Damiano Rotondo

Denis Efimov

Andrea Cristofaro

Tor Arne Johansen

Estimation in uncertain switched systems using a bank of interval observers: local vs glocal approach

Keywords: Interval observers, switched systems, mode identification, uncertain systems

This paper discusses some issues related with the design of a bank of interval observers for uncertain switched systems, in which several sources of uncertainty are considered: parametric uncertainties, unknown disturbances, measurement noise, and unknown switching signal. More specifically, this paper focuses on analyzing the interval estimation accuracy when changes of active mode induce non-positivity of the interval state estimation errors. In particular, it is shown that by combining two types of interval observers, referred to as local and global, the accuracy and reliability of the estimation can be improved. The properties of the obtained so-called glocal observer are investigated and illustrated by means of numerical simulations.

INTRODUCTION

It is a well known fact that, due to uncertainties coming either from external disturbances or from the mismatch between the model and the real system, the classical state observers cannot converge to the real value of the state in general settings [START_REF] Efimov | Design of interval observers for estimation and stabilization of discrete-time LPV systems[END_REF][START_REF] Wang | Interval observer design for LPV systems with parametric uncertainty[END_REF]. For this reason, interval observers have been considered as an appealing alternative approach, since they can take into account the information that uncertainties and disturbances are bounded in some known sets, in order to compute the set of admissible values for the state at each instant of time [START_REF] Efimov | Interval estimation for LPV systems applying high order sliding mode techniques[END_REF]. Research on interval observers is still a hot topic in present days, with several contributions appearing in the literature, concerning their integration with advanced control techniques [START_REF] Oubabas | Interval sliding mode observer design for linear and nonlinear systems[END_REF], fault diagnosis [Rotondo et al., 2018b] and fault tolerant control [Rotondo et al., 2018a] problems.

On the other hand, switched systems [START_REF] Daafouz | Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach[END_REF] represent a special class of hybrid dynamics that is applied in several fields, such as control of chemical processes [START_REF] Niu | A new control method for state-constrained nonlinear switched systems with application to chemical process[END_REF] and flight control systems [START_REF] Sakthivel | Robust reliable sampled-data control for switched systems with application to flight control[END_REF]. In the last few years, some results concerning state estimation in switched systems have appeared, see for instance [START_REF] Zhao | Multiple-mode observer design for a class of switched linear systems[END_REF], [START_REF] Ríos | Continuous and discrete state estimation for switched LPV systems using parameter identification[END_REF], [START_REF] Rios | Non-minimum phase switched systems: HOSMbased fault detection and fault identification via Volterra integral equation[END_REF], where an important difference comes from whether the hypothesis on availability of the switching signal is made or not. Some works have considered the problem of interval state estimation in switched systems. For instance, Ethabet et al. [2018b,a] have proposed an interval observer design approach for continuous-time switched systems affected by unknown inputs. [START_REF] He | Control of non-linear switched systems with average dwell time: interval observer-based framework[END_REF] have addressed control system design based on an interval observer for non-linear switched systems with Lipschitz non-linearities. [START_REF] Ifqir | Switched interval observer for uncertain continuous-time systems[END_REF] have analyzed interval estimation accuracy and robustness with respect to unknown disturbances using H ∞ objective with pole placement constraints.

However, all the above works have been developed under the assumption that the switching signal that defines the active mode of the switched system is known. This assumption is not always true [START_REF] Wang | Differentiator application in altitude control for an indoor blimp robot[END_REF], and some research has addressed the issue of determining the active mode at any moment, using only the system's input/output data, see e.g. [START_REF] Lee | On-line switching signal estimation of switched linear systems with measurement noise[END_REF], [START_REF] Hakem | Switching time estimation and active mode recognition using a data projection method[END_REF], Rotondo et al. [2017b,a]. In particular, Rotondo et al. [2017b,a] showed that this goal could be achieved using a multiple model adaptive architecture (MMAE) that relies on a set of local observers, each designed using one among the possible modes of the switched system.

With the future ultimate goal of extending the MMAE to the case where interval observers are used to estimate the switching signal while taking into account the effects of the different sources of uncertainty, this paper focuses on analyzing the interval estimation accuracy when changes of active mode induce non-positivity of the interval state estimation errors. In particular, the main contribution of this work is to show that the accuracy of the estimation can be improved by using a combination of two types of interval observers, referred to as local and global. The properties of the obtained observer, named glocal after [START_REF] Hara | Glocal (global/local) control synthesis for hierarchical networked systems[END_REF], are investigated and demonstrated by means of numerical simulations.

The paper is structured as follows. Section 2 presents some notation used in the paper, along with a useful lemma and the definition of cooperative system. Section 3 contains the theoretical results concerning the definition of the considered class of systems, and the structure of the local, global and glocal interval observers. Simulation results are shown and discussed in Section 4, whereas Section 5 presents the conclusions.

PRELIMINARIES

Denote by R and N (N 0 ) the sets of real and natural numbers (with zero included), respectively, and R + = {s ∈ R : s ≥ 0}. For two vectors x 1 , x 2 ∈ R n or matrices A 1 , A 2 ∈ R n×n , the relations x 1 ≤ x 2 and A 1 ≤ A 2 are understood elementwise. Given a matrix A ∈ R n×n , let us define A + = max{0, A}, with max understood elementwise, A -= A + -A and |A| = A + + A -(similarly for vectors). Lemma 1. [START_REF] Efimov | Design of interval observers for estimation and stabilization of discrete-time LPV systems[END_REF] Let A ≤ A ≤ A for some A, A, A ∈ R n×n and x ≤ x ≤ x for x, x, x ∈ R n , then:

A + x + -A + x --A -x + + A -x -≤ Ax (1) ≤ A + x + -A + x --A -x + + A -x -
Let us define as R n×n + the set of matrices A ∈ R n×n with nonnegative elements (A ≥ 0). Then, any solution of the system:

x(t + 1) = Ax(t) + ω(t), ω : N → R n + , t ∈ N (2)
with x(t) ∈ R n and A ∈ R n×n + , is elementwise nonnegative for all t ≥ 0 if x(0) ≥ 0. Such a system is referred to as cooperative (or monotone) [START_REF] Hirsch | Monotone maps: A review[END_REF].

THEORETICAL RESULTS

System definition

Let us consider a discrete-time uncertain switched system described by:

x(t + 1) = [A(κ(t)) + ∆A(κ(t))] x(t) (3) + [B(κ(t)) + ∆B(κ(t))] u(t) + d(t) y(t) = Cx(t) + v(t)
(4) where t ∈ N 0 stands for the sample, x ∈ R nx is the state, y ∈ R ny is the output, u ∈ R nu is the input, κ(t) ∈ {κ 1 , κ 2 , . . . , κ J } denotes the switching signal, while the signals d ∈ R nx and v ∈ R ny denote the exogenous disturbance and measurement noise, respectively, which are unknown. The matrix C ∈ R ny×nx and the matrix functions A(κ(t)) ∈ R nx×nx , B(κ(t)) ∈ R nx×nu are assumed to be known (although the instantaneous value of κ(t) is not), whereas the matrix functions ∆A(κ(t)) ∈ R nx×nx , ∆B(κ(t)) ∈ R nx×nu are unknown. The following assumption will be used in further developments.

Assumption 1. d(t) ≤ d(t) ≤ d(t) and |v(t)| ≤ V for all t ∈ N 0 and for known d(t), d(t) ∈ R nx and V ∈ R + . Moreover: ∆A(κ(t)) ≤ ∆A(κ(t)) ≤ ∆A(κ(t)) (5) ∆B(κ(t)) ≤ ∆B(κ(t)) ≤ ∆B(κ(t)) (6)
A 0 + ∆A ≤ A(κ(t)) + ∆A(κ(t)) ≤ A 0 + ∆A (7) B 0 + ∆B ≤ B(κ(t)) + ∆B(κ(t)) ≤ B 0 + ∆B (
8) for some known matrix functions:

∆A(•), ∆A(•) ∈ R nx×nx : ∆A(•) ≤ 0, ∆A(•) ≥ 0 ∆B(•), ∆B(•) ∈ R nx×nu : ∆B(•) ≤ 0, ∆B(•) ≥ 0
and some known matrices

A 0 ∈ R nx×nx , B 0 ∈ R nx×nu and: ∆A, ∆A ∈ R nx×nx : ∆A ≤ 0, ∆A ≥ 0 ∆B, ∆B ∈ R nx×nu : ∆B ≤ 0, ∆B ≥ 0 It is straightforward to show that if κ(t) = κ j , the system (3)- (4) reduces to: x(t + 1) = (A j + ∆A j ) x(t) + (B j + ∆B j ) u(t) + d(t) (9) y(t) = Cx(t) + v(t) (10)
with known matrices A j A(κ j ), B j B(κ j ) and, according to Assumption 1, matrices ∆A j ∆A(κ j ) and ∆B j ∆B(κ j ) unknown but such that:

∆A j ≤ ∆A j ≤ ∆A j ∆B j ≤ ∆B j ≤ ∆B j
for some known matrices:

∆A j ∆A(κ j ) ∈ R nx×nx : ∆A j ≤ 0 ∆A j ∆A(κ j ) ∈ R nx×nx : ∆A j ≥ 0 ∆B j ∆B(κ j ) ∈ R nx×nu : ∆B j ≤ 0 ∆B j ∆B(κ j ) ∈ R nx×nu : ∆B j ≥ 0

Local interval observers

For each subsystem ( 9)-( 10), it is possible to propose a local interval observer based on cooperativity of the interval estimation error dynamics [START_REF] Efimov | Design of interval observers for estimation and stabilization of discrete-time LPV systems[END_REF], as follows:

x j (t + 1) = A j -L j C x j (t) + B j u(t) + L j y(t) (11) -|L j |V 1 ny + d(t) + ∆A j + x j + (t) -∆A j + x j -(t) -∆A j -x j + (t) + ∆A j -x j -(t) + ∆B j + u + (t) -∆B j + u -(t) -∆B j -u + (t) + ∆B j -u -(t) x j (t + 1) = A j -L j C x j (t) + B j u(t) + L j y(t) (12) + |L j |V 1 ny + d(t) + ∆A j + x j + (t) -∆A j + x j -(t) -∆A j -x j + (t) + ∆A j -x j -(t) + ∆B j + u + (t) -∆B j + u -(t) -∆B j -u + (t) + ∆B j -u -(t)
where x j , x j are the lower and upper interval estimates of x(t) for the j-th subsystem, L j , L j ∈ R nx×ny are the observer gains to be designed, and 1 ny denotes the column vector of length n y with all elements equal to 1 .

The following proposition gives some conditions under which the local interval observer provides an interval estimation of x(t). Proposition 1. Let Assumption 1 be satisfied, and:

A j -L j C, A j -L j C ∈ R nx×nx + (13)
Then, for t 0 , t f ∈ N 0 , the relation:

x j (t) ≤ x(t) ≤ x j (t) ∀t ∈ {t 0 , t 0 + 1, . . . , t 0 + t f } (14)
holds provided that:

κ(t) = κ j ∀t ∈ {t 0 , t 0 + 1, . . . , t 0 + t f } (15) x j (t 0 ) ≤ x(t 0 ) ≤ x j (t 0 ) (16)
Proof. Consider the dynamics of the interval estimation errors e j (t) = x(t) -x j (t) and e j (t) = x j (t) -x(t):

e j (t + 1) = A j -L j C e j (t) + 4 i=1 w i j (t) (17)
e j (t + 1) = A j -L j C e j (t) + 4 i=1 w i j (t) (18)
where:

w 1 j (t) = ∆A j x(t) -∆A j + x j + (t) + ∆A j + x j -(t) (19) + ∆A j -x j + (t) -∆A j -x j -(t) w 2 j (t) = ∆B j u(t) -∆B j + u + (t) + ∆B j + u -(t) (20)
+ ∆B j -u + (t) -∆B j -u -(t) w 3 j (t) = d(t) -d(t) (21)
w 4 j (t) = |L j |V 1 ny + v(t) (22)
w 1 j (t) = ∆A j + x j + (t) -∆A j + x j -(t) -∆A j -x j + (t) (23) + ∆A j -x j -(t) -∆A j x(t) w 2 j (t) = ∆B j + u + (t) -∆B j + u -(t) -∆B j -u + (t) (24) + ∆B j -u -(t) -∆B j u(t) w 3 j (t) = d(t) -d(t) (25)
w 4 j (t) = |L j |V 1 ny -v(t) (26)
Hence, the dynamics for e j (t) and e j (t) is cooperative and ( 14) holds as long as w i j (t), w i j (t) ≥ 0 ∀i = 1, 2, 3, 4 and ∀t ≥ t 0 , which is true due to Assumption 1.

Under a change of active mode, condition (16) might not hold, in such a case Lemma 1 could not be applied anymore in order to ensure that the signals w 1 j (t) and w 1 j (t) described by ( 19) and ( 23), respectively, remain non-negative. The remaining of this section will show how, by defining a global interval observer, and using the estimated global bounds to feed the local observers, it is possible to ensure that the interval estimation errors are fed by non-negative inputs even in cases where a change of active mode causes ( 16) not to hold anymore. Remark 1. Note that Proposition 1, along with similar propositions presented in the remaining of the paper, focuses only on the interval estimation property, without considering boundedness of the observers' states. Linear matrix inequality (LMI)based conditions for designing appropriate observer gains such that boundedness is achieved can be found in the available literature, see e.g. [START_REF] Efimov | Design of interval observers for estimation and stabilization of discrete-time LPV systems[END_REF].

Global interval observer

It is possible to take into account the uncertainty about κ(t) by means of a global interval observer that guarantees the state to be always within some estimated lower and upper bounds, in spite of the varyingness of κ(t), as follows:

x(t + 1) = A 0 -L 0 C x(t) + B 0 u(t) + L 0 y(t) (27)
-|L 0 |V 1 ny + d(t) + ∆A + x + (t) -∆A + x -(t) -∆A -x + (t) + ∆A - x -(t) + ∆B + u + (t) -∆B + u -(t) -∆B -u + (t) + ∆B - u -(t) x(t + 1) = A 0 -L 0 C x(t) + B 0 u(t) + L 0 y(t) (28)
+ |L 0 |V 1 ny + d(t) + ∆A + x + (t) -∆A + x -(t) -∆A - x + (t) + ∆A -x -(t) + ∆B + u + (t) -∆B + u -(t) -∆B - u + (t) + ∆B -u -(t) Proposition 2.
Let Assumption 1 be satisfied, and:

A 0 -L 0 C, A 0 -L 0 C ∈ R nx×nx + (29)
Then, for t 0 , t f ∈ N 0 , the relation:

x(t) ≤ x(t) ≤ x(t) ∀t ∈ {t 0 , t 0 + 1, . . . , t 0 + t f } (30) holds provided that:

x(t 0 ) ≤ x(t 0 ) ≤ x(t 0 ) (31)
Proof. Due to Assumption 1, in particular Eqs. ( 7)-( 8), the following is true:

A (κ(t)) + ∆A (κ(t)) = A 0 + ∇A (κ(t)) (32) B (κ(t)) + ∆B (κ(t)) = B 0 + ∇B (κ(t))
(33) for some ∇A (κ(t)) , ∇B (κ(t)) such that:

∆A ≤ ∇A (κ(t)) ≤ ∆A ∆B ≤ ∇B (κ(t)) ≤ ∆B
Hence, the dynamics of the interval estimation errors e(t + 1) = x(t) -x(t) and e(t) = x(t) -x(t) are described by:

e(t + 1) = A 0 -L 0 C e(t) + 4 i=1 w i (t) (34) e(t + 1) = A 0 -L 0 C e(t) + 4 i=1 w i (t) (35)
where w i (t), w i (t) can be obtained from w i j (t), w i j (t) in ( 19)-( 26) by replacing ∆A j → ∇A(κ(t)), ∆A j → ∆A, ∆A j → ∆A, x j → x, x j → x, ∆B j → ∇B(κ(t)), ∆B j → ∆B, ∆B j → ∆B, L j → L 0 , L j → L 0 . The remaining of the proof follows a similar reasoning as in the one of Proposition 1.

Glocal interval observers

The information provided by the global interval observer can be fed locally to interval observers for different subsystems ( 9)-( 10), as follows:

x j (t + 1) = A j -L j C x j (t) + B j u(t) + L j y(t) (36) -|L j |V 1 ny + d(t) + ∆A j + x + (t) -∆A j + x -(t) -∆A j -x + (t) + ∆A j -x -(t) + ∆B j + u + (t) -∆B j + u -(t) -∆B j -u + (t) + ∆B j -u -(t)
x j (t + 1) = A j -L j C x j (t) + B j u(t) + L j y(t) (37)

+ |L j |V 1 ny + d(t) + ∆A j + x + (t) -∆A j + x -(t) -∆A j -x + (t) + ∆A j -x -(t) + ∆B j + u + (t) -∆B j + u -(t) -∆B j -u + (t) + ∆B j -u -(t)
We will refer to an observer in the form ( 36)-( 37) as glocal.

The advantage of considering a glocal observer lies in the fact that thanks to the introduced feed, it can be guaranteed that the dynamics of the estimation errors e j (t) = x(t) -x j (t) and e j (t) = x j (t) -x(t) will be excited by non-negative inputs even when changes of active mode induce their non-positivity at some sample. Proposition 3. Let Assumption 1 be satisfied, and for t 0 , t f ∈ N 0 :

A j -L j C, A j -L j C ∈ R nx×nx + (38)
κ(t) = κ j ∀t ∈ {t 0 , t 0 +1, . . . , t 0 +t f } (39) Then, the relation:

x j (t) ≤ x(t) ≤ x j (t)
∀t ∈ {t 0 , t 0 + 1, . . . , t 0 + t f } (40) holds provided that:

x j (t 0 ) ≤ x(t 0 ) ≤ x j (t 0 ) (41)
Moreover, let us define:

e w j (t 0 + N ) N -1 k=0 4 i=1 A j -L j C N -k-1 w i j (t 0 + k) (42) e w j (t 0 + N ) N -1 k=0 4 i=1 A j -L j C N -k-1 w i j (t 0 + k) (43) If x(t 0 ) ≤ x j (t 0 ) or x(t 0 ) ≥ x j (t 0
) and there exists N ∈ N such that:

e w j (t 0 + N ) ≥ -A j -L j C N e j (t 0 ) (44)
or:

e w j (t 0 + N ) ≥ -A j -L j C N e j (t 0 ) (45)
respectively 1 , then:

x j (t 0 + N ) ≤ x(t 0 + N ) ≤ x j (t 0 + N ) (46)
1 Conditions ( 44)-( 45) can be interpreted as requiring that the signals w i j (t 0 + k) and w i j (t 0 + k), i = 1, 2, 3, 4, are sufficiently exciting in the time interval t 0 , . . . , t 0 + N -1.

Proof: The dynamics of the interval estimation errors e j (t) and e j (t) are given by:

e j (t + 1) = A j -L j C e j (t) + 4 i=1 w i j (t) (47)
e j (t + 1) = A j -L j C e j (t) + 4 i=1 w i j (t) (48)
where w i j (t), w i j (t) can be obtained from w i j (t), w i j (t) in ( 19)-( 26) by replacing x j → x, x j → x, L j → L j , L j → L j . The proof that ( 41) implies ( 40) follows a similar reasoning as in the proof of Proposition 1. Let us notice that the response of ( 47)-( 48) is given by:

e j (t 0 + N ) = A j -L j C N e j (t 0 ) + e w j (t 0 + N ) (49) e j (t 0 + N ) = A j -L j C
N e j (t 0 ) + e w j (t 0 + N ) (50) Then, it is straightforward that (46) follows from ( 44)-( 45). Remark 2. The last result of Proposition 3 implies that in the cases when the instants of commutation are unknown, and we cannot reinitialize the interval observer ( 36)-( 37) properly for the correct value of κ, if the inputs are sufficiently rich, then the glocal interval observer will start to produce correct state bounds after some transient. In fact, if the gains L j and L j are designed such that the matrices A j -L j C and A j -L j C are Schur stable, then the terms corresponding to the free responses from initial conditions e j (t 0 ), e j (t 0 ) will converge to zero.

Hence, since the terms e w j (•), e w j (•) are always positive, if they are also sufficiently exciting (e.g., but not necessarily, v(t) is a white noise), then e j (•) and e j (•) will eventually become positive and (46) will hold.

SIMULATION RESULTS

The aim of this section is to illustrate the comparison between local and glocal observers by means of a simulation study. Let us begin introducing the following system matrices:

A(κ) = A 0 + κA • B(κ) = B 0 + κB • with A 0 = 0.4 0.2 0.2 0.3 B 0 = 4 2 A • = 0.2 0.1 -0.1 -0.3 B • = 2 -1
The unknown parameter κ is assumed to vary in the discrete set {-0.5, 0, 0.5} according to the following switching scheme: 17)-( 18), ( 34)-( 35) and ( 47)-( 48), respectively, assuming that each element of the state and input matrices is affected by bounded uncertainty between -0.05 and 0.05. The results obtained for an input u(t) = -3 + cos(0.06t) from an initial condition [0, 0]

T ≤ x(0) ≤ [0.5, 0.5] T , are depicted in Figs. 1234. It is worth to note that, as expected, the glocal bounds are more conservative than the local ones, but the latter are more likely to be violated due to changes in the system's active mode.

In a second simulation study, a statistical analysis has been performed to compare the estimation effectiveness of local and glocal observers. A family of 1000 switched systems with a fixed structure has been generated by random coefficient selection. The system matrices have been designed to depend linearly on the switching parameter κ(t), whose range is constrained to a discrete set containing three admissible values. In the simulations the parameter κ(t) is forced to undergo a switch at t = 200 and at t = 600. When a switch occurs, a transient is triggered both in the local and the glocal observers, with a consequent possible temporary violation of bounds ( 17)-( 18) and ( 47)-(48). Focusing on the time samples following the switches, we are interested in comparing the number of systems that are violating the bounds. The two scenarios are represented in the histograms in Figs. 56. In both cases, it is clear that a smaller proportion of glocal observers fails to remain within the bounds compared to local observers and, furthermore, that the rate of recovery for glocal observers is remarkably higher. In conclusion, as already mentioned, on the one hand glocal observers introduce a larger conservativeness for the computation of bounds but, on the other hand, they also guarantee a better accuracy for the identification of correct switching modes.

  Assuming that C = I, the local, global and glocal observer gains have been computed such that the corresponding closedloop matrices equal the zero matrix. The bounds for local, global and glocal observers are computed based on (

Fig. 1 .

 1 Fig. 1. Evolution of the state x 2 : estimation using a bank of local interval observers

Fig. 2 .Fig. 3 .

 23 Fig. 2. Evolution of the state x 2 : estimation using a global observer

Fig. 5 .

 5 Fig. 5. Statistical analysis of bound violation due to the switch at t = 200

This work has been supported by the Spanish State Research Agency (AEI) through the Maria de Maeztu Seal of Excellence to IRI (MDM-2016-0656) and the grant Juan de la Cierva-Formacion (FJCI-2016-29019), by the Research Council of Norway through the AMOS Center, grant number 223254 and by the University of Stavanger through the project IN-12267.


Marie-Madeleine M Mialon
email: marie-madeleine.richard@clermont.inra.fr

Gilles Renand

Isabelle Ortigues

Dominique Bauchart

J.-F F Hocquette

Luc Mounier

Thierry Noël

Didier Micol

Michel Doreau

I Ortigues-Marty

† D Bauchart

† L Mounier

§ T Noël

# D Micol

Fattening performance, metabolic indicators, and muscle composition of bulls fed fiber-rich versus starch-plus-lipid-rich concentrate diets 1

Keywords: bull fattening, carcass composition, energy, fatty acids, metabolism

Fattening performance, metabolic indicators, and muscle composition of bulls fed fiber-rich versus starch-plus-lipid-rich concentrate diets

INTRODUCTION

Bulls are often fattened using starch-rich diets to yield high BW gain (BWG). However, cereal-fed ruminants are in competition with humans for use of feed resources, and high intakes of starch-rich diets can trigger ruminal acidosis. An alternative strategy may be to feed fiber-rich diets, which give comparable performance if intake is high enough to compensate for the lower energy value, as argued by [START_REF] Bradford | Strategies for promoting productivity and health of dairy cattle by feeding nonforage fiber sources[END_REF] for dairy cattle. Alternatively, lipids present the greatest energy value among all feed ingredients and may also help to limit acidosis. Several trials have studied the effect of concentrate type on fattening performance, but very few analyzed this effect while dissociating the impact of energy intake from the type of energy source [START_REF] Mueller | Use of soybean hulls as a replacement for dry rolled corn in beef cattle feedlot receiving diets[END_REF]. Type of concentrate energy may modify dietary digestive and metabolic efficiency as well as absorbed nutrient profile. As a consequence, type of concentrate may lead to significant differences in performance, muscle metabolism, and carcass composition [START_REF] Hocquette | Responses to nutrients in farm animals: Implications for production and quality[END_REF]. Consumers often see beef negatively as high in fats rich in SFA and trans-MUFA, which are considered risk factors for human health [START_REF] Riediger | A systemic review of the roles of n-3 fatty acids in health and disease[END_REF]. A moderate incorporation of linseed in the diet can increase the content of beneficial n-3 PUFA and reduce SFA in beef [START_REF] Doreau | Enhancing fatty acid composition of milk and meat through animal feeding[END_REF].

The objectives of this study were 1) to determine the fattening performance and carcass responses of bulls fed high-concentrate diets rich either in a mixture of starch plus linseed or in fibrous by-products while separating the effects of the source and level of energy intake, 2) to relate differences in performance to metabolic activities measured in the liver and 2 muscles at slaughter, and 3) to study the effects of including feeds rich in omega-3 fatty acids (FA) on FA composition in 3 muscles.

MATERIALS AND METHODS

Animals, Experimental Design, and Dietary Treatments

In total, 140 Charolais bulls were used from weaning in a fattening trial repeated over 2 successive years, with 70 bulls of the same genetic origin in each trial. The experiment took place at the INRA experimental farm in Bourges, France. At weaning, the animals averaged 239 ± 9 d old and weighed 319 ± 27 kg. They were assigned to 10 groups of 7 animals of similar initial average BW each year. Each group was housed in a separate pen. Pens were contiguous in the same shed (7 m2 per bull) and were bedded with barley straw. Three diets composed of 81% to 87% concentrate were compared: FR (based on a fiber-rich concentrate, offered ad libitum), SL (based on a starch-and lipid-rich concentrate, offered ad libitum), and SLR (based on the same concentrate as SL but offered in restricted amounts to match the NE g intake [NE g I] of the FR group). The number of pens receiving the FR, SL, and SLR diets was 4, 4, and 2 each year, respectively. After 3 wk of adaptation to experimental treatments and progressive achievement of ad libitum feeding for FR and SL diets, bulls were fattened for a minimum of 228 d and were slaughtered at the same average age of 17 to 18 mo, as usually done for this type of animal. Experimental procedures were conducted in ac-cordance with French Ministry of Agriculture guidelines on animal welfare and use for experimental purposes (http://www2.vet-lyon.fr/ens/expa/acc_regl.html).

The FR diet concentrate consisted mainly of cereal by-products, dehydrated alfalfa, and dehydrated beet pulp. The SL and SLR diet concentrate consisted of cereals and an extruded mixture containing 500 g/kg linseed (Valorex, Combourtillé, France) to achieve a theoretical level of 12 g of omega-3 FA from linseed per kilogram of DM of concentrate. In all 3 dietary treatments, bulls were offered barley straw ad libitum in a rack in each pen. This ad libitum distribution was expected to result in a greater proportion of straw in the SLR diet because of the feed restriction. Diet ingredients and chemical composition are reported in Table 1. Net energy for gain, estimated from diet composition according to INRA (2007) feed tables, was 6.05, 7.32, and 7.04 MJ/kg DM for the FR, SL, and SLR diets. Concentrates had the same ratio of NE g to MP expressed in INRA (2007) units, equal to 16 g MP/MJ NE g . Diets were formulated according to recommendations (INRA, 2007) to meet NE g and MP requirements needed for maintenance and theoretical BW gain (1,500 g/d for FR and 1,800 g/d for SL). The theoretical BWG for the FR diet corresponds to previously observed gain with the same diet distributed ad libitum to Charolais bulls. It was assumed that the SL diet distributed ad libitum would be consumed at similar DMI as the FR diet, leading to greater expected gains. Anion-cation balance was 134 and 119 meq/kg DM for FR and SL concentrates, respectively. Bulls fed the SLR diet were offered restricted amounts of concentrate mixture to provide the same average NE and MP per unit metabolic BW (BW 0.75 ) as those of FR diet animals for similar theoretical BWG. The amount of concentrate distributed to the SLR group was thus readjusted every 2 wk on the basis of the average NE intake per kilogram of BW of the FR group over the preceding 2 wk. A commercial mineral-vitamin premix was added to the concentrates at a level of 8 and 5 g/kg concentrate DM for FR and SL diets, respectively. Both concentrates were produced as pellets after the ingredients were ground (Jacques Coeur, Joigny, France). Concentrates were distributed once daily at 0800 h using an automatic feeding system (Calan system, Drafhandel Decuyper, Brussels, Belgium). Allowances were adjusted every 2 d to ensure 10% refusals in the ad libitum-fed groups (FR and SL). Fresh water was available at all times in each pen.

Measurements and Samplings during Fattening and at Slaughter

Each bull was equipped with an electronic transponder (Dairy gate, EFEI, Villeroy, France) around its neck that opened its specific feeder, and individual concentrate intake was recorded by measuring offered amounts every day and refusals every 2 d. Straw intake was measured for each pen by weighing each bale. Individual straw intake was calculated from the average intake for the pen, assuming that bedding straw intake was negligible. Each year, 3 feed samples were composed from 8 weekly subsamples taken over 2-mo periods for chemical analyses, that is, a total of 6 samples for each feed. Feeds were ashed at 550°C for 6 h for OM determination: nitrogen was determined by the Kjeldahl procedure (AOAC, 1990); NDF and ADF were determined according to [START_REF] Van Soest | Methods of dietary fiber, neutral detergent fiber, and nonstarch polysaccharides in relation to animal nutrition[END_REF]; starch was determined by spectrophotometry after enzymatic analysis [START_REF] Faisant | Resistant starch determination adapted to products containing high levels of resistant starch[END_REF]; GE was measured by isoperibolic calorimetry (C200 model, IKA, Staufen, Germany), ether extract (EE) was measured using petroleum extract (AOAC, 1990). Body weight was determined every 14 d and at fixed hours during the whole fattening period.

At the end of fattening, bulls were transported by truck to INRA's experimental slaughterhouse 200 km away (Clermont-Ferrand, France). On arrival at about 1500 h, the bulls were housed in a straw-bedded lairage pen and were offered their usual diet with water at disposal. Feed was removed at 2000 h for an overnight fast. Bulls were slaughtered at the same average age under standard conditions in the same experimental slaughterhouse. Carcasses were processed by removal of the head, tail, feet, and abdominal and thoracic viscera. Hot carcass, internal fat (i.e., peritoneal, omental, mesenteric, and kidney fat), and splanchnic organ weights were recorded. Carcasses were chilled and stored at 4°C until 24 h postmortem. The sixth rib was excised and dissected to estimate carcass weights of bone, muscle, and fat (in kg) according to the equations proposed by [START_REF] Robelin | Estimation de la composition de la carcasse des taurillons partir de la composition de la 6ème côte[END_REF] for Charolais bulls.

Preparation of Tissue Samples

Liver samples (~50 g) were taken 35 to 40 min postmortem, cut into small pieces (5 to 10 g), and frozen in liquid nitrogen. Samples from rectus abdominis (RA), longissimus thoracis (LT), and semitendinosus (ST) muscles (120 to 150 g) were taken within 30 min postmortem, cut into small pieces (5 to 10 g), and frozen in liquid nitrogen for measurement of enzyme activities. Samples of the same muscles were taken 24 h postmortem for muscle lipid and FA analysis. All samples were ground in liquid nitrogen in a M20 mill (IKA-Werke, Staufen, Germany) to produce a fine homogeneous powder, then stored at -80°C for lipid and FA analysis.

Metabolic Enzyme Activity

Metabolic enzyme activities characterizing glycolytic (phosphofructokinase [PFK,EC 2.7.1.11] and lactate dehydrogenase [LDH,EC 1.1.1.27]) or oxidative (cytochrome c oxidase (COX, EC 1.9.3.1]) metabolism were determined spectrophotometrically on liver and muscle samples from only FR and SL bulls, as described by [START_REF] Piot | Contribution of mitochondria and peroxisomes to palmitate oxidation in rat and bovine tissues[END_REF] and [START_REF] Jurie | The separate effects of the nature of diet and grazing mobility on metabolic potential of muscles from Charolais steers[END_REF]. Tissue protein content was determined spectrophotometrically with BSA as the standard according to [START_REF] Bradford | A rapid and sensitive method for the quantitation of microgram quantities of protein utilizing the principle of protein dye binding[END_REF]. All enzyme activities were measured in duplicate at 25°C and are expressed in micromoles of molecules converted per minute and per gram of wet muscle or per gram of tissue protein.

Muscle Lipid and Fatty Acid Analysis

Muscle DM was assayed gravimetrically after drying at 80°C for 48 h. Total lipids of muscle samples were extracted by grinding 6 g of muscle powder with 2:1 chloroform-methanol (vol/vol) according to [START_REF] Folch | A simple method for the isolation and purification of total lipids from animal tissues[END_REF] and then were assayed gravimetrically. Long-chain FA (LCFA) of muscle total lipids were extracted and transmethylated at room temperature for 2 × 20 min with sodium methylate (1 M) in methanol followed by boron trifluoride in methanol (14%, vol/ vol) according to [START_REF] Glass | Alcoholysis, saponification and the preparation of fatty acid methyl esters[END_REF].

Long-chain fatty acid analysis was performed by gas-liquid chromatography on a Peri 2100-model chromatograph (Perichrom, Saulx-les-Chartreux, France) fitted with a CP-Sil 88 glass capillary column (Varian, Lake Forest, CA; length: 100 m; i.d.: 0.25 mm) with H 2 as the carrier gas under conditions described by [START_REF] Scislowski | Effects of dietary n-6 and n-3 PUFA on peroxidability of lipoproteins in steers[END_REF]. Total LCFA were quantified using C19:0 as the internal standard. Identification and calculation of the response coefficient of each individual LCFA were achieved using a quantitative mix of C4 to C24 FA methyl esters (Supelco, Bellefonte, PA).

Digestibility Trial

At the end of the experiment, the digestibility of the FR and SL diets was measured using 6 dry dairy cows (initial BW 643 ± 52 kg) because our facilities were not equipped for separating urine and feces in bulls. Cows received the 2 diets for two 3-wk periods in a crossover design. Cows were tethered and kept in individual pens with clean, fresh water and mineral blocks available at all times. A 2-wk diet adaptation period was followed by a 6-d fecal collection period. Diet composition was 13% barley straw and 87% of either the FR or SL concentrate. Feeds were the same as those given to bulls during fattening. Cows were fed in restricted amounts to keep expected NE intakes the same between diets. Straw and concentrate were given in 3 equal parts at 0900, 1100, and 1600 h. Fecal contamination by urine was avoided thanks to a urine collector attached to the vulva of the cow. Representative feed samples were taken, and the total feces of each animal was pooled to 1 sample per animal. An aliquot of feed and feces samples was dried at 103°C for DM determination. Another aliquot was dried at 60°C for 72 h and then ground through an 0.8mm screen before chemical analysis. Crude protein, ash, NDF, ADF, and GE were determined according to the above-mentioned methods. The NE content of diets was calculated from digestible energy according to equations proposed by INRA (2007). It was assumed that the NE value determined in dry cows applied to fattening bulls.

Calculations and Statistical Analysis

Total NE g I in the 3 dietary treatments was calculated from the results of the digestibility trial and not from the feed table (INRA, 2007) values. The feed efficiency during a given period was estimated by the ratio of BWG to NE g I during that period. Mean NE g I, BWG, and feed efficiency were calculated during 4 fattening periods (0 to 56 d, 56 to 126 d, 126 to 196 d, and 0 to 196 d). The 0 to 196 d period started at the end of the adaptation period and finished at the first slaughter, where all the bulls were present. Muscle and fat gain efficiencies were calculated from the whole fattening period as the ratios of carcass muscle or fat mass to NE g or digestible CP intakes. Eleven bulls were removed from the experiment due to 3 accidental causes and 8 deaths diagnosed as enterotoxemia (n = 4, 2, and 2 for the SL, SLR, and FR diets, respectively). Fattening data analysis ultimately dealt with 129 bulls, and carcass data analysis dealt with 123 bulls.

Analysis of variance was run using the MIXED procedure of SAS (SAS Inst. Inc., Cary, NC). For digestibility data, the model included diet and period and their interaction as fixed effects. For intake, growth, and carcass data, the following statistical analysis was chosen to take into account the unbalanced number of pens allocated to each of the 3 diets. Thus, the effect of the 20 pens was considered as the only fixed effect. These pen effects were appropriately combined to estimate diet effects using the "estimate" option of the MIXED procedure. This same "estimate" option was also used to calculate differences between 2 diets. The "contrast" option was ultimately used to test the significance of the diet effect combining 2 of the 3 contrasts among the above diet estimates. For data measured on muscles (lipid and FA composition and enzymatic data), the model included muscle, diet, and their interaction. Muscle was considered to be repeated on the same animal. For data measured on the liver (enzymatic data), diet was the only fixed effect. For all the data measured on bulls, diet means were compared by orthogonal contrasts: FR vs. SL, FR vs. SLR, and SL vs. SLR. Significant interactions were calculated using Student's t test to identify muscle differences and individual treatment differences. Significance was considered when P ≤ 0.05.

RESULTS

Diet Digestibility and Energy Value

The apparent total tract digestibility of the OM was 5.5% units lower (P < 0.001) for cows consuming the FR diet than for cows fed the SL diet (Table 2). SL diet digestibility was lower than expected, as discussed further below. For the FR diet, NDF and ADF digestibility was 17.6% units greater (P < 0.001) than for the SL diet, whereas CP digestibility was 19.0% units lower. Gross energy digestibility was 6.5% units greater for the SL diet than for the FR diet (P < 0.001). From these results, NE g was calculated as 6.67 and 7.59 MJ/kg DM for the FR and SL diets, respectively. For the SLR diet, NE g was recalculated as 7.30 MJ/kg DM after taking into account the greater percentage of straw in the diet (18% instead of 13% for SL), and the energy digestibility of barley straw was taken as 40% (INRA, 2007). These figures were used for subsequent calculations of NE intake and feed efficiency.

Intake, Growth Performance, and Feed Efficiency

Effect of Type of Energy in Ad Libitum-Fed Bulls (FR vs. SL).

Net energy intake did not differ between diets over the whole fattening period, although it was greater (P = 0.013) for SL bull than for FR bulls during the 0 to 56 d period (Table 3). The average BWG of bulls offered the SL diet was 6% greater (P = 0.006) than that of bulls fed the FR diet over 196 d of fattening, mostly because of strong gains in the last 70 d of fattening. Feed efficiency was greater with the SL diet than with the FR diet over the whole fattening period (P = 0.025). This difference stemmed from a strong difference in the 126-to 196-d period, where feed efficiency was 11.9% greater with the SL diet than with the FR diet (P < 0.001).

Effect of Intake Level (SL vs. SLR).

Bulls fed the SLR diet consumed a greater proportion of straw than bulls fed SL diet (18% vs. 13%). Bulls fed the SLR diet consumed daily 1.1 kg DM less (P < 0.001) than bulls fed the SL diet, and NE g I was consistently around 15% lower over the whole experimental period (P < 0.001) for SLR vs. SL bulls; SLR-fed bulls thus had a 12.5% lower BWG (P < 0.001) than SL-fed bulls. The efficiency for growth was greater for the SLR diet than for the SL diet (P = 0.01).

Effect of Type of Energy in Feed-Matched Bulls (FR vs. SLR).

Net energy intake by SLR-fed bulls was planned to be similar to that of FR-fed bulls. However, because of a lower difference in digestibility between FR and SL and a greater proportion of straw in DMI, NE g I were not as isoenergetic as planned, with NE g I ultimately 13% lower (P < 0.001) in the SLR treatment vs. the FR treatment over the whole fattening period (Table 3). Average BWG from 0 to 196 d of fattening was 7% lower (P = 0.02) with the SLR diet vs. the FR diet. Overall, feed efficiency from 0 to 196 d was 7.6% greater for the SLR diet than for the FR diet (P = 0.006).

Slaughter Performance, Carcass Traits, and Efficiency of Muscle and Fat Gain

Effect of Type of Energy in Ad Libitum-Fed Bulls (FR vs. SL).

Consistent with the greater average NE g and CP intakes, SL bulls had 3% greater BW (P = 0.039) and 6% greater HCW (P < 0.001) at slaughter than FR bulls (Table 4). The ratio of cold carcass weight to onfarm BW was also greater for SL bulls (P < 0.001). Carcass composition showed proportionally more fat and less muscle (P < 0.001) for SL bulls than for FR bulls. Muscle-to-bone ratios were similar, with a value of 5.

Consequently, muscle mass was 11 kg greater (315 vs. 304 ± 4.28 kg; P < 0.05) and carcass fat mass was 14 kg greater (75.6 vs. 61.7 ± 1.74 kg; P < 0.001) in SL bulls than in FR bulls, and fat mass in the fifth quarter was also 7.5 kg greater (SEM = 1.18; P < 0.001). The lower forestomach weights (reticulorumen and omasum) in the bulls fed the SL diet (P < 0.001) were consistent with their lower DMI. Conversely, intestinal weight was greater in the SL bulls (P = 0.029), probably because of their greater intestinal digestion compared with that of FR bulls. Liver weight was unaffected.

The efficiency of NE g use for muscle gain was not affected, whereas the efficiency of NE g use for fat gain was 18% greater for the SL diet than for the FR diet (P < 0.001). The efficiency of digestible CP transfer into muscle and fat was reduced (P < 0.001) in the bulls fed SL diet. Had digestibility not been accounted for, differences in N efficiency would have been greatly reduced. Effect of Intake Level (SL vs. SLR). Compared with SL bulls, SLR bulls had 6% lower BW at slaughter (P < 0.001), 8.6% lower HCW (P < 0.001) but with a greater carcass muscle-to-fat ratio (5.07 vs. 4.23 ± 0.11; P < 0.001), and a similar muscle-to-bone ratio of 5. Consequently, both carcass muscle and fat mass were lower in SLR vs. SL bulls (P < 0.001), as was the amount of fat in the fifth quarter (Table 4). Forestomach weight was not significantly affected by the difference in DMI, but abomasal and intestinal weights were significantly lower in SLR vs. SL bulls (P = 0.004 and P = 0.036, respectively), and liver weight tended to be lower (P < 0.06). Although muscle gain was lower in SLR bulls, efficiencies of NE g and digestible CP use for muscle gain were significantly increased (P < 0.001). Efficiency of NE g use for fat gain was not different between the 2 diets. Efficiency of digestible CP use for muscle gain was greater for the SLR diet (P < 0.001).

Effect of Energy Source (FR vs. SLR). Despite differences in NE g I and BWG, FR and SLR bulls did not differ in any body composition traits except fat depots, which tended to be lower for the SLR diet (57.5 vs. 61.7 kg for the SLR and FR bulls; SEM = 1.74; P < 0.10), and forestomach (reticulorumen, omasum) and abomasum weight, which were greater (P < 0.044) for the fiber-rich FR diet than for the SLR diet. Compared with FR bulls, SLR bulls showed more efficient NE g use for muscle and fat gain but less efficient digestible CP use for muscle and fat gain (P < 0.001).

Metabolic Enzyme Activity

Despite differences in feed efficiency between the FR and SL groups just before slaughter (d 126 to 196), the enzymatic activity of the liver (which is one of the most metabolically active organs) did not differ between the 2 groups (Table 5) on the basis of COX activity (representative of mitochondrial activity) and LDH and PFK activities (representative of glycolytic metabolism), whatever the unit of expression of the results (per g of wet muscle or per g of tissue protein).

In muscle, LDH activity was slightly greater for the SL diet compared for the FR diet in both ST (+2%) and LT (+5%; P < 0.047) muscles when results were expressed per gram of wet tissue, indicating a greater glycolytic metabolism in muscles of animals fed the SL diet (Table 6). However, when results were expressed per gram of muscle protein, the differences lost significance because of a slightly greater protein content, especially in ST muscle (+3.4%; P = 0.071) for the SL diet. For all the other measured enzyme activities, we did not find any significant differences between the diets. However, metabolic activity showed differences between the 2 studied muscles, with LT being more oxidative (because of a greater COX/LDH ratio) than ST for the FR diet, as expected. Note that this difference was negated in the SL diet, as indicated by a significant muscle × diet interaction for some variables (especially the COX/LDH ratio).

Lipids and Fatty Acids in Muscles

Total lipids and total FA (g/100 g fresh tissue) and individual FA and FA class (mg/100 g fresh tissue) contents of LT, RA and ST muscles are given in Table 7. Total lipid contents differed with muscle type and body localization, being 1.6 to 2.0 and 1.4 to 1.6 times greater in LT and RA muscles, respectively, than in ST muscle (P < 0.001). Similar variations with muscle type were noted for total FA content, which was 1.9 to 2.3 and 1.7 to 1.9 times greater in LT and RA muscles than in ST muscle, respectively (P < 0.001). Total lipid and FA contents were significantly influenced by diets, being greater with the SL diet than with the FR and SLR diets (P < 0.001) which had similar lipid and FA contents. A significant (P < 0.001) muscle × diet interaction was found for total lipids but not for total FA (Table 7).

Total SFA muscle content varied with muscle type and diet in patterns similar to those of total lipids and FA (Table 7). Saturated FA were mainly palmitic acid (16:0, ≈22% of total FA) and stearic acid (18:0, ≈16%). Total and individual SFA did not differ between the FR and SLR diets but were greater for SL than for the other 2 diets (P < 0.001), with significant muscle × diet interactions (P = 0.002 to 0.003 according to FA). The ratio of 16:0 to 18:0 was mainly influenced by muscle type, being 10.3, 17.9, and 17.2 lower in LT muscle than in RA and ST muscles from bulls given the FR, SL, and SLR diets, respectively (P < 0.001).

Total MUFA, composed of cis and trans isomers, represented 32% to 42% of total FA according to the type of muscle and diet considered (Table 7); MUFA deposition was 1.9 to 2.1 and 2.0 to 2.4 times greater in RA and LT muscles than in ST muscle, respectively (P < 0.001), whatever the dietary conditions. Cis-MUFA, which represented 88% to 93% of total MUFA, were dominated by oleic acid (18:1n-9 cis, 77% to 82%) irrespective of diet and muscle type. As for SFA, muscle deposition of total SFA was significantly (P < 0.001) influenced by dietary energy level, being 1.9 to 2.2, 1.5 to 1.8, and 1.7 to 1.8 times greater for the SL diet than for the 2 other diets for LT, RA, and ST muscles, respectively (P < 0.001). Similar diet effects were found for muscle trans-MUFA contents. However, trans-MUFA contents were 1.7, 1.6, and 1.5 times greater in RA, LT, and ST muscles of bulls given the SLR diet than in those of bulls given the FR diet (P = 0.010). All 18-carbon MUFA isomers were greater in RA and LT than in ST, and most of them were diet dependent (Table 8). The main cis isomers, oleic acid (cis-9 18:1), and cis vaccenic acid (cis-11 18:1) were greater in SL samples than in SLR samples (P < 0.001). The coelution of trans-11 (trans vaccenic acid) and trans-10 18:1, which is the major peak of trans-MUFA, is greater for the SL diet than for the SLR diet (P = 0.038) and greater for the SL and SLR diets than for the FR diet (P < 0.01).

Total PUFA, composed of n-6 PUFA, n-3 PUFA, and conjugated linoleic acids (CLA, mainly rumenic acid, cis-9, trans-11 18:2) varied according to muscle (P < 0.001) and diet (P < 0.001) and accounted for 12% to 16%, 12% to 14% and 19% to 24% of total FA for RA, LT, and ST, respectively, with ST having the lowest total FA content (Table 7). The n-6 PUFA were mainly composed of 18:2 n-6 (linoleic acid) and 20:4 n-6 (arachidonic acid). In all muscles considered, linoleic acid represented 10.9% and 9.6% of total FA in muscles from bulls fed at the lowest energy intakes (FR and SLR diets) but only 6.6% of total FA in the SL diet. Quantitatively, linoleic acid content was 16% to 20% greater in RA and LT muscles than in ST muscle, irrespective of diet (P < 0.001), whereas arachidonic acid content was greater in ST than in RA and LT. The n-3 PUFA were mainly composed of 18:3 n-3 (linolenic acid) as well as 20-and 22-carbon n-3 PUFA, mainly represented by 20:5 n-3 (eicosapentaenoic acid, EPA; 2.3 to 7.8 mg/100 g) and especially 22:5 n-3 (docosapentaenoic acid, DPA; 6.9 to 12.3 mg/100 g) but poor in 22:6 n-3 (docosahexaenoic acid, DHA; <1.3 mg/100 g; Table 7). Muscle linolenic acid, EPA, DPA, and DHA content was, in all 3 muscles, highly and mainly influenced by linseed supplementation, being greater for the SL and SLR diets (rich in linolenic acid) than for the FR diet (P < 0.001). Eicosapentaenoic acid and DPA content was mainly influenced by muscle type, being 47% to 70% and 16% to 23% greater in ST than in RA and LT, respectively (P < 0.001), irrespective of diet. In other respects, CLA content was 1.5 to 1.8 and 2.7 to 3.2 times greater in SL bulls than in FR and SLR bulls, respectively (P < 0.001), for all muscles.

The n-6:n-3 PUFA ratio and 18:2 n-6 to 18:3 n-3 ratio differed among muscles and were greater for bulls given the FR diet than for bulls fed the SL and SLR diets (P < 0.001). In other respects, PUFA:SFA ratio was 1.7 to 2.0 times greater in ST muscle than in RA and LT muscles (P < 0.001), irrespective of diet. Within a row, means without a common superscript differ (P < 0.05).

1 FR: diet composed of 88% concentrate rich in fiber and 12% straw, SL: diet composed of 87% concentrate rich in starch and lipids and 13% straw, SLR: diet composed of 83% concentrate rich in starch and lipids and 17% straw.

2 NS = not significant.

DISCUSSION

Alternative strategies to feeding high-cereal diets to fattening bulls have to focus not only on achieving high levels of growth but also on using alternative feeds that do not compete with human food, improve feed efficiency, and ensure nutritionally good-quality meat [START_REF] Hocquette | Responses to nutrients in farm animals: Implications for production and quality[END_REF][START_REF] Doreau | The contribution of animal production to agricultural sustainability[END_REF]. Three strategies were tested here on the basis of 1) using high-concentrate diets to maximize intake, 2) replacing part of the cereals with a fat source to ensure energy density and to limit the risks of acidosis, and 3) using highly digestible fiber sources. The effects of energy source were separated from those of intake level. Starch-based diets are known to increase carcass fat at similar metabolizable energy intake [START_REF] Brennan | Effects of differing ratios of corn silage and corn grain on feedlot performance, carcass characteristics and projected economic returns[END_REF], but the effect may also depend on the rate of gain [START_REF] Coleman | Silage or limit-fed grain growing diets for steers: II. Empty body and carcass composition[END_REF]. Few experiments have studied the impact of energy source in finishing cattle at controlled intakes [START_REF] Brennan | Effects of differing ratios of corn silage and corn grain on feedlot performance, carcass characteristics and projected economic returns[END_REF][START_REF] Bartoň | Growth performance and fatty acid profiles of intramuscular and subcutaneous fat from Limousin and Charolais heifers fed extruded linseed[END_REF][START_REF] Costa | Carcass fat partitioning and meat quality of Alentejana and Barrosa young bulls fed high or low maize silage diets[END_REF]. The effect of the source and amount of energy has most often been studied in growing cattle, often during winter growing programs, showing little carryover effects on body composition and fat depots over fattening (e.g., [START_REF] Sharman | Effect of starchvs. fiber-based energy supplements during winter grazing on partitioning of fat among depots and adipose tissue gene expression in growing cattle and final carcass characteristics[END_REF]. To our knowledge, there is no published experiment comparing fiber-rich and starch-plus-lipid-rich concentrate diets fed to bulls continuously over the growing and fattening phases and dissociating the effects of energy source from those of intake level.

Nutritional Value of Diets and Ad Libitum Intakes

Dry cows were used instead of bulls for digestibility measurements. A bias in results cannot be excluded because of differences in age and sex and because cows were fed in restricted amounts. However, the difference may have a low extent, as shown by [START_REF] Dulphy | Quantités ingérées et activités alimentaires comparées des ovins, bovins et caprins recevant des fourrages conservés avec ou sans aliment concentré. I. Etude descriptive[END_REF]: OM digestibility was 1% to 3% units greater in cows than in bulls receiving the same diets. In any case, NE calculations from effective digestibility measurements are likely more accurate than calculations arising from feed tables.

According to the INRA (2007) feeding system, we expected to record approximately a 17% difference in NE content between FR and SL diets. However, the digestibility trial showed more limited differences, leading to a SL diet energy value that was 12% lower than expected. This may be due to limited fiber digestion with high-starch diets because of disturbances to the ruminal microbial ecosystem, that is, fewer cellulolytic bacteria and fewer protozoa [START_REF] Dehority | Development of, and natural fluctuations in, ruminal microbial populations[END_REF]), but it is not likely to be due to fat addition, which was too low to impair ruminal fiber digestion [START_REF] Doreau | Effects of linseed lipids fed as rolled seeds, extruded seeds or oil on organic matter and protein digestion in cows[END_REF]. Table 8. Contents in cis and trans C18:1 isomers of rectus abdominis (RA), longissimus thoracis (LT), and semitendinosus (ST) muscles (M) of bulls offered experimental diets (D) 1

Fatty acid Within a row, means without a common superscript differ (P < 0.05).

1 FR: diet composed of 88% concentrate rich in fiber and 12% straw, SL: diet composed of 87% concentrate rich in starch and lipids and 13% straw, SLR: diet composed of 83% concentrate rich in starch and lipids and 17% straw.

2 Coeluted isomers.

The digestibility of the SLR diet was further reduced because of a greater proportion of straw in the diet (18% vs. 13%), but the greater straw intake contributed to limiting the difference in NE g I between the SLR and FR diets. Consequently, when dietary NE was calculated from the results of the digestibility trial, NE g I was lower in SLR bulls than in FR bulls, so the objective of the design was not reached. A time course adaptation of the ruminal microbial ecosystem may be assumed for bulls fed the SL and SLR diets, which may lead to a greater energy value for these diets after a few months of fattening, but that process was impossible to quantify here.

Ad libitum intake was the first evaluation criterion of the diets. Despite the fact that SL diet intake may have been limited by possible digestive discomfort resulting from high-cereal diets [START_REF] Mialon | Effects of the forage-to-concentrate ratio of the diet on feeding behaviour in young Blond d'Aquitaine bulls[END_REF] and by a more friable consistency, ad libitum intakes were high. Conversely, bulls fed the FR diet did not consume enough feed to achieve their growth potential. This result is especially surprising because the bulls were used to consuming the FR concentrate before weaning from as early as 8 wk of age, and the role of learning on food preferences is well known [START_REF] Provenza | Role of learning in food preferences of ruminants: Greenhalgh and Reid revisited[END_REF]. The FR diet probably resulted in a greater ruminal bulk, as suggested by a greater reticulorumen weight, but a physical limitation of intake at the ruminal level is unlikely as the diet was offered as pellets with high digestibility. We can posit that SL concentrate is more palatable than FR concentrate, independent of postingestive consequences [START_REF] Favreau-Peigné | Food sensory characteristics: Their unconsidered roles in the feeding behaviour of domestic ruminants[END_REF]. In a feedlot trial comparing highfiber and high-starch concentrates in 45% forage diets, [START_REF] Mueller | Use of soybean hulls as a replacement for dry rolled corn in beef cattle feedlot receiving diets[END_REF] observed a greater DMI for highfiber diets but similar ME intake between diets and thus a metabolic regulation of intake.

Taken together, the intake differences in NE g and digestible CP were lower than expected between FR bulls and SL or SLR bulls. Actual NE g I did not differ between the FR and SL diets but was lower in the SLR diet than in the FR (by 13%) and SL (by 15%) diets. These treatment differences will thus be discussed together.

Growth, Slaughter Characteristics, and Efficiency

The intake level at a given diet composition (SL vs. SLR) affected growth rates and body and carcass composition, as expected [START_REF] Hoch | A mechanistic dynamic model to estimate beef cattle growth and body composition. I. Model description[END_REF]. Body and carcass weights were decreased at restricted intakes, with leaner carcasses and lower visceral weights (abomasum + intestine + liver). This result is consistent with the results of [START_REF] Sami | Effects of feeding intensity and time on feed on performance, carcass characteristics and meat quality of Simmental bulls[END_REF] for Simmental bulls that were finished on corn silageconcentrate diets and slaughtered at 18 to 19 mo and with knowledge of intake level effects on visceral mass [START_REF] Ortigues | Responses of the splanchnic tissues of ruminants to changes in intake. Absorption of digestion end-products, tissue mass, metabolic activity and implications to whole energy metabolism[END_REF]. The covariance adjustment for differences in fasted BW (data not shown) indicated that differences in visceral mass were due to changes in BW. However, differences in body composition were not due to changes in weight gain but to an increased fat-to-protein gain ratio in the SL diet. The greater dressing percentage with the SL diet is not due to differences in splanchnic organ weight, which tends to be greater for SL diets. Feed efficiency (BWG/NE g ) was significantly improved at restricted intakes, along with the efficiency of digestible N depot as muscle, whereas the efficiency of NE g use for fat depot was not significantly modified, which is in line with [START_REF] Geay | Recommandations alimentaires pour les bovins en croissance et à l´engrais[END_REF]. On these bases, performance comparisons of the FR bulls vs. the SL and SLR bulls should be able to dissociate the impact of the intake level from the impact of the intake composition.

First, the increased fatness of SL (vs. FR) bulls may have stemmed from cumulating factors over the long feeding period (approximately 300 d). The numerically greater energy intake for the SL diet than for the FR diet resulted in a greater weight gain, which was more marked after 126 d of fattening, with a difference of 14.5%. Bulls fed the SL diet may have needed a fairly long period of adaptation to express changes in fat deposition. Break points are known to exist before fat, particularly in intramuscular fat depots, increases [START_REF] Carter | Intramuscular fat deposition in steers is accelerated at a set body weight[END_REF]. Charolais bulls might need to have already achieved most of their growth to efficiently use this starch-and lipids-rich diet and increase their intramuscular fat contents, as was seen in SL muscles.

Strict effects of diet composition could be identified. The most striking differences, interpreted as being due to diet composition, were noted for the proportion of muscle in the carcass and the greater efficiency of digestible N use for muscle depot. Muscle-to-fat ratio was greater for FR vs. SL bulls (4.9 vs. 4.2) at similar muscle-to-bone ratio. This diet composition effect was confirmed after covariance adjusting tissue gain for differences in empty BW (data not shown). Starch supply likely enhances fat gain. At similar metabolizable energy intake, [START_REF] Mueller | Use of soybean hulls as a replacement for dry rolled corn in beef cattle feedlot receiving diets[END_REF] did not find any differences in daily gain between fiber and starch diets. Still, isoenergetic and isonitrogenous high-starch vs. fiber-rich rations that also resulted in similar daily gains and muscle depot induced fatter carcasses with starchy diets in young bulls after 8 mo of fattening [START_REF] Costa | Carcass fat partitioning and meat quality of Alentejana and Barrosa young bulls fed high or low maize silage diets[END_REF]. Increased lipogenesis with starch diets was associated with greater ruminal propionic fermentations and possibly greater starch bypass and greater insulinemia [START_REF] Majdoub | Ryegrassbased diet and barley supplementation: Partition of energyyielding nutrients among splanchnic tissues and hind limbs in finishing lambs[END_REF]. However, [START_REF] Schoonmaker | Effect of source and amount of energy and rate of growth in the growing phase on adipocytes cellularity and lipogenic enzyme activity in the intramuscular and subcutaneous fat depots of Holstein steers[END_REF] also showed that energy source affected hyperplasia, whereas the amount of energy affected hypertrophy of fat tissues, implying that the type of energy affects adiposity when applied in the growing phase. In the present trial, NE g I were similar in the 56-to 196-d period for SL and FR bulls, but the energy source of these diets differed. Increased fatness with the SL diet could thus result from a combination of different energy sources fed from the growing postweaning phase onward and nonsignificant differences in NE g I in the last 70 d of fattening.

Lipid supplementation may influence daily gain, but the literature data do not converge (review by [START_REF] Clinquart | Utilisation des matières grasses chez les bovins à l´engraissement[END_REF]. When lipid supplementation using linseed does not result in changes in DMI but increases energy intake, daily gain is either increased [START_REF] Maddock | Effect of processing flax in beef feedlot diets on performance, carcass characteristics, and trained sensory panel ratings[END_REF] or unchanged [START_REF] Bartoň | Growth performance and fatty acid profiles of intramuscular and subcutaneous fat from Limousin and Charolais heifers fed extruded linseed[END_REF]. The greater fat content in SL bulls than in FR bulls may be due to lipid supply in addition to starch. The positive effect of dietary lipids on fat percentage in carcasses is frequently observed [START_REF] Clinquart | Utilisation des matières grasses chez les bovins à l´engraissement[END_REF] but not systematically reproduced [START_REF] Corazzin | Effect of whole linseed addition on meat production and quality of Italian Simmental and Holstein young bulls[END_REF]. In addition, linseed may have improved feed efficiency, as shown by [START_REF] Maddock | Effect of processing flax in beef feedlot diets on performance, carcass characteristics, and trained sensory panel ratings[END_REF], and protein deposition efficiency, thereby increasing the amount of energy to be deposited as fat. Indeed, in growing steers, omega-3 LCFA, which are present in linseed-containing diets, were shown to potentiate the effect of insulin on protein metabolism via the mammalian target of rapamycin (mTOR) signaling pathway and to reduce amino acid oxidation [START_REF] Gingras | Long-chain omega-3 fatty acids regulate bovine whole-body protein metabolism by promoting muscle insulin signaling to the AKt-mTor-S6K1 pathway and insulin sensitivity[END_REF].

Interestingly, the efficiency of utilization of digestible N for muscle depot was greater for the FR diet than for the SL and SLR diets, despite a greater visceral mass. This effect could be strictly attributed to differences in diet composition and/or digestibility. This pattern is opposite that of the efficiency of CP transfer into milk, which is increased by high-starch diets [START_REF] Cantalapiedra-Hijar | Dietary carbohydrate composition modifies the milk N efficiency in late lactation cows fed low crude protein diets[END_REF].

Metabolic Indicators

On a metabolic basis, a better use of nutrients can be achieved either by changes in weights of tissue or organs or by changes in the specific metabolic activity of each tissue or organ (see reviews by [START_REF] Ortigues | Whole-body fuel selection in ruminants: Nutrient supply and utilization by major tissues[END_REF] and [START_REF] Hocquette | Responses to nutrients in farm animals: Implications for production and quality[END_REF]). Genetic selection on residual feed intake (an indicator of feed efficiency) has been shown to regulate the activities of enzymes involved in FA and glucose metabolisms in the liver and in muscle tissue [START_REF] Naou | Metabolic changes and tissue responses to selection on residual feed intake in growing pigs[END_REF][START_REF] Faure | Consequences of divergent selection for residual feed intake in pigs on muscle energy metabolism and meat quality[END_REF]. Here, where gross feed efficiency (BWG/NE g ) and partial efficiency of NE g use for fat depot differed between FR and SL treatments, we hypothesized differences in muscle and liver energy metabolism activity between the SL and FR bulls. In fact, we observed no difference in specific metabolic activity in the liver and a difference in LDH activity expressed per gram of tissue in only muscles. These limited differences may be explained by several reasons: a difference in the efficiency of muscle or fat gain (<20% between SL and FR diets) that was not sufficient to alter metabolic activity, changes in other metabolic pathways (such as protein metabolism) not assessed here, and the implication of other biological mechanisms. However, note that the first enzyme to be regulated is LDH, as reported in pigs (Le [START_REF] Naou | Metabolic changes and tissue responses to selection on residual feed intake in growing pigs[END_REF]. Lactate dehydrogenase plays a pivotal role in the cross talk between skeletal muscle (conversion of glucose into lactate) and liver (neosynthesis of glucose from lactate), and thus an increased Cori cycle has been associated with lower feed efficiency (Le [START_REF] Naou | Metabolic changes and tissue responses to selection on residual feed intake in growing pigs[END_REF]. Another potential mechanism that probably regulates feed efficiency is the lower weight of the empty digestive tract for the SL diet than for the FR diet, which results from a lower fiber intake [START_REF] Fitzsimons | Visceral organ weights, digestion and carcass characteristics of beef bulls differing in residual feed intake offered a high concentrate diet[END_REF].

Effect of Energy Source on Muscle Fatty Acid Composition

Improving the nutritional quality of beef is a key challenge for the beef industry. Despite extensive hydrogenation of dietary FA in the rumen, nutritional quality can still be enhanced, especially by a greater deposition of n-3 PUFA in muscles to give a greater n-3/n-6 ratio in meat (see reviews by [START_REF] Wood | Fat deposition, fatty acid composition and meat quality: A review[END_REF] and [START_REF] Doreau | Enhancing fatty acid composition of milk and meat through animal feeding[END_REF]). Here, we report the first evidence of significant effects of muscle type and diet factors on beef total lipids and FA composition in finished cattle in which nutritional conditions varied by the level and chemical nature of dietary energy. Indeed, data reported in the literature on variations of beef lipid and FA characteristics with nutritional factors have mainly concerned the effects of basal diet, especially between grass-fed and concentrate-fed diets differing in n-6/n-3 ratio [START_REF] Dannenberger | Effect of diet on the deposition of n-3 fatty acids, conjugated linoleic-and C18:1 trans fatty acid isomers in muscle lipids of German Holstein bulls[END_REF][START_REF] Aldai | Length of concentrate finishing affects the fatty acid composition of grassfed and genetically lean beef: An emphasis on trans-18:1 and conjugated linoleic acid profiles[END_REF] and dietary lipid supplements [START_REF] Raes | Effect of dietary fatty acids on incorporation of long chain polyunsaturated fatty acids and conjugated linoleic acid in lamb, beef and pork: A review[END_REF][START_REF] Bauchart | Effects of diets supplemented with oil seeds and vitamin E on specific fatty acids of Rectus abdominis muscle in charolais fattening bulls[END_REF][START_REF] Herdmann | Effect of dietary n-3 and n-6 PUFA on lipid composition of different tissues of German Holstein bulls and the fate of bioactive fatty acids during processing[END_REF].

The greater total lipid and FA contents in LT and RA muscles than in ST muscle irrespective of dietary energy characteristics confirmed previous data comparing the nutritional qualities of 9 types of muscles from finishing Charolais cattle [START_REF] Bauchart | Qualités nutritionnelles de la viande et des abats chez le bovin: Données récentes sur les principaux constituants d'intérêt nutritionnel[END_REF]. The very significant stimulatory effect of the high dietary energy level on muscle lipid deposition, noted in all studied muscles, has never previously been reported in the bovine species. In contrast, there was a lack of effect of the chemical nature of ingredients (fiber of the FR diet and linseed oil of the SLR diet made isoenergetic to a lower-energy diet) on muscle lipid deposition (noted in all studied muscles), as previ-ously reported in cattle given lipid-supplemented diets [START_REF] Bartoň | Growth performance and fatty acid profiles of intramuscular and subcutaneous fat from Limousin and Charolais heifers fed extruded linseed[END_REF][START_REF] Herdmann | Effect of dietary n-3 and n-6 PUFA on lipid composition of different tissues of German Holstein bulls and the fate of bioactive fatty acids during processing[END_REF].

The greater deposition of lipids and of FA observed in muscles of bulls given the SL diet, which was greater in energy, would be explained by a stimulation of lipogenic pathways in intra-and intermuscular adipocytes. The hypothesis of this kind of lipogenic effect was confirmed by the greater contents, in muscle cells, of saturated and monounsaturated FA known to be synthesized preferentially by such adipose cells. On the other hand, the greater deposition of linolenic acid at the expense of linoleic acid in muscles of bulls given linolenic acidrich linseed clearly confirms the capacity of muscle cells to incorporate this dietary n-3 PUFA in their lipids, as reported earlier [START_REF] Noci | The fatty acid composition of muscle fat and subcutaneous adipose tissue of grazing heifers supplemented with plant oilenriched concentrates[END_REF], thus improving the health value of beef lipids for human consumers.

The intensity of conversion of dietary linolenic acid into n-3 long-chain PUFA by reactions of elongation and desaturation in hepatic cells and their subsequent tissue deposition is evaluated by determining EPA, DPA, and DHA contents in muscle cells. Our results clearly showed that EPA, DPA, and DHA were efficiently produced and deposited in muscle tissues, especially in lean (ST) muscle, in finishing bulls given linseed-supplemented diets (SL and SLR diets), thus confirming previous data in meat cattle given different sources of linolenic acid (see [START_REF] Dannenberger | Effect of diet on the deposition of n-3 fatty acids, conjugated linoleic-and C18:1 trans fatty acid isomers in muscle lipids of German Holstein bulls[END_REF], [START_REF] Maddock | Effect of processing flax in beef feedlot diets on performance, carcass characteristics, and trained sensory panel ratings[END_REF][START_REF] Herdmann | Effect of dietary n-3 and n-6 PUFA on lipid composition of different tissues of German Holstein bulls and the fate of bioactive fatty acids during processing[END_REF] for EPA, DPA, and DHA; see [START_REF] Bartoň | Growth performance and fatty acid profiles of intramuscular and subcutaneous fat from Limousin and Charolais heifers fed extruded linseed[END_REF] for only EPA and DPA). However, DHA content remained low, showing the low extent of the last desaturation step, which may be due to the low activity of Δ4-desaturase and to competition between DHA and other LCFA for incorporation in phospholipids [START_REF] Raes | Effect of dietary fatty acids on incorporation of long chain polyunsaturated fatty acids and conjugated linoleic acid in lamb, beef and pork: A review[END_REF]. Additionally, we demonstrate, for the first time, that such metabolic conversion of linolenic acid into LC n-3 PUFA is not dietary energy dependent because the greatest muscle deposition of DHA was still observed in bulls fed the energy-restricted SLR diet.

Compared to the FR diet, the SL diet increased the amount of total and all individual cis and trans isomers (except trans-6 18:1 to trans-8 18:1) in all muscles. However, isomer proportions changed: among trans isomers, the coelution of trans-10 18:1 and trans-11 18:1 increased, whereas trans-12 to trans-16 isomers decreased (data not shown). This result is probably due to linolenic acid supply, which has been shown to increase trans-12 18:1 to trans-16 18:1 isomers at the expense of trans-9 18:1 and trans-10 18:1 isomers in bulls fed grass [START_REF] Dannenberger | Effect of diet on the deposition of n-3 fatty acids, conjugated linoleic-and C18:1 trans fatty acid isomers in muscle lipids of German Holstein bulls[END_REF] and in culled cows fed linseed [START_REF] Habeanu | Extruded linseed and rapeseed both influenced fatty acid composition of total lipids and their polar and neutral fractions in longissimus thoracis and semitendinosus muscles of finishing Normand cows[END_REF] compared with animals fed cereal diets. In our trial, trans-9 18:1 did not change, perhaps because of the opposing effects of cereals and linseed.

Conclusion

One of the novelties of this study was to separate the effects of the source and level of energy intake on fattening performance and carcass responses in bull production. This study compared 2 concentrates differing by the source of energy, based on a mixture of starch and linseed or on fibrous byproducts, and also by the level of energy. Results show that it is possible to modulate performance and meat quality by changing the source of energy in ad libitum-fed diets. Feed efficiency was significantly improved at restricted energy intakes. High dietary energy level increased muscle FA deposition. As expected, the muscle omega-3 FA content was increased by including feeds rich in omega-3 FA, especially in lean (ST) muscle, independent of the dietary energy level.

LITERATURE CITED

3Σ

  SFA = sum of even-and odd-chain SFA from 12 to 24 C: 12:0 + 13:0 + 14:0 + 15:0 + 16:0 + 17:0 + 18:0 + 20:0 + 21:0 + 22:0 + 23:0 + 24:0; Σ cis-MUFA = cis-14:1 n-5 + cis-15:1 n-6 + cis-16:1 n-7 + cis-17:1 n-8 +Σ cis-18:1 + cis-20:1 n-11; Σ trans-MUFA = Σ trans-16:1 + Σ trans-18:1; Σ MUFA = Σ cis-MUFA + Σ trans-MUFA; Σ PUFA n-6 = trans,trans-18:2 n-6 + trans,cis-18:2 n-6+ cis,trans-18:2 n-6 + cis,cis-18:2 n-6 + 18:3 n-6 + 20:2 n-6+ 20:3 n-6 + 20:4 n-6 + 22:2 n-6 + 22:4 n-6 + 22:5 n-6; Σ PUFA n-3 = 18:3 n-3 + 20:3 n-3 + 20:4 n-3 + 20:5 n-3 + 22:3 n-3 + 22:4 n-3 + 22:5 n-3 + 22:6 n-3; Σ PUFA = Σ PUFA n-6 + Σ PUFA n-3 + Σ CLA + Σ conjugated PUFA.

Table 1 .

 1 Ingredient, measured chemical composition, and tabulated energy content of the experimental diets 1

			Diet 2
	Item	FR	SL 3	SLR 3
	Straw-to-concentrate ratio (DM basis)	12:88	13:87	18:82
	Chemical composition, g/kg DM
	OM	806	828	829
	NDF	406	249	269
	ADF	227	140	154
	Starch	70	297	282
	Crude protein	145	179	171
	Ether extract	25	41	39
	GE, MJ/kg DM	18.9	19.7	19.6
	NE, 4 MJ/kg DM	6.05	7.32	7.04

Table 2 .

 2 Feed intake and digestibility of the experimental diets measured in dry cows

			Diet 1		Diet P-
	Item	FR	SL	SEM	value
	Feed intake, kg DM/d	9.86	7.81	0.011	<0.001
	Digestibility, %
	DM	71.5	75.9	0.88	<0.001
	OM	69.7	75.2	0.92	<0.001
	NDF	66.0	48.4	1.65	<0.001
	ADF	57.7	44.1	1.73	<0.001
	CP	60.5	79.5	1.12	<0.001
	GE	71.0	77.5	0.93	<0.001

Table 3 .

 3 Feed intake, growth performance, and feed efficiency ratio for bulls offered the experimental diets during 196-d fattening

			Diet 1			Diet		Contrast
	Item	FR	SL	SLR	SEM 2	P-value	FR vs. SL	FR vs. SLR	SL vs. SLR
	Number of animals	53	50	26
	Initial BW, kg	339	337	341	5.6	0.824	0.723	0.909	0.541
	Final BW, kg	649	666	639	9.6	0.168	0.083	0.483	0.159
	Feed intake, kg DM/d
	d 0 to 56	8.08	7.52	5.93	0.173	<0.001	0.002	<0.001	<0.001
	d 56 to 126	10.94	9.49	8.68	0.234	<0.001	<0.001	<0.001	<0.001
	d 126 to 196	11.79	10.61	9.64	0.234	<0.001	<0.001	<0.001	<0.001
	d 0 to 196	10.31	9.24	8.16	0.185	<0.001	<0.001	<0.001	<0.001
	NE g intake, MJ/d 3
	d 0 to 56	53.81	57.01	44.00	1.251	<0.001	0.013	<0.001	<0.001
	d 56 to 126	72.81	71.88	63.08	1.706	<0.001	0.590	0.001	<0.001
	d 126 to 196	78.47	80.48	70.16	1.663	<0.001	0.234	<0.001	<0.001
	d 0 to 196	68.68	70.03	59.46	1.333	<0.001	0.320	<0.001	<0.001
	CP intake, kg/d	1.50	1.65	1.39	0.031	<0.001	<0.001	0.023	<0.001
	BW gain, g/d
	d 0 to 56	1,470	1,537	1,289	53.7	<0.001	0.220	0.020	<0.001
	d 56 to 126	1,784	1,786	1,796	47.8	0.812	0.958	0.866	0.575
	d 126 to 196	1,478	1,692	1,290	51.4	<0.001	<0.001	0.012	<0.001
	d 0 to 196	1,585	1,682	1,471	33.8	<0.001	0.006	0.020	<0.001
	Feed efficiency, g BW gain/MJ NE g
	d 0 to 56	27.4	26.9	29.3	0.78	0.089	0.535	0.089	0.030
	d 56 to 126	24.6	25.1	28.6	0.69	<0.001	0.435	<0.001	<0.001
	d 126 to 196	18.8	21.1	18.4	0.63	0.003	<0.001	0.669	0.071
	d 0 to 196	23.1	24.1	24.9	0.44	<0.001	0.025	0.006	0.010

Table 4 .

 4 Carcass characteristics for bulls offered the experimental diets

			Diet 1			Diet		Contrast
	Item	FR	SL	SLR	SEM 2	P-value	FR vs. SL	FR vs. SLR	SL vs. SLR
	Number of animals	50	47	26
	BW at slaughter, kg	709	732	687	9.7	0.002	0.039	0.130	<0.001
	Age at slaughter, d	540	537	532	1.7	0.002	0.067	0.006	0.051
	Empty BW, kg	625	661	602	9.1	<0.001	<0.001	0.118	<0.001
	HCW, kg	426	453	414	6.7	<0.001	<0.001	0.254	<0.001
	Cold carcass weight, % BW	57.4	59.0	57.8	0.30	< 0.001	<0.001	0.271	0.002
	Carcass composition, 3 %
	Muscle	71.3	69.6	71.7	0.34	<0.001	<0.001	0.922	<0.001
	Fat	14.8	17.0	14.2	0.36	<0.001	<0.001	0.446	<0.001
	Bone	14.2	13.6	14.4	0.12	<0.001	<0.001	0.136	<0.001
	Carcass composition 3 , kg
	Muscle	304	315	297	5.0	0.012	0.044	0.254	0.004
	Fat	61.7	75.6	57.5	2.00	<0.001	<0.001	0.106	<0.001
	Bone	60.4	61.8	59.4	0.85	0.086	0.161	0.335	0.031
	Muscle-to-fat ratio	4.84	4.23	5.07	0.136	<0.001	<0.001	0.406	<0.001
	Internal fat, kg	18.5	26.0	15.9	1.18	<0.001	<0.001	0.212	<0.001
	Organ weight, kg
	Empty digestive tract	34.8	31.9	30.6	8.45	<0.001	<0.001	<0.001	0.089
	Reticulorumen	13.5	11.2	10.6	0.33	< 0.001	<0.001	<0.001	0.151
	Omasum	5.22	3.84	4.06	0.201	<0.001	<0.001	<0.001	0.391
	Abomasum	2.16	2.20	1.96	0.064	0.012	0.550	0.044	0.004
	Intestines	14.0	14.7	13.9	0.28	0.042	0.029	0.476	0.036
	Liver	6.53	6.69	6.35	0.137	0.156	0.292	0.413	0.056
	Energetic efficiency, g/MJ
	Muscle/NE g	17.48	17.82	21.59	0.343	<0.001	0.379	<0.001	<0.001
	Fat/NE g	3.63	4.29	4.32	0.089	<0.001	<0.001	<0.001	0.803
	Protein efficiency, g/kg
	Muscle/digestible CP	1,312	940	1,086	20.2	<0.001	<0.001	<0.001	<0.001
	Fat/digestible CP	273	226	217	5.1	<0.001	<0.001	<0.001	0.168

Table 5 .

 5 LDH, PFK, and COX enzyme activities in liver for bulls offered the FR (n = 22) and SL (n = 21) diets 1

		Diet 2			Diet
	Item	FR	SL	SEM	P-value
	Activity, μmol•min -1 •g liver -1
	LDH	57.5	62.7	2.4	0.138
	PFK	3.12	2.96	0.13	0.405
	COX	48.9	48.1	2.26	0.806
	Activity, μmol•min -1 •g protein -1
	LDH	313	334	15.0	0.324
	PFK	17.0	15.8	0.78	0.297
	COX	265	258	13.4	0.704
	Protein, g/kg liver	185	189	3.4	0.503
	COX/LDH, %	86.9	77.3	4.60	0.150

Table 6 .

 6 LDH, PFK, and COX enzyme activities in longissimus thoracis (LT) and semitendinosus (ST) and muscles (M) for bulls offered the FR (n = 22) and SL (n = 21) diets (D) 1

			Diet and muscle 2
		FR		SL				P-value
	Item	LT	ST	LT	ST	SEM	M	D	M × D
	Activity, μmol•min -1 •g muscle -1
	LDH	1,019	1,014	1,070	1,035	12.7	0.267	0.047	0.413
	PFK	127	108	135	122	5.0	0.029	0.115	0.663
	COX	12.4 a	9.8 b	11.5 a,b	11.3 a,b	0.38	0.015	0.663	0.032
	Activity, μmol•min -1 •g protein -1
	LDH	4,719	4,980	4,911	4,933	65.9	0.138	0.442	0.207
	PFK	588	529	621	584	24.6	0.172	0.212	0.750
	COX	57.7	48.4	52.8	53.4	1.84	0.103	0.978	0.063
	Protein, g/kg muscle	216	204	218	211	1.8	<0.001	0.071	0.334
	COX/LDH, %	1.23 a	0.97 b	1.08 a,b	1.09 a,b	0.038	0.030	0.814	0.016
	a,b Within a row, means without a common superscript differ (P < 0.05).
	1 Lactate dehydrogenase (LDH), phosphofructokinase (PFK), and cytochrome c oxidase (COX).
	2 FR: diet composed of 88% concentrate rich in fiber and 12% straw, SL: diet composed of 87% concentrate rich in starch and lipids and 13% straw.

Table 7 .

 7 Total lipids and total fatty acids (FA) and individual FA and FA classes in rectus abdominis (RA), longissimus thoracis (LT), and semitendinosus (ST) muscles (M) from bulls fed experimental diets

	Diet and muscle 1
	Item

FR: diet composed of 88% concentrate rich in fiber and 12% straw, SL: diet composed of 87% concentrate rich in starch and lipids and 13% straw, SLR: diet composed of 83% concentrate rich in starch and lipids and 17% straw.

Ingredient composition of the concentrate (g/kg DM): dehydrated alfalfa, 224; wheat bran, 219; cereal middlings, 184; dehydrated beet pulp, 212; rapeseed meal

, 35; barley, 25; palm kernel meal, 40; molasses, 30; mineral-vitamin premix, 8; magnesium oxide, 10; dicalcium phosphate, 6; sodium chloride, 6. 3 Ingredient composition of the concentrate (g/kg DM): maize, 280; barley, 98; oats, 86; maize bran, 30; extruded mixture (50% linseed, 30% wheat bran, 20% sunflower meal), 120; soybean meal, 20; dehydrated beet pulp, 60; rapeseed meal, 214; molasses, 70; urea, 4; mineral-vitamin premix, 5; calcium carbonate, 10; sodium bicarbonate, 3.4 Calculated from feed tables(INRA, 2007).

FR: diet composed of 88% concentrate rich in fiber and 12% straw, SL: diet composed of 87% concentrate rich in starch and lipids and 13% straw.

FR: diet composed of 88% concentrate rich in fiber and 12% straw, SL: diet composed of 87% concentrate rich in starch and lipids and 13% straw, SLR: diet composed of 83% concentrate rich in starch and lipids and 17% straw.

SEM was calculated with n = 26.

Net energy for gain measured from digestibility data.

FR: diet composed of 88% concentrate rich in fiber and 12% straw, SL: diet composed of 87% concentrate rich in starch and lipids and 13% straw, SLR diet composed of 83% concentrate rich in starch and lipids and 17% straw.

SEM was calculated with n = 26.

Estimated from sixth rib composition obtained by dissection. Fat weight is the sum of internal, subcutaneous and intermuscular fat weights.

Lactate dehydrogenase (LDH), phosphofructokinase (PFK), and cytochrome c oxidase (COX).

2 FR: diet composed of 88% concentrate rich in fiber and 12% straw, SL: diet composed of 87% concentrate rich in starch and lipids and 13% straw.

1 This experiment was funded by McKey Food Services (Fleuryles-Aubrais, France), Valorex (Combourtillé, France), and the regional council of the French Centre region. The authors greatly thank the staff of INRA unit UE232 for animal care and data collection and the staff of INRA unit UMR1213 experimental farm and slaughterhouse for animal transport and care, slaughter, and data collection.