David Allouche

Sophie Barbe
email: sophie.barbe@insa-toulouse.fr

Simon De Givry

George Katsirelos

Yahia Lebbah
email: ylebbah@gmail.com

Samir Loudni
email: samir.loudni@unicaen.fr

Abdelkader Ouali
email: abdelkader.ouali@inria.fr

Thomas Schiex

David Simoncini
email: david.simoncini@ut-capitole.fr

Matthias Zytnicki

Loudni Samir

Greyc

Cost Function Networks to Solve Large Computational Protein Design Problems

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

Introduction

A protein is a sequence of basic building blocks called amino acids. There are 20 natural amino acids. Proteins are involved in nearly all structural, catalytic, sensory, and regulatory functions of living systems [START_REF] Fersht | Structure and mechanism in protein science: a guide to enzyme catalysis and protein folding[END_REF]. Performing these functions generally requires that proteins are assembled into well-defined three-dimensional structures specified by their amino acid sequence. Over millions of years, natural evolutionary processes have shaped and created proteins with novel structures and functions by means of sequence variations, including mutations, recombinations and duplications.

Protein engineering techniques coupled with high-throughput automated procedures make it possible to mimic the evolutionary process on a greatly accelerated timescale, and thus increase the odds to identify the proteins of interest for technological uses [START_REF] Peisajovich | Protein engineers turned evolutionists[END_REF]. This holds great interest for medicine, synthetic biology, nanotechnologies and biotechnologies [START_REF] Nestl | Recent progress in industrial biocatalysis[END_REF][START_REF] Pleiss | Protein design in metabolic engineering and synthetic biology[END_REF][START_REF] Grunwald | Mimicking biopolymers on a molecular scale: nano(bio)technology based on engineered proteins[END_REF]. In particular, protein engineering has become a key technology to generate tailored enzymes able to perform novel specific transformations under specific conditions. Such biochemical transformations enable to access a large repertoire of small molecules for various applications such as biofuels, chemical feedstocks and therapeutics [START_REF] Khalil | Synthetic biology: applications come of age[END_REF]8]. The development of enzymes with required substrate selectivity, specificity and stability can also be profitable to overcome some of the difficulties encountered in synthetic chemistry. In this field, the in vitro use of artificial enzymes in combination with organic chemistry has led to innovative and efficient routes for the production of high value molecules while meeting the increasing demand for ecofriendly processes [START_REF] Lewis | Chemoenzymatic elaboration of monosaccharides using engineered cytochrome p450bm3 demethylases[END_REF][START_REF] Champion | Design of α-transglucosidases of controlled specificity for programmed chemoenzymatic synthesis of antigenic oligosaccharides[END_REF][START_REF] Verges | Computer-aided engineering of a transglycosylase for the glucosylation of an unnatural disaccharide of relevance for bacterial antigen synthesis[END_REF]. Nowadays, protein engineering is also being explored to create non-natural enzymes that can be combined in vivo with existing biosynthetic pathways, or be used to create entirely new synthetic metabolic pathways not found in nature to access novel (bio)chemical products [START_REF] Fritz | Biology by design: from top to bottom and back[END_REF]. These latest approaches are central to the development of synthetic biology. One significant example in this field is the full-scale production of the antimalarial drug (artemisinin) from the engineered bacteria Escherichia coli [START_REF] Martin | Engineering a mevalonate pathway in escherichia coli for production of terpenoids[END_REF].

With a choice among 20 naturally occurring amino acids at every position, the size of the combinatorial sequence space is out of reach for current experimental methods, even for short sequences. Computational protein design (CPD) methods therefore try to intelligently guide the protein design process by producing a collection of proteins, that is rich in functional proteins, but small enough to be experimentally evaluated. The challenge of choosing a sequence of amino acids to perform a given task is formulated as an optimization problem, solvable computationally. It is often described as the inverse problem of protein folding [START_REF] Pabo | Molecular technology. Designing proteins and peptides[END_REF]: the three-dimensional structure is known and we have to find amino acid sequences that fold into it. It can also be considered as a highly combinatorial variant of side-chain positioning [START_REF] Swain | A CLP approach to the protein side-chain placement problem[END_REF] because of possible amino acid mutations.

Various computational methods have been proposed over the years to solve this problem and several success stories have demonstrated the outstanding potential of CPD methods to engineer proteins with improved or novel properties. CPD has been successfully applied to increase protein thermostability and solubility; to alter specificity towards some other molecules; and to design various binding sites and construct de novo enzymes (see for example [START_REF] Khare | Computational redesign of a mononuclear zinc metalloenzyme for organophosphate hydrolysis[END_REF]).

Despite these significant advances, CPD methods must still mature in order to better guide and accelerate the construction of tailored proteins. In particular, more efficient computational optimization techniques are needed to explore the vast combinatorial space, and to facilitate the incorporation of more realistic, flexible protein models. These methods need to be capable of not only identifying the optimal model, but also of enumerating solutions close to the optimum [START_REF] Traoré | Fast search algorithms for computational protein design[END_REF].

We begin by defining the CPD problem with rigid backbone, and then introduce the approach commonly used in structural biology to exactly solve CPD. This ap-proach relies on dead-end elimination (DEE), a specific form of dominance analysis that was introduced in [START_REF] Desmet | The dead-end elimination theorem and its use in protein side-chain positioning[END_REF], and later strengthened in [START_REF] Goldstein | Efficient rotamer elimination applied to protein side-chains and related spin glasses[END_REF]. If this polynomial-time analysis does not solve the problem, an A * algorithm is used to identify an optimal protein design.

We observe that the rigid backbone CPD problem can be naturally expressed as a Cost Function Network (CFN) and solved as a Weighted Constraint Satisfaction Problem. In this context, DEE is similar to neighborhood substitutability [START_REF] Freuder | Eliminating interchangeable values in constraint satisfaction problems[END_REF][START_REF] Lecoutre | WCSP integration of soft neighborhood substitutability[END_REF][START_REF] De Givry | Dead-End Elimination for Weighted CSP[END_REF].

To evaluate the efficiency of the CFN approach, we model the CPD problem using different combinatorial optimization formalisms. We compare the performance of the 0/1 linear programming solver cplex, and the CFN solver toulbar2, against that of a well-established CPD approach implementing DEE/A * , on various realistic protein design problems. We observe drastic differences in the difficulty that these instances represent for different solvers, despite often closely related models and solving techniques.

The Computational Protein Design approach

A protein is a sequence of organic compounds called amino acids. Each of the 20 amino acids consists of a common peptidic core and a side chain with varying chemical properties (see Figure 1). In a protein, amino acid cores are linked together in sequence to form the backbone of the protein. In water, most proteins of interest fold into a 3D shape that is determined by the sequence of amino acids. Depending upon the amino acid considered, the side chain of each individual amino acid can be rotated along up to 4 dihedral angles relative to the backbone. Anfinsen's postulated [4] that the 3D structure of a protein is entirely defined by its sequence. This structure, defined by the backbone's structure and all side-chain rotations, is called the conformation of the protein and determines its chemical reactivity and biological function.

Fig. 1 A representation of how amino acids, carrying specific side chains R and R , can link together through their core to form a chain (modified from wikipedia). One molecule of water is generated in the process.

Computational Protein Design is faced with several challenges. The first lies in the exponential size of the conformational and protein sequence space that has to be explored, which rapidly grows out of reach of computational approaches. Another obstacle to overcome is the accurate structure prediction for a given sequence [START_REF] Khoury | Protein folding and de novo protein design for biotechnological applications[END_REF][START_REF] Gront | Generalized fragment picking in rosetta: design, protocols and applications[END_REF]. Therefore, the design problem is usually approached as an inverse folding problem [START_REF] Pabo | Molecular technology. Designing proteins and peptides[END_REF], in order to reduce the problem to the identification of an amino acid sequence that can fold into a target 3D-scaffold that matches the design objective [6]. In structural biology, the stability of a conformation can be directly evaluated through the energy of the conformation, a stable fold being of minimum energy [4].

In CPD, two approximations are common. First, it is assumed that the resulting designed protein retains the overall fold of the chosen scaffold: the protein backbone is considered fixed. At specific positions chosen automatically or by the molecular modeler, the amino acid used can be modified, thus changing the side chain as shown in Fig. 2. Second, the domain of conformations available to each amino acid side chain is continuous. This continuous domain is approximated using a set of discrete conformations defined by the value of their inner dihedral angles. These conformations, or rotamers [START_REF] Janin | Conformation of amino acid side-chains in proteins[END_REF], are derived from the most frequent conformations in the experimental repository of known protein structures, the PDB (Protein Data Bank, www.pdb.org). Different discretizations have been used in constraint-based approaches to protein structure prediction [7]. More recently, continuous optimization of dihedrals has been addressed in some limited settings [START_REF] Hallen | Dead-end elimination with perturbations (deeper): A provable protein design algorithm with continuous sidechain and backbone flexibility[END_REF][START_REF] Friesen | Recursive decomposition for nonconvex optimization[END_REF].

The CPD is then formulated as the problem of identifying a conformation of minimum energy via the mutation of a specific subset of amino acid residues, i.e. by affecting their identity and their 3D orientations (rotamers). The conformation that minimizes the energy is called the GMEC (Global Minimum Energy Conformation).

In order to solve this problem, we need a computationally tractable energetic model to evaluate the energy of any combination of rotamers. We also require computational optimization techniques that can efficiently explore the sequenceconformation space to find the sequence-conformation model of global minimum energy.

Energy functions

Various energy functions have been defined to make the energy computation manageable [5]. These energy functions include non-bonded terms such as van der Waals and electrostatics terms, often in conjunction with empirical contributions describing hydrogen bonds. The surrounding solvent effect is generally treated implicitly as a continuum. Statistical terms may be added in order to approximate the effect of mutations on the unfolded state or the contribution of conformational entropy. Finally, collisions between atoms (steric clashes) are also taken into account. We have used two state-of-the-art energy functions, AMBER9 [9] and Talaris2014 [START_REF] O'meara | A combined covalent-electrostatic model of hydrogen bonding improves structure prediction with rosetta[END_REF], respectively implemented in the CPD dedicated tools osprey 2.0 [START_REF] Gainza | Osprey: Protein design with ensembles, flexibility, and provable algorithms[END_REF] and Rosetta Molecular Modeling suite 3 [START_REF] Leaver-Fay | Rosetta3: an object-oriented software suite for the simulation and design of macromolecules[END_REF].

These energy functions are formulated in such a way that the terms are locally decomposable. Then, the energy of a given protein conformation, defined by a choice of one specific amino acid with an associated conformation (rotamer) for each residue, can be written as:

E = E + i E(i r ) + i j>i E(i r , j s ) (1)
where E is the potential energy of the protein, E is a constant energy contribution capturing interactions between fixed parts of the model, E(i r ) is the energy contribution of rotamer r at position i capturing internal interactions (and a reference energy for the associated amino acid) or interactions with fixed regions, and E(i r , j s ) is the pairwise interaction energy between rotamer r at position i and rotamer s at position j [START_REF] Desmet | The dead-end elimination theorem and its use in protein side-chain positioning[END_REF]. This decomposition brings two properties:

• Each term in the energy can be computed for each amino acid/rotamer (or pair for E(i r , j s )) independently. • These energy terms, in kcal/mol, can be precomputed and cached, allowing to quickly compute the energy of a design once a specific rotamer (an amino acid-conformation pairing) has been chosen at each non-rigid position.

The rigid backbone discrete rotamer CPD problem is therefore defined by a fixed backbone with a corresponding set of positions (residues), a rotamer library and a set of energy functions. Each position i of the backbone is associated with a subset D i of all (amino-acid,rotamer) pairs in the library. The problem is to identify at each position i a pair from D i such that the overall energy E is minimized. In practice, based on expert knowledge or on specific design protocols, each position can be fixed (D i is a singleton), flexible (all pairs in D i have the same amino-acid) or mutable (the general situation).

Exact CPD methods

The protein design problem as defined above, with a rigid backbone, a discrete set of rotamers, and pairwise energy functions has been proven to be NP-hard [START_REF] Pierce | Protein design is NP-hard[END_REF]. Hence, a variety of meta-heuristics have been applied to it, including Monte Carlo simulated annealing [START_REF] Kuhlman | Native protein sequences are close to optimal for their structures[END_REF], genetic algorithms [START_REF] Raha | Prediction of amino acid sequence from structure[END_REF][START_REF] Chowdry | An object-oriented library for computational protein design[END_REF], variable neighborhood search [START_REF] Charpentier | Variable neighborhood search with cost function networks to solve large computational protein design problems[END_REF], and other algorithms [START_REF] Desmet | Fast and accurate side-chain topology and energy refinement (FASTER) as a new method for protein structure optimization[END_REF]. The main weakness of these approaches is that they may remain stuck in local minima and miss the GMEC without notice.

However, there are several important motivations for solving the CPD problem exactly. First, because they know when an optimum is reached, exact methods may stop before meta-heuristics. Voigt et al. [START_REF] Voigt | Trading accuracy for speed: A quantitative comparison of search algorithms in protein sequence design[END_REF] reported that the accuracy of metaheuristics also degrades as problem size increases. More importantly, the use of exact search algorithms is important in the usual experimental design cycle, that goes through modeling, solving, protein synthesis, and experimental evaluation: when unexpected experimental results are obtained, the only possible culprit lies in the CPD model and not in the algorithm.

Usual exact methods for CPD mainly rely on the dead-end elimination (DEE) theorem [START_REF] Desmet | The dead-end elimination theorem and its use in protein side-chain positioning[END_REF][START_REF] Dahiyat | Protein design automation[END_REF] and the A * algorithm [START_REF] Leach | Exploring the conformational space of protein side chains using dead-end elimination and the A* algorithm[END_REF][START_REF] Georgiev | The minimized dead-end elimination criterion and its application to protein redesign in a hybrid scoring and search algorithm for computing partition functions over molecular ensembles[END_REF]. DEE is used as a pre-processing technique and removes rotamers that are locally dominated by other rotamers, until a fixpoint is reached. The rotamer r at position i (denoted by i r ) is removed if there exists another rotamer u at the same position such that [START_REF] Desmet | The dead-end elimination theorem and its use in protein side-chain positioning[END_REF]:

E(i r ) + j i min s E(i r , j s ) ≥ E(i u ) + j i max s E(i u , j s ) (2)
This condition guarantees that for any conformation with this r, we get a conformation with lower energy if we substitute u for r. Then, r can be removed from the list of possible rotamers at position i. This local dominance criterion was later improved by Goldstein [START_REF] Goldstein | Efficient rotamer elimination applied to protein side-chains and related spin glasses[END_REF] by directly comparing energies of each rotamer in the same conformation:

E(i r ) -E(i u ) + j i min s [E(i r , j s ) -E(i u , j s )] ≥ 0 (3)
where the best and worst-cases are replaced by the worst difference in energy. It is easy to see that this condition is always weaker than the previous one, and therefore applicable to more cases. These two properties define polynomial time algorithms that prune dominated values. Since its introduction in 1992 by Desmet, DEE has become the fundamental tool of exact CPD, and various extensions have been proposed [START_REF] Pierce | Conformational splitting: A more powerful criterion for dead-end elimination[END_REF][START_REF] Looger | Generalized dead-end elimination algorithms make large-scale protein side-chain structure prediction tractable: implications for protein design and structural genomics[END_REF][START_REF] Georgiev | Improved Pruning algorithms and Divide-and-Conquer strategies for Dead-End Elimination, with application to protein design[END_REF]. All these DEE criteria preserve the optimum but may remove suboptimal solutions. However CPD is NP-hard, and DEE cannot solve all CPD instances. Therefore, DEE preprocessing is usually followed by an A * search. After DEE pruning, the A * algorithm allows to expand a sequence-conformation tree, so that sequence-conformations are extracted and sorted on the basis of their energy values. The admissible heuristic (lower bound) used by A * is described in [START_REF] Georgiev | The minimized dead-end elimination criterion and its application to protein redesign in a hybrid scoring and search algorithm for computing partition functions over molecular ensembles[END_REF].

When the DEE algorithm does not significantly reduce the search space, the A * search tree can be too slow or memory demanding and the problem cannot be solved. Therefore, to circumvent these limitations and increase the ability of CPD to tackle problems with larger sequence-conformation spaces, novel alternative methods are needed. We now describe alternative state-of-the-art methods for solving the GMEC problem that offer attractive alternatives to DEE/A * .

From CPD to CFN

CPD instances can be directly represented as Cost Function Networks.

Definition 1 ([13])

A Cost Function Network (CFN) is a pair (X, W) where X = {1, . . . , n} is a set of n variables and W is a set of cost functions. Each variable i ∈ X has a finite domain D i of values that can be assigned to it. A value r ∈ D i is denoted i r . For a set of variables S ⊆ X, D S denotes the Cartesian product of the domains of the variables in S. For a given tuple of values t, t[S] denotes the projection of t over S. A cost function w S ∈ W, with scope S ⊆ X, is a function w S :

D S → [0, k]
where k is a maximum integer cost used for forbidden assignments.

We assume, without loss of generality, that every CFN includes at least one unary cost function w i per variable i ∈ X and a nullary cost function w . All costs being non-negative, the value of this constant function, w , provides a lower bound on the cost of any assignment.

The Weighted Constraint Satisfaction Problem (WCSP) is to find a complete assignment t minimizing the combined cost function w S ∈W w S (t[S]), where a ⊕ b = min(k, a + b) is the k-bounded addition. This optimization problem has an associated NP-complete decision problem. Notice that if k = 1, then the WCSP is nothing but the famous Constraint Satisfaction Problem or CSP (not the Max-CSP).

Modeling the CPD problem as a CFN is straightforward. The set of variables X has one variable i per residue i. The domain of each variable is the set of (amino acid,conformation) pairs in the rotamer library used. The global energy function can be represented by 0-ary, unary and binary cost functions, capturing the constant energy term w = E , the unary energy terms w i (r) = E(i r ), and the binary energy terms w i j (r, s) = E(i r , j s ), respectively. In the rest of the paper, for simplicity and consistency, we use notations E , E(•) and E(•, •) to denote cost functions and restrict ourselves to binary CFN (extensions to higher orders are well-known).

Notice that there is one discrepancy between the original formulation and the CFN model: energies are represented as arbitrary floating point numbers while CFN uses positive costs. This can simply be fixed by first subtracting the minimum energy from all energy factors. These positive costs can then be multiplied by a large integer constant M and rounded to the nearest integer if integer costs are required.

Local consistency in CFN

The usual exact approach to solve a CFN is to use a depth-first branch-and-bound algorithm (DFBB). A family of efficient and incrementally computed lower bounds is defined by local consistency properties.

Node consistency [START_REF] Larrosa | On arc and node consistency in weighted CSP[END_REF] (NC) requires that the domain of every variable i contains a value r that has a zero unary cost (E(i r ) = 0). This value is called the unary support for i. Furthermore, in the scope of the variable i, all values should have a cost below k (∀r

∈ D i , E + E(i r ) < k).
Soft arc consistency (AC * ) [START_REF] Schiex | Arc consistency for soft constraints[END_REF][START_REF] Larrosa | On arc and node consistency in weighted CSP[END_REF] requires NC and also that every value r of every variable i has a support on every cost function

E(i r , j s ) involving i. A support of i r is a value j s ∈ D j such that E(i r , j s ) = 0.
Stronger local consistencies such as Existential Directional Arc Consistency (EDAC) [START_REF] Larrosa | Existential arc consistency: getting closer to full arc consistency in weighted CSPs[END_REF] and Virtual Arc Consistency (VAC) [START_REF] Cooper | Virtual arc consistency for weighted CSP[END_REF] have also been introduced. See [START_REF] Cooper | Soft arc consistency revisited[END_REF] for a review of existing local consistencies. As in classical CSP, enforcing a local consistency property on a problem P involves transforming P = (X, W) into a problem P = (X, W ) that is equivalent to P (all complete assignments keep the same cost) and that satisfies the considered local consistency property. Enforcing a local consistency may increase and thus improve the lower bound on the optimal cost. This bound is used to prune the search tree during DFBB.

Local consistency is enforced using Equivalence Preserving Transformations (EPTs) that move costs between different cost functions [START_REF] Schiex | Arc consistency for soft constraints[END_REF][START_REF] Larrosa | On arc and node consistency in weighted CSP[END_REF][START_REF] Larrosa | Solving weighted CSP by maintaining arc consistency[END_REF][START_REF] Cooper | Arc consistency for soft constraints[END_REF][START_REF] Larrosa | Existential arc consistency: getting closer to full arc consistency in weighted CSPs[END_REF][START_REF] Cooper | High-order consistency in Valued Constraint Satisfaction[END_REF][START_REF] Cooper | Optimal soft arc consistency[END_REF][START_REF] Cooper | Virtual arc consistency for weighted CSP[END_REF][START_REF] Cooper | Soft arc consistency revisited[END_REF]. For example, a variable i violating the NC property because all its values i r have a non-zero E(i r ) cost, can be made NC by subtracting the minimum cost from all E(i r ) and adding this cost to E . The resulting network is equivalent to the original network, but it has an increased lower bound E . Far more complex sequences or sets of EPTs can be required to enforce other local consistencies [START_REF] Cooper | Soft arc consistency revisited[END_REF].

Local consistency can be enforced in polynomial time and space as summarized in Table 1. During search, incrementality is preserved along any branch of the search tree, avoiding to repeatedly apply the same EPTs at every search node.

Unfortunately, finding the optimal sequence of EPTs with integer costs which maximizes E is NP-hard [START_REF] Cooper | Arc consistency for soft constraints[END_REF]. It is polynomial for a set of EPTs with rational costs [START_REF] Cooper | Optimal soft arc consistency[END_REF] and corresponds to optimization over the local polytope of probabilistic graphical models [START_REF] Cooper | Soft arc consistency revisited[END_REF]. In practice, during search, applying suboptimal sequences of EPTs by enforcing EDAC or VAC is the most efficient approach for solving CFNs [START_REF] Hurley | Multi-Language Evaluation of Exact Solvers in Graphical Model Discrete Optimization[END_REF].

Maintaining dead-end elimination

Dead-end elimination is the key algorithmic tool of exact CPD solvers. From an AI perspective, in the context of CSP (if k = 1), the DEE Equation 3 is equivalent to neighborhood substitutability [START_REF] Freuder | Eliminating interchangeable values in constraint satisfaction problems[END_REF]. In the context of CFN, the authors of [START_REF] Lecoutre | WCSP integration of soft neighborhood substitutability[END_REF] introduced partial soft neighborhood substitutability with a definition that is equivalent to Equation 3 for pairwise decomposed energies. DEE can be enforced in time O(n 2 d 3 ) and it is orthogonal to local consistencies, except for VAC where value removals done by DEE cannot break the VAC property [START_REF] Lecoutre | WCSP integration of soft neighborhood substitutability[END_REF]. In practice, DEE and AC * (or EDAC) will be enforced until both properties are verified, with time complexity in O(n 3 d 4 ). In order to reduce this time complexity, during search, we do not test every pair of values in every domain D i , but only one pair (i r , i u ) such that E(i u ) is minimum and E(i r ) is maximum. Thus, enforcing this restricted DEE 1 can be done in O(n 2 d) and it iterates at most n × d times with AC * [START_REF] De Givry | Dead-End Elimination for Weighted CSP[END_REF].

Exploiting tree decomposition in a hybrid best-first branch-and-bound method

Hybrid Best-First Search (HBFS) [START_REF] Allouche | Anytime Hybrid Best-First Search with Tree Decomposition for Weighted CSP[END_REF] explores the search tree in a best-first manner as in A*. However, each selected open search node is expanded by a depth-first search with a limited number of backtracks. When the limit is reached, all the remaining unexplored search nodes are inserted in the open node list. The limit is dynamically tuned in order to reduce the overhead of reconstructing the CFN corresponding to the selected open node.

The HBFS method was further extended in [START_REF] Allouche | Anytime Hybrid Best-First Search with Tree Decomposition for Weighted CSP[END_REF] to exploit a tree decomposition, resulting in the BTD-HBFS method.

Definition 2 A tree decomposition of a connected CFN (X, W) is a pair (C T , T) where T = (I, A) is a tree with nodes set I and edges set A and

C T = {C i | i ∈ I} is a family of subsets of X, called clusters, such that: (i) ∪ i ∈I C i = X, (ii) ∀ w S ∈ W, ∃ C i ∈ C T s.t. S ⊆ C i , (iii) ∀ i, j, k ∈ I, if j is on the path from i to k in T, then C i ∩ C k ⊆ C j .
Definition 3 A graph of clusters for a tree decomposition (C T , T) is an undirected graph G = (C T , E) that has a vertex for each cluster C i ∈ C T , and there is an edge

(C i , C j ) ∈ E when C i ∩ C j ∅.
The width of a tree decomposition corresponds to the size of the largest cluster minus one. As finding an optimal tree decomposition with minimum width, called treewidth, is NP-hard, we use fast approximate algorithms like the min-fill heuristic.

BTD-HBFS (Backtracking with Tree Decomposition, or BTD for short) uses a restricted variable ordering heuristic, which selects variables from a root (largest) cluster first and then continues by assigning variables in the child clusters in a depth-first manner. Each child cluster has one open node list with associated lower and upper bounds per visited assignment of its variables intersecting with its parent cluster. By doing so, it exploits the lower bounds reported by HBFS in individual clusters to improve the anytime behavior and global pruning of BTD. Given a CFN (X, W) with treewidth t, BTD computes the optimum in time O(knd t+1 ) and space O(knd 2t ) [START_REF] Allouche | Anytime Hybrid Best-First Search with Tree Decomposition for Weighted CSP[END_REF].

A parallel variable neighborhood search method guided by tree decomposition

UDGVNS (for Unified Decomposition Guided Variable Neighborhood Search) [START_REF] Ouali | Iterative Decomposition Guided Variable Neighborhood Search for Graphical Model Energy Minimization[END_REF] is a CFN solving method unifying two complete and incomplete search methods: iterative Limited Discrepancy Search (LDS) and Variable Neighborhood Search (VNS) methods. LDS [START_REF] Harvey | Limited discrepancy search[END_REF] is a heuristic method that explores the depth-first search tree in a non-systematic way by making a limited number of wrong decisions w.r.t. its value ordering heuristic. We assume a binary search tree where at each search node either the selected variable is assigned to its chosen preferred value (left branch) or the value is removed from the domain (right branch). Each value removal corresponds to a wrong decision made by the search, it is called a discrepancy. The number of discrepancies is limited by a parameter. Iterative LDS increases this parameter (by a multiplication factor of 2) at each iteration until a complete search is done. VNS/LDS [START_REF] Mladenović | Variable Neighborhood Search[END_REF][START_REF] Loudni | Solving constraint optimization problems in anytime contexts[END_REF] is a metaheuristic that uses a finite set of pre-selected neighborhood structures N s , s = 4, 5, ..., n to escape from local minima by systematically changing the neighborhood structure if the current one does not improve the current incumbent solution. The initial solution is found by depth-first search on the whole problem. Then, s variables are randomly chosen and the current solution is partially destroyed by un-assigning the selected variables and an exploration of its (large) neighborhood is performed by LDS with a fixed discrepancy. As soon as a better solution is found, then s is reset to its minimal value (4 in our experiments). DGVNS [START_REF] Fontaine | Exploiting tree decomposition for guiding neighborhoods exploration for VNS[END_REF] uses another neighborhood structure N s,c , where s is the neighborhood size and C c is the cluster where the variables will be selected from. If (s > |C c |), we complete the set of candidate variables to be unassigned by adding clusters adjacent to C c in the graph of clusters provided by a tree decomposition. The neighborhood change in DGVNS is performed in the same way as in VNS/LDS. However, DGVNS considers successively all the clusters. This ensures a better diversification by covering a large number of different regions. UDGVNS [START_REF] Ouali | Iterative Decomposition Guided Variable Neighborhood Search for Graphical Model Energy Minimization[END_REF] iterates DGVNS with an increasing discrepancy (when s = n and no better solution was found) as in iterative LDS, until a complete search is done, therefore tuning its compromise between optimality proof and anytime behavior.

The parallel version of UDGVNS relies on a master/worker model. The master process controls the communication over the entire processes and holds the centralized information, while the asynchronous worker processes explore the parts of the search space assigned by the master. The cooperation in parallel UDGVNS is achieved by sharing a single global best solution among the worker processes.

Integer linear programming for the CPD

The rigid backbone CPD problem has a simple formulation and can be easily written in a variety of combinatorial optimization frameworks. In our previous work [1], we compared the CFN approach to solvers coming from different fields, including probabilistic graphical model, 0/1 linear programming, 0/1 quadratic programming, and 0/1 quadratic optimization. Here, we present only the 01LP model. Other approaches were shown to be far less efficient than CFN or 01LP [1].

A 0/1 linear programming (01LP) problem is defined by a linear criterion to optimize over a set of Boolean variables under a conjunction of linear inequalities and equalities.

For every assignment i r of every variable i, there is a Boolean variable d ir that is equal to 1 iff i = r. Additional constraints enforce that exactly one value is selected for each variable. For every pair of values of different variables (i r , j s ) involved in a binary energy term, there is a Boolean variable p ir js that is equal to 1 iff the pair (i r , j s ) is used. Constraints enforce that a pair is used iff the corresponding values are used. Then, finding a GMEC reduces to the following 01LP:

min i, r E (ir ) k E(i r ).d ir + i, r, j, s j >i, E (ir , js ) k E(i r , j s ).p ir js s.t. r d ir = 1 (∀i) (4) s p ir js = d ir (∀i, r, j) (5)
d ir = 0 (∀i, r)E(i r ) = k (6) p ir js = 0 (∀i, r, j, s)E(i r , j s ) = k (7) d ir ∈ {0, 1} (∀i, r) (8) p ir js ∈ {0, 1} (∀i, r, j, s) (9)
It is known that the continuous LP relaxation of this model is the dual of the LP problem defined by Optimal Soft Arc Consistency (OSAC) [START_REF] Cooper | Optimal soft arc consistency[END_REF][START_REF] Cooper | Soft arc consistency revisited[END_REF] when the upper bound k used in CFN is infinite. OSAC is known to be stronger than any other soft arc consistency level, including EDAC and VAC. However, as soon as the upper bound k used for pruning in CFN decreases to a finite value, soft local consistencies may prune values and EDAC becomes incomparable with the dual of these relaxed LPs.

This model is also the 01LP model IP1 proposed in [START_REF] Kingsford | Solving and analyzing side-chain positioning problems using linear and integer programming[END_REF] for side-chain positioning. It has a quadratic number of Boolean variables. Constraints ( 6) and ( 7) explicitly forbid values and pairs with cost k (sterical clashes).

This model can be simplified by relaxing the integrality constraint on the p ir js : indeed, if all d ir are set to 0 or 1, the constraints (4) and ( 5) enforce that the p ir js are set to 0 or 1. In the rest of the paper, we relax constraint (9).

Computational Protein Design instances

In our initial experiments with CPD in [3], we built 12 designs using the CPD dedicated tool osprey 1.0. A new version of osprey being available since, we used this new 2.0 version [START_REF] Gainza | Osprey: Protein design with ensembles, flexibility, and provable algorithms[END_REF] for all computations. Among different changes, this new version uses a modified energy field that includes a new definition of the "reference energy" and a different rotamer library. We therefore rebuilt the 12 instances from [3] and additionally created 35 extra instances from existing published designs, as described in [START_REF] Traoré | A new framework for computational protein design through cost function network optimization[END_REF]. We must insist on the fact that the 12 rebuilt instances do not define the same energy landscape or search space as the initial [3]'s instances (due to changes in rotamers set).

These designs include protein structures derived from the PDB that were chosen for the high resolution of their 3D-structures, their use in the literature, and their distribution of sizes and types. Diverse sizes of sequence-conformation combinatorial spaces are represented, varying by the number of mutable residues, the number of alternative amino acid types at each position and the number of conformations for each amino acid. The Penultimate rotamer library was used [START_REF] Lovell | The penultimate rotamer library[END_REF].

Preparation of CPD instances

Missing heavy atoms in crystal structures and hydrogen atoms were added with the tleap module of the AMBER9 software package [9]. Each molecular system was then minimized in implicit solvent (Generalized Born model [START_REF] Hawkins | Parametrized models of aqueous free energies of solvation based on pairwise descreening of solute atomic charges from a dielectric medium[END_REF]) using the Sander program and the all-atom ff99 force field of AMBER9. All E , E(i r ), and E(i r , j s ) energies of rotamers (see Equation 1) were pre-computed using osprey 2.0. The energy function consisted of the Amber electrostatic, van der Waals and the solvent terms. Rotamers and rotamer pairs leading to sterical clashes between molecules are associated with huge energies (10 38 ) representing forbidden combinations. For n residues to optimize with d possible (amino acid,conformation) pairs, there are n unary and up to n.(n-1) 2 binary cost functions that can be computed independently. The resulting instances have between n = 11 and n = 120 residues, and between d = 48 and d = 198 rotamers (see Table 2).

Translation to WCSP and 01LP formats

The native CPD problems were translated to the WCSP format before any preprocessing. To convert the floating point energies of a given instance to non-negative integer costs, we subtracted the minimum energy to all energies and then multiplied energies by an integer constant M and rounded to the nearest integer. The initial upper bound k is set to the sum, over all cost functions, of the maximum energies (excluding forbidden sterical clashes). High energies corresponding to sterical clashes are represented as costs equal to the upper bound k (the forbidden cost). The resulting model was used as the basis for all other solvers (except osprey). To keep a cost magnitude compatible with all the compared solvers, we used M = 10 2 . Experiments with a finer discretization (M = 10 8 ) was used in previous experiments [START_REF] Traoré | A new framework for computational protein design through cost function network optimization[END_REF] with no significant difference in computing efforts.

Note that the approximate treewidth produced by min-fill heuristic of WCSP instances is between 4 and 113, with a mean value of 26.68 (after preprocessing by toulbar2).

All the Python and C translating scripts used, including translating from WCSP to 01LP format, are available together with the 47 CPD instances in native and WCSP formats at http://genotoul.toulouse.inra.fr/~tschiex/CPD-AIJ.

Experimental results

For computing the GMEC, all computations were performed on an Intel Xeon E5-2680 at 2.50GHz, 256 GB of RAM (except osprey on an AMD Operon 6176 at 2.3 GHz, 128 GB of RAM), and a 9,000-second time-out. We compared three solvers: DEE/A* osprey version 2.0 (cs.duke.edu/donaldlab/osprey.php), 01LP solver cplex version 12.8.0 (with parameters EPAGAP, EPGAP, and EPINT set to zero to avoid premature stop), and CFN solver toulbar2 version 1.0.1 (github. com/toulbar2/toulbar2).

The procedure of osprey starts by extensive DEE pre-processing (algOption = 3, includes simple Goldstein, Magic bullet pairs, 1 and 2-split positions, Bounds and pairs pruning) followed by A * search. Only the GMEC conformation is generated by A * (initEw=0).

We ran toulbar2 using VAC in preprocessing and HBFS with EDAC, DEE 1 , and binary branching during search (options -d: -A). The additional exploitation of a min-fill tree decomposition inside branch-and-bound is denoted as toulbar2 BTD (extra options -O=-3 -B=1). The variable neighborhood search guided by tree decomposition is denoted toulbar2 UDGVNS (extra options -O=-3 -vns). Table 2 and Figure 3.left report the number of problems solved within a given time limit. osprey solved 25 instances, cplex solved 30 (resp. 33 with using 10 cores), toulbar2 solved 40 (resp. 39 with UDGVNS). 7 instances remain unsolved by any approaches in less than 9, 000 seconds. Within the three CFN approaches, toulbar2 BTD is the fastest in terms of optimality proofs. Using 10 cores improves cplex results by solving 3 more instances and a mean speed-up factor of 2.2 on the same 30 solved instances. A different behavior was found for toulbar2 UDGVNS where the mean speed-up factor was only 1.15 in favor of the parallel version. This is because the parallelization of toulbar2 UDGVNS is to partially explore the neighborhood in parallel until a single process explores the whole problem sequentially using complete depth-first branch-and-bound and ends the search.

Figure 3.right compares the evolution of upper bounds as time passes for the different methods (except for osprey which returns one optimal solution at the end of its A* exploration). Specifically, for each instance, we normalize all energies as follows: the best, potentially suboptimal solution found by any algorithm is 1, the worst solution is 2. This normalization is invariant to translation and scaling. Again, there is a clear separation between CFN and 01LP methods, in favor of CFN approaches. Among the sequential methods, toulbar2 UDGVNS has the best anytime profile. Its parallel version toulbar2 UDGVNS using 10 cores found the best upper bound for all the 47 instances (see Table 2).

Conclusions

The simplest formal optimization problem underlying CPD looks for a Global Minimum Energy Conformation (GMEC) over a rigid backbone and altered side-chains (identity and conformation). In computational biology, exact methods for solving the CPD problem combine dominance analysis (DEE) and an A * search.

The CPD problem can also be directly formulated as a Cost Function Network, with a very dense graph and relatively large domains. We have shown how DEE can be integrated with local consistency with a reasonable time complexity. An alternative 01LP formulation leads to a much larger number of variables.

On a variety of real instances, we have shown that state-of-the-art optimization algorithms on integer programming or cost function network give important speedups compared to usual CPD algorithms combining dead-end elimination with A * . Among all the tested solvers, toulbar2 was the most efficient solver and its efficiency was further improved by exploiting a tree decomposition either for optimality proofs or for finding good anytime solutions on very large instances. In practice, the performance of toulbar2 relies mostly on its fast lower bounds, while adding DEE has a marginal effect [1]. toulbar2 has now been integrated inside the osprey CPD software and is being integrated inside Rosetta Molecular Modeling suite [START_REF] Leaver-Fay | Rosetta3: an object-oriented software suite for the simulation and design of macromolecules[END_REF]. Indeed, another comparison has shown the Rosetta CPD-dedicated Simulated Annealing implementation was outperformed by the exact CFN toulbar2 BTD approach [START_REF] Simoncini | Guaranteed discrete energy optimization on large protein design problems[END_REF] in terms of GMEC solution quality within a 100-hour time limit. Exact optimization may also be useful in practice as we recently shown using toulbar2 for the design a real self-assembling protein [START_REF] Noguchi | Computational design of symmetrical eight-bladed β-propeller proteins[END_REF].

We also showed that these CPD problems define challenging benchmarks for AI and OR researchers. Among 47 instances, 7 remains open under 9,000 seconds, having from 28 to 120 mutable residues and at most 198 rotamers per position. Larger problems may exist as most of the known proteins in the PDB database include more than 200 residues1.

In practice, it must be stressed that just finding the GMEC is not a final answer to real CPD problems. CPD energies functions represent an approximation of the real physics of proteins and optimizing a target score based on them (such as stability, affinity,. . . ) is not a guarantee of finding a successful design. Indeed, some designs may be so stable that they are unable to accomplish the intended biological function. The usual approach is therefore to design a large library of proteins whose sequences are extracted from all solutions within a small threshold of energy of the GMEC. This problem is also efficiently solved by toulbar2 [START_REF] Traoré | A new framework for computational protein design through cost function network optimization[END_REF][START_REF] Simoncini | Guaranteed discrete energy optimization on large protein design problems[END_REF].

Table 2 For each instance: protein (PDB id.), number of mutable residues, maximum domain size (maximum number of rotamers), and CPU-time for solving (with best solution found in parentheses) using cplex, cplex (10 cores), toulbar2, toulbar2 BTD, toulbar2 UDGVNS, toulbar2 UDGVNS (10 cores). A '-' indicates that the corresponding solver did not prove optimality within the 9,000-second time-out. A '!' indicates the solver stops with a SEGV signal.

Fig. 2 A

 2 Fig. 2 A local view of the combinatorial sequence exploration considering a common backbone. Changes can be caused by amino acid identity substitutions (for example D/L or R/Q) or by amino acid side-chain reorientations (rotamers) for a given amino acid. A sparse rotamer library for one amino acid is shown on the right (ARG=Arginine).

Fig. 3 (

 3 Fig. 3 (Left) A figure showing the number of problems that can be solved by each approach (Xaxis) as a function of time allowed for solving each problem (Y-axis). (Right) A figure showing normalized upper bounds (Y-axis) on 47 instances as time passes (X-axis).

  3. Allouche, D., Traoré, S., André, I., de Givry, S., Katsirelos, G., Barbe, S.,Schiex, T.: Computational protein design as a cost function network optimization problem. In: Principles and Practice of Constraint Programming, pp. 840-849. Springer (2012) 4. Anfinsen, C.: Principles that govern the folding of protein chains. Science 181(4096), 223-253 (1973) 5. Boas, F.E., Harbury, P.B.: Potential energy functions for protein design. Current opinion in structural biology 17(2), 199-204 (2007) 6. Bowie, J.U., Luthy, R., Eisenberg, D.: A method to identify protein sequences that fold into a known three-dimensional structure. Science 253(5016), 164-170 (1991) 7. Campeotto, F., Dal PalÃź, A., Dovier, A., Fioretto, F., Pontelli, E.: A constraint solver for flexible protein models. J. Artif. Int. Res. (JAIR) 48(1), 953-1000 (2013) 8. Carothers, J.M., Goler, J.A., Keasling, J.D.: Chemical synthesis using synthetic biology. Current opinion in biotechnology 20(4), 498-503 (2009) 9. Case, D., Darden, T., Cheatham III, T., Simmerling, C., Wang, J., Duke, R., Luo, R., Merz, K., Pearlman, D., Crowley, M., Walker, R., Zhang, W., Wang, B., Hayik, S., Roitberg, A., Seabra,

Table 1

 1 Time and space complexities of enforcing local consistency properties on a binary CFN (X, W ), with n = |X | variables, maximum domain size d = max i∈X |D i |, e = |W | cost functions with maximum forbidden cost k, and minimum non-zero rational cost ∈]0, 1]. Also, we report polynomial classes which are solved by these local consistencies.

	Local consistency Time complexity Space complexity	Polynomial classes
	NC	O(nd)	O(nd)	-
	AC *	O(n 2 d 2 + ed 3 )	O(ed)	-
	EDAC	O(ed 2 max(nd, k))	O(ed)	Tree-structures
	VAC	O(ed 2 k/ )	O(ed)	Tree-struct., submodular func.

Acknowledgements This work has been partly funded by the "Agence nationale de la Recherche" (ANR-10-BLA-0214, ANR-12-MONU-0015-03, and ANR-16-C40-0028).


Jeremy Vanhelst
email: jeremy.vanhelst@chru-lille.fr

Laurent Beghin

Paul S Fardy

Zekya Ulmer

Gregory Czaplicki

Jérémy Vanhelst

Laurent Béghin

Zekya Ulmer

Grégory Czaplicki

J Vanhelst

Reliability of health-related physical fitness tests in adolescents: the MOVE Program

Keywords: Assessment, Youth, Aerobic fitness, Muscular strength, Speed, Flexibility, Reproducibility

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Introduction

Physical fitness is an important determinant of health in children and adolescents (Ortega et al., 2008). Health-related physical fitness includes muscular strength (lower and upper limbs), flexibility, speed/agility, and cardiorespiratory fitness (Heyward, 1991). Positive health-related physical fitness in childhood and adolescence helps to prevent mental, nutritional, gastroenterological, cardiac, and respiratory diseases (Ortega et al., 2008).

Health-related physical fitness tests are administered in the laboratory and in the field. Laboratory testing generally has the advantage of high validity and reliability (Heyward, 1991). The disadvantage, however, is that laboratory assessment requires trained personnel, is time consuming, and necessitates costly equipment. Field tests generally are easier to administer, require less time and utilise less expensive equipment (Heyward, 1991).

The French national program "Move... A priority for your health" (http://www.bougetasante.fr/), aims to assess the levels of physical fitness in youth, ages 6 to 18 years, in their school environment. For this purpose, a set of healthrelated physical fitness field tests was chosen (http://www.bougetasante.fr/). Field tests were chosen for the study because they: (i) are easy to administer by a physical education teacher; (ii) involve minimal equipment at low cost; (iii) are safe; (iv) are easily adapted according to age; and, (v) can assess health-related physical fitness in a short period of time.

The tests selected to measure health related physical fitness included the 20-m shuttle run test, ½ mile test, basketball throw, standing long jump, 20/30/50-m sprint tests, and the shoulder stretch test. The rationale for selecting these tests has been described elsewhere [START_REF] Vanhelst | Physical fitness in children and adolescents: how can it be measured in school environment? The example of the BOUGE-Fitness test battery[END_REF]. Validity refers to the ability of the test to reflect what it is designed to measure [START_REF] Artero | Reliability of field-based fitness tests in youth[END_REF]Ortega et al., 2008). The validity of a tool is judged by comparison with a 'gold standard' method. Reliability refers to the reproducibility of values of a test in repeated trials on the same individual [START_REF] Artero | Reliability of field-based fitness tests in youth[END_REF]Ortega et al., 2008).

The tests, included in the MOVE program, have been previously validated in youth [START_REF] Castro-Piñero | Percentile values for flexibility tests in youths aged 6 to 17 years: influence of weight status[END_REF]Castro-Piñero et al., 2010;Castro-Piñero et al., 2009;Castro-Piñero et al., 2010;Castro-Piñero et al., 2009;Léger & Cadoury, 1989).

However, the reliability of physical fitness tests is also necessary. Only, the reliability of the shuttle run test was widely assessed [START_REF] Artero | Reliability of field-based fitness tests in youth[END_REF]Ortega et al., 2008). Reliability for the other field tests used in the program have not been well studied [START_REF] Artero | Reliability of field-based fitness tests in youth[END_REF]Ortega et al., 2008).

The aim of this study was to assess the reliability of health-related physical fitness field tests used in the "Move… A priority for your health" program among children and adolescents.

Methods

Study design

This ancillary study is based on the French health promotion program "Move… A priority for your health" (http://www.bougetasante.fr/). The principal aim of this program is to promote the benefits of physical activity and physical fitness on the health of French youth, ages 6 to 18 years. The program will be performed in many classes throughout France. All data obtained from the organiser (Mutualité Française) of the event were anonymous, declared to the CNIL (Commission Nationale de l'Informatique et des Libertés). The aims and objectives were explained carefully to each adolescent and to parents. After this explanation, adolescents and parents could accept or decline to participate to this study and to record anonymously their information technology data. This study obtained an agreement by the local research ethics committee (Comité de Protection des Personnes Nord Ouest IV, Lille, France), and all procedures were performed in accordance with the ethical standards of the Helsinki Declaration of 1975 (as revised in 2008) and the European Good Clinical Practice Guidelines.

A manual of operations (rational of the study, procedures of tests, and how recorded the data) was designed for and read by the physical education teacher involved in the health promotion program before the data collection started.

Instructions provided to the participants were described in the manual of operations in order to standardize procedures.

Eighty-eight children, ages 6 to 11.9, and 86 adolescents, ages 12 to 16 years participated in this study in order to assess reliability of the physical fitness tests.

Participants were asked to perform each test two times. Tests were scheduled one week apart. Retesting was performed at the same time of day to minimize circadian rhythm variability.

Anthropometric measurements

Weight was measured in shorts and T-shirts without shoes to the nearest 0.1 kg using an electronic scale (Oregon Scientific, GA 101, USA). Height was measured without shoes to the nearest 0.1 cm using a standard physician's scale.

Physical fitness assessment

1-Sprint test: the participant stands in stationery and comfortable position, feet behind the starting line, with no rocking movements. Runners were instructed to start on the whistle sound, and timers were instructed to start the stopwatch at the whistle sound and stop their stopwatch when the runner crossed the finish line. The test assesses speed (Castro-Piñero et al., 2010).

2-Basketball throw: holding the ball the participant stands at a line with feet slightly apart, facing the direction in which the ball is to be thrown with two hands. The ball is brought back behind the head and thrown as far as possible. The throwing action is similar to that used for a soccer/football sideline throw-in. The participant is encouraged to use the legs, back, and arms to assist in maximizing the distance thrown. The participant is not permitted to fall forward over the line and the feet must remain on the ground before, during, and after the throw. The distance from the starting line to where the ball landed was recorded in centimetres. The best of two attempts was recorded. This test assesses upper-body muscular strength (Castro-Piñero et al., 2009).

3-Shoulder stretch test: to test the right shoulder the participant reaches with the right hand over the right shoulder and down the back as if to pull up a zipper or scratch between the shoulder blades. At the same time the participant places the left hand behind the back and reaches up, trying to touch the fingers of the right hand. To test the left shoulder, the participant will do the same but reversing the arm positions.

A 0 score is recorded when the participant touches the fingers. If the participant exceeds this line, the tester measures with the distance in centimetres and records a positive number. If the participant cannot touch the finger, the tester measures the distance between fingers and records a negative number. This test assesses shoulder flexibility [START_REF] Castro-Piñero | Percentile values for flexibility tests in youths aged 6 to 17 years: influence of weight status[END_REF].

4-Standing long jump: in a standing position immediately behind a line and feet shoulder's width apart, the participant jumps as far as possible with feet together. A non-slip hard surface, chalk and a tape measure were used to perform the test.

Distance is recorded in centimetres. This test assesses the lower-body muscular strength (Ortega et al., 2008).

5-1/2-mile run/walk test: the participant was instructed and encouraged to complete the distance as fast as possible. Walking was permitted if the subject was unable to run the entire distance. Time was recorded to the nearest second. This test assesses cardiorespiratory fitness [START_REF] Castro-Piñero | Percentile values for aerobic performance running/walking field tests in children aged 6 to 17 years; influence of weight status[END_REF].

Statistical analysis

The data were analysed using the Statistical Package for the Social Sciences, Windows v. 11.5 (SPSS Inc., Chicago, IL) and Excel 2003 (Microsoft Inc., Redmond, WA). Data are expressed as mean (standard deviation). The level of significance was p < 0.05.

Reliability between test-retest was assessed using the intraclass correlation coefficient (ICC) according to the Fleiss method [START_REF] Fleiss | Design and Analysis of Clinical Experiments[END_REF]. The ICC was interpreted as follows: 0-0.2 indicates poor agreement; 0.3-0.4 indicates fair agreement; 0.5-0.6 indicates moderate agreement; 0.7-0.8 indicates strong agreement; and 0.8 indicates almost perfect agreement (13). Reliability was also assessed according to the method of [START_REF] Bland | Statistical methods for assessing agreement between two methods of clinical measurement[END_REF]. The analysis measures bias as estimated from mean differences, the 95% confidence interval for bias, and the limits of agreement, ± 2 standard deviations of the difference.

A dependent t-test was performed to determine whether there were significant differences between the scores performed by boys and girls.

Results

One hundred seventy-four youth participated in the study. Mean age was 11.6 ± 2.1 years (range: 8.2-16.2). Physical characteristics of the participants are presented in Table 1.

Insert Table 1

Sprint tests Time for the two tests was 5.32 ± 1.4 sec and 5.13 ± 1.35 sec, respectively (Table 2). Children have significantly better scores (p<0.001) than adolescents (4.48 ± 0.67 vs 5.8 ± 1.54 sec). The intraclass correlation coefficient between the two trials was high (children and adolescents) demonstrating good reliability (Table 2). The high concordance of the intraclass correlation between times obtained in the two sprint tests is reinforced by the Bland and Altman method.

Mean differences were within the limits of Bland and Altman and most data points were within the limits of agreement of bias (Figure 1). The mean difference was very near to 0 (-0.16 ± 0.35) seconds, and the limits of agreement were -0.88 to 0.54.

Basketball throw

Throwing distances for the two trials were 858.9 ± 244.2 and 845.5 ± 238.5 cm, respectively (Table 2). Significant differences were obtained according to age (p < 0.001), with adolescents throwing farther than children (969.9 ± 250.9 vs 750.5 ± 181.6 meters). In each age range, the intraclass correlation coefficient between the two basketball throw tests was high demonstrating good reliability (Table 2). The Bland and Altman method confirmed the results obtained from intraclass correlation.

Mean differences were within the limits of Bland and Altman and most data points were within the limits of agreement of bias (Figure 2). The mean difference was very near to 0 (-18.3 ± 158.6) meters, and the limits of agreement were -335.6 to 298.9.

Shoulder stretch test

The scores for the two shoulder stretch test were 6.1 ± 6.8 cm, and 6.9 ± 7.1 cm, respectively (Table 2). Adolescents had significantly (p<0.001) better test results than children, (8.4 ± 6.9 vs 5.5 ± 6.9 cm). The intraclass correlation coefficient between the two trials was high demonstrating good reliability in children and adolescent (Table 2). The high concordance of the intraclass correlation between data obtained in the two tests is reinforced by the Bland & Altman method.

Mean differences was within the limits of Bland and Altman and most data points were within the limits of agreement of bias (Figure 3). The mean difference was very near to 0 (0.9 ± 2.9) cm, and the limits of agreement were -4.9 to 6.6.

Standing long jump

Distances for the two jump tests were 174.9 ± 63.6 and 177.6 ± 60.8 cm, respectively (Table 2). Adolescents had significantly (p<0.001) better scores than children (202.2 ± 63.2 vs 153.60 ± 47.5 cm). The intraclass correlation coefficient between the two tests was high in each age range, demonstrating good reliability (Table 2). The Bland and Altman method confirmed the results obtained from the intraclass correlation.

Mean differences were within the limits of Bland and Altman and most data points were within the limits of agreement of bias (Figure 4). The mean difference was very near to 0 (1.8 ± 31.5) cm, and the limits of agreement were -61.3 to 64.9.

1/2-mile run/walk tests

Times for the two run/walk tests were 299.7 ± 85.4 and 298.1 ± 52.2 sec, respectively (Table 2). Significant differences were found between age ranges (p < 0.001). Adolescents had significantly (p<0.001) better scores than children (277.3 ± 105.3 vs 325.8 ± 102.3 sec). The intraclass correlation coefficient between the two trials was moderate demonstrating acceptable reliability for both age ranges (Table 2).

Mean differences were within the limits of Bland and Altman and most data points were within the limits of agreement of bias (Figure 5). The mean difference was very near to 0 (-3.21 ± 74.9) seconds, and the limits of agreement were -153.1 to 146.7.

Insert Table 2

Discussion

The aim of this study was to assess the reliability of different health-related physical fitness field tests used in the MOVE study among children, unexplored or poorly studied [START_REF] Artero | Reliability of field-based fitness tests in youth[END_REF]Ortega et al., 2008). The main finding of our study shows that the Move heath-related fitness battery administrated by physical education teachers is reliable for assessing the levels of physical fitness in youth in a school environment.

The Move health-related fitness test includes two tests for assessing cardiorespiratory fitness, the 20-m shuttle run test for adolescents and the ½ mile run/walk test for children. Reliability of the 20-m shuttle run test was not measured as it has been widely studied previously [START_REF] Artero | Reliability of field-based fitness tests in youth[END_REF]. Good reliability was found for the shuttle run test in children and adolescents ages 8-18 years [START_REF] Artero | Reliability of field-based fitness tests in youth[END_REF]. The intraclass correlation coefficient values varied from 0.78 to 0.93 [START_REF] Beets | Criterion-referenced reliability and equivalency between the PACER and 1-mile run/walk for high school students[END_REF][START_REF] Liu | The reliability and validity of the 20-meter shuttle test in American students 12 to 15 years old[END_REF]Mahar et al., 1997;Mahar et al.., 1997;[START_REF] Pitetti | Comparing two regression formulas that predict VO2 peak using the 20-m shuttle run for children and adolescents[END_REF]. Conversely, only one study examined the reliability of the ½ mile run/walk test for children ages to 5-9 years [START_REF] Rikli | The reliability of distance run tests for children in grades K-4[END_REF]. Test reliability was acceptable for children ages 8-9 years but decreased with increased age [START_REF] Rikli | The reliability of distance run tests for children in grades K-4[END_REF]. Our findings, in contrast to [START_REF] Rikli | The reliability of distance run tests for children in grades K-4[END_REF], showed better reliability in children (0.71) than adolescents (0.63). Poor reliability for this test in adolescents confirms the choice to use the 20-m shuttle run test for this age range in the Move heath-related fitness battery. The poor reliability may be explained by the lack of fun in the ½ mile run/walk test.

We observed a high reliability in standing long jump and the basketball throw tests. Our findings are in agreement with previous results (Ortega et al., 2008b).

Ortega et al examined the reliability of the standing long jump in 123 adolescents ages 13.6 ± 0.8 years old (Ortega et al., 2008b). Authors concluded that neither a learning nor a fatigue effect was found for the standing long jump test when repeated.

In contrast, [START_REF] España-Romero | Assessing health-related fitness tests in the school setting: reliability, feasibility and safety; The ALPHA Study[END_REF] showed a low reliability in children.

Authors explained that low reliability could be due to performance on the day or even learning effects, i.e. positive systematic bias [START_REF] España-Romero | Assessing health-related fitness tests in the school setting: reliability, feasibility and safety; The ALPHA Study[END_REF]. The disagreement between our results and the previous study may be due to a wider age range in the study of [START_REF] España-Romero | Assessing health-related fitness tests in the school setting: reliability, feasibility and safety; The ALPHA Study[END_REF]. For the upper-body muscular strength, there are no data available on the reliability of the basketball throw test. Our results showed a high reliability in children and adolescents, suggesting neither learning nor fatigue (negative systematic bias) effects.

To our knowledge, reliability of the sprint test and the shoulder stretch test have not been previously studied. Although the two tests have been validated (Heyward, 1991;Castro-Piñero et al., 2010), the assessment of the reliability is needed for defining the quality of the test [START_REF] Currell | Validity, reliability and sensitivity of measures of sporting performance[END_REF]. Finally, our study is the first to validate the use of the sprint and the shoulder stretch tests in the assessment of speed and flexibility in children and adolescents.

Physical education teachers were also asked to comment on the feasibility of health-related physical fitness tests. All teachers reported good feasibility in administering the tests included in the BOUGE battery in a school environment.

Teachers appreciated the possibility to assess health-related physical fitness with tests requiring low cost, small space, and the possibility to perform either in a gymnasium or on outdoor fields. Results from the French Move battery are in agreement with previous European studies assessing health-related physical fitness tests, i.e. HELENA study and The ALPHA study (Ortega et al., 2008;[START_REF] España-Romero | Assessing health-related fitness tests in the school setting: reliability, feasibility and safety; The ALPHA Study[END_REF].

Because of the high interest in health promotion and intervention programs in children and adolescents, there is a need for adequate age-appropriate measures to test and evaluate improvement of health-related physical fitness in children and adolescents. The results of our study are relevant and practical for practitioners.

These tests are chosen for many advantages: they are less expensive, safety, involving minimal equipment, easy and quickly to administer, and require little space (i.e. can be performed in school environment or hospital).

In conclusion, our study provides new information on the reliability of field tests not previously studied. Our findings show that the reliability is acceptable for a set of health-related physical fitness field tests used in the Move study among French youth.

Adding to the validity of these tests already explored in children and adolescent, our results on the reliability reinforce the interest to use these tests to assess healthrelated physical fitness in school environment.

Figure 1 .Figure 2 .Figure 3 .

 123 Figure 1. Reliability of the sprint test

Figure 4 .Figure 5 .

 45 Figure 4. Reliability of the standing long jump

Table 1 .

 1 Further information, including protocols and figures of physical fitness tests, on the health-related physical fitness battery is available in the MOVE website: http://www.prioritesantemutualiste.fr/psm/bouge-ta-sante Physical characteristics of participants(n = 174)

	Legends

Table 2 .

 2 Reliability of physical fitness tests in youth

Table 1 .

 1 Physical characteristics of participants (n = 174)

		Children	Adolescents
	N	88	86
	Age (yr)	9.8 ± 0.9	13.3 ± 1.3
	Height (cm)	138.7 ± 23.2	164.1 ± 10.5
	Weight (kg)	37.1 ± 7.7	55.1 ± 15.9

Table 2 .

 2 Reliability of physical fitness tests in youth Reliability of the 1/2-mile run/walk tests

		1 st trial	2 nd trial	Mean difference [95% IC]	P	ICC
	All
	Sprint test (sec)	5.32 ± 1.40	5.13 ± 1.35	-0.19 [-0.03; 0.37]	0.254	0.97
	Basketball throw (cm) 858.9 ± 244.2	845.5 ± 238.5	-13.4 [-0.65; 1.04]	0.603	0.93
	Shoulder stretch test (cm)	6.1 ± 6.8	6.9 ± 7.1	0.8 [0.78; 0.85]	0.297	0.91
	Standing broad long jump (cm)	174.9 ± 63.6	177.6 ± 60.8	2.7 [2.28; 3.12]	0.694	0.93
	½ mile run/walk test (sec)	299.7 ± 85.4	298.1 ± 52.2	-1.6 [-3.33; 6.53]	0.938	0.66
	Children
	Sprint test (sec)	4.68 ± 0.88	4.48 ± 0.67	-0.2 [0.15; 0.25]	0.339	0.95
	Basketball throw (cm) 750.5 ± 181.6	761.6 ± 186.2	11.1 [10.14; 12.06]	0.689	0.90
	Shoulder stretch test (cm)	4.5 ± 6.6	5.5 ± 6.9	1.03 [0.97; 1.09]	0.313	0.93
	Standing broad long jump (cm)	150.3 ± 45.1	153.6 ± 47.5	3.3 [2.79; 3.80]	0.636	0.96
	½ mile run/walk test (sec) 325.8 ± 102.3	335.5 ± 98.6	9.7 [8.93; 10.47]	0.208	0.71
	Adolescents
	Sprint test (sec)	5.98 ± 1.54	5.80 ± 1.54	-0.18 [0.16; 0.20]	0.621	0.96
	Basketball throw (cm) 969.9 ± 250.9	932.3 ± 256.1	-37.6 [36.5; 38.70]	0.333	0.93
	Shoulder stretch test (cm)	7.9 ± 6.6	8.4 ± 6.9	0.5 [0.44; 0.56]	0.635	0.88
	Standing broad long jump (cm)	200.6 ± 69.9	202.2 ± 63.2	1.6 [0.18; 3.01]	0.872	0.89
	½ mile run/walk test (sec) 277.3 ± 105.3	287.3 ± 106.1	10.1 [9.93; 10.27]	0.836	0.63

Acknowledgements

The authors thank all participating adolescents and teachers for their collaboration in the study. Authors thank also the association "SportAlim" (www.sportalim.com).

Conflict of Interest statement

The authors declared no conflict of interest.


Jérémy Vanhelst
email: jeremy.vanhelst@chru-lille.fr

Laurent Béghin

Paul Stephen Fardy

Gilles Bui-Xuan

Jacques Mikulovic

Strategies in intervention programs for obese youth: implication of the age and the type of physical activities

Keywords: Rehabilitation, Pediatrics, Obesity, Physical activity, Strategies

The aim of this study was to assess the effects of age and type of physical activity on anthropometric measures of obese youth participating in an intervention program. Subjects included 37 obese children (12.5 ± 2.9 yrs). The program consisted of a unique program of physical activity and health education. Assessments included body mass index, body composition, and ability to perform sport activities. Paired t tests were used to assess the effects of intervention and chi square was used to assess inter-action between measures.

Findings suggest significant decrease in Z scores of Body Mass Index and an improvement of the ability to perform sport activities (p < 0.05). The effectiveness of the program has more impact on children than adolescents (p < 0.05). Improvements were greater in team vs. net sports (p < 0.05). Results show that intervention strategies have to be different according to the age in order to have a favourable effect on anthropometric characteristic and the consequences of obesity childhood and adulthood. The findings suggest that the intervention program was of greater benefit for children than adolescents.

Introduction

Pediatric obesity is alarming and epidemic problem in Western industrialized countries.

Obesity in youth is associated with adverse health consequences in adults such as coronary heart disease, diabetes, and some cancers. Studies show that high normal weight in childhood predicts overweight or obesity as an adult and elevated Body Mass Index (BMI) in childhood predicted risk of hypertension in young adulthood [START_REF] Dietz | Childhood weight affects adult morbidity and mortality[END_REF]Whitaker, Wright, Pepe, Seidel, & Dietz, 1997;Filed, Cook, & Gillman, 2005). Other consequences of obesity include sleep apnea, orthopaedic complications, asthma, poor quality of life and hypertension (Wabitsch, Hauner, Heinze, Muche, Bockmann, & Parthon, 1994;[START_REF] Chin | Can the increase in body mass index explain the rising trend in asthma in children?[END_REF][START_REF] Mutius | Relation of body mass index to asthma and atopy in children: the National Health and Nutrition Examination Study III[END_REF][START_REF] Mcmurray | A school-based intervention can reduce body fat and blood pressure in young adolescents[END_REF][START_REF] Dahlberg | Strong connection between overweight/obesity and orthopedic complaints. Consequences of the obesity epidemic widen[END_REF][START_REF] Jasik | Adolescent obesity and puberty: the 'perfect storm[END_REF]Gozal & Kheirandish-Gosal, 2009).

Clinical interventions with differing methodologies have been developed to treat obesity.

Physical activity training is regarded as an effective approach recognized for longterm weight maintenance [START_REF] Van Dale | Weight maintenance and resting metabolic rate 18-40 months after a diet/exercise treatment[END_REF]. Another successful strategy is restricting diet caloric intake [START_REF] Epstein | Increasing healthy eating vs. reducing high energy-dense foods to treat pediatric obesity[END_REF].

Physical activity is widely recognized for its positive impact on health and important role in the prevention and treatment of chronic diseases such as obesity [START_REF] Ekelund | Physical activity and metabolic risk in individuals with a family history of type 2 diabetes[END_REF][START_REF] Pedersen | Evidence for prescribing exercise as therapy in chronic disease[END_REF]. Physical activity is represented by three components, the duration, the frequency and the intensity. Studies have shown that intensity, frequency and duration of activity are important factors in having a positive impact on childhood obesity [START_REF] Atlantis | Efficacy of exercise for treating overweight in children and adolescents: a systematic review[END_REF][START_REF] Horowitz | Lipid metabolism during endurance exercise[END_REF][START_REF] Achten | Determination of the exercise intensity that elicits maximal fat oxidation[END_REF][START_REF] Lazzer | Optimizing fat oxidation through exercise in severely obese Caucasian adolescents[END_REF].

However, to the best of our knowledge, there is no study assessing the effectiveness of the type of physical activity on obese youth. Such information would provide valuable information for successful program development.

The objective of this study was to assess the influence of age and type of physical activity on anthropometric measures of obese youth.

Participants and Methods

The current report is based on data derived from an intervention program on obese youth [START_REF] Vanhelst | The CEMHaVi program: control, evaluation, and modification of lifestyles in obese youth[END_REF]. The aim of the program was to improve the health of obese youth by reducing obesity and improving cardiovascular health, physical fitness, sleep, and self-esteem. Data were collected during 2008 and 2010 in Northern France. In total, 37 obese youth ages 12.5 ± 2.9 yrs (18 girls and 19 boys) participated in the study. A detailed description of the program has been published elsewhere [START_REF] Vanhelst | The CEMHaVi program: control, evaluation, and modification of lifestyles in obese youth[END_REF]. In summary, physical training consisted of many moderate to vigorous activities, including team and net sports, such as basketball, football, tennis, badminton, and handball. Physical activity consisted of 2-hour sessions once each week in a gymnasium for one year using the Conative Educational Model (Mikulovic, Bui-Xuan, & Marcellini, 2002;Bui-Xûan, 1999). The conative educational approach is based on the idea of conative curriculum which models a sense given by to one's actions (Bui-Xûan, 1999).

Identifies five impetus which lead one's actions. This model allows the resarcher to identify conative stages through observation of child's practice, and to assess progress or evolution in the three components (structural, functional and technical) forming the model. The summation of these three components is called "guiding principle" which organize five conative stages, from novice (1) to expert (5) (Bui-Xûan, 1999). Subjects identify their stage and observe their progress in the practice of sport. Progress of the intervention program is associated with a teaching activity adapted to the stage that best encourages acquiring of new skills and progressing from one stage to the next. Subjects were evaluated individually and the activity program was adapted for each subject at the stage that met the subject's ability.

The aims and objectives were explained carefully to each subject. Written, informed consent was obtained from the children and their parents. The study was approved by the local ethics committee, and all procedures were performed in accordance with the ethical standards of the Helsinki Declaration of 1975 as revised in 2008 and the European Good Clinical Practices and the European Good Clinical Practices and with the ethical standards of the sport and exercise science research [START_REF] Béghin | Quality assurance of ethical issues and regulatory aspects relating to good clinical practices in the HELENA Cross-Sectional Study[END_REF]Harris & Atkinson, 2011).

Measurements

Measurements included age, height, weight, body mass index (BMI), body composition and ability to perform sport activities. Data were collected at baseline and at the end of one year.

Patients characteristics

Body mass was measured without shoes and heavy outer garments to the nearest 0.1 kg using an electronic scale (Oregon Scientific®, GA 101, USA). Height was measured without shoes to the nearest 0.1 cm using a standard physician's scale. Body Mass Index (BMI) was calculated by weight (kg)/height (m²), and was converted to Z-score of BMI.

Total fat and fat free mass were assessed using bioelectrical impedance analysis (AKERN®, BIA101 AKERN, Italy). Following a 5 minute rest subjects were placed in a supine position with arms and legs in abduction between 30 and 40° from the trunk. Electrode tape, conductivity gel, and current electrodes were placed on the dorsal surfaces of the right hand and foot at the distal metacarpals and metatarsals, respectively [START_REF] Houtkooper | Bioelectrical impedance estimation of fat-free body mass in children and youth: a cross-validation study[END_REF]. Detector electrodes were applied at the right pisiform prominence of the wrist and between the medial and lateral malleoli at the ankle [START_REF] Kushner | Estimation of total body water by bioelectrical impedance analysis[END_REF]. Subjects were instructed to avoid eating for two hours prior to testing. Shoes, socks, watches and jewelry were removed. Subjects were non hydrated and were requested to void the bladder prior to testing. Bio electrical impedance gives a value, expressed in resistance (R). This value is incremented in the equation of Houtkooper et al. to calculate fat mass, fatfree mass for all participants [START_REF] Houtkooper | Bioelectrical impedance estimation of fat-free body mass in children and youth: a cross-validation study[END_REF].

Ability to perform sport activities (conative curriculum)

Conative curriculum is organized into five stages, from novice (1) to expert (5) in order to assess and observe the progress in the performance of sport [START_REF] Vanhelst | A conative educational model for an intervention program in obese youth[END_REF]. Ability to perform sport activities was assessed using scales developed for team sports, e.g. soccer, handball, basketball, and net sports, e.g. tennis, badminton, volleyball. The five levels in conative curriculum are described elsewhere [START_REF] Vanhelst | A conative educational model for an intervention program in obese youth[END_REF]. Measures included Z-score of BMI, the age and the stage of conative curriculum. The chi square test was used to assess the interactions between these three variables during the intervention program. A p values < 0.05 were taken to be significant with a 95% confidence interval.

Statistical analysis

Results

Subjects are described in Table 1. Significant improvements are observed between pre and post intervention for the Z score of BMI (Table 2). No significant difference was observed for change of body composition, i.e. fat and fat free mass. The conative curriculum of subjects increased significantly (p < 0.05). Thirty-five of thirty-seven subjects improved significantly in team sport (p <0.0001) (Table 3). Compared to team sports, fewer subjects improved in net sports although gains were significant (p < 0.05) (24/37) (Table 3).

The mean ages where Z score of BMI decreased, stagnated, or increased was 12.3, 15.6 and 13.9, respectively. The effectiveness of the program on anthropometric measures was greater on children than adolescents. Best results were observed in subjects equal to or less than 12 years. 100% of obese youth aged less than 12 years improved Z score of BMI whereas 20% of subjects more than 12 years of age improved their Z score of BMI (χ2 = 2.77, df = 1, p < 0.05). 95% of obese youth 12 years of age or less improved the ability to perform team sports while 57.9% of subjects improved skills in net sports (χ2 = 2.81, df = 1, p < 0.05). 100% of obese youth aged more than 12 years of age improved the ability in net and team sports.

Discussion

Adolescence is a crucial period of life where lifestyle habits are established and persist until adulthood. The purpose of this study was to assess the influence of age and type of physical activity in obese youth participating in a rehabilitation program. Results suggest that there is a difference in the effectiveness of the program according to age and type of physical activity training. The program had more effect on improving team sports vs net sports and improvements in Z score of BMI were greatest for those subjects equal to or greater than 12 years.

Results from the present study showed that intervention was more beneficial for children 12 years of age or less vs children more than12 years old. The age associated with greatest change corresponds to puberty [START_REF] Cheng | Beyond overweight: nutrition as an important lifestyle factor influencing timing of puberty[END_REF]. The effect of the pubertal development on physical changes, e.g. substrate oxidation, insulin resistance, vitamins, blood serum, BMI, adiposity has been well studied and should be taken into account in studies of overweight or obese youth [START_REF] Brandou | Comparison of the type of substrate oxidation during exercise between pre and post pubertal markedly obese boys[END_REF][START_REF] Khadgawat | The Effect of Puberty on Interaction between Vitamin D Status and Insulin Resistance in Obese Asian-Indian Children[END_REF][START_REF] Lewitt | Pubertal stage and measures of adiposity in British schoolchildren[END_REF]Molnar & Schutz, 1998). These studies concluded that pubertal status should be taken into account in studies of overweight or obese youth. Brandou et al showed that the influence of age on the ability to oxidize fat at exercise is explained by the pubertal increase in fat fee mass. Authors demonstrated in markedly obese children during puberty, the ability of fat free mass to oxidize fat at exercise decreases [START_REF] Brandou | Comparison of the type of substrate oxidation during exercise between pre and post pubertal markedly obese boys[END_REF]. This conclusion may explain the difference between the two age categories. Even if obese youth increased fat free mass at the end of the intervention program, the improvement was not sufficient to overcome the effect of decreasing of fat oxidation by the fat free mass. Our results are in accordance with the studies showing the difficulty after puberty, to use fat oxidation to enhance lipolysis and diminish adipose tissue and the consequences of obesity (Molnar & Schutz, 1998;[START_REF] Mcmurray | The interaction of obesity and puberty on substrate utilization during exercise: a gender comparison[END_REF][START_REF] Brandou | Comparison of the type of substrate oxidation during exercise between pre and post pubertal markedly obese boys[END_REF][START_REF] Maffeis | Increased fat oxidation in prepubertal obese children: a metabolic defense against further weight gain?[END_REF]. However, we cannot completely confirm these conclusions because the program does not include data on the subjects' puberty stage. Other factors, such as daily physical activity, may also explain the improvement of anthropometric measures in children and not in adolescents. [START_REF] Knuth | Temporal trends in physical activity: a systematic review[END_REF] showed that physical activity in youth decreased with increasing age, including a lower level of activity in physical education classes. In this program, whether children or adolescents, the time spent in moderate to vigorous physical activity during one week is not different (data not shown).

Another outcome of the present study was the necessity to differentiate the physical activity training according to the type of exercise. Adolescents improved their skills in team and net sports whereas children improved more in team v. net sports. No explanation on this topic is referenced in the literature. Perhaps there is less improvement in net sports because these activities, e.g. tennis, badminton, and table tennis have more complex movements than team sports. Results from our study on this topic are important in designing intervention programs for obese youth. Indeed, the intervention program has to be enjoyable in order to maintain interest and motivate subjects to adhere. The participant must never be in a failure situation which might lead to decreased activity. The child is positioned in a positive evolutionary dynamics in order to increase self-esteem that will lead a better management of overweight.

Therefore, intervention strategies have to be different according to the age of the patient. Our results show that engaging in team sports has a greater impact on anthropometric measures and on the improvement on their ability for both age categories. Therefore team sports should be preferred for children. Net sports are better for adolescents than children.

The current study is unique in that it represents a 1-year health-wellness intervention program of physical activity for obese youth with a conative educational approach. The use of the conative curriculum permits subjects to be evaluated individually and to adapt the activity program according to the subject's ability. The study is limited because no control group was included. Future research could included a larger wide participants adding a control group.

In summary, results show that the intervention should take into account differences in age when designing intervention strategies for obese youth and adolescents. Team sports as a physical activity training intervention are more favourable than net sports for this age group. Z score of BMI 5 ± 1.9 4.5 ± 1.9* -0.4 -8.7

Legends

Fat mass (kg) 39.1 ± 6.6 37.4 ± 6.4 -1.7 -4.3

Fat Free Mass (kg) 60.9 ± 6.6 62.6 ± 6.4 + 1.7 + 2.8

Conative Curriculum

Team sport 1.3 ± 0.5 3 ± 0.5* + 1.7 + 90

Net sport 1.3 ± 0.6 3 ± 0.7* + 1.7 + 52.9

  Data were analyzed using the Statistical Package for the Social Sciences, Windows 11.5 (SPSS Inc., Chicago, IL, USA), Excel 2003 (Microsoft Inc., Redmond, WA, USA) and Sphinx (Chavanod, France). Means were calculated at baseline and following intervention and were compared by paired t tests to assess the effects of the intervention program.

Table 1 .

 1 Physical characteristics of subjects (n = 37)

Table 2 .

 2 Pre and Post intervention mean differences in Z score of BMI and the stage obtained in conative curriculum(n = 37)

Table 3 .

 3 Evolution of participants after the intervention program (n = 37)

Table 1 .

 1 Physical characteristics of subjects (n = 37)

	Boys	Girls

Table 2 .

 2 Pre and Post intervention mean differences in Z score of BMI and the stage obtained in conative curriculum(n = 37)

	Pre intervention	Post intervention	Δ	Δ (%)

Table 3 .

 3 Evolution of participants after the intervention program (n = 37)

		Decrease	Stagnation	Improvement
	Team sport (n = 37)	0	2	35*
	Net sport (n = 37)	0	13	24 †
	* p <0.0001
	† p <0.05

* p <0.05

Acknowledgements

The authors thank the children and their parents for taking part in the study. There is no funding for this study. The authors declare that they have no competing interests.

The findings suggest also that the intervention program in obesity is more favourable for children (pre pubescent) than adolescents (post pubescent).

Wabitsch M, Hauner H, Heinze E, Muche R, Bockmann A, Parthon W. Body-fat distribution and changes in the atherogenic risk-factor profile in obese adolescent girls during weight reduction. Am J Clin Nutr (1994); 60: 54-60.

Whitaker RC, Wright JA, Pepe MS, Seidel KD, Dietz WH. Predicting obesity in young adulthood from childhood and parental obesity. N Engl J Med (1997); 337: 869-73.


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Groettrup

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