± 1), which is close to the value obtained by the authors after one extraction for the higher V/M. The reinterpretation of these data makes it possible to understand the dependence of the quantities of U(VI) extracted according to the V/M ratios observed by the authors.

The work of Nagao et al. (2020) [START_REF] Elias | A procedure for quantitation of total oxidized uranium for bioremediation studies[END_REF] was devoted to assessing 137 As expected, these results are slightly higher than those obtained by Nagao et al. (2020) [START_REF] Elias | A procedure for quantitation of total oxidized uranium for bioremediation studies[END_REF] , mainly for sample St4 for which Nagao et al. (2020) [23] underestimated the available 137 Cs fraction by 30%.

This higher underestimation of the available fraction of 137 Cs for sample St4 may be explained by the higher values of k'D obtained for this sample compared to the others (38, 77, 51 and 43 L kg -1 for St1, St4, St5a and St5b, respectively). The higher the k'D , the higher the number of extractions needed to recover the totality of the available fraction. This directly points out another argument in favor of the proposed method, which is the gain of time for a good estimation of k'D and 137 Cs available fraction (four extractions being enough). Additionally, even if the pool of available 137 Cs in sand that can be extracted by seawater was well determined by Nagao et al. (2020) [START_REF] Elias | A procedure for quantitation of total oxidized uranium for bioremediation studies[END_REF] for the majority of sands, this information is not sufficient to model the dynamics of recontamination of seawater. This sort of modeling is classically realized using a KD model. However, as already explained, this approach considers that all the contaminant in the solid is available. Our approach permits integrating the dynamic release of the real fraction of available 137 Cs only. As an example, simulated results of predictions made by a KD model or by our model are presented in Figure S2 for St4. For these simulations, the KD value was set equal to the RD measured at the first desorption step (322 L kg -1 ), whereas % of available 137 Cs and k'D were those presented above for St4. The water content of sand was provided by Nagao et al. (2020) [START_REF] Elias | A procedure for quantitation of total oxidized uranium for bioremediation studies[END_REF] , the contact time used for desorption (48h) was used as the time of solution renewal, and the radioactive decay of 137 Cs was considered. The results showed that our model predicts a release of 137 Cs in interstitial water 2 orders of magnitude lower than the KD model after 10 years and 7 orders of magnitude lower after 40 years. On the opposite, after 40 years, 137 Cs remaining on the sand is 2 orders of magnitude lower for the KD simulation. This result illustrates the difference in the prediction of solid/solution distribution using one model considering that all the contaminant present in the solid is available for solution transfer against another considering that only one part of this contaminant is available.

The last example used to test the method on literature data was Rigol et al.'s (1999) [START_REF] Roig | Estimating the radionuclide available fraction in m i n e r a l s o i l s u s i n g a n e x t r a c t i o n t e c hn i q u e[END_REF] work. In this paragraph, we compared the yield of extraction obtained by the authors with those obtained using equations ( 4) and (6). The objectives of this comparison were to determine (1) if the proposed method can permit decreasing the number of extraction realized by the authors (from 8 with CH3COONH4 up to 60 with CaCl2) to determine the 134 Cs available fraction and (2) if the number of extractions realized by the authors is enough to recover the totality of the 134 Cs available fraction.

The results obtained for calculation using equation ( 4) for the extractions conducted with CH3COONH4 are presented in Figure 5, whereas those obtained using equations ( 4) and ( 6) for the extractions conducted with CaCl2 are presented in Figure 6. [START_REF] Roig | Estimating the radionuclide available fraction in m i n e r a l s o i l s u s i n g a n e x t r a c t i o n t e c hn i q u e[END_REF] and calculated using equations ( 4) and ( 6).

The available fractions of 134 Cs obtained for CH3COONH4 extractions using equation ( 4) are the same as those obtained by Rigol et al. (1999) [START_REF] Roig | Estimating the radionuclide available fraction in m i n e r a l s o i l s u s i n g a n e x t r a c t i o n t e c hn i q u e[END_REF] . Interestingly, the results obtained using the four first extraction steps gave the same results as others, showing that for this kind of extractant, a lot of successive extractions are not necessary to determine the real available fraction (Tables S5 andS6).

The results concerning the CaCl2 available fraction of 134 Cs reported in Figure 6 show that for the HAT soil, in which almost all the 134 Cs is available, the results obtained using equations ( 4) or ( 6) are similar to those obtained by Rigol et al. (1999) [START_REF] Roig | Estimating the radionuclide available fraction in m i n e r a l s o i l s u s i n g a n e x t r a c t i o n t e c hn i q u e[END_REF] . For the other soils (KOM, BRA, and BIR), the available fractions calculated using equations ( 4) and ( 6) are a bit different, with results obtained by equation ( 6) being higher than those obtained by equation ( 4) and higher than those proposed by Rigol et al. (1999) [START_REF] Roig | Estimating the radionuclide available fraction in m i n e r a l s o i l s u s i n g a n e x t r a c t i o n t e c hn i q u e[END_REF] . This difference can be explained by the fact that the values proposed by Rigol et al. (1999) [START_REF] Roig | Estimating the radionuclide available fraction in m i n e r a l s o i l s u s i n g a n e x t r a c t i o n t e c hn i q u e[END_REF] were obtained after a maximum of 38 extraction steps, whereas the plateau was still not reached. In this case using equation ( 6) permitted us to really determine the available fraction even for experiments in which the plateau was not reached. The slight difference in the % of available 134 Cs obtained with equation ( 4) and the one obtained with equation ( 6) can be explained by the fact that for the CaCl2 experiments reporting Csolide versus Csolution does not always lead to a straight line, whereas with the RD versus 1/Csolution representation the break in the slope is not observable (Figure S3). This poor alignment of Csolide versus Csolution suggests that processes involved in the 134 Cs extraction cannot be simplified using a model considering a single 134 Cs available fraction at equilibrium with the solution and a non-available 134 Cs fraction. Rigol et al. (1999) [START_REF] Roig | Estimating the radionuclide available fraction in m i n e r a l s o i l s u s i n g a n e x t r a c t i o n t e c hn i q u e[END_REF] already suggested the existence of two available fractions: one immediately available and another one whose availability is diffusion limited. Moreover, CaCl2 is supposed to extract 134 Cs sorbed on the outer surface of clays and humic compounds. The sorption of Cs on the surface of clay minerals can occur under inner-sphere or outer-sphere complexes [START_REF] Takeda | Extractability of major and trace elements from agricultural soils using chemical extraction methods: Application for phytoavailability assessment[END_REF] and under outer-sphere complexes on organic compounds [START_REF] Cherif | A robust and parsimonious model for caesium sorption on clay minerals and natural clay materials[END_REF] . As outersphere complexes are highly available compared to inner-sphere complexes, we can suppose that the pool of outer-sphere complexes was removed with the first extraction, whereas the inner-sphere complexes pool was recovered with the following ones. The results obtained using equations ( 4) and ( 6) applied to the complete data set, the data set minus the four first extraction steps, and those to the four first extraction steps are available in the Supporting Information (Tables S5 andS6). The estimation of the 134 Cs available fraction using the entire data set is similar to the one using the data set minus the four first extraction steps for equation (6). Differences appear only for some soils using equation (4) (maximum 15% for BRA soil after PCaK-D treatment). The results obtained using the four first extraction steps showed that the estimated available fraction and k'D were lower than those obtained from the entire data set, except for HAT soil for which the results were the same. This result confirms that the CaCl2 available fraction can be subdivided into two fractions: one highly available and another one less available. For this experiment, using equation ( 6) for the full data set is a better way to estimate the global available fraction. The reinterpretation of Rigol et al.'s (1999) [START_REF] Roig | Estimating the radionuclide available fraction in m i n e r a l s o i l s u s i n g a n e x t r a c t i o n t e c hn i q u e[END_REF] work permitted us to go further into the validation and criticism of the proposed method, by underlying the limitation of the proposed method, if the available fraction of a contaminant is a combination of different sub-fractions with different availabilities which cannot be described by a single k'D.

Conclusions

The results obtained under simulated conditions, from experiments performed to validate the approach, and from the reinterpretation of the literature showed the robustness of the proposed method.

In this paper, the technique of successive desorption has been seen in a new light. Compared to previous studies, in which only the extracted fraction was determined, the proposed method permits determining the real percentage of the available fraction and its associated distribution coefficient (k ′ D). We demonstrated that using successive desorption or experiments conducted at different V/M can provide the same parameters. One of the main advantages of the "successive desorption" method is that the obtained parameters do not depend on the V/M ratio used for the extraction, which permits comparing the results obtained with different experimental protocols.

The % of the available contaminant and k'D can then be used to calculate the time needed to leach the available fraction of contaminated soil in natural environments, by knowing the in situ soil humidity, precipitation level, and infiltration rate.

Moreover, this method (1) confirms that using a single-step extraction can underestimate the real available fraction and (2) provides information on the use of RD as KD in modeling: if the available fraction is about 100 %, k'D is equal to RD and can be assimilated to KD.

The proposed method relies on the assumption that soil/solution system can be represented by a two-site model: one site at equilibrium with the solution and another site which does not interact with the solution. However, some limitations can be underlined for this operational and simple assumption. For example, very slow kinetic reactions may control the release in the solution of the second pool (which cannot be considered as "fixed" anymore), or different sorption sites having different equilibrium or kinetic constants may lead to different pools released at different extraction steps. In this case, a first conceptual simplification could be proposed: k'D represents the fractionation of the contaminant between the soil/solution for the sites having equilibrium or kinetic constants permitting the transfer from solid to solution with the experimental protocol used and the non-available fraction represents the sites with higher equilibrium or lower kinetic constants conducting to non-significant desorption due to the experimental protocol used. In case where this simplification is not satisfactory, more complex models (kinetics, geochemists...) [33][35] need to be used to describe the contaminant transfer from contaminated material to the solution. Nevertheless, in most cases, the method is interesting from an operational point of view to predict the transfer of contaminants in soils being easy to apply and more realistic than the KD classical approach. One perspective of this work would be to better link this macroscopic method to the process that controls the retention of contaminants in soil and to determine the influence of the soil's physicochemical parameters on the available fraction and its distribution coefficient, based on specific experiments or reinterpretation of existing literature.

Figure 1 .

 1 Figure 1. C _solid_total_final against C _solution_final for the % Solid_fixed_fraction of 30% and k'D = 10 L kg -1 theoretical

Figure 2 .

 2 Figure 2. Contaminant extracted (bars) and RD (rectangles) against V/M ratios for the

  , concerns the calculation of the classical RD, assimilated by a lot of authors to a KD value. The calculated RD, corresponding to the ratio between the solid concentration and the solution concentration at the end of each extraction (in our case

Figure 3 .

 3 Figure 3. %remaining_in_solid vs Csolution_normalized for different experiments : (a) CaCl2 (0.5 mM)

  (b). For this set of experiments, after the fourth step of extraction in a classical batch setup, the pellet was introduced in a dialysis bag having a different V/M ratio and a second 4-step successive extraction was conducted using the dialysis bag protocol.

Figure 3c ,

 3c Figure 3c,d exhibits the results obtained for batch extractions with water and ammonium acetate

Figure 4 .

 4 Figure 4. Interpretations of literature data : equation(6) applied to Zheng and Wan (2005)[START_REF] Parajuli | Variation in available cesium concentration with parameters during temperature induced extraction of cesium from soil[END_REF] data

Figure 5 .Figure 6 .

 56 Figure 5. CH3COONH4 available fractions of 134 Cs obtained by Rigol et al. (1999)[START_REF] Roig | Estimating the radionuclide available fraction in m i n e r a l s o i l s u s i n g a n e x t r a c t i o n t e c hn i q u e[END_REF] and

Table 1 .

 1 Simulated initial conditions tested

	Range of the tested simulated conditions
	k' D (L kg -1 )	1	10	100	1000
	% solid_fixed_initial (%)	0	10	30	50	70	90	99
	V/M (L kg -1 )	0.1	0.5 1	5	10	50	250	500

Table 2 .

 2 Experimental conditions tested

	Elements Extraction	Contamination Solid phase	Extractant	V/M	Contact	Exp.
		set-up				(ml/g)	time (h)
	75 Se	Batch	Spike	Silty clay	CaCl 2,	5	48,	(1a)
				loam soil	0.5 mM	5	480	(1b)
				(0-20 cm)
	137 Cs	Batch	Spike	Andosol	*UHQ water	10	24	(2a)
				(0-20 cm)
		Dialysis	Spike	Andosol	*UHQ water	22.5	24	(2b)
		bag		(0-20 cm)
	137 Cs,	Batch	In Situ	Humus	*UHQ water	26	24	(3)
	133 Cs	Batch	In Situ	Silty soil	*UHQ water	12	24	(4)
				(0-10 cm)
		Batch	In Situ	Humus	C 2 H 7 NO 2, 1M

Table 3

 3

	. k'D and available fraction (in %) deduced from linear regression and recovery after the
	first and fourth extractions
	Exp. Elements k' D (L kg -1 ) % of available	% recovery	% recovery
				fraction	of 1 st	of 3 rd (*) or
					extraction	4 th
						extraction
	(1a)	75 Se	5.0 ±0.4	2.7±0.1	49±1%	91±2%
	(1b)		5.2 ±0.6	2.7±0.1	48±2%	91±4%
	(2a)	137 Cs	26.1 ±2.7	0.7 ±0.1	27±2%	70±3%
	(2b)		21.2 ±4.7	0.7 ±0.1	83±4%	95±3%
	(3)	137 Cs	20.5 ±5.2	9.2 ±0.8	47±6%	82±11%*
		133 Cs	31.3±6.2	9.3 ±0.8	37±5%	73±10%*
	(4)	137 Cs	<LD	<LD	n.d	n.d
		133 Cs	14.9 ±0.3	1.9 ±0.1	43±4%	81±8%*
	(5)	137 Cs	7.0 ±1.0	44.4 ±1.0	75±8%	97±10%*
		133 Cs	10.6 ±0.3	53.4 ±0.4	66±7%	93±9%*
	(6)	137 Cs	8.0±2.3	44.9 ±3.5	56±7%	91±11%*
		133 Cs	2.6 ±0.1	11.8 ±0.1	81±8%	99±10%*
	Figure

  After the calculation of137 Cs concentration in solid and solution at each desorption step, based on their figure showing the extracted percentage at each extraction step, equations (4) and (6) were used to calculate the available137 Cs and its associated k'D. Equations (4) and (6) lead to the same values, only results obtained for equation(6) are presented in table S4 and Figure S1. The available fraction of 137 Cs (calculated from equation (1) knowing the slope (𝑖. 𝑒. 𝐶 𝑠𝑜𝑙𝑖𝑑_𝑓𝑖𝑥𝑒𝑑_𝑖𝑛𝑖𝑡𝑖𝑎𝑙 ) and the total initial concentration) obtained for St1, St4, St5a and St5b are 61, 25, 41 and 56 %, respectively.

	Cs availability contained in beach
	sands. For their 4 samples, they concluded, after 12 or 16 desorption steps with seawater, that 58,
	19, 37 and 51 % of 137 Cs were available in samples labeled St1, St4, St5a and St5b, respectively.

ACKNOWLEDGMENT

The authors would like to thanks to A. Rigol, M.Vidal and G.Rauret to provide us the originaldata of their work and DA Elias, JM Senko and LR Krumholz to search additional informationon U concentrations of their sediments.

Supporting information

Table S1 (Results obtained for the 224 simulated initial conditions), Table S2 (Additional information concerning the experiments performed to validate the approach), Table S3 (Calculation of available fraction for Elias et al. (2003) work), Table S4 (Estimation of available fraction (%) and its associated k'd using equation ( 6) from Nagao et al. (2020) data), Table S5 (Estimation of available fraction (%) and its associated k'd using equation ( 4) from Rigol et al.

(1999) data), Table S6 (Estimation of available fraction (%) and its associated k'd using equation The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. The authors contributed equally.


Keywords: primary ciliary dyskinesia (PCD), cilia, genetics, Kartagener syndrome, dynein, situs inversus, mutations

Cilia are evolutionarily conserved structures that play key roles in diverse cell types. Motile cilia are involved in the most prominent ciliopathy called primary ciliary dyskinesia (PCD) that combines respiratory symptoms, male infertility, and, in half cases, situs inversus. The diagnosis of PCD relies on the identification of ciliary abnormalities that mainly concern outer and/or inner dynein arms (ODA, IDA). PCD is a genetic condition, usually inherited as an autosomal recessive trait. To date, six genes have been clearly implicated in PCD. Two "major" genes, DNAI1 and DNAH5, underlie PCD in nearly half of the patients with ODA defects, whereas RPGR, DNAH11 and TXNDC3 are implicated in rare families with specific phenotypes (retinitis pigmentosa, abnormal beating of structurally normal cilia, and situs ambiguous, respectively). The relative contribution of DNAI2, is currently assessed. In all the other patients with ODA or other ultrastructural defects, the causative genes remain to be identify.

Introduction

The history of primary ciliary dyskinesia (PCD) began with the 20 th century when A. Siewert noticed the surprising association of bronchiectasis and situs inversus [START_REF] Siewert | Ueber einen fall von bronchiectasie bei einem patienten mit situs inversus viscerum[END_REF] . In 1933, this association was formalised by M. Kartagener who described the triad of sinusitis, bronchiectasis, and situs inversus. Some forty years later, B. Afzelius identified in the axoneme of respiratory cilia and sperm flagella of patients with Kartagener syndrome the underlying ultrastructural defect corresponding to an absence of dynein arms [START_REF] Kartagener | Zur pathogenese der bronchiektasien. Bronchiektasien bie situs inversus viscerum[END_REF] . By the end of the 20 th century, DNAI1, the human ortholog of the Chlamydomonas reinhardtii gene IC78, was identified as the first gene involved in PCD [START_REF] Pennarun | Loss-of-function mutations in a human gene related to Chlamydomonas reinhardtii dynein IC78 result in primary ciliary dyskinesia[END_REF] , thereby opening up a new field of research to decipher the pathophysiology of this complex disorder.

Ciliary structure Cilia are evolutionarily conserved complex structures that protrude from the apical surface of most eukaryotic cells [START_REF] Haimo | Cilia, flagella, and microtubules[END_REF] . These organelles, which are structurally related to the flagella of spermatozoa, can be classified according to the arrangement of their microtubule cytoskeleton core, called axoneme. The axoneme consists either of nine doublets only («9+0» pattern) or of nine outer-doublet microtubules surrounding a central pair of single microtubules («9+2» pattern). The «9+0» primary cilia are immotile, except in the embryonic node where they are involved in left-right asymmetry. In mammals, primary cilia are present on most cells where they have mechanosensory properties, acting as antennae, sensing the external environment, while sensory cilia play key roles in vision and olfaction. The «9+2» motile cilia are always motile, are involved in the transport of extracellular fluids; for example, ciliated epithelium can be found in the respiratory tract, the brain ependyma, the female oviduct and the male vas deferent. Most importantly, respiratory cilia propel mucus along the respiratory tract and represent, therefore, the first line of airway defences [START_REF] Satir | Overview of structure and function of mammalian cilia[END_REF] .

The axonemal proteins have been shown to be extremely conserved throughout evolution from lower eukaryotes, like the unicellular green algae Chlamydomonas, to mammals [START_REF] Hook | The dynein family at a glance[END_REF] . The axoneme of motile cilia (Fig. 1) consists of α and β tubulin heterodimers arranged in protofilaments to form microtubules. Each peripheral doublet is composed of an A microtubule (13 protofilaments) and a B microtubule (11 protofilaments) surrounding a central complex (CC) consisting of two single microtubules (C1 and C2) inside a central sheath. Nexin links and radial spokes are multiprotein complexes that interconnect the adjacent peripheral doublets to each other and to the central microtubules, respectively. The inner dynein arms (IDA) and the outer dynein arms (ODA), bound to each A peripheral microtubules with certain periodicity, are the transducers of mechanical forces necessary for ciliary motion via a number of complex cell events including phosphorylation/dephosphorylation of key proteins [START_REF] Haimo | Cilia, flagella, and microtubules[END_REF] . Detailed structural and biochemical studies of dynein arms have been performed in various species including sea urchin and Chlamydomonas reinhardtii. These studies have revealed that dynein arms are large multisubunit molecular motors formed by the assembly of heavy, intermediate and light chains (HC of 400-500 kDa, IC of 45-110 kDa and LC of 8-55 kDa, respectively). The ODA is composed of three or two HCs (α, β, γ), depending on species (only β and γ in humans), two ICs and 8 LCs. Dynein HCs provide, through ATPase activity, the energy necessary for ciliary beating. The IDAs are more complex with at least seven different isoforms: one with two HCs and each of the six other isoforms contains a different HC; each isoform includes different ICs and LCs [START_REF] Porter | Axonemal dyneins: assembly, organization, and regulation[END_REF] . Assembly and maintenance of cilia and flagella are dependent on intraflagellar transport (IFT). IFT is an intracellular motility system, by which large protein complexes called IFT particles are transported bidirectionally between the cell membrane and the outer doublet microtubules of cilia and flagella. IFT, which was first described in Chlamydomonas, has subsequently been found to be essential for the assembly of motile and sensory cilia in many organisms including mice [START_REF] Rosenbaum | Intraflagellar transport[END_REF] .

Ciliary defects

Cilia play key physiological and developmental roles in diverse cell types and organisms. In mammals, defects in primary cilia cause a wide range of disorders such as cystic diseases and/or sensorial disorders, while motile cilia are involved in the most prominent ciliopathy called primary ciliary dyskinesia (PCD). PCD (MIM 242650) is a rare respiratory disease due to impaired mucociliary clearance resulting from functional and ultrastructural abnormalities of respiratory cilia 9, 10 . It represents a heterogeneous group of genetic disorders, usually beginning in early childhood.

Approximately half of the patients with PCD display a situs inversus, thereby defining the Kartagener syndrome (MIM 244400). This complex phenotype, i.e. chronic airway infections, situs inversus and male infertility, is now clearly explained by a single event involving the axonemal structure found in motile respiratory, embryonic nodal cilia, and flagella of spermatozoa, respectively.

The diagnosis of PCD is therefore based on the identification of functional and structural abnormalities of cilia (Fig. 2). In most patients with PCD, all the cilia share the same ultrastructural defect, as expected for a congenital disease. However, depending on the patients, cilia have been shown to carry various axonemal abnormalities. The first ultrastructural defect that has been reported in patients with PCD was the absence of dynein arms that are essential for ciliary motion [START_REF] Afzelius | The immotile-cilia syndrome: a microtubule-associated defect[END_REF] . The main ciliary defect concerns dynein arms in more than 80% of cases, and involves more frequently ODA than IDA [START_REF] Chilvers | Ciliary beat pattern is associated with specific ultrastructural defects in primary ciliary dyskinesia[END_REF][START_REF] Noone | Primary ciliary dyskinesia: diagnostic and phenotypic features[END_REF] . Other axonemal abnormalities concern the central complex or the radial spokes (axonemal disorganization). In our 20-year experience, as in literature, the spectrum of ultrastructural defects in PCD is as follows: 24 to 43% of isolated ODA defects, 24 to 45% of defects involving both dynein arms, 14 to 29% of isolated IDA defects, and 4 to 18% of CC defects [START_REF] Chilvers | Ciliary beat pattern is associated with specific ultrastructural defects in primary ciliary dyskinesia[END_REF][START_REF] Noone | Primary ciliary dyskinesia: diagnostic and phenotypic features[END_REF][START_REF] Iongh | Ciliary defects in healthy subjects, bronchiectasis, and primary ciliary dyskinesia[END_REF][START_REF] Jorissen | Ultrastructural expression of primary ciliary dyskinesia after ciliogenesis in culture[END_REF][START_REF] Tamalet | Abnormal central complex is a marker of severity in the presence of partial ciliary defect[END_REF] . Ciliary motility seems to be related to the type of ciliary defects: most of the cilia are immotile when both dynein arms or outer dynein arms are affected [START_REF] Noone | Primary ciliary dyskinesia: diagnostic and phenotypic features[END_REF][START_REF] Iongh | Ciliary defects in healthy subjects, bronchiectasis, and primary ciliary dyskinesia[END_REF][START_REF] Rossman | The dyskinetic cilia syndrome; abnormal ciliary motility in association with abnormal ciliary ultrastructure[END_REF][START_REF] Pedersen | Rhinitis, sinusitis and otitis media in Kartagener's syndrome (primary ciliary dyskinesia)[END_REF][START_REF] Chilvers | Functional analysis of cilia and ciliated epithelial ultrastructure in healthy children and young adults[END_REF] , while the ciliary beating pattern seems abnormal with reduced amplitude in case of inner dynein arm defects [START_REF] Chilvers | Functional analysis of cilia and ciliated epithelial ultrastructure in healthy children and young adults[END_REF] . In case of anomalies of the central complex, the ciliary beating pattern is abnormal [START_REF] Chilvers | Ciliary beat pattern is associated with specific ultrastructural defects in primary ciliary dyskinesia[END_REF][START_REF] Rossman | The dyskinetic cilia syndrome; abnormal ciliary motility in association with abnormal ciliary ultrastructure[END_REF][START_REF] Escalier | Abnormalities of the ciliary axonemal complex in children: an ultrastructural cinetic study in a series of 34 cases[END_REF] . In 10-20% of patients, no ultrastructural defects can be found through conventional electron microscopy, although cilia are immotile [START_REF] Pennarun | Loss-of-function mutations in a human gene related to Chlamydomonas reinhardtii dynein IC78 result in primary ciliary dyskinesia[END_REF][START_REF] Satir | Overview of structure and function of mammalian cilia[END_REF][START_REF] Iongh | Ciliary defects in healthy subjects, bronchiectasis, and primary ciliary dyskinesia[END_REF][START_REF] Chao | Genetic heterogeneity of dynein-deficiency in cilia from patients with respiratory disease[END_REF][START_REF] Fliegauf | Mislocalization of DNAH5 and DNAH9 in respiratory cells from patients with primary ciliary dyskinesia[END_REF] . In these patients, the diagnosis of PCD is based on the presence of typical clinical features (including situs inversus) with the absence of ciliary motion. In these cases, a low level of nasal nitric oxide might be very helpful to assert the diagnosis of PCD. It has been proposed that the defect could concern some enzymes associated with various axonemal structures [START_REF] Porter | The 9 + 2 axoneme anchors multiple inner arm dyneins and a network of kinases and phosphatases that control motility[END_REF] . In fact, Kartagener syndrome with normal cilia is not an exceptional condition [START_REF] Greenstone | Normal axonemal structure and function in Kartagener's syndrome: an explicable paradox[END_REF][START_REF] Escudier | Unexpectedly normal cilia and spermatozoa in an infertile man with Kartagener's syndrome[END_REF][START_REF] Schwabe | Primary ciliary dyskinesia associated with normal axoneme ultrastructure is caused by DNAH11 mutations[END_REF] . As a consequence, and because of random lateralization, it is tempting to speculate that the same proportion of "true" patients with PCD, but with normal cilia and without situs inversus, should exist.

PCD inheritance

In most instance, the transmission pattern of PCD is consistant autosomal recessive inheritance of the disease [START_REF] Afzelius | The immotile-cilia syndrome: a microtubule-associated defect[END_REF] , although rare families showing autosomal dominant or X-linked modes of inheritance have also been reported [START_REF] Narayan | Unusual inheritance of primary ciliary dyskinesia (Kartagener's syndrome)[END_REF][START_REF] Krawczynski | PCD and RP: X-linked inheritance of both disorders?[END_REF][START_REF] Moore | RPGR is mutated in patients with a complex X linked phenotype combining primary ciliary dyskinesia and retinitis pigmentosa[END_REF] . The incidence of PCD ranges from 1/15,000 to 1/60,000 alive births [START_REF] Afzelius | The immotile-cilia syndrome: a microtubule-associated defect[END_REF] , while that of Kartagener syndrome is estimated to range between 1/30,000 and 1/20,000 live births. However, the frequency of the disease is markedly underestimated, especially when situs inversus is absent and/or when ultrastructure is normal.

As predicted from the high complexity of ciliary structure and function, there is ample room for genetic heterogeneity in PCD. Each of the several hundreds of proteins that constitute a cilia could potentially cause the disease. Such complexity makes approaches based on genetic linkage difficult to apply; except in case of large and/or consanguineous families, a situation which is exceptional. Alternative approaches rely on the fact that (i) the structure of the ciliary axoneme is highly conserved across species and (ii) the protein components of a protozoan axoneme, such as those found in Chlamydomonas reinhardtii, and those of mammalian cilia are highly homologous at the sequence level [START_REF] Hook | The dynein family at a glance[END_REF] . Strikingly, several immotile strains of Chlamydomonas carry axonemal ultrastructural defects that are reminiscent of those reported in patients with PCD; this observation led to the development of a candidate-gene approach based on Chlamydomonas mutants. It enabled the characterization of the first gene involved in PCD, called DNAI1 that encodes a dynein intermediate chain of the ODA [START_REF] Pennarun | Loss-of-function mutations in a human gene related to Chlamydomonas reinhardtii dynein IC78 result in primary ciliary dyskinesia[END_REF] .

PCD genes (Table I) DNAI1, which is located in the p21-p23 region of chromosome 9, comprises 20 exons spanning about 62 kb of genomic DNA. It encodes a 699-amino-acid protein orthologous to the Chlamydomonas ODA protein IC78. Mutations in DNAI1 have been found in several PCD patients including patients with Kartagener syndrome [START_REF] Pennarun | Loss-of-function mutations in a human gene related to Chlamydomonas reinhardtii dynein IC78 result in primary ciliary dyskinesia[END_REF][START_REF] Guichard | Axonemal dynein intermediate-chain gene (DNAI1) mutations result in situs inversus and primary ciliary dyskinesia (Kartagener syndrome)[END_REF][START_REF] Zariwala | Germline mutations in an intermediate chain dynein cause primary ciliary dyskinesia[END_REF][START_REF] Zariwala | Mutations of DNAI1 in primary ciliary dyskinesia: evidence of founder effect in a common mutation[END_REF] . Although allelic heterogeneity was noted in the very first studies, it was secondarily shown that the IVS1+2_3insT mutation, which accounts for about half the mutated alleles, results in fact from a founder effect [START_REF] Zariwala | Mutations of DNAI1 in primary ciliary dyskinesia: evidence of founder effect in a common mutation[END_REF] . As so far, mutations in DNAI1 have always been found in association with ODA defects and account for about 14% of those patients [START_REF] Zariwala | Mutations of DNAI1 in primary ciliary dyskinesia: evidence of founder effect in a common mutation[END_REF] .

Thanks to a genetic linkage analysis performed in one large consanguineous multiplex family, mutations have been identified in a second gene encoding a dynein heavy chain, DNAH5 33 34 . DNAH5, located on chromosome 5, codes for a protein orthologous of the Chlamydomonas γaxonemal heavy chain of the ODA. The human DNAH5 gene, which spans 250 kb, comprises 80 exons. So far, DNAH5 mutations have been found only in patients with partial or total loss of ODA associated or not with left-right asymmetry anomalies [START_REF] Olbrich | Mutations in DNAH5 cause primary ciliary dyskinesia and randomization of left-right asymmetry[END_REF][START_REF] Hornef | DNAH5 mutations are a common cause of primary ciliary dyskinesia with outer dynein arm defects[END_REF] . The DNAH5 mutation detection rate was shown to reach 49% in a subset of PCD families with documented ODA defects [START_REF] Hornef | DNAH5 mutations are a common cause of primary ciliary dyskinesia with outer dynein arm defects[END_REF] .

A third candidate gene (DNAH11) has first been involved in a patient with a complex phenotype associating cystic fibrosis, situs inversus and a paternal uniparental isodisomy of chromosome 7, a chromosome that carries both the CFTR and DNAH11 genes [START_REF] Bartoloni | Mutations in the DNAH11 (axonemal heavy chain dynein type 11) gene cause one form of situs inversus totalis and most likely primary ciliary dyskinesia[END_REF] . DNAH11, which encodes also a dynein heavy chain, comprises 82 exons, spanning more than 353 kb of the p21 region of chromosome 7. The patient was shown to be homozygous for the F508del mutation of the CFTR gene, and for the R2852X nonsense mutation in DNAH11. Notably, a missense mutation had been identified in the Dnah11 gene of the iv/iv (inversus viscerum) mouse characterized by immotile cilia of the embryonic node and random organ lateralization [START_REF] Supp | Mutation of an axonemal dynein affects left-right asymmetry in inversus viscerum mice[END_REF] . Secondarily, compound heterozygous DNAH11 mutations were identified in a large family in which five individuals have PCD and one has Kartagener syndrome. Respiratory cilia from affected individuals showed a normal axonemal ultrastructure but an abnormal ciliary beating pattern with a reduced bending capacity and a hyperkinetic beat. Mutations in DNAH11, therefore, do not result in axonemal ultrastructural defect detectable by electron microscopy, but are believed to affect motor function [START_REF] Schwabe | Primary ciliary dyskinesia associated with normal axoneme ultrastructure is caused by DNAH11 mutations[END_REF] . PCD may also be caused by mutations in RPGR (retinitis pigmentosa guanosine triphosphatase regulator), the most common gene involved in X-linked retinitis pigmentosa or TXNDC3 that codes for a protein belonging to the thioredoxin superfamily. The RPGR gene, located on the p21.1 region of the chromosome X is essential for photoreceptor maintenance and viability; it is also expressed in respiratory ciliated cells [START_REF] Hong | RPGR isoforms in photoreceptor connecting cilia and the transitional zone of motile cilia[END_REF] . In rare instances, typical symptoms of PCD have been reported in males with retinitis pigmentosa [START_REF] Krawczynski | PCD and RP: X-linked inheritance of both disorders?[END_REF][START_REF] Iannaccone | Clinical and immunohistochemical evidence for an X linked retinitis pigmentosa syndrome with recurrent infections and hearing loss in association with an[END_REF][START_REF] Zito | RPGR mutation associated with retinitis pigmentosa, impaired hearing, and sinorespiratory infections[END_REF] . More recently, a 57-bp intragenic deletion of this gene has been identified in one family in which two boys present a complex phenotype combining PCD with retinitis pigmentosa. Ciliary investigations showed immotile cilia and various ultrastructural abnormalities with partial dynein arm defects [START_REF] Moore | RPGR is mutated in patients with a complex X linked phenotype combining primary ciliary dyskinesia and retinitis pigmentosa[END_REF] . This finding, which underlines the importance of RPGR in the development of axonemal structures in photoreceptors and in respiratory cilia, represents the first clear demonstration of an X-linked transmission of the PCD phenotype. TXNDC3, which encodes a thioredoxine-nucleoside diphosphate kinase, is expressed in testis and respiratory epithelial cells. This gene was considered as a candidate for PCD because it represents the human ortholog of the sea urchin IC1 gene that encodes a component of sperm ODA [START_REF] Ogawa | Is outer arm dynein intermediate chain 1 multifunctional?[END_REF] ; it was therefore tested in a series patients with PCD and ODA abnormalities. In a young girl with PCD and situs ambiguous was identified a nonsense mutation combined, in trans, with an intronic SNP controlling the respective amounts of two physiological TXNDC3 isoforms generated by alternative splicing [START_REF] Duriez | A common variant in combination with a nonsense mutation in a member of the thioredoxin family causes primary ciliary dyskinesia[END_REF] and shown to display different binding properties to microtubules.

Just recently, several loss-of-function mutations have been identified in the DNAI2 gene of patients with ODA defect [START_REF] Loges | DNAI2 mutations cause primary ciliary dyskinesia with defects in the outer dynein arm[END_REF] , therefore confirming that DNAI2 which is located on the q25 region of chromosome 17, was indeed a good candidate gene for PCD [START_REF] Pennarun | The human dynein intermediate chain 2 gene (DNAI2): cloning, mapping, expression pattern, and evaluation as a candidate for primary ciliary dyskinesia[END_REF] .

A number of other candidate genes for PCD (such as DNAH9, HP28, DPCD, SPAG16, HFH-4) [START_REF] Zariwala | Genetic defects in ciliary structure and function[END_REF] have been selected for mutation screening in PCD patients, but, so far, no mutations have been reported. In addition, approaches based on positional cloning have pointed to several possible PCD loci (e.g. 1q23.1-q32.1, 7p14.2-12.2, 15q13.1-15.1, 15q24-25, 16p12.1-12.2, 19q13.3-qter regions) 46- 51 ; the causative genes are still to be identified.

Conclusion

The molecular basis of PCD is just beginning to be elucidated. To date, despite substantial efforts made for many years by several groups and the recent availability of huge sequence information, only six genes (DNAI1, DNAH5, DNAH11, RPGR, TXNDC3 and DNAI2) have been clearly implicated in PCD. Two of them, DNAI1 and DNAH5, which underly the disease in about 25% of the patients with PCD, represent major genes, while three others (RPGR, DNAH11, TXNDC3), are "minor" genes, implicated in only few families. The relative contribution of DNAI2 to the pathology remains to be determined. Although DNAI1 and DNAH5 mutations underlie PCD in nearly half of patients with ODA defects, for all the other patients with ODA defects or with other ultrastructural phenotypes, the genes responsible for their ciliary defect are still to be identified. This is an important task for a better management of the disease (e.g. development of new diagnostic methods and of more efficient treatments). This research should also provide new insights into the molecular mechanisms involved in the assembly and function of cilia, as well as in the determination of laterality.

Figure 1 :Figure 2 :

 12 Figure 1: Schematic representation of a transversal section of the axoneme of motile cilia

Table I :

 I Clinical and ultrastructural phenotype according to the genes involved in PCD

	Genes	Extra-respiratory phenotypic features	Ultrastructural defect	References
	DNAI1 DNAH5 DNAH11 RPGR TXNDC3 DNAI2	± situs inversus ± situs inversus ± situs inversus retinitis pigmentosa complex dynein arm defect lack of ODA lack of ODA normal axoneme situs ambiguous partial lack of ODA ± situs inversus lack of ODA	3, 30-32 34, 35 . 36, 26 29 42