Farid Errassifi

Anas Menbaoui

Hélène Autefage

Lhaj Benaziz

Saadia Ouizat

Véronique Santran

Stéphanie Sarda

Albert Lebugle

Christèle Combes

Allal Barroug

H Sfihi

C Rey

Adsorption onto nanocrystalline

come

INTRODUCTION

Adsorption of proteins and drugs on apatites are considered to play a determining role in mineralized tissues and substitutive biomaterials based on calcium phosphate apatites [START_REF] Matsumoto | Hydroxyapatite particles as a controlled release carrier of protein[END_REF][START_REF] Wilson | Mediation of biomaterial-cell interactions by adsorbed proteins: a review[END_REF][START_REF] Davies | In vitro modeling of the bone/implant interface[END_REF] . Several specific bone proteins such as osteocalcin, osteopontin, as well as generic proteins and biomolecules like albumin, phospholipids and others have been shown to adsorb on and interact strongly with apatite [START_REF] Boskey | Persistence of complexed acidic phospholipids in rapidly mineralizing tissues is due to affinity for mineral and resistance to hydrolitic attack: in vitro data[END_REF][START_REF] Hauschka | Osteocalcin-hydroxyapatite interactions in the extracellular organic matric of bone[END_REF][START_REF] Romberg | Inhibition of apatite crystal growth by bonespecific and other calcium-binding proteins[END_REF][START_REF] Goldberg | Binding of bone sialoprotein osteopontin and synthetic polypeptides to hydroxyapatite[END_REF][START_REF] Robinson | Crystal growth in dental enamel: the role of amelogenins and albumin[END_REF][START_REF] Jung | The binding of pyrophosphate and two diphosphonates by hydroxyapatite crystals[END_REF] . These phenomena are considered to control apatite crystals nucleation, growth and dissolution in vivo [START_REF] Hauschka | Osteocalcin-hydroxyapatite interactions in the extracellular organic matric of bone[END_REF][START_REF] Romberg | Inhibition of apatite crystal growth by bonespecific and other calcium-binding proteins[END_REF][START_REF] Goldberg | Binding of bone sialoprotein osteopontin and synthetic polypeptides to hydroxyapatite[END_REF][START_REF] Robinson | Crystal growth in dental enamel: the role of amelogenins and albumin[END_REF] . Many macromolecules have been classified as initiator or inhibitor of crystal growth although for a given substance the role is not so clear and could depend, for example, on the local concentration or on the state of solute or solid fractions of this given substance [START_REF] Combes | Adsorption of proteins and calcium phosphate materials bioactivity[END_REF][START_REF] Addadi | Stereochemical aspects of crystal regulation in calcium phosphate-associated mineralized tissues[END_REF] . In the biomaterial field it has been suggested that molecules interacting with calcium phosphates play a crucial role in the recruitment of cells and their expression and that they are strongly involved in the biointegration of implants [START_REF] Hlady | Protein adsorption on solid surfaces[END_REF][START_REF] Garcia | Biomimetic surfaces for control of cell adhesion to facilitate bone formation[END_REF] . Considering the treatments of bone diseases, some bone adsorbing molecules, like bisphosphonates, have been used to control bone turnover [START_REF] Jung | The binding of pyrophosphate and two diphosphonates by hydroxyapatite crystals[END_REF] , although their effect on bone cell behavior has been largely documented, the biological activity has been shown recently rather well correlated with their adsorption properties 14 . Surface properties of apatites are also largely used in separation chromatography of proteins and, in fact, preparatory and development studies for these applications have started the researches on adsorption on apatite surface [START_REF] Hjerten | Protein chromatography on calcium phosphate columns[END_REF] . The models proposed initially are still widely present in the actual explanations of the adsorption behavior of apatites, essentially base on surface charge considerations [START_REF] Rouahi | Physico-chemical characteristics and protein adsorption potential of hydroxyapatite particles: influence on in vitro biocompatibility of ceramics after sintering[END_REF][START_REF] Yin | Impact of the surface charge property on protein adsorption on hydroxyapatite[END_REF] . The aim of this report is to give several, nonexhaustive examples of different types of adsorption reactions on apatites and to present some possible applications especially for growth factors delivery. We will first describe adsorption experiments of small molecules stressing the influence of functional groups on adsorption properties, we will then analyze the effect of the adsorbent characteristics, especially the type of apatite used, and we will finally describe the adsorption process of molecules of biological origin and their applications.

MATERIALS AND METHODS

Adsorbents

The adsorption substrates were prepared according to published methods [START_REF] Rey | Nanocrystalline apatites in biological systems, characterization, structure and properties[END_REF][START_REF] Barroug | Hydroxyapatite crystals as a local delivery system for cisplatin: adsorption and release of cisplatin in vitro[END_REF][START_REF] Ouizat | Adsorption of bovine serum albumin on poorly crystalline apatite : influence of maturation[END_REF][START_REF] Benaziz | Adsorption of o-phospho-L-serine and Lserine onto poorly crystalline apatite[END_REF] . Briefly, nearly stoichiometric apatite was prepared by double decomposition at boiling temperature and alkaline pH, between a calcium nitrate solution and an ammonium phosphate solution.

Apatite nanocrystals were also prepared by double decomposition but at room temperature and physiologic pH [START_REF] Barroug | Hydroxyapatite crystals as a local delivery system for cisplatin: adsorption and release of cisplatin in vitro[END_REF] .

After filtering and washing the samples were lyophilized. They were all controlled by X-ray diffraction, chemical analyses and FTIR spectroscopy. The specific surface area was determined by BET method (nitrogen adsorption).

Adsorption experiments

Adsorption experiments were made in batches at constant temperature and known pH. A given amount of adsorbate was dissolved in aqueous solution at constant ionic strength (in KNO 3 solution). The apatite powder was added in the solution. After an equilibration period, determined from previous adsorption rate studies, the solutions were analyzed. The adsorption isotherm was determined from the equilibrium concentration in solution. The calcium and phosphate content of the solutions were measured by atomic absorption spectroscopy and spectrophotometry of the phospho-vanado-molybdic acid respectively. Details are given in the different publications [START_REF] Barroug | Hydroxyapatite crystals as a local delivery system for cisplatin: adsorption and release of cisplatin in vitro[END_REF][START_REF] Ouizat | Adsorption of bovine serum albumin on poorly crystalline apatite : influence of maturation[END_REF][START_REF] Benaziz | Adsorption of o-phospho-L-serine and Lserine onto poorly crystalline apatite[END_REF] .

RESULTS

Adsorption of small molecules -Serine and o-phosphoserine

The adsorption of these aminoacids on apatite nanocrystals gives a good example of the effect of functional groups using simple molecules [START_REF] Benaziz | Adsorption of o-phospho-L-serine and Lserine onto poorly crystalline apatite[END_REF] . These aminoacids are involved in matrix proteins of bone and it has been shown that it exists a relationship between the phosphorylation ratio of bone tissue proteins and the mineralization process. The adsorption isotherms of serine and phosphoserine on a nanocrystalline apatite are shown in figure 1. The adsorption of o-phosphoserine is well described by a classical Langmuir type isotherm and it is characterized by a rather high affinity constant. Comparatively, the adsorption of serine appears much weaker and a plateau was not reached in the domain of concentrations explored. The adsorption of serine can be described by a Freundlich type isotherm like that of other aminoacids or simple molecules weakly interacting with apatite surface such as glycine or acetic acid for example [START_REF] Barroug | Exchange reactions at calcium phosphate surface and applications to biomaterials[END_REF] .

The very high affinity of phosphoserine for apatite surface compared to that of serine can be related to the existence of the phosphate group which can interact strongly with the apatite surface. Phosphoproteins for example have been shown to play a key role in apatite nucleation in bone tissues. In the present case, it has been shown by solid-state NMR that phosphorylated amino acids, more specifically, seems to interact with nascent bone crystals in embryonic bone mineralization [START_REF] Wu | Phosphate ions in bone: identification of a calcium phosphate complex by 31 P solid-state NMR spectroscopy at early stages of mineralization[END_REF] . In the field of biomaterials, the attachment of methylmethacrylates monomers to calcium phosphates has been shown to be considerably enhanced with the esterification of alcool groups with phosphoric acid [START_REF] Subirade | Study of the mineral-organic interface between a calcium phosphate and a phosphorylated monomer[END_REF] . Among the other functional groups considered to interact strongly with apatite surface are silicate and sulfate. Generally carboxylate group interact weakly except when they are associated in polyacids.

An interesting aspect of the adsorption of phosphoserine is that the maximum amount adsorbed can considerably vary depending on the pH or the presence of mineral ions in the solution. Thus in the presence of phosphate or carbonate ions the maximum amount adsorbed decreases whereas in the presence of calcium one can adsorb much more molecules at saturation.

The adsorption of phosphoserine cannot be reversed by simple dilution of the solution and the corresponding decrease in the equilibrium concentration of the adsorbate. This phenomenon is common to many adsorption processes on apatites.

-Adsorption of a Bisphosphonate: risedronate Bisphosphonates are among the most prescribed medication for several bone diseases and more specifically osteoporosis. The adsorption isotherm of a bisphosphonate, risedronate, on hydroxyapatite is shown in figure 2.

Figure 2: Adsorption isotherm of risedronate on well crystallized hydroxyapatite (Ca/P ratio 1.64, Specific surface area: 59 m 2 .g -1 , pH=7.4 , T=37°C)

It corresponds also to Langmuir's isotherms. The follow-up of the variation of the mineral ions content of the solution indicate that the adsorption of risedronate is associated with a release of phosphate ions (Figure 3) whereas the calcium concentration remains almost unchanged. These findings are analogous to those reported by others concerning the adsorption of another bisphosphonate, zoledronate, on calcium phosphates [START_REF] Josse | Novel biomaterials for bisphosphonate delivery[END_REF] .

Considering that the dissolution of hydroxyapatite in our system is congruent (i.e. the Ca/P ratio is the same for the solid and the solution), the calculations indicate that for most of the points of the isotherm there is one phosphate ion released for every risedronate molecule adsorbed. In this case the adsorption reaction corresponds in fact to an ion exchange:

[Ri 3-] sol + [PO 4 3- ] surf ⇔ [Ri 3-] surf + [PO 4 3- ] sol
in which the risedronate ions from the solution substitute for the phosphate ions of the apatite surface. This reaction is responsible for the release of additional phosphate ions and the apparent noncongruent dissolution equilibrium of the apatite. Considering this equilibrium, the calcium concentration should decrease as the phosphate in solution increase. This is not observed and the stability and even the slight increase of the calcium content with the increase of risedronate in solution can be interpreted as an indication for the probable formation of ion pairs or complexes between risedronate molecules and calcium ions in solution.

An interesting aspect of risedronate adsorption is that the amount of molecules adsorbed at saturation can vary considerably depending on different parameters such as the temperature, the pH, the initial phosphate and calcium content in the solution. Such variations cannot be explained by the chemical equilibrium proposed.

As previously noticed the adsorption of risedronate is irreversible and the amount adsorbed is not altered by dilution of the adsorption solution or even on washing of the samples.

The adsorption of biological macromolecules appears more difficult to follow as the possible interactions with a mineral surface are more numerous that for simple molecules. One may regard a biological macromolecule as a charged object which can interact with a charge mineral surface depending respectively on the point of zero charge of the molecule and the surface charge of the mineral surface. Theoretical approaches, however, such as computational modeling, lead to multiple but precise bonding schemes involving identified groups of atoms of the molecule and of the mineral surface. In addition in many cases the adsorption of biological macromolecules has been shown to be related to phosphate ion release [START_REF] Rouahi | Physico-chemical characteristics and protein adsorption potential of hydroxyapatite particles: influence on in vitro biocompatibility of ceramics after sintering[END_REF] , like for small molecules, and some of these molecules can be purified and separated by chromatography on apatite columns using phosphate solutions with a concentration gradient for as mobile phase [START_REF] Ohta | Adsorption characteristics of proteins on calcium phosphates using liquid chromatography[END_REF] . These observations suggest that the existence of specific chemical reactions with apatite surface cannot be discarded in the description of adsorption processes.

Adsorption of biological macromolecules -Bovine serum albumin (BSA) Albumin is the most abundant protein in blood serum. It is also one of the major proteins found in bone and it is considered to be involved in enamel formation. Several studies have been made on albumin interactions with apatites [START_REF] Barroug | Hydroxyapatite crystals as a local delivery system for cisplatin: adsorption and release of cisplatin in vitro[END_REF][START_REF] Wassel | Adsorption of bovine serum albumin onto hydroxyapatite[END_REF][START_REF] Serro | Bovine serum albumin conformational changes upon adsorption on titania and on hydroxyapatoite and their relation with biomineralization[END_REF] . Like small molecules BSA adsorbs on well crystallized, nearly stoichiometric, apatite according to Langmuir's theory. However, the biological apatites are very different from stoichiometric ones: they are nanocrystalline and they exhibit a surface hydrated layer with mineral ions in non-apatitic environments. This layer is related to the precipitation process at physiological pH and its structure as well its extension depend on the ageing time in solution [START_REF] Cazalbou | Poorly crystalline apatites: evolution and maturation in vitro and in vivo[END_REF] . The data obtained for BSA adsorption (but also for phosphoserine, and risedronate, data not shown) indicate an increase of the affinity constant and a decrease of the maximum amount adsorbed at saturation with the maturation time (Figure 4). These data illustrate the variability of adsorption on apatite substrates and the need to define and characterize precisely the type of apatite used and its surface. -Heparin Heparin is a calcium complexing polysaccharide involved in the control of blood clot formation which has been proposed as carrier of growth factors. The adsorption of heparin on well crystallized stoichiometric apatite was investigated in detail. Like BSA and small molecules the adsorption equilibrium is reached relatively rapidly in about 20 minutes. The adsorption isotherms are Langmuirian (Figure 5).

The analyses of the mineral ions in solution show a complex variation (Figure 6). A constant increase of the concentration of phosphate ions as the amount of heparin in solution increases is observed. Concerning the calcium concentration, a decrease occurs at low heparin content followed by an increase when the adsorption limit is reached. This behavior seems rather different from that of risedronate although the phosphate releases seems to increase with the amount adsorbed, the calcium content with a U shaped variation appears rather strange. However, like for risedronate, the addition of calcium ions in the absorption solution was found to increase the maximum amount adsorbed whereas it decreased in the presence of phosphate ions. Additional studies by solid state NMR on apatite -rhBMP 2 BMP 2 is one of the most efficient growth factor involved in bone reconstruction. Only a very few studies have been made on the adsorption of this molecule on apatites. Boix et al. have produced a rather complete study on the adsorption of BMP on well crystallized apatites [START_REF] Boix | Adsorption of recombinant human bone morphogenetic protein rhBMP-2m onto hydroxyapatite[END_REF] . This molecule seems to follow the general characteristics of the adsorption of other molecules with a Langmuir type isotherm. Like for many other molecules for which the attachment to the apatite surface is determined by anionic carboxylate functions, the adsorption limit varies considerably with the mineral ions present in the solution. The increase of the calcium concentration in the adsorbate solution increases the adsorption limit whereas that of phosphate shows a reverse effect. This growth factor can also be attached to nanocrystalline coatings [START_REF] Autefage | Adsorption and release of BMP-2 on nanocrystalline apatite-coated and uncoated hydroxyapatite/b-tricalcium phosphate porous ceramics[END_REF] . The adsorption is also Langmurian, and most of the growth factor molecules are irreversibly bound and they are not spontaneously released in a cell culture media (Figure 7). This characteristic has also been observed for other growth factors like FGF 2 or VEGF [START_REF] Midy | Basic fibroblast growth factor adsorption and release properties of calcium phosphate[END_REF][START_REF] Midy | Adsorption of vascular endothelial growth factor to two different apatitic materials and its release[END_REF] .

DISCUSSION

These few examples illustrate the variability of the adsorption processes on apatites but common features have been observed.

Adsorption isotherms

Generally the adsorption equilibrium of molecules strongly interacting with an apatite surface is well depicted by a Langmuir isotherm (C e equilibrium concentration of the adsorbate and Q amount adsorbed):

Q=NK L C e /(1+K L C e )
characterized by two adsorption parameters, the affinity constant (K L ) and the maximum coverage (N). The empirical Freundlich isotherms:

Q=K F C e 1/n
have been found generally in the adsorption of molecules weakly bound to the apatite surfaces, and rather far from the saturation limit. It has been found for example for serine in the example given here and also for different other ions or molecules like glycine and acetate ions for example.

In a recent study on adsorption Rill et al. tested different adsorption models for the analysis of adsorption data of phosphonate-containing molecules on apatites [START_REF] Rill | Kinetic and thermodynamics of adsorption on hydroxyapatite of the 160 Tb terbium complexes of the bone-targeting ligand DOTP and BPPED[END_REF] . The best fits were given by a Langmuir-Freundlich isotherm:

Q=N(K LF C e ) n /(1+(K LF C e ) n )
and a Tóth isotherm:

Q=[N(K T C e ) n /(1+(K T C e ) n )] 1/n
which are taking into account the existence of a distribution of adsorption energies on the apatite surfaces. However for molecules of interest the simple Langmuir's isotherms are satisfactory. A major characteristic of adsorption on apatites is the absence of reversibility, often noticed, which is totally contradictory with the Langmuir theory of adsorption.

The adsorption process

Historically two types of adsorption sites have been recognized, on apatite calcium surface sites and phosphate surface sites respectively. Negatively charged molecules (or moeties) were considered to bind to calcium sites and positively charged ones to phosphate sites. The adsorption of negative molecules seems particularly important and it is involved in most chromatographic use of apatites and also in most studies involving molecules of biological interest. The zeta potential of apatites has been considered to play a major role in the adsorption process and most adsorption behaviors were, and still are, related to this surface parameter although the correlation between this global physical parameter describing the surface charge of apatite particles and chemical interactions with specific ions at an atomic level is not straightforward. It shall be considered that the global charge of a particle does not give any information on the local distribution of cations and anions at a mineral surface and in fact zeta potential does not appear as a decisive parameter: for example the adsorption of positive molecules on positive apatite surface and inversely negative molecules on negative apatite surface has been described [START_REF] Barroug | Adsorption of succinylated Lysozyme on hydroxyapatite[END_REF][START_REF] Barroug | Adsorption of catalase on hydroxyapatite[END_REF] . Similarly the isoelectric point of proteins, by itself, do not give specific information on the ionization state of the different functions of a molecules and they should be considered with caution for the prevision of an adsorption behavior related to a chemical interaction.

In several of the examples given in this report the adsorption of negative molecular ions has been related to a release of phosphate ions evidencing a chemical ion exchange reaction with the apatite surface. This process has been described in different instances, as for example in the adsorption of polyacids [START_REF] Pearce | Ion displacement following the adsorption of anionic macromolecules on hydroxyapatite[END_REF] , citrate ions [START_REF] Misra | Interaction of some alkali metal citrates with hydroxyapatite. Ion-exchange adsorption and role of charge balance[END_REF] , zoledronate [START_REF] Josse | Novel biomaterials for bisphosphonate delivery[END_REF] , or serum proteins on apatites [START_REF] Rouahi | Physico-chemical characteristics and protein adsorption potential of hydroxyapatite particles: influence on in vitro biocompatibility of ceramics after sintering[END_REF] . In the case of risedronate it has been found that one molecule adsorbed removed one phosphate ion out of the apatite surface. This chemical process seems rather general and supports a chemical description of the adsorption reaction rather than a physical one based on global electrostatic interactions. The adsorption could then be represented, for example, as a chemical equilibrium as follows (in a case of a one to one exchange):

A sol + P ap ⇔ A ap + P sol (reaction 1) with A the adsorbate in a given ionic state either in solution (sol) or on the apatite surface (ap), P phosphate group in a given ionic state either in solution or on the apatite surface. Other ion exchange possibilities have been discussed by Misra in the case of citrate adsorption [START_REF] Misra | Interaction of some alkali metal citrates with hydroxyapatite. Ion-exchange adsorption and role of charge balance[END_REF] . These descriptions seem consistent with the use of apatites in chromatography where negatively charged molecules are desorbed using phosphate solutions (and positively charged ones using calcium solutions).

The peculiar behavior of heparin deserves some additional explanations. This molecule can give soluble complexes with calcium ions. In the presence of apatite, calcium ions are complexed by heparine and apatite dissolves to reach a solubility equilibrium. During the first raising part of the adsorption isotherm these complexes are bound to the apatite surface and essentially phosphate ions are released. As the surface saturation occurs, the addition of heparin still results in Ca-complex formation but the complex cannot attach to the saturated surface and remains in solution, resulting in an increase of both calcium and phosphate concentrations in the solution. This behavior could also occur in the adsorption of citrate anions on apatites or more generally in the adsorption of calciumcomplexing molecules.

In addition to complexation other processes can disturb the adsorption equilibrium and have to be taken into account: the possible precipitation of calcium (or phosphate) salts, the dissolution equilibrium of the apatite and the surface hydrolysis reactions of apatite.

Insoluble calcium salts may sometimes form and precipitate with the adsorbate molecules, depending on their respective concentrations. Then the apatite phase is progressively destroyed as the new phase forms leading to a release of phosphate in the solution until a new equilibrium is reached. This event does not generally give a Langmuir type isotherm with a typical saturation domain. On the contrary, the addition of adsorbate solutions aliquots results in precipitation of calcium salt of the absorbate and more destruction of the apatite. In some cases however this process could result in a Langmuir-like adsorption behavior with an apparent saturation domain if there is a coating of the apatite surface by the new phase preventing further reaction. The observation of the solid phase by Xray diffraction or electron microscopy allows generally the detection of new phases formation.

The dissolution equilibrium of apatite has also to be considered. Generally apatite dissolution is congruent when the apatite/solution ratio is small enough to neglect surface reactions. However there are some conceptual divergencies on the solubility product of hydroxyapatite most often related to inhomogeneity of composition and non-stoichiometry. In the case of nanocrystalline apatites the dissolution behavior is more complex than for stoichiometric apatites and it can probably be represented by a metastable equilibrium solubility (MES) [START_REF] Chhettry | Metastable equilibrium solubility distribution of carbonated apatite as a function of solution composition[END_REF] showing a dependency of the apparent equilibrium concentrations with the amount dissolved, although the dissolution still remains congruent. The amount of calcium and phosphate in the equilibrium solution depends also, in these cases, on the maturation stage of the nanocrystals. The result of dissolution equilibriums is the existence of calcium and phosphate ions in the solution which may interfere with the adsorption equilibrium and especially with the maximum amount adsorbed and the affinity constant.

Additionally in cases where the amount of apatite with a high specific surface area is elevated in the solution, a hydrolysis of the phosphate ions on the surface may occur associated with a release of calcium in the solution. This phenomenon leads to an apparent non-congruent dissolution equilibrium which appears mainly related to a surface equilibration reaction and then depends on the solid/solution ratio. As adsorption studies are often made with rather large solid/solution ratios, this phenomenon leads to calcium and phosphate ions in solution in a ratio different from that in the solid, which may also interfere with the adsorption parameters. To avoid these anomalies a pre-equilibration of the apatite with a solution at the same pH and ionic strength than the adsorption solution can be realized, before putting the apatite in contact with the adsorption solution.

The description of adsorption as an ion exchange reaction permits to explain several characteristics of the adsorption of charged molecules on apatites and especially the apparent irreversibility of the adsorption process.

Irreversibility of the adsorption

Langmuir adsorption is generally an equilibrium and thus a reversible process. The most convenient way to determine the reversibility of adsorption is to dilute the solution in equilibrium with the apatite surface. Then the concentration of the adsorbate is reduced and a new equilibrium shall occur resulting in the release of molecules from the solid surface. The observation of a total or partial irreversibility of adsorption on apatites upon solution dilution is a common observation which has received several explanations such as a kinetic limitation due to multiple bonds of macromolecules, necessitating a rupture of all of them to release the molecule, change in configuration and surface properties. These possibilities may of course exist, but irreversibility is also observed for simple molecules such as phosphoserine or bisphosphonate for which none of these explanations seem satisfactory. Considering the ion exchange equilibrium reaction, it is apparent that the adsorption process is not only related to the concentration of the molecule in solution but also to that of the mineral ion displaced. From reaction 1 we can write:

K ex = P sol .Q/(C e (N-Q))
with K ex , the equilibrium constant of the exchange reaction, Q the amount adsorbed, C e the equilibrium adsorbate concentration, P sol the phosphate concentration in solution, N the total number of adsorption sites (i.e. the maximum of molecules adsorbed). This equation can be transformed into a Langmuir type isotherm equation: Q= NK ex (C e /P sol )/(1+K ex (C e /P sol ))

The equilibrium concentration of the adsorbate (C e ) in the traditional Langmuir equilibrium is simply replaced by the ratio C e /P sol in the exchange reaction equilibrium. This models fits well with data points obtained in our studies, in addition it explains simply the apparent irreversibility on diluting the equilibrated solution. As dilution involves a reduction of both concentrations (C e and P sol ) in equal proportion, the conditions of the equilibrium are roughly unchanged (if the very weak dissolution of apatite to re-establish the solubility equilibrium and hence the corresponding faint increase of calcium and phosphate in solution are neglected). The recently reported observation that the reversibility of the adsorption of phosphonate complexes [START_REF] Rill | Kinetic and thermodynamics of adsorption on hydroxyapatite of the 160 Tb terbium complexes of the bone-targeting ligand DOTP and BPPED[END_REF] on apatite on dilution was depending on the equilibrium concentration of the adsorbate in solution can be explained with the same arguments. In these experiments the authors were testing the reversibility at two points of the isotherm corresponding to low and high adsorbed amount. The dilution was performed with a solution saturated with respect to the apatite to avoid any dissolution of the adsorbent. Assuming an exchange reaction of a complex molecules with a phosphate ion, the dilution with a saturated solution was correlatively bringing a relative increase of phosphate ions in solution more important for the solution equilibrated with a low amount adsorbed, and thus with the lowest amount of exchanged phosphate, than for the solution at a higher equilibrium concentration and a higher amount of phosphate in solution. Thus the reverse reaction appeared slightly stronger, in relative amounts, at low adsorbate equilibrium concentration. Similarly washing an apatite sample with adsorbed molecules resulting of ion exchange does not create any reverse exchange possibility and no desorption should be expected, except for faint release effects due to the dissolution of the apatite.

An equivalent, though slightly different, description of the exchange reaction can be proposed taking into account the solubility equilibrium of the apatite: (Ca) R (P)=K sp,pp where K sp,pp is the solubility product of the apatite corresponding to one phosphate and R the Ca/P ratio of the apatite, assuming a congruent dissolution (the pH is considered constant, for example a physiological pH, and the OH contribution to the solubility is therefore also constant and included in the solubility product).

Then the adsorption isotherm may also be written as

Q= NK ex (C e (Ca) R /K sp )/(1+K ex (C e (Ca) R /K sp )) or: Q= NK b (C e .(Ca) R /(1+K b C e .(Ca) R )
where K b =K ex /K sp,pp. The adsorption process can then be described as mobilizing calcium ions from the solution to serve as a binding agent of the molecule with the mineral, instead of a phosphate exchange. The corresponding chemical equation can be written as:

A sol + RCa sol + S ap ⇔ A-RCa-S ap
where S ap represents a binding site on the apatite. These raw equations shall be adapted to each case, and there can be for example one binding calcium per molecule, which could be described in the equivalent ion exchange process as a replacement of a fraction of phosphate ion. These descriptions (ion exchange with phosphate or calcium binding) are totally equivalent from a chemical point of view although they shall be adapted to take into account the number of ions involved and their charges.

The adsorption process does not differ strongly between well crystallized apatites and nanocrystalline apatites. An interesting aspect is the variation of the adsorption parameters with the characteristics of the nanocrystals

Adsorption on apatite nanocrystals and ageing

An interesting problem, regarding nanocrystalline apatites, is the possible change of surface properties with the maturation state of the nanocrystals.

The available data on adsorption properties of apatite nanocrystals are very scarce, but those obtained with several molecules such as bovine serum albumin, phosphoserine, and risedronate suggest a general behavior and the findings reported in figure 4, in the case of albumin, were also observed in other cases: the number of adsorption sites decreases when the maturation time of the nanocrystals increases but the affinity constant increases.

The variation of the affinity has been related to a decrease of the surface energy as the hydrated layer becomes progressively transformed into apatite. Although it is very difficult to determine the surface energy of nanocrystals, several measurements on Ca-P materials have shown that hydrated Ca-P salts always had a much lower surface energy than anhydrous ones [START_REF] Wu | Determination of interfacial tension from crystallization and dissolution data: a comparison with other methods[END_REF] . Thus, the hydrated layer, which most probably reduces the surface energy of the nanocrystals in aqueous media, also weakens, to some extent, the interfacial energy released by protein adsorption. Another explanation could be that ions in the hydrated layer become less exchangeable as the maturation time increases, which is effectively observed [START_REF] Cazalbou | Poorly crystalline apatites: evolution and maturation in vitro and in vivo[END_REF] .

The decrease of the maximum amount of adsorbed molecules with maturation is more difficult to explain. It does not seem related to a decrease of the specific surface area of the crystals and the rate of coverage does not support the formation of multilayers of proteins on immature crystals. A different conformation could be suggested in the case of albumin. However the small phosphoserine exhibits the same behavior. The adsorption process by ion displacement suggests that the amount of protein incorporation could be related to the amount of labile mineral ions available in the hydrated layer and then to the extension of the hydrated layer. The adsorption process could then involve the whole hydrated layer and possibly its re-structuration and stabilization. As a support for this hypothesis it can be noted that the adsorption limit is well correlated to the development of the hydrated layer on nanocrystals as shown for example for the adsorption of phosphoserine (Figure 7). It has also been shown that the development of the hydrated layer was related to the ion exchange capability and a parallel seems to exist between ions exchange and adsorption.

Another common point to adsorptions on apatites is the variability of the adsorbed maximum amount with several physical chemical parameters.

Maximum amount adsorbed

The maximum amount adsorbed is supposed to correspond to the saturation of the surface adsorption sites. The question regarding the variations of this quantity is generally answered by reference to the surface charge model and its alterations. For example an increase of the pH produces a decrease of the surface charge and of the adsorption capabilities of negatively charged molecules.

Similarly the increase of the calcium ions concentration in solution increases the surface charge and favors the adsorption of negatively charged molecules whereas the increase of the phosphate concentration has a reverse effect. As already mentioned, this global model does not consider that the most important adsorption processes on apatite involve strong local interactions with individual ions on the surface and not simply a global electrostatic interaction between a charged surface and a charged molecule. Considering the proposed ion exchange reactions, the chemical equilibriums involved cannot explain a variation of the adsorption limit: when the concentration of absorbate increases to large values, all sites should be occupied. Such variations suppose that maximum number of sites which can be occupied (N) varies according to different factors. It is obvious that for most molecules, and this is especially true for macromolecules, the dimension is much larger than that of phosphate or calcium ion exchanged by specific molecular functions and a total replacement of all surface ions by these molecular functions is not possible. Thus there are always more possibilities of exchange and attachments than what is feasible due to sterical constrains. The effect of phosphate and calcium ions in the adsorption solution are always similar regarding the adsorption limit of negatively charged molecules: phosphate ions decrease the maximum amount of adsorbed molecules compared to a solution containing only the adsorbate, and calcium ions increase it. These added mineral ions affect the adsorption limit in a wide range (from 1 to 6 for example in the cases of heparin). If we compare with the variations observed for nanocrystals at different maturation stages it can be suggested that the mineral ions in solution may affect the hydrated layer at the surface of the apatite crystals. The strength of attachment and surface mobility of the adsorbed molecules has also to be considered and could be involved in the reorganization of molecules on the surface.

Consequences for bone mineral

Two main roles have been assigned to the interactions of proteins with apatite crystals in biological systems: initiation of crystal nucleation and inhibition of crystal growth [START_REF] Boskey | Matrix proteins and mineralization: an overview[END_REF] . Several in vitro experiments have provided support for this notion. However the classification of proteins as initiators or inhibitors of mineral formation suffers from numerous exceptions. It has been shown that the role of proteins may depend on their state and configuration. Thus, the same protein may act as an inhibitor when it is in solution and as an initiator when it is bound to a substrate. In addition most adsorbing proteins seem to show both aspects depending on their concentration 10 : at low concentrations they accelerate crystal formation whereas at high concentrations they act as inhibitors.

Most mineral binding proteins are rich in anionic groups. Phosphoproteins especially have been suggested to bind to calcium and to initiate the first nuclei for mineral formation [START_REF] Glimcher | The possible role of collagen fibrils and collagen phosphoprotein complexes in the calcification of bone invitro and in vivo[END_REF] . Due to their lower mobility compared to that of mineral ions and the relatively fast rate of formation of nanocrystals, proteins can only play a role when they are already in situ. In addition to their role in the nucleation and growth of mineral crystals, proteins may also be used to control mineral maturation. Maturation of the nanocrystals considerably reduces their surface reactivity and their action in homeostasis. Remodeling appears, therefore, as a necessity for the organism to maintain the ion reservoir function of bone. The strong variation of the surface properties of the nanocrystals with maturation and especially the change in adsorption properties suggest that some proteins could act as signals between mineral crystals and cells to control the maturation state and possibly initiate the remodeling process. This hypothesis needs, however, to be verified. The variation of the adsorption properties of bone nanocrystals with time is rarely considered in a dynamical approach of the system; but, considering the very large specific surface area of bone crystals, it could be fundamental.

The interactions between nanocrystals and the collagen matrix have not yet been elucidated at the atomic level. It seems probable that ions mobility in the hydrated layer could facilitate an intimate contact between the two main constituents of bone and could influence the mechanical properties of the tissue. The fact that the mechanical properties of bone depend strongly on its hydration state supports this hypothesis.

Considering the specific mode of interaction of drugs like bisphophonates with apatites, the study of the adsorption process allows some findings to be explained. The absence of accumulation of the drug in bone even after years of use, for example, is related to the adsorption process and the exchange equilibrium: once equilibrium concentrations have been reached in bone tissue the loading cannot continue. This would not be the case if a dissolution re-precipitation process were involved. The release after interruption of the treatment depends on the phosphate concentration in bone fluids; as it is very low this release is very slow.

It seems important to consider the dynamic of bone tissue, not only in terms of bone cell behavior but also as a regulating system involving interfacial interactions with the mineral. Without taking this aspect into account the approach will necessarily be incomplete.

Consequences for biomaterials

Adsorption on apatites and other calcium phosphates may find several uses in biomaterials [START_REF] Matsumoto | Hydroxyapatite particles as a controlled release carrier of protein[END_REF] . Generally active molecules such as growth factors are associated with biomaterials by impregnation often followed by drying. However this easy, rapid and inexpensive method does not allow a precise control of the physical state of the active molecules which may appear partly crystallized partly adsorbed or partly precipitated as calcium or phosphate salt or more likely a combination of these possible states depending on the conditions of preparation and drying. Thus the release rate is difficult to predict it can be rapid and only determined by the diffusion properties of the molecule if no interactions with the biomaterial surface have been established or depend on solubility behavior or desorption conditions. These uncertainties depending on the conditions of impregnation can lead to anomalies. For example a local excess of released BMP may activate bone resorption instead of bone formation [START_REF] Toth | Short-term osteoclastic activity induced by locally high concentrations of recombinant human bone morphogenetic protein-2 in a cancellous bone environment[END_REF] . Adsorption on the contrary leads to stable association and the molecules can only be displaced by mineral ions and/or soluble proteins with a stronger affinity for apatite surfaces but in a predicable manner. Generally, the spontaneous release is very low and the active molecules show a sustained release related to the degradation of the biomaterial. It is probable, although this has not been systematically investigated, that the release rate is related to the nature of the apatite samples and their maturation stage. Another interesting property of adsorbed growth factors is their availability for cells as demonstrated in the case of VEGF. In vivo studies have confirmed the efficiency and reproducibility of adsorbed BMP-2 in osteoinduction.

Cell adhesion on an apatite surface appears to be generally poorer than on specially treated surfaces like those of cell culture dishes. Therefore, several attempts have been made to favor cell attachment by using cell-binding proteins or specific protein sequences, such as RGD (arginine, glycine, aspartic acid), involved in cell attachment. The results generally show an improvement of cell adhesion and differentiation. It has been suggested that the osteoconductive properties of apatite could be due to the ability of its surface to bind such proteins.

CONCLUSION

This non exhaustive review of some adsorption studies, essentially made in our research groups, in the last years relates the progressive shift of our conception of the adsorption process from an electrostatic mode,l based on previous considerations largely developed, to a more focused ion exchange model. The possibilities of interactions of a molecule, especially a macromolecule, with a mineral apatite surface are of course more numerous than the simple ion exchange reactions proposed here, but our experience suggests that this is a fundamental basic reaction determining the strong adsorptive properties of many molecules and bio-macromolecules of interest and explaining some specific behaviors like the effect of phosphate and calcium ions on the adsorption equilibrium and the apparent irreversibility on dilution. The observation of such ions exchange interactions needs a precise evaluation of the amount adsorbed and of the mineral ion content of the solution which is rarely made in most adsorption studies. Among the competitive reactions which have to be taken into account we have identified the apatite dissolution equilibrium and the surface equilibration reactions of the mineral in solution which involves essentially a surface hydrolysis of phosphate species associated with a release of calcium ions. These different equilibriums can lead to different but totally equivalent descriptions of the adsorption phenomena.

Figure 1 :

 1 Figure 1: Example of adsorption isotherm of serine and phosphoserine on nanocrystalline apatite (24 hours maturation time, Ca/P ratio: 1.42; Specific surface area 155 m 2 .g -1 , pH 7.0, T=25°C).

Figure 3 :

 3 Figure 3: Variation of the calcium (B: white squares) and phosphate (A: black squares) content of the solution with the amount of risedronate adsorbed.

Figure 4 :

 4 Figure 4: variation of the adsorption characteristics of BSA on nanocrystalline apatites with the maturation time 20 .

2 )Figure 5 :Figure 6 :

 256 Figure 5 : adsorption isotherm of heparin on well crystallized nearly stoichiometric apatite.(Ca/P ratio 1.62, Specific surface area :82 m 2 .g -1 , pH=7.4 , T=25°C)

Figure 7 :

 7 Figure 7: Release of rhBMP 2 in DMEM complete culture medium with 10% fetal calf serum from adsorbed rhBMP-2 on nanocrystalline coated and uncoated Biphasic Calcium Phosphate 31 .

Figure 7 :

 7 Figure 7: Correlation between the amount of phosphoserine adsorbed and the development of the hydrated layer as measured by the intensity of the surface HPO 4 2-determined by FTIR spectroscopy.


Yunli Wang
email: wang@imft.fr

Rachid Ababou
email: ababou@imft.fr

Manuel Marcoux
email: marcoux@imft.fr

Signal Processing of Water Level Fluctuations in a Laboratory Experiment: Sloping Sandy Beach in a Wave Canal (Hydralab Project Barcelona)

In coastal processes, the strong water movements due to short periodic waves (such as sea swell) can induce irregular water level fluctuations H(t) in the swash zone, and also, within the sandy beach. In this paper, we analyze measured water level fluctuations in a wave canal with a sloping sand beach, using 7 capacitive sensors (H i (t) is the water level at sensor N°"i"). Fourier spectrum and multi-resolution wavelet analyses were used to study these water level fluctuations. Several dominant periods for the entry water level H 1 (t) were identified with Fourier analysis. The corresponding amplitudes and the corresponding phases were obtained by wavelet analysis. Then a simplified (bimodal) Fourier approximation was determined for the irregular water level fluctuations H 1 (t), which can be used as the entry condition for numerical simulations.

INTRODUCTION

Beach groundwater is a complex and dynamic system interacting with tides, waves and swash. Groundwater fluctuations driven by oceanic oscillations enhance water exchange between the ocean and coastal aquifer. Interaction between swash dynamics and groundwater may also be important with regard to onshore sediment transport and beach profile evolution. There is currently limited understanding of how the beach groundwater system responds to oceanic forcing at various frequencies.

A "wave-beach" experiment was conducted in a large water wave canal equipped with a wave generator (CIEM flume in Barcelona). The experiment was part of a European project, HYDRALAB-SANDS, undertaken in a collaboration between the HYDRALAB laboratory in Barcelona (Spain) and the OTE group in our laboratory (IMFT, Toulouse, France). The experiment was designed to measure the erosion of the swash zone in a sandy beach, with periodic water level oscillations.

In this work, we focus on a related problem, namely, the effect of surface water waves and swash zone phenomena on subsurface oscillations in the sandy porous medium, and the possible interactions between surface and subsurface oscillations. In this experiment, water level fluctuations H(t) in the sloping sandy beach were measured by 7 capacitive sensors (sensor No.1 yields H 1 (t), ..., and sensor No.7 yields H 7 (t)).

In the sequel of this paper, Fourier spectrum and multi-resolution wavelet methods are used to analyze these measured water level fluctuations Hi(t) in the sloping sandy beach, using geophysical signal analysis tools previously developed in our group [START_REF] Fatmi | Méthodologie d'analyse des signaux et caractérisation hydrogéologique : application aux chroniques de données obtenues aux laboratoires souterrains du Mont Terri[END_REF].

EXPERIMENT: DESCRIPTION

The canal is 100m long, 3m wide and 5m high. At the back end of the canal, a mechanical wave generator was designed with adjustable period and amplitude. For this experiment, the period is about 4 seconds, and the maximum amplitude is about 0.9 m. The weighted average diameter d 50 of sand grains is 0.25mm. The beach slope is 1/15.

As shown in FIG. 1. and FIG. 2. , 6 capacitive sensors were installed at intervals of about 1.5 m in the beach in order to measure groundwater level fluctuations. In particular, one sensor (No.1) was placed near the still water / beach boundary to measure the water level fluctuations corresponding to the entry condition of the model.

EXPERIMENT: MEASURED WATER LEVELS H(t)

The water level measurements at the capacitive sensors began from the static initial water level (step (1) in Fig. 3), then lasted about 30 minutes corresponding to water level fluctuations forced by the wave generator (step (2) in Fig. 3), and finally ended during the draining phase (step (3) in Fig. 3). The measured water levels H(t) shown in Fig. 3 correspond to just one "test" (the "first test", conducted the 18th of March 2008).

The measurement results show clearly two effects: the spatial decaying of the amplitudes away from the shore, and the filtering out of the shortest periods. Furthermore, the signals away from the shore (H 5 (t), H 6 (t) ,H 7 (t)) exhibit a very different behavior from those closer to the shore (see Fig. 3).

The net super-elevation of the mean groundwater in these sensors may be caused by the sloping beach favoring vertical infiltration/drainage, and swash zone run-up, as observed in coastal processes [START_REF] Turner | Tides, waves and the super-elevation of groundwater at the coast[END_REF].

Capacitive sensor

Sand-bed(beach)

-500

0 1 000 2 000 2.3 2.4 2.5 2.6 2.7 2.8 (1) (2) (3) Time(s) H 1 (m) 2.4 2.6 2.8 (1) (2) (3) H 2 (m) (1) (2)
(3)

H 3 (m) (1)
(2)

(3)

H 4 (m) 0 1000 2000 2.4 2.6 2.8 (1)
(2)

(3)

H 5 (m) Time(s) 0 1000 2000 (1)
(2)

(3)

H 6 (m) Time(s) 0 1000 2000 (1)
(2)

(3)

H 7 (m) Time(s) (a)

SIGNAL PROCESSING & ANALYZIS OF WATER LEVEL FLUCTUATIONS Analysis of Sensor No.1 (H 1 (t), entry boundary condition)

Water level fluctuations at sensor No.1 (H 1 (t)) reflect surface water levels and can be considered as the entry boundary condition with respect to all the other 'subsurface' sensors. The regular periodic wave with period T = 4 seconds produced at the wave generator, seems much less regular when it arrives at Sensor No.1, in the swash zone (see FIG. 4 and FIG. 5). To simplify such complex signals, we want to find the dominant periods of H 1 (t). Accordingly, we choose the following bimodal Fourier approximation for water level signal H 1 (t):

( ) ( ) ( ) 2 2 2 1 1 1 0 1 sin sin ϕ ω ϕ ω + + + + = t A t A H t H
(1)

FIG. 6. Reduced frequency spectrum of the water level fluctuations H 1 (t).

From FIG. 6, we can see clearly that period T 1 = 23.33 s prevails among the H 1 (t) signals. There are also three other periods which play important roles. So far, we consider that period T 1 = 23.33 s is the result of the size of the wave canal (we have analyzed independently the signals measured after the stop of the wave generator, and we have obtained the same results). On the other hand, period T 4 = 4.83 s is obviously close to the wave generator period (T 0 = 4 s).

We then used orthogonal multi-resolution wavelet analysis to verify the results of Fourier analysis and to obtain the corresponding amplitudes and phases for the dominant periodic waves. In FIG. 7, we can see that the sum of the dyadic wavelet component C7 (whose time scale is

s t T C 6 . 25 2 1 7 7 = Δ × = +
) and the dyadic wavelet component C5 (whose time scale is

s t T C 4 . 6 2 1 5 5 = Δ × = +
), agree well with the original signal. After that, we obtain the amplitudes (defined as the 90% confidence band) of the wavelet components C7 and C5: where tn * is the first 0-crossing of the signal (this method will be revised with a statistical identification of the phase in future). We obtain here:

FIG. 8. Wavelet analysis of signal H1(t): the dyadic components C7 & C5

We have now obtained all the coefficients for the analytical bimodal Fourier model of equation ( 1), as shown in Table 1. From FIG. 7, we can see that this 'analytical model' is a good approximation of the original signal, and is confirmed by wavelet analysis. The water in the tube of the capacitive sensor 7, furthest from the swash zone, is thought to be a direct measurement of 'groundwater'. From FIG. 9, it can be seen that signal H 7 (t) is totally different from H 1 (t): signal H 7 (t) clearly exhibits a slowly increasing stage (water filling) and a descending stage (water draining). The Fourier method is not directly suited for this type of strongly non periodic and non ergodic signal. Instead, we use first a moving average filter to remove the nonlinear trend, and then, we use Fourier to analyze the residuel of the original signal. The reduced Fourier spectra versus reduced frequencies of the detrended H 7 (t) are shown in FIG. 10. It can be seen that all the small period waves have disappeared; the remaining dominant period is T1 = 171 s, which is seven times longer than that of the H 1 (t) signal (T1 = 24 s).

In addition, we think that the two stages of curve of the H 7 (t) have exponential trends with different coefficients. We are currently studying this point in relation with groundwater flow models, and will discuss it in the near future.

CONCLUSIONS AND FUTURE WORK

This wave canal experiment was conducted in the frame of a European project, HYDRALAB-SANDS, in collaboration with the HYDRALAB-SANDS laboratory (Barcelona, Spain) and the OTE group at the IMFT laboratory (Toulouse, France). The experiment was especially designed to measure the erosion of the swash zone in a sandy beach, with periodic oscillations of water levels, using a wave generator. In this work, as members of the porous media group (GEMP), we have focused on a related problem: the effects of surface water waves and of swash zone processes on subsurface water in the sand beach, and the possible interactions between surface and subsurface oscillations.

We have instrumented the artificial beach of the canal with subsurface sensors (micropiezometers) to measure groundwater level fluctuations, and we have used signal processing techniques towards this goal. The results obtained so far, with spectral frequency methods and multi-resolution wavelet analyses, appear quite promising. In particular, two important periods, and their corresponding amplitudes and phases at the entry boundary were identified. A bimodal Fourier approximation of the signal was proposed. This yields a simplified version of the observed irregular water level fluctuations H 1 (t), which can be used as the entry condition for numerical simulations.

In addition, numerical simulations are currently being implemented in order to complement the experimental water level signal analyses and to compare them with various water flow models (a preliminary version of modeling results was presented in [START_REF] Wang | Oscillatory Flows through Porous Media: Free Surface Hydraulics, Wave Propagation, and Capillarity[END_REF]. The numerical models being used for these comparisons include:

FIG. 1 .

 1 FIG. 1. Schematic of the layout of the capacitive sensors in the swash zone (vertical axial section). Sensor N°1 is closest to the free water. FIG. 2. Photo of the sand beach with capacitive sensors / micro-piezometers at the HYDRALAB-SANDS wave canal (CIEM flume) in Barcelona. Incoming water waves are visible in the rear.

FIG. 3 .

 3 FIG. 3. Water levels H i (t) versus time at the 7 sensors (Test 1: 18 March 2008).

  Concerning the phases, we can directly measure them from FIG.8. A simple method was used at first, namely:

  FIG. 7. Wavelet analysis of signal H1(t): comparison of original signal, bimodalFourier signal, and 2-component wavelet.

  FIG. 9. Original signals H 7 (t) and its moving average

  (1) A 2D plane flow model based on the vertically averaged Dupuit-Boussinesq equation for unconfined groundwater flow (with fluctuating boundary conditions); (2) A 3D variably saturated flow model based on a generalized Richards' equation.

Table 1 . Coefficients of the 'analytical' bimodal approximation

 1

	Coefficients	(m)	(s)	(m)	(rad)
	Values	2.5112	24	0.0672	0.238
	Coefficients		(s)	(m)	(rad)
	Values		4.83	0.0524	0.982
	Methods	Average of the original signals Fourier Wavelet	Wavelet
	Analysis of Sensor No.7 (groundwater)

ACKNOWLEDGMENTS

This research has been conducted through a collaborative effort on a long wave canal experiment (SANDS/HYDRALAB, Barcelona, Spain) and in collaboration with the OTE group at IMFT Toulouse (D. Astruc, O. Eiff, et al., IMFT, Toulouse, France).