Weihsueh A Chiu
email: chiu.weihsueh@epa.gov

Frédéric Y Bois
email: frederic.bois@ineris.fr

An Approximate Method for Population Toxicokinetic Analysis With Aggregated Data

Keywords: 1-3 butadiene, Bayesian, inter-individual variability, Markov chain Monte Carlo simulation, population pharmacokinetics

Standard statistical models for analyzing inter-individual variability in clinical pharmacokinetics (non-linear mixed effects; hierarchical Bayesian) require individual data.

However, for environmental or occupational toxicants only aggregated data are usually available, so toxicokinetic analyses typically ignore population variability. We propose a hierarchical Bayesian approach to estimate inter-individual variability from the observed mean and variance at each time point, using a bivariate normal (or lognormal) approximation to their joint likelihood. Through analysis of both simulated data and real toxicokinetic data from 1,3-butadiene exposures, we conclude that given information on the form of the individual-level model, useful information on inter-individual variability may be obtainable from aggregated data, but that additional sensitivity and

INTRODUCTION

Population analyses of toxicokinetic data are designed to characterize inter-individual variability in the parameters or predictions of models describing the absorption, distribution, metabolism, and excretion of toxicants in the body. While such analyses are standard in pharmaceutical research [START_REF] Sheiner | Modeling of Individual Pharmacokinetics for Computer-Aided Drug Dosage[END_REF][START_REF] Sheiner | The population approach to pharmacokinetic data analysis: rationale and standard data analysis methods[END_REF] and [START_REF] Covington | The use of Markov chain Monte Carlo uncertainty analysis to support a Public Health Goal for perchloroethylene[END_REF]). Population analysis methods such as non-linear mixed effects or hierarchical Bayesian modeling require individual-level data. However, individual data from toxicokinetic studies (commonly performed in laboratory animals, but also sometimes in humans) are often unavailable due to the common practice of summarizing data in the form of average and SD (which are sufficient for some classical analyses).

Toxicokinetic analyses of older, often under-exploited, datasets therefore typically ignore population variability because models are fit using reported means and standard errors from multiple individuals, with those parameters interpreted as representing an "average individual." The increasing use of physiologically-based toxicokinetic (PBTK) models, which have many more parameters than classical pharmacokinetic models, has led to the additional practice of fixing "known" physiological variables and estimating the remaining chemical-specific parameters either from in vitro measurements or by "fitting" to aggregated data. There are several problems with such practices. First, except for the simplest models, the concept of "average" parameters is difficult to interpret because of the non-linear relationships between model parameteres and predictions. Moreover, the general presumption that population variability can be ignored in laboratory animal experiments because they are performed on groups of in-bread, genetically similar strains is questionable. Such data still may show a fairly wide range of kinetic response, especially evident in experiments that report single data points for individual animals (e.g., [START_REF] Prout | Species Differences in response to Trichloroethylene[END_REF]. Furthermore, there is typically a large amount of both uncertainty and variability in parameters in PBTK models that are treated as "known," and the selection of which parameters to fix and which to fit is difficult, especially when combining information from various sources and multiple datasets. Therefore, the practice of fitting to aggregate data in this setting can at the very least underestimate overall uncertainty and may lead to inaccurate and biased estimates (Racine-Poon and Smith 1990; Sheiner 1984; Sheiner and Ludden 1992; [START_REF] Woodruff | Optimization issues in physiological toxicokinetic modeling: a case study with benzene[END_REF].

We demonstrate here that population inferences may still be made from aggregated data if both the observed mean and variance at each time point are available and there is a priori information about the model and variance structures. In particular, we propose that the usual hierarchical Bayesian approach, briefly reviewed in Section 2, be extended by treating individual data as missing (or latent) and marginalizing over it. As described in Section 3, we approximate the corresponding (generally intractable) joint likelihood of the observed means and variances with a multivariate normal (or lognormal) distribution having the correct first and second-order moments. The form of the likelihood depends in part on the underlying measurement model for the individual data and the assumed variance structure. We derive approximations based on normal, proportional, and lognormal errors and a single level of inter-individual variability, which are commonly used in toxicokinetic models. In Section 4, we present comparisons of analyses based on individual data using the full population approach to analyses based on aggregated data using our proposed approximations for three simulated data sets and one published human toxicokinetic dataset of controlled exposures to 1,3-butadiene. We find in our examples that the aggregated analyses provide posterior predictions quite similar to individual analyses, albeit with greater posterior uncertainty, as should be expected. In Section 5, we discuss our conclusion that substantial information on inter-individual variability may remain in the aggregated data, and that such information can be recovered through appropriate analyses. Given that some information is still lost in data aggregation, we suggest that posterior analyses, including checking of model fit, sensitivity, and parameter identifiability, are of great importance to increasing confidence in conclusions drawn from analyses of aggregated data.

POPULATION MODELING OF TOXICOKINETICS

As described in [START_REF] Gelman | Physiological Pharmacokinetic Analysis Using Population Modeling and Informative Prior Distributions[END_REF], population modeling of toxicokinetics involves setting up a model in several stages. A nonlinear toxicokinetic model, with predictions denoted f , describes the absorption, distribution, metabolism, and excretion of a compound and its metabolites in the body. This model depends on several, usually known, parameters such as measurement times t, exposure E, and measured covariates φ. Each subject i in a population has a set of unknown parameters θ i . A population model describes their distribution in the population, and incorporates existing scientific knowledge about them through prior distributions on the population mean µ and variance Σ 2 . Finally, a "measurement error" model describes deviations ǫ (with variance σ 2 ) between the data y and model predictions f . This level of the hierarchical model typically also encompasses intraindividual variability as well as model misspecification, but for notational convenience we refer to it here as "measurement error." All these components are illustrated graphically in the left part of Figure 1. ***Figure 1 about here.

The posterior distribution for the unknown parameters is obtained in the usual manner by multiplying (A) the prior distribution for the population mean and variance and the "measurement" error P (µ, Σ 2 |I)P (σ 2 |I), (B) the population distribution for the indi-vidual parameters P (θ|µ, Σ 2 , I), and (C) the likelihood P (y|θ, σ 2 , I), where for notational convenience, we collapse the knowledge of f , φ, E, t, and n into prior information I:

P (θ, µ, Σ 2 , σ 2 |y, I) ∝ P (µ, Σ 2 |I)P (σ 2 |I)P (θ|µ, Σ 2 , I)P (y|θ, σ 2 , I) (1)
Here, each individual's parameters θ i have the same sampling distribution (i.e., they are iid ), so their joint prior distribution is

P (θ|µ, Σ 2 , I) = n i=1 P (θ i |µ, Σ 2 , I). (2)
We consider three different measurement models for the likelihood function, normal errors (Model I), proportional errors (Model II), and lognormal errors (Model III), as shown in

P (y|θ, σ 2 , I) = n i=1 m j=1 N j k=1 P (y ijk |θ i , σ 2 j , t jk ) ( 3
)
where n is the number of individuals and m is the number of different types of measurements, N j is the number of measurements of type j, and t jk are the times at which measurements of type j were made. Note we have assumed that the individuals each have the same experimental design, as would be expected if data were to be aggregated. jk . This full statistical model is illustrated in the middle of Figure 1. A possible treatment of the problem would be to consider the y ijk as latent variables and sample (i.e., impute) them as the other estimands, through Monte Carlo techniques, for example. The logical relationship between y ijk and (m jk , s 2 jk ) would complicate such a treatment for continuous measures (see Marjoram, Militor, Plagnol, and Taveré 2003 for discussion of such methods).

ANALYSIS OF AGGREGATED DATA

The approach we take is to marginalize over the individual measured values y ijk , which here may be considered nuisance parameters, prior to sampling via Monte Carlo. The posterior distribution we are aiming for, then, has the form

P (θ, σ 2 , µ, Σ 2 |m, s 2 , I) ∝ P (θ|µ, Σ 2 , I)P (µ, Σ 2 |I)P (σ 2 |I)P (m, s 2 |θ, σ 2 , I), (5)
with

P (m, s 2 |θ, σ 2 , I) = j,k P (m jk , s 2 jk |θ, σ 2 j , I) (6)
This marginalization is illustrated graphically on the right part of Figure 1. Because the likelihood function P (m jk , s 2 j |θ, σ 2 j , I) is conditional on θ, it is independent of the population model for inter-individual variability and only depends on the "measurement" model.

Below, we present approximations to P (m, s 2 |θ, σ 2 , I) for the different measurement models considered above. Note that from here on we generally suppress the indices j, k for clarity, and concentrate on approximations for the integral in equation [START_REF] Fenton | The sum of log-normal probability distributions in scatter transmission systems[END_REF].

Likelihood Functions for Various Measurement Models

Our general approach is to approximate (for fixed observation type j and time-point t k ) the joint distribution of m and s 2 (m and m 2 ≡ (m 2 + s 2 ) for Model III), conditional on {θ i } (i = 1 . . . n), with a bivariate normal (lognormal for Model III) distribution by matching the first and second order moments. In particular, we require that the distributions match

in terms of E[m], E[m 2 ] -E[m] 2 , E[s 2 ], E[s 4 ] -E[s 2 ] 2 , and E[ms 2 ] -E[m]E[s 2 ]
, where E is the expectation conditional on the values of {θ i }. The results of these calculations are summarized in Table 1.

Table 1 about here.

The moment matching derivations for Models I and II are straight-forward, though tedious (and available as supplementary material online). Note that in both cases, the marginal distributions for the observed mean m are exactly normal, as they are weighted sums of normal deviates. The covariance between m and s 2 is zero for Model I, and non-zero for Model II.

The derivation for lognormal errors, Model III, merits additional discussion. In this case, the mean, given by m = (1/n) f i exp(ǫ i ), has no simple closed form solution for its distribution (see [START_REF] Barakat | Sums of independent lognormally distributed random variables[END_REF][START_REF] Leipnik | On Lognormal Random Variables: I-The Characteristic Function[END_REF] for series approaches to calculating the characteristic function). Several approaches may be taken to approximate it. For large n and/or small σ 2 , the central limit theorem can be invoked to approximate the distribution for m by a normal distribution. For many applications, however, n is quite small (∼ 4), and [START_REF] Barakat | Sums of independent lognormally distributed random variables[END_REF] shows that the coefficient of skewness of the sum distribution decays only as ∼ n -1/2 . Moreover, m and √ s 2 are often of the same order, so it may be important to incorporate the fact that m must be positive. For these reasons, in many telecommunications and engineering applications, the sum of lognormal deviates is commonly approximated by a lognormal distribution by matching moments (e.g., [START_REF] Fenton | The sum of log-normal probability distributions in scatter transmission systems[END_REF]. Simulations appear to indicate that this approximation is useful for values up to σ 2 ∼ 1 (Fenton 1960; Schwartz and Yeh 1982), and we adopt this approximation here.

So as to enable use of the same approach, we take as our second "observed" value not the variance s 2 but the second moment

m 2 ≡ (1/n) f 2 i exp(2ǫ i ) = s 2 + m 2 ,
as it is also a sum of lognormal deviates. Thus, we also approximate its distribution by a lognormal distribution by matching moments, noting that it is the same form as m with σ 2 → 4σ 2 and

f i → f 2 i .
From the work cited above, this means that the lognormal approximation for m 2 is only useful for 4σ 2 ≤ 1. Therefore, in general the approximate likelihood for (m, m 2 ) is only accurate if σ ≤ 0.5.

The final step, then, is to define the correlation coefficient r of the bivariate lognormal distribution. We use the same approach as for Models I and II, matching the product moment E[mm 2 ] (equivalent to matching the central moment because we have already matched E[m] and E[m 2 ]). We have investigated this approximation in a limited number of simulations for values of n ≤ 10 and values of σ ≤ 0.5, and have found it to be acceptable as long as the f i has a relatively small coefficient of variation. If f i are too widely dispersed (e.g., VAR[ln f ] > 1), then the above formula can sometimes give a value of r > 1. In this case, however, we have found that using the above formula, but taking σ → 0 (i.e., the limit in which measurement error is negligible relative to inter-individual variability), so that r →

E[f 3 ]/ E[f 2 ]E[f 4 ],
gives reasonable results. We take the minimum value of r from the above two formulae as the one we use in our distribution for m and m 2 , as shown in Table 1. We find that this approach sometimes slightly underestimates r by up to a few percent, but ensures that r ≤ 1.

This constraint on r should be checked in posterior simulations.

Additional Issues for Consideration

Sufficiency and Identifiability

For most non-linear models, there will undoubtedly be some loss of information in data aggregation, so there may be concerns about whether there is still sufficient information to ensure parameter identifiability in the toxicokinetic and population models. However, even with individual data, a toxicokinetic model may not be fully identifiable (e.g., the estimation of decay times of a mixture of exponentials is ill-conditioned, Acton 1970), so this problem is not unique to aggregated data. At the very least, some a priori information on the system being analyzed should exist to motivate the formulation of the model and, preferably, informative prior distributions for its parameters. For instance, in their analysis of tetrachloroethylene toxicokinetics, [START_REF] Gelman | Physiological Pharmacokinetic Analysis Using Population Modeling and Informative Prior Distributions[END_REF] remarked that both the physiological model and prior distributions were necessary to ensure identifiability. At best, data from other experiments where data were not aggregated could be used to establish the appropriate model form. In toxicokinetics, if one's goal is to characterize population variability, then one presumably already has sufficient information to justify the structure of the individual-level model. So we focus in particular on parameter identifiability rather than model discrimination.

For non-linear models, these issues are necessarily case-specific, and it may not be possible to know whether parameter identifiability is a problem prior to performing an analysis.

However, posterior and sensitivity analyses can be done to check that the population parameters are identifiable given the data. The first evidence for non-sufficiency would be if the priors and posterior distributions are identical. If the posteriors are narrower, then the data add some information. A scalar measure τ of the "overlap" between marginal prior and posterior distributions was proposed by [START_REF] Garrett | Latent class model diagnosis[END_REF] for latent class models, and is adapted here for more general use. In particular, for a parameter θ, data y, and prior information I, prior distribution P (θ|I), and posterior distribution P (θ|y, I), the "overlap diagnostic" is defined as τ = min {P (θ|I), P (θ|y, I)} dθ. Additionally, it can be determined whether parameters are uniquely identifiable. For example, in the case of a model y i (t) = (α i + β i )t + ǫ it , the parameters α i and β i (and their corresponding population mean and variance) are not uniquely identifiable without informative priors, whether one has individual data or aggregated data. If one does not have informative priors, then this can be detected a posteriori by examining sensitivity of the results to different diffuse priors, and more directly through examining correlations in the posterior samples. While visual inspection of the posterior correlation matrix can be useful in simple cases such as this, in more realistic applications in which more than two parameters may be involved simultaneously, principal component analysis (PCA) should be a useful tool.

In particular, performing PCA on the posterior samples, and then comparing the posterior distributions of the principal components with their priors (i.e., applying the same centering, scaling, and rotation to samples from their joint prior distribution) should identify any nondiagonal components which are not identifiable. This should also be applicable to cases such as y i (t) = θ i + ǫ it , where variance contributions from different levels of the hierarchical model are indistinguishable after data aggregation.

Choice of Measurement Model

In standard population analyses, the choice of measurement model is influenced only by the underlying hypothesis for how the individual data deviate from model predictions. In our case, how the data are aggregated also plays a role. For most toxicokinetic data, a lognormal measurement model has been traditionally assumed for individual data points.

One could thus either use Model I by transforming y → ln y, or use Model III. A priori, Model I would be preferable because it is simpler. However, one could only use this model if the aggregation was done on the transformed data -e.g., the reported values are geometric mean and standard deviation. Typically, it is the arithmetic mean and standard deviation that are reported, so that model III would be the most appropriate. Unfortunately, model III is also the least robust of the models because of the requirement for σ 2 ≤ 0.5 and the possible lack of stability of the derived correlation coefficient. Model II then is a more robust alternative approximation that still allows for errors to be proportional to the measured value.

On a practical matter, data are probably most useful in a regime where proportional normal errors (Model II) and lognormal errors (Model III) are not easily distinguishable. Moreover, the measurement model also encompasses model misspecification, and a value of σ > 0.5 (i.e., a > 50% error) may be reason to rethink the model.

Model Checking and Model Choice

As with standard population analyses, model checking is important here. In addition to the identifiability checks described above, the most basic check is whether the model is consistent with the data. In the standard population analysis, a typical method to perform this check is to compare simulated (replicated) data y i,rep with the observed data y i,obs ( One important limitation of aggregated analyses, however, is that the structural assumptions in the population model P (θ|µΣ 2 ) and the measurement model P (y|θ, σ 2 ), which are not easy to check with individual data, are even more difficult to validate with only aggregated data. Typical techniques for assessing these assumptions include both posterior simulations as well as sensitivity analyses. For aggregated analyses, posterior simulation is of somewhat limited usefulness when checking structural assumptions because of the additional layer of latency. Sensitivity analyses take on greater importance. We illustrate this below by considering all three measurement models in our analyses.

On the related issue of model choice, there are a large number of statistical methods for model selection in both a frequentist (e.g., log-likelihood ratio test, Akaike information criterion) and Bayesian context (e.g., Bayes factors, Bayesian information criterion). These methods may be less reliable with only aggregated data. Fortunately, the formulation of toxicokinetic models is motivated primarily by a priori biological and chemical information rather than statistical measures.

In checking and choosing models, it is also important to make a distinction between the "statistical" and "practical" significance of model errors. That is, because models such as those used in toxicokinetics can never be thought of as strictly "true," statistical lack of fit may or may not have an impact on the substantive inferences for which the model is used.

Thus, the use of the model should be kept in mind when assessing either the consistency between model predictions and data or the impact of different model assumptions.

APPLICATION TO DATA ON 1,3-BUTADIENE

We first performed a number of simulations with a simple model and simulated data, as summarized in Table 2. These simulations covered all three measurement models. We generated simulated data and compared full population analysis of the individual data with analyses of the same data aggregated. Computations were performed using WinBUGS version 1.4 and MCSim (Version 5.0.0, Bois, Maszle, Revzan, Tillier, and Yuan 2005). In each case, the results of the analysis of aggregated data were quite consistent with the results of the full population analysis as well as with the underlying "true" values from which the data were generated. This offered support for the accuracy of the approach developed here.

***Table 2 about here.

Butadiene data and model

We then applied our aggregation model to actual toxicokinetic data. The data and model are described in detail in Bois, Smith, Gelman, Chang, and Smith (1999), and are summarized briefly here. Eight human volunteers were recruited and tested at National Cheng Kung University in Taiwan. The tests were conducted, under informed consent, with an Institutional Review Board-approved human subjects protocol. They were exposed to an ambient concentration C in (t) of five ppm of 1,3-butadiene for two hours and then zero thereafter. This exposure was the minimum that could be precisely measured, and was well below The toxicokinetic model was a standard two-compartment model, with a central (volume

V c
) and peripheral compartment (volume V p ) governed by the following differential equations for the amount of 1,3-butadiene in each respective compartment Q c (t) and Q p (t):

Qc (t) = K in C in (t) + K cp Q p (t) P pc V p -K cp + K in P ca Q c (t) V c -K met Q c (t) (9)
Qp (t) = K cp Q c (t) V c - K cp Q p (t) P pc V p , (10)
where, in addition to the parameters defined above, P ca is the central-to-air partition coefficient (assumed to be the measured blood-air partition coefficient P ba ); K cp is the rate constant for distribution from central to peripheral compartments; P pc is the peripheral to central partition coefficient; and K met is the metabolic rate constant. The measurement of covariates BDW , K in , and P ba greatly improves parameter identifiability in this model.

The exhaled concentration at observed time t k is given by

C ex (t k ) = 0.7 Q c (t k ) P ca V c + 0.3 C in (t k ), (11)
where a physiological dead space of 30% is assumed. Because the product P pc V p is not separable, it is treated as a single parameter to ensure identifiability. In addition, the central volume and the minute-volume are assumed to follow the scaling relations

V c = sc V c BDW (12)
K in = sc K in BDW 0.7 , (13)
so the sc V c and sc K in are the actual parameters in the model. Finally, one of the important uses of the model is the prediction of the amount metabolized AMET, which is given by were included. Although it is possible to include the missing data points in the model, it adds a level of complexity that obscures the point of this comparison, which is to compare full population analysis with an analysis using only aggregated data.

AMET = K met Q c (t)
To summarize, each individual i has seven parameters θ i = (sc V c , K cp , P pc V p , K met , P ca , sc K in , BDW ) i and four types of observations y i = (P ba,obs , K in,obs , C ex,obs (t k ), BDW obs ) i .

All errors were assumed lognormal except for BDW , for which errors were assumed to be normal:

P ba,obs = P ca exp(ǫ Pca ) ( 14)

K in,obs = K in exp(ǫ K in ) (15) C ex,obs (t k ) = C ex (t k ) exp(ǫ Cex ) (16)
BDW obs = BDW + ǫ BDW [START_REF] Marjoram | Markov Chain Monte Carlo without likelihoods[END_REF] where in the middle two cases, the model predictions are given by equations ( 13) and [START_REF] Gelman | Inference from Iterative Simulation Using Multiple Sequences[END_REF], respectively, and ǫ Pca ∼ N (0, log 1.17), ǫ K in ∼ N (0, log 1.02), ǫ Cex ∼ N (0, log GSD ex ), and ǫ BDW ∼ N (0, 0.25 kg) (the first two were based on replicate samples).

Data aggregation was performed using log-transformed measurements (thus using Error Model I) as well as un-transformed measurements (thus using Error Models II and III), the last of which are also shown in the left panel of Figure 2. Simulations for all cases were performed using the MCSim software. To ensure consistency, the original MCSim code used in [START_REF] Bois | Optimal design for a study of butadiene toxicokinetics in humans[END_REF] was obtained and modified only where needed.

Prior distributions were the same as in [START_REF] Bois | Optimal design for a study of butadiene toxicokinetics in humans[END_REF], except for the body weight parameters, which are new. The prior mean body weight was assigned a uniform distribution with min and max equal to the min and max measured body weight. The prior variance was assigned the inverse Gamma distribution with shape parameter of unity and scale parameter corresponding to a 20% coefficient of variation. All priors are listed in Table 3. As was done in [START_REF] Bois | Optimal design for a study of butadiene toxicokinetics in humans[END_REF], 50,000 iterations performed for two independent chains in each case. The first 10,000 iterations were discarded, and only every 10 iterations were stored for analysis. Convergence was monitored through the method of Gelman and Rubin (1992), and potential scale reduction factors were ≤ 1.03 in the case of individual data, and ≤ 1.01 in the aggregated data cases.

Comparisons between full population and aggregated analyses

***Figure 3 and Table 3 about here.

Table 3 and Figure 3 summarize the statistical results for both full population and aggregated analyses. There is substantial agreement between the different analyses, as shown visually in Figure 3. Posterior estimates of population parameters substantially overlap for all parameters except for the "measurement" error, which is signficantly larger in the aggregated analyses (discussed below). While difficult to see in the Figure due to the logarithmic scale, estimates of the population mean parameters (µ), summarized in Table 3, are not greatly affected by the use of aggregated data, both in terms location and scale. In most cases, the population variances (expressed as geometric standard deviations exp Σ in Table 3) are only slightly affected as well, with 95% confidence intervals substantially overlapping among the four analyses. The uncertainties in the population variance parameters exp Σ, however, are consistently greater in the aggregated analyses. Because the inverse-Gamma priors on the population variances Σ 2 have shape parameter of unity, they have infinite dispersion. Thus, greater posterior uncertainty generally leads to higher central estimates and upper confidence limits. This is reflected in the results, particularly for parameters sc V c and sc K in . It is clear that in these cases, some information was lost in the aggregation process. The parameter for "measurement" error GSD ex was slightly greater in the aggregated analyses. [START_REF] Bois | Optimal design for a study of butadiene toxicokinetics in humans[END_REF] reported that the analytical errors were estimated to be about 7%, so this increased "measurement" error reflects additional model error (e.g., due

to the approximations necessary to derive the likelihood functions) and/or intraindividual variability. Table 3 also shows the posterior uncertainty in the population variability in the dose metric AMET for the 8 individuals. The posterior predictions were very similar among the full population and aggregated analyses, although as with the population parameters, the uncertainty from the aggregated analyses is slightly greater. Overall, the results of the population analysis based on aggregated data, using the statistical models developed above, are consistent (albeit with greater overall uncertainty) with those based on individual data.

Parameter identifiability

Checks for non-identifiability were conducted on the full population analysis as well as each aggregated analysis, concentrating on the 15 population parameters (mean and variance for each of the 7 model parameters, plus residual "measurement" variance). Given the narrowing of all of these distributions from prior to posterior, one would not expect any parameters to be completely unidentifiable. Indeed, for population means, values for the overlap diagnostic τ were ≤ 0.2 except for the metabolic rate constant K met (τ ∼ 0.5) and the mean body weight (τ ∼ 0.6). Moreover, the difference between τ in individual and aggregated analyses was ≤ 0.05, indicating little information loss for estimated population means. Population variances were not as well identified, with τ ≥ 0.4. In addition, the differences between individual and aggregated analyses were greater. The largest changes in overlap were in the estimated variances of V c (τ = 0.55 for the individual analysis and τ = 0.83 -0.90 for the aggregated analyses) and P pc (τ = 0.46 for the individual analysis and τ = 0.61-0.64 for the aggregated analyses). For the other variance parameters, the overlap diagnostic τ changed by ∼ 0.1.

Further checks examined whether some parameter combinations are only weakly constrained by the data. As a visual check, the correlation matrix was calculated with mean parameters log-transformed (this is more "natural" since the population model and most of the likelihoods are lognormal) and variability parameters transformed, if necessary, to variances (e.g., GSD → (ln GSD) 2 ). All non-diagonal correlation coefficients for the population parameters were in the interval (-0.4,0.6); of the 15 × 14/2 = 105 unique non-diagonal elements, only 8 were outside the interval [-0.2,0.2]. Thus, there were some correlations, but none were extremely strong.

PCA was performed on the posteriors with the R statistical package, with centering to zero mean and scaling to unit variance (i.e., equivalent to determining the eigenvectors of the correlation matrix). Each analysis (full population and the three aggregated) had a slightly different rotation matrix, as should be expected for a non-linear model and the approximate likelihood functions used. Priors for each set of principal components were then generated by applying the same transformations to random samples from the joint prior distribution. All prior principal component [2.5%,97.5%] confidence intervals included zero (which, by definition, is the posterior mean of the principal components), so there is no conflict between priors and posteriors even after transformation. Moreover, the posterior confidence intervals were wholly contained within the prior confidence intervals, with the prior intervals substantially wider (i.e., by at least 5.9-fold). Thus, we conclude that there are no substantial parameter identifiability problems.

Checking Model Fit

Inspection of Figure 2 (middle and right panel) of the scatter in the data points relative to the scatter of the predictions suggests that full population and aggregated analyses give similar inter-individual variance in their predictions. Additional checks using the full posterior distribution of predictions for the measured mean and variance for the exhaled air concentration C ex showed good qualitative consistency between the model predictions and the underlying (aggregated) data (not shown). However, the scatter during the period of exposure (t = 0 -120 minutes) appears underestimated, perhaps due to intraindividual variability, which here was not modeled separately but lumped with "measurement" error. This feature also appears in the full population analysis, as can be seen in the middle panel of Figure 2. We also note that, for Model III, the posterior range of the "measurement" error variance σ < 0.5, as required by our approximation for the likelihood function. In addition,

for Model III, we checked the approximation for the correlation parameter r, and found that in no case did the moment-matching formula give r > 1, so the σ → 0 approximation was never used.

Sensitivity analysis is illustrated through comparison of the results from different error models. Summary statistics are quite similar, with the exception of the variance of sc V c , which had greater uncertainty in Model II. In particular, the posterior estimates for the dose metric AMET were remarkably consistent. Furthermore, graphs of the posterior distributions as well as the comparisons between data and model predictions showed little sensitivity to different error models (not shown).

Finally, we note that checks for parameter identifiability ( §4.3), model fit and sensitivity analyses are not unique to the analysis of aggregated data. They could (and should, in our opinion) be more widely applied to standard population analyses as well. For instance, parameter identifiability is usually not checked in any formal manner. Model fit is typically checked only through scatter plots of data and a single posterior prediction (e.g., using a "random sample" or using population mean parameters), as is shown in Figure 2. As reported above, we performed additional checks using the full posterior distribution. Checking of the assumed "measurement" error model, as was done here as part of the sensitivity analyses, is rarely done.

DISCUSSION

Through the use of some conceptually simple approximations, we have developed likelihood functions for the observed sample mean and variance of individual measurements, given a hierarchical population model. Our results illustrate that individual data, while preferable, are not necessarily essential to analyze population variability in a hierarchical Bayesian framework. In the cases we analyzed, the resulting posterior distributions between analysis of individual and aggregated data are very similar. This may not be too surprising with very simple normal models. Yet, we have found in our examples that the mean and variance are nearly sufficient even with a nonlinear model. However, it is important to check model fit, sensitivity to the likelihood approximation used, and parameter identifiability. For this last check, we propose principal component analysis as a broadly applicable method.

We have not yet applied our approach to more complex (e.g., PBTK) models, but results from the butadiene example are encouraging.

There are several important limitations to our approach, some of which are fundamental and some more practical. First of all, in the examples we have examined, the assumption has been made (by design for the simulated data and checked in the case of the butadiene analysis) that other sources of variability (intraindividual variability, measurement error, model uncertainty, for example) are small compared to inter-individual variability. If this assumption were not true, the analysis may not be able to disentangle inter-and intraindividual variability. However, this can be checked a posteriori with the identifiability checks described above. In addition, structural assumptions, which are not easy to test even with individual data, are even more difficult to check with aggregated data, so use of aggregated data for statistical model discrimination is not recommended. Fortunately, for toxicokinetic models there is usually a priori information on model formulation. Finally, one should always consider evaluations of the performance of aggregated analyses in the context of what the data are to be used for, as a mild loss of information or parameter non-identifiability may not necessarily have a significant impact on posterior inferences of interest. In our example with 1,3-butadiene, the predicted mean and variance for the dose metric AMET differed very little among the different analysis, even though some information on population variability was lost.

On a practical level, the analysis of aggregated data is more computationally burdensome than if individual data were available. This is due to the more complicated likelihoods, particularly for Models II and III where there is covariance, and possibly slower convergence.

For instance, on an Intel Pentium 4 2.8 GHz processor running Windows XP with 512 MB of RAM, two chains of length 50,000 run in MCSim took about 1 hour to complete for the individual data for butadiene, and about 4.5 hours for the aggregated data using Model III. While these times are not long, more complicated models and data could substantially increase the computation time and the chain length necessary for convergence. These practical limitations could be alleviated by either more efficient MCMC algorithms or faster computing power than we have used here.

Ideally, of course, individual data would always be available for analysis, and it is sound practice to use all such data. It should not be inferred from our analysis that summary data should be used when individual data are available, data aggregation always entails a degree of information loss. However, especially in a toxicological/environmental health setting where data are often gathered from multiple, usually historical, sources, the original data may be unavailable. The effort, then, should be to maximize the use of the available information, particular in the case of human data where unnecessary exposure to toxicants should be minimized. Typically, no attempt is made to extract population variability information from aggregated data, perhaps because it is presumed to be unimportant or to have been lost in the aggregation process. Our analysis shows this information is not necessarily completely lost -that when both the mean and variance are reported, significant information on population variability may remain. We have presented here an example of application to the analysis of toxicokinetic data, but aggregation of data for publication has been pervasive in biology, and occasions to test the approach we propose should be plentiful. For example, in cancer bioassays, groups of animals are exposed to predetermined doses of a carcinogen and the onset of tumors is observed. Each animal is expected to react differently to the exposure. Such inter-individual variability can be studied if time-to-event reporting of tumors is available.

y i ∼ N (f i , σ) (m, s 2 ) ∼ N (µ m , σ m , µ s 2 , σ s 2 , r) Subject i µ Σ θ i φ i t i E i f i σ 2 m,s 2 y i Subject i µ Σ θ i φ i t i E i f i Integration over y i n σ 2 m,s 2 n Subject i µ Σ θ i φ i t i E i f i σ 2
Aggregation of data y i 1.41 2.00 1.18

1.39 1.91 1.17

  ; Radine-Poon 1985; Yuh et al. 1994; Wakefield, Smith, Racine-Poon, and Gelfand 1994; Wakefield 1996; FDA 1999), it has only been since the work of Bois et al. (1996a, b) and Gelman, Bois, and Jiang (1996) that similar methods have been applied in environmental health sciences. However, there is only a handful of published population toxicokinetic analyses (recent examples include Hack, Chiu, Zhao, and Clewell 2006; Marino et al. 2006; Yokley et al. 2006;

  If individual data have been aggregated, and one only has the number of individuals n and the sample mean m jk and variance s 2 jk of individual measurements at time-point k, then one must modify the statistical model used. The individual data y ijk are considered missing or latent, and therefore treated as parameters rather than data in a Bayesian context. Thus, the standard data model becomes part of the population model, and a new data model for m and s 2 is needed. One therefore has a posterior distribution given by P (θ, σ 2 , µ, Σ 2 , y|m, s 2 , I) ∝ P (θ|µ, Σ 2 , I)P (µ, Σ 2 |I)P (σ 2 |I)P (y|θ, σ 2 , I)P (m, s 2 |y, I). (4) The additional term P (m, s 2 |y, I) is formally a δ-function (or 0-1 indicator) specifying the arithmetic relationship between the observed values y ijk and their mean m jk and variance s 2

( 8 )

 8 Values of τ near unity (i.e., 100% overlap) indicate weak identifiability from the data, whereas lower values (Garrett and Zeger 2000 proposed 0.35 as a heuristic threshold) indicated strong identifiability from the data.

  Taiwan's allowable occupational exposure of 10 ppm per eight hour work day for a working lifetime. For each individual, measurements of body weight (BDW ), minute-ventilation rate K in , and blood-air partition coefficients P ba were made along with exhaled breath measurements C ex (t k ) at a series of times t k from the beginning of exposure to about one hour post-exposure. The full dataset for C ex (t k ) is displayed in all three panels of Figure 2. ***Figure 2 about here.

  dt. The characterization of the uncertainty and variability in dose metrics such as this is important for making inferences about the population distribution of risks from exposure. In the population model, all the individual-level parameters are assumed to be lognormally distributed with geometric mean exp(µ) and log-variance parameter Σ 2 . Two modifications from the Bois et al. (1999) full population analysis were made to allow comparison between analyses of individual and aggregated data. First, population body weight parameters were estimated as part of the model. The population model was lognormal, but the likelihood function was assumed to be normal with a measurement standard deviation of 0.25 kg. Second, only time points for which measurements were available in all 8 individuals

Figure 1 :

 1 Figure 1: Graphical representation of population statistical model describing dependence relationships between variables. Square nodes are known or measured quantities, circle nodes are unknown or unobserved, solid arrows indicate a stochastic dependence, and dashed arrows indicate a logical (functional) dependence. The inverted triangle f represents the nonlinear pharmacokinetic model prediction. Individuals are labeled by the index i. It should be noted that all of the nodes may have additional dimensions in addition to i (e.g., multiple time points, tissues). The left model represents the situation where individual data y i are available. Aggregation of data leads to the middle model, where only m, s 2 , and n are available (note y i is still part of the model, but has changed from a square node, denoting a measured quantity, to a circle node, indicating an unobserved quantity). Marginalization over y i leads to the model on the right, which is used in our analyses. Approximations for the results of this marginalization for various measurement models are described in the text.

Table 1

 1

. Note that Models II and III are heteroscedastic, a common concern for toxicokinetic data. Different types of measurements j = 1 . . . m may have different errors, but errors are otherwise assumed to be iid. Since the individuals are treated as independent given θ 1...n , the total likelihood function is simply

  Gelman, Carlin, Stern, and Rubin 2003, chap. 6). Analyses of aggregated data are no different except that the quantities being compared are (m, s 2 ) rep and (m, s 2 ) obs , as in the examples we give below.

Table 1 :

 1 However, most of the time (e.g. the carcinogenic potency database of Lois Gold at Berkeley, Approximate Likelihood Functions for Aggregated Data

	Gold, Manley, Slone, and Rohrbach 1999) only the number of animals bearing tumors at
	the end of the experiment is kept and analyzed with binomial or Poisson regressions. A
	better understanding of the variabilities and uncertainties involved in such experiments would
	probably benefit society as a whole.

Table 3 :

 3 Comparison of Individual and Aggregated Analyses of 1,3-Butadiene Data. Each pharmacokinetic model parameter has an associated population mean µ and variance Σ 2 .Individual analyses used error model III[START_REF] Bois | Optimal design for a study of butadiene toxicokinetics in humans[END_REF]. Aggregated analyses for error model I used log-transformed measurements; those for error models II and III used untransformed measurements. Prior distributions on µ and Σ 2 are specified below, as are the posterior median 97.5%2.5% on µ and exp Σ based on two independent chains of 50,000 iterations, thinned by 10, with the first 10,000 iterations discarded. For the prediction AMET, GM 8 and GSD 8 are the geometric mean and geometric standard deviation of 8 individuals, respectively.

	Parameter or Priors (µ, Σ 2 )	Posteriors (µ, exp Σ) from Analyses:
	Prediction		Individual	Model I	Model II	Model III
	sc V c : µ	Unif(0.01, 0.5)	0.0637 0.0772 0.0533	0.0654 0.084 0.0517	0.0682 0.0928 0.0517	0.0665 0.086 0.0526
	sc V c : Σ 2	InvΓ(1, 0.039)	1.16 1.33 1.09	1.21 1.62 1.1	1.28 1.97 1.11	1.22 1.65 1.1
	K cp : µ	Unif(0.5, 5)	1.09 1.32 0.919	1.12 1.39 0.923	1.13 1.39 0.934	1.13 1.4 0.925
	K cp : Σ 2	InvΓ(1, 0.039)	1.16 1.34 1.09	1.18 1.4 1.1	1.19 1.41 1.1	1.18 1.4 1.1
	P pc V p : µ	Unif(10, 100)	27.9 33.2 23.9	28.8 35.3 23.8	29.2 35.1 24.2	29.2 35.7 24.1
	P pc V p : Σ 2	InvΓ(1, 0.039)	1.14 1.28 1.08	1.17 1.38 1.09	1.18 1.39 1.1	1.18 1.38 1.1
	K met : µ	Unif(0.05, 0.5)	0.224 0.346 0.144	0.23 0.37 0.136	0.228 0.37 0.137	0.23 0.368 0.136
	K met : Σ 2	InvΓ(1, 0.693)	1.66 2.52 1.38	1.74 2.93 1.4	1.75 2.89 1.4	1.72 2.88 1.4
	P ca : µ	Unif(0.1, 5)	1.3 1.57 1.09	1.52 1.09	1.3 1.53 1.09	1.28 1.53 1.08
	P ca : Σ 2	InvΓ(1, 0.039)	1.21 1.44 1.12	1.18 1.38 1.1	1.18 1.39 1.1	1.18 1.39 1.1
	sc K in : µ	Unif(0.1, 1)	0.372 0.422 0.329	0.372 0.444 0.315	0.373 0.444 0.319	0.373 0.443 0.319
	sc K in : Σ 2	InvΓ(1, 0.039)	1.17 1.33 1.11	1.24 1.5 1.14	1.23 1.49 1.13	1.23 1.48 1.13
	BDW : µ	Unif(48, 71)	61.7 68.6 54.3	61.7 68.5 54.8	61.7 68.5 54.7	61.6 68.5 54.5
	BDW : Σ 2	InvΓ(1, 0.039)	1.19 1.36 1.12	1.18 1.34 1.12	1.18 1.34 1.12	1.18 1.34 1.11
	GSD ex	LogUnif(1.01, 1.30)	1.08 1.09 1.07	1.11 1.13 1.09	1.11 1.13 1.09	1.11 1.13 1.09
	AMET: GM 8 -	0.023 0.028 0.017	0.023 0.028 0.016	0.024 0.031 0.017	0.024 0.031 0.017
	AMET: GSD 8 -	1.37 1.76 1.17

ACKNOWLEDGEMENTS

This work is partially supported by the Ministry of the Environment and Sustainable Development (BCRD-AP2004-DRC05). The authors would like to thank B. Amzal, C. Chen, T. Choi, C. Diack, J. Fox, H. Kahn, E. Parent, W. Setzer, R. Subramaniam, and P. White for helpful discussions and comments, as well as the editors and referee whose suggestions improved this paper.

given by ln κ 1,2 ∼ N (µ 1,2 , Σ 1,2 ), and measurement error models


W Sanchez

C Goin

F Brion

P E Olsson

A Goksøyr

J M Porcher

A new ELISA for the three-spined stickleback (Gasterosteus aculeatus L.) spiggin, using antibodies against synthetic peptide

Keywords: three-spined stickleback, spiggin, androgens, ELISA

The aim of this study was to develop an enzyme linked immunosorbent (ELISA) assay to quantify spiggin in the three-spined stickleback. Spiggin is a glue protein produced in the kidney of male three-spined stickleback under the control of androgens during the breeding period. Disturbances of spiggin production in male fish and abnormal induction of spiggin in female fish are considered as valuable biomarkers of exposure to (anti-)androgenic chemicals.

Polyclonal antibodies against a peptide sequence of spiggin (HRD 16) were used and the specificity of the antibodies was verified by Western blotting and direct ELISA experiments.

By using HRD 16 antibodies and spiggin standard preparation, a competitive ELISA was setup and validated. This assay appears sensitive, with a detection limit of 0.5 U/mL, and specific, as shown by the competition curves, obtained by serial dilution of male and female kidney homogenates, that were parallel to the spiggin standard curves. The ability of the spiggin ELISA to quantify spiggin induction was achieved by exposing male and female three-spined sticklebacks to 0.1 and 1 µg/L of methyltestosterone. The results show a significant dose-dependent induction of spiggin in methyltestosterone-exposed female fish compared to controls.

Introduction

Several man-made chemicals and natural substances present in the environment are able to disturb the normal physiology and endocrinology of organisms [START_REF] Arukwe | Xenobiotics, xenoestrogens and reproduction disturbances in fish[END_REF].

These substances, termed endocrine-disrupting chemicals (EDCs), have been defined as « exogenous substances that cause adverse health effects in an intact organism, or its progeny, secondary to changes in endocrine function » (Organization for Economic Cooperation and Development, 1997). Much research has been conducted on estrogenic endocrine disrupters and their environmental occurrence and effects on aquatic organisms are well described.

However, less data are available on androgenic and anti-androgenic EDCs able to mimic or antagonise, respectively, the effects of the endogenous androgenic hormones. Some studies have reported in vitro (anti-)androgenic activity in surface waters and sediment extracts of samples collected in rivers and estuaries [START_REF] Thomas | An assessment of in vitro androgenic activity and the identification of environmental androgens in United Kingdom estuaries[END_REF][START_REF] Blankvoort | Androgenic activity in surface water samples detected using the AR-LUX assay: indications for mixture effects[END_REF][START_REF] Jenkins | Identification of androstenedione in a river containing paper mill effluent[END_REF][START_REF] Soto | Androgenic and estrogenic activity in water bodies receiving cattle feedlot effluent in Eastern Nebraska, USA[END_REF]. The application of « toxicity identification evaluation » (TIE) approach which combines bioassays and chemical analysis, allowed to identify the androgenic compounds implicated in aquatic environment contamination such as androstenedione [START_REF] Jenkins | Identification of androstenedione in a river containing paper mill effluent[END_REF]. Moreover, several effluents of domestic and industrial water treatment plants discharging into environment, exhibited also androgenic activities linked to the occurrence of various androgenic EDCs such as testosterone, dehydrotestosterone, androsterone, trembolone [START_REF] Thomas | An assessment of in vitro androgenic activity and the identification of environmental androgens in United Kingdom estuaries[END_REF][START_REF] Blankvoort | Androgenic activity in surface water samples detected using the AR-LUX assay: indications for mixture effects[END_REF]. This contamination is liable for adverse effects in wildlife such as masculinisation of female common mosquito fish (Gambusia affinis) reflected by elongated anal fin rays, resembling the male gonopodium (Cody and Bortone, 1997) or female eelpouts (Zoarces viviparus) showed by a bias toward males in embryonic sex ratios of wild eelpout [START_REF] Larsson | More male fish embryos near a pulp mill[END_REF][START_REF] Larsson | Male-biased sex ratios of fish embryos near a pulp mill: temporary recovery after a short-term shutdown[END_REF]. In ligth to the data available on occurrence of androgens in environment and their effects on aquatic species, further studies are required to bridge the gap of knowledges on the molecular, physiological, morphological and behavioural effects of androgenics EDCs.

For this purpose, the three-spined stickleback (Gasterosteus aculeatus), a small teleost fish, robust to contamination, inhabiting in both northern hemisphere seawater and freshwater, can be considered as a valuable model fish species. Indeed, during its breeding period, male stickleback exhibits androgen-dependent secondary sexual characters including development of kidney hypertrophy, nuptial coloration, territorial and nest-building behaviour. At biochemical level, the kidney hypertrophies under the control of androgens to produce an hydrophobic protein named spiggin. Spiggin is a 203-kDa cysteine-rich glycoprotein synthesized, during the breeding period only, in the kidney of male fish and then secreted into the urinary bladder where it is assembled from three subunits prior its utilisation as a structural thread for nest building [START_REF] Jakobsson | An 11-ketotestosterone induced kidney-secreted protein: the nest building glue from male three-spined stickleback, Gasterosteus aculeatus[END_REF][START_REF] Jones | Molecular cloning and characterisation of spiggin. An androgen-regulated extraorganismal adhesive with structural similarities to Von Willebrand factor-related proteins[END_REF]. The spiggin gene is present, but remains silent, in female and juvenile stickleback. Following stimulation by androgens or their mimics, spiggin is readily induced. Because spiggin synthesis appears to be androgen-specific, the induction of spiggin in female or immature fish can serve as a sensitive and reliable biomarker for exposure to androgen receptor agonists in laboratory [START_REF] Katsiadaki | Detection of environmental androgens: a novel method based on enzyme-linked immunosorbent assay of spiggin, the stickleback (Gasterostus aculeatus) glue protein[END_REF] and field studies [START_REF] Allen | Effects of 17ethynylestradiol on EROD activity, spiggin and vitellogenin in three-spined stickleback (Gasterosteus aculeatus)[END_REF]. Spiggin can also be used as endpoint for the rapid and sensitive screening of androgenic and anti-androgenic endocrine disrupting compounds tested on stickleback kidney cell culture assay [START_REF] Bjorkblom | Estrogen-and androgensensitive bioassays based on primary cell and tissue slice cultures from three-spined stickleback (Gasterosteus aculeatus)[END_REF][START_REF] Jolly | Development of a stickleback kidney cell culture assay for the screening of androgenic and anti-androgenic endocrine disrupters[END_REF]. Moreover, an in vivo test, based on measurement of spiggin reduction in androgen-treated female sticklebacks, has been developed for the detection of environmental anti-androgens [START_REF] Katsiadaki | A sensitive, in vivo test for the detection of environmental anti-androgens, using the three-spined stickleback (Gasterosteus aculeatus)[END_REF].

The present paper describes the development and validation of a competitive enzyme-linked immunosorbent assay (ELISA) based on utilisation of antibodies against a synthetic peptide specific to three-spined stickleback spiggin sequence.

Materials and methods

Fish maintenance and spiggin induction

Three-spined sticklebacks and nine-spined sticklebacks (Pungitius pungitius) used in this study were male and female adults sampled, outside their breeding period, from uncontaminated outdoor lotic mesocosms located at INERIS (Verneuil en Halatte, France).

Prior to the onset of experiments, fish were acclimated in conditions for one week. The water temperature was 15°C ± 1°C and the photoperiod was a light/dark cycle of 8/16 hours. Male and female zebrafish (Danio rerio), a fish species in which spiggin synthesis is not observed, were sampled from a laboratory stock and acclimated to a temperature of 26.5°C ± 0.4°C and a 14/10 hours light/dark photoperiod. During this period, water was completely renewed and food was supplied every other day. Spiggin induction. Male and female fish were randomly distributed in 15 litres glass aquaria loaded to one fish per litre and exposed, during 21 days, to 20 µg/L of waterborne 17methyltestosterone (17 -MT) dissolved in dimethylsulfoxide (0.002 % of DMSO by aquarium). The 17 -MT concentration was chosen to allow a strong spiggin induction. The control group received no added MT and DMSO. During this exposure, water was completely renewed and food was supplied every other day.

Standard and samples preparation

After exposure, fish were sacrificed, measured, weighed and sexed. Kidneys were dissected and weighed. Kidneys were dissolved in 100 mM Tris-HCl buffer (pH 8.5) containing 10 mM ethylenediaminetetraacetic acid (EDTA), 8 M urea, 2% (w/v) sodium dodecyl sulfate (SDS), 200 mM -mercaptoethanol and 0.2 mM phenylmethylsulfonyl fluoride (PMSF) by heating at 100°C for two hours. Dissolved kidneys were stored at -80°C prior to spiggin quantification. Spiggin purification by chromatographic method is difficult because it is an hydrophobic protein that reforms into glue. However, the use of induced biological material as a standard for coating and standard curve dilutions, appears as a useful principle previously [START_REF] Katsiadaki | Detection of environmental androgens: a novel method based on enzyme-linked immunosorbent assay of spiggin, the stickleback (Gasterostus aculeatus) glue protein[END_REF]. Hypertrophied kidneys from breeding male sticklebacks exposed to 20 µg 17 -MT /L during 21 days (see part 2.1) were pooled and dissolved (1:10 [w:v]) in denaturing buffer using the same method as with the samples. To minimise non-specific interactions between standard and antibodies, dissolved kidneys were centrifuged at 14 000 x g, 4°C for 15 min. Unfortunately, denaturing buffer components interfered with classical protein quantification assays such as 280 nm UV measurement, Bradford's assay [START_REF] Bradford | A rapid sensitive method for the quantitation of microgram quantities of protein utilizing the principle of protein-dye binding[END_REF] or Lowry's assay [START_REF] Lowry | Protein measurement with the folin phenol reagent[END_REF], and prevent protein quantification. Hence, to bridge this gap, the supernatant was assigned to 50 000 U/mL according the method described by [START_REF] Katsiadaki | Detection of environmental androgens: a novel method based on enzyme-linked immunosorbent assay of spiggin, the stickleback (Gasterostus aculeatus) glue protein[END_REF]. Prior utilisation, aliquots of 20 µL were stored at -80°C.

Synthetic peptide and peptide antibody

A peptide (HRD-16) common to the spiggin subunits was synthesized by Innovagen AB (Lund, Sweden). The peptide sequence, HRDELIRDSKLHDHRC, corresponded to amino acid 161 to 176 in the three-spined stickleback spiggin protein [START_REF] Jones | Molecular cloning and characterisation of spiggin. An androgen-regulated extraorganismal adhesive with structural similarities to Von Willebrand factor-related proteins[END_REF] and was used to produce polyclonal antiserum (Agrisera, Vännäs Sweden). IgG (0.9 mg/mL) was purified from rabbit polyclonal antiserum against HRD-16 peptide (as described by [START_REF] Nilsen | Development of quantitative vitellogenin-ELISAs for fish test species used in endocrine disruptor screening[END_REF]).

Western Blot analysis

In a first time, samples were run in 10 % SDS-PAGE. While protein concentrations cannot be determined, gels were loaded with known quantities of tissue (50 µg for male kidney from three-spined stickleback and nine spined stickleback and 500 µg for all other samples). In a second time, proteins were transferred to a nitrocellulose membrane followed by a blocking step with 5 % BSA in PBS overnight at 4°C. Membranes were then incubated for 1 h at room temperature with anti-HRD-16 IgG diluted 1:80 000 in PBS, 0.05% Tween 20, 2 % BSA (PBS-T-BSA), and then incubated for 1 h at room temperature with a HRP-conjugated goat anti-rabbit serum (Bio-Rad Laboratories) diluted 1:2 000 in PBS-T-BSA. Membranes were washed and developed using luminol/H 2 O 2 as substrates (Amersham Biosciences).

Direct ELISA

Samples diluted in 0.05 M carbonate/bicarbonate buffer (pH 9.6) were coated in microtiter plates (96-well Nunc Maxisorp ; Nunc, Roskilde, Denmark) overnight at 4°C. The plates were then blocked for 1 h with 2 % BSA in PBS and then incubated 1 h, at room temperature, with primary antibody diluted in PBS, 1 % BSA. After this time, HRP-conjugated goat anti-rabbit serum diluted in PBS, 1 % was added for 1 hours at 37°C. The peroxidase activity was revealed by adding tetramethyl benzidine enzyme substrate (Interchim, France). After a 30 min incubation at 37°C, the enzyme reaction was stopped by addition of 50 µL of 1 M phosphoric acid (H 3 PO 4 ). The absorbance was read at 450 nm using a microplate reader (Power Wave x -Bio-Tek instruments).

Stickleback spiggin competitive ELISA

This competitive ELISA for three-spined stickleback spiggin is based on a competition for the anti-HRD-16 antibodies between spiggin coated on the wells of a microtiter plate and free spiggin in the sample or standard solutions. The procedure described here has been optimized.

Coating. Microtiter plates (96-well Nunc Maxisorp ; Nunc, Roskilde, Denmark) were coated with 100 µL per well of stickleback spiggin standard at a concentration of 5 U/mL in 0.05 M carbonate/bicarbonate buffer (pH 9.6). The nonspecific binding (NSB) was determined using two wells coated with carbonate/bicarbonate buffer containing BSA only. The plates were incubated overnight at 4°C. Standard and sample preincubation. Spiggin standard was serially diluted by a factor two in PBS, from 0.2 to 100 U/mL. Similarly, samples were serially diluted from 1: 50 to 1:50 000.

Diluted solution were mixed (1:1) with primary antibody solution previously diluted to 1:10 000 to obtain a final concentration of 1:20 000. The maximal binding (B 0 ) was determined using a sample containing only antibody mixed with the buffer to make a final concentration identical to the antibody concentration present in all other samples. The mixed solutions were incubated at room temperature during 30 min and subsequently incubated overnight at 4°C.

Blocking. The coated plates were washed three times with 200 µL per well of PBS-T and blocked with the same volume of PBS, 2% BSA for 1 h at room temperature.

Primary and secondary antibody incubation. The blocked plates were washed three times with PBS-T. After this washing step, 100 µL of standard/antibody or sample/antibody preincubates were introduced into the wells. The plates were sealed and incubated during 2 hours at room temperature. After this time, the plates were washed another three times with the same protocol. 100 µL of HRP-conjugated goat anti-rabbit serum were added in all wells at a dilution of 1:3 000 in PBS, 1% BSA. Plates were sealed and incubated at 37°C for 2 hours.

Development. Microtiter plates were washed five times with PBS-T and the peroxidase activity was revealed by adding 100 µL of tetramethyl benzidine enzyme substrate. The enzyme reaction was stopped after 30 min by addition of 50 µL of 1 M H 3 PO 4 , and the absorbance was read at 450 nm using a microplate reader.

Result calculation. The mean of the absorbance values for the NSB wells was subtracted from the values of all other wells on the same plate. The standard or sample dilution percentage binding was calculated using the following equation : The B i /B 0 standard data were fitted using least-squares method in a four-parameters logistic model and the equation was used to calculate the sample spiggin concentration.

Validation of ELISA method

Parallelism between standard and dilution curve. Kidney samples from control and MTexposed male and female three-spined sticklebacks were serially diluted and the parallelism between the competition curves obtained with the samples and the spiggin standard curves was assessed.

Reproducibility. Precision and reproducibility of the ELISA method were determined using a one-way analysis of variance as described by Caporal-Gautier et al. (1992a;[START_REF] Borg | Androgens in teleost fishes[END_REF]. Briefly, five independent spiggin standard curves were made in duplicate and in four independent assays using four independent spiggin standard to provide information including reproducibility of standard preparation. Each curve was fitted with a four-parameters logistic model. Intra-and interassay coefficients of variation (CV) were calculated using the following equations and expressed as a percentage for the spiggin concentration at 90, 80, 50, and 20% binding. Detection and quantification limits. The detection and quantification limits (DL and QL respectively) were determined using the standard dilution curve and were respectively represented by 90 and 80% binding [START_REF] Brion | Development and validation of an enzyme-linked immunosorbent assay to measure vitellogenin in the zebrafish (Danio rerio)[END_REF].

Matrix effect. The interferences generated by the renal tissue on the spiggin quantification were assessed. Briefly, o i B B values for kidney homogenates from non-exposed zebrafish diluted 1:1, 1:10, 1:20, 1:25, 1:40, 1:50, and 1:100 were determined.

Usefulness of ELISA method to quantify spiggin induced by graded concentration of 17 -methyltestosterone

A total number of 120 male and female three-spined sticklebacks were randomly distributed in 8 glass aquaria of 15 litres loaded to one fish per litre, and exposed, during 21 days, to 0, 0.1 and 1 µg waterborne 17 -MT /L. The 17 -MT was dissolved in DMSO added in aquarium to 0.002 %. Two control groups were also monitored during this experiment including an absolute control that received water only and a solvent control that received DMSO in the same proportion as exposed groups. During this exposure, water was completely renewed every day and food was supplied every other day. After exposure, fish were sacrificed, measured and weighed. Kidney was dissected, weighed and stored in liquid nitrogen prior spiggin quantification. Nephro-somactic index (NSI) was calculated as (kidney weight / fish weight) x 100. Spiggin was quantified in dissolved kidneys of sticklebacks using the developed ELISA method. All samples were analysed in duplicate and the results were expressed as Unit of spiggin/g of fish and the induction factors were calculated.

Statistical analysis

Data are presented as mean ± standard deviation and all statistical analysis were performed with SPSS 14 software. Normal distribution and homoscedasticity of data were verified using respectively Kolmogorov-Smirnov and Levene tests. When data sets didn't have a normal distribution and/or homogeneity of variance, the data was log-transformed, using F(x) = log(1+x), prior to parametric analysis. A one-way analysis of variance (ANOVA) followed by a Tukey post-hoc test was performed to test the position of significant differences between exposure conditions ( =0.05). Male and female differences were analysed using a t-test ( =0.05).

Results

Antibody characterisation

The ELISA method developed in this work is based on the use of antibodies against synthetic peptide from the spiggin sequence [START_REF] Jones | Molecular cloning and characterisation of spiggin. An androgen-regulated extraorganismal adhesive with structural similarities to Von Willebrand factor-related proteins[END_REF]. Prior to ELISA development and validation, the specificity of antibodies (anti-HRD-16) were assessed. The antibodies were initially characterised by western blot analysis using induced male kidney and liver and noninduced female kidney from stickleback and also BSA and HRD-16 peptide. The results showed that anti-HRD-16 antibody binds proteins only in induced male stickleback kidney.

No significant cross-reaction or non-specific binding were observed in other samples (Fig. 1A).

The antibodies were also characterised by direct ELISA analysis using HRD-16 peptide and various other biological samples with or without spiggin (Fig. 1B). The results indicated that anti-HRD-16 antibodies cross-react with HRD-16 peptide and kidney from induced male three-spined stickleback with a decrease of the signal proportional to the dilution of anti-HRD-16 antibodies in the range 1:4 000 -1:250 000. All other samples registered an absorbance below 0.5, providing evidence for the specificity of anti-HRD-16 for spiggin.

ELISA development and validation

In a first step, several standard spiggin coating concentrations and primary antibody dilutions were used in a criss-cross serial dilution test. Three combinations characterised by an optimal absorbance (between 1.5 and 2), a low spiggin coating concentration and a high dilution rate of antibody were selected (Fig. 2). To evaluate the performance of each assay condition, standard curves were generated (data not show). After this step, one combination based on 5 U/mL coating concentration and 1:20 000 primary antibody final dilution was selected to establish and validate the competitive ELISA.

The assay condition described, consistently produced a standard curve with a working range of 0.8-4.3 U/mL (80-20% binding) in diluted samples, with 50% of binding at approximately 1.7 U/mL. The specificity of the assay was assessed by comparing the slopes of standard curves and serially diluted samples (Fig. 3). The kidney of breeding male and 17 -MTexposed female sticklebacks showed a good parallelism with the spiggin standard within the working range of the assay. Conversely, HRD 16 peptide showed a lack of parallelism with the other samples which reflected a significant variation of cross-reaction of between antibodies and natural or synthetic ligands (data not shown). Under these conditions, intraand inter-assay coefficients of variation were calculated for the spiggin standard curve at 90 %, 80 %, 50 % and 20 % binding. The results are presented in Table 1. All coefficients of variation were satisfactory with a value below 20 % reflecting the reproducibility and the repeatability of the method including standard preparation. The detection and quantification limits of this assay were 0.5 and 0.8 U/mL respectively.

The matrix effect linked to other fish proteins or higher concentration of denaturing buffer was assessed. Diluted kidney samples of non-exposed zebrafish containing no spiggin were used to determine o i B B values. The results presented in Table 2 show that dilutions of sample below 1:25 provide a quantifiable signal. Hence, to avoid the matrix effect, a dilution of sample of at least 1:25 was chosen for the routine assay. Consequently, the detection and quantification limits for spiggin in kidney samples were 12.5 and 20 U/mL respectively.

Spiggin induction by graded 17 -MT concentrations

In this experiment, NSI and spiggin concentration was not gender dependent parameters.

However, male and female data were treated separately in light to strong physiological differences between both genders (Fig. 4). Non-exposed sticklebacks exhibited low values of NSI (0.3 ± 0.2 % for absolute control females to 0.6 ± 0.3 % for solvent control males) and no significant differences was observed between both control groups. After 21 days of exposure to 17 -MT, fish showed a significant increase of NSI values for both genders and both tested concentrations (1.1 ± 0.3 % for 0.1µg/L exposed females to 1.7 ± 0.3 % for 1.0µg/L exposed males). However, the response of NSI appeared as not dose-dependent and no significant differences was recorded between both 17 -MT exposed groups. Spiggin level in nonexposed sticklebacks was not detectable but 20 % of male and female fish exposed for 21 days to 0.002% DMSO exhibited a low level of spiggin with 24.2 ± 19.0 and 15.3 ± 7.8 U/g of fish respectively. Mean measured concentrations of spiggin in males exposed to 0.1 and 1 µg/L of 17 -MT were respectively 1303.5 ± 903.7 U/g of fish and 7645.9 ± 1111.3 U/g of fish. In female exposed to 0.1 µg/L of 17 -MT, the measured spiggin concentration was 2005.2 ± 2027.2 U/g of fish but 2 out 15 females were not induced. In female exposed to 1 µg/L of 17 -MT, spiggin was detected in all fish and the measured concentration was 5776.1 ± 2362.1 U/g of fish.

Discussion

Several methods have been described to assess the androgenic response of stickleback.

Among them, the measurement of kidney epithelium height (KEH) in histological sections [START_REF] Borg | Effectiveness of several androgens in stimulating kidney hypertrophy, a secondary sexual character, in castrated male three-spined sticklebacks, Gasterosteus aculeatus[END_REF] and NSI determination [START_REF] Sokolowska | Seasonal changes in brain melatonin concentration in the three-spined stickleback (Gasterosteus aculeatus): towards an endocrine calendar[END_REF]) provides a valuable information on androgen effects in kidney but appears to have low sensitivity. Very specific and sensitive methods to detect changes in spiggin mRNA, such as Northern blot analysis [START_REF] Jones | Molecular cloning and characterisation of spiggin. An androgen-regulated extraorganismal adhesive with structural similarities to Von Willebrand factor-related proteins[END_REF] and by real-time polymerase chain reaction (Geoghegan et al., 2005) have been developed. However, the response levels measured with these assays may not necessarily correlated with spiggin synthesis. ELISA have also been set up to measure spiggin level in stickleback kidney [START_REF] Katsiadaki | Detection of environmental androgens: a novel method based on enzyme-linked immunosorbent assay of spiggin, the stickleback (Gasterostus aculeatus) glue protein[END_REF]. This methodology appears to be very sensitive, less expensive than molecular biology assays and less time consuming than KEH measurement. Hence, we have focused on the establishment and validation of an immunoassay to detect and quantify spiggin in three-spined stickleback using antibodies raised against a synthetic peptide of the spiggin protein.

Competitive ELISA development requires the availability of a standard and an antibody specific of the protein of interest [START_REF] Brion | Development and validation of an enzyme-linked immunosorbent assay to measure vitellogenin in the zebrafish (Danio rerio)[END_REF]. Unfortunately, spiggin is a highly hydrophobic protein not easy to purify to obtain a pure and quantifiable standard, hence no spiggin purified standard and specific antibodies were commercially available. To bridge this methodological problem, [START_REF] Katsiadaki | Detection of environmental androgens: a novel method based on enzyme-linked immunosorbent assay of spiggin, the stickleback (Gasterostus aculeatus) glue protein[END_REF] developed an elegant strategy based on utilisation of a pool of hypertrophied kidneys as standard to obtain dilution curve, and a pool of nest material for coating the plates. This process diminishes interference between antibodies raised against spiggin from stickleback bladder, and coated material but not with other component of biological samples and could be induce overestimation of spiggin concentration. In the present work, we developed and validated an ELISA based on an alternative strategy. The selected antibodies were raised against a synthetic peptide. The chosen peptide corresponds to 161-176 amino acid sequence of the three-spined stickleback spiggin [START_REF] Jones | Molecular cloning and characterisation of spiggin. An androgen-regulated extraorganismal adhesive with structural similarities to Von Willebrand factor-related proteins[END_REF]. More recently, [START_REF] Kawahara | Multiple occurrences of spiggin genes in sticklebacks[END_REF] showed that spiggin is encoded by a multi-gene family named spg 1.1, 1.2, 1.3, 1.4, 2, 3 and 4. The chosen peptide is located in all the sequences deduced amino acid sequences from the seven spiggin cDNA except for spg 2 and 3 where the lysine in position 175 is replaced by arginine. The peptidespecific antibodies exhibited an high specificity as observed by Western Blot and direct ELISA analysis. Anti-HRD-16 antibodies showed a cross-reaction with spiggin of threespined stickleback only. Indeed, no cross-reaction was noticed with non-induced kidneys of females and with liver of induced males, indicating that antibodies recognised a androgeninduced protein synthetised in kidney of three-spined stickleback. A lack of cross-reaction was also noticed with induced kidneys of nine-spined stickleback. As most Gasterosteidae, nine-spined sticklebacks produces spiggin used in gluing plant material to form a nest [START_REF] Wootton | The biology of the sticklebacks[END_REF]. However, the lack of reactivity with anti-HRD-16 antibodies could be explained by the difference observed in spiggin amino acid sequence for these two fish species (i.e. 81 % similarity) and the lack of selected peptidic sequence in nine-spined stickleback (McDermott et al, unpublished data). Similarly, no cross-reaction was observed with sample from zebrafish : a fish species in which spiggin is not expressed. The high specificity of anti-HRD-16 antibodies for the spiggin of three-spined stickleback, allowed to use a preparation of hypertrophied kidneys from 17 -MT induced male three-spined stickleback as standard to obtain a steep standard curve and to coat the plates.

The spiggin standard used for this ELISA is a pool of hypertrophied kidneys from androgenised male three-spined stickleback dissolved in denaturing buffer and assigned an arbitrary value of 50 000 U/mL. A strong concentration of 17 -MT, a high affinity ligand for the androgen receptor widely used in aquaculture to produce predominately male populations [START_REF] Pandian | Hormonal induction of sex reversal in fish[END_REF] and able to induce spiggin [START_REF] Katsiadaki | Detection of environmental androgens: a novel method based on enzyme-linked immunosorbent assay of spiggin, the stickleback (Gasterostus aculeatus) glue protein[END_REF], was used for fish androgenisation. The utilisation of biological material containing spiggin as standard has been previously described by [START_REF] Katsiadaki | Detection of environmental androgens: a novel method based on enzyme-linked immunosorbent assay of spiggin, the stickleback (Gasterostus aculeatus) glue protein[END_REF] and appears as a valuable method which mitigates the lack of absolute standard.

The performance of the ELISA was validated through a single-laboratory validation based on international guidelines for validation of analytical methods (Eurachem, 1998;[START_REF] Thompson | Harmonized guidelines for single-laboratory validation of methods of analysis[END_REF]. Several parameters including linear range of the standard curve (i.e. calibration), intra-and inter-assay variation (i.e. precision and repeatability respectively), detection and quantification limits for standard and samples but also matrix effect were assessed for the developed spiggin ELISA. The minimal acceptable performances for each parameter were not clearly defined for spiggin ELISA. However, validation of vitellogenin ELISA was well described and the performances for each end-point of validation procedure were defined (Goksøyr et al., 2003). With intra-and inter-assay coefficients of variation below 20 % and a 6-fold working range between 0.8 and 4.3 U/mL, the developed ELISA in the present study appears as a valuable method to detect spiggin at 0.5 U/mL. Biological components of kidney samples and denaturing buffer used for sample preparation can interfere with the quantification of spiggin and a minimum dilution factor must be determined to avoid this problem. This matrix effect was measured by analysing homogenised kidneys from androgentreated male zebrafish rather than kidneys from non-treated female three-spined stickleback that could contain low level of spiggin. By using kidney samples of 17 -MT treated male zebrafish, a matrix effect was observed despite the lack of spiggin in this fish species and a dilution of 1:25 was determined to avoid this matrix effect. Consequently, the detection and quantification limits for spiggin in kidney samples were respectively 12.5 and 20.0 U/mL. Under these conditions, in non-exposed females and in non reproductive males no spiggin is detected in kidney samples. In contrast, other studies using the method of [START_REF] Katsiadaki | Detection of environmental androgens: a novel method based on enzyme-linked immunosorbent assay of spiggin, the stickleback (Gasterostus aculeatus) glue protein[END_REF], were able to measure low levels of spiggin allowing statistical variability in female control groups [START_REF] Allen | Effects of 17ethynylestradiol on EROD activity, spiggin and vitellogenin in three-spined stickleback (Gasterosteus aculeatus)[END_REF][START_REF] Hahlbeck | The juvenile three-spined stickleback (Gasterosteus aculeatus L.) as a model organism for endocrine disruption II-kidney hypertrophy, vitellogenin and spiggin induction[END_REF][START_REF] Katsiadaki | Detection of environmental androgens: a novel method based on enzyme-linked immunosorbent assay of spiggin, the stickleback (Gasterostus aculeatus) glue protein[END_REF].

The developed and validated ELISA was used to quantify spiggin in control and 17 -MTexposed stickleback. In the present work, non-exposed male and female sticklebacks maintained in non-reproductive status were characterised by low NSI values in accordance with the data previously reported in non-breeding sticklebacks [START_REF] Sokolowska | Seasonal changes in brain melatonin concentration in the three-spined stickleback (Gasterosteus aculeatus): towards an endocrine calendar[END_REF]. In these fish, no spiggin level was detected. In male stickleback, spiggin induction is correlated closely with the increase of 11-ketotestosterone level during the breeding season [START_REF] Mayer | Seasonal changes in and effect of castration/androgen replacement on the plasma levels of five androgens in the male three-spined stickleback, Gasterosteus aculeatus L[END_REF]. Outside breeding period, levels of 11-ketotestosterone and other androgens such as testosterone, 11 -hydroxytestosterone, 11-ketoandrostenedione and 11hydroxyandrostenedione are low [START_REF] Borg | Androgens in teleost fishes[END_REF][START_REF] Mayer | Seasonal changes in and effect of castration/androgen replacement on the plasma levels of five androgens in the male three-spined stickleback, Gasterosteus aculeatus L[END_REF] and could explain the lack of spiggin synthesis as shown in our study. Surprisingly, a low spiggin induction was detected in sticklebacks exposed for 21 days to 0.002 % of DMSO. This induction was quantified in 20 % of samples and the measured values were 24.2 ± 19.0 and 15.3 ± 7.8 U/g of fish in male and female respectively. However, no NSI increase was recorded in fish from solvent control group compared to absolute control that confirmed the high sensitivity of spiggin measurement. The review by [START_REF] Hutchinson | Acute and chronic effects of carrier solvents in aquatic organisms: A critical review[END_REF] showed clearly that DMSO carrier has the potential of modulating the endocrine system. A recent study by [START_REF] Mortensen | Dimethyl sulfoxide is a potent modulator of estrogen receptor isoforms and xenoestrogen biomarker responses in primary culture of salmon hepatocytes[END_REF] suggested that DMSO may act as an estrogen receptor agonist using a salmon hepatocyte in vitro system. Whether DMSO is able to activate androgen receptor in stickleback (as well as in other fish species) needs to be investigated.

In sticklebacks exposed to 0.1 and 1 µg 17 -MT /L, the present assay allowed to quantify spiggin inductions generated by both tested concentrations. Parallel to high spiggin synthesis by kidney of both 17 -MT-exposed male and female, we recorded significant increase of NSI which is in agreement with the hypertrophy of the male kidney during the breeding season. [START_REF] Katsiadaki | Detection of environmental androgens: a novel method based on enzyme-linked immunosorbent assay of spiggin, the stickleback (Gasterostus aculeatus) glue protein[END_REF] reported a rough low observed effect concentration (LOEC) of 0.1 µg 17 -MT /L using spiggin induction as end-point. At this concentration, we observed a 54 and 131-fold induction in male and female sticklebacks respectively. These fold-induction rates were not different between males and females. The effect recorded was not dose-dependent in female due to the high variability linked to the lack of response observed for 2 out of 15 exposed females. Interestingly, these 2 females exhibited low NSI values. Conversely, spiggin induction recorded was dose-dependent. Our results indicated that, out of breeding period, male and female sticklebacks exhibited no spiggin basal level (except for few fish from the solvent control group) and that spiggin response was similar between gender in term of effective concentration of 17 -MT and induction levels. Consequently, both gender can be used without distinction to assess androgenic effects of chemicals if sticklebacks are collected during non reproductive period. Hence, this result allows to decrease the fish number used for laboratory and field experiments. Evidence for spiggin induction in sticklebacks exposed to 0.1 µg/L for 21 days suggested that spiggin provides a valuable end-point to assess the androgenic effects in fish.

In summary, a sensitive and robust competitive spiggin ELISA has been developed using antibodies against synthetic peptide and kidney samples from 17 -MT -induced male threespined sticklebacks as standard. This method allows the quantification of spiggin in kidney of androgen-exposed stickleback with a high specificity. Hence, the present assay completed a set of biochemical biomarkers set-up in our laboratory and successfully applied to investigate biochemical responses of wild sticklebacks [START_REF] Sanchez | Preliminary investigation of multi-biomarker responses in three-spined stickleback (Gasterosteus aculeatus L.) sampled in contaminated streams[END_REF], and allows assessment of androgenic activity of chemicals in laboratory and to explore androgenic exposure in fieldsampled sticklebacks.

Caporal-Gautier, J., Nivet, J.M., Algranti, P., Guilloteau, M., Histe, M., Lallier, M., N'Guyen-Huu, J.J., Russotto, R., 1992a. Guide de validation analytique. Rapport de la commission SFSTP. I. Méthodologie. S.T.P. Pharma Pratiques 2-4, 205-226.

Caporal-Gautier, J., Nivet, J.M., Algranti, P., Guilloteau, M., Histe, M., Lallier, M., N'Guyen-Huu, J.J., Russotto, R., 1992b

Fig. 2 .

 2 Fig. 2. Determination of optimal concentration of three-spined stickleback (G. aculeatus) spiggin

Fig. 3 .

 3 Fig.3. Cross-reaction of kidney samples from MT-induced male and female three-spined

Fig. 4 .

 4 Fig. 4. Spiggin levels (A) and NSI (B) in kidneys from male (black bars) and female (open bars) three-spined sticklebacks (G. aculeatus) non-exposed (absolute control and solvent control) and exposed for 21 days to two concentrations of 17 -methyltestosterone (MT) under semistatic conditions. The numbers refer to the number of fish in each treatment. Males and females were analysed separately and treatments shown with the same letter do not differ significantly from each other ( =0.05). nd was not detectable.

  Fig.1

  Fig. 3

  MT-induced male nine-spined stickleback (P. pungitius ; kidney, 50 µg) ; lane 8 : non-induced female nine-spined stickleback (kidney, 500 µg).

	Fig. 1. Characterisation of HRD-16 antibodies. A : Western blot with HRD-16 antibodies diluted to
	1 : 80 000 and induced and noninduced samples from different fish species. B : Direct ELISA
	performed with induced and noninduced samples from different fish species diluted to 1 :10 000
	. Guide de validation analytique. Rapport de la commission and various dilutions of HRD-16 antibodies. Lane 1 : HRD-16 peptide (1 µg) ; lane 2 : MT-induced
	SFSTP. II. Exemples d'application. S.T.P. Pharma Pratiques 2-4, 227-239. male three-spined stickleback (G. aculeatus ; kidney, 50 µg) ; lane 3 : non-induced female three-
	Cody, R.P., Bortone, S.A., 1997. Masculinization of mosquitofish as an indicator of exposure
	to kraft mill effluent. Bull. Environ. Contam. Toxicol. 58, 429-436. spined stickleback (kidney, 500 µg) ; lane 4 : MT-induced male three-spined stickleback (liver, 500
	Eurachem, µg) ; lane 5 : MT-induced zebrafish (D. rerio ; kidney, 500 µg) ; lane 6 : non-induced zebrafish 1998. The fitness for purpose of analytical methods.
	http://www.eurachem.ul.pt/guides/valid.pdf. (kidney, 500 µg) ; lane 7 :
	Geoghegan, F., Katsiadaki, I., Williams, T.D., Lyons, B.P., Chipman, J.K., 2005. Differential
	gene expression in the three-spined stickleback Gasterosteus aculeatus in response to a
	mixture of pollutants, 13th international symposium Pollutant Responses in Marine
	Organisms, Alessandria, Italy.
	endocrine	disruptor	testing	and	screening	-	a	proposal.

Goksøyr, A., Eidem, J.K., Kristiansen, S.I.,

Nilsen, B.M., 2003.

On the need for a standardized set-up for validation studies of fish vitellogenin assays as an endpoint in

Table 2 .

 2 ELISA) with a combination of 5 U/mL of spiggin and antibody dilution of 1:20 000. CV = coefficient of variation. Determination of matrix effect using kidney sample of 17 -MT-exposed (20µg/L) male zebrafish (D rerio) diluted 1:1, 1:10, 1:20, 1:25, 1:40, 1:50 and 1:100. This tissue was chosen because it is devoid of spiggin. In the routine assay, samples were diluted 1:25 to avoid the matrix effect. Bi/B 0 = percentage binding.

	A				14	16
	Males
	Females
				15	15
	12	18	15	15
	B

Aknowledgement

This work was supported by the French Ministry of Ecology and Sustainable Development (Budget Civil de la Recherche et du Développement AP-2004) and by Biosense Laboratories AS.