Julia Contreras-García

Ángel M Pendás

Bernard Silvi

J Manuel Recio

Julia Contreras

Useful applications of the electron localization function in high pressure crystal chemistry

Keywords: A. Elements, C. Ab-initio calculation, C. High pressure, D. Equation of state, D. Phase transitions

The main features of a new computational code aimed at the topological analysis of the Electron Localization Function (ELF) in crystals are hereby presented. Besides the complete localization of all critical points, the code is able to determine the limiting surfaces which define the chemical regions associated with the so-found maxima (or attractors) of the ELF. Hence, integrations of density operators within these basins provide charges and volumes to cores, bonds, and lone pairs. Two illustrative applications have been selected. Firstly, we examine the Z dependence of basin compressibilities in the elements of the first two rows of the Periodic Table, and secondly, we focus our attention on the chemical changes across the pathway of the zinc blenderocksalt phase transition in BeO.

 A c c e p t e d ma n u s c r i p t 2

Introduction

Due to the high coordination indexes and to the numerous atom-atom contacts, the presence of different bonding types is a common and genuine feature of solids which hampers their characterization when compared with the molecular realm. Performing a rigorous qualitative and quantitative classification of these bonds, based on the same theoretical approach, has revealed itself a challenge and a source of debate [1]. The widest-spread method of approach has been to consider the topological analysis of the electron density (AIM) as developed by Bader and co-workers [START_REF] Bader | Atoms in Molecules: A. Quantum Theory[END_REF][START_REF] Pendas | [END_REF], according to which the existence of a bond is associated to the presence of a bond path in the stable structure of the solid.

Besides, it has been long recognized that further insight into the nature of the bond can be gained by resorting to the electron localization function (ELF) [4]. The ELF was introduced in 1990 by Becke and Edgecombe [5] in an attempt to analyse electron localization from a theoretical standpoint. Later on, the work carried out by Silvi and Savin [6], and the formulation of the latter [7] within the DFT framework have given value to the ELF in solid state science. Within this formalism, the ELF can be understood as a local measure of the excess of local kinetic energy of electrons due to the Pauli principle. It is expressed in terms of the local kinetic energy (t), its value for this density in a bosonic system (t W ) and the kinetic energy of the homogeneous electron gas (t TF , Thomas-Fermi): For convenience reasons it is defined in such a way that it runs from 0 to 1. It approaches 1 in those regions of space where localization is high, and tends to a value of 0.5 when the density distribution approaches to homogeneity. Within the context of our work, it is also interesting to remark that the ELF topological analysis allows a partition of the 3dimensional space in terms of non-overlapping regions with a full chemical meaning: electronic shells, bonds and lone pairs. This ability makes the ELF be an appropriate formalism to reconcile the traditional chemical language with the outcome of quantummechanical calculations.

However, the application of the ELF formalism in high-pressure condensed matter has been scarce due to major computational difficulties imposed by periodicity [4,8,9]. Our work has been focused to the development of a computational code attempting to fulfil the gap existing between the ELF topological analyses of bonding in the molecular and the crystalline realms. Localization of ELF critical points, evaluation of charges and volumes of basins, and visualization of interesting chemical entities within the ELF are some of the possibilities offered by our new code. A brief description of the main tasks of the program, examples of bonding analyses in prototypical solids, and selected applications in highpressure crystal chemistry are presented below.

The program

The program is currently performing three different ELF-related tasks once an all-electron crystalline wave function is introduced as input. The process is as follows. Firstly, the code searches the complete set of critical points within the cell. The irreducible Wigner Seitz cell The analysis of the ELF profile even allows us to identify the relationship between basins, and hence to characterize the weak interactions through the localization of the bond points between the basins. The relative value of ELF at those points sheds light into the "separation" between them, so that the higher the value of ELF at those points (so called, bip, bond interaction points), the less separated they are. Hence, a complete analysis of the attractors provides insight into the strong interactions, and a subsequent analysis of the bond points between them enables the characterization of the weak ones. The localization of the complete set of critical points as performed by our code enables in most cases the automatic localization of the bip. Thus, both the relationship between basins and the weak interactions can be efficiently identified, a task that becomes increasingly difficult as the complexity of the solid structure grows, if we follow a visual approach (most common method up to now).

Last but not least, the localization of the complete set of critical points not only provides a clear and quantitative view of the bonding in the crystal: as already found in the AIM theory of solids, the use of the cage points as vertices drives back to the common inorganic description of crystals based on polyhedra. This splitting provides a theoretical root for this description as well as, and most importantly, theoretical radii along different directions for the elements and their shells.

A c c e p t e d m a n u s c r i p t 5

Secondly, and once the attractors have been identified, the program is able to locate the boundary limit of the region of space associated to each of them, the basin, and therefore, it is able to calculate the integrals of any density operator provided. Currently implemented basin properties are charge population, volume and momenta. Work is in progress for the implementation of localization/delocalization indexes [10] and probabilities [START_REF] Chamorro | [END_REF]. Some representative results for different kinds of solids are summarized below.

Finally, visualization of the net of critical points, basins and surfaces can be obtained if desired by demanding the construction of 1, 2 and 3-dimensional grids. Several common visualization formats are available (Gnuplot, Gaussian cube, etc.).

Molecular, ionic, covalent, and metallic solids

As shown in Figure 1, ELF is able to clearly represent and differentiate between the different types of solids. Carbon dioxide, as a molecular solid, shows well differentiated chemical ELF objects that are identified as CO 2 molecules. The carbon core (K-shell) in the middle, C(C), with the expected charge of two electrons, a general picture that is reproduced in all the cases and that is not affected by the environment: cores approach the nominal value of two electrons [12]. Going then along the CO 2 molecular axis, we first find the basins corresponding to a double bond, B(C-C). Notice that it is the number of basins that determines the multiplicity and not the number of electrons per bond. Finally, we clearly identify the oxygen core, C(O), and its lone pairs, LP(O). Analysing the charge distribution one realizes that not only is the Lewis picture recovered, but that a weight is approach that of a sphere and whose charge corresponds to that of a complete transfer.

As far as metals are concerned, their ELF profile is nearly flat as represented by the surface surrounding Na cores (K and L shells) , a surface that resembles the traditional electron gas model of metals. However, this jellium is not at all homogeneous, but it presents numerous maxima, B(Na-Na) [8], as already observed in the density topological analysis of other metals [13]. It must be highlighted that these maxima, to which a low population is attributed, are in fact distributed in the cell in such a way that the positions of the interstitial attractors are close to the positions of anions in ionic compounds. In other words, the electrons behave as electrides towards whose positions electronegative atoms head to form anions in ionic crystals.

Chemical partition of compressibility

Our target systems are the crystalline phases of the elements of the first two rows of the Periodic Table . The electronic structure calculations have been carried out in the framework of the density functional theory (DFT) implemented in the CRYSTAL code A c c e p t e d m a n u s c r i p t 7 [START_REF] Saunders | CRYSTAL98 User's manual[END_REF]. A number of pressure (p)-volume (V) points have been calculated for each of the compounds, and the topological analysis of the ELF was performed with the new code in order to evaluate the rate at which the volumes of the basins decrease when pressure is applied to them. As explained above, two different types of attractors are to be found: atomic shells and bonding attractors. In analogy with the jellium model, these will be resumed in core (inner shells) and valence (electrons coming from the last shell).

We have found that it is always the valence that is the main responsible for the bulk compression in all the crystalline systems, whereas cores remain practically untouched. As far as valence behavior is concerned, there is one main factor to be taken into account:

Pauli repulsion induced by pressure. This force arises from the enhanced overlaps among localized basins upon crystal compression, and its amount depends both on the overlapping, which increases with the proximity, and on the ELF value of the basins. According to these simple ideas, the periodic trends observed in Fig. 2 (the compressibility decreases along Li, Be, C; Ne, Na, Mg; and increases for Li-Na and Be-Mg) can be razionalized as follows.

ELF basins in noble elements are well separated. In these crystals, the negligible overlap between basins allows an easy reduction of the volume as pressure is applied, and, therefore, a great compressibility is expected for this kind of compounds. A completely different picture is displayed by very low compressible compounds, such as diamond, where the basins show high ELF values separated by steep valleys. Hence, there are no large interstices without localized pairs, and the increase of energy induced by pressure prevents volume reduction. Metals represent a scenario in between: the ELF valence profile is a flat platform with intermediate localization values (see Fig. 1), and the bulk compressibility of metals is, therefore, lower than in crystals of noble elements, but higher

A c c e p t e d m a n u s c r i p t

8 than in covalent compounds. Furthermore, the order of compressibilities within compounds of the same nature also follows this trend, so lithium is more compressible than berillium since its ELF platform is around 0.27, whereas that of berillium is around 0.61.

Quantitative data of the basin response to pressure is obtained through equations of state (EOS) fittings. This is of critical importance in material design and earth studies and, therefore, it becomes interesting to find out that compressibility can also be expressed as a sum of chemically meaningful basins, just as in the case of AIM [START_REF] Pendás | [END_REF]:

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ - = = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ - = ∑ i i i i i i V p V f p V V κ κ κ 1 , 1 where V V f i i / =
is the fractional occupation of the basin in the unit cell. In all the cases we have analysed, the valence basins obey standard EOS as the Vinet one, but the cores do not, probably due to the high electron density enclosed in these small basins and/or to higher precision requirements.

EOS parameters, i.e. bulk moduli and its first pressure derivative, both evaluated at zero pressure, were determined for the ELF basins of the elements discussed above, as well as for core, valence and bond basins involved in several simple and representative compounds such as LiF (ionic), N the main contribution is associated to valence which is both bigger and more compressible.

For example, the valence compressibility in Li is 7.56x10 -2 GPa -1 and the calculated crystal value is 7.92x10 -2 GPa -1 . The contribution from the K-shell of Li is almost negligible since its charge/volume ratio is very high and strong forces are acting within it. The same applies to binary ionic and polar compounds such as LiF and BeO. We have calculated, for instance, that the oxide valence (the only valence basin) accounts for 99.2% of the BeO crystalline compressibility.

Molecular crystals, given their more complex pattern, can also illustrate how the compressibility and the chemical nature of the basins are linked. Thus, in N 2 the contributions to the crystal compressibility are mainly due to the lone pairs (98.1%) but the basin compressibilities do not follow such a clear sequence as in the previous examples (k core =1.40x10 -3 GPa -1 , f core =0.024, k bond =1.12x10 -3 GPa -1 , f bond =0.136, k lonepair =1.82x10 -2

GPa -1 , f lonepair =0.862), where all the regions were atomic shells. It is found that the compressibility of the core is slightly greater than that of the bond. This is not surprising if one realizes that in both cases the volume in which electrons are localized is very small, but the populations of core and bond are 2.08 and 3.51 electrons, respectively. In both cases electrons are subjected to very strong electrostatic repulsions, but in the second case, also strong Pauli repulsions are taking place. These results are very promising and need to be extended to more complex materials to derive general conclusions, though it is very reasonable to assume that the basic ideas can be already found in these simple compounds. The next step after the application of the new code to the microscopic interpretation of EOS in solids is to examine whether the ELF also provides an insight into chemical changes.

With this aim in mind, the pressure-induced phase transition from the zinc-blende (B3) to the rocksalt phase (B1) of BeO has been studied. Both literature surveys [16][17][18] and present computations have shown that the orthorhombic Imm2 space group is energetically favoured for the description of the transition, with a barrier of 0.51 eV at the transition pressure of 114 GPa according to our calculations. Under this symmetry, the z coordinate of Be, z Be , evolves from 0.25 in the B3 to 0 in the B1 phase, and can be taken as the transition coordinate. The energetic profile of the transition is found to proceed in just one step whose maximum is located at around z Be =0.125. Theoretical studies usually complement the energetic analysis by identifying atomic displacements and changes in distances (Figure 2b, upper curves) and coordination. In the case of study, the coordination of Be goes from a 4-fold tetrahedron to a 6-fold octahedron.

Just as for the compressibility, the chemical and structural changes taking place across the Curves at the top correspond to cores, with the same symbols as the valence curves at the bottom.

A c c e p t e d m a n u s c r i p t 4 is

 4 constructed thereto, and its topological properties are applied in order to localize all the critical points by means of recursive algorithms. Due to the great concentration of critical points around the cores, and their steep profile, the result is refined by a spherical search around the nuclei at the shell radii distances.

A c c e p t e d m a n u s c r i p t 6 given

 6 to the different resonant forms.A covalent solid like diamond displays a continuous 3D-network of tetrahedrically coordinated carbons, bound together by means of single-bond basins, B(C-C). In this case, perfect electron pairs are found, as expected from the perfect covalency of the compound (no resonant forms). Ionic compounds like LiF are characterized by the absence of bond basins, only showing closed-shell basins (K and L, C(Li), C(F), and V(F)) whose shape

A c c e p t e d m a n u s c r i p t 9 contribution

 9 2 and CO 2 (molecular), BeO (polar), etc. The value of the crystal compressibility in the solid is well reproduced by the sum of the basin contributions (errors within 1-3%). It can be seen from the equation above that two factors determine the of the different basins to the total crystalline compressibility: on the one hand the relative volume and, on the other hand, the basin compressibility. Due to both factors,

A c c e p t e d m a n u s c r i p t 10 5.

 10 B3-B1 pathway in BeO: energy profile, structural changes and ELF evolution.

A c c e p t e d m a n u s c r i p t 11 resemble 6 .A c c e p t e d m a n u s c r i p t 12 covalent

 11612 transition are merely reflected by the valence. Analysis of the ELF topology of the oxygen L shell, V(O), reveals that it is initially divided into four different basins (2+2) whose attractors point at the four coordinated Be. It is only after the transition path has been traced up to around z Be = 0.15, that two new O valence attractors appear. This fact has a catastrophic nature and reveals the onset of the new phase. The formation of the two new basins brakes the increasing in energy associated with the transformation. Furthermore, these new oxygen L-shell basins evolve along the transition in such a way that they the other four, and the valence is finally divided into six equivalent basins, which perfectly show the change in coordination occurring in the crystal. Hence, this topological change drives us back to both approaches of the phase transition, the energetic and the structural one. Summary and some prospects.The electron localization function has proved to be a very useful tool in analysing the Lewis picture of molecules, and more specifically, the nature of the bonds. Due to computational difficulties, its application in solids has until now been scarce and mainly qualitative. A new code is hereby presented which widens the application of the ELF topological analysis to all kinds of solids, allowing a microscopic interpretation of the physical and chemical changes that pressure induces upon their bonds. The integration of the ELF basins as performed by our code enables the calculation of electron shell, bond and lone pair basin compressibilities of a large variety of crystalline systems. Data obtained so far do correlate with the chemical concepts as classically established. This does not only confirm these principles, but also endows them with a theoretical background enabling future behaviour foreseeing. Our next step towards a deeper understanding of the processes taking place within solids is to carry out the analysis of phase transitions where a change in the nature of the bond occurs. Work is in progress in both CO 2 and SiO 2 , where the change from molecular to and polar-ionic networks awakes much interest due to the natural relevance of both compounds[19][20][21]. In order to provide a non-ambiguous tool to understand these changes in the bond nature, we are currently working in the development of a user-friendly index that would quantify the character of the bond based on the ELF topological analysis[1,22].7. Acknowledgements.Financial support from the Spanish MEC and FEDER program under projects MAT2006-13548-C02-02 and CTQ2006-02976 are gratefully acknowledged. JCG thanks the Spanish MEC for a FPU postgraduate grant and for funding her stay at the Laboratoire de Chimie Theorique (Universite Pierre et Marie Curie, Paris) where part of this work has been done.

A c c e p t e d m a n u s c r i p t 14 FIGURE CAPTIONS Fig. 1 .

 14CAPTIONS1 FIGURE CAPTIONS

Fig. 2 .

 2 Fig. 2. Relative volumes vs. pressure of some of the elements of the first two rows of the periodic table.

Fig. 3 .

 3 Fig.3. Evolution of the six Be-O shortest distances (upper curves) and the distances from oxygen nucleus to its valence attractors (bottom) along the transition pathway. X stands for Be or the corresponding attractor.The black circle marks the emergence of the new oxygen basin. Numbers in brackets stand for the multiplicities associated with the curves.

A c c e p t e d m a n u s c r i p t 15 Fig. 1

 151 Fig.1

Fig. 2

 2 Fig. 2

A c c e p t e d m a n u s c r i p t 16 Fig. 3

 163 Fig. 3


E Holbig
email: eva.holbig@uni-bayreuth.de

L Dubrovinsky

V Swamy

R Wirth

V Prakapenka

A Kuznetsov

Stiffening of nanoscale anatase Ti 0.9 Zr 0.1 O 2 upon multiple compression cycles

Keywords: A. oxides, A. nanostructures, D. elastic properties, D. equation of state, D. mechanical properties

 for nanoscale anatase, but yielding much lower pressures (12 GPa) for the onset of partial amorphization.

Introduction

Anatase TiO 2 in the macrocrystalline and nanocrystalline form is widely used as material in pigments, plastics, cosmetics, electronics, and catalysts industries. It is a wide band-gap semiconductor used for electrochemical dye solar cells [START_REF] Bach | Solid-state dye-sensitized mesoporous TiO 2 solar cells with high photon-to-electron conversion efficiencies[END_REF] and exhibits a good performance in photocatalysis [START_REF] Hoffmann | Environmental Applications of Semiconductor Photocatalysis[END_REF][START_REF] Fox | Heterogeneous Photocatalysis[END_REF]. For all technical applications, the microstructure of the material is an important tool for tuning the properties and among the materials used one can find thin films as well as mesopouros, nanocrystalline or polycrystalline materials. The crystallite size has a strong effect on the relative stability of anatase and other TiO 2 modifications like rutile, brookite or high pressure polymorphs TiO 2 II and MI phase [START_REF] Pischedda | Ultrastability and enhanced stiffness of similar to 6 nm TiO 2 nanoanatase and eventual pressureinduced disorder on the nanometer scale[END_REF][START_REF] Banfield | TiO 2 Accessory Minerals -Coarsening, and Transformation Kinetics in Pure and Doped Synthetic Nanocrystalline Materials[END_REF][START_REF] Ranade | Energetics of nanocrystalline TiO 2[END_REF][START_REF] Swamy | Size-dependent pressure-induced amorphization in nanoscale TiO 2[END_REF]. Nanoscale anatase remains stable to much higher pressures compared to the microcrystalline or single crystal counterpart [START_REF] Swamy | Compression behavior of nanocrystalline anatase TiO 2[END_REF] and when the crystallite size is smaller than the critical value of ~ 10 nm, pressure induced amorphization takes place at pressures of ~ 20 to 24 GPa [START_REF] Swamy | Size-dependent pressure-induced amorphization in nanoscale TiO 2[END_REF].

The bulk modulus of anatase varies strongly with the crystallite size of the starting material and also in response to doping with Zr. In former studies using the diamond anvil cell apparatus (DAC) and synchrotron powder X-ray diffraction (XRD) the authors fitted experimental pressure-volume data to the second-order Birch-Murnaghan Equation of State (EoS) and determined K 0 = 178(1) GPa [START_REF] Swamy | Bulk modulus of anatase[END_REF] and K 0 = 190(10) GPa [START_REF] Arlt | High-pressure polymorphs of anatase TiO 2[END_REF] for the bulk modulus of microscale anatase TiO 2 . In comparison, the values for nanoscale anatase are much higher with K 0 = 243(3) GPa [START_REF] Swamy | Compression behavior of nanocrystalline anatase TiO 2[END_REF] and K 0 = 237(3)

GPa [START_REF] Pischedda | Ultrastability and enhanced stiffness of similar to 6 nm TiO 2 nanoanatase and eventual pressureinduced disorder on the nanometer scale[END_REF]. The data suggest that anatase becomes stiffer when the crystallite size is decreased to the nanometer scale. Additionally, doping with Zr of nanoscale anatase leads to an even higher bulk modulus of K 0 = 266(6) GPa for Ti 0.9 Zr 0.1 O 2 [START_REF] Holbig | Compression behavior of Zr-doped nanoanatase[END_REF]. The fact that Zrdoping of nanoanatase produces the least compressible form of anatase is opposite to the expectation from the comparison of elastic constants for TiO 2 and ZrO 2 polymorphs.

While ZrO 2 polymorphs show a smaller bulk modulus than the corresponding TiO 2 forms, the incorporation of Zr into TiO 2 anatase results in an increasing bulk modulus. Furthermore, the compression behavior of Zr-doped nanoanatase Ti 0.9 Zr 0.1 O 2 shows another interesting phenomenon. Analysis of the X-ray diffraction data shows a significant change in compression behavior at pressures > 4 GPa. The slope of the ratio of lattice parameters a/c strongly increases, the slope of the ratio of the apical and equatorial bond length of the octahedra changes from negative to positive, and the z-coordinate of the oxygen atom, the only free atomic coordinate, changes its trend [START_REF] Holbig | Compression behavior of Zr-doped nanoanatase[END_REF]. The authors suggested that the anomalous compression behavior of the sample is related to the In order to study these phenomena in more detail and to find out, whether the pressure induced changes of structural parameters are reversible upon decompression, we carried out DAC experiments on anatase Ti 0.9 Zr 0.1 O 2 with crystallite size of ~ 12 nm, performing multiple cycles of compression and decompression within the stability field of the material, which is up to 13 GPa.

Experimental method

Experiments on a mixture of nanoscale anatase Ti 0.9 Zr 0.1 O 2 and LiF were carried out in the diamond anvil cell, at the synchrotron facility GeoSoilEnviroCARS 13 IDD at the Advanced Photon Source (APS), Argonne, Illinois; details of the experimental setup, starting material and XRD data processing are as in ref. [START_REF] Holbig | Compression behavior of Zr-doped nanoanatase[END_REF]. An X-ray beam with a wavelength of 0.3344 Å and a size of 6×15 µm was used. The distance sample to detector was 201 mm. The seats of the DAC were made from cBN and allowed the collection of diffraction data to d = 1 Å. Unlike other DAC samples [START_REF] Holbig | Compression behavior of Zr-doped nanoanatase[END_REF], the sample was loaded without any compression applied during the loading process, then compressed at room temperature to 12 GPa, decompressed to 0.5 GPa, compressed to 12 GPa and decompressed to ambient conditions.

In order to prepare a quenched sample to be observed by TEM, a second experiment with the same setup of the DAC was performed on the pure Zr-doped nanoanatase, using Raman spectroscopy. The material was loaded together with a small ruby-sphere, and sample pressures were determined from the pressure dependent shift of the ruby fluorescence R 1 line [START_REF] Mao | Calibration of the Ruby Pressure Gauge to 800-Kbar under Quasi-Hydrostatic Conditions[END_REF]. The pressure-induced frequency shifts were monitored while the sample was compressed and decompressed in the same way as the previous experiment. After the experiment, the sample was prepared for TEM analysis, using a FEI FIB200TEM Focused Ion Beam (FIB) device [START_REF] Wirth | Focused ion beam (FIB): Applications in micro-and nanoanalysis in geosciences and applied mineralogy[END_REF]. The produced foil with a thickness of ~ 50 nm was analyzed at the FEI Tecnai TM G 2 F20 X-Twin transmission electron microscope at the GeoForschungszentrum, Potsdam. The crystallite size of the doped anatase was measured before and after the experiment, using high-resolution TEM and convolution-based profile fitting of XRD data. Fig. 2 shows the pressure-volume data of the sample as refined from XRD data and results of the fitting to a second order EoS with the first derivative of the bulk modulus, K 0 ' fixed to 4. The bulk modulus of the material was determined during the first compression to K 0 = 211(7) GPa, upon the decompression the bulk modulus was decreased to K 0 = 199(3) GPa and it was increased upon the second compression to K 0 = 249 (9) GPa. The results show that the precompressed sample is stiffer compared to the uncompressed sample. The figure also shows the data of the previous experiment performed on the same material, described by Holbig et al. [START_REF] Holbig | Compression behavior of Zr-doped nanoanatase[END_REF]. It is worth noting at this point that the experiment Holbig et al. [START_REF] Holbig | Compression behavior of Zr-doped nanoanatase[END_REF] was performed on a sample which was compacted and precompressed between diamond anvils during the sample loading. The bulk modulus was measured as K 0 = 266(6) GPa, confirming the hypothesis that precompressed samples are stiffer than originally uncompressed samples.

Fig. 3 presents the values of the ratio of lattice parameters a/c as a function of the pressure. The slope of the curve is linear for the first compression and more or less also for the decompression. Upon the second compression however, the slope becomes steeper at pressure > 5 GPa, which is comparable to the results reported by Holbig et al.

[11] (line 3' in Fig. 2). The anomalous compression behavior for nanoscale Zr-doped anatase reported before is therefore reproduced in this study.

The XRD data of the sample at ambient conditions at the beginning (a) and at the end (b) of the experiment were used to estimate the crystallite size and to see, whether a change of the microstructure can be observed. We used the TOPAS-ACADEMIC software [START_REF] Yang | ZrO 2 -TiO 2 , Ceramic Humidity Sensors[END_REF] for convolution-based profile fitting [START_REF] Xu | Influence of high pressure and high temperature on the structure of ZrO 2 nanosolids[END_REF] and refined the microstructure.

The source emission profile and instrumental contribution to peak broadening were determined by means of the diffraction spectrum of a CeO standard. The effects of crystallite size and strain on the peak broadening were analyzed using the double-Voigt approach [START_REF] Balzar | Voigt-Function Modeling in Fourier-Analysis of Size-Broadened and Strain-Broadened X-Ray-Diffraction Peaks[END_REF] and the maximum (upper limit) strain values e 0 as well as the integralbreadth based volume-weighted mean column height L Vol_IB of coherently diffracting domains [START_REF] Xu | Influence of high pressure and high temperature on the structure of ZrO 2 nanosolids[END_REF] were obtained simultaneously. The estimate of crystallite size from L Vol_IB depends on the shape and the size distribution of the crystallites. For monodisperse IB . [START_REF] Popa | An analytical approximation for a size-broadened profile 1 3[END_REF]18] The strain of the material increased strongly during the experiment from e 0 = 0.13(3) % at the beginning to 0.26(4) % at the end. The crystallite size appears bigger at the end of the experiment but we attest no physical meaning to it. We suggest that the increasing strain slightly biases towards itself the relative contributions to the peak broadening due to a reduced data quality for b). Another confirmation of the additionally induced strain is the relationship between a and c lattice parameters (table 2). The unit cell at the end of the experiment is deformed with an elongation of the a parameter and shortening of the b parameter. At the same time the unit cell volume and pressure are practically the same. Fig. 4 shows high-resolution TEM images of the starting material as well as the quenched sample of the second experiment, performed on pure anatase Ti 0.90 Zr 0.10 O 2 . The crystallite sizes are 12(±3) nm for both samples and therefore remain more or less constant during the experiment. The crystallites of the quenched sample show spherical crystal shape and are defect free. There are several lines of evidence suggesting that the crystallites are surrounded by amorphous rims and that amorphization takes place gradually upon compression. Pressure induced amorphization was observed before by Swamy et al. [START_REF] Swamy | Size-dependent pressure-induced amorphization in nanoscale TiO 2[END_REF], who claimed that anatase with crystallite size of < 10 nm transforms upon compression to a high density amorphous phase, which transforms to a low density amorphous phase upon the quenching process. In contrast, coarser samples undergo transformations to crystalline high pressure polymorphs. Partial amorphization was suggested earlier for experimental studies (e.g. [START_REF] Pischedda | Ultrastability and enhanced stiffness of similar to 6 nm TiO 2 nanoanatase and eventual pressureinduced disorder on the nanometer scale[END_REF]), but could not be detected by the insitu XRD analysis because the broad amorphous features would be hidden in the background signal -a phenomenon that applies also for this study. Partial amorphization was theoretically predicted by Pischedda et al. [START_REF] Pischedda | Ultrastability and enhanced stiffness of similar to 6 nm TiO 2 nanoanatase and eventual pressureinduced disorder on the nanometer scale[END_REF], who performed molecular dynamics computations, using a simple Buckingham potential and computed compression of a single anatase nanoparticle in a box of 10 nm dimension in excess of the nanoparticle volume. At 25 GPa, the simulations suggest the appearance of disorder in the surfaceshell region (about 30-40 % of the atoms), surrounding a more rigid crystalline core, which also contains some defects. In our study, the TEM analysis of the material after compression shows in fact features that can be assigned as rims of amorphous material with a thickness of several nanometer (Fig. 4, right), confirming the suggested appearance of partial amorphization. However, the TEM image shows a part of the sample where several crystallites overlap and the features seen could be the consequence of that. To avoid overlap of crystallites, TEM foils with a thickness of 10-15 nm would be necessary.

A c c e p t e d m a n u s c r i p t 3 nanocrystallinity

 3 and proposed that Zr-doping and the tendency of clustering of Zr-atoms could affect the structural parameters and influence the elastic properties.

A c c e p t e d m a n u s c r i p t 4 3.

 4 Results and discussionThe lattice parameters of Zr-doped nanoscale anatase at zero pressure were refined to a = 3.8110(3), c = 9.6101[START_REF] Mao | Calibration of the Ruby Pressure Gauge to 800-Kbar under Quasi-Hydrostatic Conditions[END_REF] Šand V = 139.57(2) ų. Tab. 1 presents refined lattice parameters of anatase and LiF as well as the pressure, Fig.1shows representative results of full profile refinements at low and high pressures, indicating the high quality of the fit.

A c c e p t e d m a n u s c r i p t 5 spherical

 5 crystallites with diameter D, the following equation is applicable: D = 4/3 L Vol-

A c c e p t e d m a n u s c r i p t 6 TheA c c e p t e d m a n u s c r i p t 10 Tab. 2 .A c c e p t e d m a n u s c r i p t 11 Figure captions Fig. 1 .Fig. 2 .

 610211captions12 Figure captions

Fig. 3 .

 3 Fig. 3. Ratio of the lattice parameters a/c of nanocrystalline Zr 0.1 Ti 0.9 O 2 anatase. Symbols as in Fig. 2.

Fig. 4 .A c c e p t e d m a n u s c r i p t 11 Fig. 1 A c c e p t e d m a n u s c r i p t 12 Fig. 2 .A c c e p t e d m a n u s c r i p t 13 Fig. 3 .A c c e p t e d m a n u s c r i p t 14 Fig. 4 .

 4111122133144 Fig. 4. High-resolution TEM image of the starting material Zr 0.1 Ti 0.9 O 2 anatase (left) and the sample after the experiment (right). Both images indicate average crystallite sizes of 12nm. C marks a crystalline area, A marks the suggested amorphous rim.

Acknowledgments

We want to thank S. Saxena for the organization of the SMEC conference and N. Miyashima for TEM analysis of the starting material. This work was supported by the Elitenetzwerk Bayern of the state of Bavaria, Germany. GeoSoilEnviroCARS is supported by the National Science Foundation -Earth Sciences (EAR-0217473), Department of Energy -Geosciences (DE-FG02-94ER14466) and the State of Illinois. Use of the APS was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. W-31-109-ENG-38.

A c c e p t e d m a n u s c r i p t


Anie Azroyan

Kamel Laghmani

Gilles Crambert

David Mordasini

Alain Doucet

Aurélie Edwards
email: aurelie.edwards@upmc.fr

REGULATION OF PENDRIN BY pH: DEPENDENCE ON GLYCOSYLATION Running title: Mathematical Modeling of Pendrin Activity

Keywords: pendrin, anion exchanger, mathematical modeling, transport kinetics, glycosylation, pH B-IC, type-B intercalated cells, CCD, cortical collecting duct, DIDS, 4,4'diiosothiocyanatostilbène-2,2'-disulfonate

Mutations of the anion exchanger pendrin are responsible for Pendred syndrome, an autosomal recessive disease characterized by deafness and goiter. Pendrin is highly expressed in kidney collecting ducts, where it acts as a chloride/bicarbonate exchanger and thereby contributes to the regulation of acid-base homeostasis and blood pressure. This study aimed to characterize the intrinsic properties of pendrin. Mouse pendrin was transfected in HEK293 and OKP cells; its activity was determined by monitoring changes in intracellular pH induced by variations of trans-membrane anion gradients. Combining measurements of pendrin activity with mathematical modeling, we found that its affinities for Cl -, HCO 3 -and OH -vary with intracellular pH, resulting in increased activity at low intracellular pH. Pendrin maximal activity was also stimulated at low extracellular pH, suggesting the presence of intra-and extracellular proton regulatory sites. We identified 5 putative pendrin glycosylation sites, only two of which are used. Mutagenesis-induced disruption of pendrin glycosylation did not alter its cell surface expression, polarized targeting to the apical membrane and basal activity, but fully abrogated its sensitivity to extracellular pH. The hereto unknown regulation of pendrin by external pH may constitute a key mechanism in controlling ionic exchanges across the collecting duct and inner ear.

INTRODUCTION

Pendred syndrome is an autosomal recessive disease characterized by deafness and goiter [START_REF] Reardon | Pendred syndrome[END_REF]. It is associated with mutations of the PDS gene which encodes pendrin, an anion exchanger that is a member of SLC26 family (Slc26a4). Pendrin exchanges extracellular chloride against either intracellular bicarbonate or iodide or formate [START_REF] Kraiem | Sulfate transport is not Impaired in Pendred syndrome thyrocytes[END_REF][START_REF] Royaux | Pendrin, the protein encoded by the Pendred syndrome gene (PDS), is an apical porter of iodide in the thyroid and is regulated by thyroglobulin in FRTL-5 cells[END_REF][START_REF] Scott | Human pendrin expressed in Xenopus laevis oocytes mediates chloride/formate exchange[END_REF]. The Cl -/I -and Cl - /HCO 3 -exchange functions of pendrin account for its role in iodide organification in the thyroid and in pH homeostasis of endolymph respectively, which are altered in Pendred syndrome [START_REF] Kopp | Pendred syndrome and iodide transport in the thyroid[END_REF][START_REF] Maciaszczyk | Phenotypes of SLC26A4 gene mutations: Pendred syndrome and hypoacusis with enlarged vestibular aqueduct[END_REF]. Even though patients with Pendred syndrome display no clinical signs beyond the thyroid and inner ear, pendrin is expressed in many tissues including mammary glands [START_REF] Rillema | Prolactin regulation of the pendrin-iodide transporter in the mammary gland[END_REF], uterus [START_REF] Suzuki | Expression of PDS/Pds, the Pendred syndrome gene, in endometrium[END_REF], testis [START_REF] Bidart | Expression of Na+/I-symporter and Pendred syndrome genes in trophoblast cells[END_REF], placenta [START_REF] Bidart | Expression of Na+/I-symporter and Pendred syndrome genes in trophoblast cells[END_REF], and kidneys [10]. Kidneys even display a higher expression level of pendrin mRNAs than the thyroid gland and inner ear.

In the kidney, pendrin is expressed at the apical border of the type-B intercalated cells (B-IC) present in the cortical collecting duct (CCD). B-ICs play a major role in the regulation of acid-base balance by mediating bicarbonate secretion through an apical Cl -/HCO 3 -exchanger functioning in series with a basolateral plasma membrane H + -ATPase. Recent studies have shown that HCO [START_REF] Royaux | Pendrin, the protein encoded by the Pendred syndrome gene (PDS), is an apical porter of iodide in the thyroid and is regulated by thyroglobulin in FRTL-5 cells[END_REF] -secretion in CCDs is abolished in pendrin knockout mice, which indicates that apical Cl -/HCO 3 -exchange in B-ICs is fully mediated by pendrin [10,[START_REF] Wall | NaCl restriction upregulates renal Slc26a4 through subcellular redistribution: Role in Cl-conservation[END_REF]. Accordingly, both the expression and the activity of the apical anion exchanger are upregulated in CCD after induction of metabolic alkalosis by either administration of aldosterone or NaHCO 3 loading, and aldosterone-induced metabolic alkalosis is more severe in pendrin knockout mice than in controls [START_REF] Verlander | Deoxycorticosterone upregulates PDS (Slc26a4) in mouse kidney: Role of pendrin in mineralocorticoid-induced hypertension[END_REF] .

In addition, B-ICs are sites of chloride reabsorption through the apical Cl -/HCO 3 -exchanger in series with basolateral chloride channels ClCK. Chloride reabsorption in CCDs is fully abolished in pendrin knockout mice [START_REF] Wall | NaCl restriction upregulates renal Slc26a4 through subcellular redistribution: Role in Cl-conservation[END_REF], indicating that pendrin-mediated transcellular transport in B-ICs is the only pathway for chloride reabsorption in CCDs. Moreover, the expression of pendrin in the kidney of rats fed different amounts of chloride is inversely correlated with the urinary excretion of chloride, independently of the accompanying cation and acid-base status [START_REF] Quentin | The Cl-/HCO3-exchanger pendrin in the rat kidney is regulated in response to chronic alterations in chloride balance[END_REF]14]. This suggests a major role for pendrin in the regulation of chloride balance.

Finally, it was reported recently that coupling of pendrin with the Na + -driven Cl -/HCO 3 exchanger (NDCBE/Slc4a8) mediates electroneutral reabsorption of NaCl in the CCD [START_REF] Leviel | The Na+-dependent chloride-bicarbonate exchanger SLC4A8 mediates an electroneutral Na+ reabsorption process in the renal cortical collecting ducts of mice[END_REF]. The presence of this thiazide-sensitive pathway for NaCl reabsorption, which operates in parallel with the amiloride-sensitive epithelial sodium channel, likely accounts for the fact that isolated alteration of Cl -transport in the distal nephron can impact blood pressure [START_REF] Kahle | WNK4 regulates apical and basolateral Cl-flux in extrarenal epithelia[END_REF][START_REF] Schambelan | Mineralocorticoidresistant renal hyperkalemia without salt wasting (type II pseudohypoaldosteronism): Role of increased renal chloride reabsorption[END_REF][START_REF] Take | Increased chloride reabsorption as an inherited renal tubular defect in familial type II pseudohypoaldosteronism[END_REF][START_REF] Yamauchi | Disease-causing mutant WNK4 increases paracellular chloride permeability and phosphorylates claudins[END_REF] and that pendrin knockout mice are protected against mineralocorticoid/salt-induced hypertension [START_REF] Verlander | Deoxycorticosterone upregulates PDS (Slc26a4) in mouse kidney: Role of pendrin in mineralocorticoid-induced hypertension[END_REF]. The importance of pendrin in mediating Na + and Cl -reabsorption and HCO 3 -secretion in the CCD, and in regulating acid-base balance, extracellular volume and blood pressure, underlies the need to characterize its intrinsic properties, which have remained poorly documented until now. The purpose of this study was to functionally characterize pendrin using in vitro expression models. Our major findings are that pendrin activity is modulated by pH and that this regulation depends on pendrin glycosylation. 0.1% Tween 20 for 1 h and then incubated overnight with primary anti-pendrin antibody diluted 1:5000 in TBS 0.1% Tween 20. Blots were then washed 3 times with TBS 0.1% Tween 20, and incubated with horseradish peroxidase-conjugated goat anti rabbit IgG (Promega, Madison, WI, USA)) 1:10000 in TBS 0.1% Tween 20. Blots were washed as described above and assayed with ECL using SuperSignal Substrate (Pierce, Rockford, IL, USA) and captured on a light sensitive imaging film (Kodak).

The anti-pendrin antibody (gift from Dr D Eladari), a rabbit polyclonal antibody directed against a peptide corresponding to the C-terminal domain of mouse pendrin (amino acids 630 to 643), has been characterized previously [START_REF] Wagner | Regulation of the expression of the Cl-/anion exchanger pendrin in mouse kidney by acid-base status[END_REF][START_REF] Knauf | Identification of a chloride-formate exchanger expressed on the brush border membrane of renal proximal tubule cells[END_REF]. Immunofluorescence. OKP cells plated at confluent density on 12 mm transwell porous cell culture inserts (0.4 µm pore , Costar) for 7 days and HEK293 cells grown on glass coverslips were washed twice with an ice-cold PBS solution at pH 8 containing 1 mM MgCl 2 and 0.1 mM CaCl 2 , and were then placed at 4°C for 1h in PBS solution containing 1 mg/ml EZ-Link Sulfo-NHS-LC-LC-Biotin (Pierce). After 3 washes with PBS, cells were fixed with 4% paraformaldehyde (Electron Microscopy Sciences, Hatfield, PA) for 30 min at room temperature, then washed 3 times with PBS and permeabilized with 0.1% Triton X100 for 15 min. Cells were blocked for 30 min with 3% normal goat serum (Vector Laboratories) and incubated with anti-pendrin antibody diluted 1:400 in 3% normal goat serum for 1h. After 3 washes with PBS, cells were incubated for 1h in the dark with FITC-conjugated goat anti-rabbit IgG diluted 1:100 and Cy5-conjugated streptavidin (Sigma Aldrich) at 1:100. Filters were excised from the filter cup with a razor blade and mounted with Vectashield H1200 (Vector Laboratories) mounting media containing 4.6-diamidino 2-phenylindole dihydrochloride for nuclei staining. Slides were visualised with a Zeiss LSM 510 laser-scanning microscope using appropriate filters (Carl Zeiss, Germany). Intracellular pH measurement. Activity of pendrin in transfected cells was assessed based on the rate of variation of intracellular pH (pH i ) in response to the generation of transmembrane gradients of Cl -, HCO 3 -or OH -concentration. The activity of pendrin was calculated as the difference between the rate of pH variation in transfected cells and that in non-transfected cells in the same experimental series. Changes in transmembrane ion gradients were obtained by varying the composition of the extracellular medium, as indicated in the Results section. For pH i measurements, HEK293 cells grown to confluence on glass coverslips coated with 0.5 mg/ml poly D-lysine (Sigma) were incubated for 30 min at 37°C in the presence of 5 µM pH sensitive dye 2',7'-bis(2-carboxyl)-5(6)-carboxy-fluorescein (BCECF) (Invitrogen) in isotonic solutions. Changes in intracellular pH were monitored at excitation wavelengths of 500 and 450 nm, at 37°C, in a FluoroMax3 spectrofluorometer (Jobin Yvon, Horiba). Three-point calibration curves (pH 6.0, 7.0 and 8.0) were established using KCl/nigericine. Cl --containing solutions consisted of NaCl at concentrations varying from 0.5 mM to 120 mM, Na-gluconate, KCl, and K-gluconate. All solutions contained 0.2 mM KH 2 PO 4 , 0.8 mM K 2 HPO 4 , 1 mM Cagluconate, 1 mM Mg-gluconate and 10 mM HEPES. For Cl --free solutions, all Cl -containing salts were replaced with gluconate salts. For HCO 3 --containing solutions Na-gluconate was replaced isosmotically with NaHCO 3 . Bicarbonate containing solutions were prepared extemporarily to intracellular pH measurements. The actual concentration of bicarbonate was calculated as explained in Appendix A.

The intrinsic buffering power (β i; mM H + /pH unit) was measured in transfected and nontransfected HEK293 cells using the NH 4 + pulse method. To eliminate all pendrin activity the measurements were done in the presence of 0.5 mM DIDS. Cells were initially loaded with BCECF in Na + -and bicarbonate-free isotonic solutions. NaCl was iso-osmolarily replaced with NMDGCl. The ∆pHi of cell alkalinisation was measured after the addition of 20 mM NH [START_REF] Scott | Human pendrin expressed in Xenopus laevis oocytes mediates chloride/formate exchange[END_REF] Cl by iso-osmolar replacement of NMDGCl. The base equivalent transport flux was cal-culated by multiplying the buffering power (mM H + /pH unit) by the transport rate (pH unit/min) and expressed in mM/min.

When tested, pharmacological agents (Sigma Aldrich) were added simultaneously with BCECF. They were dissolved in DMSO (Sigma, 1% final concentration), and the same concentration of DMSO was added to controls. Measurement of intracellular chloride concentration. Pendrin-transfected HEK293 cells grown to confluence on glass coverslips were labelled for 24 hours with 5 mM SPQ (6methoxy-N-(3-sulfopropyl)-quinolinium, inner salt) (Molecular Probes) in sterile DMEM medium supplemented with 10% bovine serum. Afterwards, cells were washed extensively in isotonic buffer at pH 7.4, prior to 30 min incubation in the same buffer at 37°C. The isotonic buffers were either Cl --free solutions or Cl --containing solutions consisting of NaCl at concentrations varying between 4 mM and 120 mM. After incubation cells were washed again 5 times and SPQ fluorescence was measured in a FluoroMax3 spectrofluorometer at excitation and emission wavelengths of 365 nm and 443 nm respectively. Calibration curves were established using KCl/nigericine (5 µM)/tributyltine (10 µM). For calibration Cl --containing solutions consisted of KCl at concentrations varying from 4 mM to 120 mM, Na-gluconate, Mggluconate, Ca-gluconate, K-gluconate and Hepes. Statistics. Values are expressed as means ± S.E. The significance of differences between mean values was evaluated using paired or unpaired t test or analysis of variance as appropriate. p< 0.05 was considered statistically significant. A c c e p t e d M a n u s c r i p t Licenced copy. Copying is not permitted, except with prior permission and as allowed by law.

RESULTS

Expression of pendrin protein in HEK293 cells. We first determined the expression of pendrin protein and its location in HEK293 cells stably transfected with mouse pendrin cDNA. Figure 1 shows that all the cells derived from a single clone displayed pendrin-positive staining. Pendrin immunoreactivity was mainly present at the plasma membrane since it colocalized with biotin. In contrast, non-transfected or mock-transfected cells did not show any positive stain for pendrin (data not shown).

Measurements of pendrin activity. We next characterized the functional expression of pendrin by determining the rate of ion transport in either Cl -/OH -or Cl -/HCO 3 -exchange mode in pendrin cDNA-transfected cells. Previous studies demonstrated that pendrin functions in Cl - /OH -, Cl -/HCO 3 -, or Cl -/formate electroneutral exchange mode [START_REF] Soleimani | Pendrin: an apical Cl{-}/OH{-}/HCO3{-} exchanger in the kidney cortex[END_REF][START_REF] Shcheynikov | The Slc26a4 transporter functions as an electroneutral Cl-/I-/HCO3exchanger: role of Slc26a4 and Slc26a6 in I-and HCO3-secretion and in regulation of CFTR in the parotid duct[END_REF]. Cl -/OH -exchange. Cells were first incubated in a Cl --free medium for 30 min at 37°C and then monitored for changes in intracellular pH (pH i ) after addition of extracellular Cl -. Figure 2A shows that the addition of extracellular Cl -(120 mM) caused a more rapid cellular acidification in pendrin-transfected cells than in non-transfected cells. This phenomenon was reversed after the cells were switched back to a Cl --free medium (Figure 2B). The initial rate of cell acidification, corresponding to the forward rate of Cl -/OH -exchange, was ~0.3 and ~0.04 pH unit.min -1 in transfected and non-transfected cells respectively. The backward rate of Cl - /OH -exchange was ~0.2 in transfected cells and ~0.03 pH unit.min -1 in non-transfected cells.

Cl -/HCO 3 -exchange. In these series of experiments, cells were first incubated in a bicarbonate-free and Cl --containing medium for 30 min at 37°C, and then monitored for pH i changes after switching to a bicarbonate-containing and Cl --free medium. As shown in Figure 2C, the concomitant addition of bicarbonate (25 mM) and removal of chloride from the medium caused a transient acidification of both pendrin-transfected and non-transfected cells that is likely accounted for by CO 2 entry. Afterwards, a more rapid intracellular alkalinisation was observed in pendrin-transfected cells than in non-transfected cells. The initial rate of cell alkalinisation, corresponding to the rate of Cl -/HCO 3 -exchange, was ~0.8 and ~0.2 pH unit.min -1 in transfected and non-transfected cells respectively.

We also confirmed that pendrin is inhibited by 4,4'-diiosothiocyanatostilbène-2,2'-disulfonate (DIDS), as previously described [START_REF] Soleimani | Pendrin: an apical Cl{-}/OH{-}/HCO3{-} exchanger in the kidney cortex[END_REF]. Pendrin activity determined under forward Cl - /HCO 3 exchange mode was fully inhibited by 0.5 mM DIDS: (in mM.min -1 ± SE) Control, 20.1 ± 1.0; DIDS, 1.4 ± 1.4; n = 6, p < 0.001.

Effect of pH on pendrin activity. We examined whether pendrin is regulated by pH by measuring its activity while either the extracellular (pH e ) or the intracellular (pH i ) pH was varied. In the first series of experiments, the cells were incubated in a Cl --free medium at pH e = 7.4; their pH i rose to an equilibrium value of 7.85. At t = 0, the cells were suddenly exposed to a 120 mM Cl -medium of variable pH e . The bath switch resulted in Cl -influx and OH -efflux. As shown in Figure 3A, the initial flux of OH -out of the cell was found to increase with decreasing pH e .

To examine the effect of intracellular pH on the activity of the exchanger, the cells were incubated in a 120 mM Cl -medium at variable pH e (6.0, 7.4, and 8.0); their equilibrium pH i then reached varying values (6.2, 7.0, and 7.5). At t = 0, the cells were exposed to a Cl --free medium at a fixed pH e of 8.0, resulting in Cl -efflux and OH -influx into the cells. The initial rate of cell alkalinization was seen to increase with decreasing pH i , as displayed in Figure 3B.

A decrease in extracellular or intracellular pH enhances the gradient for OH -efflux or influx, respectively, and therefore might account for the observed increase in pendrin activity.

To evaluate whether the pH dependence reflects a true regulation of pendrin or a concentration gradient effect, we then sought to determine the kinetics parameters of pendrin.

Kinetic parameters of pendrin. To calculate the affinities of pendrin to Cl -, OH -and HCO 3 -, we first determined pendrin activity by measuring pH i variations in the presence of different anion concentrations, in several exchange modes. In all experiments, the activity of pendrin was calculated as the difference in the initial rate of pH i variation between pendrin-transfected and non-transfected cells. Next, the affinities were calculated based on a theoretical model of pendrin-mediated ion transport.

Activity of pendrin as a function of external chloride. Cells were pre-incubated in a Cl -free medium, then switched to a medium containing different concentrations of Cl -(0.5 to 100 mM), and the initial rate of acidification was measured. As expected, increasing extracellular Cl -concentration increased pendrin activity in a saturable fashion. Linearizing the data according to the Lineweaver-Burk equation yielded an apparent external Cl -affinity of 1.35 mM and a V max of 0.3 pH unit.min -1 (Figure 4A).

Activity of pendrin as a function of internal chloride. To determine the apparent intracellular affinity of pendrin for Cl -, we measured the initial rate of alkalinisation during backward Cl -/OH -exchange. Thus, after pre-incubation in Cl --free medium, the cells were switched to a medium containing various concentrations of Cl -and the change in pH i was monitored. When pH i equilibrium was achieved, the cells were switched back to a Cl --free medium and the initial rate of alkalinisation was determined. The internal concentration of Cl -at the onset of the alkalinisation phase was determined by SPQ fluorescence in separate experiments. Using this protocol we were able to vary the intracellular concentration of Cl -from 0.5 to 50 mM. This was accompanied by a saturable activation of pendrin, and an apparent internal Cl -affinity of 24 mM and a V max of 0.2 pH unit.min -1 were derived from the Lineweaver-Burk plot (Figure 4B).

Activity of pendrin as a function of external bicarbonate. Following pre-incubation in a bicarbonate-free and Cl --containing medium, the cells were switched to a Cl --free medium containing various concentrations of HCO 3

-and the initial rate of alkalinisation was measured. Bicarbonate was added at concentrations ranging from 1 to 25 mM, and the corresponding actual concentrations of HCO 3 -in the medium were calculated as described in Appendix A. A Lineweaver-Burk plot of the data gave an apparent external HCO 3 -affinity of 2.6 mM and a V max of 0.8 pH unit.min -1 (Figure 4C).

The curves representing the initial flux across pendrin as a function of external or internal anion concentrations (Figure 4A-C) were then used to determine the kinetic parameters of the exchanger. We examined different models (such as the bi bi cyclic reaction scheme, the sixstate ping-pong model, an eight-state exchanger scheme) and obtained the best fit to the data using the ping-pong mechanism depicted in Figure 5. According to this scheme, after Cl - binds to the empty carrier on one side, it is translocated to the other side; only after it is released can the other ion (HCO 3 -or OH -) bind to the carrier and be translocated back in the opposite direction. Note that this kinetic scheme is identical to that assumed for the Cl -/HCO 3 exchanger AE1 [START_REF] Weinstein | A mathematical model of the outer medullary collecting duct of the rat[END_REF]. To fully characterize dynamic transport across pendrin, 4 kinetic parameters per ionic species must be determined: the external and internal binding affinities, and the forward and backward translocation rates.

The flux equations are given in Appendix B. As discussed therein, the experimental curves in this study can only yield 6 independent parameters, out of a total of 10 (6 affinities and 4 independent translocation rates). We therefore assumed that the internal and external binding affinities of each ion are equal, and we fixed the forward (external) Cl -translocation rate (denoted ). The remaining 6 independent parameters (the affinities to Cl -, HCO A c c e p t e d M a n u s c r i p t

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OH -; the forward rates for HCO 3 -and OH -; and the backward rate for Cl -) were then fitted to the experimental data.

Analysis of the experimental results revealed that it was not possible to fit the data shown in Figures 4A and4B simultaneously without accounting for the modulating effect of internal pH (~ 8.0 in the Cl -influx experiments, vs. ~ 7.0 in the Cl -efflux experiments) on pendrin activity. Moreover, assuming that the kinetic parameters of pendrin are independent of pH i , the model predicts that the driving force in the experiment displayed in Figure 3B remains constant, that is, the flux should remain approximately the same as pH i varies between 6.2 and 7.5. Thus, these two sets of results strongly suggest that pH i variations intrinsically modify the kinetics of the transporter, independently of transmembrane concentration gradients. We accounted for this effect by assuming that the binding affinities of Cl -and OH -vary with internal pH.

Fitted parameter values are given in Table 1. As described in Appendix B, the fitted values of the affinities, and of the translocation rates relative to , depend very little on the value of . The affinity of pendrin for Cl -and OH -was respectively calculated as 3 mM and 1.4x10 -6 M at pH i = 8.0, and as 75 mM and 2.6x10 -7 M at pH i = 7.0. Predicted flux values based upon these parameters are in good agreement with measured values, as displayed in We then sought to interpret the effect of external pH depicted on Figure 3A. If pH e had no intrinsic effect on the kinetic parameters of pendrin, the mathematical model would predict a constant flux in these experiments. Indeed, the 'effective" concentration of Cl -(i.e., its concentration divided by its affinity) in the bath was much greater than that of OH -both in the bath and within the cell, so that the intracellular concentration of OH -was the rate-limiting factor that determines the magnitude of the flux. Given that the initial pH i was constant in these experiments, the flux at t = 0 should have remained constant in the absence of an intrinsic effect of pH e . The fact that the flux decreased with increasing pH e strongly suggests that lowering pH e stimulates pendrin activity.

Glycosylation of pendrin.

Immunodetection of mouse pendrin transiently expressed in HEK293 cells reveals two bands at ~130 kDa and ~90 kDa (Figure 6A). Treatment with endoglycosidase H, which hydrolyzes only the high mannose sugars, did not alter the 130 kDa band and slightly reduced to ~85 kDa the apparent molecular weight of the lower band, consistent with core deglycosylation of pendrin. Conversely, upon treatment with N glycosidase F, which removes all glycosides, the ~130 kDa band disappeared and the ~90 kDa band moved to the same lower molecular weight seen after endoglycosidase H treatment, which corresponds to the expected molecular weight of the non-glycosylated protein (Figure 6B). These results confirm that the higher molecular weight band is the complex glycoprotein and the lower band is the core glycosylated protein.

In silico analysis of mouse pendrin (NetNGlyc 1.0 Server) predicted five putative Nlinked glycosylation sites at asparagines 167, 172, 241, 475 and 567. Site-directed mutagenesis, in which asparagine was substituted for alanine, showed that only the first two sites, N167 and N172, account for the full glycolsylation of pendrin (Figure 6B).

We next evaluated the role of glycosylation on the membrane targeting, the polarization, and the activity of pendrin. These experiments were performed in OKP cells stably transfected with either wild type or N167A/N172A double mutant pendrin, because OKP cells exhibit a much higher transfection rate (up to 80%) compared to HEK293 cells, and they are polarized when grown on filters. Figure 7A-C shows that in polarized OKP cells (as in HEK293 cells; see Figure 1), wild type pendrin colocalized with biotin at the plasma membrane. Moreover, pendrin was preferentially expressed at the apical cell border (Figure 7D), as in native collect-ing duct B-ICs. A similar pattern of apical membrane expression was observed with the N167A/N172A double mutant pendrin (Figure 7E-H).

Membrane expression of pendrin with disrupted N-linked glycosylation sites in stably transfected, non-polarized OKP cells was confirmed by cell surface biotinylation followed by avidin bead precipitation and immunoblotting. Results show that pendrin was expressed at a lesser level in cells expressing the N167A/N172A double mutant pendrin than in cells expressing the wild type pendrin, but the fraction of pendrin expressed at the cell surface was similar in the two cell lines (Figure 8A). Furthermore, the functional pendrin activity in these two OKP cell lines, as determined under the forward Cl -/OH -exchange mode at pH e 7.4, was proportional to their expression level of pendrin at the cell surface (Figure 8B). However, in contrast to the wild type pendrin, the activity of which increases at low pH e in OKP cells as in HEK293 cells, the activity of the N167A/N172A double mutant pendrin did not increase at pH e 6.0 (Figure 8B).

Altogether these results indicate that glycosylation is not required for the expression of pendrin at the apical cell surface and its activity, but that it is a determinant of its sensitivity to external pH.

DISCUSSION

Pendrin has been shown to play a key role in maintaining the homeostasis of the inner ear [25] and in regulating the renal chloride balance [START_REF] Quentin | The Cl-/HCO3-exchanger pendrin in the rat kidney is regulated in response to chronic alterations in chloride balance[END_REF]14]; hence the importance of fully characterizing its structure and function. Pendrin expression in Xenopus laevis oocytes or in HEK293 cells previously demonstrated that it can function in several distinct modes including Cl -/I -, Cl -/OH -, Cl -/HCO 3 -and Cl -/formate exchange [START_REF] Soleimani | Pendrin: an apical Cl{-}/OH{-}/HCO3{-} exchanger in the kidney cortex[END_REF][START_REF] Scott | The Pendred syndrome gene encodes a chloride-iodide transport protein[END_REF], and that it is sensitive to DIDS [START_REF] Soleimani | Pendrin: an apical Cl{-}/OH{-}/HCO3{-} exchanger in the kidney cortex[END_REF]. In this study, we sought to characterize the glycosylation properties of pendrin, its kinetic behaviour, and its regulation by pH. Stable expression of mouse full-length pendrin in HEK293 cells enabled us to examine its function as a Cl -/OH -and Cl -/HCO 3 -reversible exchanger.

We found that the activity of pendrin was significantly higher in the Cl -/HCO 3 -exchange mode, that is, its predominant transport mode in the kidney collecting duct [27]. In rabbit CCD, Schuster [START_REF] Schuster | Cyclic adenosine monophosphate-stimulated anion transport in rabbit cortical collecting duct. Kinetics, stoichiometry, and conductive pathways[END_REF] estimated the K m for luminal chloride as 4-11 mM based upon his flux measurements, and as 1.7 mM based upon the fluxes reported in another study [START_REF] Garcia-Austt | Deoxycorticosterone-stimulated bicarbonate secretion in rabbit cortical collecting ducts: effects of luminal chloride removal and in vivo acid loading[END_REF]. However, it is important to note that the K m values measured in these previous studies are apparent transepithelial kinetic parameters and cannot be considered as true affinity constants in the enzymatic sense; the measured fluxes included a contribution by other transporters, such as basolateral anion exchangers. In contrast, our values were obtained in heterologous expression systems and reflected only the activity of pendrin. Moreover, they were corrected to account for variations in gradients and driving forces as external and/or internal concentrations were themselves varied. The apparent Cl -affinity values that we measured (1.35 mM at pH i = 8.0, 24 mM at pH i = 7.0) are significantly lower than the true affinity values that we calculated (3 and 75 mM, respectively). From a physiological standpoint, the relatively high affinity of pendrin for external Cl -at high pH values could play an important role in the kidney collecting duct: it would allow the exchanger to function at very low Cl -concentrations and secrete bicarbonate in states of alkalosis.

The pendrin affinity values obtained in this study may also be compared to those that have been reported for the Cl -/HCO 3 -exchanger AE1. Based upon previously published experimental data [30, 31], Weinstein [START_REF] Weinstein | A mathematical model of the outer medullary collecting duct of the rat[END_REF] calculated a K m of 50 mM for Cl -and 198 mM for HCO 3 -, with the assumption that internal and external affinities were equal. In a later study, Knauf et al. [START_REF] Knauf | Substrate-dependent reversal of anion transport site orientation in the human red blood cell anion-exchange protein, AE1[END_REF] estimated the true K m of AE1 as 20 mM for external Cl -(vs. 48 mM for internal Cl -), and as 2 mM for external HCO 3 -(vs. 340 mM for internal HCO 3 -

). These AE1 affinity values are comparable to those that we determined for pendrin at physiological pH values (i.e., pH i ~ 7.0).

Importantly, we characterized the effect of intracellular (pH i ) and extracellular (pH e ) pH on the kinetics of the transporter. We measured pendrin activity at pH values varying from 6 to 8; note that during ischemic episodes, intracellular pH levels may drop as low as 6.2 [START_REF] Garlick | Studies of acidosis in the ischaemic heart by phosphorus nuclear magnetic resonance[END_REF]. Pendrin as a Cl -/HCO 3 -exchanger is known to contribute to the regulation of intracellular and extracellular pH [27]. Conversely, we established for the first time that pendrin is regulated by pH. More specifically, we found that pendrin activity in vitro is significantly higher at acid pH e . Mathematical analysis of the fluxes showed that the effects of pH e can be accounted for assuming that a low pH e accelerates ion translocation, possibly via allosteric modifications. The effects of pH i on pendrin kinetics could be explained by a pH i -induced modification of binding affinities. The affinity of pendrin for Cl -was predicted to increase by a factor of 25 as pH i decreased from 8.0 to 7.0, whereas that for OH -was reduced by a factor of 5.

The regulation of AE isoforms by pH was previously established by several investigators [START_REF] Sterling | Transport activity of AE3 chloride/bicarbonate anion-exchanger proteins and their regulation by intracellular pH[END_REF][35][START_REF] Zhang | The cytoplasmic and transmembrane domains of AE2 both contribute to regulation of anion exchange by pH[END_REF]. In particular, the study of Sterling and Casey [START_REF] Sterling | Transport activity of AE3 chloride/bicarbonate anion-exchanger proteins and their regulation by intracellular pH[END_REF] demonstrated that AE1 and AE3 isoforms are essentially insensitive to pH, whereas AE2 appears to be slightly inhibited by acid pH and more significantly activated by high pH. Although the latter findings would sug-gest that pH exerts opposite effects on AE2 and pendrin, it should be noted that in contrast to our present measurements of pendrin activity, pH i and pH e were varied simultaneously in the study of Sterling and Casey; thus, we can not rule out the possibility that pH i and pH e exert inverse regulatory effects on AE2. Interpreting flux measurements for an acid-base transporter is complicated by the combined effect of ionic concentrations on the driving force and potential pH regulation sites. Our mathematical model enabled us to show that pH-mediated changes in pendrin activity were not due to variations in transmembrane gradients but to an intrinsic pH effect. In the kidney, the stimulating effect of low extracellular pH on pendrin activity suggests that the exchanger is constitutively activated, since urine is known to be acid. This may also be the case in the endolymphatic sac of the inner ear, where pendrin has been shown to contribute to pH buffering by secreting bicarbonate [START_REF] Wangemann | Loss of cochlear HCO3-secretion causes deafness via endolymphatic acidification and inhibition of Ca2+ reabsorption in a Pendred syndrome mouse model[END_REF]. The endolymph is known to be acidic (pH ~ 6.6-7.1) [38-40], and endolymphatic pH homeostasis is necessary for the prevention of hearing loss. Thus, the constitutive stimulation of pendrin in the endolymphatic sac may represent an important regulation pathway in the inner ear.

Our results indicate that pendrin is glycosylated exclusively at asparagines 167 and 172, which are located in the second putative extracellular loop of pendrin. N-glycosylation of membrane proteins plays a role in their correct folding and their targeting to the membrane [START_REF] Asano | The role of N-glycosylation in the targeting and stability of GLUT1 glucose transporter[END_REF][START_REF] Fishburn | Differential glycosylation and intracellular trafficking for the long and short isoforms of the D dopamine receptor[END_REF]. Some studies also suggest that glycosylation may have a role in maintaining the transporter in an active form within the membrane [START_REF] Hoover | N-Glycosylation at two sites critically alters thiazide binding and activity of the rat thiazide-sensitive Na+:Cl-cotransporter[END_REF][START_REF] Paredes | Activity of the renal Na+-K+-2Cl-cotransporter is reduced by mutagenesis of N-glycosylation sites: role for protein surface charge in Cl-transport[END_REF]. Hence, the role of Nglycosylation sites varies among different proteins. In contrast to the rat Na + -Cl -thiazidesensitive co-transporter (Slc12a3) which displays diminished surface expression and activity when its N-glycosylation sites are disrupted [START_REF] Hoover | N-Glycosylation at two sites critically alters thiazide binding and activity of the rat thiazide-sensitive Na+:Cl-cotransporter[END_REF], N-glycosylation of pendrin does not appear to be a pre-requisite for its targeting to the cell surface and polarized expression at the apical cell border. Although N-glycosylation is not required for the basal transport activity of pendrin, mutation of the two N-glycosylated asparagines (Asn) to alanines (Ala) abrogates the external pH dependence of pendrin activity. Several hypotheses can be put forward to account for this effect: 1) the sugar residues are the proton sensor; however, to our knowledge, this has never been reported before; 2) the loss of the sugar residues modifies the conformation of the protein and masks the proton sensor; 3) the replacement of Asn by Ala modifies the conformation of the protein and masks the proton sensor, independently of the loss of the sugar residues; 4) mutated Asn are the proton sensor responsible for the modulation of pendrin activity. Further experiments are needed to address these hypotheses.

In summary, we characterized both experimentally and theoretically the kinetic behaviour of pendrin. We showed for the first time that pendrin activity is modulated by both internal and external pH, and that the dependence on external pH is lost by mutagenesis-induced disruption of N-glycosylation sites. The sensitivity of pendrin to pH may serve as a key mechanism in controlling ionic exchanges across the plasma membrane of type-B intercalated cells in the kidney collecting duct.

Appendix A. Bicarbonate Concentration

Bicarbonate and carbonic acid form an acid/base pair. In water, carbonic acid and carbon dioxide are inter-converted:

O H CO k k CO H H HCO 2 2 d h 3 2 3 + + ⎯ ⎯ → ⎯ ⎯ ⎯ ⎯ ← ⎯→ ⎯ ⎯⎯ ← + -
where k d and k h are the H 2 CO 3 dehydration and hydration rates, respectively taken as 18 and 0.037 s -1 [START_REF] Pocker | Stopped-flow studies of carbon dioxide hydration and bicarbonate dehydration in water and water-d2. Acid-base and metal ion catalysis[END_REF]. We assume that the dissociation of H 2 CO 3 is rapid and at equilibrium. Thus, the acid-base concentration ratio is given by:

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + = - ] CO H [ ] HCO [ log pKa pH 3 2 3 (1) That is, ( 2
)
pH pKa 3 3 2 10 x ] HCO [ ] CO H [ - - =
The temporal concentration variations can be written as:

] CO [ k ] HCO [ k dt ] CO H [ d dt ] HCO [ d 2 h 3 d 3 2 3 + - = + - - (3)
] CO [ k ] HCO [ k dt ] CO [ d 2 h 3 d 2 - + = - (4)
Adding Eqs. (3-4) yields:

( 0 ] CO [ ] CO H [ ] HCO [ d ) t d 2 3 2 3 = + + - (5) tot 2 3 2 3 C ] CO [ ] CO H [ ] HCO [ = + + - (6)
where the constant C tot is the total concentration of all bicarbonate species (i.e., HCO 3 -+ H 2 CO 3 + CO 2 ). Combining Eqs. ( 2) and ( 6), we obtain:

) 10 1 ]( HCO [ C ] CO [ pH pKa 3 tot 2 - - + - = (7)
Substituting Eqs. ( 2) and ( 7) into Eq. ( 3) and rearranging yields an equation for the time derivative of [HCO 3 -] only: Integration of Eq. ( 8) yields the concentration of bicarbonate as a function of time:

tot pH pKa h 3 pH pKa pH pKa h pH pKa d 3 C 10 1 k ] HCO [ ) 10 1 ( ) 10 1 ( k ) 10 ( k dt ] HCO [ d ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + + + - = - - - - - - (8
( )

) t k exp( ) k 1 ( k C ] HCO [ 1 2 2 tot 3 - - + = - (10)
In our experiments, the total concentration of bicarbonate species is equal to the initial concentration of HCO 3 -(denoted ). Equation (10) can therefore be expressed as:

o 3 ] HCO [ - ) t k exp( ) k 1 ( k ] HCO [ ] HCO [ 1 2 2 o 3 t 3 - - + = - - (11)
where the subscript "t" denotes any time t, and "o" the starting point of the experiment. As demonstrated by Eq. ( 11), the equilibrium ("eq") concentration of HCO

= + + = = - - - - (12)
That is, HCO 3 -concentration at equilibrium is 6.73% lower than that at the starting point. Given that exp(-3) = 0.05, we can also estimate the time needed to reach 95% of the equilibrium concentration (t 95 ) as:

- - = β = β (14b) i OH i i e OH e e K ] OH [ , K ] OH [ - - = α = α (14c)

General Equations

Following the approach of Weinstein [START_REF] Weinstein | A mathematical model of rat ascending Henle limb. I. Cotransporter function[END_REF], we assume that anion binding occurs much faster than translocation, so that the concentration of bound carrier on each side is calculated based on the equilibrium binding constants. Thus, if x e and x i respectively denote the concentration of unloaded carrier on the external and internal sides, the concentration of carrier bound to Cl -on the external and internal sides is calculated as and , respectively.

Similarly, the concentration of carrier bound to HCO 3 -and OH -is given by and on the external side, and by and on the internal side. If x total represents the density of total carrier, conservation of total carrier can then be written as: Substituting Eq. ( 18) into ( 16) yields: The net fluxes of Cl -, HCO 3 -and OH -into the cell can then be calculated as:

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ σ η γ - η γ = γ - γ = - = e i i Cl
⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ σ η α - η α = α - α = - = e i i

Cl -/OH -exchange: Cl -influx

In the first set of Cl -/OH -exchange experiments, the dpH i /dt variations are proportional to the efflux of OH -. Before addition of Cl -to the bath at t = 0, the intracellular concentration of Cl -is negligible. Thus, we assume that immediately after t = 0. In addition, there is no bicarbonate (i.e., ). Under these conditions, Eq. (20c) yields the OH -efflux as:

0 ĩ γ 0 e i = β = β ) 1 ( P )
α + α + α + α + α + + α γ γ α = (21)
After rearrangement, the flux can be rewritten as:

α + + α + α + α + + γ γ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ α + + = (22)
In other words,

K ] Cl [ ] Cl [ J J + = - - , (23a)
where the maximal flux and apparent affinity are given by:

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ α + + = ) / 1 1 ( P P P P x J i e Cl i OH e Cl i OH total max , efflux OH (23b) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ α + + α + α + α + = ) / 1 1 ( P P ) / 1 1 ( P ) 1 ( P K K i e Cl i OH

Cl -/OH -exchange: Cl -efflux

In the second set of experiments, the the dpH i /dt variations are proportional to the influx of OH -. By symmetry with the preceding set of experiments, we have:

app , i Cl e e max , lux inf OH lux inf OH K ] Cl [ ] Cl [ J J + = - - , (24a)
where the maximal flux and apparent affinity are given by:

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ α + + = ) /
⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ α + + α + α + α + = ) / 1 1 ( P P ) / 1 1 ( P ) 1 ( P K K e i Cl e OH e i i OH i e OH i Cl app , i Cl (24c)
Cl -/HCO 3 -exchange In the Cl -/HCO 3 -exchange experiments, the dpH i /dt variations are proportional to the net flux of HCO 3 -into the cell; it can be shown that the net flux of OH -is negligible in comparison. Before addition of HCO 3 -to the bath at t = 0, the intracellular concentration of HCO 3 is negligible. Under these conditions, immediately after t = 0, and there is no HCO 3 efflux. The flux of HCO 3 -into the cell is given by: 0

γ + γ + γ + γ + γ + + γ β γ β = (25)
Rearranging Eq. 25 yields:

)] / 1
γ + + γ + γ + γ + + β β ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ γ + + = (26)
Thus, the HCO 3 -influx can be expressed as: where the maximal flux and apparent affinity are given by:

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ γ + + = )] / 1

Parameter Fit

For the 3 species considered here, there is a total of 4 x 3 = 12 parameters (notwithstanding the total carrier density x total , which is not an intrinsic property of pendrin). However, these parameters are not all independent; since there is no net flux across the exchanger when external and internal concentrations are equal, we have: Thus, the number of independent parameters (in addition to x total ) is 10. As shown in Eqs. [START_REF] Shcheynikov | The Slc26a4 transporter functions as an electroneutral Cl-/I-/HCO3exchanger: role of Slc26a4 and Slc26a6 in I-and HCO3-secretion and in regulation of CFTR in the parotid duct[END_REF][START_REF] Weinstein | A mathematical model of the outer medullary collecting duct of the rat[END_REF]27), the 3 maximum fluxes and the apparent external affinities for HCO 3 -and Cl -are constant in each set of experiments, that is, they do not depend on variable concentrations. In contrast, the apparent internal affinity for Cl -(Eq. 24c) is a function of the intracellular pH (i.e.,

) which is variable. This means that our experiments can yield a total of 6 parameters, and that the others have to be assumed. We therefore assumed that the internal and external binding affinities of a given ion are equal, as is usually done [START_REF] Weinstein | A mathematical model of rat ascending Henle limb. I. Cotransporter function[END_REF], and we fixed the forward Cl - translocation rate ( ). The remaining 6 parameters were fitted to the data shown in Figures 4A-C using the non-linear data fitting optimization procedure lsqnonlin on Matlab®.

i α e Cl

P

The forward Cl -translocation rate ( ) was varied between 10 +2 s -1 (i.e., the turnover rate for the Na + -K + -ATPase) and 10 +6 s -1 (i.e., that of an ion channel) [START_REF] Weinstein | A mathematical model of rat ascending Henle limb. I. Cotransporter function[END_REF] . For each value of , the remaining six parameters were fitted to the experimental data. The error function was the same in all cases, and the affinity values and the ratios of the translocation rates to were found to be almost insensitive to the value of . The value of was then fixed at 10 +4 s -1 , a mid-range value. The fitted parameter values corresponding to = 10 +4 s -1 are shown in Table 1. Changes in pH i in pendrin-transfected (black traces) or non-transfected (grey traces) HEK293 cells were induced by modifying the composition of the extracellular medium, as shown on top of each diagram. The initial rate of pH i variation was determined over the first 20 sec period. The insets illustrate the transport mode of pendrin in each condition. In the absence of bicarbonate, pendrin was studied either under forward (A) or backward (B) Cl -/OH -exchange mode. In the presence of bicarbonate, it was measured under forward Cl -/HCO 3 -exchange mode (C). Fig. 3. pH dependence of pendrin activity. A. After pre-incubation in a Cl --free medium at pH 7.4, cells were exposed to a medium containing 120 mM Cl -at different pH values, and the initial rate of intracellular acidification was monitored. B. Cells were first incubated in a medium containing 120 mM Cl -at pH 6.0, 7.4 or 8.0. After equilibration of intracellular pH, at 6.2, 7.0 and 7.5 respectively, cells were exposed to a Cl --free medium at pH 8.0, and the initial rate of intracellular alkalinisation was measured. The parameters were fitted to the data shown in Figure 4, and correspond to an external pH of 7.4. The Cl -forward rate ( ) was fixed at 10,000 s -1 ; the ratios of the other rates to were found to be independent of its value. Note that the HCO 3 -and OH -backward rates are not independent parameters; they can be obtained by using Eq. ( 28).

Biochemical

  Journal Immediate Publication. Published on 12 Nov 2010 as manuscript BJ20101411 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20101411

Biochemical

  Journal Immediate Publication. Published on 12 Nov 2010 as manuscript BJ20101411 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20101411A c c e p t e d M a n u s c r i p t Licenced copy. Copying is not permitted, except with prior permission and as allowed by law.

13 Biochemical

 13 Journal Immediate Publication. Published on 12 Nov 2010 as manuscript BJ20101411 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20101411A c c e p t e d M a n u s c r i p t Licenced copy. Copying is not permitted, except with prior permission and as allowed by law.

  Publication. Published on 12 Nov 2010 as manuscript BJ20101411 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20101411 A c c e p t e d M a n u s c r i p t Appendix B. Kinetic Parameter Evaluation As depicted on Figure 5, the transport of a given species (e.g., Cl -, HCO 3 -, or OH -) across pendrin is characterized by 4 parameters: the external and internal binding constants () and the forward and backward translocation rates ( ), where the superscripts "e" and "i" respectively denote the extracellular and intracellular compartments. The nondimensional external and internal concentrations of chloride (γ), bicarbonate (β), and OH -(α) are defined as:

15 Biochemical

 15 Journal Immediate Publication. Published on 12 Nov 2010 as manuscript BJ20101411 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20101411 A c c e p t e d M a n u s c r i p t

  that Eq. (23) represents a Michaelis-Menten relationship, in accordance with the kinetic curve shown in Figure4A.

  Publication. Published on 12 Nov 2010 as manuscript BJ20101411 THIS IS NOT THE VERSION OF RECORD -see doi:10.1042/BJ20101411A c c e p t e d M a n u s c r i p t Licenced copy. Copying is not permitted, except with prior permission and as allowed by law.

FIGURE LEGENDS Fig. 1 .Fig. 2 .

 LEGENDS12 FIGURE LEGENDS

Fig. 4 . 3 -.

 43 Fig. 4. Pendrin activity as a function of anion concentration. Pendrin activity was measured (black squares) as described in Figure 3 in the presence of different concentrations of Cl -, OH -and HCO 3 -. Also displayed are calculated values (white squares), computed using the mathematical model of pendrin-mediated ion transport. Insets show the Lineweaver-Burk plots of the measured data.

Fig. 5 .

 5 Fig.5. Kinetic scheme of pendrin. Pendrin-mediated ion transport across the cell membrane is represented according to a ping-pong mechanism. Pd° and Pd* refer to the free and ionbound forms of pendrin, and P Cl and P HCO3 are the translocation rates of chloride and bicarbonate respectively (see Appendix B for details).

Fig. 6 .

 6 Fig. 6. Glycosylation of pendrin. A. Electrophoretical profile of pendrin in HEK293 cells transiently transfected with pendrin, in the absence of treatment or after treatment with endoglycosidase H, N glycosidase F, or sham treatment. Note that non-transfected cells display a non specific band at ~ 130 kDa. B. Electrophoretical profile of HEK293 cells transiently transfected with wild type pendrin (WT), or mutated pendrin with disruption of either only N167 or both N167 and N172 glycosylation sites.

Fig. 7 .

 7 Fig. 7. Immunolocalization of pendrin in stably transfected OKP cells. Confluent OKP cells stably transfected with either wild type (A-D) or N167A/N172A double mutant pendrin (E-H) were biotinylated and then stained for surface biotin (A & E, streptavidin-Cy5) and pendrin (B & F, anti-pendrin antibody followed by FITC-conjugated goat anti-rabbit IgG).

Fig. 8 .

 8 Fig. 8. Membrane expression and activity of pendrin with disrupted N-linked glycosylation sites. A. Pendrin immunoblot of biotinylated and whole cell proteins in OKP cells stably transfected with either wild type or N167A/N172A double mutant pendrin. The upper panel shows the blot and the lower panel shows the densitometry measurements of all the bands in each lane. B. Pendrin activity, measured under forward Cl -/OH -exchange mode at different external pH values (6.0, 7.4, and 8.0) in OKP cells stably transfected with either wild type or N167A/N172A double mutant pendrin . Values are means ± SE from 6-9 samples in 2-3 experiments.

Figure 1 .

 1 Figure 1. Immunolocalization of pendrin in stably transfected HEK293 cells. Confluent HEK293 cells transfected with pendrin were biotinylated and then stained for surface biotin (A, streptavidin-Cy5), nucleus (B, 4.6-diamidino 2-phenylindole dihydrochloride), and pendrin (C, anti-pendrin antibody followed by FITC-conjugated goat anti-rabbit IgG). The stained slides were visualized by confocal microscopy. D shows the merge of the three labellings.

Figure 2 .

 2 Figure 2. Representative traces showing pendrin-mediated changes in intracellular pH.Changes in pHi in pendrin-transfected (black traces) or non-transfected (grey traces) HEK cells were induced by modifying the composition of the extracellular medium, as shown on top of each diagram. The initial rate of pHi variation was determined over the first 20 sec period. The insets illustrate the transport mode of pendrin in each condition. In the absence of bicarbonate, pendrin was studied either under forward (A) or backward (B) Cl-/OH-exchange mode. In the presence of bicarbonate, it was measured under forward Cl-/HCO3-exchange mode (C).

Figure 3 .

 3 Figure 3. pH dependence of pendrin activity.A. After pre-incubation in a Cl --free medium at pH 7.4, cells were exposed to a medium containing 120 mM Cl-at different pH values, and the initial rate of intracellular acidification was monitored. B. Cells were first incubated in a medium containing 120 mM Cl-at pH 6.0, 7.4 or 8.0. After equilibration of intracellular pH, at 6.2, 7.0 and 7.5 respectively, cells were exposed to a Cl --free medium at pH 8.0, and the initial rate of intracellular alkalinisation was measured.

Figure 4 .Figure 5 .

 45 Figure 4. Pendrin activity as a function of anion concentration. Pendrin activity was measured (black squares) as described in Figure 3 in the presence of different concentrations of Cl-, OH-and HCO3-. Also displayed are calculated values (white squares), computed using the mathematical model of pendrin-mediated ion transport. Insets show the Lineweaver-Burk plots of the measured data. A c c e p t e d

Figure 6 .

 6 Figure 6. Glycosylation of pendrin. A. Electrophoretical profile of pendrin in HEK293 cells transiently transfected with pendrin, in the absence of treatment or after treatment with endoglycosidase H, N glycosidase F, or sham treatment. Note that nontransfected cells display a non specific band at ~ 130 kDa. B. Electrophoretical profile of HEK293 cells transiently transfected with wild type pendrin (WT), or mutated pendrin with disruption of either only N167 or both N167 and N172 glycosylation sites.

Figure 7 .

 7 Figure 7. Immunolocalization of pendrin in stably transfected OKP cells. Confluent OKP cells stably transfected with either wild type (A-D) or N167A/N172A double mutant pendrin (E-H) were biotinylated and then stained for surface biotin (A & E, streptavidin-Cy5) and pendrin (B & F, anti-pendrin antibody followed by FITC-conjugated goat anti-rabbit IgG). The stained slides were visualized by confocal microscopy. C & G show the merges of the two labellings. D & H. show x-z reconstructions of confocal microscopy merge image stacks.

Figure 8 .

 8 Figure 8. Membrane expression and activity of pendrin with disrupted N-linked glycosylation sites. A. Pendrin immunoblot of biotinylated and whole cell proteins in OKP cells stably transfected with either wild type or N167A/N172A double mutant pendrin. The upper panel shows the blot and the lower panel shows the densitometry measurements of all the bands in each lane. B. Pendrin activity, measured under forward Cl-/OH-exchange mode at different external pH values (6.0, 7.4, and 8.0) in OKP cells stably transfected with either wild type or N167A/N172A double mutant pendrin . Values are means ± SE from 6-9 samples in 2-3 experiments.

A c c e p t e d M a n u s c r i p t

Table 1 Pendrin kinetic parameters

 1 Ratio of Cl -backward rate to Cl -forward rate,

	e Cl Cl P i P	1.239

Licenced copy. Copying is not permitted, except with prior permission and as allowed by law.© 2010 The Authors Journal compilation © 2010 Portland Press Limited

© 2010 The Authors Journal compilation © 2010 Portland Press Limited

ACKNOWLEDGEMENTS

The authors are grateful to Kent A. Riemondy, University of Colorado, for providing the pendrin transfection plasmid.