Robert Cori

Anne Micheli

Dominique Rossin

Avalanche polynomials

The avalanche polynomial on a graph, introduced in [5], capture the distribution of avalanches in the abelian sandpile model. Studied on trees, this polynomial could be defined by simply considering the size of the subtrees of the original tree. In this article, we study some properties of this polynomial on plane trees. In [5], they show that two different trees could have the same avalanche polynomial. We show here that the problem of finding a tree with a prescribed polynomial is NP-complete. In a second part, we study the average and the variance of the avalanche distribution on trees and give a closed formula.

Introduction

Self-organized criticality is a concept introduced by Bak, Tang and Wiesenfeld [START_REF] Bak | Self-organized criticality: an explanation of 1/f noise[END_REF] to describe the behavior of natural systems like earthquakes [START_REF] Chen | Self-organized criticality in a crackpropagation model of earthquakes[END_REF][START_REF] Sornette | Self-organized criticality and earthquakes[END_REF], forest fires. A simple model that verifies this paradigm is the Abelian Sandpile Model on the 2-dimensional lattice [START_REF] Dhar | Algebraic aspects of abelian sandpile models[END_REF][START_REF] Creutz | Abelian sandpiles[END_REF][START_REF] Dhar | Inverse avalanches in the abelian sandpile model[END_REF]. This model is based on a cellular automaton where each cell has a number of sand grains on it and one cell topples whenever the number of grains is greater or equal to four. In this toppling, the cell gives one grain to each of its neighbor. Thus, some other cells may topple and the sequence of toppling is called an avalanche.

This model was also considered by combinatorists [START_REF] Biggs | Chip firing and the critical group of a graph[END_REF][START_REF] Biggs | Chip-firing and the chromatic polynomial[END_REF][START_REF] Cori | On the sandpile group of dual graphs[END_REF][START_REF] Goles | Universality of the chip-firing game[END_REF] but on general graphs. In [START_REF] Cori | Avalanche polynomials on some families of graphs[END_REF], a polynomial was introduced to encode the distribution of avalanches that was previously studied from another point of view [START_REF] Bak | Self-organized criticality: an explanation of 1/f noise[END_REF][START_REF] Dhar | Abelian sandpile model on the bethe lattice[END_REF][START_REF] Daerden | Sandpiles on a sierpinski gasket[END_REF][START_REF] Goh | Cascading toppling dynamics on scale-free networks[END_REF][START_REF] Maes | The abelian sandpile model on an infinite tree[END_REF]. In this paper, we study the inverse problem. Given the distribution D of avalanches, can we find a tree whose avalanche distribution is D ? Moreover we study the average and the variance of this distribution on plane trees.

2 Avalanche polynomial on a plane tree

Definition and main result

The avalanche polynomial [START_REF] Cori | Avalanche polynomials on some families of graphs[END_REF] encodes the size of avalanches in the abelian sandpile model. Let T = (V, E, r) be a tree rooted at r ∈ V whose vertexset is V = {v 1 , . . . , v n+1 }, and edge-set E. Without loss of generality we can take r = v n+1 . Let v ∈ V be a vertex. A subtree T ′ rooted at v is a tree whose vertices are descendants of v in T . The maximal subtree is the subtree containing all descendants of v. The size of a tree is its number of vertices.

We label the vertices v i according to the following algorithm [START_REF] Cori | Avalanche polynomials on some families of graphs[END_REF] (see Figure 1):

1. Label the root 0 2. The label of a child v of a vertex labeled µ is µ+|maximal subtree rooted at v|.

In [START_REF] Cori | Avalanche polynomials on some families of graphs[END_REF], the authors show that the avalanche polynomial is also defined by Av T (q) = i≥1 p i q i , where p i is the number of vertices labeled i in T . In the sequel we will either speak of the polynomial or its sequence of labels. Av T (q) = q 5 + 2q 6 + 3q 7 + 3q 8 + 2q 9 + 4q 10 + 4q 11 In [START_REF] Cori | Avalanche polynomials on some families of graphs[END_REF], they show that the avalanche polynomial is not a tree invariant by exhibiting two different trees with the same avalanche polynomial. In the sequel, we study the problem of finding a tree for a given polyonomial.

Theorem 1 Given a polynomial P (q), finding whether there exists a tree T whose avalanche polynomial is P (q) is NP-complete.

Proof of theorem 1

We show that the 3-PARTITION problem can be reduced to our problem.

Definition 1 The 3-PARTITION problem I n,C is the following:

• INPUT : C ∈ N, (a 1 , a 2 , . . . , a 3n ) be non-negative integers such that C 4 < a i < C 2 . • OUTPUT :
1. A partition of the integers into n parts of equal sum C.

NO if there is no such partition.

This is a well-known example of NP-complete problem ( [START_REF] Garey | Complexity results for multiprocessor scheduling with resource constraints[END_REF]). Our proof has several steps:

1. We associate a polynomial P to each instance of 3-PARTITION problem (see Definition 2).

2. We show that P is an avalanche polynomial by exhibiting a tree T P with Av T P (q) = P . Furthermore, the structure of T P gives a solution to 3-PARTITION. (see Lemma 1)

3. Then, we prove that T P is the unique tree whose avalanche polynomial is P (see Lemma 2,[START_REF] Biggs | Chip-firing and the chromatic polynomial[END_REF][START_REF] Chen | Self-organized criticality in a crackpropagation model of earthquakes[END_REF][START_REF] Cori | Avalanche polynomials on some families of graphs[END_REF].

Definition 2 Let I n,C be an instance of the 3-PARTITION problem on a 1 , . . . , a 3n . P (q) is the polynomial associated to I n,C :

P (q) = nq C+1 + 3n i=1 q C+1+a i + 3n i=1 (a i -1)q C+a i +2
Lemma 1 The polynomial P (q) associated to an instance I n,C of the 3-PARTITION problem is an avalanche polynomial. Moreover, the tree given in Figure 2 yields a solution to the 3-PARTITION problem.

Proof 1 Let Π k = (α(k), β(k), γ(k)) be a partition of {1, . . . , 3n} in n parts such that a α(k) + a β(k) + a γ(k) = C
Note that P (q) is the avalanche polynomial of the tree T P in Figure 2. The nodes at height 1 in T P have 3 children, whose labels are a part of Π k . Hence, there exists at least a solution to the Avalanche Polynomial Problem which yields a solution to the 3-PARTITION problem. To prove Theorem 1, we ensure the unicity thanks to the following remark: each value a i (and C) can be multiplied by a polynomial integer factor λ = λ(n). The avalanche polynomial becomes:

0 C + 1 C + 1 + a α(1) C + 2 + a α(1) C + 2 + a α(1) C + 1 + a β(1) C + 2 + a β(1) C + 2 + a β(1) C + 1 + a γ(1) C + 2 + a γ(1) C + 2 + a γ(1) C + 1 C + 1 + a α(n) C + 2 + a α(n) C + 2 + a α(n) C + 1 + a β(n) C + 2 + a β(n) C + 2 + a β(n) C + 1 + a γ(n) C + 2 + a γ(n) C + 2 + a γ(n) a α(1) -1 a β(1) -1 a γ(1) -1 n a α(n) -1 a β(n) -1 a γ(n) -1
P λ (q) = nq λC+1 + 3n i=1 q λC+1+λa i + 3n i=1 (λa i -1)q λC+λa i +2
Note that λ is polynomial ensures that our transformation is a polynomialtime reduction. With the following substitutions (a i → λa i and C → λC), the tree of Figure 2 is a solution of P λ . We are going to prove that, taking λ large enough, every tree such that Av T (q) = P λ (q) yields a solution to the 3-PARTITION problem. Let I be the set of all vertices labeled λC + 1 + λa i and L the set of those labeled λC

+ λa i + 2, λ ≥ 2. Note that if λ > 1 then |I| = 3n, |L| = n(λC -3) and I L = ∅.
Lemma 3 If λ > 2 then the leaves of every solution tree are in L.

Proof 3 Let v be a leaf of a solution tree labeled l v . Then its parent p is labeled l v -1. If l v = λC + 1 + λa v there does not exist any vertex labeled λC + λa v . Otherwise λC + λa v = λC + λa p + 1 + δ (δ ∈ {0, 1}). Hence, λ(a v -a p ) = 1 + δ which contradicts λ > 2. p cannot be labeled λC + 1 since λa v = 1.
Lemma 4 If λ > 3n then all vertices of L are leaves.

Proof 4 Suppose that there exists an internal vertex in L. Take v as the one with the greatest label l v = λC + λa v + 2. Let ν be a child of v. If ν is a leaf, then its label is l v + 1 = λC + λa v + 3. But there is no such vertex since λ > 3. Hence ν is an internal node. But v is the greatest internal node of L and the label of ν is greater than l v , hence ν ∈ I.

Then v is either a child of the node labeled λC + 1 or not. The two cases are shown in Figure 3.

Suppose that the parent p of v is labeled λC + 1 + λa p + δ, δ = 0, 1. The size σ of the subtree rooted at v is given:

1. either by the difference between its label and the label of its parent,

σ = λC + λa v + 2 -(λC + 1 + λa p + δ) = λ(a v -a p ) + (1 -δ),

or by the sum of the size of the t child-trees of v plus 1 (to take v into account):

σ = 1+ t i=1 ((λC + λa s i + 1) -(λC + λa v + 2)) = 1-t+ t i=1 λ(a s i -a v ) ? λC + 1 + λa p + δ λC + λa v + 2 λC + 1 + λa s1 λC + 1 + λa st λ(a s1 -a v ) λ(a st -a v ) 0 λC + 1 λC + λa v + 2 λC + 1 + λa s1 λC + 1 + λa st λ(a s1 -a v ) λ(a st -a v )
Figure 3: Two different shapes of trees that appear in Lemma 4.

Hence λ(a v -a p ) + (1 -δ) = 1 -t + t i=1 λ(a s i -a v ), and λ t i=1 a s i -(t + 1)a v + a p = t -δ. But t ≤ |I| = 3n (the number of values a i ). Hence t -δ < 3n. Taking λ > 3n concludes whenever p is labeled λC + λa p + 1 + δ, δ = 0, 1.
Note that when p is labeled λC + 1, taking a p = 0 and δ = 0 in the preceding proof concludes.

Lemma 5 If λ > 3n, then the nodes of I are children of one of the vertices labeled λC + 1.

Proof 5 Let v ∈ I be a vertex labeled λC + λa v + 1. By Lemmas 3 and 4, the λa v -1 vertices labeled λC + λa v + 2 are leaves, hence children of v. Note that if k vertices v 1 , . . . , v k have the same label than v then there are k(λa v -1) vertices labeled λC + λa v + 2. These vertices are children of the v i , 1 ≤ i ≤ k. The size of each maximal subtree rooted at v i is less or equal than λa v since the size of the subtree is the label of v minus the label of its parent p, and the label of p is at least λC + 1. Hence each v i has exactly

λa v -1 children labeled λC + λa v + 2.
Suppose that the parent p of v is labeled λC + 1 + λa p then the size of the subtree rooted at v is λ(a va p ) < λa v .

Thus the parent of v is labeled λC + 1.

2.3 Avalanche polynomial on plane tree of height at most 2.

We showed in the last section that finding a tree whose avalanche polynomial is given is NP-complete. In this part, we show that considering only trees of height at most 2, then the problem becomes poynomial. Moreover we give a linear time and space algorithm to solve it. A tree of height 2 and its labeling is given in Figure 4 and its associated polynomial is P (q) = n i=1 q a i + (a i -1)q a i +1 . Note that if one of the a i is equal to 1 then it is a leaf rooted at the vertex labeled 0.

The following algorithm takes as input a polynomial P (q) = n i=1 a i q i and output either:

• A tree T of height at most 2 whose avalanche polynomial is P .

• NO if no such tree exists.

1. Create the root with label 0. 2. Find a child of the root by taking the first non-nul coefficient a j . If j = 1 we have found a j leaves of the root. If j > 1 we have a j nodes. Each of these nodes must have j -1 children labeled j + 1. Hence a j+1 must be greater than a j (j -1). If not, output NO and exit.

3. Subtract a j q j + a j (j -1)q j+1 from the polynomial; we take this new polynomial as P 4. If P = 0 output the tree and exit.

5. Goto 2.

0 3 Avalanche polynomial on plane trees

a 1 a 1 + 1 a 1 + 1 a 2 a 2 + 1 a 2 + 1 a n a n + 1 a n + 1 a 1 -1 a 2 -1 a n -1
In this section, we study the avalanche polynomial on plane trees. The aim of this section is to find the average distribution of avalanches on a random tree. We first give the closed expression for the number of avalanches of a given size in plane trees. Unfortunately, this formula does not help to retrieve informations on the distribution, thus we give a recursive formula for the distribution and deduce the mean and the variance of this distribution.

Definition

Let us note

C k = 1 k+1 2k
k the k-th Catalan number. Let T n be the set of rooted plane trees with n edges. |T n | = C n . We extend the definition of avalanche polynomial to the set of plane trees (see Figure 5): (2q + q 2 + q 3 )t 2 (5q + 2q 2 + 4q 3 +2q 4 + q 5 + q 6 )t 3 Remark 1 Note that :

A(t, q) = i≥0 T ∈T i Av T (q)t i = p≥0 A p (q)t p (1)
A(t, 1) = p≥0 A p (1)t p = p≥0 pC p t p
In fact, the coefficient of t p in A(t, 1) is the number of rooted plane trees of size p + 1 times the number of vertices (excepting the roots). Hence it is pC p .

Closed formula

In this section, we exhibit a decomposition of the rooted plane trees which yields a closed formula for the avalanche polynomial.

Theorem 2 The coefficients of the polynomials A n (q) are given by:

[q v ]A n (q) = j -1+ √ 1+8v 2 k k=1 p∈Π n,v,k C p 1 -1 k i=2 C p i -p i-1 C n-p k +1 (2)
where

Π n,v,k = {(p 1 , . . . , p k ); p i < p i+1 , p k ≤ n, k i=1 p i = v} Proof 6
The coefficient [q v ]A n (q) represents the number of vertices labeled v in every plane trees of size n + 1.

Let x be such a vertex labeled v in a tree T and y 0 = x, y 1 , . . . , y k = x n+1 be the path joining the root x n+1 labeled 0 to the vertex x in T . Let lab be the function which maps any vertex y of T onto lab(y), the label of y in T . The proof is based on the study of rooted plane trees which have a given path.

• Note that k ≤ -1+ √ 1+8v 2
because the labels of the vertices of the path from the root to x take minimal values when the maximal subtree of T rooted at y k-1 is reduced to the path y 0 , . . . , y k-1 .

Then the labels of the vertices on this path are

k, k + (k -1),k + (k - 1) + (k -2), ..., k(k+1) 2 and if k > -1+ √ 1+8v 2
then the last label is stricly greater than v.

• The sequence of labels of the vertices y l is stricly decreasing by definition.

• The sequence of the differences (lab(y l )lab(y l+1 )) is stricly increasing. This relies on the fact that each difference is the size of the maximal subtree rooted at y l+1 and that the subtrees are nested. Moreover, lab(y k-1 )-lab(y k ) ≤ n as this is the size of the maximal subtree rooted at y k-1 . Finally, k i=1 lab(y i-1 )lab(y i ) = lab(y 0 )lab(y k ) = v.

Let k be an integer such that k ≤ -1+ √ 1+8v 2 and let (p 1 , . . . , p k ) be a stricly increasing sequence such that p k ≤ n and k i=1 p i = v. Let P be a path of vertices {y 0 , . . . , y k } labeled lab(y 0 ) = v, lab(y 1 ) = lab(y 0 )p 1 , lab(y 2 ) = lab(y 1 )p 2 , . . . , lab(y k ) = lab(y k-1 )p k = 0 (see Figure 6). Denote by F i,1 (resp. F i,2 ) the forest hanging on y i at the left (resp. right) of the edge (y i , y i-1 ).

Lemma 6

The number of plane trees of size n + 1 having P as subpath is

C p 1 -1 k i=2 C p i -p i-1 C n-p k +1 .
Proof 7 Note first that the size of the maximal subtree hanging on y i is y iy i+1 = p i+1 . Then the number of vertices of the forest

F i,1 ∪ F i,2 is p i+1 -p i -1 for i ∈ {1, . . . , k -1}. The number of such pair of forests {F i,1 , F i,2 } is C p i+1 -p i .
The size of the maximal subtree rooted at y 0 is y 0y 1 = p 1 . There are C p 1 -1 such trees.

The remaining nodes are in the forests F k,1 and F k,2 which union has np k vertices. So that the number of such forests is C n-p k +1 .

0 y k-1 y k-2 y 1 y 0 = v F k,1 F k,2 F k-1,1 F k-1,2 F k-2,1 F k-2,2 F 1,1 F 1,2 F 0 Figure 6: A tree with its subpath P Remark 2 The coefficient of t n q in A(t, q) is C n and the coefficient of t n q 2 is C n-1 .
Proof 8 There are two different proofs of these results, the first one consists in taking v = 1 or v = 2 in Equation ( 2).

The second one relies on the following property:

Lemma 7 Let T ′ be a tree. Let S T ′ be the set of trees T of size n + 1 where T ′ is a subtree of T rooted at the root of T . Then The bijection between the trees of S T ′ and plane trees of size n -|T ′ | + 1 is given in Figure 7.

|S T ′ | = C n-|T ′ |+2 . 0 T 1 T ′ T 2 0 T 1 T 2
For v = 1 take T ′ as a single edge. For v = 2 take T ′ as a path of length 2.

Functional equation

Lemma 8

The polynomial A p (q), p ≥ 0 -the distribution of avalanches on plane trees of size p + 1-is defined by the following recurrence:

A p+1 (q) = p k=0 C k C p-k q k+1 + C p-k q k+1 A k (q) + C k A p-k (q) (3)
This yields a functionnal equation for A(t, q):

A(t, q) = (1 - √ 1 -4t)(1 - √ 1 -4qt) 4t +q 1 - √ 1 -4t 2 A(qt, q) + 1 - √ 1 -4t 2 A(t, q) (4)
Proof 10 The proof relies on the following decomposition of rooted plane trees (see Figure 8). A tree T p+1 of size p + 2 can be decomposed into a tree T k of size k + 1 and a tree T p-k of size p + 1k as shown in Figure 8. Hence, the root of the tree T k is the leftmost child of the root of T p-k in T p+1 . Furthermore, the root of T k is labeled k + 1 the number of vertices of T k . This vertex contributes to the term C k C p-k q k+1 in A p+1 (q). The avalanche polynomial of T k is A k (q). In T p+1 the label of a vertex of the subtree T k is increased by k + 1. They contribute to the term C p-k q k+1 A k (q) in A p+1 (q). The last term takes into account the labels of the vertices of T p-k which stay unchanged since the root of T p-k is the root of T p+1 . 1) yields a functionnal equation for A(t, q):

0 k + 1 T k T p-k
A(t, q) = (1 - √ 1 -4t)(1 - √ 1 -4qt) 4t + p≥0 p k=0 (C p-k q k+1 A k (q)t p+1 + C k A p-k (q)t p+1 ) = (1 - √ 1 -4t)(1 - √ 1 -4qt) 4t +q 1 - √ 1 -4t 2 A(qt, q) + 1 - √ 1 -4t 2 A(t, q)
3.4 Average of the distribution of avalanches Proposition 1 The average size of an avalanche on a plane tree of size n is asymptotically equal to

√ π 4 n 3/2 . Proof 11 A(t, q) = n m a m,n q m t n
The mean size of avalanches on all plane trees of size n is given by

M n = m ma m,n m a m,n = ∂A ∂q (t, 1) n [A(t, 1)] n = ∂A ∂q (t, 1) n nC n (5)
Equation ( 4) yields:

∂A ∂q (t, 1) = 1 - √ 1 -4t 2 √ 1 -4t + 1 - √ 1 -4t 2 A(t,
∂A ∂q (t, 1) = ( √ 1 -4t -1)(2t -1) 2(4t -1) 2 Since ( √ 1 -4t -1)(2t -1) 2 = t + i≥0 (C i+1 -2C i )t i+2 , ∂A ∂q (t, 1) = t i≥0 4 i (i + 1)t i + i,j≥0 (C i+1 -2C i )4 j (j + 1)t i+j+2 = t i≥0 4 i (i + 1)t i + k≥1 4 k t k+1 k-1 i=0 (C i+1 -2C i ) k -i 4 i+1 Since k-1 i=0 C i+1 -2C i 4 i+1 = - kC k 4 k , k-1 i=0 i(C i+1 -2C i ) 4 i+1 = (2 + 5k + k 2 )C k 4 k -2, ∂A ∂q (t, 1) = i≥1 4 i-1 (i + 2) -(-1 + i + 2i 2 )C i-1 t i
Substitution of ∂A ∂q (t, 1) in Equation ( 5) yields:

M n = 4 n-1 (n + 2) nC n - (n + 1) 2 2n Since C n ∼ 4 n √ πn 3 , M n ∼ √ π 4 n 3/2 .

Variance

The variance of the distribution is given by

h ∂ 2 A ∂q 2 (t,1) i n nCn + M n -M 2
n where M n denotes the mean size (computed in the last section).

Hence we only need the expression of

∂ 2 A ∂q 2 (t, 1) n . ∂ 2 A ∂q 2 (t, 1) = t(1 - √ 1 -4t) (1 -4t) 3/2 + 1 - √ 1 -4t 2 2t ∂A ∂t (t, 1) + 2 ∂A ∂q (t, 1) +t 2 ∂ 2 A ∂t 2 (t, 1) + 2 ∂ 2 A ∂q 2 (t, 1) + 2t ∂ 2 A ∂t∂q (t, 1)
Thus we need the other derivatives ∂A ∂t (t, q), ∂A ∂q (t, q), ∂ 2 A ∂t 2 (t, 1) and ∂ 2 A ∂t∂q (t, 1). Substituting their expression in ∂ 2 A ∂q 2 (t, 1) yields:

∂ 2 A ∂q 2 (t, 1) = -1/2 -1 + √ 1 -4 t 10 t + √ 1 -4 t -1 -32 t 2 + 32 t 3 (-1 + 4 t) 4
Since :

(

1 -4t) -4 = n≥0 4 n 6 (n + 1)(n + 2)(n + 3)t n (1 -4t) -7/2 = n≥0 (n + 1)(2n + 1)(2n + 3)(2n + 5)4 n C n 152 2n t n
We obtain: In fact the distribution show strange peaks and after a renormalization (scaling in x by a factor 1/n for the distribution on trees of size n and rescaling the ordinate between 0 and 1) it gives the curves in Figure 9 and 9. In the following figures, we draw a curve for A 10 (q), A 20 (q),... Moreover for such a polynomial A n (q) = i≥0 p i q i we put points at coordinates (i/n, p i /p 1 ) since p 1 is the maximum. Let's recall from Remark 2 that p 1 = C n . The grey scale goes from white (for the first polynomial) to black (for the last one).

V n = 4

Conclusion

The Figures [START_REF] Dhar | Abelian sandpile model on the bethe lattice[END_REF] and ( 9) point out some convergence of the renormalized distribution. A question arises naturally:

• Is it possible to retrieve the asymptotic of the coefficients from their closed form ?

Note first that the peaks that appear at integer abscissa x, x ≪ √ n do not converge to 0. In fact consider the trees made of a path π 0 = 0, π 1 , . . . , π x of length x and a plane tree of size nx rooted in π x . The label of π x is n+(n-1)+(n-2)+. . .+(n-x+1) thus tends to x after the renormalization by n. Moreover there are C n-x-1 such trees. Since p 1 = C n the peak is higher than C n-x-1 /C n ∼ (1/4) x-1 .

Figure 1 :

 1 Figure 1: Example of an avalanche polynomial of a tree

Figure 2 :

 2 Figure 2: A solution to the 3-PARTITION problem

Lemma 2 Proof 2

 22 The root has n children, each one labeled λC + 1. By definition, the smallest value is the label of a child of the root. Hence the n vertices labeled λC +1 are children of the root. But n(λC +1) = ( λa i ) + n, the number of vertices. Hence all other vertices are children of one of the vertices labeled λC + 1.

Figure 4 :

 4 Figure 4: Labeled tree of height 2

Figure 5 :

 5 Figure 5: First terms of A(t, q)

Figure 7 :

 7 Figure 7: Bijection between S T ′ and plane trees

Figure 8 :

 8 Figure 8: Decomposition of a plane tree

Figure 9 :

 9 Figure 9: Distribution for the first 500 and 1000 polynomials


Dr Yang Sun

Kais Dhbaibi

Dr Hortense Lauwick

Dr Claudia Lalli

Dr Gregory Taupier

Dr Yann Molard

Dr Rafael Gramage-Doria

Dr Sylvie Dérien

Dr Jeanne Crassous
email: jeanne.crassous@univ-rennes1.fr

Dr Mathieu Jérôme Achard
email: mathieu.achard@univ-rennes1.fr

Dr K Dhaibi

Asymmetric Ruthenium Catalysis Enables Fluorophores with Point Chirality

A novel enantiopure π-allylruthenium(IV) precatalyst allowed the enantioselective and stereospecific allylations of indoles and gave access to indolin-3-ones containing vicinal stereogenic centers. Facile separation of diastereoisomers exhibiting opposite CPL activities in diverse solvents including water demonstrated the potential of these sustainable transformation and of the newly prepared molecules.

10.

Introduction

Owing to their potential applications in material sciences by inducing circularly polarized luminescence (CPL), chiral organic emitters have recently attracted considerable attention. [START_REF]Circularly Polarized Luminescence of Isolated Small Organic Molecules[END_REF] While metal-based and lanthanides complexes have demonstrated strong interest in both generating strong CPL activity and efficient phosphorescence or long-lived emission for incorporation into CP-OLEDs, [START_REF] Doistau | [END_REF] fluorescent fully organic π-conjugated systems have shown wider variability and easier processability. [3] Most reports in the literature deal with axially, planar or helically chiral fluorophores (Figure 1). [START_REF]Circularly Polarized Luminescence of Isolated Small Organic Molecules[END_REF] Additionally, reports dealing with central chirality mainly arise from chiral pool scaffolds thus hampering access to both enantiomers. [4] While these simple molecules display moderate signals in their monomeric state, dimerization, immobilization, aggregation and other strategies allowed the enhancement of the CPL dissymmetry factor, glum through diverse mechanisms. [5] However, the synthesis of such chiral compounds usually necessitates multi-step methodologies and generates several types of wastes. Thus, alternative ecofriendly and straightforward approaches minimizing steps and wastes are highly desirable. Among the high-value added chemicals, indoxyl derivatives containing the indolin-3-one core structure and a quaternary stereogenic center at the 2-position are an attractive class of compounds with interesting tunable photophysical properties. [6] Owing to the presence of a rigid conjugated electrondonor acceptor fragment nearby the quaternary stereogenic center, several indolin-3-ones exhibit impressive photoemissive properties. [6a-g] However, chiroptical properties of such compounds have never been studied. Catalysts enabling regioenantio-and stereo-selective alkylation from acyclic unactivated allylic alcohols are so far unknown. The development of such systems would allow the access to pure indolin-3-one stereoisomers minimizing steps with water as the only side product of the overall reactions (Figure 1e). In this regard, transition metal-catalyzed allylations become a powerful strategy to access a broad variety of high value-added products and various transition metal complexes were developed to achieve regio-and enantio-selective allylation of indole derivatives at the C or the N positions. [7] Among them, reports dealing with iridium precatalysts dominate this field. [8][9][10] Even if these classes of catalysts have proven to activate branched allylic alcohols enantioselectively, the use of linear derivatives to date still require activated linear allylic substrates. Similarly, various palladium precatalysts were found to be able to activate allylic alcohols including enantio-and stereo-selective alkylations with regioselectivity in favor of the less hindered terminal allyl carbon. [11] Efficient rhodium-, nickel-or gold-based catalysts have provided interesting results for the alkylation of indole derivatives. [12][13][14] Since the pioneering discoveries of Watanabe and coworkers, ruthenium-based catalysts have emerged as promising complementary systems to perform regioselective allylic substitution in favor of the branched products and various enantioselective or stereospecific protocols have been reported from activated allylic derivatives. [15][START_REF] Trost | Stereospecific allylation of activated allylic derivatives: a)[END_REF][17][18] Ruthenium precatalysts containing sulfonate or carboxylate moieties developed by Pregosin, Kitamura and us were found to activate allylic alcohols. [6e,15d,17,18] Despite our recently discovered allylationoxidation sequence of branched 2,3-disubstituted indoles via a semi-pinacol rearrangement of the resulting hydroxyindolenines in the presence of a well-defined ruthenium(IV) allyl complex [Ru(Cp*)(DPPBS)(η 3 -propenyl)][PF6]

Ru-1 bearing DiPhenylPhosphinoBenzene Sulfonate (DPPBS) ligand, an enantioselective version is yet to be reported. [6e] Herein, we describe a first report on the rutheniumcatalyzed activation of acyclic, either linear crotyl alcohol or branched but-3-en-2-ol, allowing the straightforward access to useful chiral indolin-3-one emitters via regio-, stereo-and enantioselective allylation reactions and their photophysical (absorption and emission) and chiroptical properties (Electronic Circular Dichroism -ECD and CPL activities. Interestingly, we examined how switching the nature of the allylic alcohol can generate the four different stereomers possessing two asymmetric carbons, and how stereoisomerism influences the chiroptical properties, both in organic solvents and in water.

Results and Discussion

We first focused on the synthesis of the π-allyl ruthenium(IV) precatalyst. After treatment of equimolar amount of our recently reported (Sa)-sulfo-binepine 1-H with [Ru(Cp*)(CH3CN)3]PF6 Ru-2 at room temperature, sharp multiple signals were observed in 1 H NMR. [19] A hydride signal located at -7.53 ppm (JPH=31 Hz) of a cationic hydridoruthenium(IV) species arising from the protonation-anionation of the ruthenium(II) center by the sulfonic acid moiety was observed. [11g,20] Chelate formation was evidenced by the modification of the diastereotopic proton signals for the two CH2 moieties of the sulfobinepine ligand and by 31 P NMR (Figure S1). Interestingly, a broad signal located at no less than 25 ppm in 1 H NMR accounting for the ruthenium(II) precursor was also noticed (Scheme 1). Even if we suspect a tridentate κ 3 -P,O,O coordination mode of the ligand or a dimer formation, [19] these formal 16e species undergoes rapid aggregation in less than 15 mins leading to the disappearance of the signals both in 1 H and 31 P NMR; THF signals arising from sulfo-binepine synthesis being only visible in 1 H NMR. Addition of allyl alcohol 2a (2 equiv.) to this mixture led to the formation of a yellowish solution and reappearance of characteristic signals in NMR spectroscopy which upon concentration led to the precipitation of the expected stable allylruthenium(IV) complex [Ru(Cp*)(1)(η 3 -propenyl)][PF6] Ru-3 as only one diastereoisomer; diallylated ether along with other side products remaining in solution. In Scheme 1. Synthesis of the well-defined (Sa,SRu) Ru-3 ruthenium(IV) complex. Scheme 2. Monitoring the substoichiometric reaction with linear 2c and branched 2b allylic alcohols. contrast, replacing allyl alcohol in the experiment described above by the addition of 4 equivalents of but-3-en-2-ol 2b resulted in a complex mixture (Scheme 2). Formation of the dibranched diallylated ether 3b was observed at room temperature 1 H NMR reaching around 50% conversion after one hour along with the formation a major ruthenium species located in 31 P NMR at 42.7 (s) ppm and traces of butadiene 4. [21] Complete consumption of both ether 3b and alcohol 2b acting both as nucleophiles and allylic sources occurred after 16 hours to fully generate butadiene 4. [22] All these reactions are proposed to be reversible but the low miscibility of water in CD2Cl2 facilitates these processes. [21,22] An unstable allyl ruthenium(IV) was the only observable species located at 39 ppm in 31 P NMR with characteristic π-allyl signals in [START_REF]Circularly Polarized Luminescence of Isolated Small Organic Molecules[END_REF] H NMR in the same range as Ru-3 and previously reported Ru-1. When the reaction was carried out in the presence of the linear crotyl alcohol 2c, same π-allylruthenium species were observed along with butadiene at the end of the reaction during NMR analyses. However, these allylic species were only detected at the end of these reactions raising the question of the enantioselective outcomes in the presence of other nucleophiles.

Table 1. Stereospecific versus enantioselective allylation of indole 5a [a] Entry ROH Solvent, T(°C) er [b] Absolute Configuration ratio 6a/7a [c] conv.(yield) [d] 1 [a] Experimental conditions: all reactions were performed under an inert atmosphere of argon at indicated temperature and carried out with indole 5a (0.4 mmol), allylic alcohols 2 (0.4 mmol), metallic precursor (Sa,SRu) Ru-3 (3 mol%) in a closed Schlenk tube in deaerated solvent (0.5 mL). [b] er of 6a was determined by chiral HPLC analysis (Chiralcel OJ). [c] Determined by 1 H NMR of the crude reaction mixture. [d] Conversions were determined by GC and numbers in parentheses correspond to the isolated yield of the product 6a after column chromatography.

[e] reaction was carried out in the presence of the racemic Ru-1 precatalyst.

Having established that both crotyl alcohol 2c and methyl vinyl carbinol 2b can be activated in the presence of the sulfobinepine containing catalyst, we next attempted, the reactions of these alcohols in the presence of indole 5a and the allylic ruthenium precatalyst Ru-3 (Table 1). Treatment of indole 5a with equimolar amount of the rac. but-3-en-2-ol 2b in the presence of catalytic amount of the well-defined ruthenium Ru-3 complex afforded the chiral allylated indole 6a in isolated yield up to 90% (Table 1, entry 1). Traces of linear product 7a was also detected in the crude reaction mixture by 1 H NMR reaching a Branched/Linear of compounds 6a/7a ratio of 97:3. Chiral HPLC analysis demonstrated the formation of a racemic mixture. In contrast, treatment of the enantiomerically enriched(-),(R)-but-3en-2-ol 2b (87% ee) with indole gave the allylated indole 6a with 93:7 e.r. (Table 1,entry 2). [23] The absolute configuration (R) was determined by comparison with previously reported data confirming a net retention of configuration. [10a,12] Noteworthy that the racemic chiral at ruthenium Ru-1 complex led to similar results confirming a stereospecific process (Table 1, entry 3). [START_REF] Trost | Stereospecific allylation of activated allylic derivatives: a)[END_REF]24] In contrast, treatment of the crotyl alcohol 2c (93:7 E/Z ratio) with indole 5 under similar reaction conditions gave the same product 6a in 86% isolated yield. Regioselectivity was slightly eroded reaching a 92:8 6a/7a ratio. However, product 6a was obtained with 8:92 e.r. in favor of the (S) enantiomer (Table 1, entry 4). Increasing reaction temperature, lowered concomitantly regioand enantio-selectivities whereas reaction performed at room temperature lowered conversion (Table 1, entries 5,6,7). It is important to note that for these entries, the obtained enantiomeric ratios are similar to the obtained regioselectivities correlated to the E/Z ratio of the starting material 2c indicating a selective approach toward the unsaturated enantiotopic faces and the absence of isomerization processes. Taken together, these results demonstrate that racemic and both enantiomers can be selectively obtained with the same enantiopure precatalyst (Sa,SRu)-Ru-3 by simply varying the nature of the unactivated allylic alcohol. A fast nucleophilic attack prior to isomerization might account for these results and a putative model of activation is described in Figure 2. Reminiscent to the so-called "memory effect", [24] if concerted activation of the alcohol occurs on the same side of the sulfonate moiety as previously suggested by Pregosin, Kitamura and us, the corresponding π allyl ruthenium species should be obtained. [6e,17] Owing to the longer Ru-C(allyl) bond length for the substituted terminal allyl carbon in the corresponding π-allyl ruthenium species featuring Cp* ligand, a higher reactivity of this carbon center toward nucleophiles favors the branched selectivity. [17,18] Thus, a racemic mixture of the corresponding allylated species is expected. In contrast, starting from crotyl alcohol containing a mixture of cis/trans isomers (93% trans), an enantiomeric ratio close to 7:93 should be expected. In continuation, with the influence of chirality toward modification of properties, we next investigated the application of these transformations towards the straightforward access to chiral emitters. We thus applied these procedures to access to the four stereoisomers of indolin-3-ones with the same precatalyst (Sa,SRu)-Ru-3. [6e] 2-methylindole 5b (4 mmol scale) was then tested in the presence of allylic alcohols 2 (Scheme 3). When using as low as 0.5% of precatalyst Ru-3 loading, complete conversions were obtained during allylations from either crotyl alcohol 2c or enriched(-),(R)-but-3-en-2-ol 2b which was by analyses with branched/linear ratio of 92:8 and 97:3, respectively. Noteworthy, that at this scale, water droplets deposit at the top of the Schlenk tube allowing roughly visual appreciation of the conversion by naked eyes. Since obtained 2,3-disubstituted indole intermediates are sensitive toward oxidation at position 3 of the indole nucleus and owing to the low steric hindrance of the methyl group at position 2, free rotation around the allylic fragment is expected allowing formation of both diastereoisomers arising from solid state oxidation. [6e] Thus, the resulted crude mixtures were then suspended in SiO2 and stirred under an air atmosphere to afford after oxidation and semi pinacol rearrangement, the corresponding allylated indolin-3-ones 8. Completion of the reactions were achieved after 24 hours affording 66% overall yields after purification. Owing to the presence of vicinal stereogenic centers, the diastereoisomers were easily separated by trivial purification by column chromatography affording the four distinct stereoisomers to further evaluate the influence of the stereogenic centers on their optical properties. Absolute configurations were unambiguously determined by X-ray analysis from the crystallization of (S,R)-8. [START_REF]Deposition numbers[END_REF] Scheme 3. Access to the four stereoisomers of allylated indolin-3-one 8 and molecular structure of (S,R)-8 (CCDC 2205725).

First, the optical and chiroptical properties were evaluated at the ground state by means of UV-vis absorption and ECD spectra. The absorption spectra of compounds (R,S)-8, (S,S)-8, (S,R)-8 and (R,R)-8 [START_REF]R)-8 and (R,R)-8, the first stereodescriptor designates the stereochemistry at the quaternary center[END_REF] recorded in dichloromethane solution at room temperature are depicted on Figure 3. All compounds display a broad band centered at 378 nm (ε ~ 3800 M -1 cm -1 ) that can be attributed to an intramolecular charge-transfer (ICT) transition, in agreement with the previously reported optical behaviour of indolin-3-one analogues. [6e] In addition, small shoulders of moderate intensity (ε ~ 650-1500 M -1 cm -1 ) are present around 300, 318 and 330 nm. ECD spectra of each enantiomeric pair of compounds display mirror-image relationship. Furthermore, the two epimeric species generated during the reaction show chiroptical responses that are similar in amplitude and opposite in signs, indicating that the response is mainly governed by the chiral cyclic scaffold and the configuration at the quaternary carbon stereocenter, with low contribution of the pendant chiral allyl chain. For instance, (S,R)-8 exhibits first a positive ECD band at the higher energy (Δε =+4 M -1 cm -1 at 317 nm) with some visible vibronic structuration, and a second negative band at lower energy (Δε = -5.9 M -1 cm -1 at 365 nm). The absorption dissymmetry factor (gabs = /) spectra depicted on Figure S3 display almost perfect mirror-image Table 2. Photophysical data for compounds (R,S)-8, (S,S)-8, (S,R)-8 and (R,R)-8 in CH2Cl2. [a] Compounds max (M -1 cm - relationship for each enantiomeric pair (R,S)-8/(S,R)-8 and (S,S)-8/(R,R)-8 and values around 1.9-5.3 × 10 -3 . It should be noticed that optical rotation values, registered for all four stereoisomers and summarized in the Table 2, enable to distinguish between the two different diastereomers (within the measurement errors), with the (R,S)-8 [(S,R)-8] displaying higher values compared to (R,R)-8 [(S,S)-8], but with the sign being governed by the cyclic chiral scaffold.

The chiroptical properties of these compounds were also examined at the excited state and the unpolarized and circularly polarized luminescence spectra were recorded first in CH2Cl2 (Figure 4). All the compounds display non-structured emission spectra in the blue region with a maximum around 443-442 nm with mirror-image CPL signals and emission dissymmetry factor (glum = 2/) values between 4.310 -4 and 5.310 -4 (see detailed values on Table 2), with positive signals for (R,S)-8/(R,R)-8 and negative ones for (S,S)-8/(S,R)-8 demonstrating that the simple separation of a set of diastereoisomers allows a rapid overview of the opposite CPL activities. Solvent dependence in fluorescence (Figure 5a) and CPL (Figure 5b) was 10.1002/chem.202203243

Accepted Manuscript

Chemistry -A European Journal

This article is protected by copyright. All rights reserved. could be predictable and one can speculate a diminished response for glum in polar solvent due to the strengthening of the electric dipole transition moment. [START_REF] Zheng | [END_REF]28] Indeed, the emission dissymmetry factors show a higher response in toluene and THF solvents with a glum of 8.8×10 -4 at 427 nm and 7.210 -4 at 437 nm, respectively, for (S,R)-8, conversely the CPL show an almost two-fold decrease in DCM |glum| = 4.8×10 -4 . In contrast, absolute quantum yields follow the opposite trend showing a higher response in water and DCM solvents. Interestingly, these chiral chromophores are CPL active in water (glum = 6.610 -4 ); small organic molecules that show CPL responses in water are scarce and could be considered as interesting building blocks for biologically relevant applications that require aqueous solubility. [29][30][31][32] On the other hand, CPL stimuli-responsive materials are of great interest due to their possible incorporation in security technologies and their potential application as smart CPL sensors. [33][34][35][36][37]

Conclusion

In conclusion, we have synthesized an enantiopure πallylruthenium(IV) precatalyst Ru-3 allowing the enantioselective and stereospecific allylations of indole by switching the nature (branched versus linear) of the acyclic allylic alcohols generating water as the only side product of the reaction. Extension of this transformation was applied to the one-pot two-steps preparation of the four indolin-3-one stereoisomers. This novel methodology enabled straightforward preparation of enantiomerically enriched indolin-3-ones possessing two asymmetric carbons, whose chiroptical properties are governed by the chiral cyclic scaffold rather than the chiral chain. By this method, we could show that the simple separation of enantioenriched diastereoisomers with central chirality are able to display opposite significant CPL activity, with dissymmetry factors up to 8.8 × 10 -4 in toluene solvent and appealing solvatochromism. We believe that this methodology expands the access to still rare chiral fluorophores in water.

Experimental section

Preparation of the [Ru(Cp*)(1)(η 3 -propenyl)][PF6] complex (Sa,SRu)-Ru-3 (Sa)-Sulfo-binepine [19] 1-H (0.054 g, 0.115 mmol) and [Ru(Cp*)(MeCN)3][PF6] Ru-1 (0.058 g, 0.115 mmol). were added to a 15 mL Schlenk tube. The Schlenk tube was evacuated and filled with argon three times followed by the addition of deaerated dichloromethane (2 mL). The resulted orange homogeneous solution was stirred for 15 min. Allyl alcohol 2a (15 μL ~ 2 eq.) was added and the solution immediately turned yellow. After stirring for additional 14 h, concentration afforded a pale-yellow precipitate. Removal of the solution and washing with dry, degassed n-hexane led to a yellow powder (0.082 g, 78%); 1 H NMR (400 MHz, CD2Cl2) δ 8. 22 (ddd, J= 7.9, 4.3, 1.3 Hz, 1H), 8.13 (d, J= 8.1 Hz, 1H), 8.06 (d, J= 8.3 Hz, 1H), 7.85 (d, J= 8.2 Hz, 1H), 7.71 (t, J= 7.7 Hz, 1H), 7.59 (t, J= 7.5 Hz, 1H), 7.52-7.45 (m, 3H), 7.36-7.28 (m, 3H), 7.23 (d, J= 8.7 Hz, 1H), 7.20 (d, J= 8.6 Hz, 1H), 6.95 (t, J= 8.4 Hz, 1H), 6.63 (dd, J= 8.4, 1.3 Hz, 1H), 5.32-5.28 (m, 1H, CH allyl), 4.70 (dd, J= 13.5, 4.9 Hz, 1H, CH2 binepine), 4.10 (d, J= 7.1 Hz, 1H, CH2 allyl), 4.04 (dd, J= 16.8, 14.1 Hz, 1H, CH2 binepine), 3.86-3.80 (m, 1H, CH2 allyl), 3.60 (d, J= 10.9, 2.9 Hz, 1H, CH2 allyl), 3.38 (d, J= 14.0 Hz, 1H, CH2 binepine), 3.24 (dd, J= 13.5, 5.2 Hz, 1H, CH2 binepine), 1.61-1.58 (m, 1H, CH2 allyl), 1.61 (d, J= 1.8 Hz, 15H) ; 13 C NMR (100 MHz, CD2Cl2) δ 145.8 (d, JP-C=10.2 Hz, Cq), 136.3 (d, JP-C=3.0 Hz, Cq), 134.2 (d, JP-C=2.3 Hz, Cq), 133.7 (d, JP-C=2.4 Hz, Cq), 133.5 (d, JP-C=3.4 Hz, Cq), 133.4 (d, JP-C=2.4 Hz, CH), 133.1 (d, JP-C=2.3 Hz, Cq)

Stereospecific allylation of indole 5a:

In a Schlenk tube under an inert atmosphere of argon, indole 5a (47 mg, 0.4 mmol, 1 eq.), dichloromethane (1 mL) and (-)-(R)-but-3-en-2-ol 2b (87% ee) (34 µL, 0.4 mmol, 1 eq.) were successively added and the resulting solution was stirred for five minutes. Ruthenium precatalyst Ru-3 (10 mg, 3 mol%) was added and the Schlenk was immediately heated at 30°C for 16 hours. Then, the reaction was cooled to room temperature, monitored by GC analysis and stopped. The reaction mixture was filtrated on silica gel with pentane/diethyl ether eluant (2:3) in order to eliminate the catalyst affording allylated indole 6a as colorless oil with branched/linear selectivity ~ 98:2 (90% yield).

Enantioselective allylation of indole 5a: In a Schlenk tube under an inert atmosphere of argon, indole 5a (47 mg, 0.4 mmol, 1 eq.), dichloromethane (1 mL) and crotyl alcohol (93% (E)) 2c (34 µL, 0.4 mmol, 1 eq.) were successively added and the resulting solution was stirred for five minutes. Ruthenium precatalyst Ru-3 (10 mg, 3 mol%) was added and the Schlenk was immediately heated at 30°C for 16 hours. Then, the reaction was cooled to room temperature, monitored by GC analysis and stopped. The reaction mixture was filtrated on silica gel with pentane/diethyl ether eluant (2:3) in order to eliminate the catalyst affording allylated indole as colorless oil with branched/linear selectivity ~ 92:8 (86% yield). 4, 136.7, 126.9, 122.1, 120.5, 120.4, 119.7, 119.3, 112.8, 111.2, 35.0, 20.3. NMR analyses of 3-(but-3-en-2yl)-1H-indole are in agreement with previously reported data. [17a] (S)-3-(but-3-en-2-yl)-1H-indole(S)-6a from 2c (93% (E)): Enantiomeric excess was determined by HPLC with Chiralcel OJ column (95:5 n-hexane:i-PrOH, 1.0 mL/min, 254 nm, 25 ℃); tr (minor) = 37.49 min, tr (major) = 41.05 min, 8:92 er, 84% ee. Absolute configuration was attributed by comparison of the optical rotation with previously reported data. [10a,12] . (R)-3-(but-3-en-2-yl)-1H-indole (R)-6a from (R)-2b (87% ee) : Enantiomeric excess was determined by HPLC with Chiralcel OJ column (95:5 n-hexane:i-PrOH, 1.0 mL/min, 254 nm, 25 ℃); tr (major) = 37.11 min, tr (minor) = 42.76 min, 93.5:6.5 er, 87% ee. Absolute configuration was attributed by comparison of the optical rotation in chloroform with previously reported data. [10a,12] Procedure for the one-pot allylation-oxidation sequence from 2-methylindole 5b : In a Schlenk tube under an inert atmosphere of argon, 2-methylindole 5b (500 mg, 3.8 mmol, 1 eq.), dichloromethane (6 mL) and allylic alcohols 2 (3.8 mmol, 1 eq.) were successively added and the resulting solution was stirred for five minutes. Ruthenium precatalyst Ru-3 (17 mg, 0.5 mol%) was added and the Schlenk was immediately heated at 30°C for 16 hours. After cooling, completion of the allylation step was monitored by GC chromatography indicating conversion > 95%. Then the resulting solution was transferred in a flask containing SiO2 (8 g) and CH2Cl2 (50 mL). The resulting mixture was concentrated using a rotary evaporator to give a white solid. The reaction mixture was placed in air under stirring at 60°C for two hours and at room temperature for additional 16 hrs. 3, 161.4, 139.4, 137.5, 124.8, 121.5, 119.0, 117.3, 112.9, 69.2, 45.0, 22.9, 14.4. ) [START_REF]Circularly Polarized Luminescence of Isolated Small Organic Molecules[END_REF] H NMR (400 MHz, CD2Cl2) δ 7.51 (d, J= 7.7 Hz, 1H), 7.43 (ddd, J= 8.3, 7.0, 1.4 Hz, 1H), 6.86 (d, J= 8.3 Hz, 1H), 6.81-6.77 (m, 1H), 5.68 (ddd, J= 17.1, 10.3, 8.4 Hz, 1H), 5.02 (ddd, J= 17.2, 1.9, 1.0 Hz, 1H), 4.92 (dd, J= 10.3, 1.9 Hz, 1H), 4.67 (brs, 1H), 2.47 (p, J= 7.2 Hz, 1H), 1.26 (s, 3H), 1.11 (d, J= 6.9 Hz, 3H); 13 C NMR (100 MHz, CD2Cl2) δ 205.0, 160. 9, 139.4, 137.4, 124.8, 121.3, 119.0, 116.4, 112.9, 69.1, 45.1, 21.3, 14.

3-(but-3-en-2-yl)-1H-indole 6a :

Figure 1 .

 1 Figure 1. overview of different classes of CPL emitters

Figure 2 .

 2 Figure 2. Putative model accounting for allylic alcohols activation from (Sa,SRu) Ru-3 precatalyst and preferential nucleophile approach

  This article is protected by copyright. All rights reserved. 15213765, ja, Downloaded from https://chemistry-europe.onlinelibrary.wiley.com/doi/10.1002/chem.202203243 by Portail BibCNRS INC, Wiley Online Library on [12/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

Figure 3 .

 3 Figure 3. UV-vis (bottom) and ECD (top) spectra of (R,S)-8 (red)/(S,S)-8 (green) and (S,R)-8 (blue) /(R,R)-8 (black) in dichloromethane solutions (298 K, C ~10 - 5 M).

(Figure 4 .

 4 Figure 4. CPL (top) and normalized fluorescence (bottom) spectra of (S,S)-8 (green), (R,S)-8 (red), (S,R)-8 (blue) and (R,R)-8 (black) in dichloromethane solutions (λex = 375 nm).

  Figure 5. a) Normalized emission (solid line) and absorption (dashed line) spectra of (S,R)-8 in toluene (Magenta), THF (Blue), DCM (black), DMF (green), ethanol (orange) and water (red). b) CPL spectra of (R,R)-8 (solid lines) and (S,R)-8 (dashed lines) in toluene (Magenta), THF (Blue), DCM (black), DMF (green), ethanol (orange) and water (red) (298K, C ~10 -5 M).

  , 131.1 (s, CH), 131.0(d, JP-C=6.4 Hz, CH), 130.7 (d, JP-C=7.0 Hz, CH), 130.6 (s, CH), 129.6(d, JP-C=13 Hz, Cq), 129.4 (d, JP- This article is protected by copyright. All rights reserved. 15213765, ja, Downloaded from https://chemistry-europe.onlinelibrary.wiley.com/doi/10.1002/chem.202203243 by Portail BibCNRS INC, Wiley Online Library on [12/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License C=6.7 Hz, Cq), 129.3 (d, JP-C=2.2 Hz, CH), 129.1 (d, JP-C=1.0 Hz, CH), 129.0 (d, JP-C=1.4 Hz, CH), 127.8 (d, JP-C=4.1 Hz, CH), 127.8 (s, CH), 127.5 (d, JP-C=5.0 Hz, CH), 127.4 (d, JP-C=8.1 Hz, CH), 127.3 (s, CH), 127.2 (s, CH), 126.9 (d, JP-C=1.3 Hz, CH), 124.3 (s, Cq), 123.9 (s, Cq), 109.7 (d, JP-C=1.0 Hz, Cq, C5Me5), 96.6 (s, CH, allyl), 79.1 (d JP-C=3.3 Hz, CH2, allyl), 52.6 (d, JP-C=4.5 Hz, CH2, allyl), 28.6 (d, JP-C=28.5 Hz, CH2, binepine), 28.5 (d, JP-C=22.3 Hz, CH2, binepine), 10.3 (s, CH3, C5Me5); 31 P NMR (160 MHz, CD2Cl2) δ 36.2 (s), -144.5 (hept, J=705 Hz); HRMS calcd for [M-PF6] + C41H40O3PSRu 745.14738, found : 745.1474 (0 ppm).

  Complete conversion were observed by GC and NMR analyses with branched/linear selectivity > 97:3 from 2b and branched/linear selectivity of 92:8 from 2c. Purification by silica gel column chromatography (pet. ether: Et2O = 7 : 3) allowed the separation of the two diastereoisomers (66% overall yield); HRMS calcd for [M+Na] + C13H15NONa 224.10458, found : 224.1048. (S)-2-((R)-but-3-en-2-yl)-2-methylindolin-3-one (S,R)-8 from (R)-2b (87% ee) : Yellow solid; er= 5.5:94.5; [𝛼] 𝐷 20 =-298 (c 0.004, CH2Cl2)1 H NMR (400 MHz, CD2Cl2) δ 7.54 (dt, J= 7.7, 1.0 Hz, 1H), 7.44 (ddd, J= 8.3, 7.1, 1.4 Hz, 1H), 6.89 (dt, J= 8.3, 0.8 Hz, 1H), 6.79 (ddd, J= 7.8, 7.0, 0.8 Hz, 1H), 5.93-5.79 (m, 1H), 5.21-5.17 (m, 1H), 5.16-5.12 (m, 1H), 4.70 (brs, 1H), 2.65-2.41 (m, 1H), 1.26 (s, 3H), 0.80 (d, J= 6.7 Hz, 3H) ; 13 C NMR (100 MHz, CD2Cl2) δ 205.

  Enantiomeric excess was determined by HPLC with Chiralcel ODH column (99:1 n-hexane:i-PrOH, 1.0 mL/min, 254 nm, 25 ℃); tr (minor) = 15.5 min, tr (major) = 18.(E)): Yellow solid; er= 93.7:6.3; [𝛼] 𝐷 20 =+ 250 (c 0.24, CH2Cl2). Enantiomeric excess was determined by HPLC with Chiralcel ODH column (99:1 n-hexane:i-PrOH, 1.0 mL/min, 254 nm, 25 ℃); tr (major) = 15.0 min, tr (minor) = 19.2 min, 88% ee. 2b (87% ee) : Yellow oil; er= 7.7:92.3; [𝛼] 𝐷 20 =+ 173 (c 0.004, CH2Cl2

  9. Enantiomeric excess was determined by HPLC with Chiralcel ODH column (99:1 n-hexane:i-PrOH, 1.0 mL/min, 254 nm, 25 ℃); tr (major) (E)): Yellow oil, er= 94.9:5.1, containing ~ 6% of racemic 2-(but-2-en-1-yl)-2-methylindolin-3-one side product, [𝛼] 𝐷 20 =-160(c 0.24, CH2Cl2). Enantiomeric excess was determined by HPLC with Chiralcel ODH column (99:1 n-hexane:i-PrOH, 1.0 mL/min, 254 nm, 25 ℃); tr (minor) = 17.5 min, tr (major) = 21.2 min, 88% ee.

15213765, ja, Downloaded from https://chemistry-europe.onlinelibrary.wiley.com/doi/10.1002/chem.202203243 by Portail BibCNRS INC, Wiley Online Library on [12/11/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

Acknowledgements ((optional))

10.1002/chem.202203243

Accepted Manuscript

We thank the Centre National de la Recherche Scientifique (CNRS) and the University of Rennes. Part of this work has been performed using the PRISM core facility (Biogenouest©, UMS Biosit, Université de Rennes 1 -Campus de Villejean, 35043 RENNES Cedex, FRANCE). The author thank T. Roisnel for Xray diffraction analysis.

Keywords: chirality • enantioselectivity • stereoselectivity • fluorescence • CPL

Entry for the Table of Contents

Through the use of a well-defined enantiopure π-allylic ruthenium(IV) precatalyst, facile access to enantioenriched indolin-3-one emitters was achieved.


est destinée au dépôt

  Applicability of OECD test guideline 201 to graphene-related materials (GRMs): new insights into GRMs dispersions stability and possible modifications of the standard protocol G Caorsi, F Candotto Carniel, Emmanuel Flahaut, E Vázquez, M Prato, M Tretiach To cite this version: G Caorsi, F Candotto Carniel, Emmanuel Flahaut, E Vázquez, M Prato, et al.. Applicability of OECD test guideline 201 to graphene-related materials (GRMs): new insights into GRMs dispersions stability and possible modifications of the standard protocol. International Congress of Toxicology (ICT2022), Sep 2022, Maastricht, Netherlands. hal-03850073

Applicability of OECD test guideline 201 to graphene-related materials (GRMs): new insights into

GRMs dispersions stability and possible modifications of the standard protocol G. Caorsi 1 , F. Candotto Carniel 1 , E. Flahaut 2 , E. Vázquez 3 , M. Prato 4 , M. Tretiach 1 Proceedings of the 16 th International Congress of Toxicology (ICT2022), Sept. 18-21, 2022 Graphene-related materials (GRMs) are used in many innovative applications thanks to their unique physicochemical properties. The increasing development of GRMs-containing products and the resulting future widespread availability could lead to the unintended release of GRMs with unknown consequences for the environment.

According to REACH, all new substances manufactured or imported in the EU must undergo a battery of ecotoxicological bioassays [OECD Test Guidelines (TG)] to assess their potential risk to aquatic organisms. However, these tests were developed to assess the toxicity of water-soluble substances, whereas GRMs are not. GRMs dispersed in aqueous media tend to aggregate and settle, changing their bioavailability over time. Therefore, this work aims to assess the applicability of TG201 to GRMs by studying the GRMs Dispersions Stability (GDS) in the TG201 medium. GDS was evaluated by examining the sedimentation and aggregation of GRMs by Turbiscan and flowcytometry (FCM) analyses, respectively, over the 72 hours test period. The following factors affecting GDS were tested: (i) particle composition and (ii) concentration, (iii) turbulence, and (iv) medium composition. The effects of (i)-(iii) were tested using dispersions of few-layer graphene (FLG), graphene oxide (GO), and reduced GO (rGO) at 4-20 mg L-1, that were or were not subjected to various methods to maintain turbulence (bubbling, shaking, and stirring). The effect of (iv) was tested by comparing GDS in distilled water, 5 commercial mineral waters with different ionic contents, and TG201 medium eventually added with dispersants [Suwannee River Natural Organic Matter (SRNOM), carboxymethylcellulose (CMC), and sodium deoxycholate (SDC)]. In addition, GRMs dispersions were used to evaluate the algal growth inhibition, i.e. the TG201 endpoint. Turbiscan analyses revealed that FLG had the fastest sedimentation rate in the first 3 hours, while GO was the most stable, independent of (ii). Visual inspections and FCM revealed that magnetic stirring increased GDS the most. However, turbulence always increased the formation of loose, stable, and more complex aggregates. Similarly, GRMs dispersions in high ionic content media had a greater increase in GRMs particles with high complexity over the 72 hours than in those with low content, e.g. the TG201 medium. In contrast, the addition of SRNOM to the TG201 medium increased the GDS of all dispersions. Our results show that GRMs dispersions are not stable under the standard TG201 conditions and therefore do not meet the TG requirement of a stable and homogeneous dispersion throughout the test. Therefore, modifications of the test protocols to improve the applicability of TG201 to GRMs, such as the use of SRNOM, will be presented. Finally, these data on GDS will help predict the GRMs behaviour during ecotoxicological testing, an important factor for the correct interpretation of TG201 results, and the fate of GRMs in freshwater environments.


Céline Souilhol

Sarah Cormier

Marie Monet #

Sandrine Vandormael-Pournin

Anne Joutel #

Charles Babinet

Michel Cohen-Tannoudji

The NAS transgenic mouse line allows visualization of Notch pathway activity in vivo

Keywords: arte ria l vascu la r system, develop ing centra l nervous system, li m b bud, N otch reporte r m ouse, RBP-Js, som itogenesis, sm ooth

The Notch signalling pathway plays multiple and important roles in mammals. However, several aspects of its action, in particular the precise mapping of its sites of activity, remain unclear. To address this issue, we have generated a transgenic line carrying a construct consisting of a nls-lacZ reporter gene under the control of a minimal promoter and multiple RBP-Ju binding sites. Here we show that this transgenic line, we named NAS for Notch Activ ity Sensor, d isp lays an expression profile that is consisten t w ith curren t know l edge on N otch activ ity sites in m i ce, even though it m ay not report on all these sites. M oreover, w e observe that NAS transgene expression is abolished in a RBP-Jo defic ien t background ind ica tin g that it indeed requ ires N otch /RBP-JN signa llin g pathw ay activ ity . Thus, the NAS transgen ic lin e constitu te s a valuab le and versatile too l to gain fu rthe r in sigh ts in to the com pl ex and various function s of the N otch signa llin g pathw ay.

Keyw ords:

Introduction

The N otch signa llin g pathw ay plays a fundam ental ro le in num erous developm enta l processes in m etazoans (A rtavan is- [START_REF] A Rtavan Is-Tsakonas | N otch signa lin g[END_REF]Artavanis-Tsakonas et al., 1999;[START_REF] Lai | Notch s igna l i ng : contro l of cel l communicat ion and cel l fate[END_REF]. Depending on the context, signalling through the Notch pathway impinges on a wide variety of cellular responses such as binary cell fate decisions, stem cell maintenance, induction of differentiation, proliferation or apoptosis.

Accordingly, genetic alterations of Notch pathway components have been implicated in various pathologies in humans, including cancer [START_REF] Garg | Mutat ions in NOTCH1 cause aort i c valve disease[END_REF]Gridley, 2003;Joutel and Tournier-Lasserve, 1998;[START_REF] Radtke | The ro le of Notch in tumorigenes is : oncogene or tumour suppressor?[END_REF]. Jk/CBF1/Su(H). RBP-JnterICD and co-factors assemble into a complex that activates the expression of target genes, while in the absence of act iva ted Notch, RBP-Jae recru i t s repressor complexes to the cis-regulatory region of the Notch target genes.

Numerous studies have been performed in order to decipher the in vivo functions of the Notch pathway in vertebrates. In particular, genetic studies in mice have pointed to many roles for the Notch pathway: in somite formation and patterning (reviewed in (Aulehla and Herrmann, 2004;[START_REF] Weinmaster | Modulat ion of notch s igna l i ng dur ing somitogenesis[END_REF]), vasculature development and arterial identity acquisition (reviewed in (Shawber and Kitajewski, 2004)), neurogenesis (reviewed in [START_REF] Yoon | Notch s igna l i ng in the mammalian centra l nervous system: ins ights f rom mouse mutants[END_REF]) or lymphoid progenitors differentiation (reviewed in [START_REF] Radtke | Notch regula t i on of lymphocyte development and funct i on[END_REF]). To dissect out the cellular responses directly controlled by the Notch pathway, it is important to identify cells in which the pathway is activated at a given time during development and in adult tissues. However, acquisition of such knowledge is hampered by several limitations. First, the Notch pathway involves a complex set of proteins. In rodents for example, there are four Notch receptors, five ligands of the Delta/Serrate/Jagged family and two recently identified new ligands, DNER and F3 contactin [START_REF] Eiraku | DNER acts as a neuron-speci f i c Notch l i gand dur ing Bergmann gl ia l development[END_REF][START_REF] Hu | F3/contact i n acts as a funct iona l l i gand for Notch dur ing ol igodendrocyte maturat ion[END_REF]. The corresponding genes are expressed at many sites and exhibit complex and often overlapping expression patterns. Second, Notch signalling activity is modulated by numerous accessory proteins acting either at the extracellular s ide (such as members of the Fr inge fami ly , [START_REF] Johnston | A fami ly of Fr inge genes impl i ca ted in boundary determinat ion and the Notch pathway[END_REF])) or at the intracellular side (such as Mind Bomb or Neuralized, (Le [START_REF] Borgne | The ro les of receptor and l i gand endocytos i s in regula t i ng Notch s igna l i ng[END_REF]) and is therefore highly context-dependent (Artavanis-Tsakonas et al., 1995;[START_REF] Schweisguth | Notch s igna l i ng act iv i t[END_REF]. Third, the crosstalk between the Notch pathway and other signal-transduction pathways (see for example (Dahlqvist et al., 2003;[START_REF] Gustafsson | Hypoxia requi res notch s igna l i ng to mainta in the undi f f e rent i a ted cel l state[END_REF]) make the outcome of Notch activation difficult to predict. As a consequence, Notch pathway activity cannot be simply deduced from the expression profiles of its components. Thus, activation of direct target genes could represent a more reliable readout of Notch activity. The best characterized Notch target genes are members of the Hairy/enhancer of split (Hes) family that encode basic helix-loop-helix transcription factors (Iso et al., 2003b). However, several additional direct target genes have been recently characterised (see for example [START_REF] Anthony | B ra in lip id -b ind ing prote in is a direct target of N otch signa lin g in rad ia l g lia l cells[END_REF][START_REF] Krebs | Notch s igna l i ng regula tes le f t -r ight asymmetry determinat ion by induc ing Nodal express ion[END_REF][START_REF] Raya | Notch act iv i t y induces Nodal express ion and mediates the establ i s hment of le f t -r ight asymmetry in vertebrate embryos[END_REF]Reizis and Leder, 2002)), suggesting that visualization of Notch activity using this approach may necessitate the prior identification of the target genes activated in the system under study.

As an alternative approach, we generated a RBP-Je/Notch transgenic reporter mouse that we named NAS for Notch pathw ay

Activ ity

Sensor transgen ic m ouse. In th is m ouse lin e , iden tifica tio n of lacZ expressing cells or tissue is expected to ref l e c t the dis t r i bu t i on of transcr ip t i ona l l y act ive RBP-Jo /N ICD nuclear complexes and there fore potent ia l l y those cel l s or t i s sues where Notch s igna l l i ng is at work. Here, we descr ibe the lacZ expression pattern in NAS mice and show that it is consistent with various previously identified sites of Notch pathway activity.

Results and discussion

Generation of a RBP-Jn/Notch reporter mouse

To assess the activity of the RBP-Je/Notch signalling pathway in the whole organism, we generated an RBP-Ji-dependent transgenic reporter mouse. The Escherichia coli lacZ reporter gene was chosen because it is sensitive and allows detection at the single cell level. A modified version of the lacZ gene, coding for a nuclear ß-gal, was used in order to discriminate transgene activity from the cytoplasmic non-specific activity observed in certain cells. To drive the expression of the "nlacZ" gene, we used the well-characterized TP1 promoter, which consists of 12 multimerized RBP-JP binding motifs upstream from a minimal promoter [START_REF] Kato | Invo lvement of RBP-J in bio log i ca l funct i ons of mouse Notch1 and i t s der iva t i ves[END_REF][START_REF] Minoguchi | RBP-L, a transcr i p t i on factor re la ted to RBP-Jkappa[END_REF] (fig. 1). The TP1 promoter is transactivated in a RBP-J dependent manner by the activated forms of the four mammalian Notch receptors [START_REF] Kato | Funct iona l conservat ion of mouse Notch receptor fami ly members[END_REF][START_REF] Shimizu | Funct iona l divers i t y among Notch1, Notch2, and Notch3 receptors[END_REF] and thus, has been often used to read out Notch pathway activity in various ex vivo studies (see for example (Gupta-Rossi et al., 2001;Joutel et al., 2004)) as well as in a recent in vivo study [START_REF] Kohyama | Visua l i z a t i on of spat io temporal act iva t i on of Notch s igna l i ng : l i ve monitor ing and s ign i f i c ance in neura l development[END_REF]. The resulting construct, TP1-nlacZ, was microinjected in mouse zygotes and two transgenic lines were established. Transgene expression was monitored by X-gal staining of E9.5 to E17.5 embryos and 1 to 4 weeks old mice. No transgene expression was observed in one of the two l i nes , there fore i t was discarded. In the other l i ne , rest r i c t ed and dynamic express ion of nl acZ gene was obser ved ( f i g. 2a-d) . At a gi ven st age, t r ansgeni c em br yos exhi bi t ed i dent i cal pr of i l es of expr essi on. However , som e var i at i on i n t he i nt ensi t y of X-gal st ai ni ng was obser ved bet ween em br yos of t he sam e l i t t er ( f i g. 2c) , whi ch i s l i kel y t o r ef l ect genet i c backgr ound het er ogenei t y am ongst l i t t er m at es. Thi s i s f ur t her subst ant i at ed by our pr el i m i nar y obser vat i on t hat backcr ossi ng t wi ce t hi s t r ansgeni c l i ne ont o C57Bl / 6 backgr ound r educes X-gal st ai ni ng var i abi l i t y bet ween l i t t er m at es ( dat a not shown) . I n t he r est of t he m anuscr i pt , we wi l l descr i be t he m ai n f eat ur es of t he expr essi on pr of i l e of t hi s l i ne. Because t hi s pr of i l e i s consi st ent wi t h si t es wher e act i vi t y of t he Not ch si gnal l i ng pat hway was pr edi ct ed f r om pr evi ous st udi es ( see bel ow) , we nam ed t hi s t r ansgeni c l i ne NAS f or Notch pathway Act iv i t y Sensor transgenic l i ne .

TP1-nl acZ t r ansgene expr essi on i s dependent on t he pr esence of RBP-J l

I t was essent i al t o dem onst r at e t hat l acZ expr essi on i n t he NAS t r ansgeni c l i ne i ndeed r esul t s f r om act i vi t y of t he Not ch/ RBP-J r pat hway.

To t hat end, we t r ansf er r ed TP1-nl acZ t r ansgene i nt o a RBP-J g nul l backgr ound. RBP-J ∆ del et ed al l el e was pr oduced by Cr e m edi at ed r ecom bi nat i on of a condi t i onal RBP-J r f f l oxed al l el e [START_REF] Han | Induc ib le gene knockout of transcr i p t i on factor recombinat ion s igna l bind ing prote in -J reveals i t s essent ia l ro le in T versus B l i neage decis i on[END_REF] . Mi ce car r yi ng t he TP1-nl acZ transgene in a RBP-Js ∆/ + backgr ound wer e i nt er cr ossed and em br yos wer e r ecover ed at 10 days post -coi t um , shor t l y bef or e l et hal i t y due t o t he absence of RBP-J e f unct i on [START_REF] Oka | Disrupt i on of the mouse RBP-J kappa gene resul t s in ear ly embryonic death[END_REF] . As pr evi ousl y descr i bed f or RBP-J 5 knock-out em br yos, RBP-J o and see bel ow) , whi l e no l acZ expr essi ng cel l s wer e det ect ed i n t he cor r espondi ng r egi ons of RBP-J e ∆/ ∆ em br yos ( f i g. 2g-h) .

Thi s shows t hat i n vi vo TP1-nl acZ t r ansgene act i vat i on i s m edi at ed by RBP-J t , at l east at t hi s st age. Mor eover , RBP-J i s expect ed t o f unct i on as a t r anscr i pt i onal r epr essor of TP1nl acZ t r ansgene i n absence of Not ch act i vi t y ( f i g. 1b) . W e f i nd t hat depl et i on of RBP-J c does not l ead t o t r ansgene der epr essi on t hat woul d have r esul t ed i n wi despr ead NAS act i vat i on.

l acZ expr essi on dur i ng som i t ogenesi s

Not ch si gnal l i ng pl ays i m por t ant r ol es i n t he pr ocess of som i t ogenesi s. Hence, def i ci ency i n cor e com ponent s ( Not ch1, Delta -l i ke (Dl l ) 1, Dl l3 , Preseni l i n -1, Kuzbanian and RBP-J )

as wel l as in targets and modulators (Hes7, Mesp2 and Lunat ic

Fr inge) of the Notch pathway al l resul t s in perturbat i ons of somite fomation and pattern ing ( fo r rev iew see (Auleh la and Herrmann, 2004;[START_REF] Weinmaster | Modulat ion of notch s igna l i ng dur ing somitogenesis[END_REF]) . In te res t i ng l y , the NAS reporte r transgene is expressed dur ing somitogenesis .

At E9.5, a str i pe of X-gal posi t i ve cel l s was detected in the poster i o rmost region of newly formed somites ( f i g . 2a, i ) . In the presomit i c mesoderm (PSM), a band of l acZ expr essi ng cel l s was al so obser ved at t he boundar y-f or m i ng r egi on of t he pr ospect i ve som i t e ( f i g. 2i ar r ow) . A si m i l ar expr essi on pr of i l e was obser ved dur i ng som i t ogenesi s of ol der em br yos ( f i g. 2c, d, j ) . On E11. 5 t ai l t r ansver se sect i ons, ß-gal posi t i ve cel l s wer e m ai nl y f ound at t he post er i or bor der of t he new som i t es ( f i g. 2k) . I n t he PSM, TP1-nl acZ t r ansgene expr essi on was det ect ed bef or e a cl ef t was f or m ed ( ar r owheads on f i g. 2k) , consi st ent wi t h t he r epor t ed cr i t i cal r ol e of Not ch si gnal l i ng pat hway i n i nt er -som i t es boundar y f or m at i on 1998) ) . To addr ess t hi s possi bi l i t y, we l ooked by i n si t u hybr i di zat i on at t he di st r i but i on of l acZ m RNA i n t he t ai l of E10. 5-11. 5 em br yos. A si ngl e band of l acZ t r anscr i pt s was det ect ed i n PSM i n t he cl ef t -f or m i ng ar ea ( ar r owheads f i g. 2l ) i ndi cat i ng t hat i t i s t he m ai n si t e of TP1-nl acZ t r ansact i vat i on and t hat ß-gal st abi l i t y i s m ost l i kel y r esponsi bl e f or t he st ai ni ng obser ved i n t he m or e ant er i or som i t es. Such act i vat i on i s l i kel y t o ensue f r om si gnal l i ng t hr ough Not ch1 r ecept or si nce accum ul at i on of act i vat ed Not ch1 at t he cl ef t f or m i ng r egi on bet ween som i t es S-1 and S0 has been r ecent l y vi sual i zed usi ng an ant i body 2005) . I t shoul d be however not ed t hat cycl i cal pr oduct i on of act i vat ed Not ch1 det ect ed i n t hese st udi es i n a m or e post er i or r egi on of PSM usi ng t he sam e ant i body i s not r ef l ect ed by a det ect abl e NAS r epor t er t r ansgene t r ansact i vat i on.

l acZ expr essi on i n t he hear t and t he ar t er i al vascul ar syst em

The Not ch pat hway, no l acZ expr essi on was obser ved, and t hi s at al l em br yoni c st ages anal ysed. I n t he devel opi ng vascul at ur e, t r ansgene expr essi on was f i r st det ect ed i n t he caudal r egi on of t he dor sal aor t a and i n vi t el l i ne and um bi l i cal ar t er i es at E9. 5-E10 ( f i g. 2b, m ) . Tr ansver se sect i ons i n t he t r unk r egi on showed a pat chy X-gal st ai ni ng di st r i but ed ar ound t he aor t a cl ose t o t he l um en ( f i g. 2m ) . Expr essi on was al so obser ved i n t he per i car di ac r egi on. At E9. 5-E10, scat t er ed st ai ni ng was f ound i n t he t hi r d br anchi al ar ch ( ar r ows i n f i g. 2a, b) . Then at E10. 5, ß-gal posi t i ve cel l s wer e det ect ed i n t he r egi on l i ni ng t he l um en of t he upper par t of t he car di ac out f l ow t r act and of t he br anchi al ar ch ar t er i es di r ect l y br anchi ng f r om i t ( f i g. 2n) . Sect i ons of E10. 5 showed t hat t r ansgene expr essi on i n t he hear t was r est r i ct ed t o t he endocar di um of t he out f l ow t r act ( dat a not shown) . I n t he f ol l owi ng days, l acZ express ion progressed to i l i a c arter i e s and major vesse ls of the head ( f i g . 2o) . At E12.5, X-gal sta in ing was observed throughout dorsa l aorta , being more in tense in the caudal region ( f i g . 2e, p) . At E17.5, transgene express ion was almost absent f rom the abdominal aorta but was detected in in te rcos ta l arter i e s branching direc t l y f rom i t ( f i g . 2q) as wel l as in many other smal l arter i e s of the embryo. At th i s stage, as wel l as in postnata l mice, the dis t r i bu t i on and ovoid shape of X-gal posi t i v e nucle i assoc ia ted with vessels was evocat ive of smooth muscle cel l s (SMCs) . Spira les of posi t i v e nucle i enci rc l i ng var ious vesse ls , such as ta i l or pia l arter i e s , were detected ( f i g . 2r,s ) . Many cerebra l microvesse ls were s imi la r l y decorated with X-gal posi t i v es nucle i , which l i ke l y correspond to per icy tes ( f i g . 2t) .

l acZ expr essi on i n ot her si t es

I n addi t i on t o t he t wo m ai ns si t es descr i bed above, r est r i ct ed and dynam i c expr essi on of TP1-nl acZ t r ansgene was obser ved i n sever al ot her t i ssues. For exam pl e, dur i ng l i m b devel opm ent , scat t er ed ß-gal expr essi ng cel l s wer e f i r st det ect ed at E10, i n t he sur f ace ect oder m of t he vent r al si de of f or el i m b buds ( f i g. 3a devel opm ent has been r ecent l y pr ovi ded t hr ough condi t i onal m ut agenesi s [START_REF] Pan | Notch1 and 2 cooperate in l imb ectoderm to rece ive an ear ly Jagged2 s igna l regula t i ng in te rd ig i t a l apoptos i s[END_REF] .

Rest r i ct ed t r ansgene expr essi on was al so obser ved i n t he devel opi ng cent r al ner vous syst em ( CNS) . I n t he f or ebr ai n, expr essi on was det ect ed i n t he caudal t hi r d of t he m edi al wal l of E11. 5 and E12. 5 cor t i cal hem i spher es ( f i g. 3d and 2o) . Thi s r egi on i ncl udes t he cor t i cal hem , whi ch i s i m por t ant f or t el encephal on pat t er ni ng. I n t he hi ndbr ai n, X-gal l abel l ed cel l s accum ul at ed on bot h si des of vent r al m i dl i ne st r uct ur es of E10. 5 em br yos ( f i g. 3e) . At E11. 5, ß-gal posi t i ve cel l s wer e or gani zed i nt o wel l def i ned st r i pes ( f i g. 3f , i ) . A f i r st bi l at er al st r i pe cl ose t o t he f l oor pl at e was obser ved i n t he hi ndbr ai n ( bl ack ar r ows i n f i g. 3f and f i g. 3i ) . A second st r i pe was obser ved i n t he hi ndbr ai n i n a m or e l at er al posi t i on ( f i g. 3f , em pt y ar r ow i ndi cat es i t s ant er i or l i m i t ) .

This str i pe extended poster io r l y in to most of the neura l tube of E11.5 ( f i g . 3f ,h ) and E12.5 ( f i g . 3g, arrow) embryos.

Sect ions ind ica ted that TP1-nl acZ t r ansgene i s expr essed i n t he vent r i cul ar zone ( f i g. 3h, i ) as ar e Not ch r ecept or s and l i gands i n t he m i dgest at i on em br yoni c m am m al i an CNS ( Li ndsel l et al . , 1996;[START_REF] Myat | A chick homologue of Serrate and i t s re la t i onsh ip with Notch and Delta homologues dur ing centra l neurogenesis[END_REF] . I nt er est i ngl y, bi l at er al st r i pes of expr essi on i n t he vent r i cul ar zone of t he hi ndbr ai n and spi nal cor d have been r epor t ed f or chi ck Del t a-1 and J agged-1 [START_REF] Myat | A chick homologue of Serrate and i t s re la t i onsh ip with Notch and Delta homologues dur ing centra l neurogenesis[END_REF] di f f er ent Not ch r ecept or s and l i gands m i ght be i nvol ved i n t he pr oduct i on of di st i nct neur al phenot ypes. A det ai l ed anal ysi s wi l l be necessar y t o est abl i sh t he pr eci se r el at i ons bet ween t he TP1-nl acZ t r ansgene and t he expr essi on pr of i l es of com ponent s of t he Not ch pat hway. I n post nat al br ai ns, weak t r ansgene expr essi on, besi des t he vessel s associ at ed cel l s, was obser ved i n t he Pur ki nj e cel l l ayer of cer ebel l um ( f i g. 3j , ar r ow) . A st r ong l ayer -speci f i c X-gal st ai ni ng was al so det ect ed i n a vent r ol at er al r egi on of t he cor t ex, whi ch i s l i kel y t o cor r espond t o t he ent or hi nal cor t ex ( f i g. 3k and ar r ow i n f i g. 2r ) . Sect i ons i ndi cat ed t hat t r ansgene expr essi on was r est r i ct ed t o an i nt er m edi at e cor t i cal l ayer ( f i g. 3l ) .

Anot her si t e of expr essi on was t he devel opi ng t oot h. At E17. 5, a strong sta in ing was observed on the lab ia l sur face of the inc i so r buds ( f i g . 3m). Sect ions ind ica ted that transgene express ion was rest r i c t ed to stra tum in te rmedium cel l s under ly ing ta l l columnar ameloblas ts secret ing the enamel matr ix ( f i g . 3n) . Simi la r observat ions were made on postnata l develop ing molar ( f i g . 3o No obvi ous t r ansgene expr essi on was obser ved i n som e si t es wher e RBP-J t / Not ch si gnal l i ng has been pr evi ousl y shown t o be act i ve. For exam pl e, l ym phoi d or gans wer e not l abel l ed by Xgal st ai ni ng, whi l e a r ol e f or Not ch dur i ng l ym phoi d pr ecur sor di f f er ent i at i on has been cl ear l y est abl i shed ( r evi ewed i n ( Radt ke et al . , 2004) . The r easons t hat m ay account f or t hi s di scr epancy ar e yet unknown but a possi bi l i t y woul d be t hat t he TP1-nl acZ const r uct cannot be t r ansact i vat ed i n cer t ai n t i ssues because of posi t i on ef f ect si l enci ng. The st r uct ur e of t he t r ansgene i t sel f m ay al so conf er som e quant i t at i ve or qual i t at i ve r est r i ct i ons t o i t s act i vat i on by t he RBP-J o/ Not ch pat hway. I n t he pr om ot er r egi on of Not ch t ar get genes, spaci ng and or ienta t i on of RBP-J-bind ing s i tes as wel l as the i r assoc ia t i on with other DNA binding s i tes modulate the transcr i p t i ona l response mediated by act iva ted Notch receptors [START_REF] Cave | A DNA transcrip tion code for ce ll-specific gene activa tion by notch signa lin g[END_REF][START_REF] Ong | Col labora t i on between disc re te prote in domains and binding s i te archi tec tu re on the promoter determine target selec t i v i t y of vertebrate notch prote ins[END_REF] . Hence, m ouse Hes-1 pr om ot er cont ai ns pai r ed hi gh af f i ni t y RBP-J e bi ndi ng si t es i n a head-t o-head or i ent at i on and changi ng t hei r or i ent at i on abr ogat es i t s Not ch m edi at ed act i vat i on i n cul t ur ed cel l s [START_REF] Ong | Col labora t i on between disc re te prote in domains and binding s i te archi tec tu re on the promoter determine target selec t i v i t y of vertebrate notch prote ins[END_REF] , 1996) . Due t o t he ar t i f i ci al st r uct ur e of t he TP1-nl acZ pr om ot er r egi on, i t was ant i ci pat ed t hat t r ansgene expr essi on pr of i l e m i ght not r epor t on al l Not ch act i vi t y. Thi s i s t he case, however our f i r st sur vey of t he l acZ expr essi on pr of i l e i n NAS m i ce i ndi cat es t hat a num ber of known si t es of Not ch act i vi t y expr ess t he t r ansgene.

I t should be noted that a more extens ive analys i s of TP1-nl acZ expr essi on m i ght r eveal ot her si t es of Not ch act i vi t y.

Gener at i on and char act er i zat i on of ot her Not ch r epor t er t r ansgeni c l i nes car r yi ng var i ous RBP-J r bi ndi ng si t es and di f f er ent r epor t er genes conf i gur at i on shal l al so pr ove t o be usef ul f or ext ensi ve vi sual i zat i on of Not ch act i vi t y i n vi vo.

I n t hi s r espect , i t shoul d be m ent i oned t hat sor t i ng of Not ch r esponsi ve haem at opoi et i c st em cel l s was r ecent l y achi eved t hanks t o t he use of a t r ansgeni c l i ne har bour i ng f our copi es of RBP-J o bi ndi ng si t es l i nked t o EGFP [START_REF] Duncan | Integra t i on of Notch and Wnt s igna l i ng in hematopoiet i c stem cel l maintenance[END_REF] .

However t he expr essi on pr of i l e of t hi s l i ne apar t f r om t he adul t bone m ar r ow has not been r epor t ed so f ar . Fi nal l y, com par i son of TP1-nl acZ expr essi on pr of i l es wi t h t hat of t r ansgeni c l i nes car r yi ng a r epor t er gene under t he cont r ol of r egul at or y r egi ons of di r ect Not ch t ar get genes m i ght al so hel p t o def i ne t he r el at i ve cont r i but i on of RBP-J i / NI CD com pl exes t o t he t r anscr i pt i onal r egul at i on of i ndi vi dual t ar get genes.

I n addi t i on t o i t s use i n t he descr i pt i on of Not ch pat hway act i vi t y dur i ng nor m al devel opm ent and i n adul t t i ssues, NAS t r ansgeni c m i ce m ay be usef ul i n addr essi ng ot her i m por t ant bi ol ogi cal quest i ons. For exam pl e, i t shoul d hel p f or genet i c or dr ug scr eens f or Not ch si gnal l i ng m odul at or s i n m i ce. I t shoul d al so hel p t o eval uat e i n vi vo t he cr osst al ks bet ween Not ch and ot her si gnal l i ng pat hways or t o f i ne t une t he invo lvement of the former in var ious pathogenic processes ( tumorigenes is , developmental anomalies , etc…). Future work using the NAS transgenic l i ne wi l l certa in l y help to gain new ins ights in to the complex funct i ons of the Notch s igna l l i ng pathway in the mouse.

Methods

Construction of the RBP-nlsLacZ transgene and production of transgenic mice.

TP1-nlacZ construct was derived from plasmid pGa981-6 [START_REF] Minoguchi | RBP-L, a transcr i p t i on factor re la ted to RBP-Jkappa[END_REF] and plasmid pSKTNLSLACZ (a gift from S. Tajbakhsh). The hexamerized 50 bp EBNA2 response element of the TP-1 promoter in front of the minimal ß-globin promoter was recovered from pGa981-6 plasmid and put in front of the nlsLacZ gene from pSKTNLSLACZ coding for a nuclear ßgalactosidase (ßgal) (fig. 1a). StuI-NotI linearized construct was microinjected into (C57BL/6xSJL/J) 2 fertilized eggs, which were then transferred to pseudo-pregnant females. Transgenic embryos and animals were identified by PCR and Southern blot analysis of tail or placental DNA using lacZ oligonucleotides (lacZ1 : 5'-GTC GTT TTA CAA CGT CGT GAC T-3' ; lacZ2 : 5'-GAT GGG CGC ATC GTA ACC GTG C-3') and probe as described in [START_REF] Cohen-Tannoudji | Unexpected position -dependent expression of H -2 and beta 2m i crog lobu lin /la cZ transgenes[END_REF]. Stable lines, harbouring single integration of the transgene, were established by cross ing transgenic founders with (C57BL/6xSJL / J ) F1 mice.

Embryos were recovered f rom mating between N1 or N2 transgenic males with wild -type females . The age of the embryos was determined accord ing to the appearance of the vagina l plug (day 0.5) and conf i rmed by morphologica l cr i t e r i a .

Whole mount ß-galactosidase staining.

Embryos as well as organs dissected from postnatal mice were fixed for 30-60 minutes at room temperature in either 4% paraformaldehyde or 2% paraformaldehyde and 0.2% glutaraldehyde in PBS. From E12.5 onwards, embryos and organs were cut in halves after 30 min in the fixative solution in order to improve the penetration of fixative and staining solutions and then returned to the fixative solution for another 30 min. After fixation, samples were rinsed several times with PBS and incubated overnight at 32°C in X-Gal staining solution (PBS containing 0.01% Tween20, 2mM MgCl 2 , 4mM K 4 Fe(CN) 6 , 4mM K 3 Fe(CN) 6 , and 4mg/ml of X-gal (Invitrogen)).

Then, samples were rinsed several times with PBS, postfixed in 4% paraformaldehyde and stored at 4°C in a 1/1 mixture of 4% paraformaldehyde and glycerol. Pictures of embryos and organs were taken using a SMZ1500 stereomicroscope (Nikon) equipped with an AxioCam color (Zeiss).

Production of RBP-Jc null embryos.

RBP-J f / f males, carrying an exons 6 and 7-floxed RBP-J allele [START_REF] Han | Induc ib le gene knockout of transcr i p t i on factor recombinat ion s igna l bind ing prote in -J reveals i t s essent ia l ro le in T versus B l i neage decis i on[END_REF], were crossed to ZP3-Cre females [START_REF] De Vries | Express ion of Cre recombinase in mouse oocytes : a means to study maternal ef fec t genes[END_REF] in order to produce mice carrying a deleted RBP-JB ∆ allele, which were then crossed with TP1-nlacZ transgenic mice. Embryos were collected from intercrosses between RBP-J R/ + , TP1-nlacZ transgenic mice and monitored individually for ßgalactosidase activity. Genotype of each embryo was determined by PCR analysis of placental DNA using lacZ and RBP-JR primers (WT1: 5'-GTT CTT AAC CTG TTG GTC GGA ACC-3' ; WT2: 5'-GTC TGA GGC TTG ATG TTC TGT ATT GC-3'; G1: 5'-GTG GCA AAG CCC TTA AAA AT-3' ; -2: 5'-GAG ATA GAC CTT GGT TTG TT-3').

Embryo in situ hybridization and histology.

Whole mount RNA in situ hybridization was carried out according to (Wilkinson and Nieto, 1993). Embryos were fixed in 4% paraformaldehyde in PBS overnight at 4°C, dehydrated in methanol and stored at -20°C. RNA probes were labeled with digoxigenin and visualized with BM Purple according to the manufacturer's instruction (Roche Biosciences). The lacZ hybridization probe used included the full ORF. For histology, X-gal reacted samples were either embedded in 4% agarose and cut at 50 tm thickness using a Leica VT1000 S Vibratome or embedded in paraffin and cut at 12 am thickness using a Leica RM 2155 microtome. Some sections were counterstained with eosin.

Figures Legends

Figu re deficient embryos recovered 10 days after mating do not express the TP1-nl acZ t r ansgene. Magni f i ed vi ews of r egi ons i ndi cat ed by boxes i n ( f ) show t he absence of l acZ expr essi ng cel l s i n car di ac ( g) and t ai l ( h) r egi ons. Det ai l of t he st ai ni ng of t he t ai l of E9. 5 i ) and E11. 5 ( j , boxed r egi on i n ( d) ) NAS em br yos. Ar r ows poi nt t o t he band of ß-gal posi t i ve cel l s i n t he PSM. ( k) Vi br at om e t hi ck sect i on of X-gal st ai ned E11. 5 t ai l showi ng a r ow of NAS expr essi ng cel l s i n t he PSM ( ar r ows) at t he t i m e when cl ef t st ar t s t o f or m ( ar r owhead) .

( l ) W hol e m ount i n si t u hybr i di zat i on of E10. 5 t ai l showi ng t hat l acZ m RNA i s det ect ed essent i al l y i n t he boundar y f or m i ng r egi on of t he PSM ( ar r owhead) . ( m ) Sect i on i n t he t r unk r egi on ( ar r ow i n ( b) ) of E10 em br yo showi ng TP1-nl acZ expr essi on i n t he wal l s of dor sal aor t a ( da) and vi t el l i ne ar t er y ( va) . ur : ur ogeni t al r i dge. ( n) Upper vi ew of t he hear t r egi on of E10. 5

NAS em br yo f r om whi ch t he head has been cut of f . TP1-nl acZ expr essi on i s f ound i n t he di st al por t i on of t he out f l ow t r act ( of t ) and i n t he br anchi al ar ch ar t er i es ( ba) . nt : neur al t ube. ( o-p) Enl ar ged vi ews cor r espondi ng t o boxed r egi ons i n ( e) showi ng TP1-nl acZ expr essi on i n dor sal aor t a ( da) and caudal ar t er y ( ca) ( p) and i n head ar t er i es ( o) of E12. 5 em br yo. Ar r ow i n ( o) poi nt s t o X-gal st ai ni ng i n t he r egi on of cor t i cal hem . ( q) Det ai l of t he X-gal st ai ni ng of E17. 5 NAS em br yo. TP1-nl acZ expr essi on i s bar el y det ect abl e i n t he dor sal aor t a ( ao) whi l e i t i s cl ear l y vi si bl e i n t he i nt er cost al ar t er i es ( i ca) br anchi ng di r ect l y f r om i t . ( r )

Ventra l view of dissected bra in f rom a 4 weeks old NAS mouse showing the sta in ing in cerebra l arter i e s and in entorh ina l cortex (ar row) . Inset shows a magnif i ed view of the branching of the r ight sy lv ian artery to the Wil l i s polygon. (s -t)

Detai l s of pia l arter i e s (s ) cerebra l cortex microvesse l ( t ) X-gal sta in ing f rom 4 weeks old NAS mouse.

  Notch is a large single spanning transmembrane protein composed of an extracellular domain containing epithelialgrowth-factor-like repeats and an intracellular domain (NICD) containing ankyrin motifs, a transactivation domain and nuclear localisation signals. Interaction of the extracellular domain of Notch receptors with membrane-bound ligands encoded by Delta and Serrate/Jagged family genes triggers the proteolytic cleavage of the Notch receptor and the release of NICD from the membrane. NICD then translocates into the nucleus where it interacts with the DNA-binding protein RBP-

r

  ai sed agai nst a novel NI CD epi t ope gener at ed by a-secr et ase cl eavage of Not ch1 ( Hupper t et al . , 2005; Mor i m ot o et al . ,

  Figu re 1: Rationa le of a N otch pathw ay activ ity sensor

Figure 2 :

 2 Figure 2: TP1-nlacZ expression pattern during somitogenesis

Figure 3 :

 3 Figure 3: TP1-nl acZ expr essi on pat t er n i n devel opi ng l i m bs,

  Not ch pat hway i s i nvol ved i n m ul t i pl e aspect s of car di o-

	Human Notch genes are l i nked to Alagi l l e ' s	Syndrome, a
	developmental disorder with vascular defects , to CADASIL , a
	cerebra l arter i opathy as wel l as to congenita l aort i c valve
	disease (Garg et al . , 2005; J out el and Tour ni er -Lasser ve,
	1998) . ß-gal expr essi on was obser ved i n t he em br yoni c and
	post nat al	vascul at ur e.	I nt er est i ngl y,	TP1-nl acZ t r ansgene
	showed ar t er i al speci f i c expr essi on, as do m any com ponent s of
	t he Not ch pat hway ( r evi ewed i n ( I so et al . , 2003a; Shawber and
	vascul ar devel opm ent i ncl udi ng vascul ar r em odel l i ng, ar t er i al /
	venous speci f i cat i on, m at ur at i on of vascul ar sm oot h m uscl e
	cel l s

and epi t hel i al -m esenchym al t r ansi t i on dur i ng hear t devel opm ent ( f or r evi ew see

( Shawber and Ki t aj ewski , 2004)

) . Ki t aj ewski , 2004) ) . I n t he case of pl acent al and yol k-sac ar t er i es however , we not ed t hat , cont r ar y t o com ponent s of t he

  ) . ß-gal expr essi ng cel l s t hen accum ul at ed at t he t i p of t he l i m b bud and t r ansgene expr essi on becam e pr ogr essi vel y ious evidence that J agged2 i s i ni t i al l y expr essed t hr oughout t he l i m b ect oder m and t hen r est r i ct ed t o t he AER soon af t er i t s f or m at i on and t hat Not ch1 i s weakl y expr essed i n t he AER at E10. 5[START_REF] Lan | Defects in l imb, cranio fac ia l , and thymic development in Jagged2 mutant mice[END_REF] Si dow et al . , 1997; Val secchi et al . , 1997) . I n addi t i on, bot h spont aneous and t ar get ed J agged2 m ut ant s di spl ay abnor m al t hi ckeni ng of t he AER[START_REF] Lan | Defects in l imb, cranio fac ia l , and thymic development in Jagged2 mutant mice[END_REF] Si dow et al . , 1997) suggest i ng t hat Not ch si gnal l i ng i n t he l i m b ect oder m m i ght be r egul at i ng t he num ber of AER pr ogeni t or cel l s. Dem onst r at i on t hat Not ch si gnal l i ng act s i n t he ect oder m at an ear l y st age of l i m b

r est r i ct ed t o t he api cal ect oder m al r i dge ( AER) ( f i g. 3b-c; see al so f i g. 2j ) . Thi s expr essi on pat t er n i s i n agr eem ent with prev

Concl udi ng r em ar ks

  ) . TP1-nl acZ t r ansgene i s com posed of t wel ve head-

	transgenic mouse l i ne is a bona f i de sensor of Not ch act i vi t y
	i n sever al t i ssues. Thi s concl usi on i s f ur t her subst ant i at ed
	by t he r ecent dem onst r at i on t hat TP1-nl acZ expr essi on i n
	ar t er i es i s abol i shed i n Not ch3 def i ci ent m i ce, whi l e i t i s
	m ai nt ai ned i n ot her si t es ( Monet et al . ,	m anuscr i pt i n
	pr epar at i on) . The obser vat i on t hat onl y par t of t he TP1-nl acZ
	expr essi on pr of i l e i s m edi at ed by Not ch3 r ecept or , hi ghl i ght s
	t he abi l i t y of NAS r epor t er t r ansgene t o r espond t o si gnal l i ng
	The	use	of	r epor t er	const r uct s	com pr i si ng	m ul t i pl e
	t r anscr i pt i on f act or	bi ndi ng si t es j oi ned t o a m i ni m al
	t ypes.	Havi ng dem onst r at ed t hat	t r ansgene expr essi on i s
	dependent	on	t he	pr esence	of		f unct i onal	RBP-J n i we
	i nvest i gat ed l acZ expr essi on and f ound a st r i ki ng coi nci dence
	bet ween NAS r epor t er t r ansgene act i vat i on and a num ber of
	Al t oget her ,	t hese	dat a	st r ongl y	suggest	t hat	t he	NAS

t o-t ai l hi gh af f i ni t y RBP-J d bi ndi ng si t es j oi ned t o a m i ni m al pr om ot er and, t her ef or e, i s ver y di f f er ent f r om pr om ot er s of di r ect Not ch t ar get genes. I t i s t hus possi bl e t hat , i n cer t ai n cel l ul ar cont ext s, l ow l evel of act i vat ed Not ch r ecept or woul d not be suf f i ci ent t o ensur e ef f i ci ent t r ansgene act i vat i on, whi l e i n syner gy wi t h ot her t r anscr i pt i on f act or s, i t woul d act i vat e endogenous Not ch t ar get genes.

I n concl usi on, t he NAS m i ce per m i t t he r eadout of t he act i vi t y of RBP-J u/ Not ch si gnal l i ng pat hway i n vi vo i n var i ous cel l known si t es of act i vi t y of com ponent s of t he Not ch pat hway. t hr ough t he di f f er ent Not ch r ecept or Mor eover , t he anal ysi s of TP1-nl acZ expr essi on i n Not ch3 -/ -i ce has per m i t t ed us t o cl ear l y est abl i sh t hat t he f unct i on of Not ch3 i n ar t er i al SMCs i s m edi at ed t hr ough a RBP-J f -dependent pat hway, al t hough i t s act i on i s i ndependent of Hes/ Hr t genes ( Monet et al . , m anuscr i pt i n pr epar at i on) . pr om ot er has pr oven t o be ver y usef ul t o st udy ot her pat hways such as f or exam pl e t he W nt / ß-cat eni n/ LEF pat hway ( DasGupt a and Fuchs, 1999; Mar et t o et al . , 2003) or si gnal l i ng t hr ough NF-kB ( Schm i dt -Ul l r i ch et al .

Acknowledgments

We thank T. Honjo and K. Tanigaki (Kyoto, Japan) for the RBP-JB flox mice and the pGa981-6 plasmid, B. Knowles (Bar Harbor, USA) for the ZP3/Cre transgenic line and S. Tajbakhsh for the pSKTNLSLACZ plasmid. We also thank C. Brou for helpful discussions, J. Artus, J.L. de la Pompa, S. Tajbakhsh and M. Wassef for critical reading of the manuscript. This work was supported by the Centre National de la Recherche Scientifique, the Association pour la Recherche contre le Cancer (ARC), the Institut Pasteur GPH07 on stem cells and the Agence National de la Recherche (contract n° JC05_41835). C. S. and M. M. received grants from CNRS ("Bourse de Doctorat pour les Ingénieurs") and the "Ministère de l'Education Nationale, de la Recherche et de la Technologie" respectively, and S.C. received grants from the Pasteur-Negri-Weizmann Council and the ARC.