Mayerling Martinez
email: mayerling.martinez@ensicaen.fr

Eric Hug

Characterization of deformation twinning in polycrystalline cobalt A quantitative analysis

Keywords: polycrystalline cobalt, twinning, hcp metal, grain size, grain orientation

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

Introduction

Deformation twinning represents an important deformation mode in polycrystalline hexagonal close packed (hcp) metals. There are multiple twin systems in hexagonal metals and hence it is expected that different twin types could operate conditioning on loading conditions and the c/a ratio [START_REF] Partridge | The crystallography and deformation modes of hexagonal close-packed metals[END_REF]. Depending on the crystal parameters of the hexagonal structure, a given twin system may induce either a dilatation or a contraction along the caxis, which are called tension or compression twins, respectively. The most commonly activated system in hcp metals is the 101 2 type, because the corresponding twinning shear magnitude is the lowest. For cobalt, with a ratio c/a < √3, this corresponds to a tension twin, which is expected to be activated when tensile stress is applied parallel to the c-axis. Besides the 101 2 type, others twin modes have been observed in hexagonal metals: 112 1 and 112 2 twins in titanium and zirconium [START_REF] Bozzolo | Misorientations induced by deformation twinning in titanium[END_REF][START_REF] Xu | Dislocation mediated variant selection for secondary twinning in compression of pure titanium[END_REF][START_REF] Kumar | Role of microstructure on twin nucleation and growth in HCP titanium: A statistical study[END_REF][START_REF] Bingert | Deformation twinning in polycrystalline Zr: Insights from electron backscattered diffraction characterization[END_REF], 101 1 and 101 3 types in magnesium [START_REF] Yoshinaga | Deformation Mechanisms in Magnesium Single Crystals Compressed in the Direction Parallel to Hexagonal Axis[END_REF], and 101 1 , 101 3 and 112 1 types in cobalt [START_REF] Zhang | Deformation twinning in polycrystalline Co during room temperature dynamic plastic deformation[END_REF][START_REF] Martinez | TEM analysis of the deformation microstructure of polycrystalline cobalt plastically strained in tension[END_REF].

In order to have a wider understanding of twinning in hexagonal metals, efforts have been made recently to provide statistical analysis of the occurrence of twinning under various conditions of load, using an automated electron backscattering diffraction (EBSD) technique. Beyerlein et al. [START_REF] Beyerlein | Statistical analyses of deformation twinning in magnesium[END_REF] focused on the study of 101 2 twins in high purity Mg. The samples were deformed in a compression test up to 3% strain and the relationships between orientation of grains, grain size, thickness and numbers of twins were established.

Capolungo et al. [START_REF] Capolungo | Nucleation and growth of twins in Zr: A statistical study[END_REF] published a similar study for the 101 2 twins in Zr. Samples of polycrystalline Zr were loaded in compression to 5% and 10% strain in this study. More recently, [START_REF] Kumar | Role of microstructure on twin nucleation and growth in HCP titanium: A statistical study[END_REF] published a study concerning Ti, the samples were also deformed in a compression test and the study was extended to several types of twins, namely 101 2 , 112 1 , and 112 2 . The 101 2 twinning is possible on six equivalent 101 2 twinning planes with a specific shear direction of the 〈101 1〉 type. The mechanism of activation of specific twin variants in Mg and Mg alloys has been studied by several authors [START_REF] Hong | Role of {10-12} twinning characteristics in the deformation behavior of a polycrystalline magnesium alloy[END_REF][START_REF] Guo | Understanding of variant selection and twin patterns in compressed Mg alloy sheets via combined analysis of Schmid factor and strain compatibility factor[END_REF][START_REF] Nave | Microstructures and textures of pure magnesium deformed in plane-strain compression[END_REF].

Two reports concerning a statistical analysis of twinning in polycrystalline Co have been published so far. Zhang et al. [START_REF] Zhang | Deformation twinning in polycrystalline Co during room temperature dynamic plastic deformation[END_REF] performed a statistical analysis, based on EBSD, of the frequency of different types of twins for samples after compression and dynamic plastic deformation test. The second study, by Martinez et al. [START_REF] Martinez | TEM analysis of the deformation microstructure of polycrystalline cobalt plastically strained in tension[END_REF], presents an analysis using identification of twins by transmission electron microscopy (TEM) after a monotonous tensile test. These two studies led to the conclusion that the most important twin mode, regardless the deformation mode, is the 101 2 type. Others studies dealing with twinning in Co were rather focused on high resolution transmission electron microscopy studies of twin/matrix interfaces of different types of twins [START_REF] Zhang | Twin boundaries showing very large deviations from the twinning plane[END_REF][START_REF] Sun | Structural characterization of {1013} twin boundaries in deformed cobalt[END_REF][START_REF] Sun | Structural characterization of twin boundaries in deformed cobalt[END_REF].

The aim of the present study is to reach a better understanding of the twinning process in hcp cobalt. The use of the electron backscattered diffraction technique in strained polycrystalline cobalt allowed acquiring an important quantity of data, thus allowing a statistical analysis considering aspects such as grain orientation, twin volume fraction, twinning modes and twin variants. These are interesting aspects recently explored for other hexagonal metals, but not yet for polycrystalline cobalt. The objective in the present work is to present a statistical analysis of the features based on a grain by grain investigation of the twinning in a large number of grains.

Material and Experimental details

Rolled sheets of polycrystalline cobalt (99.9 wt. % purity) were selected to study deformation twinning. The as-received material was annealed under secondary vacuum at 1100 °C for 1 h. The characterization of the initial state was performed in the previous study by EBSD [START_REF] Martinez | TEM analysis of the deformation microstructure of polycrystalline cobalt plastically strained in tension[END_REF][START_REF] Fleurier | Size effects and Hall-Petch relation in polycrystalline cobalt[END_REF]. The analysis of initial material shows that the samples contain about 8.5% of residual fcc cobalt (Figure 1a). The results indicated (Figure 1b) the typical basal {0001} texture of hexagonal rolled metals [START_REF] Wang | Texture analysis in hexagonal materials[END_REF], with basal poles tilted ±30-50° away from the normal direction [START_REF] Martinez | TEM analysis of the deformation microstructure of polycrystalline cobalt plastically strained in tension[END_REF]. The mean grain size is around 19 µm (~295 µm 2 ).

The microstructure of samples plastically strained at a value of 0.04 was studied by EBSD coupled to a Scanning Electron Microscope (SEM). Three distinct stages are present on the work-hardening curve of polycrystalline cobalt: a nonlinear elasticity stage, a second one linked to basal slip mechanisms, and a last one associated to the mechanical twinning generalization. The chosen strain level (4%) corresponds to the work hardening stage during which twinning is the predominant deformation mechanism [START_REF] Martinez | TEM analysis of the deformation microstructure of polycrystalline cobalt plastically strained in tension[END_REF]. Interrupted tensile tests were performed parallel to the rolling direction (RD) of the sheet at the strain rate of The samples for EBSD analysis were prepared by mechanical grinding until 1 µm diamond paste, followed by a final electrolytic polishing using a solution of glycerol, perchloric acid and ethanol at a voltage of 20 V. The EBSD data were obtained using the ZEISS Supra 55 system operating at 20 kV with a 0.2 µm step size. The microscope was equipped with the TSL/EDAX data acquisition software and the CDD camera DigiView 3. The data were collected from different scans covering the total surface area around 0.5 mm2 , allowing the analysis of 500 grains.

The fraction of twinned grains was measured, one twinned grain being considered as a grain that contains at least one visible twin. The extent of twin formation regarding the grain orientation and the grain size area was determined. The grain size orientation is defined in the present work as the misorientation angle between the c-axis of the grain and the direction of the macroscopic stress applied to the samples. The calculation of the area of the grain includes any twinned regions. The twin area fraction was determined, as well.

Grain area and twin area data are based on 2D analysis of the material. For each twinned grain the number of variants was also determined. Table 1 shows the shear stress associated to some twin mode and other crystallographic parameters. Tenupol5, with an electrolyte consisting of 90% glacial acetic acid and of 10% perchloric acid at a voltage of 50 V.

Results and Discussion

Microstructure and twin variant analysis

The present analysis concerns the study of deformation twinning on samples plastically strained in the twinning work hardening stage and the description of morphology and types of twin variants. Figure 1 represents the pole figure and a general view of the strained sample obtained by EBSD analysis. The grayscale (Figure 1d) represents the quality of the Kikuchi pattern. Twins are also represented in two colors and one can readily see that a high proportion of grains are twinned. The most common twin encountered are tension twins, the 101 2 type that is represented in red, and the 112 1 type represented in blue.

Twins exhibit variable sizes, some of them occupying the whole grain and others ending inside the grain. Twins of a 101 2 type have lenticular or irregular shapes while the twins of 112 1 type are very long and feature extremely flat interfaces. In some grains different variants of the same type of twin are present. In others cases, the two types of twins with their different variants can be observed. No twins appear to cross grain boundaries, or to be connected to each other at grain boundaries, as it was previously observed for Mg and Mg alloys [START_REF] Beyerlein | Statistical analyses of deformation twinning in magnesium[END_REF][START_REF] Ghaderi | Sensitivity of deformation twinning to grain size in titanium and magnesium[END_REF]. Double twinning and others twin modes have already been observed in cobalt [START_REF] Zhang | Deformation twinning in polycrystalline Co during room temperature dynamic plastic deformation[END_REF][START_REF] Martinez | TEM analysis of the deformation microstructure of polycrystalline cobalt plastically strained in tension[END_REF], however, there is no evidence of these twin modes in our samples, using the EBSD experimental conditions with the step size of 0.2 µm. TEM is a more suitable technique to reveal the presence of small single twins or double twins, as show at the end of this section.

According to the histogram of grain area in Figure 1e, grain surface area is principally in a range reaching about 650 µm 2 . Theoretically, the 101 2 twinning is possible on six equivalent 101 2 twinning planes with a specific shear direction of 〈101 1〉 (six equivalent twin variants, or three twin variant pairs). The disorientation relationship between identical variants is 0°, between twins of the same variant around 7° and for twins of different variants about 60° [START_REF] Nave | Microstructures and textures of pure magnesium deformed in plane-strain compression[END_REF][START_REF] Dixit | Microstructural evolution of pure magnesium under high strain rate loading[END_REF][START_REF] Pei | Extension twin variant selection during uniaxial compression of a magnesium alloy[END_REF].

Consequently, according to the misorientation between T1a and T1b, we can conclude that these twins constitute a variant pair. The difference in the misorientation relationship is certainly due to the orientation spread induced by the slip activity. Regarding the frequency, in one third of the cases where several twins were encountered inside a grain, the 101 2 variant pairs were identified.

One can also observe two others twin types (labelled T2a and T2b), which exhibit extremely flat interfaces and correspond to the 112 1 mode. According to the color code and the pole figure, 〈101 0〉 clearly appears to be a common axis to M and T2a and to M and T2b (only the relation of M and T2a is indicated in the Figure 2c, blue circle). The twins are rotated away from the axis at 34° around the same 〈101 0〉 axis. For this twin type we can conclude that a twin/twin misorientation of about 68° corresponds to a misorientation of a variant pair for the 112 1 twins, which is very near to the theoretical value of 68.4°, calculated according to the relationship between the twinning shear and the lattice parameters [START_REF] Partridge | The crystallography and deformation modes of hexagonal close-packed metals[END_REF]. These twins are always present together with at least one 101 2 twin variant.

The coherency can be also evaluated using the pole figures of the planes. The traces of the T2a and T2b twin boundary planes are shown on the 112 1 pole figure (Figure 2c). Each trace is aligned along one normal of the 112 1 planes indicating their coherency. The analysis of coherency for 101 2 twins using pole figures is more difficult because of their irregular shape. In addition it is known that 101 2 twins are not always coherent in cobalt [START_REF] Sun | Structural characterization of twin boundaries in deformed cobalt[END_REF][START_REF] Ostapovets | On the relationship between the "shuffling-dominated" and "shear-dominated" mechanisms for twinning in magnesium[END_REF]. The deviations for the habit planes of 101 2 twins have been also observed in magnesium [START_REF] Zhang | Twin boundaries showing very large deviations from the twinning plane[END_REF], some hypothesis have been proposed but there is no consensus regarding these deviations [START_REF] Sun | Structural characterization of twin boundaries in deformed cobalt[END_REF][START_REF] Ostapovets | On the relationship between the "shuffling-dominated" and "shear-dominated" mechanisms for twinning in magnesium[END_REF].

It has to be stressed here that the twin morphology in cobalt is much more irregular than that observed for magnesium, titanium or zirconium. According to observations in, twins observed in Mg alloys, Zr and Ti are rather lenticular shape, and for larger grains the presence of multiple parallel twins is facilitated.

The flat interfaces of the 112 1 twin are certainly a consequence of its high twinning shear in comparison to that of the 101 2 mode (Table 1). It was observed that the 112 1 twins are present in general in large grains with a grain area over 1000 µm 2 in the half of the cases where these twins were encountered. Also, when a variant pair is present inside a grain they are systematically connected to each other. Guo et al. [START_REF] Guo | Understanding of variant selection and twin patterns in compressed Mg alloy sheets via combined analysis of Schmid factor and strain compatibility factor[END_REF] studied the variant selection using a combined analysis of Schmid factor (m) and local strain accommodation factor (m') during compression of Mg at room temperature. The local strain accommodation refers to the relationship between twinning planes normal and twining shear directions. According to these analyses, twin occurrence is governed not only by the orientation of the grains, but also and mainly by strain accommodation. For the case of multiple twinning in the same grain, the selection of a variant of higher misorientation (≈ 60°) gives the best strain accommodation, while for a variant pair with misorientation of 7.4° the strain accommodation is the worst. Other studies concerning variants selection of twins in Mg alloys ponder not only the strain and the orientation in the grain, where the twins form or could form, but also the strain accommodation, that is or would be required in neighboring grains [START_REF] Jonas | The role of strain accommodation during the variant selection of primary twins in magnesium[END_REF][START_REF] Mu | Variant selection of primary, secondary and tertiary twins in a deformed Mg alloy[END_REF]. The analysis shows that the twin selected depends not only on the value of the Schmid factor. The twin variant selected is the one that requires the least accommodation work in most of the neighboring grains.

Considering these previous studies [START_REF] Guo | Understanding of variant selection and twin patterns in compressed Mg alloy sheets via combined analysis of Schmid factor and strain compatibility factor[END_REF][START_REF] Jonas | The role of strain accommodation during the variant selection of primary twins in magnesium[END_REF][START_REF] Mu | Variant selection of primary, secondary and tertiary twins in a deformed Mg alloy[END_REF], the results concerning the variant selection of twin in strained cobalt can be explained as follows. First the higher occurrence of twins (two-third of the cases) with mutual misorientation of 60° is expected, because this corresponds to the best strain accommodation inside the grain. Second, the presence of a still considerable occurrence of variant pairs (in one-third of the cases), could be related to a lowest accommodation work in most of the adjacent grains.

In order to make a complete characterization of twins variants activated during deformation, the samples were also observed using TEM, as depicted in Figures 4 and5.

The 101 1 and 101 3 compression twins were observed. The occurrence of these twins was low and their size small, in the order of few hundred nanometers, so as their detection using EBSD could be easily neglected, as in our experiments. The image depicted in Figure 4 shows an example of the 101 3 compression twin and the diffraction pattern showing the corresponding misorientation. The twin and the matrix are related by a rotation of 64° about the 〈12 10〉 axis. The observations revealed a presence of stacking faults in both the matrix and the twin, but their density seems to be higher in the latter case, as revealed by the intensity of streaks in the diffraction pattern. Two types of double twinning were encountered in these samples, namely the 101 3 -101 2 and the 101 1 -101 2 modes. An example of the latter case is captured in Figure 5. Double twinning occurs as follows [START_REF] Ando | Relationship between deformation twinning and surface step formation in AZ31 magnesium alloys[END_REF]: the basal plane of the matrix first rotates by 56° around the 〈12 10〉 axis to form the 101 1 twin, then rotates again around the same axis by 86° to form the second order 101 2 twin. The final misorientation, between the matrix and the double twinning, is then 38°. The image shows a double-twin, in the process of formation, so that in the diffraction patterns (not showed here) we can measure the three typical misorientations mentioned. More details and descriptions concerning single and double twins can be encountered in [START_REF] Martinez | TEM analysis of the deformation microstructure of polycrystalline cobalt plastically strained in tension[END_REF]. The grain misorientation angle distribution obtained by EBSD experiments is shown in Figure 6. The plot axis starts at 10° in order to avoid the intragranular misorientation associated with the presence of dislocations and internal stresses. There are three misorientation angle peaks at around 71°, 86° and 34°, by order of intensity. The peak located at 71° is associated with the phase transformation during cooling after annealing.

Cobalt exhibits a face-centered cubic structure at high temperatures. During cooling the metal transforms into the hexagonal structure at 437 °C. The transformation is martensitic and occurs in the {111} type planes of the fcc structure so that this angle can be interpreted as a result of phase transformation following the Shoji-Nishiyama orientation relationship between the fcc and hcp phases [START_REF] Zhu | Observation of twins in polycrystalline cobalt containing facecenter-cubic and hexagonal-close-packed phases[END_REF]. The two other peaks at around 86° and 34° correspond to the tension twins. They have the same rotation axis 〈12 10〉, with a rotation of 86° for the 101 2 twin and 34° for the 112 1 twin. Plotting of both boundaries (86° and 34°) on orientation maps showed that they are correlated with boundaries having the morphologies consistent with twins [START_REF] Lou | Non-Schmid-based {10-12} twinning behavior in polycrystalline magnesium alloy[END_REF][START_REF] Xu | Effect of twinning on microstructure and texture evolutions of pure Ti during dynamic plastic deformation[END_REF].

Statistical analysis of twinning

The present section aims at a statistical analysis of twinning in polycrystalline cobalt and a comparison with previous works concerning other hexagonal metals. The analysis was made using 500 grains covering about 0.5 mm 2 . For the analysis, the 101 2 and 112 1 tension twins and their variants were considered, with special emphasis in the first twin type. The features considered here are the grain area, grain orientation, fraction of twinned grains, twin area fraction, and number of twin variants. The result indicates that 46% of grains are twinned, and that 8% of grains contain two types of tensile twins.

Grain orientation effects on twinning

In order to investigate the orientation effect for each grain, the angle between the c-axis and the load axis was determined. This orientation data allow us to determine whether a grain is favorably oriented to deform by generating tensile twins.

Regarding the orientation of grains, it was observed that grains that have their c-axis almost parallel to the direction of the applied load are all twinned (Figure 7a), and contain tension twins as expected. However, about 35% of grains are not conveniently oriented for twinning. These grains with their c-axis perpendicular to the loading axis also contain tension twins, which is unexpected, since their Schmid factor is in average lower than the values corresponding to grains with their c-axis parallel to the loading axis. Tension twins appeared over the whole range of orientations, regardless the orientation of the grains, even for those grains for which the orientation is consistent with a deformation through the formation of compression twins. The influence of grain orientation in the twin area fraction is depicted in Figure 7b.

According to our results, there is a decrease in twin area fraction when the grain is less favorably oriented to twinning. The frequency of a grain of a given orientation to twin in one or more variants is captured in Figure 7c. Here we consider that a grain with more than one variant contains different variants of the same twin type, one or several variant pairs, mixtures of different tensile twins, or combinations of two or more of previous cases (Figure 2 and3). We can observe that grains with their c-axis almost parallel to the load axis contain in majority of cases more than one variant, while the grains that are less favorably oriented, with their c-axis perpendicular to the macroscopic loading direction, display in most of cases one single variant. Increasing the misorientation angle between the c-axis and the loading axis reduces the probability of a grain to exhibit more than one variant.

Our results can be compared with the influence of orientation on the twinning mechanisms of others plastically strained hexagonal metals. The study by Lou et al. [START_REF] Lou | Non-Schmid-based {10-12} twinning behavior in polycrystalline magnesium alloy[END_REF] concerns the effect of different loading conditions on twinning in magnesium. The samples were subjected to dynamic plastic deformation with the compression axis taken with different angles to the c-axis. The observed behavior of Mg is similar to that of Co: the twins are activated in grains during deformation even if the initial orientation does not in theory favor the 101 2 twinning.

Similar behavior was reported for Mg [START_REF] Beyerlein | Statistical analyses of deformation twinning in magnesium[END_REF] and Zr [START_REF] Capolungo | Nucleation and growth of twins in Zr: A statistical study[END_REF] in studies using the Schmid factor analysis. A geometric Schmid factor was calculated with respect to the orientation of the macroscopic loading direction, using the twin plane and the shear direction of each twin variant for each grain. Twinning occur in both types of grains, the favorably oriented with a high Schmid factor (≥ 0.37) and not so favorably oriented, with lower Schmid factor (≤ 0.37). Concerning the specific twins that are formed in grains, the majority of the twins activated are those with a higher Schmid factor, but it is not always the case [START_REF] Beyerlein | Statistical analyses of deformation twinning in magnesium[END_REF][START_REF] Capolungo | Nucleation and growth of twins in Zr: A statistical study[END_REF].

The presence of twins with low Schmid factor, revealed in the above mentioned studies, and the presence of unexpected high number of twinned grains not favorably oriented, as reported here, can be explained by a deviation in a local grain stress state from a macroscopic stress state, and to local stress fluctuations within the grain, produced by interaction with its neighborhood.

Another parameter evaluated as a function of orientation was the twin area fraction. While Capolungo et al. [START_REF] Capolungo | Nucleation and growth of twins in Zr: A statistical study[END_REF] found for Zr that the twin thickness is insensitive to or only slightly dependent on the grain orientation, Beyerlein et al. [START_REF] Beyerlein | Statistical analyses of deformation twinning in magnesium[END_REF] reported for Mg that in more favorably oriented grains the twins are thicker (the thickness correspond to the minor axis of an ellipse fitted to each twin). If we extrapolate the thickness to the twin area fraction we can conclude that the behavior of cobalt is similar to that of magnesium, since the twin area fraction increases in more favorable oriented grains.

The influence of grain orientation on the frequency of twinning variants (Fig. 7c) shows that grains favorably oriented for twinning present more twin variants than those unfavorably oriented. The grain orientation effect on the variant selection has been also reported for Zr and Mg [START_REF] Beyerlein | Statistical analyses of deformation twinning in magnesium[END_REF][START_REF] Capolungo | Nucleation and growth of twins in Zr: A statistical study[END_REF]. These analyses consider the Schmid factor of each twin formed in different grains. It is seen that the favorable variants are those with the higher 20 Schmid factor, but the number of activated variants in a grain is not clearly evident form these studies, hence no conclusion about this aspect in different hcp metals can be drawn.

Grain size area effects on twinning

The influence of the grain size area on various twinning parameters is expressed in the histograms displayed in Figure 8. We decided to include only the grain size area under 650 µm 2 because for larger grains only few cases were present, which do not need to be statistically significant. The variations of fraction of twinned grains with the grain area are presented in Figure 8a.

It is clearly observed that the frequency increases with the area, and that the correlation between these parameters is strong. The trend for of the twin fraction area displays some fluctuation, but it can be concluded that the twin fraction area tends to decrease with increasing the grain area (Figure 8b). The number of variants present in one twinned grain was determined, as well (Figure 8c). The grains with small area (≤ 50 µm 2 ) exhibit only one variant, while larger grains have the tendency to twin into two or more variants.

It is usually found that materials with a larger average grain size twin more easily. The effect of grain size on twinning has already been described for other hexagonal metals [START_REF] Kumar | Role of microstructure on twin nucleation and growth in HCP titanium: A statistical study[END_REF][START_REF] Beyerlein | Statistical analyses of deformation twinning in magnesium[END_REF][START_REF] Capolungo | Nucleation and growth of twins in Zr: A statistical study[END_REF][START_REF] Ghaderi | Sensitivity of deformation twinning to grain size in titanium and magnesium[END_REF][START_REF] Barnett | Influence of grain size on the compressive deformation of wrought Mg-3Al-1Zn[END_REF]. In those studies, three different hexagonal metals were studied: Mg and Mg alloys, Ti, and Zr. If we consider a similar grain area, up to 1000 µm 2 , the correlation follows the same behavior in our present research. There is a positive correlation between the grain size and the fraction of twinned grains in all hcp metals. The origin of size effect on twinning is not completely understood, but some explanations have been suggested.

Ecob and Ralph [START_REF] Ecob | The effect of grain size on deformation twinning in a tectured zinc alloy[END_REF] related this effect to the concentration of dislocations in neighboring grains, while Barnett [START_REF] Barnett | Non-Schmid behaviour during secondary twinning in a polycrystalline magnesium alloy[END_REF] considered that the number of twins is directly related to the grain boundary surface, so that a reduction of grain size will correspond to a reduced twinning.

Concerning the twin area fraction or twin volume, the results show slight discrepancies.

The grain size is compared considering again the same range for grain size area, going up to 1000 µm 2 . The grain area shows a strong positive influence on this parameter in titanium [START_REF] Kumar | Role of microstructure on twin nucleation and growth in HCP titanium: A statistical study[END_REF][START_REF] Ghaderi | Sensitivity of deformation twinning to grain size in titanium and magnesium[END_REF], the effect in magnesium is less pronounced [START_REF] Beyerlein | Statistical analyses of deformation twinning in magnesium[END_REF][START_REF] Ghaderi | Sensitivity of deformation twinning to grain size in titanium and magnesium[END_REF], and is absent in zirconium [START_REF] Capolungo | Nucleation and growth of twins in Zr: A statistical study[END_REF].

For cobalt, the twin area fraction was calculated using 2D images and compared with the grain area. In our case the twin area fraction decreases in a non-monotonous way with the grain area, which is a completely different result comparing to other hcp metals.

Previous studies on other hexagonal metals considered also additional parameters, as the number of twins per grain. It increases with grain size for all three metals but it is strongest for zirconium. The shape of twins in cobalt for a plastic strain of 0.04 is rather irregular, and some twins seem to be the result of twin coalescence (see in Figure 1, white arrows). In our work, we decided to estimate the number of twin variants, rather than number of twins, even if for each variant several twins can be present (see Figure 2, and 3).

At the strain level studied here, the smaller grains are less frequently twinned and present fewer twins variant. However, up to six different variants can be found for largest grain size. Concerning the presence of multiple variants (as in the present work) or multiple twins, the correlation is also positive in all hexagonal metals. The reason for such positive correlation with grain size is certainly linked to the presence of more grain boundaries being imperfect surfaces, giving nucleation sites for twinning. This is supported by atomistic simulations by Wang et al. for magnesium [START_REF] Wang | An atomic and probabilistic perspective on twin nucleation in Mg[END_REF].

Conclusions

Polycrystalline cobalt was deformed by monotonous tensile test in the twinning work hardening stage to study the twinning deformation behavior using EBSD. The statistical analysis of twinning characteristics was performed over more than 500 grains and led to the following conclusions:

-The twin type more frequently activated is by far the 101 2 compression mode and this type was used for statistic considerations.

-Several variants of the 101 2 mode are frequently present inside a grain. The variants with higher occurrence are those with a mutual misorientation of about 60°, which correspond to the best strain accommodation inside the grain.

-Grain size seems to have less impact on twinning characteristics in comparison to orientation of grains. The twin frequency and the number of variant increase with grain size while the twin area fraction decreases.

-It is shown that the grains which are favorably oriented twin more frequently, exhibit a higher twin fraction area and several twin variants. Surprisingly, grains with their c-axis at 90° from the load axis are also twinned. This is probably related to a local state of stress different from the macroscopic one. These unfavorably oriented grains present lower twin area fraction and most of the time only one twin variant.

Figure 1 .

 1 Figure 1. Microstructure of polycrystalline cobalt: (a) distribution of phases after annealing (grain boundaries are shown in black); (b) pole figure showing texture component after annealing, (c) pole figure after straining at 4%; (d) representation of the Image Quality maps after straining at 4%, the grey scale represents the quality of the Kikuchi pattern from high (white) to low (black). Tension 101 2 twins are represented in red and 112 1 in blue; (e) grain area distribution of polycrystalline samples.

Figure 2 .

 2 Figure 2. Image of a grain with its c-axis nearly parallel to the direction RD of the macroscopic stress. The EBSD map shows the co-existence of several types of twins: (a) inverse pole figure map of the grain, (b) image showing the color code associated to (c) pole figure showing the crystallographic relationship between the matrix and the twins.

Figure 3 .

 3 Figure 3. Image of a grain showing the co-existence of several variants of the same type of twin and related inverse pole figures.

Figure 3

 3 Figure 3 shows an example of a grain with multiple variants corresponding to the 101 2

Figure 4 .

 4 Figure 4. TEM image of the morphology of 101 3 compression twin and the corresponding

Figure 5 .

 5 Figure 5. TEM images of the morphology of a 101 1 -101 2 double-twin in polycrystalline

Figure 6 .

 6 Figure 6. Grain boundary misorientation angle distribution for polycrystalline cobalt strained in misorientation tension to 4%.

Figure 7 .

 7 Figure 7. Effects of grain orientation on (a) fraction of twinned grains, (b) twin area fraction and (c) number of variants in the grain.

Figure 8 .

 8 Figure 8. Effects of grain size area on (a) fraction of twinned grains, (b) twin fraction area and (c) number of variants in the grain.

Table 1 .

 1 Twins characteristics of some twins in cobalt[START_REF] Zhang | Deformation twinning in polycrystalline Co during room temperature dynamic plastic deformation[END_REF].

	Twin plane	Rotation Angle Axis	Magnitude of the twinning shear	Twin type
	101 2	86°	〈12 10〉	0.13	Tension
	112 1	34°	〈12 10〉	0.62	Tension
	101 1	56°	〈12 10〉	0.14	Compression
	101 3	64°	〈12 10〉	0.35	Compression
	Samples were also examined by TEM. Conventional bright field images were made with a
	Jeol 2010 TEM operating at 200 kV. Samples for TEM observations were prepared by
	mechanical polishing and then electropolished by the twin jet method in a Struers

× 10 -4 s -1 . The samples were dog bone shaped with a gauge section of 20 mm in length and 10 mm in width. Strain was measured by a traditional clip-on extensometer.


Ndaye Ndour

Jean-Marc Janot

Laurence Soussan

Zaineb Bouaziz

Damien Voiry

Sebastien Balme
email: sebastien.balme@umontpellier.fr

Impact of Polyelectrolytes on Lysozyme Properties in Colloidal Dispersions

In this work, we investigated the impact of different polyelectrolytes (polyacrylic acid, polystyrene sulfonate, dextran sulfate, and chondroitin sulfate) on lysozyme properties when they form colloidal complexes. To this aim, we characterized (i) the size and stability of the different polyelectrolytelysozyme complexes upon addition of NaCl (different concentrations) by diffusion light scattering, and (ii) the structure and accessibility of lysozyme active site in such complexes by fluorescence quenching and time resolved fluorescence analysis. We then used these results to explain the antibacterial activity variations among colloidal complexes and compared with free lysozyme. Our findings show that colloidal complexes that are more prone to swelling (i.e., lysozyme complexed with polystyrene sulfonate) are less stable upon salt addition. In these colloids, the enzymatic site is also more accessible. However, the antibacterial activity does not depend on the swelling properties because no large structural modification of the active site occurs.

Introduction

Polyelectrolyte (PE)-protein complexes have been widely studied due to their numerous applications, such as protein delivery, catalysis, biosensing, and protein separation [START_REF] Cooper | Polyelectrolyte-protein complexes[END_REF]. These complexes adopt different structures (colloidal suspension, gel, and turbid solution [START_REF] Cousin | The model Lysozyme-PSSNa system for electrostatic complexation: Similarities and differences with complex coacervation[END_REF]) depending on the balance of negative/positive charges. This balance is usually governed by the ratio of protein/PE concentrations and pH [START_REF] Park | Effects of Protein Charge Heterogeneity in Protein-Polyelectrolyte Complexation[END_REF]. In water media, PE/protein complexes are typically governed by electrostatic interactions, and often become instable at high ionic strength when the salts shield the PE charges [START_REF] Cousin | The model Lysozyme-PSSNa system for electrostatic complexation: Similarities and differences with complex coacervation[END_REF][START_REF] Gummel | Counterions release from electrostatic complexes of polyelectrolytes and proteins of opposite charge: A direct measurement[END_REF]. In several cases, hydrogen (H-) bonds can compete with electrostatic interactions [START_REF] Cooper | Polyelectrolyte-protein complexes[END_REF]. Regardless of the nature of the application, a key point of these complexes is the structural modification of the complexed proteins. More specifically for catalysis or biosensing as well as for drug delivery and entrapment, the enzyme active site must be preserved and must remain accessible [5,6] [7,8].

Lysozyme is a model of hard protein with a well-known structure [START_REF] Arai | The behavior of some model proteins at solid-liquid interfaces 1. Adsorption from single protein solutions[END_REF][START_REF] Koo | Pressure-induced protein adsorption at aqueous-solid interfaces[END_REF]. It is composed of 129 amino acid residues divided in two main domains: the α-domain made of α-helices, and the β-domain that consists mainly of β-sheets. Between these domains a loop completes the enzymatic site that catalyzes the hydrolysis of the glycosidic β (1-4) linkages between N-acetylglucosamine and N-acetylmuramic acid into peptidoglycans, contributing to lysozyme antibacterial property. From an energetic point of view, lysozyme exhibits a high internal energy of about 60 kJ mol -1 due to the large ratio of β-sheets and the four disulfide bonds [START_REF] Koo | Pressure-induced protein adsorption at aqueous-solid interfaces[END_REF]. As lysozyme is less prone to unfold, it is considered a hard protein.

Lysozyme typically maintains its antibacterial properties after adsorption on inorganic material [START_REF] Balme | Structure, orientation and stability of lysozyme confined in layered materials[END_REF] or in the form of amyloid structures obtained after heating at pH 2 for several hours [START_REF] Bouaziz | Structure and antibacterial activity relationships of native and amyloid fibril lysozyme loaded on layered double hydroxide[END_REF]. For this reason, lysozyme is employed for many applications, from medicine to food industry [START_REF] Wu | What is new in lysozyme research and its application in food industry? -A review[END_REF]. More recently, lysozyme has been used to solubilize nanoparticles, such as gold [START_REF] Wei | Time-dependent, protein-directed growth of gold nanoparticles within a single crystal of lysozyme[END_REF] and copper [START_REF] Ghosh | Blue-emitting copper nanoclusters synthesized in the presence of lysozyme as candidates for cell labeling[END_REF], opening new avenues for the development of affordable alternatives to gold for sensing [START_REF] Hu | Recent advances in the analytical applications of copper nanoclusters[END_REF][START_REF] Guo | Fluorescent copper nanoparticles: Recent advances in synthesis and applications for sensing metal ions[END_REF].

Lysozyme is often used as a model for basic studies of PE-protein complexes [START_REF] Cousin | The model Lysozyme-PSSNa system for electrostatic complexation: Similarities and differences with complex coacervation[END_REF]. Such complexes can adopt many different structures (gel, microgel micelle, colloid, precipitate, coacervate) by tuning the lysozyme/PE ratio as well as the PE nature and length [START_REF] Cousin | The model Lysozyme-PSSNa system for electrostatic complexation: Similarities and differences with complex coacervation[END_REF][START_REF] Johansson | Interaction between lysozyme and poly(acrylic acid) microgels[END_REF][START_REF] Johansson | Interaction between lysozyme and colloidal poly(NIPAM-co-acrylic acid) microgels[END_REF][START_REF] Wu | Folding Behaviors of Protein (Lysozyme) Confined in Polyelectrolyte Complex Micelle[END_REF]. When mixed with polystyrene sulfonate (PSS) at a [-]/[+] ratio of about 1 ([-] and [+] refer to the concentration of PE and lysozyme, respectively, at neutral pH), such complexes adopt a colloid structure, while lysozyme maintains its antibacterial activity. However, these complexes become unstable in the presence of increasing salt concentrations. With the increase of the [-]/[+] ratio in PSS, lysozyme unfolds and loses its activity [START_REF] Cousin | The model Lysozyme-PSSNa system for electrostatic complexation: Similarities and differences with complex coacervation[END_REF].

To improve the stability of PE-protein complexes in the presence of salts, methoxypoly(ethylene glycol) -block-poly(l-aspartic acid sodium salt) has been used to form micelle structures [START_REF] Wu | Folding Behaviors of Protein (Lysozyme) Confined in Polyelectrolyte Complex Micelle[END_REF].

However, encapsulation in the micelle structure modifies the lysozyme α-helix/β-sheet ratio [START_REF] Wu | Folding Behaviors of Protein (Lysozyme) Confined in Polyelectrolyte Complex Micelle[END_REF].

Consequently, the structure dependence of lysozyme when associated with PE has only been investigated through large structural modifications or antibacterial activity. On the other hand, we recently reported that amyloid fibrillation and/or adsorption of lysozyme on layered material modifies its global structure, whereas the integrity of the active site is less affected [START_REF] Balme | Structure, orientation and stability of lysozyme confined in layered materials[END_REF][START_REF] Bouaziz | Structure and antibacterial activity relationships of native and amyloid fibril lysozyme loaded on layered double hydroxide[END_REF]. Several questions remain unanswered, especially about the correlation between enzymatic activity and the integrity and accessibility of the active site in PE-lysozyme (PE-LYS) complexes.

To address these issues, we studied PE-LYS colloids because these complexes are suitable for several applications in catalysis, drug delivery, and entrapment. We considered four different PEs: poly(sodium 4-styrenesulfonate) (PSS), poly(acrylic acid) (PAA), dextran sulfate (DS), and chondroitin 4-sulfate (CS). First, for each PE, we characterized the PE-LYS complex stability in function of the salt concentration by diffusion light scattering. Then, we evaluated the integrity and accessibility of the enzymatic site by fluorescence quenching and time resolved fluorescence analysis.

Finally, we analyzed the antibacterial activity of the different PE-LYS complexes.

Materiel and methods

Material

Lysozyme (M=14300 g mol -¹, 6297), PSS (Mw~70000 g.mol⁻¹, 243051), PAA (Mw~100000 g.mol⁻¹, 523925), CS sodium salt from bovine trachea (27042), DS sodium salt from Leuconostoc spp (Mw~6500-10000 g mol⁻¹, D 4911), NaCl (S7653), acrylamide (01700), and hydrazine (225819) were purchased from Sigma-Aldrich. CuSO4 (22-

Polyelectrolyte-Lysozyme (PE-LYS) colloid complex preparation

PE-LYS complexes were obtained by adding 50 µl of lysozyme solution (concentration = 10 mg ml -1 ) and 320 µl of PE (PAA, PSS, CS or DS, concentration = 0.5 mg ml -1 ) to 14.63 ml of deionized water.

The resulting colloids were named PAA-LYS, PSS-LYS, CS-LYS, and DS-LYS.

Antibacterial experiments

Non-pathogenic Staphylococcus epidermidis (CIP53.124, from Pasteur Institute Laboratory, Lyon, France) was chosen as surrogate microorganism of bacterial contamination.

Preparation of the bacterial suspensions used for antibacterial tests:

For each experiment, a new bacterial suspension was prepared from a frozen S. epidermidis aliquot. The frozen inoculum (2 mL) was first transferred in LB medium (10 mL). at 37 °C under constant stirring (110 rpm) for 3h. Then, it was inoculated in fresh LB medium (5% v/v) and incubated at 37 °C under constant stirring (110 rpm) overnight until the bacteria reached the stationary growth phase. Afterwards, bacteria were pelleted by centrifugation (3300 g, 4°C, 20 min) to remove nutrients, and avoid bacterial development in the reactor. The recovered bacterial pellets were suspended in spring water (Cristaline Sainte Cécile, France:

[Ca 2+ ] = 39 mg L -1 , [Mg 2+ ] = 25 mg L -1 , [Na + ] = 19 mg L -1 , [K + ] = 1.5 mg L -1 , [F -] < 0.3 mg L - 1 , [HCO3 -] = 290 mg L -1 , [SO4 2-] = 5 mg L -1 , [Cl -] = 4 mg L -1 , [NO3 -] < 2 mg L -1
). The bacterial concentration in the suspensions was determined from the absorbance at 600 nm by using a previously obtained calibration curve. Bacterial cells were finally diluted in spring water to obtain a bacterial suspension in which the cell concentration was about 10 4 CFU mL -1 . Each bacterial suspension was instantly used for the antimicrobial tests.

Counting viable bacteria. Bacteria were counted using the conventional method of colony counting on agar plates. Each S. epidermidis sample was diluted by a factor of 10 in spring water. Each dilution was spread on LB nutrient agar plates, and plates were incubated at 37°C for 24h to allow bacterial colonies to form. Knowing that each colony stemmed from one initial bacterium, the bacterial concentration in each sample was calculated as the mean number of counted colonies divided by the inoculated volume on LB agar plates, by taking into account the corresponding dilution factor. The quantification limit was 10 CFU mL -1 . Each counting was done in duplicate and independently.

Assessment of the antibacterial properties of free lysozyme, and PE-LYS colloids: Bactericidal tests were carried out in a batch mode, in glass Erlenmeyer flasks (25 mL). Reactions were performed in sterile conditions, at 37° C, and under constant stirring (110 rpm) on a rotary shaker. For each test, 9 mL of bacterial suspension was mixed with 1 mL of lysozyme solution or PE-LYS colloid suspensions (prepared in deionized water). The final lysozyme concentration was 3 µg L -1 of lysozyme equivalent.

The initial bacterial concentration C0 was precisely determined by the counting method and the mean C0 was 9.8 ± 0.4 x 10 3 CFU mL -1 . At the end of the test (3h of incubation at 37° C), the concentration of viable bacteria was measured again using the counting method. Changes in the bacterial concentration were correlated with the bactericidal performances of the tested material. The bacterial concentration decrease was expressed in log-removal values; the log-removal was defined as the logarithm (base 10) ratio of the bacterial concentration C (CFU mL -1 ) measured at 3h to the initial bacterial concentration C0 (CFU mL -1 ). In the case of total removal, a log-removal value of -log (C0) (i.e., -4.0) was attributed.

Physical characterization

The UV absorbance spectra were recorded on a JASCO V-570 UV-Vis spectrophotometer at 1 nm s -1 scanning rate.

The diffusion coefficients of PE-LYS colloidal complexes were measured by diffusion light spectroscopy (DLS) (Nanophox, Sympatec, France) at 25°C. From the raw data, the diffusion coefficients were obtained using the Quickfit software [START_REF] Krieger | QuickFit 3.0 : A data evaluation application for biophysics[END_REF]. A Levenberg-Marquardt non-linear fit without constraint box was used. Two criteria were considered for the fit quality: 1) the R 2 , and 2) the symmetrical distribution of the residual function. The hydrodynamic radius (rH) of the colloids was deduced from the diffusion coefficient (D) using the Stoke-Einstein equation (equation 1) and assuming a spherical shape:

= (1)
where kB, T and η, are the Boltzmann constant, the temperature, and the viscosity, respectively.

Time-resolved and steady state fluorescence data were obtained using the time-correlated singlephoton counting technique with a previously described home-made set-up [START_REF] Tangaraj | Adsorption and photophysical properties of fluorescent dyes over montmorillonite and saponite modified by surfactant[END_REF][START_REF] Balme | Highly efficient fluorescent label unquenched by protein interaction to probe the avidin rotational motion[END_REF]. Briefly, the excitation wavelength was achieved using a SuperK EXTREME laser (NKT Photonics, model EXR- counts in total. Decay analysis was performed using a Levenberg-Marquardt algorithm. For the analysis, the fluorescence decay law at the magic angle IM(t) was assumed as the sum of exponentials.

Fluorescence lifetime values were calculated from data collected at the magic angle by iterative adjustment after convolution of a pump profile (scattered light) with a sum of exponentials. All details about the calculation of fluorescence lifetime values are given elsewhere [START_REF] Balme | Highly efficient fluorescent label unquenched by protein interaction to probe the avidin rotational motion[END_REF].

Results and discussion

Impact of salinity on PE-LYS colloid stability

PE-LYS complexes were prepared in water using low protein concentration (33 µg ml -1 ). The used [-]/[+] ratio was about 0.01 for PSS and PAA, and about 0.2 for CS and DS. Indeed, it was shown that at

[-]/[+] ratios <1, PSS-LYS complexes adopt a colloidal structure [START_REF] Cousin | The model Lysozyme-PSSNa system for electrostatic complexation: Similarities and differences with complex coacervation[END_REF]. Dynamic light scattering was used to investigate the impact of increasing NaCl concentrations on the diffusion coefficient and stability of PE-LYS colloids (Fig. 1). First, at low NaCl concentrations, the PEs could not be detected by DLS, and lysozyme diffusion coefficient was about 128 µm 2 s -1 . For the PE-LYS complexes, the fit of the autocorrelation function required two components that depend on the salt concentration (Fig. 2).

In water, the fastest component (D1 = 13.72 µm 2 s -1 , 10.27 µm 2 s -1 , 9.76 µm 2 s -1 , and 14.55 µm 2 s -1 for PAA-LYS, PSS-LYS, CS-LYS, and DS-LYS, respectively) represented the predominant species in the solution (respectively 99.8%, 99.7%, 99.6% and 99.8% according to the pre-exponential factor and assuming a spherical shape for all PE-LYS complexes). It corresponded to spherical colloids with a hydrodynamic radius of 16 nm, 21 nm, 22 nm, and 15 nm for PAA-LYS, PSS-LYS, CS-LYS, and DS-LYS, respectively. Such PE-LYS colloids have been already described [START_REF] Cooper | Polyelectrolyte-protein complexes[END_REF][START_REF] Park | Effects of Protein Charge Heterogeneity in Protein-Polyelectrolyte Complexation[END_REF][START_REF] Cousin | Polyelectrolyte-protein complexes: Structure and conformation of each specie revealed by SANS[END_REF]. The slower component (D2 = 3.80 µm 2 s -1 , 3.02 µm 2 s -1 , 3.48 µm 2 s -1 , 3.90 µm 2 s -1 for PAA-LYS, PSS-LYS, CS-LYS and DS-LYS, respectively) corresponded to larger objects. These large colloids could be assigned to small colloid aggregates that coexist through a dynamic equilibrium. For all PE-LYS colloids, NaCl addition induced a shift of the correlation function toward longer times until signal loss that occurred when the colloids were totally destroyed. For all PE-LYS colloids, the values of the diffusion coefficients D1 and D2 decreased with the increase of NaCl concentration (Fig. 2). This indicates that the size of the two components of the complexes grew. This observation is not surprising because electrostatic interactions are predominant in the formation of PE-LYS colloids. With the increase of the salt concentration, the PE charges were shielded, inducing two effects. The first one was the swelling of colloids due to the introduction of hydrated ions in the PE-LYS complex. This ultimately led to the colloid dissociation, as indicated experimentally by the loss of the DLS signal. The second effect was the colloid aggregation that was characterized by the decrease of the diffusion coefficient. These two effects co-existed because the aggregation allowed minimizing the colloid global energy, counterbalancing their destabilization due to swelling. Interestingly, the colloid aggregation and stability depended on the PE nature. PAA-LYS complexes were the least affected by NaCl addition, and the colloids were not dissociated in the presence of 300 mM NaCl. On the other hand, PSS-LYS complexes were dissociated in the presence of 200 mM NaCl. Although the electrostatic interactions are the primary factor responsible for colloid formation, weak interactions also can play a role.

Typically, PAA carboxylic acid moieties are involved in H-bond formation, whereas PSS is prone to hydrophobic interactions. As lysozyme is a hard protein, it should not be unfolded in the complex.

Consequently, its surface should be globally hydrophilic and more prone to H-bond formation than to hydrophobic interactions. H-bonds enter in competition with the screening charge due to the increased salt concentration, thus limiting colloid swelling. In PAA-LYS complexes, the aggregation phenomenon is sufficient to counterbalance the colloid destabilization. Like PAA, DS and CS also can form H-bonds with lysozyme. However, they are less charged than PAA, and this could explain why DS-LYS and CS-LYS colloidal complexes were less stable than PAA-LYS complexes. Moreover, dynamic light scattering experiments showed that upon NaCl addition, DS-LYS colloids were more stable than CS-LYS colloids that were dissociated in the presence of 100 mM NaCl. This result can be explained by the number of anionic moieties on each saccharide unit (2 for DS and 1 for CA).

Accessibility and integrity of lysozyme active site

The active site of lysozyme is located between the αand β-domains of the protein. It contains three tryptophan residues (Trp62, Trp63, and Trp108) that are important for the enzymatic activity [START_REF] Nishimoto | Internal motion of lysozyme studied by time-resolved fluorescence depolarization of tryptophan residues[END_REF].

Analysis of its accessibility and integrity showed that at 345 nm, Trp63 fluorescence was quenched by neighboring disulfide bonds, while 92% of the total fluorescence signal was due to the Trp62 and Trp108 residues. Their photophysical properties are strongly affected by the environment inside the active site, and thus by structural modifications [START_REF] Balme | Structure, orientation and stability of lysozyme confined in layered materials[END_REF][START_REF] Bouaziz | Structure and antibacterial activity relationships of native and amyloid fibril lysozyme loaded on layered double hydroxide[END_REF]. Moreover, the fluorescence emission of these Trp residues is quenched when a molecule, such as acrylamide, enters the active site [START_REF] Tokunaga | Analysis of core region from egg white lysozyme forming amyloid fibrils[END_REF]. Therefore, they represent ideal probes to investigate PE impact on the active site accessibility and integrity and for correlations with the antibacterial activity.

Quantification of the fluorescence decay of free lysozyme (Fig. 3a) showed that in water, the mean lifetime ( ) of lysozyme was 2.34 ns. However, the fluorescence decay fit required four components, in agreement with our previous work [START_REF] Bouaziz | Structure and antibacterial activity relationships of native and amyloid fibril lysozyme loaded on layered double hydroxide[END_REF]. The shorter one (τ4 = about 0.01 ns with a yield of 2%) could be assigned to the contribution of Trp28 and Trp111, two residues located outside the active site [START_REF] Yamashita | The Steady State and Time-resolved Fluorescence Studies on the Lysozyme-Ligand Interaction[END_REF]. The three other components (τ1 = 3.64 ns, τ2 = 1.62 ns and τ3 = 0.48 ns with yields of 41 %, 48% and 9%, respectively) were assigned to Trp62 and Trp108. Indeed, complexation with PAA and DS modified significantly the mean lifetime ( ) compared with PSS and CS (Table 1). Conversely, τ1 and τ2 values and/or their yields were affected by all PEs. This could be explained by two hypotheses: (i) PE penetration inside the active site and interaction with the Trp residues, and/or (ii) modification of the active site structure. These hypotheses were tested using the acrylamide test. Indeed, if the active site is crowded by PE molecules, acrylamide will not quench the Trp fluorescence. Addition of acrylamide induced fluorescence quenching in free lysozyme and also in all PE-LYS colloidal complexes (Fig. 3b). This effect involved both dynamic and static processes that can be expressed by the following equation:

= (1 + )(1 + ) (2)
where and are the fluorescence intensity at the quencher concentration =0 and = respectively, is the Stern-Volmer constant (eq. 3) relative to the collisional quenching process [START_REF] Edwards | Exposure of tryptophanyl residues in ??-lactalbumin and lysozyme -Quantitative determination by fluorescence quenching studies[END_REF],

and is the constant of the formation of a ground-state non-fluorescent complex. The Stern-Volmer constant can be obtained from the linear dependence of as a function of (Fig. 3c). The Stern-Volmer constant reached 4.65 M -1 for free lysozyme and decreased for PE-LYS colloids (Table 2). A lower could be due to a structural modification or a reduced accessibility of the active site due to PE presence. To elucidate the origin of reduction, the quenching rate constant (kq) was calculated from the fluorescence lifetime value ( ) (eq. 3):

= 1 + = 1 + (3)
Comparison of the quenching rate constant (kq) values (Table 2) showed that they were decreased when lysozyme was complexed with PE. This could directly be interpreted as a decrease of the acrylamide/Trp collisions. The decrease of dynamic quenching could originate from (i) a modification of the active structure site, and/or (ii) a decrease of the active site accessibility due to PE steric effect.

As Trp quenching by acrylamide involved also static processes, the KS was calculated by plotting the

! "#
as a function of acrylamide concentration (Fig. 3d). For free lysozyme in water, a linear dependence was observed with KS= 2.04 M -1 . This linear dependence was maintained only when lysozyme was complexed with PSS, but with a lower KS value (1.22 M -1 ). This means that the active site is more accessible in PSS-LYS complexes compared with the PE-LYS made with PAA, CS and DS. In conclusion, our results show that PEs modified the physical properties of the Trp62 and Trp108 residues, and that the active site accessibility was reduced in PE-LYS complexes. The first information is that the active site was not fully crowded by the PE because acrylamide could still quench Trp fluorescence. This means that the fluorescence lifetime changes can be assigned to a structural modification of the active site. This is quite consistent with the fluorescence lifetime results. Indeed, if PE molecules were present inside the active site, their interaction with the Trp residues should have modified the fluorescence lifetime values, especially PSS due to the presence of aromatic moieties.

However, our findings indicate that the fluorescence lifetime values were not strongly affected by the PE, although the photophysical property changes were significant. In addition, it is unlikely that PE molecules can enter in the active site due to steric hindrance. Thus, the most probable explanation of the fluorescence lifetime value changes is a structural modification of the active site. Indeed, the active site is located between the βand the α-domains of the protein. It is constituted by amino acids involved in these domains and in the loop that connects them, thus making it prone to local structural modifications that do not affect the global protein integrity. In some cases, structural modifications of lysozyme especially in the α-domain do not strongly affect the active site, as previously shown for the lysozyme amyloid structure [START_REF] Bouaziz | Structure and antibacterial activity relationships of native and amyloid fibril lysozyme loaded on layered double hydroxide[END_REF]. This result is consistent with previous reports in which structural modification of lysozyme confined in a PE matrix was highlighted by circular dichroism [START_REF] Wu | Folding Behaviors of Protein (Lysozyme) Confined in Polyelectrolyte Complex Micelle[END_REF]. The second information is that PEs also play a role in the active site accessibility. Indeed, the acrylamide test results showed that lysozyme active site in PE-LYS complexes formed with PSS is more accessible compared with complexes formed with PAA, CS and DS. This is consistent with the high stability of PAA-LYS colloids upon salt addition (Fig. 1a). Indeed, the interactions (electrostatic and H-bonds) between PAA and LYS are stronger, making the colloid structure more compact.

Consequently, acrylamide cannot easily diffuse inside these colloids to form the non-fluorescence complex. Conversely, PSS-LYS colloids swell with the increase of salt concentration, because they are less compact. Therefore, acrylamide can easily diffuse inside the structure. Overall, our results clearly demonstrate that colloids based on CS and DS follow the same trend: the combination of electrostatic interactions and H-bond formation makes these colloids less prone to the formation of acrylamide/Trp complexes.

Antibacterial activity of PE-LYS colloids

To assess the antibacterial activity of the PE-LYS colloidal complexes against the Gram-positive S.

epidermidis, experiments were performed with the same lysozyme (free or in the colloids) concentration (i.e., 3 µg L -1 of lysozyme equivalent). The blank experiment (i.e., bacterial suspension without free lysozyme and PE-LYS) showed that the bacterial concentration remained nearly constant at the end of the 3h incubation (Table 3). As expected, free lysozyme had a strong anti-microbial activity, as indicated by the 2 log-removal value (per absolute value). The PE-LYS colloids exhibited about 1 log-removal values (i.e., 90% of bacteria were killed).. Therefore, our results confirm that lysozyme complexed with PE retains some catalytic activity, and are in agreement with what previously reported for PSS-LYS [START_REF] Cousin | The model Lysozyme-PSSNa system for electrostatic complexation: Similarities and differences with complex coacervation[END_REF]. It is interesting to note that the PE nature did not influence the log-removal value, indicating that the change in antibacterial activity was not due to a structural modification of the active site, but rather to a decrease of the number of accessible sites, in line with the fluorescence results (section 3.2). PAA-LYS at 3h

1.1 ± 0.1 x 10 3 -0.9

PSS-LYS at 3h

1.2 ± 0.2 x 10 3 -0.9

DS-LYS at 3h

9.6 ± 0.3 x 10 2 -1.0

CS-LYS at 3h

1.2 ± 0.1 x 10 3 -0.9

Conclusion

We investigated the properties of lysozyme involved in colloids with different polyanions. Our results

highlight that the PE nature strongly influences the size and stability of PE-LYS colloidal complexes as well as the antibacterial properties of lysozyme when complexed with PEs. Colloids made with PAA, where both electrostatic interactions and H-bond formation are involved, were more compact and more stable than those obtained with PSS. However, the enzyme active sites were less accessible to acrylamide. The complexes formed with polysaccharides (DS and CS) also involved electrostatic interactions and H-bond formation. This led to a compact complex structure that did not allow the formation of Trp-acrylamide complexes. However, due to their lower charge density, compared with DS (and PAA), CS are less stable upon salt addition. On the basis of the fluorescence results, the decreased antibacterial activity observed when lysozyme was complexed with PEs can be explained by the reduced accessibility and a structural modification of the enzyme active site. Our results highlight the role of the PE-LYS structure as a key factor for understanding lysozyme activity.

  Photonics, model DUV). The repetition rate was set to 38.9 MHz; the excitation pulse duration on this

Figure 1 :

 1 Figure 1: Autocorrelation curves obtained by DLS for (a) PAA-LYS complexes, (b) PSS-LYS

Figure 2 :

 2 Figure 2: Diffusion coefficients measured by DSL as a function of NaCl concentration. D1 is the

Figure 3 :

 3 Figure 3: (a) Fluorescence decay (symbol) and fit (line) of free lysozyme (LYS) (orange), PAA-LYS

Concentration (CFU mL - 1 )

 1 Log-removal values (-)

Table 1 :

 1 Fluorescence lifetime (τi), results (mean ± standard deviation) for free lysozyme (LYS) and PE-LYS, obtained with an excitation wavelength of 294 nm and recorded at 345 nm.Calculation of the fluorescence decays of lysozyme within PE-LYS complexes also required four components. The value and yield of the shorter component τ4 were not significantly modified in the PE-LYS complexes compared with free lysozyme, suggesting that no large protein structural modification occurred close to the location of Trp28 and Trp111 inside the protein chain. Conversely, lysozyme complexation with PE affected differently the value and the yield of the other components.

		τ1 (ns)	τ2 (ns)	τ3 (ns)	τ4 (ns)	Y1	Y2	Y3	Y4	χ 2	(ns)
						(%)	(%)	(%)	(%)
	LYS	3.64±0.	1.62±0.	0.48±0.	0.01±0.	41	48	9		2 1.1	2.34±0.2
		25	12	05	01					7	6
	PAA-	3.86±0.	1.33±0.	0.40±0.	0.01±0.	33	44	20		4 1.1	1.93
	LYS	22	11	04	01					2	±0.25
	PSS-	4.46±0.	1.62±0.	0.45±0.	0.02±0.	36	45	17		2 1.1	2.39±0.2
	LYS	3	13	05	01					1	8
	CS-LYS	4.17±0.	1.58±0.	0.46±0.	0.01±0.	40	44	14		2 1.1	2.43±0.1
		26	11	02	01					5	9
	DS-LYS 4.62±0.	1.70±0.	0.46±0.	0.02±0.	41	42	15		2 1.0	2.68±0.2
		30	10	04	01					7	2

Table 2 :

 2 Values of the Stern-Volmer constant, quenching constant , and static quenching

	constant Ks.
		* +, -./⁻¹	2 3 ((% 4 )-. × 6/⁻¹	*6 -./⁻¹
	LYS	4.65	2.03	2.04
	PAA-LYS	1.40	0.72	N.A.
	PSS-LYS	2.67	1.12	1.22
	DS-LYS	3.11	1.16	N.A.
	CS-LYS	2.55	1.05	N.A.

Table 3 :

 3 Bacterial log-removal values (mean ± standard deviation n=3) obtained after incubation of Gram positive S. epidermidis with free lysozyme (LYS) and PE-LYS colloidal complexes for 3 hours.

Acknowledgements

The authors would like to acknowledge the "Institut Européen des Membranes (IEM)-UMR 5635" for supporting this study through the health project PS1-2017.