João Serôdio
email: jserodio@ua.pt

Johann Lavaud

A model for describing the light response of the non-photochemical quenching of chlorophyll fluorescence

Keywords: Chlorophyll fluorescence, modelling, non-photochemical quenching, photoacclimation, photoprotection, xanthophyll cycle

The operation of photosynthetic energy-dissipating processes is commonly characterised by measuring the light response of the non-photochemical quenching (NPQ) of chlorophyll fluorescence, or NPQ vs. E curves. This study proposes a mathematical model for the quantitative description of the generic NPQ vs. E curve. The model is an adaptation of the Hill equation and is based on the close dependence of NPQ on the xanthophyll cycle (XC). The model was tested on NPQ vs. E curves measured in the plant Arabidopsis thaliana and the diatom Nitzschia palea, representing the two main types of XC, the violaxanthinantheraxanthin-zeaxanthin (VAZ) type and the diadinoxanthin-diatoxanthin (DD-DT) type, respectively. The model was also fitted to a large number of published light curves, covering the widest possible range of XC types, taxa, growth conditions, and experimental protocol of curve generation. The model provided a very good fit to experimental and published data, coping with the large variability in curve characteristics. The model was further used to quantitatively compare the light responses of NPQ and of PSII electron transport rate, ETR, through the use of indices combining parameters of the models describing the two types of light-response curves.

Their application to experimental and published data showed a systematic large delay of the build-up of NPQ relatively to the saturation of photochemistry. It was found that when ETR reaches saturation, NPQ is on average still below one fifth of its maximum attainable level, which is only reached at irradiances about three times higher. It was also found that organisms having the DD-DT type of XC appeared to be able to start operating the XC at lower irradiances than those of the VAZ type.

Introduction

Photosynthesis requires a balance between maximizing light absorption and minimizing damages caused by excessively absorbed light energy. Under natural conditions, exposure to sunlight involves unavoidable risks to the photosynthetic apparatus due to the formation of reactive oxygen species of photosynthetic origin produced under excess light [START_REF] Osmond | Too many photons: photorespiration, photoinhibition and photooxidation[END_REF][START_REF] Ort | When there is too much light[END_REF][START_REF] Demmig-Adams | Photoprotection in an ecological context: the remarkable complexity of thermal energy dissipation[END_REF]. The sustainment of prolonged photosynthetic activity under high solar irradiances is ensured by the regulation of the repartition of absorbed light energy between photochemistry and energy-dissipating pathways.

The latter function as photoprotective process against permanent damages to the photosynthetic apparatus, or photoinhibition, and are therefore of considerable interest for understanding the resistance of photoautotrophs to environmental stress [START_REF] Demmig-Adams | Photoprotection in an ecological context: the remarkable complexity of thermal energy dissipation[END_REF][START_REF] Lavaud | Fast regulation of photosynthesis in diatoms: mechanisms, evolution and ecophysiology[END_REF][START_REF] Li | Sensing and responding to excess light[END_REF].

One of the most important photoprotective processes is the non-photochemical quenching (NPQ). NPQ groups several pathways among which the thermal dissipation of excess energy (or q E , the energy-dependent quenching, [START_REF] Müller | Non-photochemical quenching. A response to excess light energy[END_REF] is considered as the most important. q E takes place in the light-harvesting antenna of the photosystem II (PS II). It relies on the presence of specific PS II antenna proteins (PsbS in plants, [START_REF] Li | A pigment-binding protein essential for regulation of photosynthetic light harvesting[END_REF]; LhcSR in green microalgae, [START_REF] Peers | An ancient light-harvesting protein is critical for the regulation of algal photosynthesis[END_REF]; Lhcx in diatoms, [START_REF] Bailleul | An atypical member of the light-harvesting complex stress-related protein family modulates diatom responses to light[END_REF], the building of a transthylakoid proton gradient (ΔpH), and the subsequent enzyme-mediated operation (deepoxidation) of the xanthophyll cycle (XC) [START_REF] Goss | Regulation and function of xanthophyll cycle-dependent photoprotection in algae[END_REF]. The XC produces deepoxidised forms of xanthophylls which are essential regulatory partners of q E , especially in some groups of microalgae (like the diatoms) [START_REF] Lavaud | Fast regulation of photosynthesis in diatoms: mechanisms, evolution and ecophysiology[END_REF][START_REF] Li | Sensing and responding to excess light[END_REF][START_REF] Goss | Regulation and function of xanthophyll cycle-dependent photoprotection in algae[END_REF]. In plants, green algae and some Heterokontophyta (brown algae, Chrysophyceae), the XC is based on the reversible conversion of pigment violaxanthin (Vx) to the q E -involved zeaxanthin (Zx), passing through the intermediate form antheraxanthin (Ax) (VAZ type of XC); in other algal groups, like the diatoms, dinoflagellates, Xanthophyceae and Haptophyta, the XC consists in the conversion between only two pigments, diadinoxanthin (DD) and the q E -involved diatoxanthin (DT) (DD-DT type of cycle) [START_REF] Olaizola | Short-term response of the diadinoxanthin cycle and fluorescence yield to high irradiance in Chaetoceros muelleri (Bacillariophyceae)[END_REF][START_REF] Lavaud | General features of photoprotection by energy dissipation in planktonic diatoms (Bacillariophyceae)[END_REF][START_REF] Lavaud | Fast regulation of photosynthesis in diatoms: mechanisms, evolution and ecophysiology[END_REF]. In phycobilisome-containing organisms, there is no XC (cyanobacteria) or its presence is uncertain (red algae) [START_REF] Goss | Regulation and function of xanthophyll cycle-dependent photoprotection in algae[END_REF].

The operation of NPQ processes is usually quantified using variable chlorophyll fluorescence (Pulse Amplitude Modulation fluorometry, PAM), by calculating the fluorescence index NPQ, which is based on the relative difference between the maximum fluorescence measured in the dark-adapted state, F m , and upon exposure to light, F m ' (see Table 1 for notation):

' ' NPQ m m m F F F   (1)
This index is a rearrangement of the Stern-Volmer equation and reflects the assumption that the reciprocal of fluorescence yield is proportional to the Zx or DT concentration (Bilger and Björkman 1990;[START_REF] Lavaud | Influence of the diadinoxanthin pool size on photoprotection in the marine planktonic diatom[END_REF][START_REF] Baker | Chlorophyll fluorescence as probe of plant photosynthetic productivity[END_REF]. The NPQ index has been routinely used to quantify the operation of photoprotective processes as well as the extent of photoinhibitory damages. Under experimental conditions allowing to assume that the prevailing processes causing the quenching of fluorescence are of photoprotective nature, NPQ has been used as a measure of the overall photoprotective capacity of the photosynthetic apparatus (e.g. Dimier et al. 2007b;[START_REF] Lavaud | Photoprotection capacity differs among diatoms: Possible consequences on the spatial distribution of diatoms related to fluctuations in the underwater light climate[END_REF].

One common way to characterise the operation of photoprotective processes or the susceptibility to photoinhibition is to quantify the light response of NPQ. This is done by constructing NPQ vs. E curves that record the development of NPQ with increasing incident irradiance. These curves are analogous to the more frequently measured light-response curves of the PSII electron transport rate (ETR) in the sense that they represent the variation of steady state photosynthetic activity between different light levels, thus not informing on the kinetics of NPQ generation, but on the NPQ attainable under each irradiance. The shape of NPQ vs. E curve varies widely, both regarding its overall shape as well as the absolute NPQ values reached. Typically, NPQ increases monotonically with irradiance, varying from zero (measured in darkness) to maximum values that vary greatly with taxonomical groups, physiological state, environmental constraints, or light levels applied. The curve presents a variable degree of sigmoidicity, ranging from cases when NPQ starts to increase steeply from the lowest light levels, following a simple saturation-like pattern (no sigmoidicity), to cases when NPQ remains close to zero for a range of low light levels, then showing an abrupt increase only for intermediate irradiances before stabilizing at maximum values (highly sigmoid). Often, although the stabilization of NPQ is evident, a constant value is not reached within the range of irradiances applied and the maximum attainable NPQ cannot be estimated.

Light-response curves of NPQ have been analysed and interpreted on the basis of arbitrarily chosen features, by qualitatively describing its shape (e.g. low or high sigmoidicity), or by selecting NPQ values reached at particular E levels (e.g. NPQ at maximum applied E).

The absence of an adequate descriptive model impedes the characterization of the curve along the whole range of irradiances applied. Also, the lack of a commonly-used set of descriptive

Materials and Methods

Model rationale

The model proposed to describe the light-response curve of NPQ is an adaptation of the Hill equation, originally derived in the context of ligand binding to macromolecules with multiple binding sites. This equation describes the variation of the number of filled binding sites with the increase in ligand concentration, and is routinely used to characterise the cooperativity of enzymatic reactions [START_REF] Voet | response curves of NPQ and ETR in VAZ and DD-DT types of XC[END_REF]. The use of the Hill equation for modelling the NPQ vs. E curve is based on the main assumption that NPQ is mostly due to the operation of the XC coupled to the build-up of the transthylakoid ΔpH, or energy-dependent quenching (q E ;[START_REF] Müller | Non-photochemical quenching. A response to excess light energy[END_REF], and that the other potential components of NPQ, the quenching due to state transitions (q T ) or to photoinhibition (q I ) are not expected to significantly affect the NPQ vs. E curves (see Discussion). The analogy underlying this rationale is to consider the epoxidized XC pigments Vx and DD as representing the macromolecule of the Hill model, and the transthylakoidal ΔpH-dependent protonation of specific light-harvesting complex (LHC) antenna sites as corresponding to the ligand concentration that bind to their multiple binding sites. At steady state, each irradiance level corresponds to a stable transthylakoidal ΔpH and resulting Vx or DD de-epoxidation and activation through protonation of LHC sites (the socalled 'activation' of Zx and DT; [START_REF] Horton | Allosteric regulation of the light-harvesting system of photosystem II[END_REF][START_REF] Goss | The importance of a highly active and ΔpHregulated diatoxanthin epoxidase for the regulation of the PS II antenna function in diadinoxanthin cycle containing algae[END_REF][START_REF] Lavaud | In diatoms, the transthylakoid proton gradient regulates the photoprotective non-photochemical fluorescence quenching beyond its control on the xanthophyll cycle[END_REF][START_REF] Horton | Photosynthetic acclimation: does the dynamic structure and macro-organisation of photosystem II in higher plant grana membranes regulate light harvesting states?[END_REF], and thus to a defined NPQ value. The NPQ vs. E curve is thus proposed to be described by the equation:

n n n m E E E E   50 NPQ ) ( NPQ (2)
where NPQ m is the maximum NPQ value reached during the light curve, E 50 is the irradiance level for which NPQ attains 50% of NPQ m , and n is the Hill coefficient, characterizing the sigmoidicity of the curve. Whilst the parameters E 50 and n are directly adopted from the Hill equation (originally having only these two parameters), a third parameter, NPQ m , had to be considered to account for the variability in the absolute values of NPQ. Under the analogy with the ligand binding context of the Hill equation, NPQ(E) is considered to represent the fraction of Vx or DD molecules de-epoxidized into Zx or DT and which have been 'activated'. As such, E 50 represents the irradiance level necessary to de-epoxidize and 'activate' 50% of convertible Vx or DD pool (ligand concentration resulting in half occupation of binding sites) necessary to reach the maximal NPQ level, NPQ m . Of potential importance for the characterization of the physiological processes underlying the NPQ vs. E curve is the sigmoidicity parameter n, which measures the type and extent of the reaction cooperativity. In the case of n < 1, the curve displays a saturation-like increase asymptotically towards NPQ m , indicating the presence of a negatively cooperative reaction; if n > 1, the curve starts to present a sigmoidal shape, the sigmoidicity increasing with n, indicating a positively cooperative, or allosteric, reaction; if n =1, the model is reduced to the Michaelis-Menten equation, indicative of a non-cooperative reaction.

Measurement of light-response curves

To test the adequacy of the model, Eq. 2 was first fit to NPQ vs. E curves generated for organisms representative of the two types of XC, a plant (A. thaliana; VAZ type of XC) and a diatom (N. palea; DD-DT type of XC), grown under light conditions expected to induce large variations in NPQ absolute values and in the shape of the NPQ light-response curve. Plants of A. thaliana (ecotype Columbia) were grown under controlled growth chamber conditions for 4-5 weeks under a 16:8 h light/dark cycle and 70% relative humidity. The light/dark temperatures were 22/20 °C. Three irradiance levels were applied: 10 ('low light', LL), 75 ('moderate light', ML) and 150 μmol photons m -2 s -1 ('high light', HL). The diatom Nitzschia palea (Kütz.) W.

Smith (collection of the Department of Biology, University of Aveiro) was grown photoautotrophically in unialgal semi-continuous batch 100 mL cultures in sterile natural seawater enriched with f/2 nutrients [START_REF] Guillard | Studies of marine phytoplanktonic diatoms. I. Cyclotella nana Hustedt and Detonula confervaceae (Cleve) Gran[END_REF]. Cultures were grown at 20 °C, under 20 (LL), 100 (ML) and 400 µmol photons m -2 s -1 (HL) in a 12:12 h light/dark cycle. Cells were harvested by centrifugation (3000 × g, 10 min) during the exponential phase of growth, and were resuspended in fresh growth medium supplemented with NaHCO 3 to a final concentration > 10 µg Chl a ml -1 .

Light-response curves of NPQ and ETR were generated by exposing the samples to 7-12 levels of actinic light, up to 920 μmol m -2 s -1 . Samples were dark-adapted for 30 min before the start of the light curve to allow determination of fluorescence levels F o (minimum fluorescence) and F m , required for the calculation of NPQ (Eq. 1). Samples were light-activated before the start of each light-response curve, through exposure to low light of 54 μmol photons m -2 s -1 until a steady state in fluorescence was reached (minimum 15 min). Under each light level, a saturation pulse (0.8 s for A. thaliana and 0.6 s for N. palea) was applied and fluorescence levels F s (steady state fluorescence) and F m ' were recorded and used to calculate NPQ (Eq. 1) and ETR, using [START_REF] Genty | The relationship between the quantum yield of photosynthetic electron transport and quenching of chlorophyll fluorescence[END_REF]

: ' ' ETR m s m F F F E   (3)
A different sample (plant leaf or algal culture aliquot) was used for measuring NPQ and ETR under each light level. Three replicated measurements were made for each light level. Lightresponse curves of ETR were described by fitting the model of [START_REF] Eilers | A model for the relationship between light intensity and the rate of photosynthesis in phytoplankton[END_REF], and by estimating the parameters α (the initial slope of the curve), ETR m (maximum ETR) and E k (the light-saturation parameter). The parameter E k is commonly interpreted as a measure of the light level to which a sample is acclimated to, and commonly used to characterise its photoacclimation status [START_REF] Behrenfeld | In search of a physiological basis for covariations in light-limited and light-saturated photosynthesis[END_REF]).

Chlorophyll fluorescence yield was measured using a PAM fluorometer comprising a computer-operated PAM-Control Unit (Walz) and a WATER-EDF-Universal emitter-detector unit (Gademann Instruments GmbH, Germany), using a modulated blue light (LED-lamp peaking at 450 nm, half-bandwidth of 20 nm) as source for measuring, actinic, and saturating light [START_REF] Cruz | Relationship of rapid light curves of variable fluorescence to photoacclimation and non-photochemical quenching in a benthic diatom[END_REF]. Fluorescence was measured using a 6 mm-diameter Fluid Light Guide fiberoptics. In the case of N. palea, the fiberoptics was connected to a fluorescence cuvette (KS-101, Walz, Effeltrich, Germany).

Published light-response curves

The model was also fitted to published NPQ vs. E curves, covering a wide range of taxonomic groups (higher plants, mosses, green algae, diatoms, dinoflagellates, others), XC types (VAZ, DD-DT, absence of XC), mutants with variable degrees of impairment of the XC operation, habitats (land and aquatic higher plants; planktonic and benthic microalgae), growth conditions (e.g. low and high light), physiological state (heat stress or XC inhibitors) and fluorescence light-response curve measuring protocols (steady state and rapid light curves, RLCs). Only species with a known functional XC were considered. Studies presenting light curves having less than seven data points were not considered, because of the large errors in the model fitting and parameter estimation. For each study, when three or more light curves were available for each species and experimental treatment, only the two curves presenting the most extreme (higher and lower) NPQ values were used. Detailed information on the data used in the metaanalysis is summarised in Table 3. When available, the corresponding ETR vs. E curves were also characterised by fitting the model of [START_REF] Eilers | A model for the relationship between light intensity and the rate of photosynthesis in phytoplankton[END_REF] and by estimating its parameters.

Some studies have reported the formation of NPQ in the dark [START_REF] Perkins | The application of variable chlorophyll fluorescence to microphytobenthic biofilms[END_REF]. This phenomenon was observed on diatoms [START_REF] Jakob | Activation of diadinoxanthin de-epoxidase due to a chlororespiratory proton gradient in the dark in the diatom Phaeodactylum tricornutum[END_REF]) and brown algae [START_REF] Mouget | Suitability of the Fluorescence Monitoring System (FMS, Hansatech) for measurement of photosynthetic characteristics in algae[END_REF], and results in NPQ vs. E curves showing a distinctive bi-phasic pattern, with NPQ decreasing from initial high values measured in the dark to a minimum under low to moderate light levels (e.g. [START_REF] Geel | Estimation of oxygen evolution by marine phytoplankton from measurement of the efficiency of photosystem II electron flow[END_REF][START_REF] Serôdio | Rapid light-response curves of chlorophyll fluorescence in microalgae: relationship to steady-state light curves and non-photochemical quenching in benthic diatom-dominated assemblages[END_REF]. Being relevant only for a limited number of taxonomic groups and physiological conditions, this type of NPQ lightresponse curve was not considered in the present study.

Model fitting and parameter estimation

The light-response curve models were fitted using a procedure written in Microsoft Visual Basic and based on Microsoft Excel Solver. Model parameters were estimated iteratively by minimizing a least-squares function, forward differencing, and the default quasi-Newton search method. The model can be easily fitted using commonly available software packages. On preliminary tests, this method was compared with the fitting procedures implemented in Sigmaplot 9.0 (Systat Software, Inc., San Jose, USA) and Statistica 8.0 (Statsoft, Inc., Tulsa, USA) and no significant differences were found between the estimates of model parameters.

The standard errors of the parameter estimates were calculated following [START_REF] Ritchie | Fitting light saturation curves measured using modulated fluorometry[END_REF] and are asymptotic standard errors. For nonlinear models such as the one here tested, asymptotic standard errors may not be adequate, as they possibly underestimate the actual parameter uncertainty and cannot evaluate the eventual asymmetry of the confidence regions of estimated parameters [START_REF] Johnson | Nonlinear least-squares fitting methods[END_REF]. A number of alternative approaches exist, the best being based on Monte Carlo methods, such as the Boostrap (Press et al. 1996;[START_REF] Johnson | Nonlinear least-squares fitting methods[END_REF]). However, the benefits of pursuing alternative methods, requiring substantially more computation time, depend on the magnitude of the uncertainty associated to parameter estimation. In this study, the use of asymptotic standard errors was justified by the finding that they were on average relatively low, in a majority of cases below 10% of parameter estimates (see below, Results), in which case they can be considered acceptable [START_REF] Tellinghuisen | Stupid statistics![END_REF].

Results

Model fitting to NPQ vs. E curves

The light-response curves of NPQ measured in the plant A. thaliana and in the diatom N. palea acclimated to different growth light conditions showed a wide range of curve shapes, varying between two main types: curves with low sigmoidicity, presenting a simple saturation-like pattern (e.g. Fig. 1a, HL), and curves with high sigmoidicity, presenting an initial period of low values, followed by a phase of rapid increase leading to a stage of plateau of maximum values (e.g. Fig. 2a,HL). In all cases, the model provided an excellent fitting to the experimental data throughout the whole range of light levels explaining always more than 99.1% of the data variability (Table 2). Although the residuals (Figs. 1b,2b) showed in some cases a clearly nonrandom pattern of variation, values were typically low, between ± 5%. The fitting of the model resulted in a large variation of model parameters with species and growth light conditions, following some consistent trends. Both for A. thaliana and N. palea, the increase in growth light resulted in an increase in NPQ m (Fig. 1a, 2a; Table 2). This increase in NPQ m could be detected despite the fact that in most cases the curves did not reach their maximum values within the range of irradiances applied (e.g. Fig. 1a). Another effect of increasing growth light was the increase in the irradiance level for which the curves reached maximum values. For LL-grown samples, maximum NPQ was reached for lower irradiances, with the curves showing an overall lower sigmoidicity, while for HL-grown samples, curves reached saturation at much higher light levels. This trend could be well described by model parameter E 50 , which increased with growth light in both species (Table 2).

The most noticeable difference between the NPQ light-response curves of A. thaliana and N. palea was the apparent curve sigmoidicity, with less sigmoid curves being found for the former and more sigmoid curves (and a larger variation) for the latter. This variation in curve sigmoidicity was well characterized by the model parameter n, which averaged 1.2 for A. thaliana (varying from 0.98 to 1.44), whilst reaching an average value of 2.11 for N. palea (varying from 1.61 to 2.61). However, a different pattern of variation was found for each species, with n decreasing with growth light in A. thaliana, and increasing in N. palea (Table 2).

Model fitting to published NPQ vs. E curves

The compilation of published light-response curves of NPQ allowed gathering a large number of datasets covering a wide range of NPQ absolute values and curve shapes. The model provided a very good fit to the published data, coping with the large diversity in curve characteristics resulting from different combinations of maximum NPQ values attained (NPQ m ), irradiance range of NPQ build-up (E 50 ), and curve sigmoidicity (n) (Table 3). Considering all cases, the model explained more than 96% of data variability, independently of type of XC (and XC impaired mutants), species, growth conditions, and experimental protocol used for the generation of light curves. A summary of the meta-analysis carried out on the data set of published NPQ vs. E curves is presented in Table 4. NPQ m was the most variable parameter (c.v. 112.5%), mostly responding to growth conditions, averaging 2.89 but reaching maximum values above 9 for diatoms and even higher for some mosses (Table 3). E 50 ranged from 30-40 μmol photons m -2 s -1 to above 3500 μmol m -2 s -1 , in all cases attaining values well above growth irradiances (see below). However, with few exception (the diatoms Skeletonema costatum and Phaeocystis antarctica, and the high light-grown A. thaliana), all values of E 50 above 1200 μmol m -2 s -1 were obtained for A. thaliana mutants with impaired operation of the XC (Table 3).

n was the least variable parameter (c.v. 50.8%), meaning that the curve shape remained relatively unaltered, and that the variability in the NPQ vs. E curves was mainly due to changes in NPQ maximum values and in NPQ onset along the irradiance range. n averaged 1.7, corresponding to a noticeable degree of sigmoidicity, although values around 1.0 (no sigmoidicity) or slightly lower (mostly mutants with impaired XC) as well as above 3.0 (very high sigmoidicity) were also found (Table 3).

Despite the low number of data points forming most NPQ vs. E curves, standard errors of parameter estimates were on average relatively low (15.6, 27.3 and 12.2% of estimates for NPQ m , E 50 and n, respectively). However, standard errors were typically much higher in the cases when XC was impaired (24.5, 43.9 and 13.5% for NPQ m , E 50 and n, respectively), indicating that a high level of precision in the estimation of model parameters can be expected for samples under natural conditions.

When comparing different XC types, no clear differences were found between model parameters, due to the large overlap of their range of variation. Model parameters appeared to depend mostly on growth conditions, as larger variations could be found within the same species than amongst different taxonomic groups. The model also described very well the lightresponse curves of NPQ for composite samples (phytoplankton, microphytobenthos). Model parameters varied independently from each other, as no significant correlations were found between NPQ m , E 50 or n, either when considering all data pooled together, or when considering for separate for each XC type.

Considering the published data, the effects of growth light levels on model parameters were identical to those described for the experimental data of this study. When compared to lower light conditions, NPQ light-response curves of samples acclimated to high light showed higher values of NPQ m [START_REF] Bilger | Role of the xanthophyll cycle in photoprotection elucidated by measurements of light-induced absorbance changes, fluorescence and photosynthesis in leaves of Hedera canariensis[END_REF][START_REF] Burritt | Antioxidant metabolism during acclimation of Begonia × erytrophylla to high light levels[END_REF][START_REF] Müller-Moulé | Ascorbate-deficient mutants of Arabidopsis grow in high light despite chronic photooxidative stress[END_REF][START_REF] Ralph | Rapid light curves: a powerful tool to assess photosynthetic activity[END_REF][START_REF] Rodríguez-Calcerrada | Acclimation to light in seedlings of Quercus petraea (Mattuschka) Liebl. and Quercus pyrenaica Willd. planted along a forest-edge gradient[END_REF][START_REF] Cruz | Relationship of rapid light curves of variable fluorescence to photoacclimation and non-photochemical quenching in a benthic diatom[END_REF] and, with the exception of [START_REF] Ralph | Rapid light curves: a powerful tool to assess photosynthetic activity[END_REF], all these studies showed a similar increase in E 50 with growth light. The model also fitted very well the light-response curves of NPQ with impaired functioning of the XC, illustrating the usefulness of estimating model parameters to characterize quantitatively the effects on NPQ of inhibitors (e.g. [START_REF] Bilger | Role of the xanthophyll cycle in photoprotection elucidated by measurements of light-induced absorbance changes, fluorescence and photosynthesis in leaves of Hedera canariensis[END_REF], mutations (e.g. [START_REF] Niyogi | Arabidopsis mutants define a central role for the xanthophyll cycle in the regulation of photosynthetic energy conversion[END_REF], or changes in temperature [START_REF] Ralph | Zooxanthellae expelled from bleached corals at 33 ºC are photosynthetically competent[END_REF].

Finally, the model was also found to be adequate to describe NPQ vs. E curves generated under non-steady state conditions, i.e. derived from RLCs. The comparison of the model parameters estimated for light curves of different light steps showed the same pattern on VAZ and DD-DT samples, with shorter light steps resulting in lower NPQ m and higher E 50 , whilst n not showing any consistent trend [START_REF] Ralph | Rapid light curves: a powerful tool to assess photosynthetic activity[END_REF][START_REF] Perkins | Light response curve methodology and possible implications in the application of chlorophyll fluorescence to benthic diatoms[END_REF].

Relationship between NPQ and ETR light-response curves

To illustrate the application of the model to evaluate to what extent the NPQ response to light is related to the photoacclimation status, the light levels required for induction of NPQ and for photochemistry or ETR saturation were compared. A simple form of achieving this is by the direct comparison of model parameters E 50 and E k estimated for the two types of light-response curves. These parameters have the advantage of being measured in the same scale (PAR irradiance, µmol photons m -2 s -1 ) and of being independent of the units used to measure photosynthetic rates, ETR or NPQ, which can vary with the method in use (the case of photosynthesis) or instrument settings (the case of ETR).

For the experimental data obtained in this study, the increase in growth irradiance induced a substantial change in the photoacclimation status, noticeable by a clear change in the ETR vs E curves. As a result, the increase observed for E 50 was followed by a similarly large increase in E k , (due to the decrease of α and the increase of ETR m ), both in A. thaliana (Fig. 3) and in N. palea (Fig. 4). However, E 50 was found to be in all cases higher than E k , by 3.7 and 2.5 times, on average, for A. thaliana and N. palea, respectively (2.90 for the whole data). This result indicates that the light-induced build-up of substantial values of NPQ started only after linear electron transport reached near saturation. Furthermore, it shows that a large fraction of E 50 variability was related to variations in the photoacclimation status due to different growth light conditions, as E 50 increased linearly with E k , both for the plant as for the diatom (although the correlation was not statistical significant, but a clear linear trend is obvious; Fig. 5). This analysis also showed that the slope of the regression line of E 50 on E k was higher for A. thaliana than for N. palea, indicating that, for the same photoacclimation status (the same E k ) the plant requires a higher light level for NPQ to reach 50% of its maximum capacity. Or, in other words, that NPQ is induced latter in the range of irradiances in the plant than in the diatom.

Interestingly, the analysis of the subset of published data presenting both NPQ and ETR light-response curves, showed the same generic trend. When pooling together the published and experimental data for samples with fully operational XC (i.e. excluding mutants or samples treated with XC inhibitors) and E k estimates based only on steady state light curves (i.e.

excluding RLCs as E k estimation is largely dependent on light step duration; [START_REF] Serôdio | Rapid light-response curves of chlorophyll fluorescence in microalgae: relationship to steady-state light curves and non-photochemical quenching in benthic diatom-dominated assemblages[END_REF], the ratio E 50 /E k was found to be higher on organisms having a VAZ type of XC and to differ significantly from those having a DD-DT type (3.32 and 2.39, respectively; t-test P = 0.038; Fig. 6a).

Another way to compare the light responses of NPQ and ETR is to calculate the fraction of NPQ that is formed when ETR approaches saturation (i.e. when E = E k ), or:

m k Ek NPQ ) ( NPQ NPQ E  (4)
Low values of NPQ Ek indicate that when photochemistry saturates, NPQ is still not significantly developed (corresponding to high E 50 /E k ), whilst high values indicate that NPQ responds more promptly to light increase and the approach of ETR saturation (corresponding to low E 50 /E k ).

Considering both published and experimental data (the data subset used above for comparing E 50 /E k ), NPQ Ek averaged 0.16, and remained below 0.35, indicating that when E = E k , NPQ hardly reached over one third of the maximum attainable level. Confirming the expected inverted relationship between NPQ Ek and E 50 /E k , significantly lower values were found for organisms with a VAZ type of XC than for those with the DD-DT type (0.14 and 0.21, respectively; t-test, P = 0.023; Fig. 6b).

Model fitting and parameter estimation

Despite the usually reduced number of data points in the analyzed NPQ light-response curves (average 9.7, maximum 13), the model proposed in this study was found to be easily fitted to experimental curves, in most cases yielding parameter estimates virtually independently from the start values used in the iterative fitting procedure (although realistic start values allows a more rapid and precise parameter estimation). The main problem found when trying to fit Eq. 2 to NPQ vs. E curves occurred when the curves were very close to linear, showing no clear features like sigmoidicity or saturation. This resulted in that a similarly good fit could be reached with different combinations of model parameters values. Still, this occurred only in relatively small number of cases, like the case of the diatom Skeletonema costatum [START_REF] Lavaud | Fast regulation of photosynthesis in diatoms: mechanisms, evolution and ecophysiology[END_REF]) and some A. thaliana mutants with severe impairment of XC operation, for which some degree of uncertainty remain associated to the presented parameter estimates.

This problem seems to result from the common situation of having light-response curves constructed with the main purpose of characterizing the ETR vs. E curves, NPQ having only a secondary interest. As it often happens that the NPQ approaches its maximum for light levels much above the range used for measuring ETR, the NPQ vs. E curve may result truncated and its complete shape may not be available for model fitting. Yet, the relationship established between NPQ and ETR light curves in similar data may be used to impose boundaries to the model parameter estimates, and thus help to reach a single set of meaningful values.

Discussion

Model assumptions

The model proposed for describing the NPQ vs. E curve is based on the main assumption that NPQ is mostly due to q E , the 'energy-quenching' associated to the build-up of the transthylakoid ΔpH and the operation of the XC. This assumption is generally supported by the finding of strong linear relationships between NPQ and de-epoxidized xanthophylls in all groups investigated (plants, green algae, diatoms, Chrysophyceae) and under a wide range of experimental conditions. However, besides q E , NPQ also quantifies the fluorescence quenching caused by state transitions (q T ) or by photoinhibition (q I ) which may potentially significantly affect the NPQ vs. E curves. q T is relevant in phycobilisome-containing organisms (cyanobacteria and red algae) [START_REF] Campbell | Chlorophyll fluorescence analysis of cyanobacterial photosynthesis and acclimation[END_REF]Mullineaux and Emlyn-Jones 2004), although not as much in higher plants and green algae [START_REF] Pfannschmidt | Acclimation to varying light qualities: toward the functional relationship of state transitions and adjustment of photosystem stoichiometry[END_REF][START_REF] Eberhard | The dynamics of photosynthesis[END_REF][START_REF] Ruban | Dynamics of higher plant photosystem cross-section associated with state transitions[END_REF], and it does not occur for the Heterokontophyta [START_REF] Lavaud | Fast regulation of photosynthesis in diatoms: mechanisms, evolution and ecophysiology[END_REF]. When occurring, q T is not significant in light conditions triggering q E -related NPQ (Mullineaux and Emlyn-Jones 2004;[START_REF] Tikkanen | State transitions revisited -a buffering system for dynamic low light acclimation of Arabidopsis[END_REF][START_REF] Ruban | Dynamics of higher plant photosystem cross-section associated with state transitions[END_REF]. With the exception of some land plants (overwintering conifers and tropical evergreen species), q I origin is not clearly defined and it requires particular conditions such as prolonged environmental stress [START_REF] Müller | Non-photochemical quenching. A response to excess light energy[END_REF][START_REF] Demmig-Adams | Photoprotection in an ecological context: the remarkable complexity of thermal energy dissipation[END_REF][START_REF] Horton | Photosynthetic acclimation: does the dynamic structure and macro-organisation of photosystem II in higher plant grana membranes regulate light harvesting states?[END_REF].

The effects of q T or q I on the light-response curve of NPQ would likely consist in a general change in curve shape, through the increase of NPQ at low light levels (for q T ) and of NPQ m (for q I ). However, these components of NPQ may be expected not to significantly affect the NPQ vs. E curves measured under the usually applied experimental protocols. This is because the duration of the light steps commonly applied (≤ 2-3 min, and much shorter in the case of RLCs) correspond to light doses clearly different than those required to induce both q T or q I [START_REF] Campbell | Chlorophyll fluorescence analysis of cyanobacterial photosynthesis and acclimation[END_REF][START_REF] Müller | Non-photochemical quenching. A response to excess light energy[END_REF][START_REF] Demmig-Adams | Photoprotection in an ecological context: the remarkable complexity of thermal energy dissipation[END_REF][START_REF] Horton | Photosynthetic acclimation: does the dynamic structure and macro-organisation of photosystem II in higher plant grana membranes regulate light harvesting states?[END_REF][START_REF] Ruban | Dynamics of higher plant photosystem cross-section associated with state transitions[END_REF].

The same reasoning applies to another implicit assumption of the model, that during the generation of a light curve q E is due solely to the development of the ΔpH and the subsequent de-epoxidation of the present (and susceptible of being de-epoxidized) pool of xanthophylls. In fact, it is well established that exposure to high light can induce the de novo synthesis of XC pigments (e.g. [START_REF] Olaizola | Short-term response of the diadinoxanthin cycle and fluorescence yield to high irradiance in Chaetoceros muelleri (Bacillariophyceae)[END_REF][START_REF] D'haese | Non-photochemical quenching kinetics during the dark to light transition in relation to the formation of antheraxanthin and zeaxanthin[END_REF][START_REF] Lavaud | General features of photoprotection by energy dissipation in planktonic diatoms (Bacillariophyceae)[END_REF][START_REF] Demmig-Adams | Photoprotection in an ecological context: the remarkable complexity of thermal energy dissipation[END_REF]. This process causes the accumulation of de-epoxidized forms, which could result in the linear increase of NPQ in the high-light part of the curve.

Again, the de novo synthesis requires the prolonged exposure to very high irradiances (e.g. [START_REF] Lavaud | General features of photoprotection by energy dissipation in planktonic diatoms (Bacillariophyceae)[END_REF][START_REF] Demmig-Adams | Photoprotection in an ecological context: the remarkable complexity of thermal energy dissipation[END_REF][START_REF] Lavaud | Fast regulation of photosynthesis in diatoms: mechanisms, evolution and ecophysiology[END_REF], well above the light doses applied during the construction of NPQ light-response curves.

Nevertheless, even if significant q T , q I or de novo pigment synthesis do occur, the resulting curve may still be of the same general shape and describable by the model. In fact, this study showed that the model fits very well to data obtained in a wide range of experimental conditions, in which the occurrence of any of these processes cannot be completely ruled out (Table 3). In this case, however, care should be taken in interpreting and comparing the model parameters estimated for different species or condition, as they may be affected differently by processes other than the build-up of the ΔpH and the XC. In the case of organisms with impaired operation of the XC (mutants or inhibitor-treated samples), the model was nevertheless shown to be of value, providing a useful quantitative characterization of the light response of NPQ.

Another major assumption of the model is that the formation of q E , through the deepoxidation of Vx or DD generated by the acidification of the lumen relates to incident irradiance following the generic conditions of application of the Hill equation, i.e. that NPQ can be considered as allosterically regulated by irradiance through the build-up of the transthylakoidal ΔpH. This assumption is partially supported by the finding that, in isolated plant chloroplasts, the regulation of q E is of allosteric nature, resulting in response curves of q E as a function of ΔpH of sigmoidal shape, shown to be adequately described by the Hill equation [START_REF] Pfündel | The pH dependence of violaxanthin deepoxidation in isolated pea chloroplasts[END_REF][START_REF] Ruban | Kinetic analysis of nonphotochemical quenching of chlorophyll fluorescence. 1. Isolated chloroplasts[END_REF][START_REF] Takizawa | The thylakoid proton motive force in vivo. Quantitative, noninvasive probes, energetics, and regulatory consequences of light-induced pmf[END_REF][START_REF] Pérez-Bueno | The Lhcb protein and xanthophyll composition of the light harvesting antenna controls the ΔpH-dependency of nonphotochemical quenching in Arabidopsis thaliana[END_REF]. This sigmoidicity is attributed to the protonation of binding sites of the LHC protein Psbs induced by lumen acidification, and subsequent conformational changes within the LHC, switching the de-epoxidized xanthophylls to an 'activated' state. It is taken as an indication of allosteric regulation of q E , resulting from proton binding showing positive cooperativity, and the 'activated' de-epoxidized xanthophylls Zx [START_REF] Horton | Allosteric regulation of the light-harvesting system of photosystem II[END_REF][START_REF] Horton | Photosynthetic acclimation: does the dynamic structure and macro-organisation of photosystem II in higher plant grana membranes regulate light harvesting states?[END_REF][START_REF] Li | Sensing and responding to excess light[END_REF] or DT [START_REF] Goss | The importance of a highly active and ΔpHregulated diatoxanthin epoxidase for the regulation of the PS II antenna function in diadinoxanthin cycle containing algae[END_REF][START_REF] Lavaud | In diatoms, the transthylakoid proton gradient regulates the photoprotective non-photochemical fluorescence quenching beyond its control on the xanthophyll cycle[END_REF] acting as a positive effector.

The strong physiological basis of the proposed model is likely to explain its success to cope with a large diversity of light-response curve characteristics. Other mathematical models have also been used to successfully describe NPQ vs. E curves, namely an exponential saturation function, the Michaelis-Menten function, and a hyperbolic tangent function [START_REF] Ritchie | Fitting light saturation curves measured using modulated fluorometry[END_REF]). However, these models have only been tested on a reduced dataset, and on light curves of low sigmoidicity. Interestingly, the model that yielded the better fit to experimental data was the Michaelis-Menten equation [START_REF] Ritchie | Fitting light saturation curves measured using modulated fluorometry[END_REF], a particular case of the model proposed in the present study.

Model fitting to NPQ vs. E curves

The usefulness of the model was demonstrated by the possibility to estimate NPQ m despite the fact that in most cases the curves did not reach a saturation plateau within the range of irradiances applied (e.g. Fig. 1a). When assuming NPQ to represent mostly q E , the maximum NPQ reached by a sample quantifies its photoprotective potential via the dissipation of excessive light energy. By applying the model, curves measured under different experimental conditions can be readily compared, and changes in NPQ m (e.g. following changes in growth light conditions) can be quantified, which would be otherwise impossible. The accurate estimation of NPQ m is also required for quantifying E 50 , which, in some cases of strict relationship (e.g. for most Heterokontophyta; [START_REF] Lavaud | General features of photoprotection by energy dissipation in planktonic diatoms (Bacillariophyceae)[END_REF][START_REF] Lavaud | Fast regulation of photosynthesis in diatoms: mechanisms, evolution and ecophysiology[END_REF], is interpretable as the light level corresponding to the de-epoxidation and 'activation' of the xanthophyll convertible pool necessary to induce half of the maximal NPQ. The size of the xanthophyll convertible pool can be very different in VAZ and DD-DT organisms varying with species and growth conditions, ranging between 50 and 70% [START_REF] Lavaud | Fast regulation of photosynthesis in diatoms: mechanisms, evolution and ecophysiology[END_REF][START_REF] Goss | Regulation and function of xanthophyll cycle-dependent photoprotection in algae[END_REF]. Again, the fit of Eq. 2 to NPQ vs. E curves provided an adequate form of characterizing how promptly the XC is ΔpH-activated when responding to an increase in incident irradiance. However, while NPQ m and E 50 can be grossly estimated by visual inspection of the curves (at least when saturation is reached for the light levels applied), the curve sigmoidicity can hardly be characterized quantitatively without the fit of the model and estimation of n. The sigmoidicity coefficient was found to vary around 1.5-2.0, values corresponding to positive cooperativity and thus indicating the allosteric regulation of NPQ by light. Minimum n values averaged about 1 (reaching significantly lower values only for cases of XC impairment), indicate that negative cooperativity is not involved in the regulation of processes underlying NPQ. These results generally support that the allosteric nature known for the more fundamental regulation of q E by ∆pH in plants [START_REF] Ruban | Kinetic analysis of nonphotochemical quenching of chlorophyll fluorescence. 1. Isolated chloroplasts[END_REF][START_REF] Li | Sensing and responding to excess light[END_REF]) holds for the relationship of NPQ to irradiance in a large diversity of photosynthetic organisms.

The Hill coefficient has been interpreted as representing the number of allosteric regulators [START_REF] D'haese | Non-photochemical quenching kinetics during the dark to light transition in relation to the formation of antheraxanthin and zeaxanthin[END_REF]). Considering the diversity of factors likely to contribute to the NPQ vs. E curve (Demmig-Adams and Adams 2006; [START_REF] Eberhard | The dynamics of photosynthesis[END_REF][START_REF] Horton | Photosynthetic acclimation: does the dynamic structure and macro-organisation of photosystem II in higher plant grana membranes regulate light harvesting states?[END_REF][START_REF] Li | Sensing and responding to excess light[END_REF]), some of them not fully identified in some photosynthetic taxa [START_REF] Lavaud | Fast regulation of photosynthesis in diatoms: mechanisms, evolution and ecophysiology[END_REF], n should be considered simply as an empirical coefficient informing on the degree of allostery and serving as a practical descriptor of the curve shape.

Relationship of NPQ light response to photoacclimation status

The modelling of the NPQ vs. E curves opens the new possibility of quantitatively comparing the light responses of NPQ and of photochemistry or ETR. Photosynthesis and ETR lightresponse curves are very commonly used as a form of characterizing the photoacclimation status of photosynthetic organisms, through the estimation of the parameters of a number of available models [START_REF] Henley | Measurement and interpretation of photosynthetic light-response curves in algae in the context of photoinhibition and diel changes[END_REF][START_REF] Behrenfeld | In search of a physiological basis for covariations in light-limited and light-saturated photosynthesis[END_REF][START_REF] Ralph | Rapid light curves: a powerful tool to assess photosynthetic activity[END_REF][START_REF] Guarini | Modelling the dynamics of the electron transport rate measured by PAM fluorimetry during Rapid Light Curve experiments[END_REF][START_REF] Perkins | The application of variable chlorophyll fluorescence to microphytobenthic biofilms[END_REF]. By describing the NPQ vs. E curve by a small set of meaningful parameters, the light response of NPQ can be characterized relatively to the one of ETR or photosynthetic rate. This possibility is useful for the definition of the light levels corresponding to the onset of NPQ (e.g. activation of the XC) relatively to the saturation of photochemistry. As the light response of NPQ may depend greatly on the photoacclimation status, the characterization and comparison of NPQ vs. E curves should be preferably normalized to parameters indicative of photochemistry saturation. Furthermore, the comparison of the NPQ and ETR light responses is also of interest because it provides insight on the way an organism combines the responses of photochemistry and of photoprotective processes to changes in ambient light. However, without adequate parameterization of the NPQ light-response, this question can be answered only approximately.

Despite its simplicity, the indices E 50 /E k and NPQ Ek here proposed provide an efficient form of comparing the light levels for which NPQ reaches significant values and photochemistry reaches saturation. The application of these indices allowed quantifying the delay of the light response of NPQ relatively to the saturation of photochemistry. Under the assumption that NPQ mostly represents q E , it showed that it takes about three times the irradiance at E k for half of q E to develop and that, at E k , the formation of q E is still at relatively low levels, providing typically less than one fifth of maximum photoprotective capacity. For the cases when q E is strictly related to the XC operation (e.g. in most of Heterokontophyta; [START_REF] Lavaud | General features of photoprotection by energy dissipation in planktonic diatoms (Bacillariophyceae)[END_REF][START_REF] Lavaud | Fast regulation of photosynthesis in diatoms: mechanisms, evolution and ecophysiology[END_REF], the values of the indices E 50 /E k and NPQ Ek can be interpreted in terms of the de-epoxidation state of the convertible pool of xanthophylls and their 'activation' upon LHC protonation. Yet, the modelling of the NPQ vs. E curve may allow for the development of other indices that better characterize this relationship.

Interestingly, the meta-analysis carried out in this study showed consistent differences between the relationships of NPQ light response to photoacclimation status in organisms with VAZ and DD-DT types of XC. The fact that these differences were found despite the diversity in taxa and growth conditions may indicate that they are due to fundamental differences in the way the two types of organisms cope with high light, especially regarding the underlying q E mechanism and regulation of the XC, illustrating the advantages provided by the quantitative description of the NPQ vs E curve.

(programme 'chercheurs invités') to both. We thank two anonymous reviewers for critical 576 comments on the manuscript. of [START_REF] Eilers | A model for the relationship between light intensity and the rate of photosynthesis in phytoplankton[END_REF] fitted to the ETR vs. E curves are presented. Estimates of the parameters of the curves fitted to the NPQ vs. E curves are presented in Table 2.

  parameters makes it difficult to compare curves measured in different studies or experimental conditions or taxonomic groups. The present study proposes a simple mathematical model for the quantitative description of the generic NPQ vs. E curve, by means of the estimation of a small number of physiologically-meaningful parameters. The model is based on the close, but not absolute, dependence of NPQ on the operation of the XC, through the light-induced de-epoxidation of PS II antenna pigments Vx or DD. To illustrate the main features and variability of the NPQ vs. E curve, as well as the interpretation of model parameters, light-response curves were measured on a plant (Arabidopsis thaliana (L.); VAZ type XC) and a diatom (Nitzschia palea (Kütz) W. Smith; DD-DT type XC) grown under experimental conditions expected to induce a large variability in curve shape and NPQ absolute values. The adequacy of the model was further tested by fitting it to published NPQ vs. E curves measured on a large variety of photosynthetic organisms and experimental conditions, and covering the widest possible range of NPQ values and curve shapes. The usefulness of the model was also illustrated by exploring the relationship between NPQ vs. E curves and the photoacclimation status, characterized by light-response curves of the PSII electron transport rate, ETR.

  irradiance (µmol photons m -2 s -1 ) E 50 -Irradiance level corresponding to 50% of NPQ m in a NPQ vs. E curve E k -Light-saturation parameter of the ETR vs. E curve ETR -PSII relative electron transport rate ETR m -Maximum ETR in a ETR vs. E curve F o , F m -Minimum and maximum fluorescence of a dark-adapted sample F s , F m ' -Steady state and maximum fluorescence of a light-adapted sample NPQ -Non-photochemical quenching NPQ m -Maximum NPQ value reached in a NPQ vs. E curve NPQ Ek -Fraction of NPQ m reached when E = E k n -Sigmoidicity coefficient of the NPQ vs. E curve PSII -Photosystem II RLC -Rapid light-response curve VAZ -Vx-Ax-

Fig. 1 .

 1 Fig. 1. Fitting of Eq. 2 to light-response curves of NPQ measured in the plant A. thaliana grown

Fig. 2 .

 2 Fig. 2. Fitting of Eq. 2 to light-response curves of NPQ measured in the diatom N. palea grown

Fig. 3 .

 3 Fig. 3. Comparison between the light-response curves of NPQ and of ETR of A. thaliana grown

Fig. 4 .

 4 Fig. 4. Comparison between the light-response curves of NPQ and ETR of N. palea grown

Fig. 5 .

 5 Fig. 5. Relationship between the parameter E 50 of Eq. 2 fitted to the NPQ vs. E curves and the parameter E k of the[START_REF] Eilers | A model for the relationship between light intensity and the rate of photosynthesis in phytoplankton[END_REF] model fitted to the ETR vs. E curves, for the plant A. thaliana (circles) and the diatom N. palea (squares) grown under high (white), moderate

Fig. 6 .

 6 Fig. 6. Comparison between the ratios E 50 /E k (a) and NPQ(E k )/NPQ m (b) as calculated for the published (excluding cases with impaired XC operation) and experimental (this study) light-

Table 2 .

 2 Summary of the results of the fitting of the model to NPQ vs. E curves measured in A. thaliana and N. palea grown under low (LL), moderate (ML) and high light (HL). Parameter estimates ± one standard error.

				Model parameters
			NPQ m	E 50	n	r 2
	A. thaliana	LL	3.91 ± 0.82	209.9 ± 8.31	1.44 ± 0.52	0.999
		ML	4.63 ± 0.24	542.0 ± 49.2	1.21 ± 0.04	0.999
		HL	5.90 ± 1.04	1141.0 ± 372.1	0.98 ± 0.06	0.998
	N. palea	LL	2.70 ± 0.10	91.7 ± 7.01	1.61 ± 0.19	0.991
		ML	3.65 ± 0.05	312.6 ± 5.59	2.16 ± 0.05	0.999
		HL	3.86 ± 0.11	551.4 ± 15.8	2.55 ± 0.08	0.999

Table 3 .

 3 Results of fitting of Eq. 2 to published NPQ vs. E curves. Composite: samples containing organisms with different XC types. LC: light curve protocol

	(SS: steady state LL; RLCx: rapid light curve, x seconds light step; N-SLC: non-sequential light curve). Treatment: conditions applied before the measurement
	of the light curves (PAR, temperature); growth conditions when more than one curve available for the same taxon (HL: high light; LL: low light; DTT: XC
	inhibitor dithiothreitol; LL/HL: transfer from LL to HL; Dense: plants from dense forest stand; Edge: plants from forest edge; IL: intermittent light; CL:
	continuous light; wt: wild type; aba1, crr6, CRR6, lut1, lut2, lut2, npq1, npq2, npq4, npq5, vtc2: mutants; LI-1, Sf-2, Col-0, Ws-2: Arabidopsis accessions;
	Mixing: water column mixing). Parameter estimates ± one standard error.
							Model parameters
	XC type	Taxon		LC	Treatment	NPQ m	E 50	n	r 2	Reference
	VAZ	Magnoliophyta	Arabidopsis thaliana	SS	wt 10 ºC	2.07 ± 0.04	113.6 ± 6.0	1.11 ± 0.08 0.998 Havaux and
		(flowering plants)			wt 25 ºC	2.98 ± 0.40	1118.0 ± 293.8 1.09 ± 0.11 0.996	Kloppstech
					npq1 10 ºC	1.68 ± 0.25	636.5 ± 587.0	0.40 ± 0.06 0.998	(2001)
					npq1 25 ºC	1.16 ± 0.22	867.1 ± 557.5	0.63 ± 0.10 0.995
				SS	Li-1	3.76 ± 0.18	563.8 ± 40.6	1.83 ± 0.16 0.998 Jung and
					Sf-2	4.12 ± 0.16	661.9 ± 33.7	2.03 ± 0.13 0.999	Niyogi (2009)
					Col-0	3.29 ± 0.19	683.7 ± 55.0	1.84 ± 0.16 0.998
					Ws-2	3.32 ± 0.19	599.8 ± 49.1	1.96 ± 0.21 0.997
				SS	wt	2.06 ± 0.08	184.1 ± 13.4	2.21 ± 0.32 0.993 Lokstein et al.
					lut1	1.52 ± 0.06	195.5 ± 13.7	2.28 ± 0.33 0.994	(2002)
					lut2	1.76 ± 0.10	231.0 ± 22.2	1.72 ± 0.22 0.995
					aba1	2.36 ± 0.19	251.1 ± 43.2	1.14 ± 0.13 0.996
					lut2aba1	1.17 ± 0.07	214.7 ± 30.6	1.08 ± 0.10 0.997

Table 4 .

 4 Summary of the meta-analysis of the results of the fitting of the model to published NPQ vs. E curves (listed in Table3). Mean values ± one standard error.

	Model parameters

Acknowledgements

We thank Glória Pinto, Eleazar Rodriguez and Armando Costa for helping with the seeding of the Arabidopsis plants. This study was supported by FCT -Fundação para a Ciência e a Tecnologia, grant SFRH/BSAB/962/2009, to J. Serôdio, by the French consortium CPER-Littoral to J. Lavaud, and by the CNRS -Centre National de la Recherche Scientifique


M Ammar
email: ammar@satie.ens-cachan.fr

F Mazaleyrat

J P Bonnet

P Audebert

A Brosseau

G Wang

Y Champion

Synthesis and characterization of core-shell structure silica-coated Fe 29.5 Ni 70.5 nanoparticles

In view of potential applications of magnetic particles in biomedicine and electromagnetic devices, we made use of the classical Stöber method -base-catalysed hydrolysis and condensation of tetraethoxysilane (TEOS) -to encapsulate FeNi nanoparticles within a silica shell. An original stirring system under high power ultrasounds made possible to disperse the otherwise agglomerated particles. Sonication guaranteed particles to remain dispersed during the Stöber synthesis and also improved the efficiency of the method. The coated particles are characterized by electron microscopy (TEM) and spectroscopy (EDX) showing a core-shell structure with a uniform layer of silica. Silica-coating does not affect the core magnetic properties. Indeed, all samples are ferromagnetic at 77 K and room temperature and the Curie point remains unchanged. Only the coercive force shows an unexpected non-monotonous dependence on silica layer thickness.

1.

Introduction

Magnetic-metal nanoparticles encapsulated in a dielectric inorganic material are considered to have practical applications in electromagnetic devices, biology and fundamental study to improve the local physical investigation of magnetic nanostructures. In the core-shell structure, the core size-dependant magnetic susceptibility at room temperature combined with the chemical stability of the silica coatings suggests that the resulting nanocomposite may be a good candidate for biomedical applications, such as magnetic separation, drug targeting, image contrast in magnetic resonance imaging and hyperthermia therapy [1,2,[START_REF] Richards | Nanofabrication Towards Biomedical Applications[END_REF]. Magnetic fluids dedicated for clinical applications are typically colloidal suspensions of iron, magnetite, iron-nickel and cobalt nanoparticles coated with biocompatible surfactants [START_REF] Behrens | [END_REF]. Actually, there are two fundamental criteria to prevent the catalysis of damaging reactions within cells, the reduction of the toxicity of the vector conveying the solution due to its oxidative alteration and its chemical time stability. Accordingly, the silica coating of magnetic nanoparticles is one of promising tool to ensure this specific biocompatibility and leads to low toxicity material. Magnetic-dielectric nanocomposites have also attracted sustained interest over one century owing to their unusual combined magnetic and electric properties. In fact, due to their metallic nature, eddy currents limit application of magnetic nanoparticles at high frequency. The coating by an insulating shell on the surface of soft magnetic nanoparticle cores such as FeNi confers to the material a high permeability independent of the frequency even in GHz range [5]. Such materials are typically suited for applications in telecommunication [6]. On the other hand, the ability to control magnetic interactions is an important consequence of the coating of magnetic particles, which has been explored in details by several authors for particles in solution [7] and close-packed thin films [8]. Coating thickness controls both insulation of nanoparticles and interparticle distance and, therefore, the interparticle interactions [9]. This provided substantially reliable results to study magnetic nanostructure of nanoparticles using electron holography [10]. Several synthetic routes for producing magnetic nanoparticles have been explored during the last decade including chemical vapor condensation (CPVD), powder pyrolysis and sonochemical synthesis [11,12,13]. However, nanoparticles synthesized by these methods frequently display a relatively poor cristallinity or polydispersity in their shape or/and size, which affects their magnetic properties. Evaporation-cryo-condensation process has been developped to overcome some of these problems. In the present work, cryogenic melting has been used to produce Fe 29.5 Ni 70.5 nanoparticles and consequently to guarantee more cristallinity and a better stability in the elemental chemical composition. Additionally, several approaches, such as the sol-gel process [14], co-precipitation [15,16,17], metal-dielectric cosputtering deposition [18] or metal ion deposition, have been used to prepare magneticinsulator nanocomposites. Our present approach is to start from metallic nanoparticles and to coat them with an inorganic-dielectric polymer in order to control the morphology of the shell. In this paper, a modified Stöber approach has been used to encapsulate in silica the asprepared metallic FeNi particles. In fact, we have introduced high-power sonochemistry not only in the dispersion step, but also during the synthesis to improve the effectiveness of the classical Stöber method [19,20].

2.

Experimental details Synthesis of Fe 29.5 Ni 70. 5 nanoparticles FeNi nanoparticles with well-defined morphology and homogeneous chemical composition were synthesised using the cryogenic melting technique. This method consists in sliding down a feeding bar of metal (Fe 29.5 Ni 70.5 ) into a Radio Frequency (RF) reactor. A drop of molten metal forms at the edge and falls onto the inductors where it is levitated to complete transformation into nanocrystalline powders. In order to have sufficient vapour pressure, the metal must be heated up by several hundred degrees over its melting temperature (over 2000°C for Fe, Ni). The size of particle depends critically on the metal vapour pressure. The gas produced from the cryogenic liquid carry the particles into a canvas filter. Technical details are reported in [21]. The as-obtained iron-nickel nanopowders are composed of spherical particles with an average diameter of about 55 nm (deduced from microscopy, standard deviation 20 nm). From Electron Energy Loss Spectroscopy (EELS) the chemical composition is homogeneous from one particle to another as well as inside the nanoparticles. The fraction of iron x = 0.295 is of particular interest since large amounts can be produced with no deviation in chemical composition [22]. Because metallic nanoparticles are pyrophoric in air, they are collected in hexane where an oxide layer of approximately 2 nm forms, making possible their manipulation without risk. The magnetization of as-prepared iron-nickel particles (75 Am 2 /kg) is 20% lower compared to the bulk alloy magnetization, which confirms the non-magnetic nature of the oxide layer observed from electron microscopy and analysed using XPS (X-Ray Photoemission Spectroscopy). Essentially Nickel Hydroxides Ni(OOH) and Ni(OH 2 ), iron oxide Fe 2 O 3 and FeO were detected [22].

Synthesis of Silica-coated Fe 29.5 Ni 70.5 nanoparticles

The silica shell onto FeNi core was synthesized according to the Stöber method [23] (sol-gel reaction) without any silane coupling agent (like 3-aminopropyltrimethoxysilane which is sometimes used for noble metals nanoparticules silica coating [24]). Indeed, oxide shell covering FeNi nanoparticles is expected to enhance the SiO 2 shell binding. Ethanol (95-96% synthesis grade) and Ammonia solution (28% analytical grade) were purchased from SDS/CARLO ERBA, tetraethylorthosilicate (TEOS) ≥ 98% (GC) from FLUKA. All reagents were used as received without further purification. Ultrasonic dispersion was carried out with a Bandelin 200W (variable from 10 to 100%) ultrasonic processor (Sonopuls HD 2200) fitted out with a horn of 13×3 mm. All experiments were made in glass flask equipped with a cooling jacket to keep the mixture temperature constant. Typically, 80 mg of raw Fe 29.5 Ni 70.5 nanoparticles were first sonicated in 50 ml of ethanol during 90 minutes under a controlled ultrasonic power of 3 W/cm 3 . Then, various volumes of TEOS and ammonia 28% (NH 4 OH) were successively introduced into the suspension and the mixture was again sonicated for 90 minutes under a power of 0.5 W/cm 3 to complete the solgel reaction (Figure 1). Finally the suspensions are centrifuged at 3000 rpm for 10 minutes, the solvent is discarded, and the FeNi nanoparticles are ultrasonically redispersed in 50 ml of ethanol. This purification process (centrifugation/dispersion under sonication) was repeated three times. The particles were then transferred into ethanol to avoid any further growth or chemical modification of the silica layer. Subsequently, an amount of the coated nanoparticles were dried under reduced pressure and moderate temperature to remove remaining solvent and to prepare samples for the physical characterization. Four samples with different reagent concentrations have been produced (see table 1).

Characterization and techniques

Thermal degradation analyses were made with a Perkin-Elmer Pyris 6-TGA instrument using standard ceramic crucibles and sample mass of 1-29mg. The samples were heated at a rate of 10 °C min -1 from room temperature to 1000 °C in an air flow of 10 ml min -1 or an argon flow of 80 ml min -1 . The analyser was coupled to a permanent magnet producing a gradient field in the crucible to measure the Curie temperature (T c ). These measurements are conducted under argon flow to avoid adventitious oxidation of the nanoparticles. Fourier Transform Infra-Red spectra (FTIR) were recorded with a Thermoelectron Corporation NEXUS spectrometer equipped with an attenuated total reflectance probe (ATR) covering the wavenumber range 4000-700 cm -1 . The morphology and size of the particles were analysed by conventional and high resolution electron microscopy (HRTEM) using a TECNAI F20 microscope (operating at 200 kV with a point-to-point resolution of 0.24 nm), on the powders deposited onto a microscopy grid coated with an amorphous carbon film. Powders were also characterized by Electron Energy Loss Spectra (EELS) in a Gatan Image Filter (GIF 2000) spectrometer coupled to the TECNAI F20. Fitting and integration windows of 30 eV were used for all the chemical maps and the spectra were obtained with an energy resolution of 1.2 eV. Elemental chemical analysis of the nanocomposites was also performed using Energy Dispersive X-rays (EDX) attached to the same system. The quasi-static hysteresis loops with an applied magnetic field of -300 kA/m < H < 300 kA/m were acquired using a home-made Vibrating Sample Magnetometer (VSM) between room and liquid nitrogen temperature.

3.

Results and discussion

Fourier Transform Infrared (FTIR) spectroscopy was used to identify the functional groups present on the surface of FeNi@SiO2 nanoparticles. Comparison of uncoated and silicacoated particles FT-IR spectra (Figure 2) shows a pronounced change detected in the 1300-700 cm -1 region, which clearly indicates the presence of the silica coating. The peaks at 970 and 1070 cm -1 correspond to the characteristic Si-O-Si bond, typically attributed to the Si-O - symmetric stretching and Si-O-Si asymmetric stretching respectively, in agreement with [25]. Analysis of bonding configurations from FTIR data suggest also the existence of Si-O-C or/and ≡Si-O-Si≡ functions (bands under 1000 cm -1 ). Nevertheless, the spectra are obviously dominated by the Si-O-Si bonding vibrations, for all coated samples. The presence of this type of strained bond is a clear evidence of the mechanical stress in the silica sheath, which in turn may strain the FeNi nanoparticles. The chemical composition was examined using Energy-Dispersive X-ray (EDX) spectroscopy, which shows a Fe 29.5 Ni 70.5 core coated by silica shell (Figure 3). The copper lines in this figure are due to the copper grid used as TEM sample holder. An atomic ratio of Si/O = 1/0.6 was obtained on the core-shell structure, indicating that the off-stoichiometric silica shell is silicon-rich in nature. The structural evolution study suggests that the silica layer grows without affecting the integrity of the FeNi core. Indeed, the spectra do not reveal other elements except those present initially in the FeNi core, the oxide layer, the silica shell and the copper grid. Figure 4 shows TEM pictures of FeNi@SiO 2 particles synthesized using various TEOS volumes. Observation of figure 4 images (a), (b), (c) and (d) clearly shows the shell thickness dependence on TEOS concentration (see also table 1). Additionally Energy Filtered in scanning TEM mode, which one can see an illustration on the inset (f) of figure 4, comes to support the elementary chemical nature of the silica-layer surrounding the nanoparticles. In fact, the image exhibits a chemical cartography obtained from EELS and undeniably shows the formation of silica uniformly on the FeNi core.

The properties of oxidation-resistance of the FeNi@SiO 2 composite were tested by TGA. Figure 5 shows the typical curves of thermal analysis of metallic materials [26]. Correspondingly, the weight increment of the coated particles (sample 5) caused by FeNi oxidation decreased from 28% to 5% relative to that of the uncoated FeNi particles (sample 1). It is clear that a thicker shell of silica can protect the nickel-iron from oxidation more efficiently. For instance the oxidation of the FeNi core of FeNi@SiO 2 composites (sample 4) proceeds at ~430 °C which is 250 °C higher than for as-prepared FeNi nanoparticles. The weight loss, observed for coated samples starting from RT, is attributed to the surface dehydration of the silica monolayer and the loss of others organic compounds which are volatile in this range of temperature [27].

For many applications of core-shell particles, such as electromagnetic devices [28], it is of essential importance to control precisely the thickness of the shell. In the system under consideration, the simplest approach to vary shell thickness is to use different amounts of TEOS. Consequently, we investigate the effect of adding various amounts of TEOS in a single step. Figure 4 (e), which features a typical high resolution image (HRTEM) for sample 4, reveals a core-shell structure with an uniform amorphous silica coating (thickness 15 nm). For comparison, the thickness of silica-shell is deduced from magnetic characterization. In fact, the volume of SiO 2 can be estimated using where V and m are for volume and weight, respectively, ρ SiO2 is the silica density estimated experimentally (2270 kg/m 3 ) and M s (Am 2 /kg) is the specific magnetic moment at saturation; "coated" indicates the coated sample, and "free" corresponds to the raw FeNi powder. Assuming that the nanoparticles are monodisperse and 55 nm in diameter, the theoretical thickness t MAG required to increase the radius R of the seed particle to a final radius R+t MAG is given by [START_REF] Clausis | Die mechannistische Wärmelehre II[END_REF]

        - = = ) ( ) (
          -         + = 1 1 3 2 FeNi FeNi SiO MAG m V R t ρ where 2 SiO Coated FeNi m m m - =
is the weight of the effective magnetic component in the nanocomposite. The bulk Fe 29.5 Ni 70.5 density was used (8450 kgm -3 [START_REF] Bozorth | Ferromagnetism D[END_REF]). Figure 6 shows the dependence of the thickness of silica shell, deduced from TEM analysis and magnetic measurements, on TEOS volume. Interestingly, the two data are consistent with a quantitative silica formation on the nanoparticles for thin silica layer up to 20 nm. Above this limit t MAG presents a discrepancy compared to t TEM for thicker silica layer (beyond 20 nm). This could be explained by the presence of free silica nanoparticles synthesized when a large amount of TEOS is added. After centrifugation, the calculated volumic amount of silica coating the nanoparticles is underrated and therefore, the deduced silica-shell thickness is erroneous.

4.

Magnetic properties

The TGA recordings under constant magnetic field are presented in figure 7. Due to the neutral atmosphere (argon flow), oxidation was inhibited. Up to 600 °C we observe a weak weight drop due to a chemical desorption from the silica shell for coated particles as reported in [27]. Comparable weight loss is observed for uncoated sample 1 due to the desorption of organic chains adsorbed in the oxidized FeNi surface during the passivation step of the nanoparticles. The TGA traces show a characteristic feature for all samples which reveals a typical ferromagnetic-to-paramagnetic transition at the Curie temperature (T c ). Noticeably, the nanocomposites (sample 2 to 5) exhibit a broaden transition. Obviously, this makes difficult the extraction of T c which roughly maintains a stable value of 605 °C (± 5 °C) for all samples in agreement with the literature [START_REF] Bozorth | Ferromagnetism D[END_REF].

A comparative measurement of hysterisis loops at 300 K (RT) and 77 K was performed for both uncoated and silica-coated nanoparticles using VSM as mentioned previously. Magnetization curves are reported in figure 8 and the main quantities are listed in table 2 (specific saturation magnetization, remanent magnetization and coercivity at 77 K and RT). All curves at RT saturate approximately at the same applied field than those measured at 77 K. For the same operating temperature, loops for coated samples appear to have a component whose magnetization continues to increase with increasing field up to 200 kA/m, whereas the raw FeNi powder saturates much faster than the nanocomposites. In fact the interparticle interactions are modulated by the thickness of the coating layer which isolates the particles. As a result the nanocomposite hardens magnetically and its saturation becomes difficult [6,18,[START_REF] Salgueirino-Maceira | [END_REF]. For all samples there is only a slight deviation regarding the saturation magnetization between 77 K and RT because RT/T c ≈ 0.3. Furthermore, the coating quality is examined in saturation magnetization versus silica-layer thickness plots as an inset in figure 8 (right side). It is clearly seen that the specific magnetization decreases with increasing the thickness of silica-shell. Accordingly diamagnetic contribution of silica leads to a lower saturation magnetization than the core-free FeNi particles (table 2).

The inset, left side of figure 8, illustrates the coercive field versus the thickness of silica-shell at 77 K and RT. Noticeably, the temperature dependence of coercivity indicates a slight increase for all samples when temperature decreases which is consistent with an increase of anisotropy regardless of its origin. On the one hand, for randomly oriented nanoparticles with cubic anisotropy, the coercive field should be H c ≈ 0.64K 1 /J s [33]. If we consider the bulk Fe 30 Ni 70 magnetocristalline anisotropy K 1 ≈ 700 J/m 3 [START_REF] Bozorth | Ferromagnetism D[END_REF] and the measured saturation magnetization J s = 0.8 T, we find H c ≈ 560 A/m which is in disagreement with the experimental coercivity. On the other hand, the morphology and size effect are believed to be the reason of high coercivity observed for all samples (22 kA/m < H c < 32 kA/m, see table 2). According to the pioneering work of Néel [START_REF] Néel | [END_REF], for soft magnetic nanoparticles a dissymmetry of some atomic layers is sufficient in order to make the contribution of demagnetizing field becoming dominant and to lead to an enhancement of the coercivity. Shape anisotropy effect is due to the asphericity of the nanoparticles below a critical size. The coercive field in an elongated spheroidal single-domain particle is given by H c =2K s /J s [36] where

( ) 0 2 2µ s a b s J N N K - =
is the shape anisotropy. N b and N a represent the demagnetizing coefficients along the two axes of an ellipsoid of revolution [37]. For an asphericity 0.86<γ<1.14, If we assume a coercive field H c = 33 kA/m, we find an asphericity of 13%. The result is consistent with TEM observations (figure 4) where 0.80<γ<1.2 was found. The coercive field dependence on silica layer thickness shows a non-monotonous evolution. For thin silica-layer a sensitive drop in coercivity is observed followed by an increase before recovering the initial value. This is probably due to a competition between dipole-dipole interaction and magnetoelastic anisotropy. In the one hand, dipolar interactions are reduced as the distance between magnetic cores is increasing. In the other hand, it has been shown by FTIR the existence of stress in the silica shell. As the thickness of the shell increases, the stress experienced at the surface of FeNi nanoparticles is enhanced yielding an increasing magneto-elastic anisotropy. These two contributions balanced for a thickness of ~15 nm. Classically, for ultrafine nanoparticles (~10 nm or less) dispersed in non-magnetic material, anhysteretic loops are expected because of the superparamagnetic behavior of the nanoparticles, as already reported [38,39]. For the FeNi nanoparticles described in this paper, the shape anisotropy dominates the magnetocristalline anisotropy (K s = 20 kJ/m 3 >> K 1 ) so the critical size for which the superparamagnetism is observed at room temperature is given by

      - = γ
nm K T k D s B sp 27 150 3 ≈ = π compared with nm K T k B 72 150 3 1 ≈ π [40],
where T is the measuring temperature and k B the Boltzmann constant. Considering the mean size of the nanoparticles (55 nm), this is in line with the hysteresis observed for all samples (figure 8). Because part of the particles is smaller than 27 nm and because some are nearly spheroidal (γ<1.05) a superparamagnetic contribution is not excluded. Another interesting feature is the remarkable stability of the squareness ratio regardless of temperature and coating (see table 2). The M r /M s ratio is noticeably lower than 0.5 predicted for single domain particles according to Néel and Stoner [41,42]. Actually, this low value is typical of vortex-like magnetic structure composed of an out of the plane uniformly magnetized core surrounded by a crown of curling spins [10].

Alternatively to a coherent rotation, the magnetization process consists initially into an irreversible switch of the vortex core followed by a screw-like rotation of the external curling spins [43].

Conclusions and perspectives

The preparation of silica-coated FeNi particles was successfully achieved by a combination of two original synthetic procedures, a cryogenic evaporation of master alloy Fe 29.5 Ni 70.5 to obtain nanoparticles with well-defined size and composition, and subsequently a modified classical Stöber method which permits to encapsulate the latter within a silica shell. The coating can be accomplished through a direct, simple, one-step procedure. FTIR, EDX and EELS analysis are consistent with the presence of silica in the nanocomposites synthesized. Consequently the silica-shell thickness could be conveniently controlled through the TEOS volume added to the colloidal FeNi solution. Our study allowed us to correlate the shell-silica thickness with the evolution of the magnetic properties of the final nanocomposite. The magnetic investigations demonstrate the possibility of making property-tunable magnetic nanoparticles ready for surface engineering in particular with bioactive molecules or for electromagnetic device applications aiming to enhance frequency limits. These aspects will undoubtedly require further longer-term ageing studies. In particular, the chemical stability must be ensured before any in-vivo applications are intended. Electronic holography experiments are in course to confirm the expected vortex structure of the FeNi nanoparticles. (a-d) Representative transmission electron micrographs of the silica-coated FeNi nanoparticles corresponding respectively to the sample 1, 2, 4, 5 (e) HRTEM pattern for the silica@FeNi (sample 3) which shows the presence of a 15 nm thick silica layer lying at the particle surface (f) Typical EFTEM analysis using metallic silicon as the silica source (Si Kedge), displays the chemical cartography showing a silica-rich shell (sample 3).

Figure 1 .

 1 Figure 1. Illustration of the silica-coated Fe 29.5 Ni 70.5 nanoparticles stepwise synthesis protocol.

Figure 2 .

 2 Figure 2. Thermal gravimetric curves (TGA) of FeNi@SiO 2 nanocomposites (sample 1 to 5) under air flow. Thermal nanopowder alteration obviously depends on the amount of silica in the sample.

Figure 3 .

 3 Figure 3. FTIR spectra recorded from different samples FeNi@SiO 2 (sample 1 to 5) related to various volumes of TEOS in range of 750-2500 cm -1 . The main resonances are identified in the figure and discussed in the text in relation with the dominating Si-O-Si vibrations on solid surface.

Figure 4 .

 4 Figure 4. In the inset of top, EDX spectrum of Fe 29.5 Ni 70.5 core-free nanoparticles.In the inset of bottom, EDX of silica portion of a FeNi@SiO 2 nanoparticles when the beam was focused on silica edges.

Figure 5 .

 5 Figure 5.(a-d) Representative transmission electron micrographs of the silica-coated FeNi nanoparticles corresponding respectively to the sample 1, 2, 4, 5 (e) HRTEM pattern for the silica@FeNi (sample 3) which shows the presence of a 15 nm thick silica layer lying at the particle surface (f) Typical EFTEM analysis using metallic silicon as the silica source (Si Kedge), displays the chemical cartography showing a silica-rich shell (sample 3).

Figure 6 .

 6 Figure6. Plot of silica-layer thickness as function of various volume of precursor TEOS, estimated from HRTEM analysis (t TEM ) and magnetic characterization (t MAG ) (see also table1).

Figure 7 .

 7 Figure 7. Thermal gravimetric curves (TGA) of FeNi@SiO 2 nanocomposites (sample 1 to 5) under argon flow. See table 2 for Curie temperatures assessed from curves.

Figure 8 .

 8 Figure8. Magnetic quasi-static hysterisis loops for samples with various silica-shells (sample 1 to 5). On the left, magnetization curves recorded at 300 K. The inset on the lower right corner illustrates the changes in the M s as a function of the silica-shell thickness. On the right the M-H curves recorded at 77 K. The inset on the lower right corner illustrates the changes in the coercive field as a function of the silica-shell thickness.

Figure 2

 2 Figure 2

Figure 3

 3 Figure 3

Figure 4

 4 Figure 4

Figure 5

 5 Figure 5

Figure 6

 6 Figure 6

Figure 7 13

 7 Figure 7

Figure 8

 8 Figure 8

Table 1 .

 1 Summary of the FeNi@SiO 2 synthesis, presenting the various volumes of reagents used. The Silica-layer thickness was estimated using HRTEM analysis (t TEM ) and magnetic investigation (t MAG ).

		Silica Coating (after dispersion
		under ultrasounds (3 w/cm 3 ))	t (nm)
		TEOS(µl)	NH 4 OH(ml)	t TEM	t MAG
	Sample 1	0	0	0	0
	Sample 2	50	0.35	3	4
	Sample 3	100	0.7	8	9
	Sample 4	200	1.4	15	17
	Sample 5	500	3.5	33	24

Table 2 .

 2 Magnetic properties for uncoated FeNi (sample 1) and silica-coated FeNi (sample 2 to 5) nanoparticles. M s is the specific saturation magnetization, M r remanent magnetization, T c Curie temperature and H c coercive field.

			M s (Am 2 /kg)	M r /M s	H c (kA/m)
									T c (°C)
		77 K	300 K	77 K	300 K	77 K	300 K
	Sample 1	80	76	0.32	0.34	33.9	31.8	598
	Sample 2	72	65	0.30	0.30	28.2	22.1	608
	Sample 3	58	54	0.26	0.28	28.8	24.4	607
	Sample 4	40	39	0.27	0.28	33.8	31.1	607
	Sample 5	32	29	0.28	0.31	34.3	32.2	607
									OH
	FeNi	Ethanol 90 min Ultrasound		FeNi	TEOS NH 4 OH Ultrasound 90 min	FeNi@SiO 2	O	Si O OH Si Si O OH O

Acknowledgements

This work was supported by the Institut d'Alembert IFR-CNRS-UMR 8531, 61 Av. Du President Wilson 94235 Cachan, France.