Christine Vauthier
email: christine.vauthier@u-psud.fr

Bjorn Persson

Peter Lindner

Bernard Cabane

Protein

Keywords: core-diffuse shell nanoparticles, mesh size, BSA, fibrinogen, C3, adsorption isotherm, dextran, poly(alkylcyanoacrylate)

Introduction

Colloidal particles are often used to carry molecules that are pharmaceutically active from the point of administration to a target site in the body. The requirements for such a particle are threefold (a) it should carry a sufficient number of active molecules; (b) it should avoid the body's mechanisms for recognition of foreign particles; (c) it should be able to deliver the active molecules to the target. In order to perform these functions, most colloidal carriers rely on a core-diffuse shell structure. Typically, the core is made of a hydrophobic polymer that dissolves or traps the active molecules. The diffuse shell (also called corona) is made of hydrophilic polymers that "hide" this hydrophobic core [START_REF] Vauthier | Methods for the preparation and manufacture of polymeric nanoparticles[END_REF].

Colloidal carriers that are injected into the blood stream find themselves in a concentrated protein solution. The most abundant protein, serum albumin, is present in blood at a concentration of 4%. Consequently, the first event that takes place when a particle is injected in the blood is the adsorption of proteins, mainly serum albumin. Subsequently, other proteins may either displace the bound serum albumins or bind to the absorbed serum albumin layers [START_REF] Olivier | Stability of orosomucoidcoated polyisobutylcyanoacrylate nanoparticles in the presence of serum[END_REF][START_REF] Cedervall | Detailed identification of plasma proteins adsorbed on copolymer nanoparticles[END_REF][START_REF] Noh | Volumetric interpretation of protein adsorption: competition from mixtures and the Vroman effect[END_REF]. Recognition and elimination of these foreign particles by the body defense mechanisms including macrophages may then occur through the absorption of specific proteins, e.g. the C3 protein of the complement system [START_REF] Sahu | Structure and biology of complement protein C3, a connecting link between innate and acquired immunity[END_REF]. Upon binding, the C3 protein will change conformation, expose a reactive site, and release a signaling molecule that triggers the chain of bio-chemical events called the complement activation cascade [START_REF] Law | The internal thioester and the covalent binding properties of the complement proteins C3 and C4[END_REF]. This will lead to the elimination of the particles by the macrophages [START_REF] Vonarbourg | Parameters influencing the stealthiness of colloidal drug delivery systems[END_REF].

There are indications that some chemical characteristics of the diffuse shell have an effect on complement activation. Indeed a chain length effect has been found for diffuse shell made of PEG or polysaccharides [START_REF] Vittaz | Effect of PEO surface density on long-circulating PLA-PEO nanoparticles which are very low complement activators[END_REF][START_REF] Bertholon | Complement activation by core-shell poly(isobutylcyanoacrylate)-polysaccharide nanoparticles: influences of surface morphology, length, and type of polysaccharide[END_REF]. Also, an effect of the grafting density of hydrophilic chains on the particle surfaces has been found in the case of PEG chains [START_REF] Vittaz | Effect of PEO surface density on long-circulating PLA-PEO nanoparticles which are very low complement activators[END_REF]. The nature of the hydrophilic chains may also be important. These effects may be caused by interactions of C3 with albumins that are already adsorbed [START_REF] Andersson | Binding of C3 fragments on top of adsorbed plasma proteins during complement activation on a model biomaterial surface[END_REF]. Indeed, since the absorption of the C3 complement protein takes place after that of serum albumin, it will be influenced by the amount of bound serum albumins, their configurations at the surface, and their accessibility. Thus, in order to design the diffuse shell for avoiding complement activation, we need to know more about the adsorption of albumin.

Recently we have synthesized a collection of nanometric-sized drug carriers through self-assembly of block copolymers. As a hydrophobic block we chose poly(isobutylcyanoacrylate) (PIBCA), which is a bioerodible and bioeliminable polymer that has already been used to deliver in vivo a number of drug molecules [START_REF] Vauthier | Design aspects of poly(alkylcyanoacrylate) nanoparticles for drug delivery[END_REF][START_REF] Nicolas | Synthesis of poly(alkylcyanoacrylate)-based colloidal nanomedicines[END_REF]. As a hydrophilic block, we chose dextran, which is a polysaccharide known to restrict protein adsorption [START_REF] Osterberg | Protein-rejecting ability of surface-bound dextran in end-on and side-on configurations: comparison to PEG[END_REF][START_REF] Monchaux | Development of dextran-derivative arrays to identify physicochemical properties involved in biofouling from serum[END_REF]. The selfassembly of these copolymers does yield particles with a core-diffuse shell structure that is determined by the respective lengths of the hydrophobic and hydrophilic blocks [START_REF] Bertholon | Complement activation by core-shell poly(isobutylcyanoacrylate)-polysaccharide nanoparticles: influences of surface morphology, length, and type of polysaccharide[END_REF][START_REF] Bertholon | Characterization of dextran-poly(isobutylcyanoacrylate) copolymers obtained by redox radical and anionic emulsion polymerization[END_REF]. By changing the conditions of polymerization, we have produced two types of particles that differ only by the core size and by the density and extension of the diffuse shell. Remarkably, these two types have very different effects on complement activation. This opens the possibility of finding how the characteristics of the diffuse shell control protein adsorption and complement activation.

In this paper we report characterizations of these polymer particles by Small Angle Neutron Scattering (SANS), measurements of the adsorption of the abundant blood proteins, serum albumin, through rocket-immunoelectrophoresis [START_REF] Laurell | Quantitative estimation of proteins by electrophoresis in agarose gel containing antibodies[END_REF] and radial immunodiffusion [START_REF] Mancini | Immunochemical quantitation of antigens by single radial immunodiffusion[END_REF], measurements of fibrinogen-induced aggregation through SANS, and measurements of the activation of the complement system, through 2-D immunoelectrophoresis [START_REF] Bertholon | Complement activation by core-shell poly(isobutylcyanoacrylate)-polysaccharide nanoparticles: influences of surface morphology, length, and type of polysaccharide[END_REF][START_REF] Boackle | Potentiation of factor H by heparin: a rate-limiting mechanism for inhibition of the alternative complement pathway[END_REF]. We attempt to answer the following questions:

(a) Does the diffuse shell limit protein adsorption, what is the location of the adsorbed proteins, and what is their configuration?

(b) What is the relation between the number of hydrophilic chains that protrude out of the core and the number of proteins that can be adsorbed? (c) Is there a relation between the number or the configuration of adsorbed proteins and the activation of the complement system?

Materials and Methods

Preparation of nanoparticles

PIBCA nanoparticles were prepared by redox radical emulsion polymerization (RREP) according to the method of Bertholon et al. [START_REF] Bertholon | Complement activation by core-shell poly(isobutylcyanoacrylate)-polysaccharide nanoparticles: influences of surface morphology, length, and type of polysaccharide[END_REF][START_REF] Bertholon | Characterization of dextran-poly(isobutylcyanoacrylate) copolymers obtained by redox radical and anionic emulsion polymerization[END_REF]. The polymerization initiated on dextran produces bloc-copolymers which self-assemble into nanoparticles with a core-diffuse shell structure.

Two dispersions were prepared named A and B, differing by the amount of initiator (dextran-cerium). Nanoparticles A were obtained in 8 mL of nitric acid 0.2M containing 0.137 g of dextran (molar mass 69300 Da). The solution was placed under vigorous magnetic agitation at 40°C and purged with nitrogen for 10 min. Then, 2 mL of a solution of cerium ammonium nitrate (0.08 M in nitric acid 0.2M) and 0.5 mL of isobutylcyanoacrylate (IBCA) were added successively and the polymerization was allowed to proceed for 1 h at 40°C. For nanoparticles B, the volume of nitric acid 0.2M was 9.3 mL, the amount of dextran was 0.0502g and the volume of cerium ammonium nitrate was 0.7 mL. All other conditions were the same.

Immediately after polymerization, the nanoparticle dispersions were cooled down to room temperature using an ice bath. They were purified by dialysis (Spectra/Por ® membrane 100 000 g/mol molecular weight cut off) against 1 L of water 4 times to remove unreacted reagents and to raise the pH to a neutral value. Further purification included a first centrifugation at 720×g for 10 min followed by a second centrifugation at 17000×g for 15min to remove any aggregates. After the second centrifugation, the lower part of the supernatant (340 µl) was collected as fractions A middle and B middle respectively and the upper part of the supernatant (600 µl) as fractions A top and B top respectively. The volume fractions of the dispersions were around 1%.

Particle sizes and structures

Quasi-elastic light scattering (QELS).

The hydrodynamic radii of the nanoparticles were measured through QELS using a Zetasizer ZS90 instrument (Malvern, France). Measurements were performed at 25°C at a scattering angle of 90°. The intensity correlation function was fitted through the instrument software to yield a volumeweighted distribution of particle sizes. From this distribution we calculated the total volume and total surface area of the nanoparticles, and the radius that describes the corresponding hydrodynamic volume/surface ratio. This radius is identical to the z-averaged radius of the particles defined by equation 1.

R z = Σ N i R i 3 / Σ N i R i 2 [ 1 ] .
Dispersions were diluted in Milli ® Q water filtered over a 0.22 µm membrane prior to the measurement.

Scanning electron microscopy (SEM).

Images of freeze-dried nanoparticle dispersions were obtained using a scanning electron microscope LEO 1530 (LEICA) equipped with a Gemini column. Prior to observation, freeze dried samples were mounted on supports and coated with a 2nm Pt/Pd layer using a Cressington sputter coater 208HR apparatus (Cressington, France) operating under argon atmosphere. The sizes of more than 300 individual nanoparticles were measured to determine the mean radius and the parameters of the size distribution.

Small Angle Neutron Scattering (SANS).

Scattering patterns from liquid nanoparticle dispersions were obtained using the instrument D11 at the ILL. The experiments yielded scattering patterns consisting of intensities as a function of scattering vector q. Since the dispersions were isotropic, the scattering patterns were averaged over all directions of q, yielding spectra of intensity I vs. magnitude q of the scattering vector, which is related to wavelength  and scattering angle  by q = (4/) sin(/2). The range of q values was 6 x 10 -3 to 9 x 10 -2 nm -1 . In this range, the interference patterns probe variations of the density of scattering length (r) with a resolution of 10 nm. Scattering is then produced by the difference between the scattering density of a particle, (r), and that of the solvent,  s . For the characterization of the particles, the dispersions were made in H 2 O, as the difference of scattering density between the particles and H 2 O was sufficient to produce strong scattering [START_REF] Vauthier | Configuration of bovine serum albumin adsorbed on polymer particles with grafted dextran corona[END_REF]. Spectra were fitted with a calculated curve for a log-normal distribution of spheres. The z-averaged value (R z ) was calculated using equation 1. Other experiments were made with dispersions made in H 2 O-D 2 O mixtures that matched the scattering density of the PIBCA-dextran nanoparticles, in order to enhance the contrast of the adsorbed proteins [START_REF] Vauthier | Configuration of bovine serum albumin adsorbed on polymer particles with grafted dextran corona[END_REF].

Composition of the nanoparticles

The monomer compositions of the PIBCA-dextran copolymers were determined through ( 1 H) NMR spectroscopy. The copolymers were dissolved at 40 °C in dimethyl-d 6 -sulfoxide (DMSO, d 6 ) (Carlo Erba) at the concentration of 20 mg/mL. Spectra were then recorded on a 300 MHz Brucker instrument (Brucker, France). The composition was deduced from the spectra by calculating the ratio between the integral of dextran peaks (4.3 -5 ppm) and that of the CH peak of PIBCA (1.8 -2.0 ppm) [START_REF] Pirker | Characterization of polybutyleyanoacrylate nanoparticles. part II: determination of polymer content by NMR-analysis[END_REF]. The molecular weight of the PIBCA part of the copolymer was calculated from the composition in dextran and PIBCA deduced from the NMR spectra and the known molecular weight of dextran (69 300 g/mol), assuming that the copolymer was composed of one chain of PIBCA and one chain of dextran as shown by Bertholon at al. [START_REF] Bertholon | Characterization of dextran-poly(isobutylcyanoacrylate) copolymers obtained by redox radical and anionic emulsion polymerization[END_REF].

BSA adsorption through immunomethods.

Nanoparticles at a volume fraction of 0.5% were incubated with different concentrations of BSA in 10 mM phosphate buffer for 3 hours at 37 °C. After incubation, the amount of non-adsorbed BSA was determined using immunochemical methods including immunoelectrophoresis [START_REF] Laurell | Quantitative estimation of proteins by electrophoresis in agarose gel containing antibodies[END_REF] and radial immunodiffusion [START_REF] Mancini | Immunochemical quantitation of antigens by single radial immunodiffusion[END_REF] as previously described [START_REF] Vauthier | Configuration of bovine serum albumin adsorbed on polymer particles with grafted dextran corona[END_REF].

In both cases, agarose gel plates (12 cm×8.5 cm) were prepared on Gelbond ® films for agarose gel (GE healthcare, BioScience, Sweden). The agarose solution (13 mL) at a concentration of 1% contained 0.3 mL of the bovine serum albumin antisera (Sigma, France) diluted at 1/5 in a saline phosphate buffer (10 mM, NaCl 140 mM, KCl 25 mM, pH 7.5). For the radial immunodiffusion technique, the gel was prepared in the saline phosphate buffer (10 mM, NaCl 140 mM, KCl 25 mM, pH 7.5) whereas tricine buffer (lactate calcium 1 mM, Tris 63 mM, Tricine 27 mM, pH 8.6) was used to prepare gels for the immunoelectrophoresis method. Wells holding 5µL sample were formed using a 2mm diameter punch on the gel plates. After deposition of the samples in the wells (5µL) including standard solutions of BSA and nanoparticles incubated with the different concentrations in BSA, gels were placed in a humid chamber and let to diffuse in a quiet place for 48 h at room temperature in the case of the radial immunodiffusion technique. The conditions for the immunoelectrophoresis were 18 h, 230 V, 12mA (Electrophoresis power supply EPS 600, Amersham, Pharmacia Biotech, Orsay, France) using Tricine buffer as the running buffer for the electrophoresis performed in a Pharmacia LKB Multiphor II apparatus (Amersham, Pharmacia Biotech, Orsay, France). At the end of both types of experiments, the gels were dried using Watmann ® filter papers and stained with coomassie blue to reveal of the formation of BSA-antibody immunoprecipitate. Each gel contained a set of 5-6 standard solutions of BSA of concentrations ranging from 20 to 900µg/mL for internal calibration purpose. In the case of the radial immunodiffusion technique, the calibration curve is a linear relationship between the square of the diameter of the immunoprecipitation ring and BSA concentration in the well for BSA concentrations ranging from 100 to 900 µg/mL. In the case of the immunoelectrophoresis, the calibration curve is a linear relationship between the height of the immunoprecipitation peak and the concentration in BSA in the well in the range of BSA concentrations comprised between 20 and 200 µg/mL. In both cases, calibration curves with correlation coefficients above 0.99 were obtained with a good reproducibility.

Fibrinogen induced aggregation of the nanoparticles

Phosphate buffer 100mM, pH 7.4 containing different concentrations of fibrinogen (human fibrinogen from Sigma) was added to nanoparticle dispersions at a volume ratio of 1/10. Final concentrations of fibrinogen ranged from 0 to 2mg/mL. The behaviour of the dispersion during the addition of the fibrinogen was observed for eventual precipitation. The microscopic aspects of the dispersions containing 2mg/mL fibrinogen were observed with an optical microscope using the phase contrast mode (Olympus BH2). Dispersions that appeared homogeneous by microscopic observations were characterized by QELS and SANS.

Activation of the complement system

Activation of the complement system induced by the nanoparticles was evaluated using a 2D immunoelectrophoresis method as described in previous publications [START_REF] Bertholon | Complement activation by core-shell poly(isobutylcyanoacrylate)-polysaccharide nanoparticles: influences of surface morphology, length, and type of polysaccharide[END_REF][START_REF] Boackle | Potentiation of factor H by heparin: a rate-limiting mechanism for inhibition of the alternative complement pathway[END_REF].

Briefly, the nanoparticles (400 cm² in 100 µl, as calculated from the hydrodynamic radius of the nanoparticles) were incubated with 50 µl human serum and 50 µl veronal buffer containing 0.15 mM calcium chloride and 0.5 mM magnesium chloride for 1 hour at 37 °C. After incubation, 5 μL of each sample was subjected to a first electrophoresis on a 1% agarose gel. The second-dimension electrophoresis was carried out on Gelbond ® films in 1% agarose gel plates containing a polyclonal antibody to human C3 (Complement C3 antiserum rose in goat, Sigma, France), recognizing both C3 and C3b. The films were finally dried and stained with Coomassie blue to reveal the presence of C3 and C3b which have reacted with the antibody (Sigma).

The complement activation factor was calculated from the ratio of the area of the peak attributed to C3b over the sum of the areas of the peaks attributed to C3b and to C3. This ratio was then normalized on a scale ranging from 0 to 100 in which 100 indicated total activation and 0 the spontaneous activation measured in absence of nanoparticles.

Results

Characterization of the nanoparticles

In order to understand what characteristics of the nanoparticles determined protein adsorption, we determined their geometric dimensions and their compositions. From these data we calculated, for each type of nanoparticle dispersion, the average thickness of the diffuse shell and the surface density of chains in the diffuse shell at the core surface.

Particle radii according to SEM, SANS and QELS.

SEM images of the particles show that they are globular and polydisperse in sizes (Figure 1). In the case of the B particles, we were able to measure individual particle radii, and to obtain the distribution of these radii (Table 1). In the case of type A particles the smaller particles were not imaged in SEM. 2.

For type A dispersions, the scattered intensity follows Guinier's law at small q values and then continues with the q -4 decay predicted by Porod's law for dense particles, without any of the oscillations that are expected for monodisperse spheres. These features are the usual behavior when there is a single population of nanoparticles with sizes broadly distributed around a mean value, since each spectrum is the sum of intensities scattered by all particles in the dispersion [START_REF] Lindner | Neutrons, X-Rays and Light: Scattering methods applied to soft condensed matter[END_REF]. Accordingly, we fitted each spectrum with the calculated scattering curves for spheres with lognormal distributions of radii. From these distributions we calculated the specific surface area, for comparison with protein adsorption measurements, and the corresponding radius, R z , for 1). For B middle the fit is obtained with a similar distribution plus a population of larger particles (parameters in Table 1).

comparison with the hydrodynamic radius determined through QELS (Table 1). As expected, nanoparticles isolated from the lower part of the supernatant (fractions A middle ) were of larger size than those isolated from the top part (A top ).

The spectrum of the B middle nanoparticles is different: it has a power-law decay at low q values which is characteristic of a population of aggregated particles. Accordingly, we fitted this spectrum with the scattering curve calculated for a log-normal distribution of spheres plus a population of larger particles (Table 1). This was consistent with QELS measurements presented next.

QELS measurements yield the distribution of hydrodynamic radii of nanoparticles (Figure 3). For A middle , A top and B top ,, QELS shows a single population of nanoparticles with a lognormal distribution, from which we calculated the z-averaged hydrodynamic radii (Table 1). These radii characterize the Brownian motions of particles with their diffuse shells and the solvent that is trapped by the diffuse shells. Hence the hydrodynamic thickness of the diffuse shell can be calculated as a difference between the average hydrodynamic radius and the average core radius. However, since the populations of nanoparticles are polydispersed, the results from different methods can be compared only if they make the same average of the distribution of radii. Thus, we compared the z-averaged diffuse shell radius calculated from the distribution of particle sizes measured through QELS with the z-averaged core radius calculated from the distribution that fits the SANS spectrum. The difference of these radii was taken as the diffuse shell thickness (Table 1). We found that this thickness was larger than the end-to-end distance of dextran polymers that have the same molar mass M w as the dextran block of the copolymers used here. Indeed, extensive light scattering measurements on dilute aqueous dextran solutions yield the law given in equation 2 for the radius of gyration R g , in nm, as a function of the molar mass M w in Da [START_REF] Ioan | Structure properties of dextran. 2. dilute solution[END_REF].

R g = 0.4 (M w ) 0.3 [2]
The low value of the exponent is due to the fact that dextran polymers are branched. According to this law, the radius of gyration of the dextran polymers used here should be 11 nm. For a Gaussian chain, the corresponding end-to-end distance would be 28 nm, and for a branched polymer it would still be about the same. As shown in Table 1, the calculated value of the diffuse shell thickness of A middle nanoparticles (49 nm) is larger than this length, indicating that the dextran chains were stretched as a result of their confinement in the diffuse shell. In contrast, for the smaller nanoparticules (Atop and Btop), the diffuse shell thickness (respectively 21 and 17nm) is smaller than this value. In this case the small thickness results from the high curvature of the nanoparticle surfaces [START_REF] Garvey | A comparison of the adsorbed layer thickness obtained by several techniques of various molecular weight fractions of poly(vinyl alcohol) on aqueous polystyrene latex particles[END_REF][START_REF] Lafuma | Bridging of colloidal particles through adsorbed polymers[END_REF].

In the case of Bmiddle nanoparticles, the distribution of hydrodynamic radii was bimodal with a population of large aggregates (2-4 µm) (Figure 3). These aggregates contributed a very small fraction of the surface area but to a larger fraction of the light scattering intensity. Consequently, the precision of surface area determinations can be considered to be comparable to that of the other measurements.

Composition of the particles

The compositions in dextran and PIBCA of the copolymer forming the nanoparticles were determined by NMR. NMR spectra from the A and B type dispersions were similar to those obtained in previous work [START_REF] Bertholon | Characterization of dextran-poly(isobutylcyanoacrylate) copolymers obtained by redox radical and anionic emulsion polymerization[END_REF]. The composition of each copolymer was deduced from the integration of peaks due to the characteristic protons of dextran and PIBCA (Table 2). The fraction of PIBCA found in type A copolymers was much lower than that found in type B copolymers. This result agrees with the fact that type A copolymers were prepared with a higher concentration of dextran in the original solution. In addition, there was also a smaller difference between the middle and top fractions of each dispersion. In a previous work [START_REF] Bertholon | Characterization of dextran-poly(isobutylcyanoacrylate) copolymers obtained by redox radical and anionic emulsion polymerization[END_REF], we have shown that the copolymer was composed of one chain of dextran and one chain of PIBCA. Knowing the molecular weight of dextran (69300 g/mol), and the composition of the copolymer we calculate the degree of polymerization and the molecular weight of the PIBCA moiety. Results summarized in table 2 showed that the Mw of the PIBCA part of the type B copolymers were much larger than those in type A copolymers (Table 2).

We can then calculate the number N of PIBCA chains in the core of a nanoparticle according to the core volume V core and the PIBCA chain volume v P-chain or the mass per chain and the specific mass of PIBCA d = 1300 kg/m 3 : [START_REF] Cedervall | Detailed identification of plasma proteins adsorbed on copolymer nanoparticles[END_REF] This can be combined with the core surface area to yield the area per chain at the core surface, or its inverse, the surface density of dextran chains that are tied to the core:

N  V core v P  chain  4  3 R 3 v P  chain
a P  chain  S core N  3v P  chain R [ 4 ]
In this equation, the radius R is that corresponding to the specific surface area, i.e. the ratio of the total volume of all the cores to the total surface area of all the cores. This radius is given as "R z " in Table 2. The resulting values of the surface area per dextran chain are given in Table 2. These values show that the B type particles have a very large surface area per chain, due to the very high molar mass of their PIBCA chains.

Finally, we calculate the volume fraction of dextran chains in the diffuse shell according to the volume of one dextran chain: [START_REF] Sahu | Structure and biology of complement protein C3, a connecting link between innate and acquired immunity[END_REF] We can also calculate the average mesh size  of the diffuse shell according to the scaling law [START_REF] Cabane | Mesh size of aqueous TMOS gels[END_REF]

 dextran  N v D  chain V corona
 b   dextran    1 d  d f         [ 6 ]
where b is the length of the statistical segment of the dextran chain (b = 1 nm) [START_REF] Guizard | Molecular and crystal structure of dextrans: a combined electron and X-ray diffraction study. 1. the anhydrous high-temperature polymorph[END_REF], d is the space dimension (d = 3) and d f is the fractal dimension of the dextran polymers (approximately d f = 2) [START_REF] Ioan | Structure properties of dextran. 2. dilute solution[END_REF].

The values of  dextran and  are also listed in Table 2. In the case of the A top particles, the calculated values of  dextran and  were excessively high, due to the very low degree of polymerization of the PIBCA block. Since this degree of polymerization is an average, it is likely that copolymers with the smaller PIBCA blocks remained in the aqueous phase, and that the A top nanoparticles contained less dextran than assumed by equations /3/ and /5/.

Adsorption of BSA

Adsorption isotherms through radial immunodiffusion and rocket immunoelectrophoresis:

The adsorption of BSA on the nanoparticles at a volume fraction of 0.5% in aqueous dispersion was determined through two methods: radial immunodiffusion and rocket immunoeletrophoresis. Both methods measure the concentration of BSA that remains in the dispersion upon equilibrium with the nanoparticles. Although the analysis is performed without previous separation of the nanoparticles from the incubation medium containing BSA, only the free BSA will be able to penetrate in the gel during either radial diffusion or electrophoresis and will be quantified by the two methods. As shown in previous work [START_REF] Vauthier | Configuration of bovine serum albumin adsorbed on polymer particles with grafted dextran corona[END_REF][START_REF] Olivier | Preparation and characterization of biodegradable poly(isobutylcyanoacrylate) nanoparticles with the surface modified by the adsorption of proteins[END_REF], adsorption equilibrium was reached after 1 hour of incubation and both methods yield very similar adsorption isotherms. The amount of adsorbed BSA was calculated for each initial concentration of BSA in the solution, and then the results were converted into adsorption isotherms. The isotherms given by each type of nanoparticles have a similar shape (Figure 4) with a first section of high affinity binding (i.e., the amount adsorbed equals the initial amount) followed by a plateau that indicates saturation of the nanoparticle surfaces (i.e., the adsorbed amount saturates regardless of the total amount of BSA). It was found that the concentration of the adsorbed BSA at the beginning of the plateau varied slightly for the different nanoparticles considered in this work (Table 3). These values were of the same order of magnitude than that found in a previous work considering the same type of nanoparticles prepared by another polymerization method [START_REF] Vauthier | Configuration of bovine serum albumin adsorbed on polymer particles with grafted dextran corona[END_REF][START_REF] Olivier | Preparation and characterization of biodegradable poly(isobutylcyanoacrylate) nanoparticles with the surface modified by the adsorption of proteins[END_REF]. They were close to those given in the literature for different types of surfaces, excepted for those which were coated with a dense brush of polyethylene glycol [START_REF] Gaucher | Effect of poly(N-vinyl-pyrrolidone)-block-poly(D,Llactide) as coating agent on the opsonization, phagocytosis, and pharmacokinetics of biodegradable nanoparticles[END_REF][START_REF] Bosker | BSA adsorption on bimodal PEO brushes[END_REF][START_REF] Roach | Surface tailoring for controlled protein adsorption: effect of topography at the nanometer scale and chemistry[END_REF][START_REF] Norde | BSA structural changes during homomolecular exchange between the adsorbed and the dissolved states[END_REF].

Structural effects of adsorbed BSA:

The amounts of adsorbed BSA were too small (in comparison with the polymer mass per nanoparticle) to be determined through SANS. Indeed, attempts were made to measure the scattering of the adsorbed BSA using the contrast match technique, as in previous work [START_REF] Vauthier | Configuration of bovine serum albumin adsorbed on polymer particles with grafted dextran corona[END_REF]. SANS experiments were performed with dispersions in blends of H On the other hand, SANS at full contrast and QELS were used to evidence structural effects such as aggregation or dissociation of particles that could be caused by the adsorption of BSA. The main effect was found with the dispersion B middle , which was initially aggregated (figures 2 and 3). Upon addition of BSA, the QELS data indicated that the population of very large aggregates (radii 2-4 µm) was strongly reduced, and the population of nanoparticles shifted to lower sizes (Figure 5). Similarly, the average radius measured through SANS at full contrast also shifted to lower values. For all other dispersions (A middle , A top and B top) , there were no effects of BSA adsorption: the distributions of hydrodynamic radii remained the same, and the spectra from dispersions with BSA were nearly identical to those of the initial nanoparticles. Vertical axis: populations of particles P(R i ), normalized to 100 %. Note the reduction in magnitude of the population of very large aggregates and the shift to lower radi of the main population. For all other dispersions, the addition of BSA had no effect on the measured radii (see the text).

Interactions of the nanoparticles with fibrinogen

Addition of fibrinogen in type B dispersions induced a strong precipitation of the nanoparticles. In contrast, type A dispersions remained homogeneous during and after addition of fibrinogen. Observations through optical microscopic confirmed that large precipitates were formed in type B dispersions while type A dispersions which remained homogenous at the macro-and microscopic scales (Figure 6). The analysis of the type A dispersions by QELS revealed only a slight increase in the hydrodynamic radius of the nanoparticles. After the addition of 2 mg/mL of fibrinogen, the hydrodynamic radius of dispersion A middle increased from 112 to 123 nm while that of dispersion A top increased from 60 to 66 nm. SANS also detected a slight aggregation of A top , due to the presence of oligomers (up to 5 particles per aggregate) but not in the case of A middle .

Figure 6: Macroscopic and microscopic images of the nanoparticle dispersions as they appeared right after the addition of fibrinogen at a concentration of 2 mg/mL to the different dispersions of nanoparticles. Scale bar: 50 µm.

Activation of the complement system.

Finally, the capacity of the different nanoparticles to activate the complement system was measured by analyzing the C3 protein of the complement in serum by 2D immunoelectrophoresis. The two fractions of nanoparticles A induced a similar and weak activation of the complement system shown on the gel by the larger peak on the left side which corresponds to the native C3 protein. The complement activation factor was around 30.1 ± 0.4 and 27 ± 3 for nanoparticles A middle and A top respectively (Figure 7). The electrophoregrams of nanoparticles B middle and B top clearly showed that the two fractions of the nanoparticles B have a very different capacity to activate the complement system. Fraction B middle induced an almost complete activation of the complement shown by the almost absence of the peak of C3 protein on the left side of the gel and the presence of a large peak on the right side corresponding to the activated form of the protein C3, i.e. C3B. The complement activation factor (95 ± 6) was closed to the maximum value (100) (Figure 7). The presence of two peaks of proteins on the electrophoregram of the serum incubated with nanoparticles B top indicated that the activation of the complement system produced by these nanoparticles was much lower than that found for nanoparticles B middle . The complement activation factor was much lower (41 ± 7) but remained significantly higher than those obtained with nanoparticles A middle and A top. .

Discussion

The aim of this discussion is to deal with the questions raised in the introduction, regarding the effects of the diffuse shell on the adsorption of small proteins (BSA), fibrinogen, and the larger proteins that trigger the activation of the complement system. The discussion is based on the characteristics of the diffuse shells (listed in Table 2), the characteristics of the proteins (listed in Table 4 below), the measured adsorption of BSA (Table 3), the occurrence of fibrinogen-induced aggregation and the measurements of complement activation. Not find yet BSA 3GHG [START_REF] Id 3ghg Kollman | Crystal structure of human fibrinogen. the protein data bank[END_REF] 2A73 [START_REF] Id 2a ; Janssen | Structures of complement component C3 provide insights into the function and evolution of immunity. the protein data bank[END_REF] *calculated from the amino acid sequence

Does the diffuse shell limit the adsorption of small proteins such as BSA?

We have measured the adsorption of BSA on nanoparticles that have very different diffuse shells: Atype diffuse shells have a very high surface density of dextran chains (spaced by about 2 nm); B-type diffuse shells have a low surface density of dextran chains (spaced by about 6 nm). Yet all these particles adsorb a substantial amount of BSA, comparable to the amounts adsorbed on other surfaces [START_REF] Vauthier | Configuration of bovine serum albumin adsorbed on polymer particles with grafted dextran corona[END_REF][START_REF] Roach | Surface tailoring for controlled protein adsorption: effect of topography at the nanometer scale and chemistry[END_REF][START_REF] Norde | BSA structural changes during homomolecular exchange between the adsorbed and the dissolved states[END_REF][START_REF] Norde | The adsorption of human plasma albumin and bovine pancreas ribonuclease at negatively charged polystyrene surfaces: 1 adsorption isotherms: effects of charge, ionic strength, and temperature[END_REF][START_REF] Forcini | Surface enrichment of proteins at quartz/water interfaces: a neutron reflectivity study[END_REF][START_REF] Do Serro | Bovine serum albumin adsorption on titania surfaces and its relation to wettability aspects[END_REF][START_REF] Verrecchia | Adsorption/desorption of human serum albumin at the surface of poly(lactic acid) nanoparticles prepared by a solvent evaporation process[END_REF]. Hence these diffuse shells do not prevent the adsorption of small proteins. Still, there are differences in the adsorption isotherms of the 4 types of nanoparticles. In order to interpret these differences, it is instructive to use a thermodynamic model for the adsorption. The simplest one is the Langmuir model, which assumes equilibrium between a solution of free proteins and a collection of independent adsorption sites at the nanoparticle surfaces. The equilibrium adsorption is ruled by two parameters: the affinity  of the protein for the surface sites, which has the dimensions of an inverse concentration, and the saturation value of the adsorption,   (1-), where   is the adsorbed amount for a full protein monolayer, and  is the fraction of the surface area that is unavailable for adsorption because of the dextran chains. The model yields the following equation for the adsorbed amount, , as a function of the concentration  of free protein in the solution (equation 7).

   0 1     1  [START_REF] Vonarbourg | Parameters influencing the stealthiness of colloidal drug delivery systems[END_REF] In order to use this equation, we must determine   , and for this we must make an assumption regarding the configuration of the adsorbed proteins. BSA can be approximated as a prism-shaped object, with dimensions 8.4 x 8.4 x 3.8 nm 3 [START_REF] Yampolskaya | Proteins at fluid interfaces: adsorption layers and thin liquid films[END_REF]. Adsorption in a "flat" configuration requires a free area of 70 nm 2 , which is certainly not available at the surfaces of the A-type particles, and rather unlikely at the surfaces of the B-type particles. Adsorption in an "edge" configuration requires a free area of 26 nm 2 , which may be more easily found if the adsorption site need not be circular (see below). In the following, we assume that BSA is adsorbed on all particles in the "edge" configuration. A full monolayer in this configuration would contain   = 3.66 mg/m 2 of adsorbed protein. With this choice, the Langmuir model parameters are as given in Table 3 above. Accordingly, the fraction (α) of the core surface that is unavailable for adsorption is only 0.2 in the case of A middle , and 0.7 in the case of A top .

How do the BSA molecules manage to adsorb on surfaces that already have a high density of hydrophilic chains? The first step in protein adsorption is the diffusion of the protein through the diffuse shell to the surface. This diffusion may be prevented if the overall dimensions of the protein are much larger than the mesh size of the diffuse shell. Thus, the dimensions of BSA (Table 4) must be compared with the average mesh sizes of the diffuse shells (Table 2). For type A particles, the average mesh size is  = 4 nm, and there are of course considerable fluctuations around this value. Therefore, diffusion of BSA through the mesh is difficult but certainly not impossible. For type B particles, the average mesh sizes are  = 8 nm and 47 nm, and therefore diffusion of BSA through these diffuse shells is not restricted. In case of type B particles, the mesh size (47 nm) of the dextran brush is of the same order of magnitude than the thickness of the diffuse shell (48 nm). Completely free path from the end of the diffuse shell to the surface of the core may exist on the surface of this nanoparticle which can give almost free access of the core surface to proteins. The next step is the binding of the protein to the core surface. At first sight, it appears that the surface is too crowded with dextran chains for this to occur. For A middle particles, the area per chain at the core surface is only 3.9 nm 2 and for A top it is 2.8 nm 2 (Table 2). The required area for a BSA macromolecule adsorbed in the "edge" configuration is much larger, equal to 26 nm 2 . A simple statistical calculation indicates that a BSA macromolecule is very unlikely to find an area of this magnitude available for adsorption at the core surface. Consider the insertion of an object with area S 1 into a system with area S having N randomly distributed "hard" points. The density of points on the surface, ρ, is given in equation 8.

  N S

. [START_REF] Vittaz | Effect of PEO surface density on long-circulating PLA-PEO nanoparticles which are very low complement activators[END_REF] The probability of a successful insertion, P insert (where the object does not overlap any of the points) is given by equation 9

N N insert N S S S P                 1 1 1 1  [ 9 ]
For a large surface with many "hard points" (N∞) this yields:

P insert  exp  S 1   [10]
The dimensionless argument of the exponential is the mean number of points per inserted disc. The free energy difference gives a measure of the process of inserting macromolecules of different area in the presence of these points. Using the experimental numbers, we find a probability of insertion equal to 1x10 -3 in the case of A middle particles and even lower for A top . (Table 5). A similar mismatch has already been observed for other particles with hydrophilic diffuse shells [START_REF] Gaucher | Effect of poly(N-vinyl-pyrrolidone)-block-poly(D,Llactide) as coating agent on the opsonization, phagocytosis, and pharmacokinetics of biodegradable nanoparticles[END_REF][START_REF] Bosker | BSA adsorption on bimodal PEO brushes[END_REF][START_REF] Oksuka | Surface characterization of functionalized polylactide through the coating with heterobifunctional poly(ethylene glycol)/polylactide block copolymers[END_REF]. However, this mismatch could be explained in different ways:

(i) -The BSA macromolecules can change conformations, which make it possible for them to fit into crowded areas. Indeed it is well known that BSA does not retain its native conformation upon adsorption [START_REF] Andersson | Binding of C3 fragments on top of adsorbed plasma proteins during complement activation on a model biomaterial surface[END_REF][START_REF] Norde | BSA structural changes during homomolecular exchange between the adsorbed and the dissolved states[END_REF][START_REF] Roach | Interpretation of protein adsorption: surface-induced conformational changes[END_REF][START_REF] Shang | pH-dependent protein conformational changes in albumin: gold nanoparticle bioconjugates: a spectroscopic study[END_REF][START_REF] Wangoo | Interaction of gold nanoparticles with protein: a spectroscopic study to monitor protein conformational changes[END_REF]] (ii) -The surfaces of albumin macromolecules have "patches" of positive electrical charges that are attracted to negative charges at the nanoparticle core surface [START_REF] Id 1e ; Bhattacharya | Binding of the general anesthetics propofol and halothane to human serum albumin high resolution crystal structures. the protein data bank[END_REF]. (iii) -The BSA macromolecules can take conformations that make it possible for them to bind to the diffuse shells of dextran.

We conclude that the diffuse shells of dextran are not able to prevent the adsorption of small flexible proteins, even when the density of chains within the diffuse shell is quite high

Does the diffuse shell limit the adsorption of larger proteins?

Fibrinogen is a large protein that binds to "foreign" surfaces and causes them to aggregate through a bridging mechanism [START_REF] Sit | Surface-dependent differences in fibrin assembly visualized by atomic force microscopy[END_REF]. Hence, resistance to aggregation by fibrinogen is a good predictor of resistance to adsorption of large proteins. In this respect, the two particle types are quite dissimilar. Type B particles were strongly aggregated by fibrinogen, whereas A top are only weakly aggregated, and A middle not at all. These differences are in line with the protection of the particle cores by dextran chains.

First, the diffusion of fibrinogen through the diffuse shell of dextran depends on its dimensions (a thin cylinder with diameter 3.2 nm and length 47 nm) (Table 4). The diameter is comparable or smaller than the mesh size of the diffuse shell for all particles, but the length is much larger. Hence, diffusion of fibrinogen through the diffuse shell is not restricted if it diffuses along its length. Next, the binding of a fibrinogen macromolecule requires an area of about 10 nm 2 , compared with an area per dextran chain of 3 to 4 nm 2 for A particles and 30 nm 2 per dextran in B particles (table 2). From the statistical argument given above, we find an insertion probability of 0.06 for A middle particles and 0.7 on B middle particles (Table 5). Hence the adsorption of fibrinogen is indeed prevented by high surface density of dextran chains in the case of type A particles, but not in the case of type B particles. This is in good agreement with the observation of fibrinogen induced aggregation in the case of B particles only.

Complement C3 protein is also a large protein (molar mass 180000) with dimensions 15.2 x 9 x 8.4 nm 3 . The adsorption of C3 is the first event that triggers the activation of the complement cascade [START_REF] Sahu | Structure and biology of complement protein C3, a connecting link between innate and acquired immunity[END_REF][START_REF] Law | The internal thioester and the covalent binding properties of the complement proteins C3 and C4[END_REF]. The dimensions of C3 are larger than the mesh size of type A diffuse shells, but smaller than those of type B diffuse shells. As in the case of BSA, diffusion through the diffuse shells of type A particles may be difficult, but not impossible due to the fluctuations of dextran chain conformations. However, the binding of C3 requires an area of 80 nm 2 . The probability of finding an area of this magnitude at the nanoparticle surfaces is practically zero for type A particles (Table 5). On the other hand, this insertion probability at the core surface is 0.1 for B middle , and 0.05 for B top (Table 5).

Thus, we have two factors that may explain the differences in complement activation between the nanoparticles. Both yield a satisfactory correlation. Figure 8a presents the correlation between diffuse shell mesh size and complement activation, while Figure 8b presents the correlation between the insertion probability at the core surface and complement activation. The correlation appears surprisingly good for the mesh size, and worse for the insertion probability at the core surface. A possible interpretation for this effect is that the C3 protein does not need to reach the actual core surface in order to trigger complement activation. Indeed, the dextran diffuse shell may contain albumin macromolecules that have changed conformations in order to bind to dextran chains. These bound albumins may be recognized by the C3 proteins and in this way trigger the complement cascade.

Conclusion

As presumed, the characteristics of the diffuse shells determine the interactions of the core-diffuse shell nanoparticles with serum proteins. The three investigated proteins are very different, and their behaviors are not at all the same. BSA diffuses through the diffuse shell and binds at the core surface even when the density of hydrophilic chains is quite high. This may be due to conformational flexibility of the protein and to attractions between opposite charges located at the protein surface and at the core surface. Fibrinogen manages to diffuse through the diffuse shell because it has the shape of a long cylinder. However, its adsorption at the core surface is restricted by the density of hydrophilic chains. The binding of fibrinogen to neighboring nanoparticles leads to the formation of aggregates of the nanoparticles. We also measured the activation of the complement cascade which is triggered by adsorption of protein C3. From these measurements, we inferred that C3 is repelled by diffuse shells that have a dense mesh of hydrophilic chains. If it manages to diffuse through this mesh, then it may bind to albumins that are already bound to the core surface or to the diffuse shell. In this case, the complement cascade is activated. In order to prevent aggregation caused by fibrinogen and recognition by the C3 protein of the complement system, it is necessary to keep these two proteins away from the core surface and from small proteins which adsorbed first during the opsonization process. This requires diffuse shells that have a very high density of hydrophilic chains.

Figure 1 :

 1 Figure 1: Scanning electron micrographs of Type B nanoparticles. Lyophilized powder coated with a 2 nm thick Pt/Pd layer. Scale bar = 200 nm.

Figure 3 .

 3 Figure3. Distributions of hydrodynamic radii for the nanoparticles according to QELS. Horizontal axis: hydrodynamic radii R i . Vertical axis: populations of particles P(R i ), normalized to 100 %. In each graph, the blue (short-doted line) curve is the volume-weighted distribution, obtained from the instrument software. The red (long-doted line) curve is the surface-weighted distribution, and the green (solid line) curve is the distribution of volume/surface ratios, both calculated from the volume-weighted distribution. The average radius calculated from the ratio of total volume/total surface is the zaverage hydrodynamic radius R z , which is then compared with the core radius R z * extracted from TEM or R z ** extracted from SANS.

Figure 4 :

 4 Figure 4: Adsorption isotherms of BSA on the different preparations of nanoparticles after incubation in 10 mM phosphate buffer (pH 7.4) for 3 hours at 37°C. The nanoparticles were used at a volume fraction of 0.5%. Doted line: simulation of the amount of BSA adsorbed on the nanoparticle surface calculated from the Langmuir adsorption equation [7].

Figure 5 .

 5 Figure 5. Effect of added BSA on the population of aggregates within the B middle dispersion, according to QELS. The concentrations of BSA are indicated in the Figure. Horizontal axis: hydrodynamic radii R i .Vertical axis: populations of particles P(R i ), normalized to 100 %. Note the reduction in magnitude of the population of very large aggregates and the shift to lower radi of the main population. For all other dispersions, the addition of BSA had no effect on the measured radii (see the text).

Figure 7 :

 7 Figure 7: Activation of the complement system evaluated from 2D immunoelectrophoresis experiments after incubation of the different nanoparticles with human serum in veronal buffer supplemented with calcium chloride and magnesium chloride. The concentration in nanoparticles was adjusted to obtain an equivalent surface area of 2000 cm²/mL in the test tube. Upper part: immunoelectrophoregram shown by the analysis of the C3 proteins after incubation of the serum with the different nanoparticles. Lower part: complement activation factor deduced from the analysis of the immunoelectrophoregrams.

Figure 8 :

 8 Figure 8: Relation between complement activation induced by the nanoparticles and the mesh size of the diffuse shell (a) and the insertion probability of the C3 protein at the core surface (b).

Table 1 :

 1 RadiiSANS spectra of the dispersions in H 2 O measure the core radii of the nanoparticles. SANS spectra of dispersions A middle A top and B middle are shown in Figure

		QELS	SEM*	SANS**	Diffuse shell
		R z (nm)	STD (nm) R z *(nm) STD (nm)	R z **	STD (nm)	thickness
					(nm)		(nm)
	A middle	112	32		63	20	49**
	A top	4 7	2 4		2 6	8	21**
	B middle	88	40	37	4 0	20	48**
	B top	4 9	1 2	3 2			17*

of the nanoparticles as determined by QELS, SEM and SANS (R z calculated with equation 1). Diffuse shell thicknesses were deduced from comparing QELS with either SEM (*) or SANS (**). The experimental error was estimated as ± 5 nm for QELS measurements and as ± 2 nm for SANS measurements.

Table 2 :

 2 Summary of the characteristics of the copolymers composing the nanoparticles and calculation of the characteristics of the diffuse shell of dextran: area per dextran chain at the surface of the core of the nanoparticles, volume fraction of dextran in the diffuse shell and mesh size formed by dextran chains in the diffuse shell .

	Sample %PIBCA	Mw	PIBCA degree of	Area per chain	Volume fraction of	Mesh size
			PIBCA #	polymerization	at the core	dextran in the	of diffuse
					surface (nm²)	diffuse shell	shell
							(nm)
	A middle	48 ± 1	63969	418	3.9 ± 0.6	0.24 ± 0.01	4 ± 0.2
	A top	22 ±	19 546	128	2.8 ± 0.6
		0.5
	B middle	83 ± 2 338 347	2211	32 ± 5	0.02 ± 0.001	47 ± 2
	B top	75 ± 2 207 900	1359	25 ± 5	0.13 ± 0.01	8 ± 0.3

# calculated from the composition of the copolymer

Table 3 :

 3

	Sample Adsorbed amount  mg/m²	Langmuir fit parameters		Experimental value
		Beginning of plateau	End of plateau	 mL/µg Affinity	0 mg/m2 Monolayer	unavailable α Fraction	Fraction unavailable
	A middle	2.1 ± 0.2	3.0 ± 0.2	0.02	3.66	0.2	0.18
	A top	1.0 ± 0.1	2.4 ± 0.3	0.02	3.66	0.7	0.34
	B middle	2.7 ± 0.4	3.4 ± 0.2	0.04	3.66	0	0.07
	B top	1.4 ± 0.3	2.8 ± 0.5	0.04	3.66	0.5	0.23

BSA adsorbed at the plateau of saturation deduced from the adsorption isotherms and from simulations performed with a log normal distribution of the particle size and various thickness of the adsorbed layer. The monolayer adsorption is calculated for BSA molecules in the "edge-on" configuration (see Discussion).

  2 O + D 2 O. The isotopic compositions were close to the average scattering density of the nanoparticles. The shapes of spectra obtained at the different contrasts with and without BSA were similar. The composition of the solvent that matched the nanoparticles was 29.3 % D 2 O, 70.7% H 2 O in absence of BSA and 29.7% D 2 O, 70.3% H 2 O in presence of BSA. The slight increase of the average scattering density of the nanoparticles with BSA can be attributed to the contribution of the protein. However the precision of this determination was not nearly as good as that of the immunodiffusion methods.

Table 4 .

 4 Physical characteristics of the proteins

	Protein	BSA [33]	Fibrinogen [34,35]	Complement C3 [5]
	MM	67 000	340 000	184 342* [36]
			Dimer consisting of three pairs of	Chain α 110 000
			polypeptide chains (Aα, Bβ and	Chain β 75 000
			γ) 2	1 disulfide bond between
				chains
	Specific		1.38
	density
	PI	4.7	5.8	5.7
	Shape	Prism/hard shape	Cylinder	Elongated curve shape*
	Dimensions	8 x 8 x 3.8	diameter 3.2,	15.2 x 9 x 8.4*
	(nm)		length 47.5
	Plasma	40	2.6 -3	1.2
	concentration
	mg/mL
	PBD ID	HSA: 1E78 [37]

Table 5 .

 5 Comparison of the diffuse shell mesh sizes with the protein dimensions. Insertion probabilities of the proteins at the core surfaces, based on the area per dextran chain at the core surface (see table2).

	Sample diffuse shell	diffuse shell	diffuse shell	P insert for BSA	P insert for	P insert for C3
		mesh size /	mesh size /	mesh size /		Fibrinogen
		BSA	fibrinogen	C3
	A middle	1.1	1.3	0.5	1 x 10 -3	6 x 10 -2	4 x 10 -9
	A top				1 x 10 -4	2 x 10 -2	1 x 10 -12
	B middle	12.4	14.7	5.6	4 x 10 -1	7 x 10 -1	1 x 10 -1
	B top	2.0	2.4	0.9	3 x 10 -1	6 x 10 -1	5 x 10 -2

Acknowledgments

The authors wish to thank Henkel Biomedical for constant support in giving the monomer used in this study, and Nicolas Tsapis at the University of Paris South, UMR CNRS 8612 for his assistance in scanning electron microscopy. This work was supported by ILL proposal 9-12-176.


Joo-Eun Jee

Aleix Comas-Vives

Chiara Dinoi

Gregori Ujaque

Rudi Van Eldik

Agusti Lledos

Rinaldo Poli
email: poli@lcc-toulouse.fr

Agustí Lledós

Nature of Cp*MoO 2 + in Water and Intramolecular Proton-Transfer Mechanism by Stopped-Flow Kinetics and Density Functional Theory Calculations

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The precise structure of aqua complexes and ions in water solution is rarely known. For instance, molybdic acid (H2MoO4) is commonly represented as Mo(OH)6, MoO2(OH)2(H2O)2 and MoO3(H2O)3, [1][2][3][4][5][6] while its first protonation product has been described as Mo(OH)5(H2O) + or MoO2(OH)(H2O)3 + , 1,4,5 although the isomeric formulation MoO(OH)3(H2O)2 + could also be envisaged. To the best of our knowledge, the factors regulating the relative energy of a transition metal dihydroxo complex and its isomeric aqua-oxo form (Scheme 1) are not well understood. In terms of the rate and mechanism of water exchange reactions, the correct assignment of such species is of utmost importance since it is well known that water exchange reactions follow the reactivity order M-OH2 >> M-OH >> M=O. In the organometallic area, the complex Cp*2Zr(OH)2 is a stable compound, 8 whereas Cp*2ZrO is a reactive intermediate. 9 On the other hand, Cp*2WO and Cp*2Ta(O)H are stable compounds that exchange water through Cp*2W(OH)2 and Cp*2Ta(OH)2H intermediates. 10 Finally, the closely related oxo and dihydroxo complexes [CpMoO(PMe3)2] + and [( 5 -C5Et5)Mo(OH)2(dppe)] + have been isolated and structurally characterized. 11,12 In these systems, Cp, Cp* and related chelates are expected to have a drastic influence of the rate and mechanism of the water exchange process on the basis of data reported in the literature for water exchange on [Cp*Rh(H2O)3] 2+ and [Cp*Ir(H2O)3] 2+ , which is 14 orders of magnitude faster than for the corresponding hexaaqua complexes and proceeds according to a more dissociative substitution mode. 13,14 Some of us have initiated an investigation of the aqueous chemistry of high oxidation state organometallic compounds, focusing initially on Cp*Mo derivatives in a variety of oxidation states (VI, V, IV, and mixed-valence clusters). 15 High oxidation state oxomolybdenum compounds are employed in a variety of catalytic reactions, such as olefin epoxidation, the selective oxidation of alcohols to aldehydes, the dehydrogenation and isomerization of alkenes, and even reductive processes such as the hydrosilylation of carbonyl compounds. 16 Organometallic versions of these systems have shown high activities, notably in olefin epoxidation. [17][18][19][20] It would therefore be of interest to adapt these catalytic processes to an aqueous environment. To this end, knowledge of the nature of the Cp*Mo VI aqua ion under different pH conditions is very useful.

A previous investigation of the aqueous speciation of Cp*Mo VI has given the results summarized in Figure 1. 21 In particular, the rate of conversion of compound Cp*MoO2(OH) (generated quantitatively by the rapid protonation of Cp*MoO3 -at pH ≤ 2) to the final cationic product was found to be first order in [H + ]. The interpretation of this result leaves two possibilities as detailed in Scheme 2, both involving a proton addition pre-equilibrium to yield an intermediate cationic dihydroxo complex. The first possibility (path a) involves a rapid equilibrium rearrangement to an aqua-oxo isomer, followed by rate-determining loss of a water ligand, whereas the second one (path b) involves the intramolecular isomerization process as a rate-determining step. The [Cp*MoO(OH)2] + ion is likely a strong acid in water (pKa1 < 0), since most multiprotic inorganic oxo acids (e.g. H2CO3, H2SO3, H3PO4, …) are characterized by a pKa of ca.

4-5 and the pKa2 (acid dissociation of Cp*MoO2(OH)) is 3.65. Thus, the aquation state of the final cationic product is uncertain, [Cp*MoO2(H2O)n] + with either n = 0 or 1. The two possibilities cannot be distinguished on the basis of the kinetics experiment, nor by use of 1 H NMR spectroscopy because only the large solvent resonance was observed under all pH conditions, providing only negative evidence for water coordination (the resonance of the coordinated water molecule could either be overshadowed by the much stronger solvent resonance, of the ligand exchange is in the fast regime leading to a single averaged resonance). IR spectroscopy is also useless for such dilute solutions in a strongly absorbing medium. Subsequent attempts to crystallize a salt of the [Cp*MoO2(H2O)n] + ion and to determine its aquation state by X-ray crystallography have not been successful, always yielding instead the neutral dinuclear compound Cp*2Mo2O5. 22 In fact, the low solubility product of this compound drives its precipitation by combination with the thermodynamically unfavorable (at low pH, see Figure 1) anionic hydrolysis product, Cp*MoO3 -. Another point that has remained unexplained from the previous study 21 concerns the greater thermodynamic stability of the dioxo cation, Cp*MoO2 + (or its water adduct) relative to the oxo dihydroxo isomer, Cp*MoO(OH)2 + .

In this contribution, we present a more detailed stopped-flow kinetics investigation of the generation of the [Cp*MoO2(H2O)n] + ion in the low pH regime, including variable temperature and variable pressure experiments, as well as a DFT computational study aimed at establishing (i) the aquation state of this ion and (ii) the mechanism of the slow process which leads to its generation. The results of this theoretical investigation are potentially of more general interest, as they illustrate the effect of the medium on the relative stability of oxo and dihydroxo transition metal species.

Results and Discussion

(a) Aquation state of [Cp*MoO2(H2O)n] +

The reaction shown in Equation 1 was studied computationally by DFT methods on the full systems (i.e. no ligand simplification was adopted). Both complexes were optimized in the gas phase. These two minima are shown in Figure 2. The unsolvated species give rise to a bent geometry, with the Mo-Cp* ring centroid axis forming an angle of 136.9° from the MoO2 plane, which is only slightly smaller than the same angle in the water adduct (141.9°). Relative to the ideal planar structure (optimized independently under constrained Cs symmetry), this configuration is more stable by only 2.9 kcal mol -1 . The electronic structure of two-legged piano stool complexes has been analyzed before, [23][24][25] including the effect of the coordination environment 26,27 and spin state 28,29 Although this addition process is entropically disfavored, the free energy difference of the reaction is still exergonic by 28.1 kcal/mol. The inclusion of solvent effects by means of the CPCM method changes significantly the results. The energetic difference remains in favor of the water adduct but the gain is reduced to 10.1 kcal/mol. Having the Cp*MoO2 + and the H2O molecules separated in the gas phase is a very energy costing process because a strong cation-dipole interaction is broken. Adding solvent effects stabilize the separated reactants by interacting with the dielectric continuum of the polar medium, leading to a considerable decrease in the energy difference between the isolated species and the aqua complex.

The conclusion of this investigation is to establish the nature of the acidic form of Cp*Mo VI in water as the aqua complex [Cp*MoO2(H2O)] + , although the dissociation of the water ligand to afford the fully consistent with the previously established scheme (Figure 1), because the rate law for the acidification reaction can be expressed as in Equation 2(the equilibrium Ka1 is rapidly maintained on the time scale of k-1 and k-2). 21 At low [H + ] (Ka1 -1 [H + ] << 1), the rate law further simplifies to Equation 3, which accounts for the linear dependence observed under such conditions. The small intercept could be ascribed to a minor contribution of the parallel k-1 path. It is useful to remind the reader here that at low pH the k-1 pathway, corresponding to direct loss of OH -from Cp*MoO2(OH), should be negligible (k-1 = 6.32•10 -7 s -1 ) compared to the k-2 pathway, correponding to protonation and isomerization of the

[Cp*MoO(OH)2] + intermediate, e.g. k-2Ka1 -1 [H + ] = 1.73 s -1 at pH 1.
Alternatively, the intercept can also be due to a contribution of the back reaction. i.e. the k2 path.

kobs = {k-1 + k-2Ka1 -1 [H + ]}/{1 + Ka1 -1 [H + ]} Equation 2 kobs ~ k-1 + k-2Ka1 -1 [H + ] (if [H + ] small) Equation 3
The fit of the data in Figure 3 with the expression of Equation 4, for which the small contribution of the intercept was ignored, resulted in k-2 = 28  1 s -1 (logk-2 = 1.44) and Ka1 = 3.6  0.6 M, from which pKa1 = -0.56. It follows that k-2 is almost 8 orders of magnitude larger than k-1 and that pKa (i.e. pKa2-pKa1) = 4.1. These values are consistent with expectations, since as mentioned above the pKa of a typical inorganic diprotic oxoacid is ≥ 4. Thus, the new results described here fully confirm the validity of the previously proposed kinetic scheme (Figure 1), where a rapid pre-equilibrium protonation precedes a slow step, which is now known to be the intramolecular proton transfer, see next sections. It is worth to mention that the proton transfer to the oxo ligands in compound Re(O)I(2,7-nonadiyne) by CF3SO3H in MeCN was shown to be relatively slow (11.9 M -1 s -1 at -40°C). 31 kobs

~ k-2Ka1 -1 [H + ]/{1 + Ka1 -1 [H + ]} (if k-1 negligible) Equation 4
It should be noted that the individual values of Ka1 and k-2 obtained by the above analysis give rise to a ratio k-2/Ka1 = 7.8, in relatively good agreement with the previously determined value (17.2). 21 The discrepancy may be attributed to the difference in ionic strength used in these studies. However, one point remains to be discussed on the thermodynamics of the system, before we can turn to the kinetics.

The combination of the individual rate constants for the tautomerization of the cationic system in both directions (k2 and k-2 as shown in Scheme 3) yields the tautomerization equilibrium constant, K2 = k2/k-2 = 1.8•10 -5 , which corresponds to a free energy difference of 6.5 kcal mol -1 in favor of the oxo aqua isomer.

The combination of this value with the experimentally determined pKa1 value (-0.56) according to the thermodynamic cycle shown in Scheme 3 (the deprotonation of the two isomeric cations affords the same neutral hydroxo complex) yields the thermodynamic proton dissociation constant of the dioxo aqua species, Ka1' = 6.5•10 -5 M (pKa1' = 4. 19). This compares well with the value calculated from the k-2/Ka1 determined in the previous study (Ka1' = 2.9•10 -5 M; pKa1' = 4.54). Note that this value is also given by the expression (k+1/k-1)Ks, from the thermodynamic cycle in Figure 1. At first sight, it may appear unreasonable that the first acid dissociation constant of this aqua complex is weaker than the second one.

However, this observation can be rationalized if the water ligand is extensively dissociated due to the labilization caused by the Cp* chelate as referred to above. In this case, the calculated pKa1' value must be treated as an apparent pKa value since it includes the equilibrium constant for the dissociation of water, which is expected to be large in order to offset the observed pKa value. Thus the effective thermodynamic acidity of the cationic complex is a weighted average of the coordinated water molecule acidity, which is expected to be intrinsically very high, and the acidity of the free water molecule (pKa = 15.6). The hypothesis of an extensive water dissociation from the cationic complex is not inconsistent with the computational study, since the water adduct is calculated as only 10.1 kcal/mole more stable than the dissociated species according to the CPCM, but this calculation does not consider explicit interactions of the adduct and the separate fragments with additional water molecules. For instance, the stabilization of a water molecule by hydrogen bonding to additional water molecules is expected to contribute significantly to the equilibrium energetics (the solvation free energy of a water molecule in water has recently been estimated at -6.3 kcal/mol). 32 It is also interesting to recall that an electrospray mass spectrometric investigation of a H2O-MeOH solution of Cp*Mo VI at low pH (ca. 4 and 1) revealed the presence of both Cp*MoO2 + and Cp*MoO2(H2O) + species, as well as the related Cp*MoO2(MeOH) + adduct. 33,34 Whether the rapid equilibrium highlighted at the left hand side of Scheme 3 involves only species Cp*MoO2 + and Cp*MoO2(H2O) + , or whether also a methanol solvate is present, does not affect the measured values of all rate and equilibrium constants, nor their significance.

Scheme 3

In general it is expected that ground state labilization caused by metal-carbon bonds in the trans position to coordinated water molecules will not only drastically accelerate the water exchange process, but will also significantly increase the pKa value of the coordinated water as found in the present case.

Bond weakening of the M-OH2 bond will cause a decrease in the acidity of the coordinated water molecule. 7,14 In addition, the bond strength will follow the order M=O >> M-OH >> M-OH2 as mentioned before. Thus, the combination of bond labilization and pH will control the lability of coordinated water and lead to apparent pKa values that seem to be 'abnormal'.

It is also interesting to analyze the Cp*Mo VI system in terms of the isolobal analogy between the O 2- and Cp* -ligands. Thus, the Cp*MoO2 + system is isolobally related to MoO3, Cp*MoO2(OH) to HMoO4 -, and Cp*MoO3 -to MoO4 2-. Interestingly, while the MoO4 2-and HMoO4 -are always described as tetrahedral ions, aqueous MoO3 is described as having coordination number 6 (either as MoO3(H2O)3 or MoO2(OH)2(H2O)2), possibly because an octahedral environment is found for MoO3, 35 as well as for its water adduct MoO3•2H2O, 36 in the solid state. However, equilibria with 5-or 4-coordinate species may in fact exist. A comparison between the pKa of HMoO4 -(3.48) 4 and Cp*MoO2(OH) (3.65) suggests that the Cp* -ligand is a marginally better electron donor than the isolobal O 2-ligand for this system in an aqueous solvent. This means that the Mo center is electron-richer in Cp*MoO2 + than in MoO3 as supported by the Mulliken charges in Mo atom (+1.38 vs. +1.88). In combination with the greater steric bulk of the Cp* ligand vs. the oxo ligand, this may lead to a weaker interaction between [Cp*MoO2] + and water.

The pressure dependence of the reaction was studied at 0.4 M acid for which the data are shown in Figure 5. The obtained activation parameter, ΔV ‡ slope is -9.1  0.2 cm 3 mol -1 . The activation parameters for the slope of the plots in Figure 4 and Figure 5

(d) Computational study of the intramolecular proton transfer process

In order to validate the intramolecular proton transfer mechanism and find the possible origin of the negative activation parameters (entropy and volumes), we carried out calculations on the initial (1a) and end product (2a) of Equation 5, as well as on the transition state (ts1a), in the absence and in the presence of additional water molecules. The gas phase and water solution energy profiles obtained in the absence of additional water molecules are shown in Figure 6, whereas the optimized 1a and ts1a species are shown in Figure 7. The barrier height is quite high, having a value of 43.1 kcal/mol in the gas phase, whereas the reaction is endoergic by 10.6 kcal/mol. Both results disagree with the experimental evidence, since the isomerization process is rather facile and the oxo-aqua complex is the thermodynamically more stable product. When the non-specific solvent effects are accounted for by use of the CPCM method, the barrier is nearly the same (43.9 kcal/mol), whereas the reaction is endoergic by 7. Relative energy profile (in kcal mol -1 ) in gas phase and water solution for the starting complex(1a), transition state (ts1a) and product (2a) of Equation 5. In order to further probe the mechanistic details of this reaction, we considered that the explicit inclusion of water molecules could afford an easier proton transfer pathway, as the system contains both donor and acceptor sites for the establishment of hydrogen bonds with water molecules. Many theoretical works have already reported the active participation of water chains in tautomerization [37][38][39] and proton exchange processes. 40,41 The mechanism is described as a water-assisted reaction in which one or more water molecules act as bifunctional catalyst. Recent theoretical studies of the tautomerization process between the hydrated oxide, [MO(H2O)] + , and the dihydroxide [M(OH)2] + cations (M = V, Nb and Ta) also point out that the participation of water acting as proton donor and acceptor can effectively lower the barrier height for the isomerization process. 42 The same water-catalysis has been found for the isomerization of UO2(OH)2. 43 The resulting energy profiles with one additional water molecule are shown in Figure 8. In Figure 9 the main geometric characteristics of the optimized structures are depicted. First of all, the interaction of the additional water molecule with systems 1a and 2a gives rise to a significant energetic stabilization (15.5 and 8.1 kcal mol -1 in the gas phase and in water solution, respectively, for the dihydroxo complex 1b; 21.0 and 11.3 kcal mol -1 under the same conditions for the oxo aqua complex 2b).

The stabilization of 2b is slightly greater than that of 1b, which renders the isomerization process less endothermic relative to the situation of the isolated system (E = +5.1 and +4.0 kcal mol -1 in the gas phase and in water solution). The corresponding free energy difference in the gas phase is +3. 2b, on the other hand, are essentially unchanged relative to those of 1a and 2a. Thus, the structural rearrangement in ts1b is not as marked as in ts1a, with respect to the relative reactants. It is worth to mention that a very slow rate of intramolecular proton transfer was reported for complex Re(O)( 18 OH)(MeC≡CMe)2 in benzene solution. 44 Although the rate of transformation was shown not to strongly depend on the presence or absence of stoichiometric amounts of ethanol, trace amounts of CF3SO3H strongly accelerate the reaction. It is possible that the transformation could also be accelerated by excess water. Another slow intramolecular proton transfer process was reported for trans- 45 Another noteworthy characteristic of ts1b is that the proton originating from the donating O-H group has already migrated onto the water molecule (1.088 Å), whereas the proton that eventually ends up in the aqua ligand is still bonded to the added water molecule (1.026 Å). These distances suggest that the transition state involves the interaction between a hydronium ion (H3O + ) and the neutral Cp*MoO2(OH) molecule, through the establishment of two hydrogen bonds (1.382 Å to the oxo ligand and 1.591 Å to the hydroxo ligand). We have reported a similar transition-state in hydrogenation performed by gold catalysts for the heterolytic cleavage of H2 assisted by a solvent molecule (ethanol). 46 In conclusion, the explicit consideration of a water molecule confirms the feasibility of the rearrangement of 1b to 2b by solvent assisted intramolecular proton transfer. Relative energy profiles (in kcal mol -1 ) in gas phase and water solution for the starting complex (1b), transition state (ts1b) and product (2b) of Equation 6. On the basis of the above results, we have imagined that the addition of a second water molecule could further lower the energy of the transition state. An eight-membered transition-state (ts1c) having two water molecules acting as proton and donor acceptors concurrently between the two complexes 1c and 2c (Equation 7) may further reduce the necessary geometric reorganization to reach the transition state.

[Ru IV (tpy)(O)(O=P(Ph)2CH2CH2PPh2)(H2O)] 2+ in MeCN solution.
The resulting energy profiles in the gas phase and water solution on this system are shown in Figure 10 and the optimized structures for the related species are drawn in Figure 11. As already seen on going from the water-free to the H2O adduct, going from the mono to the bis(water) adduct further stabilizes the oxoaqua isomer relative to the dihydroxo isomer. The oxo-aqua complex is now only 1.4 kcal mol -1 less stable than the dihydro isomer in the gas phase (cf. 5.1 and 10.6 kcal mol -1 for the mono(water) and water-free system, respectively), and actually more stable by a small margin (0.4 kcal mol -1 ) in water solution.

The gas phase free energy is still in favor of the dihydroxo isomer, but only by 2.4 kcal mol -1 .

Undoubtedly, the correct relative energy can be obtained at this level of theory, provided the effect of the water solvation is considered by the explicit inclusion of a sufficient number of water molecules in the calculation. Although the relative free energy computed by including two water molecules is still a bit far from the experimental value of 6.5 kcal mol -1 in favor of the oxo aqua isomer, the explicit inclusion of water molecules in the calculations moves the energetic balance in the right direction. In conclusion, our calculations indicate an intrinsic preference of the system for the dihydroxide form (gas phase). The nonspecific interactions (continuum calculations) are not sufficient to reverse this stability order, whereas a reversal, in agreement with the experiment, is observed upon inclusion of the specific interactions (hydrogen bonds) with the water solvent. Undoubtedly, the correct relative energy can be obtained at this level of theory, provided the effect of the water solvation is considered by the explicit inclusion of a sufficient number of water molecules in the calculation. For the sake of completion, we have pursued the study by adding a third water molecule to the system. In this case, however, the optimization of both the hydroxo and the oxo aqua isomers 1d and 2d

resulted in an optimized structure where the water proton is completely transferred to the water cluster, isomer (1.025 Å in 2b vs. 0.997 Å in 1b, 1.132 Å in 2c vs. 1.049 Å in 1c; these distances are essentially identical in 1a and 2a). This suggests that [Cp*MoO2(H2O)] + is intrinsically more acidic than its dihydroxo isomer, which may seem in contradiction with the experimental evidence (oxo aqua isomer: pKa = 4.19; dihydroxo isomer: pKa = -0.56). However, as argued above, the high effective pKa value of [Cp*MoO2(H2O)] + is proposed to result from an equilibrium with [Cp*MoO2] + and free H2O. Thus, these computational results indirectly validate the water dissociation hypothesis.

The calculations agree with the experimental evidence that the cationic systems, [Cp*MoO(OH)2] + and [Cp*MoO2(H2O)] + , can be deprotonated in a slightly acidic medium. However, the predominant species in very acidic media is a cationic complex. As a very simple way of modeling the effect of lowering the pH, we have added an extra proton to the system, i.e. using the [H3O(H2O)2] + cluster as a model of the medium. The resulting system is dipositive. This is a rough simulation of a low pH aqueous solution but can give some insights of what occurs when increasing the acidity of the medium. Several theoretical studies have addressed the question of the nature of the hydronium species in solution and its solvation shell. [47][48][49][50] The [H3O(H2O)2] + cluster has been used as a model of the hydronium species in solution in other reactions involving transition metal complexes. 51,52 Different structures were optimized, exploring several starting points, and the various optimized species are shown in Figure 13. For species 1e and 2e, the hydronium ion (H3O + ) is located in the second coordination sphere, whereas species 1e2, 1e3 and 2e2 feature this ion in the first coordination sphere, directly interacting with the molybdenum complex.

Obviously, these are not necessarily all the possible minima, but probably the most favored ones. In no case was the proton of the cationic complex ([Cp*MoO2(H2O)] + or [Cp*MoO(OH)2] + ) transferred to the medium, conversely of what occurred for the monopositive system with three water molecules. This is not a surprising result, the medium (modeled here as [H3O(H2O)2] + ) being too acidic in the gas phase to accept an additional proton, because it has an excess of positive charge. Nevertheless, this approach gives a nice representation of what occurs when lowering the pH value because the cationic species become now favorable and can be obtained as real minima in the potential energy surface for both isomers.

Concerning the relative energies, placing the hydronium ion in the first coordination sphere carries an energy cost of ca. 2 kcal/mol, relative to having it in the second sphere (e.g. going from 1e to 1e2 and 1e3 for the dihydroxo complex, and from 2e to 2e2 for the oxo aqua complex). On the other hand, the dihydroxo isomer is more stable than the oxo aqua species by 5.3 kcal mol -1 (1e vs. 2e structure). As discussed before, we believe that a larger number of water molecules (at least the complete first solvation sphere) should be included in order to reproduce the experimental relative stability.

The experimental data also show that the dominant species at pH > 5 is the anionic complex [Cp*MoO3] -. 21 We suggest that when increasing the hydroxide concentration, the proton of the [Cp*MoO2(OH)] complex can be easily transferred to hydroxide in solution, analogously to what occurs to one proton of the aqua complex when water molecules are added to the system. Nevertheless, although theoretical calculations reported here provide some relevant energy trends, geometries and activation barriers, a complete theoretical analysis of the species present in solution as a function of pH is beyond the scope of this study, mainly because of the intrinsic difficulty of simulating an aqueous solution at a given pH. More information could be extracted from dynamics simulations.

Conclusions

A combination of kinetic and computational investigations on the Cp*Mo VI system in acidic aqueous medium has greatly improved our understanding of what factors regulate the properties of the oxo dihydroxo ([Cp*MoO(OH)2] + ) and dioxo aqua ([Cp*MoO2(H2O)] + ) isomers in solution. The computational study shows that the dihydroxo isomer is favored for the isolated system in the gas phase, but the subsequent introduction of the solvent model (by CPCM) and especially the explicit introduction of water molecules in the calculations attenuate and even reverse this stability trend. The study further suggests that the medium strongly affects the water dissociation energy cost from the dioxo aqua isomer (10.1 kcal mol -1 in water solution vs. 39.7 kcal mol -1 in the gas phase). A generalization of these trends suggests that the dihydroxo species for any given system have a better chance to be stable in apolar organic solvents, whereas a rearrangement to oxo complexes accompanied by water dissociation may be favored in stronger dielectric solvents.

The above trend also rationalizes the unusually low acidities that are sometimes found for high oxidation state cationic complexes. While the water ligand in the oxo aqua isomer, [Cp*MoO2(H2O)] + , is an intrinsically stronger proton donor than the hydroxo ligand in the dihydroxo isomer, [Cp*MoO(OH)2] + , the much lower observed acidity for the former (pKa = 4.19; vs. -0.56 for the latter) is related to a water dissociation equilibrium. In turn, this is related to the coordination sphere and particularly to how the ligands are able to satisfy the electron deficiency at the metal center upon loss of the water lone pair donation. In the present system the extremely high lability of the coordinated water molecule can be ascribed to the trans labilization effect of the Cp* chelate, which in turn favors the formation of the dioxo complex and is responsible for the apparent high pKa value of the oxo aqua isomer. We are not aware of any other analogous study in the literature.

Concerning the isomerization mechanism leading from the dihydroxo to the oxo aqua species, the direct intramolecular proton transfer from the dihydroxo to the aqua complex can be ruled out due to the high calculated barrier for the direct proton transfer, viz. 43.9 kcal mol -1 including solvent effects. The assistance of either one or two water molecules renders proton transfer feasible by dramatically lowering the barrier height. The mechanism involving assistance by two water molecules even yields a lower energy for the transition state than for the reactant and product when including the CPCM, suggesting that this is indeed a very facile process. The assistance by amphiphilic external molecules, such as water, is increasingly found to be crucial to lower activation barriers of intramolecular proton transfer rearrangements.

Synopsis

Combined protonation kinetics and DFT studies bring to light the regulating factors for the relative energy of dihydroxo vs. oxo aqua isomers, the water dissociation equilibrium, and abnormal acid dissociation constants, for the organometallic "Cp*MoO2(OH) + H + " system.

  Scheme 1

Figure 1 .

 1 Figure 1. Thermodynamic and kinetic parameters related to the Cp*Mo VI system in a H2O-MeOH (80:20) solution. 21

[ 1 Figure 2 .

 12 Figure 2. Optimized structures of the [Cp*MoO2] + and [Cp*MoO2(H2O)] + (2a) complexes.

[

  Cp*MoO2] + intermediate may be a facile process. As mentioned in the Introduction, from a kinetics point of view, the Cp* ligand is known to exert a strong trans effect on ligand dissociation processes. The introduction of the Cp* ligand on the very inert hexa-aqua complexes of Ir(III) and Rh(III), i.e. on going from the [M(H2O)6] 3+ to the [Cp*M(H2O)3] 2+ complexes (M = Rh, Ir), increases the water exchange rate by 12-14 orders of magnitude.13 A 17 O NMR investigation of the water exchange process for the Cp*Mo VI aq system as a function of pH is currently ongoing in our laboratories and will be reported in detail in a separate contribution, but we are already able to state that this appears to be an extremely fast process. Therefore, the mechanism of the low-pH transformation leading from Cp*MoO2(OH) to [Cp*MoO2(H2O)] + may be formulated as path b in Scheme 2, the slow step being the intramolecular proton transfer process, leading from the intermediate dihydroxo complex [Cp*MoO(OH)2] + to the final product. (b) Protonation kinetics in the low pH regime In an effort to determine the first acid dissociation constant of [Cp*MoO(OH)2] + (pKa1), the acidification kinetics of [Cp*MoO3] -was studied at low pH (down to zero), where the complex is present in the [Cp*MoO2(OH)] form (pKa2 = 3.65, see Figure 1). Consistent with the previous study, 21 acidification kinetics showed a linear [H + ] dependence up to 0.35 M (pH = 0.45), but a slight saturation effect was visible at concentrations up to 1 M (pH down to 0) as shown in Figure 3. This behavior is

1 Figure 3 .

 13 Figure 3. Plots of kobs versus [H + ] for the acidification of [Cp*MoO3] -with HNO3 in the range 0.01 to

Cp*MoO 2 (

 2

( c )

 c Activation parameters for the low-pH transformationThe temperature and pressure dependence of the acidification process for the protonation reaction in the low acidity range have also been investigated. The data were collected only in the pH range where the rate depends linearly on [H + ], see Figure4. The obtained activation parameters are ΔH ‡ slope = 5.1  0.1 kcal mol -1 and ΔS ‡ slope = -37  1 cal mol -1 K -1 . The double logarithmic plots (logk vs. pH) are linear with slopes very close to unity, demonstrating that the intercept plays a minor role in fitting the data.

Figure 4 .

 4 Figure 4. (a) Plots of kobs versus [H + ] for the acidification of [Cp*MoO3] -with HNO3 in the temperature

Figure 5 .

 5 Figure 5. Plot of ln(kobs) versus pressure for the acidification of [Cp*MoO3] -with HNO3 in the range 10

Figure 6 .

 6 Figure 6. Relative energy profile (in kcal mol -1 ) in gas phase and water solution for the starting

Figure 7 .

 7 Figure 7. Optimized structures of the dihydroxo complex (1a) and the proton transfer transition state

Figure 9 .

 9 Figure 9. The most likely cause of such dramatic decrease in activation barrier is the smaller distortion of

[Figure 8 .

 8 Figure 8. Relative energy profiles (in kcal mol -1 ) in gas phase and water solution for the starting

Figure 9 .

 9 Figure 9. Optimized structures of the starting complex (1b, above), transition state (ts1b, middle) and

[Figure 10 .

 10 Figure 10. Relative energy profiles (in kcal mol -1 ) in gas phase and water solution for the starting

Figure 11 .

 11 Figure 11. Optimized structures of the starting complex (1c, above), transition state (ts1c, middle) and

Figure 13 .

 13 Figure 13. Optimised structures of the [Cp*MoO(OH)2] + and [Cp*MoO2(H2O)] + complexes interacting with the [(H3O)(H2O)2] + cluster (relative energies in kcal mol -1 in parentheses).

  represent those for k-2/Ka1. Since nothing is presently known about the temperature dependence of Ka1, it is difficult to speculate about the meaning of the reported activation parameters. It is reasonable to speculate that Ka1 should not show a significant pressure dependence since it involves no changes in electrostriction and at the most can be slightly positive. The overall significantly negative activation entropy and volume values favor a process in which significant

bond formation or charge creation occurs. According to the slow reaction for path (b) of Scheme 2, formation of the aqua complex involves bond formation between OH and H, as well as shortening of the Mo-O bond during conversion of Mo-OH to Mo=O. These processes are suggested to account for the observed volume collapse and decrease in entropy on going to the transition state.

Table of Contents graphics

	OH	?	O
	M	M
	OH		OH 2

Acknowledgement. We gratefully acknowledge the European Commission for funding this work through the AQUACHEM Research Training Network (Contract n° MRTN-CT-2003-503864). Financial support from the Spanish MEC through Project CTQ2005-09000-C02-01 and from Generalitat de Catalunya through grant 2005SGR00896 is gratefully acknowledged. A.C.-V. acknowledges the Spanish MEC for a FPU fellowship.

which thereby becomes a H7O3 + hydronium ion and interacts via hydrogen bonding with the neutral Cp*MoO2(OH) complex, see Figure 12. These results confirm the trend reported in 2b and 2c, where the O-H bond became more elongated as more water molecules were added in the system. This trend reflects the acidity of the cationic species, thus a more water-rich environment favors the proton transfer to the medium. The two structures 1d and 2d are isomers in terms of the arrangement of the hydrogen-bonded water molecules. Structure 2d is more stable than 1d by 1.8 kcal mol -1 in water solution. It is interesting to note that the protonated water molecule (H3O + ) interacts with the OH group in structure 2d, whereas it prefers an oxo ligand in structure 1d. Although this difference is fairly small and the final point depends on the starting point in the optimization, this difference may be attributed to the fact that in 2d there is an additional hydrogen bond. Moreover, the O(OH) interacting with H3O + in 2d presents a more negative Mulliken charge than the O interacting with H3O + in 1d: -1.11 vs. -0.89. Computational details. Calculations were carried out using the Gaussian 03 package 54 at the DFT level by means of the B3LYP functional. [55][56][57] For the Mo atom, the LANL2DZ pseudopotential 58 was used with the addition of f polarisation functions. 59 The 6-31G(d) basis set was used for C atoms whether for O atoms additional diffuse functions were added due to their anionic character (6-31+G(d)). For the hydrogens, the 6-31G(d,p) basis set was employed. IRC calculations were made in order to get the two minima linked by every transition-state. [60][61][62] Solvent effects were included by means of CPCM single point calculations. 63,64 Additional spheres were included for all the hydrogens except for the Cp* hydrogens by means of the SPHEREONH option.

Frequency calculations were made in order to get the free Gibbs energy. The temperature used was 298.15 K.