Alessandro Barbiero
email: alessandro.barbiero@unimi.it

Confidence intervals for reliability of stress-strength models in the normal case

Keywords: asymptotically normal, independent normal, parametric bootstrap, Monte Carlo simulations, stress-strength, variance estimation asymptotically normal, independent normal, parametric bootstrap, Monte Carlo simulations, stress-strength, variance estimation

Confidence intervals for reliability of stress-strength models in the normal case

the term "stress-strength". In the simplest terms this can be described as an assessment of "reliability" of a "component" in terms of random variables Y representing "stress" experienced by the component and X representing the "strength" of the component available to overcome the stress. According to this simplified scenario, if the stress exceeds the strength (Y > X) the component would fail; and vice versa. Reliability is defined as the probability of not failing: R = P(Y < X). The reliability problem arises in the fields of aeronautical, civil, mechanical and electronic engineering. For example, X may be the breakdown voltage of a capacitor, while Y may represent the voltage output of a transverter [START_REF] Hall | Approximate one-sided tolerance limits for the difference or sum of two independent normal variates[END_REF]; or X may be the chamber burst strength and Y the operating pressure for a rocket-motor [START_REF] Reiser | Statistical Inference for Pr(Y < X): The Normal Case[END_REF].

The beginning point of this idea was introduced by [START_REF] Birnbaum | On a use of the Mann-Whitney statistic[END_REF] and developed by [START_REF] Birnbaum | A distribution-free upper confidence bound for P(Y < X) based on independent samples of X and Y[END_REF]. The latter paper does for the first time include P(Y < X) in its title. The formal term "stress-strength" appears for the first time in the title of the paper by [START_REF] Church | The Estimation of Reliability from Stress-Strength Relationships[END_REF]. In the course of time, there have been attempts to introduce further elements of adherence to reality, including various generalizations and applications; many papers are devoted both to merely probabilistic problems associated with the evaluation of R and the construction of efficient and reliable estimators of this parameter, based on sample values with various assumptions on the distributions of X and Y . So the research has not only dealt with the problems of deriving theoretical expressions for P(Y < X) and its modifications and extensions under various distributional assumptions, but also with estimation of these probabilities based on samples of various structure, providing for approximations to variances and confidence bounds [START_REF] Kotz | The stress-strength model and its generalizations -Theory and Applications[END_REF]. Many of these works presume that both random variables has distributions belonging to the same family (such as normal, exponential, log-normal, Weibull, etc.) and more importantly they assume independence between them. Some authors, however, considered the case in which X and Y admit a specified form of dependence (bivariate normal, bivariate exponential, etc.): see for example [START_REF] Mukherjee | Estimation of failure probability from a bivariate normal stress-strength distribution[END_REF]; [START_REF] Nadarajah | Reliability For A Bivariate Gamma Distribution[END_REF]; [START_REF] Roy | Estimation of failure probability under a bivariate normal stress-strength distribution[END_REF]. [START_REF] Harris | The Theory of Optimal Confidence Limits for Systems Reliability with Counterexamples for Results on Optimal Confidence Limits for Series Systems[END_REF] emphasize the fact that in many applications the "reliability" has to be very close to one for the device to have any possibility of "useful" life: this implies that very large samples may be needed to obtain sufficiently precise estimates of reliability, since we are dealing with extreme tails of distributions.

In this paper we will consider the estimation of reliability when X and Y are independent random variables and their distribution belongs to a known family (normal) with unknown parameters. Based upon ML estimators, we will consider and refine approximate interval estimators already appeared in literature, we will propose an original bootstrap interval estimator and empirically investigate and compare their performance in terms of coverage and accuracy through an extensive simulation study.

The paper is structured as follows: in Section 2 we describe available methods for interval estimation of reliability for an independent setup; in Section 3 we describe our proposals; in Section 4 we describe the simulation design, show the results and discuss them; in Section 5, we present a real application, in Section 6 we give some final remarks.

Available methods

We will now briefly introduce the concept of "reliability" for a stress-strength model and summarize the methods available in literature for its interval estimation. We will confine ourselves to the parametric case only.

Let the strength be modeled by r.v. X and the stress by r.v. Y . Let us suppose that X follows a continuous distribution with vector of parameters θ θ θ and Y follows a continuous distributions with vector of parameters λ λ λ . The reliability of a stress-strength model is formally defined as

R = P(Y < X) = P(Y -X < 0)
and the following expression can be used to obtain the reliability:

R = +∞ -∞ f x (x,θ θ θ ) x -∞ f y (y,λ λ λ )dydx
where f x and f y denote the p.d.f. of X and Y respectively. For independent normal r.v. X ∼ N(µ x , σ x ) and Y ∼ N(µ y , σ y ), the reliability presents the easy expression

R = Φ   µ x -µ y σ 2 x + σ 2 y   (1)
where Φ denotes the standard normal c.d.f.

A straightforward procedure for getting conservative confidence intervals for the reliability R was described by Chang [START_REF] Chang | Reliability bounds for the stress-strength model[END_REF]. The basic idea was to start from confidence intervals for the parameters of the two r.v. and then numerically obtain a lower and upper bound for reliability from the lower and upper bounds of these intervals. Chang's method provides for the reliability of a stress-strength model with two independent normal variables the following conservative 100

• (1 -2α) 2 % interval: R, R = inf Ω R, sup Ω R =   Φ   µ x -µ y σ 2 x + σ 2 y   , Φ   µ x -µ y σ 2 x + σ 2 y     (2)
where

Ω = µ x ≤ µ x ≤ µ x , µ y ≤ µ y ≤ µ y , σ 2 x ≤ σ 2 x ≤ σ 2 x , σ 2 y ≤ σ 2 y ≤ σ 2 y and (µ x , µ x ) and (σ 2 x , σ 2
x ) are a (1α) confidence interval for µ x and σ 2

x respectively, and analogously for the Y parameters. Yet, Chang's method is overly conservative producing CIs that are unnecessarily wider. [START_REF] Reiser | Statistical Inference for Pr(Y < X): The Normal Case[END_REF] examine statistical inference for P(Y < X), where X and Y are independent normal variates with unknown means and variances. Two approximate methods for obtaining confidence intervals and an approximate Bayesian probability interval are described. The actual coverage probabilities of these intervals are examined by simulation. Specifically, they first consider

δ = µ x -µ y σ 2 x + σ 2 y
Since R is a monotonic function of δ , finding a CI for R is equivalent to finding a CI for δ .

They argue that it seems more reasonable to base inference on a normal approximation to δ than on the normal approximation to R since δ is unbounded, while R is bounded in (-1, 1).

An approximate (1α) CI they propose is given by

(Φ(δ L ), Φ(δ U )) (3)
where δ L and δ U are the lower and upper bound of the interval

δ ± 1 M + δ 2 2 f z 1-α/2 with δ = x -ȳ s 2 x + s 2 y f = (s 2 x + s 2 y ) 2 / s 2 x n -1 + s 2 F o
= δ -1 M + δ 2 2 f z 1-α .
The simulations show that the coverage is not badly influenced by unequal sample sizes. [START_REF] Church | The Estimation of Reliability from Stress-Strength Relationships[END_REF] obtain confidence intervals for P(Y < X) under the assumptions that X and Y are independently normally distributed and the distribution of Y is known. [START_REF] Downton | The Estimation of Pr(Y < X) in the Normal Case[END_REF] derives the minimum variance unbiased estimator of P(Y < X) under the same assumptions. Approximations to this "best" estimator are obtained, and they are suggested as alternatives to the asymptotically equivalent estimator used by Church and Harris to obtain confidence intervals for that probability; they generalize the estimator to the case the distribution of Y is unknown. [START_REF] Weerahandi | Testing Reliability in a Stress-Strength Model When X and Y Are Normally Distributed[END_REF] derive approximate confidence intervals for the reliability, based upon generalized p-values, when X and Y are independently normally distributed and all the parameters are unknown. [START_REF] Irwin | New Approximate Inferential Methods for the Reliability Parameter in a Stress-Strength Model: The Normal Case[END_REF] propose an approximate (one-sided) CI for R by first computing a lower bound for δ and then transforming it to a lower bound for R as done by [START_REF] Reiser | Statistical Inference for Pr(Y < X): The Normal Case[END_REF]. The proposal involves noncentral t with a non-integer number of degrees of freedom and requires a numerical solution. More in detail, if we denote with F(x; d f , ξ ) the noncentral t cumulative distribution function with d f degrees of freedom and noncentrality parameter ξ , a first lower bound δ 1L is the solution of the equation

F( m1 δ ; f1 , m1 δ 1L ) = 1 -α where m1 = n(1 + q1 ) q1 + n/m ; f1 = (n -1)( q1 + 1) 2 q2 1 + (n -1)/(m -1) ; q1 = s 2 1 /s 2 2
whereas a second lower bound δ 2L is the solution of the equation

F( m2 δ ; f2 , m2 δ 2L ) = 1 -α where m2 = m(1 + q2 ) q2 + m/n ; f1 = (m -1)( q2 + 1) 2 q2 2 + (m -1)/(n -1) ; q2 = s 2 2 /s 2 1
The actual lower bound for R is obtained as Mukherjee and Mahiti (1998) develop an interval estimation procedure on the basis of the asymptotic normality of the maximum likelihood estimator (ML) of R and also provide interval estimation procedures based on variance stabilizing transformations such as logit and arcsine.

RL = Φ(min {δ 1L , δ 2L }). (4
Specifically, they consider the case of two independent Weibull distributions. For the same setup, Krishnamoorthy and Lin (2010) propose an alternative method using a generalized variable approach.

In the next Section, we will provide some new procedures to obtain an approximate CI for R.

The proposals

We will now describe our new method for the interval estimation of reliability, based upon two independent samples from X and Y , denoted as x and y, of size n and m respectively. The first is based upon parametric bootstrap, the second ones upon asymptotic results.

A parametric bootstrap procedure

Our first method is a straightforward extension and application of parametric bootstrap for the i.i.d. case [START_REF] Efron | An Introduction to the Bootstrap[END_REF] to a two-sample case. It works as follows:

1. estimate the parameters of the r.v. X and Y , through θ θ θ and λ λ λ (e.g. maximum likelihood)

2. estimate R as R = +∞ -∞ f x (x, θ θ θ ) x -∞ f y (y, λ λ λ )dydx;
For normal r.v. R has an analytical expression depending upon the parameters of X and Y (see Equation ( 1)), and can be easily estimated e.g. through (see [START_REF] Downton | The Estimation of Pr(Y < X) in the Normal Case[END_REF]) (or X * ∼ N( x, s 2 x )) and similarly for Y * . Since all procedures depend on only the sample means and variances, for the well-known properties of the normal distribution, for this case we only have to generate X * ∼ N( x; s 2

R = Φ   x -ȳ s 2 x + s 2 y   or R = Φ   x -ȳ σ 2 x + σ 2 y   , 6
x /n) and S * 2 x ∼ s 2 x χ 2 n-1 /(n -1); similarly, Ȳ * and S * 2 y can be generated.

4. estimate R * , using the same expression for the estimator used in 2.

5. repeat steps 3. and 4. B times (B sufficiently large, e.g. 2, 000), thus obtaining the bootstrap distribution R * 6. estimate a (1α) bootstrap percentile CI for R from R * distribution, taking the α/2 and

1 -α/2 quantiles: R * α/2 , R * 1-α/2 (5) or a (1 -α) bootstrap percentile lower bound for R as R * α
The procedure is quite easy, even if time-consuming, due to the bootstrap step which requires a huge number of runs (2, 000 is a recommended value for percentile bootstrap). Here it is applied to the normal case; indeed, it only preferably requires that the reliability has got a known expression for the two distributions; otherwise the reliability estimate R has to be numerically computed, and the bootstrap estimates R * too. It is a general purpose algorithm, since it can be applied to all possible distribution families; anyway it requires an a priori parametric hypothesis about the distribution of X and Y , which is needed in order to estimate the parameters and the model reliability. The interval estimation is indeed performed only recalling the (parametric) bootstrap principle, which is independently applied to the two samples,

with no concern about the different sample size, and then used to get a bootstrap distribution for R * , which is an estimate for the unknown distribution of R.

Actually, only [START_REF] Irwin | New Approximate Inferential Methods for the Reliability Parameter in a Stress-Strength Model: The Normal Case[END_REF] results: their extensive simulation studies showed that the test based on parametric bootstrap method is liberal, i.e. its size is far greater than the nominal level. We will see that the bootstrap method can provide acceptable results, even if not as good as other approximate methods; yet it turns out as an alternative approach when all the parameters are unknown.

Confidence intervals based upon asymptotic results

Another way to obtain approximate confidence intervals for reliability is to recall some asymptotic results and/or to use some variance stabilizing functions. Asymptotic confidence intervals can be easily obtained. The asymptotic variance of the ML estimator R can be derived following the same steps used in [START_REF] Mukherjee | Estimation of failure probability from a bivariate normal stress-strength distribution[END_REF], and it can be estimated by

v( R) = 1 2πs 2 e -( x-ȳ) 2 /s 2 s 2 x /n + s 2 y /m + 1/2 ( x -ȳ) 2 s 4 (s 4 x /n + s 4 y /m)
where s 2 = s 2 x + s 2 y . A confidence interval for R can be then built using the variance estimate above; however, for the same reason recalled by Reiser and Guttman, it may be better to adopt some specific modifications in order to produce better CI. For example, it is possible to find first the estimate of the asymptotic variance of the ML estimator of δ , d =

xȳ σ 2

x + σ 2 y , that can be obtained as:

v( d) = 1 s 2 s 2 x /n + s 2 y /m + 1 2 ( x -ȳ) 2 s 4 (s 2 x /n + s 2 y /m)
and can be employed to construct an approximate (1α) CI for d:

(d L , d U ) = ( d ± z 1-α/2 v( d))
and then an approximate (1α) CI for R:

(Φ(d L ), Φ(d U )) (6)
or an approximate (1α) lower bound as

Φ( d -z 1-α v( d)).
The variance estimate of R can be employed to build a CI for R by previously "stabilizing" it through a proper transformation. For a normalizing transformation g( R), the approximate 8 variance can be obtained, according to the delta method, as

V (g( R)) [g (R)] 2 V ( R)
Then, see Krishnamoorthy and Lin (2010), for the logit transformation g

(R) = ln R 1-R we get the approximate (1 -α) CI e L (1 + e L ) -1 , e U (1 + e U ) -1 (7)
where L and U are the lower and upper bound of the CI:

  ln R 1 -R ± z 1-α/2 v( R) R(1 -R)  
For the arcsin transformation, the approximate (1α) CI is given by

sin 2 (L), sin 2 (U) (8)
where L and U are the lower and upper bound of the CI:

sin -1 R ± z 1-α/2 v( R) 4 R(1 -R)
Analogously, an approximate (1α) lower bound can be obtained for R recalling the logit and arcsin transformations. The three latest confidence intervals are based upon the asymptotic properties of the ML estimator, so we expect they may fail or show poor results when the sample sizes n and m are small. The simulation study we present in the next Section will point out if and when this expectation is well-founded.

Simulation study

The simulation study we performed aims at empirically checking the statistical properties of the proposed estimators and its competitors, specifically coverage and average length at a nominal level (95%). The simulation study works as follows:

1. set the parameters for the r. • Reiser and Guttman approximate CI (RG, Eq.3)

• Guo and Krishnamoorthy approximate CI (GK, Eq.4)

• bootstrap percentile CI (B, Eq.5)

• approximate CI based on asymptotic variance of d (AS, Eq.6)

• approximate CI based on logit transformation (LO, Eq.7)

• approximate CI based on sin transformation (SIN, Eq.8)

We considered different scenarios, each corresponding to a different combination of distributional parameters (and thus different reliabilities), reported in Table 1, and sample sizes.

Without any loss in generality, we fixed Y ∼ N(µ y = 0, σ y = 1) and varied the parameters of X ∼ N(µ x , σ x ). We set the parameters in order to get a high value for the reliability, since, as we have stressed before, in real practice we usually look for high reliability for the study component/system.

parameter values Actually, the reliability estimator employed is not unbiased, and the MC relative error is an estimate of its relative bias

µ x 2 3 4 2 3 4 µ y 0 0 0 0 0 0 σ x 1 1 1 3 3 3 σ y 1 1 1 1 1 1 R 0.
µ x = 2 µ x = 3 µ x = 4 µ x = 2 µ x = 3 µ x = 4 σ x = 1 σ x = 3 σ x = 1 σ x = 3 σ x = 1 σ x = 3 σ x = 1 σ x = 3 σ x = 1 σ x = 3 σ x = 1 σ x = 3 n = 10, m = 10 n = 20, m =
(E( R) -R)/R.
The results of the simulation study are reported in Tables 3 and4 (coverage and average length of the two-sided CIs) and Tables 5 and6 (coverage and average lower bound of onesided CIs). The MC percentage relative bias of R is reported in Table 2.

With regard to the behavior of R, even if the ML estimator is only asymptotically unbiased, its MC bias is here shown to be negligible, since its absolute value is always smaller than 1.5%.

As we would have expected, sample sizes affect it significantly: for n = m = 50 it decreases to 0.25%. The MC bias is also strongly affected by the experimental conditions: in particular, it takes negative values when the true R is closer to 1, while takes the greatest positive values when R is nearer to 0.5.

Looking at the results for two-sided CIs, it is clearly visible that Reiser and Guttman inferential procedure gives very good results, which seem not to be affected by the samples' sizes and by their discrepancy, even if one can note a slight departure of coverage rate from the nominal level when n = 10 and m = 50. The asymptotic normal CI provide very good results too, in terms of coverage, which is always very close to the nominal level, yet its performance is a bit worse than Reiser and Guttman's. The bootstrap proposal show on average a good performance, assuring a coverage always greater than 90% even for small samples; moreover, it is the method that provides, on average, the shortest confidence interval, under each experimental 11 From the simulation results for one-sided confidence intervals, the overall superiority of GK procedure emerges, followed closed behind by RG and LO. also take into account the additional computation time this already time consuming method could bring. With regard to the SIN procedure, its performance is not totally satisfactory and reliable. One should also note an overall light worsening of the performance of asymptotic procedures passing from two-sided to one-sided CIs: this may be ascribed to the fact that asymptotic CIs overcover on one-tail and undercover on the other, and so overall coverage probabilities of asymptotic two-sided CIs turn out to be close to the nominal level 1α. This behavior has been detected by Krishnamoorthy and Lin (2010) for the Weibull case.

µ x = 2 µ x = 3 µ x = 4 method µ x = 2 µ x = 3 µ x = 4 σ x = 1 σ x = 3 σ x = 1 σ x = 3 σ x = 1 σ x = 3 σ x = 1 σ x = 3 σ x = 1 σ x = 3 σ x = 1 σ x = 3 n = 10, m = 10 n = 20, m =
method µ x = 2 µ x = 3 µ x = 4 method µ x = 2 µ x = 3 µ x = 4 σ x = 1 σ x = 3 σ x = 1 σ x = 3 σ x = 1 σ x = 3 σ x = 1 σ x = 3 σ x = 1 σ x = 3 σ x = 1 σ x = 3 n = 10, m = 10 n = 20, m =
method µ x = 2 µ x = 3 µ x = 4 method µ x = 2 µ x = 3 µ x = 4 σ x = 1 σ x = 3 σ x = 1 σ x = 3 σ x = 1 σ x = 3 σ x = 1 σ x = 3 σ x = 1 σ x = 3 σ x = 1 σ x = 3 n = 10, m = 10 n = 20, m =
method µ x = 2 µ x = 3 µ x = 4 method µ x = 2 µ x = 3 µ x = 4 σ x = 1 σ x = 3 σ x = 1 σ x = 3 σ x = 1 σ x = 3 σ x = 1 σ x = 3 σ x = 1 σ x = 3 σ x = 1 σ x = 3 n = 10, m = 10 n = 20, m =
5 An example of application

Conclusions

In this paper we propose a bootstrap approach and some approximate methods for the interval estimation of reliability in a stress-strength model, where both stress and strength are normally distributed with unknown parameters. We empirically investigate the performance of these bounds) of two existing methods specifically conceived for the normal set-up. Our bootstrap proposal performs slightly worse than the other approximate methods in terms of coverage, but provides narrower intervals. Yet, the advantage of the bootstrap method versus its competitors lies in the actual computation of CI, which does not require further formulas or approximations, but simply reuses the formula employed for point estimation. With regard to the estimators based on asymptotic results, their performance has been here satisfactory even for moderate sample sizes, however, a particular attention should be devoted if extending these results to other parametric families. The new bootstrap proposal can be easily extended, especially to the other family distributions for which an expression for the reliability R is analytically derivable;

it can be used in the independent set-up, as described here, but also generalized -with proper modifications -to the dependent set-up: future research shall then investigate the performance of the bootstrap interval estimator towards the existing ones for other parametric monovariate and bivariate families.

  this paper is to propose confidence intervals for the probability P(Y < X), where X and Y are independent random variables and when sample values x and y are observed. The recent years have seen a lot of publications on this subject: the basic impetus to these developments can be attributed to the specific practical problem of applied statistics summarized by 1

  ML estimator of R 3. draw independently a bootstrap sample x * of size n from a r.v. X * with the same distribution family of X and parameter θ θ θ and a bootstrap sample y * of size m from a r.v. Y * with the same distribution family of Y and parameter λ λ λ . In the normal case, X * ∼ N( x, σx 2 )

  independently a sample x of size n from X and a sample y of size m from Y 4. estimate R and a CI (either two-sided or one-sided) for R 5. check out if the CI computed at the previous step contains R; compute its length 6. repeat steps 3-5 nSim (10, 000) times and compute the overall CI coverage and average length The confidence intervals empirically investigated by simulation are:

  based on asymptotic results, perform well even for small sample sizes. It is also interesting to observe that for sample sizes moderately large (n = m = 50, depending upon the other parameters) the performances of the different confidence intervals tend to get closer, in terms of both coverage ( 95%) and average length.From the simulation study, it is interesting to note if and how the value of R and the sample sizes n and m affect the performance of the interval estimators. With regard to the coverage, as already said, the samples' sizes and their discrepancy seem not to heavily affect the results (but, as expected, the overall best results are for n = m = 50); the same can be told about the experimental conditions: the values of µ x and σ x seem not to systematically affect the performances of the compared procedures. Even in the "worst" scenario (µ x = 4, σ x = 1, with R very close to 1) the methods keep working satisfactorily. Yet LO, for some scenarios, namely µ x = 4 and σ x = 1, provides unreliable results. With regard to the average width, this is clearly influenced by the sample sizes and experimental conditions. The results get better (i.e. the CI are more precise) as the sample sizes increase and the reliability R gets closer to 1.

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  methods and other existing ones, through a simulation study comprising different artificial scenarios. The results show the superiority (in particular when building one-sided tolerance 17

  α) confidence lower bound can be obtained as Φ(δ l ) with δ l

	and
	M =	s 2 x + s 2 y x /n + s 2 s 2 y /m
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have considered the bootstrap method for reliability estimation, specifically as a way to derive approximate test for reliability, at least for the normal case; yet, they have observed that the parametric bootstrap does not give satisfactory 7 Page 12 of 26 URL: http://mc.manuscriptcentral.com/lssp E-mail: comstat@univmail.cis.mcmaster.

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Table 1 :

 1 Parameters for the simulation study

	9214 0.9831 0.9977 0.7365 0.8286 0.8970
	The Monte Carlo (MC) relative bias of R has been taken under control by checking out the
	condition
	E MC ( R) -R /R ≤ 2%
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Table 2 :

 2 Simulation results: R percentage relative bias

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Table 3 :

 3 Simulation results: CI coverage rate 12

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	RG	0.958	0.949	0.958	0.943	0.951	0.951	RG	0.956	0.943	0.952	0.946	0.956	0.949
	GK	0.964	0.952	0.964	0.950	0.958	0.957	GK	0.959	0.947	0.956	0.952	0.959	0.950
	B	0.887	0.891	0.863	0.874	0.851	0.850	B	0.919	0.914	0.924	0.898	0.920	0.889
	AS	0.952	0.945	0.953	0.938	0.941	0.947	AS	0.953	0.942	0.950	0.943	0.950	0.948
	LO	1.000	0.960	1.000	0.984	1.000	1.000	LO	0.962	0.945	0.970	0.955	0.981	0.958
	SIN	0.906	0.908	0.883	0.895	0.860	0.889	SIN	0.922	0.926	0.919	0.917	0.904	0.901
	n = 10, m = 20 RG GK	0.947 0.952 F 0.940 0.944 o	0.945 0.953	0.936 0.941	0.940 0.948	0.939 0.949	n = 50, m = 10 RG GK	0.926 0.946	0.950 0.960	0.926 0.939	0.950 0.955	0.917 0.929	0.950 0.957
	B	0.883	0.879 r 0.858	0.872	0.850	0.865	B	0.876	0.926	0.855	0.917	0.848	0.917
	AS	0.942	0.934	0.942	0.930	0.936	0.932	AS	0.923	0.950	0.922	0.948	0.914	0.950
	LO SIN n = 10, m = 50 RG GK B	0.977 0.894 0.944 0.953 0.890	0.954 0.906 P 1.000 0.869 0.947 0.941 0.951 0.952 0.889 0.879 e 0.975 0.896 0.941 0.950 0.874 e r 1.000 0.848 0.938 0.955 0.864	0.992 0.887 0.939 0.952 0.859	LO SIN n = 50, m = 20 RG GK B	0.946 0.885 0.950 0.953 0.912	0.951 0.935 0.954 0.959 0.923	0.965 0.856 0.948 0.952 0.900	0.954 0.923 0.955 0.958 0.916	0.989 0.83 0.949 0.953 0.895	0.960 0.923 0.954 0.959 0.913
	AS LO SIN n = 20, m = 10 RG GK B AS LO SIN	0.939 0.956 0.901 0.942 0.952 0.875 0.934 0.980 0.891	0.945 0.953 0.913 0.949 0.951 0.908 0.947 0.951 0.923	0.939 0.970 0.879 0.943 0.952 0.857 0.937 1.000 0.864	0.939 0.966 0.897 0.948 0.952 0.894 0.946 0.958 0.912	0.930 0.987 0.850 0.946 0.959 0.856 0.941 1.000 0.848 R e 0.932 0.984 0.889 0.945 0.948 0.875 0.943 0.968 0.899 v n = 50, m = 50 AS LO SIN RG GK B AS LO SIN i e w	0.949 0.956 0.917 0.962 0.962 0.940 0.961 0.965 0.941	0.954 0.954 0.934 0.956 0.959 0.939 0.956 0.956 0.944	0.946 0.974 0.891 0.957 0.960 0.937 0.956 0.966 0.924	0.955 0.958 0.926 0.957 0.959 0.927 0.956 0.957 0.935	0.948 0.983 0.872 0.954 0.957 0.932 0.954 0.976 0.913	0.953 0.961 0.921 0.953 0.956 0.923 0.950 0.957 0.929
	n = 20, m = 20 RG GK B AS LO	0.948 0.950 0.888 0.947 0.962	0.932 0.935 0.896 0.931 0.935	0.950 0.955 0.889 0.948 0.984	0.933 0.939 0.877 0.926 0.948	0.953 0.954 0.886 0.949 1.000	0.934 0.936 0.869 0.930 0.953	O n l y
	SIN	0.897	0.908	0.893	0.893	0.871	0.883
			Table 5: Simulation results: one-sided CI coverage rate
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  condition. The little departure of coverage from the nominal level is a known issue of bootstrap interval estimation, see[START_REF] Schreuder | Reliability of Confidence Intervals Calculated by Bootstrap and Classical Methods Using the FIA 1-ha Plot Design[END_REF]. The CI based on logit transformation gives always coverages greater than the nominal level, especially for high values of R; on the other hand, its average width is the largest. The CI based on sin transformation almost always give coverages never greater than 95%, even for the largest samples' sizes; its performance in terms of both coverage and average width looks surprisingly similar to the bootstrap interval estimator. It is worthwhile noting that the two approximate methods proposed (LO and SIN),

								50
	RG	0.775	0.535	0.902	0.637	0.963	0.725	RG	0.845	0.597	0.948	0.701	0.987	0.787
	GK	0.769	0.530	0.897	0.631	0.960	0.717	GK	0.842	0.594	0.947	0.697	0.986	0.784
	B	0.817	0.565	0.934	0.681	0.980	0.776	B	0.858	0.612	0.956	0.723	0.990	0.811
	AS	0.778	0.537	0.905	0.641	0.965	0.729	AS	0.845	0.597	0.949	0.702	0.987	0.788
	LO	0.749	0.533	0.827	0.625	0.746	0.696	LO	0.843	0.597	0.945	0.699	0.984	0.782
	SIN	0.806	0.556	0.927	0.667	0.977	0.759	SIN	0.856	0.607	0.956	0.715	0.990	0.804
	n = 10, m = 20 RG GK	0.802 0.795 F 0.542 0.536 o	0.921 0.916	0.645 0.637	0.973 0.971	0.732 0.724	n = 50, m = 10 RG GK	0.820 0.811	0.634 0.630	0.932 0.926	0.739 0.735	0.978 0.975	0.823 0.820
	B	0.833	0.571 r 0.943	0.689	0.984	0.783	B	0.844	0.644	0.949	0.750	0.986	0.835
	AS	0.804	0.544	0.923	0.648	0.975	0.737	AS	0.822	0.635	0.933	0.739	0.979	0.823
	LO SIN n = 10, m = 50 RG GK B	0.790 0.826 0.820 0.811 0.844	0.540 0.562 P 0.896 0.939 0.547 0.932 0.540 0.926 0.576 0.949 e 0.635 0.673 0.650 0.641 0.693 e r 0.933 0.983 0.978 0.975 0.986	0.709 0.766 0.737 0.728 0.786	LO SIN n = 50, m = 20 RG GK B	0.814 0.839 0.847 0.844 0.860	0.635 0.640 0.643 0.642 0.651	0.920 0.946 0.949 0.947 0.957	0.738 0.747 0.746 0.745 0.756	0.964 0.986 0.987 0.986 0.990	0.822 0.832 0.828 0.827 0.839
	AS LO SIN n = 20, m = 10 RG GK B AS LO SIN	0.822 0.814 0.839 0.804 0.796 0.834 0.806 0.792 0.827	0.549 0.546 0.567 0.592 0.589 0.610 0.593 0.592 0.604	0.934 0.920 0.946 0.922 0.917 0.944 0.924 0.924 0.940	0.653 0.641 0.678 0.697 0.693 0.721 0.698 0.694 0.713	0.979 0.964 0.986 0.974 0.971 0.985 0.975 0.933 0.984 R e 0.741 0.716 0.770 0.784 0.781 0.810 0.785 0.777 0.803 v n = 50, m = 50 AS LO SIN RG GK B AS LO SIN i e w	0.847 0.845 0.857 0.867 0.867 0.874 0.867 0.867 0.873	0.644 0.644 0.649 0.647 0.647 0.654 0.648 0.648 0.652	0.949 0.945 0.956 0.960 0.960 0.964 0.960 0.959 0.964	0.746 0.746 0.753 0.749 0.748 0.758 0.750 0.749 0.755	0.987 0.984 0.990 0.991 0.991 0.993 0.991 0.990 0.993	0.829 0.827 0.836 0.831 0.830 0.841 0.831 0.830 0.838
	n = 20, m = 20 RG GK B AS LO	0.831 0.829 0.850 0.832 0.826	0.602 0.599 0.618 0.602 0.602	0.940 0.939 0.952 0.941 0.931	0.705 0.702 0.728 0.706 0.703	0.983 0.982 0.988 0.983 0.975	0.791 0.788 0.816 0.792 0.786	O n l y
	SIN	0.847	0.613	0.951	0.721	0.988	0.809
		Table 6: Simulation results: one-sided CI average lower bound
							15

ca Communications in Statistics -Simulation and Computation

  The LO intervals here, in fact, allows almost always coverages greater than the nominal level, even if in some cases they are too conservative, providing also smaller lower bounds. The lower bounds based on asymptotic results provide satisfactory results, which only partially suffer from the finiteness of sample sizes. The bootstrap procedure gives worse results than in the two-sided cases: it attains coverage rates close to the nominal level only for large sample sizes, whereas they are

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	F o
	r
	P
	e e r
	R e v i e w
	O n
	l y
	often smaller than 90%; it tends to give higher lower bounds than its competitors. Its "crude"
	use is not suggested; some proper modifications should be made, but the practitioner should
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Table 7 ,

 7 taken from[START_REF] Duncan | Quality and Industrial Statistics[END_REF], gives the results of measuring shear strength for spot welds for two different gauges of steel. Although not a stress-strength situation in the sense discussed in the introduction, this problem does fit our formulation, and we use it to show how the inferential procedures work on a practical case. Denoting with X and Y the r.v. modeling the strength of the two gauges of steel, the estimates computed on the data are x = 975, ȳ = 480, σ 2x = 33055 and σ 2 y = 7345. Assuming X and Y are independently normally distributed, the maximum likelihood estimator R has value 0.9931. The confidence intervals calculated according each of the methods described in the previous sections are reported in Table8, in Table9the one-sided confidence intervals; they show that the proposed bootstrap methods provides the narrowest interval, confirming what we have already seen in the simulation study, while the LO method provides the largest one. RG, GK and AS bounds are very close to each other.

Table 7 :

 7 Data on shear strengths of two gauges of steel method lower bound upper bound lower bound upper bound lower bound upper bound

		90%		95%		99%
	RG	0.9216	0.9994	0.8925	0.9997	0.8147	0.9999
	AS	0.9262	0.9994	0.8993	0.9997	0.8277	0.9999
	SIN	0.9511	1.0000	0.9389	1.0000	0.9115	1.0000
	LO	0.8308	0.9998	0.7200	0.9999	0.4205	1.0000
	B	0.9587	0.9999	0.9443	1.0000	0.9266	1.0000

Table 8 :

 8 Results for reliability on Duncan data: 90, 95, and 99% confidence intervals.

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ca Communications in Statistics -Simulation and Computation

	method 90%	95%	99%
	RG	0.9473 0.9216 0.8496
	GK	0.9416 0.9154 0.8467
	AS	0.9499 0.9262 0.8599
	SIN	0.9636 0.9511 0.9232
	LO	0.9120 0.8308 0.5478
	B	0.9685 0.9569 0.9303
	F o
	r
	P
	e e r
		R e v i e w
				O n
				l y

Table 9 :

 9 90, 95, and 99% lower bounds for reliability on Duncan data.

URL: http://mc.manuscriptcentral.com/lssp E-mail: comstat@univmail.cis.mcmaster.caCommunications in Statistics -Simulation and Computation

Acknowledgments

I would like to thank the referees for their helpful comments and suggestions.

I wish to dedicate this paper to the cherished memory of my mother and to my father.


Giulia Maria Camerino

Maria Antonietta Pellegrino

Lorenza Brocca

Claudio Digennaro

Diana Conte Camerino

Sabata Pierno
email: spierno@farmbiol.uniba.it

Roberto Bottinelli

Statin or fibrate chronic treatment modifies the proteomic profile of rat skeletal muscle

Keywords: hypolipidemic drugs, skeletal muscle, side effects, myopathy, proteomic analysis

Statins and fibrates can cause myopathy. To further understand the causes of the damage we performed a proteome analysis in fast-twitch skeletal muscle of rats chronically treated with different hypolipidemic drugs. The proteomic maps were obtained from extensor digitorum longus (EDL) muscles of rats treated for 2-months with 10mg/kg atorvastatin, 20mg/kg fluvastatin, 60mg/kg fenofibrate and control rats. The proteins differentially expressed were identified by mass spectrometry and further analysed by immunoblot analysis. We found a significant modification in 40 out of 417 total spots analysed in atorvastatin treated rats, 15 out of 436 total spots in fluvastatin treated rats and 21 out of 439 total spots in fenofibrate treated rats in comparison to controls. All treatments induced a general tendency to a down-regulation of protein expression; in particular, atorvastatin affected the protein pattern more extensively with respect to the other treatments.

Energy production systems, both oxidative and glycolytic enzymes and creatine kinase, were downregulated following atorvastatin administration, whereas fenofibrate determined mostly alterations in glycolytic enzymes and creatine kinase, oxidative enzymes being relatively spared. Additionally, all treatments resulted in some modifications of proteins involved in cellular defenses against oxidative stress, such as heat shock proteins, and of myofibrillar proteins. These results were confirmed by immunoblot analysis. In conclusions, the proteomic analysis showed that either statin or fibrate administration can modify the expression of proteins essential for skeletal muscle function suggesting potential mechanisms for statin myopathy.

A c c e p t e d M a n u s c r i p t

Introduction

Hypocholesterolemic drugs, such as statin and fibrate, are widely prescribed medications effective to reduce blood lipids level. Statins potently inhibit the 3-hydroxymethyl-glutaryl-coenzyme A (HMG-CoA) reductase, the rate-limiting enzyme for the synthesis of mevalonate and therefore cholesterol [START_REF] Goldstein | Regulation of the mevalonate pathway[END_REF]. Fibrates by acting on the peroxisome proliferator-activated receptor (PPAR)-α, lower serum triglyceride levels and increase high-density lipoprotein (HDL)-cholesterol [START_REF] Cannon | Combination therapy in the management of mixed dyslipidaemia[END_REF].

Statins and fibrate are generally well tolerated by patients, however they can potentially produce serious adverse effects especially on skeletal muscle. The clinical evidence of statin-associated muscle disorders range from benign myalgia to severe myopathy with elevation of serum creatine kinase (CK) and muscle weakness. Life-threatening rhabdomyolysis with muscle necrosis and electrolyte alteration, myoglobinuria and renal failure is extremely rare [START_REF] Bellosta | Safety of statins: focus on clinical pharmacokinetics and drug interactions[END_REF][START_REF] Rosenson | Statins: can the new generation make an impression?[END_REF][START_REF] Antons | Clinical perspectives of statin-induced rhabdomyolysis[END_REF]. A population-based study describes that the relative risk of myopathy associated with the use of fibrates in monotherapy is 5-fold higher compared with statin [START_REF] Graham | Incidence of hospitalized rhabdomyolysis in patients treated with lipid-lowering drugs[END_REF]. However, the risk of rhabdomyolysis with cerivastatin monotherapy was 10-fold greater than with other statins, and in combination with gemfibrozil, was increased more than 1400-fold [START_REF] Farmer | Learning from the cerivastatin experience[END_REF][START_REF] Gaist | Lipid-lowering drugs and risk of myopathy: a population-based follow-up study[END_REF][START_REF] Thompson | Statin-associated myopathy[END_REF]. Thus, the fear of rare but serious muscle toxicity remains a major impediment to the appropriate use of these drugs considering the ample number of patients worldwide now receiving statins for hypercholesterolemia. In addition statins exhibit antiinflammatory and antineoplastic pleiotropic effects that may expand their clinical value as well as the need to identify the mechanism of muscle side effects and possibly to find suitable countermeasures [START_REF] Martin | Statin-induced inhibition of the Rho-signaling pathway activates PPARalpha and induces HDL apoA-I[END_REF][START_REF] Weitz-Schmidt | Statins as anti-inflammatory agents[END_REF][START_REF] Demierre | Statins and cancer prevention[END_REF]. Indeed, the precise molecular mechanisms behind statin-associated myopathy have not been fully elucidated, although various hypotheses suggested either the alteration of muscle cell membrane function due to impairment of cholesterol synthesis, the deficits in energy metabolism associated with ubiquinone deficiency [START_REF] Evans | The myotoxicity of statins[END_REF] or the reduction of small GTPbinding proteins involved in myocytes preservation [START_REF] Vaughan | Update on statins: 2003[END_REF]. Different studies have shown that statin and fibrate can modify gene and protein expression in skeletal muscle [START_REF] Cornwell | Profiling of hepatic gene expression in rats treated with fibric acid analogs[END_REF]. For instance, an up-A c c e p t e d M a n u s c r i p t 4 regulation of ryanodine receptor, suggestive of intracellular calcium increase, was found in muscle biopsies of statin treated patients showing evident structural damage [START_REF] Mohaupt | Association between statin-associated myopathy and skeletal muscle damage[END_REF]. Our previous studies have demonstrated that statin and fibrate affect skeletal muscle function also by modifying calcium homeostasis and resting chloride conductance (gCl). Indeed, lipophilic statin increased intracellular calcium via mitochondria and sarcoplasmic reticulum release [START_REF] Liantonio | Fluvastatin and atorvastatin affect calcium homeostasis of rat skeletal muscle fibers in vivo and in vitro by impairing the sarcoplasmic reticulum/mitochondria Ca2+-release system[END_REF], thereby affecting contractile function. In turn these drugs reduced resting gCl [START_REF] Pierno | Effects of HMG-CoA reductase inhibitors on excitation-contraction coupling of rat skeletal muscle[END_REF][START_REF] Sirvent | Simvastatin triggers mitochondria-induced Ca2+ signaling alteration in skeletal muscle[END_REF], a parameter sustained by the ClC-1 chloride channel and modulated by calcium-dependent PKC [START_REF] Pierno | Statins and fenofibrate affect skeletal muscle chloride conductance in rats by differently impairing ClC-1 channel regulation and expression[END_REF][START_REF] De Luca | Aging and chloride channel regulation in rat fast-twitch muscle fibres[END_REF][START_REF] Bryant | Chloride channel regulation in the skeletal muscle of normal and myotonic goats[END_REF][START_REF] Pierno | Potential risk of myopathy by HMG-CoA reductase inhibitors: a comparison of pravastatin and simvastatin effects on membrane electrical properties of rat skeletal muscle fibers[END_REF][START_REF] Pierno | Effects of chronic treatment with statins and fenofibrate on rat skeletal muscle: a biochemical, histological and electrophysiological study[END_REF][START_REF] Pierno | Disuse of rat muscle in vivo reduces protein kinase C activity controlling the sarcolemma chloride conductance[END_REF]. This parameter is normally high in fast-twitch muscles and is important to guarantee muscle membrane potential and excitability [START_REF] Pierno | Statins and fenofibrate affect skeletal muscle chloride conductance in rats by differently impairing ClC-1 channel regulation and expression[END_REF][START_REF] De Luca | Aging and chloride channel regulation in rat fast-twitch muscle fibres[END_REF][START_REF] Bryant | Chloride channel regulation in the skeletal muscle of normal and myotonic goats[END_REF]. We also found that fenofibrate directly inhibit the ClC-1 chloride channel [START_REF] Pierno | Statins and fenofibrate affect skeletal muscle chloride conductance in rats by differently impairing ClC-1 channel regulation and expression[END_REF].

To better understand the mechanisms underlying myotoxicity and the diverse effects of statin and fibrate, we applied the proteomic approach to analyse skeletal muscle adaptation to chronic drug treatment. Since statins inhibit many enzymatic reactions downstream of mevalonate production, they may affect a wide range of intracellular functions. Also fenofibrate by acting on peroxisome proliferator-activated receptors (PPARs) has pleiotropic biological effects. In addition, skeletal muscle adaptation is per se very complex because it depends on the activation of genetic programs codifying for proteins belonging to different functional categories [START_REF] Spangenburg | Molecular regulation of individual skeletal muscle fibre types[END_REF]. This widens the panorama of potential sites of antilipidemic drug side effects and justifies the difficulties in understanding the mechanisms of myotoxicity. Therefore, since complex modifications of the protein pattern are likely to occur following both statin and fibrate administration, we believe that a global proteomic approach may prove very helpful to clarify the molecular mechanisms underlying myopathy. Thus, the proteomic analysis, by identifying differentially expressed protein following drug administration appears the approach of choice to address the complexity of muscle adaptations and to reveal the underlying mechanisms in statin and fibrate muscle damage. Despite the high resolutive power of the 2DE approach and the large number of proteins whose differential expression could be studied (~450), not all the protein expressed in the muscle could be examined, such as those with an isoelectric point higher than 8-9 and little represented proteins such as membrane proteins.

A c c e p t e d M a n u s c r i p t 5 However, this approach has been demonstrated widely useful in a number of recent works [START_REF] Gelfi | The human muscle proteome in aging[END_REF][START_REF] Brocca | Amino acid supplements improve native antioxidant enzyme expression in the skeletal muscle of diabetic mice[END_REF][START_REF] Brocca | Is oxidative stress a cause or consequence of disuse muscle atrophy in mice? A proteomic approach in hindlimb-unloaded mice[END_REF][START_REF] Moriggi | Long term bed rest with and without vibration exercise countermeasures: effects on human muscle protein dysregulation[END_REF].

Such a proteomic approach is novel in skeletal muscle. The few proteomic studies reported in the literature have regarded other tissues, such as liver and interestingly showed that statin treatment can modify the expression of the cholesterol biosynthesis pathway enzymes as well as of carbohydrate metabolism enzymes, cellular stress proteins and protein involved in calcium homeostasis [START_REF] Steiner | Proteomics to display lovastatin-induced protein and pathway regulation in rat liver[END_REF][START_REF] Steiner | Cholesterol biosynthesis regulation and protein changes in rat liver following treatment with fluvastatin[END_REF]. Statin by inhibiting cholesterol biosynthesis may also affect glutathione peroxidase liver production, whose expression level and catalytic activity were reduced. The consequence of this loss may be an increased sensitivity of the cells to peroxide [START_REF] Kromer | Statin-induced liver injury involves cross-talk between cholesterol and selenoprotein biosynthetic pathways[END_REF].

Here we report the effects of chronic treatments with fluvastatin, atorvastatin and fenofibrate in rats on the proteomic maps of the extensor digitorum longus (EDL) muscle. Although there are some reports showing that fast-twitch muscles are primarily affected in statin myopathy [START_REF] Westwood | Rosuvastatin: characterization of induced myopathy in the rat[END_REF], whereas type I muscle fibers are mainly affected by fibrates [START_REF] Souza | Agonists of the peroxisome proliferator-activated receptor alpha induce a fiber-type-selective transcriptional response in rat skeletal muscle[END_REF], we focused the proteomic analysis on the fast-twitch EDL muscle because we previously showed that this muscle is a toxicological target of both statins and fibrates [START_REF] Pierno | Statins and fenofibrate affect skeletal muscle chloride conductance in rats by differently impairing ClC-1 channel regulation and expression[END_REF]. The results reveal various metabolic pathways involved in the response to antilipidemic drugs, which may concur to myotoxicity.

A c c e p t e d M a n u s c r i p t 6

METHODS

Animal care and treatments

The animal study protocol was conducted in accordance with the Italian Guidelines for the use of laboratory animals, which conforms to the European Community Directive published in 1986 (86/609/EEC). Adult male Wistar rats (Charles River Laboratories, Calco, Italy), weighing 300-350 g, were housed individually in appropriate metabolic cages in an environmentally controlled room and received commercial rodent chow (30 g/day) (Charles River, 4RF21) and water ad libitum. Rats were randomly assigned to 4 experimental groups of 8 animals each: 1) fluvastatin 20mg/kg/day treated animals (FLUVA), 2) atorvastatin 10mg/kg/day treated animals (ATO), 3) fenofibrate 60 mg/kg/day treated animals (FENO), 4) control animals (CTRL) treated with the vehicle (0.5% carboxymethylcellulose in aqueous solution) used to dissolve the drugs. Fluvastatin (Lescol, Novartis), atorvastatin (Torvast, Pfizer), and fenofibrate (Lipsin, Caber) were administered orally by using an esophageal cannula, once a day for two months [START_REF] Pierno | Statins and fenofibrate affect skeletal muscle chloride conductance in rats by differently impairing ClC-1 channel regulation and expression[END_REF]. During the treatment the body weight and vital parameters (health conditions, water and food consumption) were normal in all treated rats. Skeletal muscle performance was evaluated daily by testing in each rat the righting reflex, i.e. the ability of the rat to straighten itself on four legs when turned on the back. The observation of the righting reflex can help to detect severe myotonic-like signs or alteration of muscle function. As previously observed, the righting reflex was normal during the entire treatment period in all the animals. No mortality was observed. At the end of the 2-months treatment rats were sacrificed by cervical dislocation and the extensor digitorum longus (EDL) muscle was carefully dissected from each rat and immediately frozen in liquid nitrogen, then stored at -80°C until proteomic analysis. The contralateral EDL muscle of all fluvastatin, atorvastatin and fenofibrate treated rats was immediately placed in a appropriate muscle bath chamber to measure the resting chloride conductance (gCl) by the 2-intracellular microelectrode technique [START_REF] Pierno | Statins and fenofibrate affect skeletal muscle chloride conductance in rats by differently impairing ClC-1 channel regulation and expression[END_REF]. Histological A c c e p t e d M a n u s c r i p t 7 analysis was also performed on four tibialis anterior muscles dissected from randomly selected treated rats of each experimental group as previously described [START_REF] Pierno | Effects of chronic treatment with statins and fenofibrate on rat skeletal muscle: a biochemical, histological and electrophysiological study[END_REF].

Proteome analysis (2-DE)

2.2.1. Sample preparation. The methods of proteome analysis are mostly the same as those previously used [START_REF] Brocca | Is oxidative stress a cause or consequence of disuse muscle atrophy in mice? A proteomic approach in hindlimb-unloaded mice[END_REF]. Muscle samples previously stored at -80°C, were pulverized in a steel mortar with liquid nitrogen to obtain a powder that was immediately resuspended in a lysis buffer [8M urea, 2M thiourea, 4% CHAPS, 65mM DTT, 40mM Tris base (Healthcare, Germany) and a cocktail of protease inhibitors (Sigma-Aldrich, Italy)]. The samples were vortexed, frozen with liquid nitrogen and thawed at room temperature four times; then the samples were incubated with DNase and RNase for 45 min at 4°C to separate proteins from nucleic acids and finally spun at 35000 g for 30 min. Protein concentration in the dissolved samples was determined with a protein assay kit (2D quant Kit, Healthcare). In order to perform proteome analysis, a sample mix was obtained for each experimental group (CTRL, FLUVA, ATO, FENO). Each sample mix contained an equal protein quantity taken from each muscle sample of CTRL, FLUVA, ATO, FENO.

Two-dimensional electrophoresis.

Isoelectrofocusing was carried out using IPGphor system (Ettan IPGphor isoelectric Focusing Sistem -Healthcare). IPG gels strips, pH 3-11 NL (non linear) 13 cm, were rehydrated for 14h, at 30 Volt and at 20°C, in 250 μl of reswelling buffer [(8 M urea, 2 M thiourea, 2% (w/v) CHAPS, 0.1% (v/v) tergitol NP7 (Sigma, Italy), 65 mM DTT, 0.5% (v/v) pharmalyte 3-11NL (Healthcare), tergitol NP7 (Sigma)] containing 100 g protein sample. Strips were focused at 20000 Vhr, at constant temperature of 20°C and the current was limited to 50 A° per IPG gel strip. After isoelectrofocusing the strips were stored at -80°C until use or equilibrated immediately for 10-12 min in 5 ml of equilibration buffer [50 mM Tris pH 6.8, 6 M urea, 30% (v/v) glycerol, 2% (w/v) SDS, 3% (w/v) iodoacetamide (Healthcare)]. Then, the immobiline IPG gel strips were applied to 15% SDS-PAGE without a stacking gel. The separation was performed at 80 A c c e p t e d M a n u s c r i p t 8 V for 17h at room temperature. The 2D gels were fixed for 2h in fixing solution [(ethanol 40% (v/v) acetic acid 10% (v/v) (VWR International, Italy)], stained with fluorescent staining (FlamingoTM Fluorescent Gel Stain by BIO-RAD, Italy) for 3h and destained with 0.1% (w/v) Tween 20 (VWR International) solution for 10 minutes. Triplicate gels of each mix sample were obtained, visualized using a Typhoon laser scanner (Healthcare) and analyzed with Platinum Software (Healthcare). The analysis was performed comparing FLUVA, ATO and FENO with CTRL. For each analysis one gel was chosen as the master gel, and used for the automatic matching of spots in the other 2D gels.

Only spots present in all gels used for the analysis were considered. The software provided normalized volume for each spot (representing protein amount). A good reproducibility of the spots among the triplicate gels of each experimental group was found. Plotting the spot volumes for matched spots on a linear scale, in fact, regression analysis yielded correlation coefficients in the range 0.75-0.8. The volumes of each spots in the triplicate gels were averaged and the average volume used for statistical comparison among spots was considered significant if P < 0.05. The average volumes of each differentially expressed spot were used to determine the volume ratios reported in the figures and tables.

Protein identification

2.3.1. Electrophoresis fractionation and in situ digestion. 2D gels were loaded with 300 µg of proteins per strip and the electrophoretic was carried out with the same conditions described above.

After staining with Colloidal Coomassie (Thermo scientific, UK) spots were excised from the gel and washed in 50mM ammonium bicarbonate pH 8.0 in 50% acetonitrile (VWR International) to a complete destaining. The gel pieces were re-suspended in 50mM ammonium bicarbonate pH 8.0 containing 100 ng of trypsin (Sigma-Aldrich) and incubated for 2 hr at 4°C and overnight at 37°C.

The supernatant containing the resulting peptide mixtures was removed and the gel pieces were reextracted with acetonitrile. The two fractions were then collected and freeze-dried. applied to the metallic sample plate and air dried. Mass calibration was performed by using the standard mixture provided by the manufacturer. Mass signals were then used for database searching using the MASCOT peptide fingerprinting search program (Matrix Science, Boston, USA) available on the net.

LCMSMS analysis.

When the identity of the proteins could not be established by peptide mass fingerprinting, the peptide mixtures were further analyzed by LCMSMS using the LC/MSD Trap XCT Ultra (Agilent Technologies, Palo Alto, CA) equipped with a 1100 HPLC system and a chip cube (Agilent Technologies). After loading, the peptide mixture [7 µl in 0.5% TFA (VWR International)] was first concentrated and washed (i) at 1 μl/min onto a C18 reverse-phase precolumn (Waters, USA) or (ii) at 4 μl/min in 40 nl enrichment column (Agilent Technologies chip), with 0.1% formic acid (VWR International) as the eluent. The sample was then fractionated on a C18 reverse-phase capillary column (75 Mm x 20 cm in the Waters system, 75 Mm x 43 mm in the Agilent Technologies chip) at a flow rate of 200 nl/min, with a linear gradient of eluent B [0.1% formic acid in acetonitrile (VWR International)] in A (0.1% formic acid) (VWR International) from 5 to 60% in 50 min. Elution was monitored on the mass spectrometers without any splitting device.

Peptide analysis was performed using data-dependent acquisition of one MS scan (m/z range from 400 to 2000 Da/e) followed by MS/MS scans of the three most abundant ions in each MS scan.

Dynamic exclusion was used to acquire a more complete survey of the peptides by automatic recognition and temporary exclusion (2 min) of ions from which definitive mass spectral data had previously been acquired. Moreover a permanent exclusion list of the most frequent peptide A c c e p t e d M a n u s c r i p t 10 contaminants (keratins and trypsin peptides) was included in the acquisition method in order to focus the analyses on significant data.

Immunoblot analysis

The validation of expression changes of the proteins as judged by 2-DE analysis was carried out by standard 1-D immunoblotting. About 30 µg of muscle samples prepared and used for 2D electrophoresis were loaded on 15% polyacrylamide SDS-PAGE gels. The proteins were electrotransferred from gels to nitrocellulose membranes (4.5 µm pore size,Healthcare product, Germany) and the Western blot analysis was performed. Nitrocellulose membranes were blocked in 5% milk in TBS (Tris 0.02M, Nacl 0.05 M pH 7.4-7.6) for 1 h and then incubated in primary antibody (diluted in 5% milk) at 4°C overnight. The membranes were probed with antibody specific to ATP synthase (rabbit-anti ATP synthase, 1:2500, from Abcam, Italy), isocitrate dehydrogenase (rabbit-anti Isocitrate Dehydr, 1:500, from Abcam), Pyruvate kinase (rabbit polyclonal anti pyruvate kinase, 1:1000, from Abcam), Glyceraldehyde 3-P dehydrogenase (rabbit polyclonal anti GAPDH, 1:1000, from Abcam), Triosephosphate isomerase (goat polyclonal anti Triosephosphate isomerase 1:1000, from Biocompare, Italy), Creatine Kinase M (rabbit-anti CK M, 1:1000, from Abcam) Hsp1 (mouse-anti Hsp27, 1:1000, from Abcam). After several rinses in TTBS (0.1% Tween-20 in TBS, VWR International), the membranes were incubated in HRP-conjugated secondary antibody (diluted in 5% milk), rabbit-anti-mouse (1:800, from Dako, USA), rabbit-antigoat (1:5000, from Abcam) or goat-anti-rabbit (1:5000, from Millipore, Italy) for 1 h at room temperature. The protein bands were visualized by an enhanced chemiluminescence method in which luminol was excited by peroxidase in presence of H 2 O 2 (ECL Plus, Healthcare product). The content of single protein investigated was assessed by determining the brightness-area product (BAP) of the protein bands. [START_REF] Farrell | High resolution two-dimensional electrophoresis of proteins[END_REF]. The lysates were applied onto 8% poyacrylamide SDS-PAGE gels prepares according to the method described by Talmadge and Roy (1993) [START_REF] Talmadge | Electrophoretic separation of rat skeletal muscle myosin heavy-chain isoforms[END_REF].

Analysis of MHC isoforms content

Electrophoresis was run for 2 h at 200V and then for 24 h at 250 V. The gels were stained with Coomassie blue staining. In the region of MHC isoforms, four bands were separated that corresponded, in order of migration from the fastest to the slowest, to MHC-1 (or slow), MHC-2B, MHC-2X and MHC-2A (or fast). Densitometric analysis of these isoforms were performed to establish the relative proportion of the MHC isoforms identified in the sample [START_REF] Pellegrino | Bottinelli R Orthologous myosin isoforms and scaling of shortening velocity with body size in mouse, rat, rabbit and human muscles[END_REF].

Creatine kinase determination

Blood was collected by cardiac puncture, soon after animal death, in ethylenediaminetetraacetic acid (EDTA, Sigma) rinsed centrifuge tubes. The blood was centrifuged at 600 g for 10 min at 15°C and the plasma was separated and stored at -20°C until assay. Creatine kinase determination was performed by standard spectrophotometric analysis by using diagnostic kit (Sigma-Aldrich, Milan, Italy) within 7 days from plasma preparation [START_REF] Pierno | Effects of chronic treatment with statins and fenofibrate on rat skeletal muscle: a biochemical, histological and electrophysiological study[END_REF].

Statistical analysis

Data were expressed as mean ± S.E.M. Statistical significance of the differences between means was assessed by Student's t-test or by one-way ANOVA followed by Student-Newman-Keuls test (for data in Fig. 3). A probability of less than 5% was considered significant (P<0.05).

RESULTS

Analysis of skeletal muscle proteomic map

A c c e p t e d M a n u s c r i p t 12 Proteomic maps of EDL muscles, for each animal of each group (control rats, statin and fibrate treated rats), were obtained using 2D gel electrophoresis. The comparison between 2D maps of treated and control rats enabled us to identify the differentially expressed proteins which were thereafter identified by MALDI. Such proteins are indicated by circles and numbers in the control maps of EDL as reported in Fig. 1. The full set of information regarding the differentially expressed proteins is reported in Table 1. The differentially expressed proteins were grouped on the basis of their functional role in the following categories: energy production system (oxidative metabolism, glycolytic metabolism and creatine kinase), myofibrillar proteins, detoxification systems and other proteins (Fig. 2A-2C). The proteomic map of control rat showed about 450 spots. In EDL of atorvastatin treated rat about 417 spots were found. The comparison between the protein spots common to atorvastatin and CTRL maps showed that the 9.6 % (40 spot) of spots were significantly different. Of the 40 spots (15 identified by mass spectra analysis) 2.5% (n=1) were up-regulated and 97.5% (n=39) were down-regulated. In EDL of fluvastatin treated rat about 436 spots were found.

Compared to control only the 3.4% (15 spot) of the spots showed significant differences in protein expression. Of the 15 spots (6 identified by mass spectra analysis) 12.5% (n=2) were up-regulated and 86.6% (n=13) were down-regulated. In EDL of fenofibrate treated rat about 439 spots were found. In fenofibrate maps the percent of significantly different spots was 5% (21 spots), compared to CTRL. Of the 21 spots (12 identified by mass spectra analysis) 14% (n=3) were up-regulated and 86% (n=18) down-regulated. Several of the differentially expressed proteins reported in Figure 1 and Table 1, were found in multiple spot localizations (see, for example, glyceraldehyde 3phosphate dehydrogenase in fenofibrate map and creatine kinase and pyruvate kinase in atorvastatin map) and therefore appear more than once in Fig. 2. The presence of multiple spots of a protein is frequent in 2D gels and is due to the existence of isoforms or to post-translational modifications of proteins. Different isoforms of the same protein might differ both for molecular weight and isoelectric point, or different molecular weight. Mass spectrometry was not able to identify all isoforms of some proteins or the nature of their post-translational modifications. To make sure that A c c e p t e d M a n u s c r i p t 13 the change in expression of the identified spot or spots of a given protein was representative of the global change of that protein, the expression of the most relevant proteins was confirmed by western blot on one dimensional gels. In the latter gels, in fact, all the spots of a protein which are separated in 2D gels migrate in a single band.

Energy production system

The larger group of differently expressed proteins was involved in the three energy production systems: oxidative metabolism, glycolitic metabolism and creatine kinase. EDL of atorvastatin treated rats showed a down regulation of four proteins involved in oxidative metabolism [isocytrate dehydrogenase 3 (-5,49 ratio), NADH dehydrogenase 1 (-1,98 ratio), oxoglutarate dehydrogenase (-1,9 ratio), ATP synthase (β subunit) (-6,43 ratio)]. The glyceraldehyde 3 phosphate dehydrogenase, enolase 3 and three isoforms of pyruvate kinase (spot number 8, 9 and 10), that are involved in glycolytic metabolism, were also down-regulated (-3,30, -3,17, -3,01 -1,377 and -2,39 ratio, respectively) (Table 1). EDL of fluvastatin treated animals did not show significant alterations of proteins involved in energy production systems, except for 2 isoforms of β enolase 3 (protein of glycolitic system) that was less expressed if compared to control (-2,20 and -1,73 ratio in spot number 1 and 2 respectively) (Table 1). In contrast, the fenofibrate maps showed small alterations of the enzymes involved in oxidative metabolisms and a marked down-regulation of proteins involved in the glycolytic metabolism. The ATP synthase, in particular the mitochondrial β subunit (-2,29 ratio), which belongs to the oxidative system, was down-regulated. Triosephosphate isomerase, β enolase 3, and 2 isoforms of glyceraldehde 3 phosphate dehydrogenase (spot number 22 and 23), which belongs to glycolytic systems, were down-regulated (-1,91; -4,09; -2,35 and -6,08 ratio respectively). On the contrary the pyruvate kinase was up-regulated (2.17 ratio) (Table 1).

EDL of fenofibrate and atorvastatin treated rats showed a significant down-regulation of creatine The troponin T fast and α-2 actin were down-regulated following fenofibrate treatment (-3,21 and -1,95, respectively). In fluvastatin treated muscles myozenin 1 was down regulated (-1,64 ratio). The troponin T fast was down-regulated following atorvastatin treatment (-2,29 ratio) (Table 1). The adaptations in myofibrillar protein isoforms, consistent with the lack of variation in MHC isoform composition, did not show any trend of a shift in muscle phenotype (Fig. 3).

Detoxification system

Statin and fibrate had an impact on detoxification and on antioxidant proteins. The heat shock protein 1 was, indeed, down-regulated after treatment with atorvastatin and fenofibrate (-3,26 and -1,85 ratio, respectively). The carbonic anhydrase III was under-expressed after fluvastatin and atorvastatin treatments (-1,78 ratio and -2.66, respectively). The map of EDL muscle treated with fluvastatin showed a overexpression of chaperonin 60 (1,57 ratio) (Table 1).

Other proteins

The atorvastatin map showed a down regulation of serum albumin, a known plasma protein carrier (-2,03 ratio). The muscles treated with fenofibrate showed an important reduction of the expression of MSF mitochondrial factor, an important stimulation factor (-6,62 ratio) (Table 1).

Immunoblot analysis

To validate the results of 2-DE analysis comparative immunoblotting of some of most relevant changed proteins was carried out. Comparative analysis of immunoreactive bands of ATP synthase, isocitrate dehydrogenase, pyruvate kinase, glyceraldehyde 3-P dehydrogenase, triosephosphate A c c e p t e d M a n u s c r i p t 15 isomerase, creatine kinase, Hsp1 in the different treatments, confirmed, at the level of the whole protein, the change in expression of the protein spot/s revealed by 2D gels (Fig. 4).

Biological and functional indexes of skeletal muscle toxicity

To verify the possible impairment of skeletal muscle due to statin or fibrate chronic treatment we examined the release of creatine kinase (CK) from myocytes into the bloodstream. Thus, we measured CK level in plasma of all treated rats and compared those with control. Fluvastatin at the higher dose (20mg/kg) significantly increased (about 3-fold) the plasma CK content, while no significant effect was found in the rats treated with the lower dose (Table 2). Also atorvastatin and fenofibrate, at the doses tested, significantly increased plasma CK level about 3-fold or 2-fold, respectively, with respect to control (Table 2). The histopathological analysis of tibialis muscle did not show any modification of muscle section (data not shown), as previously described [START_REF] Pierno | Effects of chronic treatment with statins and fenofibrate on rat skeletal muscle: a biochemical, histological and electrophysiological study[END_REF].

Moreover, as already demonstrated [START_REF] Pierno | Effects of chronic treatment with statins and fenofibrate on rat skeletal muscle: a biochemical, histological and electrophysiological study[END_REF], in all the rats treated with fluvastatin, atorvastatin or fenofibrate the resting gCl was significantly reduced (no more than 30%) with respect to the control value (data not shown).

DISCUSSION

Taking advantage of the high resolving power and of the very large number of proteins sampled by the proteomic analysis, this novel study demonstrates that statins and fibrate administration induce complex modifications of the protein pattern of skeletal muscle, suggesting an effect on a wide range of biological functions (Supplementary Fig. S1). In parallel, other studies performed by using combined genomic and lipidomic analysis showed changes in muscle metabolism (dysregulation of calcium binding proteins and phospholipase C pathway, defective mitochondrial metabolism and activation of pro-apoptosis pathway, dysregulation of cell membrane lipids) contributing to muscle toxicity [START_REF] Laaksonen | A systems biology strategy reveals biological pathways and plasma biomarker candidates for potentially toxic statin-induced changes in muscle[END_REF]. Our results showed a down-regulation of several muscle proteins and this effect was

Myofibrillar proteins

Muscle plasticity is a particular feature of skeletal muscle by which different stimuli (disuse, drugs, etc.) can induce phenotype transition. For instance, hindlimb unloading of rodents, a model of muscle disuse, induce a slow-to-fast transition of postural muscles, i.e. increased expression of fast isoforms of myosin heavy chain (MHC) and increase of resting gCl in soleus muscle [START_REF] Desaphy | Antioxidant treatment of hindlimb-unloaded mouse counteracts fiber type transition but not atrophy of disused muscles[END_REF]. A coordinated expression existed among MHC isoforms, metabolic enzymes and isoforms of other myofibrillar and non-myofibrillar proteins [START_REF] Nemeth | Succinate dehydrogenase activity in fibres classified by myosin ATPase in three hind limb muscles of rat[END_REF][START_REF] Schiaffino | Molecular diversity of myofibrillar proteins: gene regulation and functional significance[END_REF][START_REF] Flück | Molecular basis of skeletal muscle plasticity--from gene to form and function[END_REF]. Therefore, in most myopathic conditions the change in expression of many proteins can be related to the activation of a single gene expression

Muscle cellular energy metabolism

Both statins and fenofibrate induced critical alterations of energy metabolism enzymes: atorvastatin down-regulated different oxidative and glycolytic enzymes, whereas fenofibrate mainly affected glycolytic enzymes. This latter finding can be a consequence of the inhibition of the specific targets of the two drugs. Otherwise, the prevalent effect of atorvastatin on the oxidative metabolism pathway can be related to the already described statin-mediated mitochondrial involvement [START_REF] Liantonio | Fluvastatin and atorvastatin affect calcium homeostasis of rat skeletal muscle fibers in vivo and in vitro by impairing the sarcoplasmic reticulum/mitochondria Ca2+-release system[END_REF][START_REF] Sirvent | Simvastatin triggers mitochondria-induced Ca2+ signaling alteration in skeletal muscle[END_REF][START_REF] Laaksonen | A systems biology strategy reveals biological pathways and plasma biomarker candidates for potentially toxic statin-induced changes in muscle[END_REF]]. Yet, since fenofibrate have no effects on calcium released by mitochondria [START_REF] Liantonio | Fluvastatin and atorvastatin affect calcium homeostasis of rat skeletal muscle fibers in vivo and in vitro by impairing the sarcoplasmic reticulum/mitochondria Ca2+-release system[END_REF], likely slight effect on the oxidative metabolism were observed here. and ATP synthase, involved in the mitochondrial respiratory chain, were also altered by atorvastatin treatment. As already suggested, ubiquinone reduction may be responsible for statin induced muscle damage [START_REF] Sirvent | Simvastatin triggers mitochondria-induced Ca2+ signaling alteration in skeletal muscle[END_REF]. For instance it has been shown that simvastatin was able to reduce ubiquinone level and mitochondrial function in human skeletal muscle [START_REF] Päivä | High-dose statins and skeletal muscle metabolism in humans: a randomized, controlled trial[END_REF]. Although controversial data have been reported [START_REF] Nakahara | Myopathy induced by HMG-CoA reductase inhibitors in rabbits: a pathological, electrophysiological, and biochemical study[END_REF][START_REF] Vaklavas | Molecular basis of statin-associated myopathy[END_REF], it has proposed that muscle cell treatment with ubiquinone can restore statininduced muscle damage [START_REF] Nakagawa | CoA reductase inhibitor-induced L6 myoblast cell death: involvement of the phosphatidylinositol 3-kinase pathway[END_REF]. Thus the observation that NADH dehydrogenase was down-regulated in the proteomic map of atorvastatin treated skeletal muscles strongly support the hypothesis of mitochondrial involvement [START_REF] Liantonio | Fluvastatin and atorvastatin affect calcium homeostasis of rat skeletal muscle fibers in vivo and in vitro by impairing the sarcoplasmic reticulum/mitochondria Ca2+-release system[END_REF]. An other novelty of the present study is the down-regulation and defect of the catalytic subunit of ATP synthase due to atorvastatin treatment, which may lead to ATP level reduction and consequent metabolic stress. Accordingly, a reduction of intracellular ATP content has been already described in human myocytes due to atorvastatin [START_REF] Nishimoto | Comparing myotoxic effects of squalene synthase inhibitor, T-91485, and 3-hydroxy-3-methylglutaryl coenzyme A (HMG-CoA) reductase inhibitors in human myocytes[END_REF]. Here we also find a minor involvement of ATP synthase in fenofibrate treated rats supporting the lesser participation of mitochondria in skeletal muscle damage induced by fenofibrate [START_REF] Liantonio | Fluvastatin and atorvastatin affect calcium homeostasis of rat skeletal muscle fibers in vivo and in vitro by impairing the sarcoplasmic reticulum/mitochondria Ca2+-release system[END_REF].

Glycolytic metabolism.

Both fenofibrate and statins resulted in a down-regulation of glycolytic enzymes expression. The beta enolase was down-regulated in all treatments, the PK was down-regulated in rats treated with atorvastatin and glyceraldehyde-3-phosphate dehydrogenase was down-regulated following atorvastatin and fenofibrate treatments. Another glycolytic enzyme, such as the triose-phosphate isomerase, essential for energy production, was down-regulated after fenofibrate treatment. The slow-down of glycolysis can be justified by the increased ß-oxidation pharmacologically induced by PPAR mediated fibrate or statin activation [START_REF] Wang | Statins enhance peroxisome proliferator-activated receptor gamma coactivator-1 alpha activity to regulate energy metabolism[END_REF]. The downregulation of glycolytic enzymes is a symptom of energy production failure, and can contribute to muscle damage. Interestingly a general impairment of energy metabolism have been observed in conditions of muscle atrophy [START_REF] Brocca | Is oxidative stress a cause or consequence of disuse muscle atrophy in mice? A proteomic approach in hindlimb-unloaded mice[END_REF], which may develop also during statin myopathy [START_REF] Hanai | The muscle-specific ubiquitin ligase atrogin-1/MAFbx mediates statin-induced muscle toxicity[END_REF]. Moreover, it has been shown that hereditary muscle glycogenoses in humans are characterized by defective glycolytic enzymes, including beta enolase, and leads to different degree of myopathy, ranging from cramps to myoglobinuria [START_REF] Dimauro | Muscle glycogenoses[END_REF][START_REF] Toscano | Tarui disease and distal glycogenoses: clinical and genetic update[END_REF]. The PK is a key enzyme in the glycolytic pathway, being responsible for the synthesis of pyruvate and ATP formation; it is allosterically inhibited by the increase in acetyl CoA, which in this condition may be induced by the block of cholesterol pathway in the cytosol. Interestingly, in fenofibrate treated rats the PK is up-regulated, although many enzymes of the glycolytic pathway are down-regulated, possibly because the oxidative and cholesterol pathway are not affected.

A c c e p t e d M a n u s c r i p t

Energy production system: creatine kinase

Muscle damage induced by statin and fibrate is associated with an increase of creatine kinase (CK) level in the plasma. For instance, other authors found a plasma CK increase in correlation with histological damage due to cerivastatin induced skeletal muscle damage [START_REF] Schaefer | Evaluation of ubiquinone concentration and mitochondrial function relative to cerivastatininduced skeletal myopathy in rats[END_REF]. Here we found an increase of plasma CK in all treated rats not followed by histological modification likely because the drug we used were less toxic. Moreover we found a decrease of CK expression in muscle treated with atorvastatin and fenofibrate. Since phosphocreatine, produced by CK, is an energy reservoir for different tissues and especially for skeletal muscle, the decrease in CK, together with the observed down-regulation of oxidative and glycolitic enzymes, suggest a general impairment of energy metabolism, which in turn could decrease protein synthesis, an ATP-requiring process.

Interestingly, it has been shown that in transgenic mice lacking either the cytoplasmic or mitochondrial CK, muscle atrophy and damage occur [START_REF] Momken | Impaired voluntary running capacity of creatine kinase-deficient mice[END_REF]. Surprisingly, no modification of CK expression was found in fluvastatin treated rats, in accord with the minor impact of this drug of the whole proteomic pattern.

Detoxification systems

Statin administration and, to some extent, fibrate administration down-regulated detoxification systems: heat shock protein 1, which protects cells against free radicals produced by stress stimuli, as well as carbonic anhydrase that protects cells against oxidative damage by binding free radicals [START_REF] Cabiscol | Carbonic anhydrase III. Oxidative modification in vivo and loss of phosphatase activity during aging[END_REF][START_REF] Räisänen | Carbonic anhydrase III protects cells from hydrogen peroxide-induced apoptosis[END_REF]. An effect of statin on HSPs expression has been previously observed in other tissues, such as human placental cells line [START_REF] Tartakover-Matalon | Impaired migration of trophoblast cells caused by simvastatin is associated with decreased membrane IGF-I receptor, MMP2 activity and HSP27 expression[END_REF] and rat retina during ischemia [START_REF] Schmeer | Statins modulate heat shock protein expression and enhance retinal ganglion cell survival after transient retinal ischemia/reperfusion in vivo[END_REF]. Together with the decrease of muscle plasmalogens, a sub-class of ether phospholipids involved in protection against oxidative damage [START_REF] Laaksonen | A systems biology strategy reveals biological pathways and plasma biomarker candidates for potentially toxic statin-induced changes in muscle[END_REF], these effects suggest an accentuated sensitivity of statin-treated muscles to oxidative stress. Oxidative stress has been pinpointed as a likely trigger of many conditions of muscle wasting [START_REF] Moylan | Oxidative stress, chronic disease, and muscle wasting[END_REF][START_REF] Powers | Oxidative stress and disuse muscle atrophy[END_REF].

A c c e p t e d M a n u s c r i p t 20

Other proteins

Although our previous studies have demonstrated no modification of mitochondrial activity in fibrate-induced myopathy [START_REF] Liantonio | Fluvastatin and atorvastatin affect calcium homeostasis of rat skeletal muscle fibers in vivo and in vitro by impairing the sarcoplasmic reticulum/mitochondria Ca2+-release system[END_REF], here we found a down-regulation of the mitochondrial stimulation factor (MSF) important for the synthesis and folding of mitochondrial ATP-dependent protein precursor [START_REF] Hachiya | MSF, a novel cytoplasmic chaperone which functions in precursor targeting to mitochondria[END_REF], likely suggesting an alteration in the number of these organelles in fenofibratetreated muscles. We also found a down-regulation of serum albumin in atorvastatin-treated muscles likely supporting the lack of its scavenger activity in the muscle. At this regard the effects of statin on albumin expression is controversial: simvastatin has been found to increase albumin synthesis contributing to reduce cardiovascular risk since it transport plasma lipids [START_REF] Ha | Effects of statins on the secretion of human serum albumin in cultured HepG2 cells[END_REF].

Concluding remarks

By using a proteomic approach we identified new toxicological markers of myopathy induced by hypolipidemic drugs (Supplementary Fig. S1). The major observations of this study are the following: 1) in line with our previous studies [START_REF] Pierno | Statins and fenofibrate affect skeletal muscle chloride conductance in rats by differently impairing ClC-1 channel regulation and expression[END_REF] atorvastatin was found to affect the proteomic profile of the EDL muscle more deeply than fluvastatin, likely due to its structural or pharmacokinetic characteristics; 2) atorvastatin mainly impaired the metabolic pathways responsible for energy production and particularly the key enzymes of the mitochondria, while fenofibrate essentially affected the glycolytic metabolism. Such a perturbation in energy metabolism and ATP synthesis may have a profound impact on protein synthesis and cell viability [START_REF] Klawitter | Effects of lovastatin on breast cancer cells: a proteo-metabonomic study[END_REF]; 3) considering the pivotal role attributed to oxidative stress in many myopathies, the impairment of detoxification systems could play a major role in the development of myopathy; 4) since an impaired glycolytic metabolism was observed without alteration of MHC expression, the effects of statin and fenofibrate are independent of phenotype-specific gene reprogramming. This work adds important novel information regarding the molecular and functional mechanism of druginduced muscle damage and opens the way to the discovery of new drug targets to counteract muscle toxicity. Typical 2D pattern gel image of proteins extract of control EDL muscles. The protein spots found to be differentially expressed in EDL muscles of control vs. EDL muscles of treated rat (with fluvastatin, atorvastatin or fenofibrate) are circled and numbered. The numbers enable to identify the spots using Figure 3 and Table 1. In the table are showed: the spot number corresponding to the number reported in figure 2; the name of proteins; the accession number corresponding to NCBI; the related fold changes of proteins are expressed in average ratio of change relative to the control (V Treated/V ctrl); MOWSE score; P value; the experimental Pi; the experimental MW; the biochemical pathway group membership.

A c c e p t e d M a n u s c r i p

A c c e p t e d M a n u s c r i p t 9 2. 3 . 2 .

 932 MALDI MS analysis. MALDI mass spectra were recorded on an Applied Biosystem (Italy) Voyager DE-PRO mass spectrometer equipped with a reflectron analyzer and used in delayed extraction mode. 1 l of peptide sample was mixed with an equal volume of -cyano-4hydroxycynnamic acid as matrix [10 mg/ml in 0.2% TFA in 70% acetonitrile (VWR International)],

  A c c e p t e d M a n u s c r i p t 11 About 6 µg of each muscle sample were dissolved in lysis buffer containing 8 M, 2M thiourea, 4 % CHAPS, 65 mM DTT and 40 mM Tris base

  kinase [-1,62 ratio for fenofibrate map (spot number 16) and -2,17; -2,90 ratio for atorvastatin map (spot number 16 and 17)] compared to CTRL.

  All treatments resulted in some alteration in myofibrillar protein expression. The troponin T type IVc was down-regulated in muscles treated with fenofibrate (-1,84 ratio), and fluvastatin (-1.71).

  western blot experiments. Proteins involved in energy production and in detoxification systems were the major sets of differentially expressed proteins and their changes could lead to the generation of myopathy. Atorvastatin induced a modification of a larger number of proteins than fluvastatin and fenofibrate. The reason may be related to the different chemical structure or the longer half-life of atorvastatin in comparison to the other drugs tested.

  program aimed to coordinately adapt muscle contractile machinery, energy production and cytoskeleton. To test if statin or fibrate can produce phenotype transition, we measured MHC isoform distribution in the EDL muscle. The lack of any change in MHC isoform distribution indicates that the large changes in the protein pattern due to statin and fibrate administration occur independently from such major gene expression program, suggesting more a toxic action than a functional adaptation of the treatments. This observation especially applies to changes in energy production systems which are generally under the same control as MHCs, but deeply change following statin and fibrate treatments. The observed changes in myofibrillar and cytoskeleton proteins (Troponin type IVc, Troponin T fast, α-2 actin, myozenin) do not have a straightforward interpretation in the frame of known structural or functional alteration of statin myopathy, but confirm that statins and fibrates can act directly on proteins independently from muscle phenotype.

4. 2 . 1 .

 21 Oxidative metabolism. Two biochemical pathways part of the oxidative metabolism, such as the Krebs cycle and the mitochondrial respiratory chain, are affected by atorvastatin treatment. Indeed two enzymes that participate to Krebs cycle, such as isocitrate dehydrogenase (which converts isocitrate in oxoglutarate) and the oxoglutarate dehydrogenase (which converts ketoglutarate in succinyl CoA) are down-regulated. Both enzymes are NAD dependent and their down-regulation can affect NADH production, then blocking the pathway and ATP production during mitochondrial electron transport. In consequence the acetyl CoA may accumulate in the mitochondria due to the block of the Krebs cycle and in the cytosol, because it is the first substrate of cholesterol synthesis that is inhibited by the statin. Increase of acetyl-CoA is known to inhibit the pyruvate kinase (PK) and to slow the glycolysis. The enzymes NADH dehydrogenase (ubiquinone)

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Figure 2

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A c c e p t e d M a n u s c r i p t 31 Table1

 31 Proteins differentially expressed and related changes in EDL muscles of rats following treatment with statins or fenofibrate.

Figure 1 Camerino

 1 Figure 1 Camerino Click here to download high resolution image

  Figure 2A Click here to download high resolution image

Figure 4 Camerino

 4 Figure 4 Camerino Click here to download high resolution image

Table 2

 2 Effects of two months chronic treatment with statins or fenofibrate on rat plasma creatine kinaseThe values of creatine kinase (CK) measured in plasma of control and treated rats are expressed as mean  S.E.M. from the number (N) of animals as indicated. Data showed significant differences by ANOVA test (F= 11.7, df = 4/35, P<0.001) followed by Bonferroni t-test.Table1 Proteins differentially espressed and related changes in EDL muscles of rats following treatment with statins or fenofibrate.

	Spot n°	Protein name	accession num. Fold change MOWSE P value Th Pi Th MW	pathway
	Fluvastatin
	1	Enolase 3	gi126723393	-2,20323	90	0,0491	7,08	47326 glycolitic metabolism
	2	enolase 3	gi126723393	-1,7359	412	0,039	7,08	47326 glycolitic metabolism
	3	troponin T class IVc beta-2	gi207403	-1,711174	383	0,0258	9,36	28595 myofibrillar systems
	4	myozenin 1	gi157819165	-1,64106	216	0,049	8,57	31379 myofibrillar systems
	5	carbonic anhydrase III	gi31377484	-1,78059	497	0,0203	6,89	29698	detoxification systems
									detoxification
	6	chaperonin 60	gi1778213	1,57865	389	0,0492	5,78	61029	systems
	Atorvastatin
		isocitrate dehydrogenase 3 (NAD+) alpha
	7	precursor	gi16758446	-5,49956	221	0,0014	6,47	40044 oxidative metabolism
	8	pyruvate kinase	gi16757994	-3,01587	870	0,0023	6,63	584	glycolitic metabolism
	9	pyruvate kinase	gi16757994	-1,37775	976	0,033	6,63	58294 glycolitic metabolism
	10	pyruvate kinase	gi16757994	-2,39449	1008	0,0082	6,63	58294 glycolitic metabolism
		NADH dehydrogenase (ubiquinone) 1 alpha
	11	subcomplex 10-like	gi32996721	-1,98637	309	0,0172	7,14	40804 oxidative metabolism
	12	ATP synthase subunit beta, mitochondrial	gi1374715	-6,43293	510	0,0012	4,95	51710 oxidative metabolism
		oxoglutarate (alpha-ketoglutarate) dehydrogenase
	13	(lipoamide) precursor	gi62945278	-1,90863	333	0,0298	6,3	117419 oxidative metabolism
	14	glyceraldehyde 3-phosphate-dehydrogenase	gi56188	-3,3096	316	0,0076	8,43	36098 glycolitic metabolism
	2	enolase 3	gi126723393	-3,179	412	0.047	7,08	47326 glycolitic metabolism
	15	Fast skeletal muscle troponin T	gi136385	-2,29568	267	0,019	6,19	30732 myofibrillar systems
									energy production
	16	creatine kinase	gi6978661	-2,17813	530	0,0043	6,58	43220	system
									energy production
	17	creatine kinase	gi6978661	-2,90683	480	0,019	6,58	43220	system
	18	carbonic anhydrase III	gi31377484	-2,66095	375	0,0032	6,89	29698 detoxification system
	19	heat shock protein 1	gi94400790	-3,26578	265	0,0024	6,12	24860 detoxification system
	20	Serum albumin	gi124028612	-2,03454	162	0,0361	6,09	70682	transport protein

In the table are showed: the spot number corresponding to the number reported in figure

2

; the name of proteins; the accession number corresponding to NCBI; the related fold changes of proteins are expressed in average ratio of change relative to the control (V Treated/V ctrl); MOWSE score; P value; the experimental Pi; the experimental MW; the biochemical pathway group membership.

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Table 1 Camerino

 1

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Aknowledgements

The Italian "Progetti di ricerca scientifica di Ateneo" 2009 is gratefully acknowledged. The authors wish to thank Prof. Jean-François Desaphy for the helpful comments on this manuscript.

Conflicts of interest

The authors declare no conflicts of interest.

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