Alexandre Bazin

A Depth-first Search Algorithm for Computing Pseudo-closed Sets

Keywords:

The question of the lower bounds for the delay in the computation of the Duquenne-Guigues implication basis in non-lectic orders is still open. As a step towards an answer, we propose an algorithm that can enumerate pseudo-closed sets in orders that do not necessarily extend the inclusion order using depthfirst searches in a sequence of closure systems. Empirical comparisons with NextClosure on the runtime and number of closed sets computed are provided.

Introduction

Implications, linked to closure operators, are not only interesting mathematical objects worth studying in their abstract form but they also find their application in database theory and data mining in the form of functional dependencies and certain association rules. Implications are essentially relations between elements of a powerset 2 E and, as often with this type of constructs, their number is exponential in |E| and most of them are redundant. As such, the interest revolves around finding smaller, non redundant sets of implications. The smallest such set, the subject of this work, is the Duquenne-Guigues basis.

The Duquenne-Guigues basis is constructed through the enumeration of socalled pseudo-closed sets. This enumeration has been studied most notably in the field of Formal Concept Analysis (FCA) and known results on counting, recognizing and computing these objects are mentioned in Section 2. [START_REF] Babin | Computing Premises of a Minimal Cover of Functional Dependencies is Intractable[END_REF]. The biggest open question concerns the delay of this enumeration in the general case. Indeed, it has been shown that pseudo-closed sets cannot be enumerated with a polynomial delay in the lectic or reverse lectic orders unless P = NP [START_REF] Distel | On the Complexity of Enumerating Pseudo-intents[END_REF][START_REF] Babin | Computing Premises of a Minimal Cover of Functional Dependencies is Intractable[END_REF] but no such result exists for other orders.

Two algorithms (and their variants) can be used to compute pseudo-closed sets. The first and most popular, NextClosure [START_REF] Ganter | Finding All Closed Sets: A General Approach[END_REF], uses the lectic order and thus cannot enumerate with a polynomial delay unless P = NP. The second [START_REF] Obiedkov | Attribute-incremental Construction of the Canonical Implication Basis[END_REF] uses an incremental approach and is not necessarily limited to the lectic order. Both algorithms, however, have to enumerate closed sets along with pseudoclosed sets. As the number of closed sets can be exponential in the number of pseudo-closed sets, this severely reduces hopes of obtaining a good delay with these methods. We believe that the need to compute all closed sets is linked to the way pseudo-closed sets are recognized, which forces an enumeration in orders that extend the inclusion order. That is why we propose here an algorithm that can enumerate pseudo-closed sets in orders that do not necessarily extend the inclusion order. Section 2 covers the basic required notions on lattices, closure operators and implications. In Section 3, we present a new way of recognizing a pseudoclosed set that does not require explicit knowledge of all its subsets and also propose an algorithm for finding a single pseudo-closed set. In Section 4, we describe an algorithm for computing the Duquenne-Guigues basis of a closure operator. Section 5 presents empirical results on the number of closed sets that our algorithm computes and comparisons with NextClosure.

Preliminaries

Lattices and Closure Systems

In this section, we recall the basic notions of lattice theory we will use in this work. For a deeper understanding of the subject, we refer the reader to [START_REF] Birkhoff | Lattice Theory[END_REF].

Definition 1. Let (E, ≤) be a partially ordered set. For any S ⊆ E, we call infimum (noted S) the greatest e ∈ E such that ∀s ∈ S, e ≤ s. Dually, we call supremum (noted S) the smallest e ∈ E such that ∀s ∈ S, s ≤ e. A lattice is a partially ordered set in which any pair of elements has a unique infimum and a unique supremum.

For example, (2 X , ⊆) is the Boolean lattice composed of the subsets of X ordered by inclusion. Definition 2. Let L = (E, ≤) be a lattice. For any x, y ∈ E, we say that x is a lower (resp. upper) cover of y if x is maximal (resp. minimal) such that x ≤ y (resp. y ≤ x). An element e ∈ E is said to be meet-irreducible (resp. join-irreducible) if it has a single upper (resp. lower) cover.

The sets of meet-and join-irreducibles of L are denoted by M(L) and J (L) respectively. Any element e ∈ E is the infimum (resp. supremum) of {m ∈ M(L) | e ≤ m} (resp. {j ∈ J (L) | j ≤ e}). As such, both sets completely represent the lattice.

a b c d e o1 × × o2 × × × o3 × × × o4 × × o5 × ×
E → 2 E that is idempotent (c(c(X)) = c(X)), extensive (X ⊆ c(X)) and monotone (X ⊆ Y ⇒ c(X) ⊆ c(Y )) is a closure operator.
A set S ∈ 2 E such that S = c(S) is said to be closed under c. The derivation operator • ′′ , associated to the context, is the composition of the two operators

• ′ : 2 O → 2 A O ′ = {a ∈ A | ∀o ∈ O, (o, a) ∈ R} and • ′ : 2 A → 2 O A ′ = {o ∈ O | ∀a ∈ A, (o, a) ∈ R} Example 1.
In the remainder of this work, we will abuse set notations for attribute sets and use, for example, abc to denote {abc}. In the context depicted in Table 1, the set of closed attribute sets is {∅, b, c, d, e, ab, bd, ce, de, bcd, bde, abcde}.

Implications

Now, let us present some definitions and results on implications. Multiple notions of bases have been studied in the literature [START_REF] Bertet | The Multiple Facets of the Canonical Direct Unit Implicational Basis[END_REF] but the one we are interested in is the basis of minimum cardinality called the Duquenne-Guigues basis [START_REF] Guigues | Familles minimales d'implications informatives résultant d'un tableau de données binaires[END_REF].

∀A → B ∈ I, A ⊆ Y ⇒ B ⊆ Y
Definition 9. A set P ∈ 2 E is pseudo-closed if it
is not closed and it contains the closure of all its proper subsets that are pseudo-closed.

Definition 10. The Duquenne-Guigues basis is the set

B = {P → c(P ) | P is pseudo-closed} Example 4. The Duquenne-Guigues basis corresponding to the context shown in Table 1 is {a → ab, bc → bcd, be → bde, cd → bcd, abd → abcde, bcde → abcde}.
Computing the Duquenne-Guigues basis is thus enumerating all the pseudoclosed sets for a particular closure operator. Having shown that the closed and pseudo-closed sets together form a closure system, Ganter proposed to use NextClosure [START_REF] Ganter | Finding All Closed Sets: A General Approach[END_REF], arguably the best-known and all-around most efficient algorithm. It enumerates pseudo-closed sets in the so-called lectic order, a total order that extends the order induced by the inclusion relation. As such, when the algorithm reaches a new pseudo-closed set, it has already computed the closure of all its subsets that are pseudo-closed and can, thus, recognize it. Other algorithms have been proposed such as variations on NextClosure [START_REF] Borchmann | A Generalized Next-Closure Algorithm -Enumerating Semilattice Elements from a Generating Set[END_REF][START_REF] Stumme | Attribute Exploration with Background Implications and Exceptions[END_REF][START_REF] Bazhanov | Comparing Performance of Algorithms for Generating the Duquenne-Guigues Basis[END_REF] based on the lectic order, the one in [START_REF] Bazin | Computing the Duquenne-Guigues Basis: An Algorithm for Choosing the Order[END_REF] which can enumerate in any order that extends the inclusion or the attribute-incremental algorithm in [START_REF] Obiedkov | Attribute-incremental Construction of the Canonical Implication Basis[END_REF]. All of these share the same property: they compute all the closed sets. The number of closed sets being potentially exponential in the number of pseudo-closed sets, none of these algorithms have a polynomial delay. Some aspects of pseudo-closed sets have been studied in relation to their computation. We know that |B| can be exponential in |A| and |R| [START_REF] Kuznetsov | On the Intractability of Computing the Duquenne-Guigues Basis[END_REF]. The problem of deciding whether a set is pseudo-closed given a context has been considered in [START_REF] Kuznetsov | Counting Pseudo-intents and #Pcompleteness[END_REF]1] and found to be coNP-complete. Special cases in the form of particular classes of lattices have been explored in [START_REF] Janssen | Minimum Implicational Basis for Meet-semidistributive Lattices[END_REF][START_REF] Wild | Optimal Implicational Bases for Finite Modular Lattices[END_REF][START_REF] Duquenne | The Core of Finite Lattices[END_REF]. In [START_REF] Distel | On the Complexity of Enumerating Pseudo-intents[END_REF], the authors proved that it is impossible to enumerate pseudo-closed sets in the general case in the lectic order with a polynomial delay unless P = NP and went on to remove the restriction on the order but were unable to find a lower bound. Thus, the question of the complexity of enumerating pseudo-closed sets in non-lectic orders is still open. To the best of our knowledge, the problem of enumerating pseudo-closed sets in orders that do not extend the inclusion order has not yet been studied in the literature.

Computing a Pseudo-closed Set

Recognizing Pseudo-closed Sets

As mentioned in Section 2.2, given a formal context, the problem of recognizing a pseudo-closed set is coNP-complete. When enumerating in orders that extend the inclusion order, we are faced with the easier problem of recognizing pseudo-closed sets given a context, a set S and the knowledge of the closures of all the subsets of S encapsulated in the implication set I = {A → B | A is pseudo-closed and A ⊂ S}. It is solved by computing I(S) and S ′′ . However, if we want to enumerate in orders that do not extend the inclusion order, we cannot suppose we have all the information on the subsets and we thus have to be able to recognize a pseudo-closed set given only partial information, i.e. an implication set I ⊆ {A → B | A is pseudo-closed and A ⊂ S}.

Looking back at the definition of a pseudo-closed set, we acknowledge that the minimal amount of information (about the closures of the subsets) needed to recognize a pseudo-closed S is one that ensures that S contains the closures of all its pseudo-closed proper subsets. Using implications as information, this minimal amount of information is an implication set of minimal cardinality for which we know with certainty that adding new implications will not change the logical closure of S. In other words, it is an implication set I ⊆ B of minimal cardinality such that I(S) = S implies L(S) = S for any I ⊆ L ⊆ B. Proposition 2. A set P is pseudo-closed if and only if it is not closed and there exists an implication set I ⊆ B such that P ∈ Φ I and all its lower covers in Φ I are closed.

Proof ⇒. Let us suppose P is pseudo-closed and I = B \ {P → c(P )}. From the definition of a pseudo-closed set, we have that P is not closed and P → c(P ) does not follow from I so P ∈ Φ I . We then have that all the lower covers of P in Φ I are closed (otherwise it would contain another pseudo-closed set that is not in I).

⇐. Let us suppose P is not closed and I ⊆ B is an implication set such that P ∈ Φ I and all the lower covers of P in Φ I are closed. From P belonging to Φ I , we deduce that if A → c(A) ∈ I and A ⊂ P , then c(A) ⊂ P . For any set S ⊂ P in Φ I , we have S ⊆ C where C is a lower cover of P . If S = c(S), we necessarily have c(S) ⊆ C because C is closed. As every pseudo-closed set not in I is necessarily in Φ I (otherwise it would not contain the closure of one of its pseudo-closed proper subsets), P contains the closure of all its strict subsets that are pseudo-closed and is thus pseudo-closed. Definition 11. A pseudo-closed set P ∈ Φ I for a closure operator c is said to be recognizable under I if all its lower covers in Φ I are closed.

We use Rec(I) to denote the set of pseudo-closed sets that are recognizable under I.

Example 5. In our running example, given I = {cd → bcd, be → bde} the lower covers of bc and bcde in Φ I are respectively {b, c} and {bcd, bde, ce}. All of these sets being closed, both bc and bcde are recognizable pseudo-closed sets under I. However, we have abd ∈ Rec(I) because one of its lower covers, ad, is not closed.

Proposition 3. ∀I ⊂ B, Rec(I) = ∅.
Proof Let P be minimal among pseudo-closed sets that are not premises of implications in I. If there is a lower cover C of P in Φ I that is not closed, then there is a non-closed set A ⊆ C in Φ I such that A → c(A) holds in the context. If c(A) ⊂ P then P is not minimal. If c(A) ⊆ P , then P is not pseudo-closed. Both cases lead to contradictions so all the lower covers of P are closed and P is recognizable from I. Since we have I ⊂ B, the set of pseudo-closed sets that are not a premise in I is not empty, so it has minimal elements. Hence,

Rec(I) = ∅ if I ⊂ B.
Viewing I as the set of implications "already found" at a given step during an enumeration, this property ensures we always have additional pseudo-closed sets to find if the basis is not completed.

As every element of Φ I is the intersection of meet-irreducibles, the number of lower covers of a set is bounded by |M(Φ I )|. The intersection and the closure sets can both be computed in time polynomial in the size of the context so deciding whether a set is a recognizable pseudo-closed set is polynomial in the size of M(Φ I ).

Finding a Pseudo-closed Set

Now that we know how to recognize pseudo-closed sets, we want to be able to find one efficiently. We do not want to force an enumeration order more restrictive than the one imposed by the recognizability of a pseudo-closed set and randomly testing sets would be inefficient. Proposition 4. The lattice Φ I contains a recognizable pseudo-closed set P if and only if there is a maximal chain C = X 1 ⊂ ... ⊂ X n of non-closed sets that cannot be extended by proper subsets of X 1 with X 1 = P and X n ∈ M(Φ I ).

Proof ⇒. Let P ∈ Φ I be a recognizable pseudo-closed set. Since P is in Φ I , there must be a ∧-irreducible S such that P ⊆ S and c(P ) ⊆ S. Obviously, S itself and any T ∈ Φ I such that P ⊆ T ⊆ S are not closed. P being the minimal element of the chain follows from the definition of a recognizable pseudo-closed set.

⇐. Let us suppose the lattice contains a maximal chain of non-closed sets with a ∧-irreducible as its maximal element and P as its minimal element. The set P being minimal in the maximal chain of non-closed sets, all its lower covers are closed. As such, it is a recognizable pseudo-closed set. We can thus find a pseudo-closed set by first finding a non-closed meetirreducible X in Φ I and then computing the non-closed elements of the chain in a depth-first manner.

. Algorithm 1 terminates and returns a recognizable pseudo-closed set.

Proof There is a finite number of meet-irreducibles and elements so the algorithm performs a finite number of recursive calls. As per Propositions 2 and 4, the set returned is a recognizable pseudo-closed set.

Computing all Pseudo-closed Sets

From Section 3.2, we know how to find a recognizable pseudo-closed set given a context, an implication set I and M(Φ I ). In practice (and in the case we are interested in), we begin with only a closure operator on 2 E and an empty set of implications. The lattice Φ ∅ = (2 E , ⊆) has |E| obvious meet-irreducibles: {E \{e} | e ∈ E} so applying Algorithm 1 to obtain a first pseudo-closed set only requires polynomial time. As a matter of fact, it corresponds to the algorithm proposed in [START_REF] Distel | On the Complexity of Enumerating Pseudo-intents[END_REF] for computing the lectically first pseudo-closed set (without the order requirement). After the first implication is found and I is not empty anymore, we have to explicitly compute M(Φ I ). Once this is done, we can apply Algorithm 1 to compute a new pseudo-closed set. Repeating this process will eventually yield the Duquenne-Guigues basis which, as per Proposition 4, has been computed once all the meet-irreducibles are closed. We deliberately keep our options open regarding the actual implementation of the computation of the meet-irreducibles. The best general-case algorithm is the one proposed by Wild [START_REF] Wild | Computations with Finite Closure Systems and Implications[END_REF] which computes the meet-irreducibles of Φ I from those of Φ I\{I} , which makes it efficient for our purpose. However, there are other algorithms for special cases. In particular, Gély and Nourine [START_REF] Gély | About the Family of Closure Systems Preserving Non-unit Implications in the Guigues-Duquenne Base[END_REF] showed that we can compute M(Φ I ) from M(Φ I\{I} ) in polynomial time when the premise of I is a singleton. More recently, Beaudou et al. [START_REF] Beaudou | Algorithms for kmeet-semidistributive lattices[END_REF] proposed an algorithm adapted to k-meet-semidistributive lattices.

Experimental Results

We implemented Algorithm 2 and used it to compute the Duquenne-Guigues bases of randomly generated closure operators. These were derivation operators corresponding to randomly generated formal contexts (O, A, R) such that (o, a) is in R with a probability d = n/|A|. We call d the density of the context. The contexts contained 50 objects and a varying number of attributes. For each values of |A| and d, 1000 random contexts were generated. This section presents results on the number of closed sets computed and comparisons with NextClosure.

Number of Closures

For each closure operator, we compared the number of closed sets computed by Algorithm 2 to the total number of closed sets.

σ closed = number of closed sets computed number of unique closed sets Figure 2 shows the values of σ closed (sorted in increasing order) for the 11000 contexts with 12 attributes and a density varying from 1/12 to 11/12. We observe that Algorithm 2 computes less closed sets than the total number of closed sets in 42% of the contexts. The best and worst cases are respectively σ closed = 0.03 and σ closed = 10.1.

Figure 3 shows the average number of closed sets total and computed (left) and the corresponding average σ closed (right) for each density d between 1/12 and 11/12. We observe that Algorithm 2 is most efficient on contexts with a density above 7/12 while, in sparser contexts, it computes many times more closed sets than necessary. This is most likely due to the fact that denser contexts more often contain "clusters" of closed sets that are never computed, thus compensating for the multiple occurrences of the other ones.

Runtime

Even though the runtime depends heavily on the implementation, it can give insight into what needs to be improved. We compare the runtimes of Algorithm 2 and NextClosure through the ratio σ runtime = runtime for Algorithm 2 runtime for NextClosure Figure 4 shows the average runtimes of NextClosure and Algorithm 2 together with the values of σ runtime for random contexts containing 13 attributes with densities between 1/13 and 12/13. The variations of the average runtime unsurprisingly correlates with the numbers of closed sets enumerated (Figure 3). This means that Algorithm 2 becomes more efficient than NextClosure once it starts enumerating less closed sets, i.e. once the context is dense enough.

Discussion

The proposed algorithm allows for the computation of the Duquenne-Guigues basis in orders that do not extend the inclusion order. Moreover, it does not necessarily enumerate all the closed sets even though it can find some of them multiple times. While this is certainly a step towards more efficient algorithms for this problem, the version presented here suffers from high runtimes on contexts (closure operators) that are not dense enough. These runtimes are due to

• the difficulty of computing the meet-irreducibles elements of Φ I∪{I} from those of Φ I

• the fact that closed sets can be found multiple times when performing the depth-first searches along non-closed chains As previously mentioned, computing the meet-irreducibles elements of Φ I∪{I} from those of Φ I can be done in polynomial time when the premise of I is a singleton. It would be interesting to isolate other special cases as it could lead to for each density between 1/13 and 12/13. Right: values of σ runtime for each density significant improvements on the runtime. Furthermore, studying the evolution of M(Φ I ) when I grows would help us bound the delay as it is a function of both the number of meet-irreducibles and their structure. Of course, it would also be beneficial to investigate better general-case algorithms for this particular problem.

Concerning the computation of the non-closed chain, we could, potentially, always find a non-closed set first and thus never compute a single closed set with Algorithm 1 before reaching the pseudo-closed set. Achieving that in every case is probably impossible but heuristics could be used to find a non-closed set faster, which would considerably speed up the computation.

Proposition 1 .

 1 Let X, Y ∈ 2 E be sets and c a closure operator. The set c(X)∩ c(Y ) is closed under c. Throughout this paper, we will use Φ c = ({X | X = c(X)}, ⊆) to denote the lattice of sets closed under a closure operator c ordered by the inclusion relation. The most commonly used closure operator in FCA literature is the derivation operator • ′′ that we will use as an example in this work. Definition 5. A formal context is a triple C = (O, A, R) where O is a set of objects, A a set of attributes and R ⊆ O × A a binary relation that associates sets of attributes to objects.

Example 2 .Definition 8 .

 28 Let I = {a → ab, bc → bcd} be an implication set. We have I(ad) = abd and I(ac) = abcd. An implication set I is a basis for a closure operator c if Φ I = Φ c . In FCA, an implication A → B is said to hold in a formal context when A ′ ⊆ B ′ . Example 3. The implications a → ab, b → b and ad → abcd hold in the example context. The implication b → b holds trivially in any context.

Example 6 .

 6 Let I = {cd → bcd, be → bde, bcde abcde} be a subset of the Duquenne-Guigues basis of our running example. The lattice Φ I , depicted in Figure1, contains 8 meet-irreducibles M(Φ I ) = {abcd, abde, abc, ace, ade, bcd, bde, ce} and 2 recognizable pseudo-closed sets Rec(Φ I ) = {bc, a}. Both abde > abd > ad > a and abcd > abc > bc are examples of maximal non-closed chains between a meet-irreducible and a pseudo-closed set.

Figure 1 :∅

 1 Figure 1: Lattice Φ I for I = {cd → bcd, be → bde, bcde → abcde} abcde

  Computing the intersections of a set with meet-irreducibles is in O(|E| × |M(Φ I )|) and the algorithm performs at most |E| recursive calls. Isolating the maximal elements can be done in O(|M(Φ I )| 2 ). Thus, we can compute a new pseudo-closed set in time polynomial in |M(Φ I )| times the complexity of computing a closure. The actual runtime of Algorithm 1 heavily depends on the order in which the meet-irreducibles are considered. If the first intersection always results in a nonclosed lower cover, the pseudo-closed set is reached after |E| closures whereas finding the non-closed set last can produce |E| × |M(Φ I )| unnecessary closed sets.

Algorithm 2 ,Proposition 6 .

 26 described in pseudocode, computes the Duquenne-Guigues basis of a given closure operator. Algorithm 2 AllP C(E, c) Require: A closure operator c on 2 E Ensure: The Duquenne-Guigues basis B corresponding to c I = ∅ M = {E \ {e} | e ∈ E} while ∃S ∈ M such that S = c(S) do P = Descent(S, M, c) I = I ∪ {P → c(P )} M = M(Φ I ) end while return I Algorithm 2 terminates and returns the Duquenne-Guigues basis of the input closure operator. Proof Propositions 5 and 2 ensure every iteration of the while loop adds a new implication I ∈ B. Proposition 4 ensures the while loop stops when I = B. The number of implications in B being finite, the algorithm terminates and returns the Duquenne-Guigues basis of the context.

  Wild's algorithm computes the meet-irreducibles of Φ I from those of Φ I\{I} by intersecting elements of M(Φ I ) ∩ M(Φ I\{I} ) (meet-irreducibles that stay) with elements of M(Φ I\{I} )\(M(Φ I )∩M(Φ I\{I} )) (meet-irreducibles removed by the new implication). Hence, it performs less than |M(Φ I\{I} )| 2 intersections. It then recognizes meet-irreducibles among the resulting sets. This can be done in polynomial time by checking whether a set is maximal among those that do not contain some element e. As such, both computing M(Φ I ) and finding a new pseudo-closed set can be done in time polynomial in |M(Φ I\{I} )|. Unfortunately, |M(Φ I\{I} )| can be exponential in |I|.

Figure 2 :

 2 Figure 2: Sorted values of σ closed for 11000 randomly generated contexts with 12 attributes and a density between 1/12 and 11/12 (1000 contexts for each density). The red line is σ closed = 1.

Figure 3 :

 3 Figure 3: Left: average number of unique closed sets (blue) and computed closed sets (green) for each density. Right: average values of σ closed for each density. The red line is σ closed = 1.

Figure 4 :

 4 Figure 4: Left: average runtime in milliseconds of NextClosure (green) and Algorithm 2 (blue) for each density between 1/13 and 12/13. Right: values of σ runtime for each density

Table 1 :

 1 ≤ ... ≤ c n is maximal if c i+1 is an upper cover of c i for any 1 ≤ i < n.

	Definition 4. Let E be a set. An operator c : 2

A Formal Context Definition 3. In a lattice (E, ≤), a chain is a set C ⊆ E such that any two elements of C are comparable. A chain C = c 1

  Definition 6. An implication is a pair(A, B) ∈ 2 E × 2 E , often noted A → B.

	Definition 7. Let I be a set of implications. We denote by I(•) the closure
	operator, sometimes called logical closure, that maps a set X to its smallest
	superset Y such that

Acknowledgements

The author was supported by the European Union and the French Région Auvergne-Rhône-Alpes under the European Regional Development Fund (ERDF).

Bibliography

[1] Mikhail A. Babin and Sergei O. Kuznetsov. Recognizing Pseudo-intents is coNP-complete. In Marzena Kryszkiewicz and Sergei A. Obiedkov, editors, Concept Lattices and Applications, volume 672 of CEUR Workshop Proceedings, pages 294-301. CEUR-WS.org, 2010.


Fatima-Zohra El

Laurent Yon

Marlène Guérin

Seloua El Ouezzani

Abdelilah Alaoui

Nicolas Chartrel

Youssef Anouar
email: youssef.anouar@univ-rouen.fr

Rabia Magoul

Immunocytochemical distribution of EM66 within the hypothalamic parvocellular paraventricular nucleus: Colocalization with CRH and TRH but no plasticity related to acute stress and thyroidectomy in the rat

Introduction

The hypothalamic paraventricular nucleus (PVN) is known to be involved in the neuroendocrine adaptive response to stress through parvocellular effector neurons synthesizing and releasing into the pituitary portal blood the corticotropin-releasing hormone (CRH) [START_REF] Harbuz | Stress responsiveness of hypothalamic corticotropin-releasing factor and pituitary pro-opiomelanocortin mRNAs following high-dose glucocorticoid treatment and withdrawal in the rat[END_REF][START_REF] Herman | Regulatory changes in neuroendocrine stressintegrative circuitry produced by a variable stress paradigm[END_REF][START_REF] Karalis | CRH and the immune system[END_REF]. The CRH-containing neurons of the parvocellular PVN (pPVN) have a high potential for phenotypical plasticity, allowing them to modify their neuroendocrine output depending upon circumstances [START_REF] Tilders | Phenotypic plasticity of CRF neurons during stress[END_REF]. Indeed, in addition to CRH, they are able to elaborate several other accessory neuropeptides, such as vasopressin, cholecystokinin, enkephalin, neurotensin or oxytocin, each probably subserving a complementary function to CRH in the control of the pituitary and each depending on different regulatory mechanisms for their expression [START_REF] Sawchenko | Corticotropin-releasing factor: coexpression within distinct subsets of oxytocin-, vasopressin-, and neurotensinimmunoreactive neurons in the hypothalamus of the male rat[END_REF][START_REF] Mezey | Cholecystokinin in the medial parvocellular subdivision of the paraventricular nucleus. Coexistence with corticotropin-releasing hormone[END_REF][START_REF] Lightman | Changes in hypothalamic preproenkephalin A mRNA following stress and opiate withdrawal[END_REF][START_REF] Antoni | Vasopressinergic control of pituitary adrenocorticotropin secretion comes of age[END_REF][START_REF] Watts | Physiological regulation of peptide messenger RNA colocalization in rat hypothalamic paraventricular medial parvicellular neurons[END_REF].

The pPVN neurons also contain the hypophysiotropic thyrotropinreleasing hormone (TRH), the central regulator of the hypothalamuspituitary-thyroid (or thyrotropic) axis [START_REF] Ishikawa | Immunocytochemical delineation of thyrotrophic area: origin of thyrotropin-releasing hormone in the median eminence[END_REF][START_REF] Merchenthaler | Mapping of thyrotropin-releasing hormone (TRH) neuronal systems of rat forebrain projecting to the median eminence and the OVLT. Immunocytochemistry combined with retrograde labeling at the light and electron microscopic levels[END_REF][START_REF] Fekete | Association of cocaine-and amphetamineregulated transcript-immunoreactive elements with thyrotropin-releasing hormonesynthesizing neurons in the hypothalamic paraventricular nucleus and its role in the regulation of the hypothalamic-pituitary-thyroid axis during fasting[END_REF][START_REF] Abel | Critical role for thyroid hormone receptor beta2 in the regulation of paraventricular thyrotropin-releasing hormone neurons[END_REF][START_REF] Ronald | The TRH neuron: a hypothalamic integrator of energy metabolism[END_REF] which plays an essential role in the maintenance of metabolic homeostasis in response to alterations in metabolism and external environment. The TRH neurons have a primary role in the regulation of the thyroid hormone (TH) production through release of TRH at the median eminence to stimulate pituitary TSH release. TSH then stimulates the thyroid gland to produce T4 and T3. TSH, in turn, regulates the activity of TRH neurons in the hypothalamus by a classical negative feedback pathway [START_REF] Segerson | Thyroid hormone regulates TRH biosynthesis in the paraventricular nucleus of the rat hypothalamus[END_REF][START_REF] Kakucska | Thyrotropin-releasing hormone gene expression in the hypothalamic paraventricular nucleus is dependent on feedback regulation by both triiodothyronine and thyroxine[END_REF][START_REF] Tapia-Arancibia | Evidence for α1-adrenergic stimulatory control of in vitro release of immunoreactive thyrotropin-releasing hormone from rat median eminence: in vivo corroboration[END_REF]. TRH neurons represent a neuron population completely distinct from the CRH neurons [START_REF] Ceccatelli | Distribution and coexistence of corticotropinreleasing factor-, neurotensin-, enkephalin-, cholecystokinin-, galanin-and vasoactive intestinal polypeptide/peptide histidine isoleucine-like peptides in the parvocellular part of the paraventricular nucleus[END_REF]. However, they express glucocorticoid receptors indicating that they may be under corticotrope axis control [START_REF] Ceccatelli | Coexistence of glucocorticoid receptor-like immunoreactivity with neuropeptides in the hypothalamic paraventricular nucleus[END_REF].

The secretogranin II-derived peptide EM66 is among the neuropeptides strongly expressed within the pPVN as well as in the external median eminence (ME), suggesting a probable hypophysiotropic role for this neuropeptide in the control of the corticotrope axis [START_REF] Boutahricht | Immunohistochemical distribution of the secretogranin II-derived peptide EM66 in the rat hypothalamus: a comparative study with jerboa[END_REF][START_REF] Yamani | EM66-containing neurones in the hypothalamic parvicellular paraventricular nucleus of the rat: no plasticity related to acute immune stress[END_REF]. As a first approach to investigate such a role, our previous results showed that EM66 does not participate to the phenotypical plasticity of pPVN neurons in response to acute inflammatory stress in rat [START_REF] Yamani | EM66-containing neurones in the hypothalamic parvicellular paraventricular nucleus of the rat: no plasticity related to acute immune stress[END_REF]. The patterns of distribution of the EM66-containing neurons and the CRH neurosecretory cells within the pPVN and their terminals in the ME are very similar, suggesting an eventual colocalization of these two neuropeptides in this hypothalamic neuroendocrine area [START_REF] Yamani | EM66-containing neurones in the hypothalamic parvicellular paraventricular nucleus of the rat: no plasticity related to acute immune stress[END_REF] and thus a possible functional interaction between CRH and EM66 within the pPVN in the regulation of the corticotrope axis.

To explore a possible EM66-CRH coexpression within the PVN as well as the ME (site of CRH release) of rat, we used in the present work a double immunofluorescence procedure followed by confocal microscope analysis. In order to investigate also an eventual neuroendocrine plasticity involving EM66 in response to stress and since the stress-induced neuroendocrine response seems to be stressor-specific [START_REF] Djordjević | Different activation of ACTH and corticosterone release in response to various stressors in rats[END_REF], we analyzed by immunohistochemistry EM66 expression within the pPVN neurons of rats submitted to different stressful circumstances such as acute immobilization and thermal stress. Such stressors are known to activate the corticotrope axis and represent interesting stressful stimulus inducing an increase in parvocellular CRH mRNA expression and ACTH hypersecretion followed by hypercorticosteronemia [START_REF] Wong | Acute-stress-induced facilitation of the hypothalamo-pituitary-adrenal axis[END_REF].

The similarity of the distribution pattern of TRH-containing neurons and the EM66 neuronal system within pPVN as well as ME suggests their possible coexpression in this neuroendocrine area and thus an eventual interaction in the regulation of the thyrotrope axis. Thyroidectomy is known to induce a significant increase in the number of TRH-containing neurons within the parvocellular aspect of the PVN and plasma TSH concentration [START_REF] Koibuchi | Thyroidectomy induces Fos-like immunoreactivity within thyrotropin-releasing hormone-expressing neurons located in the paraventricular nucleus of the adult rat hypothalamus[END_REF]. In this context, we evaluated by double immunofluorescence EM66-TRH coexpression within the PVN and the ME and studied the effect of short-term thyroidectomy on EM66 expression in the rat pPVN.

Material and methods

Animals

Male Wistar rats weighing 250-300 g were maintained under controlled conditions of temperature (24 °C) and photoperiod (12 h light/12 h dark). The diet was supplied ad libitum. Animal manipulations were performed according to the recommendations of the Local Ethical Committee.

Stress procedures

Rats were randomly assigned to three groups. A control group consisted of six animals (n = 6) sacrificed 24 h after intracerebroventricular (icv) injection of 100 μg/10 μl volume of colchicine (necessary to visualize EM66, CRH and TRH-immunoreactive cell bodies) (AP: -0.9 mm, length: 1.8 mm, height: -4.5 mm, according to Paxinos and Watson [START_REF] Paxinos | The rat brain in stereotaxic coordinates[END_REF]). The second group of rats (n = 6) was exposed to acute immobilization stress for 2 h according to the method of Kvetnansky and Mikulaj [START_REF] Kvetnansky | Adrenal and urinary catecholamines in rats during adaptation to repeated immobilization stress[END_REF] by fixing all four limbs to a board with adhesive tape. The heads were also fixed at the neck area, thus limiting their motion. This was followed by colchicine icv injection as described above. Rats of the third group (n = 5) were exposed to acute cold stress by keeping animals at 5 °C for 4 h, followed by colchicine treatment, and sacrificed 24 h after.

Thyroidectomy procedure

The surgical procedure was performed under pentobarbital anesthesia (35 mg/kg ip) as previously described [START_REF] Koibuchi | Thyroidectomy induces Fos-like immunoreactivity within thyrotropin-releasing hormone-expressing neurons located in the paraventricular nucleus of the adult rat hypothalamus[END_REF]. Briefly, in thyroidectomized rats (n= 6), thyroid glands were surgically removed. In the sham-control animals (n=6), the thyroid glands were just exposed.

All the experimental rats were kept alive during 6 days with food and water available ad libitum, and treated with colchicine 24 h before sacrifice.

Tissue processing

The expression of EM66, TRH, and CRH within hypothalamic cells and fibers was studied by immunohistochemistry, using respectively, rabbit polyclonal antibodies raised against recombinant EM66 [START_REF] Anouar | Identification of a novel secretogranin II-derived peptide (SgII (187-152)) in adult and fetal human adrenal glands using antibodies raised against the human recombinant peptide[END_REF][START_REF] Montero-Hadjadje | Biochemical characterization and immunocytochemical localization of EM66, a novel peptide derived from secretogranin II, in the rat pituitary and adrenal glands[END_REF], and a TRH synthetic peptide (13482, Abnova Taïwan) and sheep polyclonal antibodies raised against a CRH synthetic peptide (110-81721, Novus Biologicals). The animals were anesthetized with an intraperitoneal injection of sodium pentobarbital (35 mg/kg) and perfused through the aorta with 50 ml of a saline solution followed by 300 ml of a fixative solution containing 4% paraformaldehyde and 0.2% picric acid in 0.1 M phosphate buffer (PB), pH 7.4. The brains were dissected, cut into 5 mm thick slabs and post-fixed for 48 h at 4 °C with the same fixative. Brain sections (60 μm) at the hypothalamic level were cut on a vibratome and rinsed with phosphate-buffered saline (PBS).

Immunohistochemical (IHC) procedures

Single IHC labeling

The tissue sections were rinsed several times in PBS and processed for indirect immunohistochemistry. Tissue slices were incubated overnight at 4 °C with the primary EM66 antiserum diluted 1:2000 in PBS containing 0.3% Triton X-100. The sections were rinsed in PBS for 30 min and incubated for 2 h at room temperature with a biotinylated goat anti-rabbit (GAR) antiserum (Vector Laboratories, Paris, France) diluted 1:400. Finally, brain sections were incubated for 2 h at room temperature with standard avidin-biotin peroxidase (Vector Laboratories) diluted 1:400 in PBS. The peroxidase activity was revealed according to the method of Shu et al. [START_REF] Shu | The glucose-oxidase DAB-nickel method in peroxydase histochemistry of the nervous system[END_REF] using diaminobenzidine tetrahydrochloride (DAB, Sigma-Aldrich) as chromogen, and intensified with nickel ammonium sulfate (Sigma-Aldrich). The reaction was stopped by rinsing in PB. Sections were deposited on gelatin-coated slides, air-dried, dehydrated in graded alcohol and mounted in Eukit (O. Kindler GmbH & Co, Freiburg, Germany). The sections were examined under a Nikon Microphot-FX microscope (Tokyo, Japan) and photomicrographs were taken with a Leitz microscope (Leica, Heidelberg, Germany).

Double IHC labeling

Tissue slices were treated for 90 min with normal donkey serum diluted at 1:100 in a solution containing 1% BSA and 0.3% Triton X-100 in PBS, to reduce non-specific labeling. For EM66-CRH doubleimmunolabeling, sections were then incubated for 2 h at room temperature with a mixture of the two primary antibodies diluted 1:800 and 1:100, respectively. The immunoreactivities were revealed with a mixture of two secondary antibodies, Alexa Fluor 488-conjugated donkey anti-rabbit IgG (Invitrogen) diluted 1:100 and Alexa Fluor 594conjugated donkey anti-sheep IgG (Invitrogen) diluted 1:100. For EM66-TRH double-immunolabeling, a sequential approach [START_REF] Gasman | Regulated exocytosis in neuroendocrine cells: a role for subplasmalemmal Cdc42/N-WASP-induced actin filaments[END_REF] was used since both antibodies were raised in rabbit. Indeed, the saturation step was performed with normal goat serum, diluted 1:100 for 90 min at room temperature, before incubation with the TRH primary antisera (1:100, 2 h at room temperature). Tissue sections were rinsed in PBS and then incubated for 90 min at room temperature with Alexa Fluor 488-conjugated GAR IgG (Invitrogen) diluted 1:100. An intervening 15 min paraformaldehyde (2%) treatment was used between the first (TRH) and the second (EM66) immunolabeling procedures to allow fixation of the TRH-GAR immunoreactive complexes. The sections were then washed and treated with normal goat serum, diluted 1:100 for 90 min at room temperature. Subsequently, they were incubated overnight at 4 °C with the EM66 primary antibody diluted 1:800 and then incubated for 90 min with Alexa Fluor 594-conjugated GAR IgG (Invitrogen) diluted 1:100. Selected sections for double immunolabeling were incubated for 2 min with 1 μg/ml 4,6-diamino-2-phenylindole (DAPI, Sigma) to stain nuclei. Immediately after, tissue slices were rinsed in PBS, fixed again and buffer/glycerol (1:1) coverslipped to be examined using a Leica SP2 upright confocal laser scanning microscope (DMRAX-UV) equipped with the Acousto-Optico Beam Splitter system (Leica).

To verify the specificity of the immunoreactions, control tests were performed including omission of primary antibodies (substitution of the primary antibodies with PB) incubation with non-immune serum instead of the primary antibodies, and preincubation of the EM66 antiserum (diluted 1:800 or 1:2000 for respectively immunofluorescent or immunoenzymatic methods) with purified recombinant EM66. For the IHC procedure of TRH-EM66 labeling, omission of the primary EM66 antisera was performed in order to check the absence of unspecific Alexa Fluor 594-conjugated GAR IgG immunoreactive signal.

Statistical analysis

Quantification of EM66-IR cell bodies within the pPVN of control, stressed or thyroidectomized rats was performed on all PVN sections per animal and an average value was calculated for each animal. The magnification used for such measurements was × 100 and × 250. The results are expressed as mean ± SEM. Statistical significance was determined using Student's unpaired t-test.

Results

EM66-IR neurons in the rat pPVN and ME

The distribution pattern of EM66-IR neurons within the pPVN of control rats confirmed previously reported data [START_REF] Boutahricht | Immunohistochemical distribution of the secretogranin II-derived peptide EM66 in the rat hypothalamus: a comparative study with jerboa[END_REF][START_REF] Yamani | EM66-containing neurones in the hypothalamic parvicellular paraventricular nucleus of the rat: no plasticity related to acute immune stress[END_REF]. Indeed, most of the EM66-IR neurons were concentrated within the medial nuclei of the pPVN along its rostrocaudal extent (data not shown). As previously reported [START_REF] Boutahricht | Immunohistochemical distribution of the secretogranin II-derived peptide EM66 in the rat hypothalamus: a comparative study with jerboa[END_REF][START_REF] Yamani | EM66-containing neurones in the hypothalamic parvicellular paraventricular nucleus of the rat: no plasticity related to acute immune stress[END_REF], the median eminence (ME) exhibited a dense plexus of EM66-IR fibers in its external zone with a preferential distribution around capillaries.

Colocalization of EM66 and CRH-IR neurons within the pPVN and the ME

Co-incubation of hypothalamic slices with the anti-EM66 and the anti-CRH antibodies revealed that CRH-IR neurons within the pPVN contain EM66 immunoreactivity (Fig. 1A-H), indicating that the EM66 peptide occurs in corticotrope neuroendocrine cells. CRH and EM66 co-localization appears in cytoplasmic compartments (Fig. 1D andH, arrowhead). However, the CRH-EM66 colocalization is not observed in all cells since some CRH-IR cells did not exhibit any EM66-IR (Fig. 1E-H, asterisk) and some EM66-IR neurons did not display any CRH-IR (Fig. 1E-H, thick arrow). In the external zone of the ME, site of neurohormone release, numerous nerve terminals were positively labeled for EM66 and CRH (Fig. 2A andB). Moreover, it is clear that EM66 is coexpressed with CRH in some axon terminals, with a privileged distribution around capillaries (Fig. 2C, arrowhead). No immunoreaction was observed when primary antibodies were omitted, replaced by nonimmune serum or pre-incubated with the EM66 peptide in the case of the EM66 antibody.

Colocalization of EM66 and TRH-IR neurons within the pPVN and the ME

Co-incubation of hypothalamic sections with the anti-EM66 and anti-TRH antibodies revealed that numerous TRH-IR neurons within the pPVN were also immunolabeled for EM66 (Fig. 3D, H andL, arrowhead), indicating that the EM66 peptide is expressed in thyrotrope neuroendocrine cells. However, some TRH immunopositive cells were devoid of EM66-IR (Fig. 3E-H, thick arrow). Conversely, some EM66-IR neurons did not display any TRH immunoreactivity (Fig. 3E-H, asterisk). Furthermore, the external zone of the ME displayed intense colabelings of EM66 and TRH in fiber terminals, with a privileged distribution around capillaries (Fig. 4A-D). No immunoreactivity was observed when the EM66 antibody was omitted, replaced by non-immune serum or pre-incubated with the EM66 peptide. In contrast, non-specific labeling of cells bordering the third ventricle was observed in the presence and absence of the TRH antibody (Fig. 3B andD, and data not shown).

Effect of acute immobilization or cold stress on EM66 neuronal population in the rat pPVN

The distribution pattern of EM66-IR neurons within the pPVN remained unchanged in the various experimental conditions (control vs stressed groups). Indeed, acute immobilization (2 h) as well as acute cold stress (4 h) had no apparent effect on the EM66 immunoreactivity within the pPVN compared to control rats (data not shown). A quantitative analysis confirmed these observations showing no significant change in the number of EM66-IR cell bodies within the pPVN of immobilization stressed compared to control animals (Fig. 5A). Similarly, rats exposed to acute cold stress showed no significant variation in the number of EM66-IR cell bodies compared to control animals (Fig. 5B).

Effect of thyroidectomy on EM66-IR neurons in the rat pPVN

Six days after thyroidectomy, no apparent change in the density of EM66-immunopositive cell bodies was observed between sham and thyroidectomized rats (data not shown). A statistical analysis confirmed the lack of difference in the number of EM66-IR cell bodies within the pPVN of sham versus operated animals (Fig. 5C).

Discussion

In line with previously published data [START_REF] Boutahricht | Immunohistochemical distribution of the secretogranin II-derived peptide EM66 in the rat hypothalamus: a comparative study with jerboa[END_REF][START_REF] Yamani | EM66-containing neurones in the hypothalamic parvicellular paraventricular nucleus of the rat: no plasticity related to acute immune stress[END_REF], the present results show that in colchicine-treated rats EM66 immunoreactivity is concentrated within pPVN cell bodies as well as in terminals of the external layer of the median eminence, suggesting a hypophysiotropic role for this peptide. Indeed, these hypothalamic structures are well known to be involved in multiple neuroendocrine regulations, in particular the control of stress and the thyroid axis [START_REF] Lechan | Update on thyrotropin-releasing hormone[END_REF][START_REF] Paulmyer-Lacroix | Régulation de la fonction corticotrope dans les situations de stress[END_REF]. One argument in favor of such roles for EM66 is that EM66-IR is colocalized with CRH and TRH within pPVN hypophysiotropic neurons. CRH-and TRH-containing axon terminals located around capillary vessels of the ME also contained EM66-IR. These data suggest that EM66 may be co-released with CRH and TRH into the portal circulation and therefore, that EM66 could be an accessory peptide which modulates the effects of CRH and TRH on anterior pituitary cells, and thus participates to the control of corticotrope and thyrotrope axis activity in rat. Taking into account the fact that the TRH neuronal population of the pPVN is completely distinct from the CRH neurosecretory system [START_REF] Ceccatelli | Distribution and coexistence of corticotropinreleasing factor-, neurotensin-, enkephalin-, cholecystokinin-, galanin-and vasoactive intestinal polypeptide/peptide histidine isoleucine-like peptides in the parvocellular part of the paraventricular nucleus[END_REF], colocalization of EM66 with CRH and TRH within parvocellular neurons argues for the occurrence of at least two distinct EM66 neuronal populations in the rat pPVN.

To evaluate a possible hypophysiotropic role for the EM66 neuropeptide in relation with the corticotrope and/or thyrotrope axis in rat, we studied the effect of acute stressors and thyroidectomy on the distribution of EM66 immunoreactivity in the pPVN of the rat hypothalamus. There are indications that various experimental stress paradigms may evoke different neural and neuroendocrine responses [START_REF] Pacak | Heterogenous neurochemical responses to different stressors: a test of Selye's doctrine of non specificity[END_REF]. We analyzed the effects of some of these paradigms such as acute immobilization stress and cold exposure which represent strong neurogenic stressors, and thyroidectomy which has extensively been studied in rat [START_REF] Koibuchi | Thyroidectomy induces Fos-like immunoreactivity within thyrotropin-releasing hormone-expressing neurons located in the paraventricular nucleus of the adult rat hypothalamus[END_REF][START_REF] Ceccatelli | Response of hypothalamic peptide mRNAs to thyroidectomy[END_REF][START_REF] Ma | Induction of Fos expression by acute immobilization stress is reduced in locus coeruleus and medial amygdale of Wistar-Kyoto rats compared to Sprague-Dawley rats[END_REF][START_REF] Jiang | Sympathetic nervous system mediates cold stress-induced suppression of natural killer cytotoxicity in rats[END_REF]. Immobilization and cold exposure represent interesting stressful stimuli inducing an array of peripheral and central responses associated with increased activity of the hypothalamic-pituitaryadrenal (HPA) axis [START_REF] Wong | Acute-stress-induced facilitation of the hypothalamo-pituitary-adrenal axis[END_REF][START_REF] Jiang | Sympathetic nervous system mediates cold stress-induced suppression of natural killer cytotoxicity in rats[END_REF] which is evidenced by an increase in parvocellular CRH mRNA and ACTH hypersecretion followed by hypercorticosteronemia [START_REF] Bartanusz | Up-regulation of vasopressin mRNA in paraventricular hypophysiotrophic neurons after acute immobilization stress[END_REF][START_REF] Dronjak | Immobilization and cold stress affect sympatho-adrenomedullary system and pituitary adrenocortical axis of rats exposed to long-term isolation and crowding[END_REF][START_REF] Wu | Cold and novel environment stress affects AVP mRNA in the paraventricular nucleus, but not the supraoptic nucleus: an in situ hybridization study[END_REF]. The same acute stressors are also known to up-regulate the expression of other pPVN neuropeptides such as vasopressin which may play a role in the regulation of pituitary-adrenal responses to immobilization and cold stress [START_REF] Bartanusz | Up-regulation of vasopressin mRNA in paraventricular hypophysiotrophic neurons after acute immobilization stress[END_REF][START_REF] Wu | Cold and novel environment stress affects AVP mRNA in the paraventricular nucleus, but not the supraoptic nucleus: an in situ hybridization study[END_REF].

Using protocols thoroughly validated previously [START_REF] Yamani | EM66-containing neurones in the hypothalamic parvicellular paraventricular nucleus of the rat: no plasticity related to acute immune stress[END_REF][START_REF] Boutahricht | Biochemical characterization and immunocytochemical localization of the secretogranin II-derived peptide EM66 in the hypothalamus of the jerboa (Jaculus orientalis): modulation by food deprivation[END_REF][START_REF] Barakat | Immunocytochemical detection of CCK and CRH neuropeptides in the hypothalamic paraventricular nucleus of the jerboa (Jaculus orientalis): modulation by immobilization stress[END_REF][START_REF] Barakat | Vasopressin-containing neurons of the hypothalamic parvicellular paraventricular nucleus of the jerboa: plasticity related to immobilization stress[END_REF][START_REF] Barakat | Oxytocin-containing neurons in the hypothalamic parvicellular paraventricular nucleus of the jerboa: no plasticity related to acute immobilization[END_REF], the present work showed that acute immobilization (2 h) or cold exposure (5 °C, 4 h) did not affect the EM66 immunoreactivity evaluated by the number of EM66-IR neurons within the pPVN. Consistent with these results, other paradigms such as acute immune stress induced by an ip injection of LPS, known to increase cytokines in brain and plasma [START_REF] Tilders | Activation of the hypothalamus-pituitary-adrenal axis by bacterial endotoxins: routes and intermediate signals[END_REF][START_REF] Elmquist | Mechanisms of CNS response to systemic immune challenge: the febrile response[END_REF], or central injection of cytokines as IL-1β known to be associated with HPA axis activation, did not affect the number of EM66-IR neurons of the pPVN [START_REF] Yamani | EM66-containing neurones in the hypothalamic parvicellular paraventricular nucleus of the rat: no plasticity related to acute immune stress[END_REF]. Similarly, vasopressin mRNA expression remained unchanged in CRH neurons of pPVN after acute immune stress [START_REF] Yamani | EM66-containing neurones in the hypothalamic parvicellular paraventricular nucleus of the rat: no plasticity related to acute immune stress[END_REF][START_REF] Juaneda | CCK mRNA expression in neuroendocrine CRH neurons is increased in rats subjected to an immune challenge[END_REF]. Our data suggest that EM66, like vasopressin, does not participate to the phenotypic plasticity of CRH parvocellular neurons in response to acute stress; thus it may not be essential in this short-term adaptation of PVN neurons. Since chronic stress as well as adrenalectomy were reported to induce a sharp increase in parvocellular vasopressin mRNA [START_REF] De Goeij | Repeated stress-induced activation of corticotropin-releasing factor neurons enhances vasopressin stores and colocalization with corticotropin-releasing factor in the median eminence of rats[END_REF][START_REF] De Goeij | Repeated stress enhances vasopressin synthesis in corticotropin releasing factor neurons in the paraventricular nucleus[END_REF][START_REF] Makino | Increased expression of corticotropin-releasing hormone and vasopressin messenger ribonucleic acid (mRNA) in the hypothalamic paraventricular nucleus during repeated stress: association with reduction in glucocorticoid receptor mRNA levels[END_REF], we cannot exclude that the stressor stimulus duration plays a critical role in the control of the phenotypical plasticity of PVN neurons and neuropeptide expression. It will be useful to study an eventual impact of chronic stressors on EM66 expression within the pPVN. These data provide an additional evidence for the complexity of the phenotypical and/or secretory plasticity of neurons within the pPVN [START_REF] Pirnik | Fos expression variances in mouse hypothalamus upon physical and osmotic stimuli: co-staining with vasopressin, oxytocin, and tyrosine hydroxylase[END_REF] and thus of the regulatory mechanisms of the stress response in rat.

Number of EM66-IR cells

In fact, multiple regulations take place in the paraventricular nucleus of the hypothalamus, which is known to be the feedback site for several peripheral hormones, including thyroid hormones [START_REF] Segerson | Thyroid hormone regulates TRH biosynthesis in the paraventricular nucleus of the rat hypothalamus[END_REF]. As soon as hypothyroidism develops, a dramatic increase in TRH mRNA expression is observed, which is reversed by T4 administration [START_REF] Ceccatelli | Response of hypothalamic peptide mRNAs to thyroidectomy[END_REF][START_REF] Calza | Thyroid hormone-induced plasticity in the adult rat brain[END_REF]. The plasma TSH concentration following thyroidectomy is also increased, suggesting that plasma levels of TSH correlate directly with activation of TRH neurons located in the pPVN [START_REF] Koibuchi | Thyroidectomy induces Fos-like immunoreactivity within thyrotropin-releasing hormone-expressing neurons located in the paraventricular nucleus of the adult rat hypothalamus[END_REF]. Since our results showed an important EM66 expression within TRH-containing parvocellular cells and ME terminals, EM66 may represent an accessory peptide which could regulate the thyrotrope activity and which could be sensitive to peripheral hormones of this axis. The present study showed that thyroidectomy (1 week) did not affect the number of EM66-IR neurons in the pPVN, as it is also the case for CRH and Enk [START_REF] Koibuchi | Thyroidectomy induces Fos-like immunoreactivity within thyrotropin-releasing hormone-expressing neurons located in the paraventricular nucleus of the adult rat hypothalamus[END_REF]. However, it is known that 4 to 7 weeks of hypothyroidism provokes a decrease in CRH mRNA expression within pPVN and that T4 restoration reverses this effect, suggesting that the thyrotrope axis regulates the corticotrope function after prolonged hypothyroidism [START_REF] Ceccatelli | Response of hypothalamic peptide mRNAs to thyroidectomy[END_REF][START_REF] Sanchez-Franco | Thyroid hormone action on ACTH secretion[END_REF]. A reciprocal action of the corticotrope axis on the thyroid activity is also possible since cold stress is known to induce an increase in TSH release in rat [START_REF] Uribe | The systemic inhibition of nitric oxide production rapidly regulates TRH mRNA concentration in the paraventricular nucleus of the hypothalamus and serum TSH concentration. Studies in control and cold-stressed rats[END_REF]. In addition to TRH and CRH, other hypothalamic peptides are affected by thyroid hormone levels, and their expression depends on short-or long-term hypothyroidism. For instance, 4 and 7 weeks of hypothyroidism elicits a dramatic decrease in galanin mRNA in the pPVN. Likewise, VIP mRNA which is undetectable in the PVN of normal animals, is upregulated after 4 and 7 weeks of thyroidectomy [START_REF] Ceccatelli | Response of hypothalamic peptide mRNAs to thyroidectomy[END_REF]. However, other pPVN peptides such as neurotensin, enkephalin and vasopressin are not altered by 4 and 7 weeks of hypothyroidism [START_REF] Ceccatelli | Response of hypothalamic peptide mRNAs to thyroidectomy[END_REF]. It remains to be determined whether EM66 neuropeptide expression could be altered following a long-term duration of hypothyroidism, in order to unravel a potential role of EM66 in the control of the thyrotrope axis and/or in a thyrotrope-corticotrope interaction.

Conclusion

The present study revealed for the first time the occurrence of EM66 in the CRH-and TRH-containing neurons of the rat pPVN as well as in their terminals at the external layer of the ME. Since the TRH neuronal population of the pPVN is known to be completely distinct from the CRH neurosecretory system, our data strongly suggest the existence of at least two distinct EM66 neuronal populations in the rat pPVN. Functionally, EM66 levels do not depend on acute immobilization or cold exposure stresses, as we have previously shown also for an acute immune challenge. In addition, EM66 expression is insensitive to short term hypothyroidism induced by one-week thyroidectomy. These data indicate that EM66 does not participate to the phenotypic plasticity of hypothalamic parvocellular neurons in response to acute stress and to a short duration hypothyroidism. Additional investigations will be conducted to determine the putative regulation of EM66 expression in the pPVN in response to chronic stressors and to long-term hypothyroidism.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Confocal microscopy of CRH-and EM66-IR neurons in rat pPVN. CRH and EM66 cell bodies respectively immunolabeled with Alexa fluor 594 (red color, A and E, thin arrows) and Alexa fluor 488 (green color, B and F, thin arrows) and nuclei stained by DAPI (blue color, C and G, thin arrows) were visualized in the same sections. CRH and EM66 colocalization (merge, D and H, arrowheads) appeared to concern only some cytoplasmic compartments. Neurons containing only either CRH (E-H, asterisk), or EM66 (A-D, thick arrows) were also observed. Scale bar, (A-D) 7.5 μm and (E-H) 10 μm.

Fig. 3 .Fig. 4 .

 34 Fig. 3. Confocal microscopy of TRH-and EM66-IR neurons in pPVN of rat. EM66 immunolabeling with Alexa fluor 594 (A, E and I), TRH immunostaining with Alexa fluor 488 (B, F and J) and DAPI nuclei fluorescence (C, G and K) were visualized in the same sections. Colocalization of TRH and EM66 is shown in the merged photomicrograph (D, H and L, arrowheads). High-powered magnification clearly evidenced EM66 and TRH colocalization within pPVN neurons (inset H, L). Neurons containing either TRH only (E-H, thick arrow) or EM66 (E-H, asterisk), were also observed. Scale bars, (A-D) 75 μm, (E-H) 50 μm and (I-L) 10 μm.

Fig. 5 .

 5 Fig.5. Effects of acute stresses or thyroidectomy on EM66 pPVN neuronal populations. (A) Comparison of the number of EM66-IR neurons within the pPVN of control vs experimental animals (rats immobilized for 2 h; n = 6 in both groups). Student t-test revealed no significant change in the average number of EM66-IR cells between the two groups. (B) Comparison of the number of EM66-IR neurons within the pPVN of control and cold stressed rats (5 °C for 4 h). The histograms showed no significant difference in the number of EM66-IR neurons between control and stressed groups (n = 5 in both groups). (C) Comparison of the number of EM66-IR neurons within the pPVN of sham-operated vs thyroidectomized rats (n = 6 in both groups). No significant change in the average number of EM66-IR cells was noted. Values are shown as mean ± SEM.

Acknowledgments

This study was supported by an exchange program supported by CNRST (Morocco) and INSERM (France), the GDRI Neuro "Groupement de Recherche International de Neurosciences" supported by CNRST (Morocco) and CNRS and INSERM (France), and the FP7 program Neuromed.