Patrick Bosc

Didier Dubois

Olivier Pivert

Henri Prade

Martine De Calmès

Fuzzy Summarization of Data Using Fuzzy Cardinalities

Keywords: Fuzzy query, fuzzy cardinality, fuzzy prediction, fuzzy association rule

The paper investigates the following knowledge extraction method from a database. A set of a small number of attributes of interest are chosen. The idea is to figure out to what extent one of the attributes (the "output attribute" B) is influenced by the others (called "input attributes" A i ). Each of the input attribute domain are supposed to be equipped with a fuzzy partition made of a relatively small number (2 to 5) of fuzzy sets A i j or B k respectively. These fuzzy partitions are supposed t o be meaningful for the user and/or to be in agreement with the way the attribute values are scattered. For a given tuple (A 1 j ,..., A n j , B k ), we compute the fuzzy cardinality of the set of items of the database which are A 1 j and ... and A n j and B k , and of the set of items which are A 1 j and ... and A n j . From which we can easily obtain the fuzzy-valued confidence and support of the association rule "if x is A 1 j and ... and A n j , then x is B k ". In order to obtain more interesting association rules, the B k are not chosen beforehand, but on the basis of a possibilistic case-based reasoning machinery which provides the fuzzy set of possible output values for a class of situations described in terms of labels A i j of the fuzzy partitions of the input attributes. Thus a set of fuzzy association rules summarizing a database can be obtained.

Introduction

Querying a database in order to retrieve items satisfying some requirements, and extracting knowledge from a database are two types of operations which are often complementary for the users. Indeed in a querying session, a user may be interested in knowing what are the possible values of an attribute (e.g. the price) for some class of items specified in terms of other attributes (e.g. the size, the location of houses to be rent), or in knowing if there are many items available in the database which satisfy the requirements he has in mind). The two types of operations can be related at the processing level also. This will be illustrated in the following, where we are more particularly interested in summarizing a part of a database in terms of fuzzy association rules, which will be built by using flexible querying and fuzzy prediction techniques.

During the last years, the number and volume of databases have tremendously increased and the need for extracting some "condensed" information has received attention. The related research area, called knowledge discovery in databases (KDD) or data mining, aims at the discovery of useful information from large collections of data. The discovered knowledge can be rules describing properties of data, frequently occurring patterns, clusterings of the objects in the database, etc. Among the recent works, a great deal of attention has been paid to the discovery of a specific type of rules called association rules [START_REF] Agrawal | Mining association rules between sets of items in large databases[END_REF]. Association rules are of the type "when the properties A and B are satisfied in the data, then property C is also satisfied". Let us give a simple formalization of the problem.

Given a schema R = {A 1 , ..., A n } of attributes with respective domains D 1 , ..., D n , a relation r can be represented by a Boolean matrix in which a row corresponds to a tuple and a column to an attribute value. An association rule about r is an expression of the form: X ⇒ B, where X ⊆ R and B ∈ R \ X. The intuitive meaning of the rule is that if a row of the matrix r has a 1 in each column of X, then the row tends to have a 1 also in column B. This semantics is captured by the measures of frequency (or support) and confidence. Given W ⊆ R, we denote by sup(W, r) the frequency of W in r: the fraction of rows that have a 1 in each column of W. The frequency of the rule X ⇒ B in r is defined to be sup(X ∪ {B}, r) and the confidence of the rule is sup(X ∪ {B}, r)/sup(X, r).

In the discovery of association rules, the task is to find all rules X ⇒ B such that the frequency of the rule is at least equal to a given threshold σ and the confidence of the rule reaches at least another threshold θ. In other words, one wants to obtain rules that are sufficiently frequent and valid.

As stated by R. Yager [START_REF] Yager | Database discovery using fuzzy sets[END_REF], the use of fuzzy logic seems particularly interesting in the context of knowledge discovery inasmuch as it allows to express properties about the current content of a database as statements of the natural language, thus providing knowledge that can be easily understood by nonexperts. In this paper, we propose an extension of the notion of an association rule, based on the aggregation of sufficiently close data into fuzzy sets and on the use of fuzzy cardinalities.

The paper is organized into five sections. Section 2 presents the notion of a fuzzy association rule based on fuzzy cardinalities. Section 3 describes an aggregation procedure which is performed on a non fuzzy relational database. It aims at replacing the initial database by a fuzzy relational database which summarizes it. This summarization is made in terms of labels of fuzzy partitions of the attribute domains which are supposed to be given and to be meaningful for the user. This aggregation procedure is augmented with the computation of the fuzzy cardinalities of the sets of items to which a given fuzzy label in a cell of the new relation is applicable. Section 4 describes how it should be possible to generate linguistic summaries of interest (in the form of fuzzy association rules) from the summarized fuzzy relational database built in the previous section and the associated fuzzy cardinalities. Section 5 shows how a possibilistic case-based prediction method can help to choose and use a meaningful partition for the output attribute domain. Section 6 reports some experiment results.

Fuzzy association rules based on fuzzy cardinalities

The starting point is to aggregate sufficiently close data into fuzzy sets, on the basis of fuzzy partitions which are meaningful for a user.

Another key idea is to view fuzzy sets as a way for describing the different possible labellings that can be made by a user for borderline data.

Notations

Let R be a (non fuzzy) relation involving attributes A, B, C, ... In fact, we assume that the user is interested in possible summaries (association rules) involving a given subset of attributes. We only consider the projection of R on this subset, and for notational simplicity, we use a 3 element subset of attribute, say A, B and C, in the following, which is sufficiently general for discussing the main issues.

Let (a i , b j , c k ) denote a tuple of R(A, B , C) projected on attributes A, B and C. Let DA, DB, DC be the attribute domains. We assume that each domain is equipped with a fuzzy partition (A 1 , A 2 , ..., A na ), (B 1 , B 2 , ..., B n b ), (C 1 , C 2 , ..., C nc ) respectively. Each fuzzy set in a partition is assumed to be normalized. Each partition is ordered, and a fuzzy set, say A i , can only overlap with its predecessor A i-1 or its successor A i+1 (when they exist).

We further assume that a finite scale (with m + 1 levels) is used for assessing the membership degrees, namely 1 = σ 1 > ... > σ m > 0. Each level corresponds to a different possible understanding of A r as the crisp level cut (A r ) σ i . The use of a finite scale then greatly facilitates the computation of fuzzy cardinalities, as it is shown in the following, without being a serious limitation in practice.

Principle

The approach corresponds to a straightforward extension of the usual definition of an association rule. Its principle is the following: the validity of the rule (A, A r ) ⇒ (B, B s ) depends on the number of tuples which are A r on the one hand and on the number of tuples which are A r and B s on the other hand.

For instance, using scalar cardinalities, the validity of the rule (A, A r ) ⇒ (B, B s ) can be defined as:

|A r ∩ B s | / |A r | = Σ t ∈ R min(µ Ar (t), µ Bs (t))/Σ t ∈ R µ Ar (t)
which is nothing but a straightforward extension of the usual definition of the confidence.

Remark. It is worth noticing that the principle consisting in: i) rewriting the data by means of a more general vocabulary, and ii) trying to discover properties in the rewritten database, has also been advocated in a "nonfuzzy context". For instance, in [START_REF] Han | Discovery of multiple-level association rules from large databases[END_REF], the authors use a hierarchy of (Boolean) concepts in order to "rewrite" a relation so as to discover different types of rules. See also [START_REF] Srikant | Mining generalized association rules[END_REF] where the notion of a generalized association rule is introduced. Nevertheless, the fact of using linguistic labels (i.e., fuzzy sets) to rewrite the data allows to discover more robust rules. The key point, with a fuzzy partition, is that the borderline data are taken into account in each of the two classes, which decreases the sensitivity to the boundaries.

The general principle described above has been advocated by Yager [START_REF] Yager | Database discovery using fuzzy sets[END_REF], and more recently by Kacprzyk [START_REF] Kacprzyk | Fuzzy logic for linguistic summarization of databases[END_REF]. These authors use scalar relative cardinalities to compute the degree of validity of a summary (i.e., of a fuzzy association rule). Scalar fuzzy cardinality, which amounts to the addition of membership degrees, considers a collection of several elements with small membership grades whose sum is 1, as equivalent to one element with full membership for instance; this might be debatable or even misleading from a user point of view. In this paper, we present an alternative fuzzy approach based on the use of fuzzy cardinalities. This approach constitutes an extension of those described in [START_REF] Dubois | Fuzzy sets in data summaries -Outline of a new approach[END_REF][START_REF] Bosc | Résumés de données et ensembles flous -Principe d'une nouvelle approche[END_REF].

Summarizing a relation

From the relation R (restricted to A, B and C), we build a new relation R su (for "R summarized") by a procedure involving two main steps which are now described. The idea is to perform a kind of information compression.

The labelling step

For each tuple (a i b j c k ), we replace it by one or several tuples of fuzzy sets (A r , B s , C t ) subject to the constraint:

A r (a i ) > 0, B s (b j ) > 0, C t (c k ) > 0.

Thus (a i b j c k ) may be replaced by one tuple (A r B s C t ) if all the three degrees of membership are equal to 1, or by several (up to 2 3 = 8) in case one or several of the element(s) in the tuple belong to two fuzzy sets. For instance where we keep track of the membership degrees (A r stands for 1/A r ). This corresponds t o all the possible "readings" of the tuple (a i , b j , c k ) in terms of the vocabulary provided by the fuzzy partitions. In a data mining context, it is not necessary to store the summarized relation R su . The only additional data that have t o be stored are the fuzzy cardinalities, whose computation is described in the following subsection.

, if A r (a i ) = 1, B s (b j ) = 0.8, B s+1 (b j ) = 0.2, C t-1 (c k ) = 0.6, C t (c k ) = 0.

Fusion step and computation of fuzzy cardinalities

We

i or not. If ∃ i, x' = λ i > λ i+1 then F Ar is modi- fied into: 1/0 + ... + 1/n-1 + 1/n + λ 1 /(n+1) + ... + λ i /(n+i) + λ i /(n+i+1) + ... + λ k /(n+k+1) + 0/(n+k+2) + ... .
Otherwise, ∃ j, λ j > x' > λ j+1 (we assume that λ 0 = 1) and F Ar becomes:

1/0 + ... + 1/n-1 + 1/n + λ 1 /(n+1) + ... + λ j /(n+j) + x'/(n+j+1) + λ j+1 /(n+j+2) + ... + λ k /(n+k+1) + 0/(n+k+2) + ... .

Note that the fuzzy cardinalities computed this way are such that ∀i, j, λ i ≠ 0, λ j ≠ 0, i > j ⇒ λ i ≥ λ j . If, for the computation of F Ar (resp. F Bs et F Ct ), one takes into account the value x' (resp. y' the degree related to B s , and z' the degree related to C t ), the computation of F ArBs (resp. F ArCt , F BsCt and F ArBsCt ), takes into account the value min(x', y') (resp. min(x', z'), min(y', z'), min(x', y', z')), thus reflecting the fact that the tuple to fuse is both A r and B s (resp. A r and C t , B s and C t , A r and B s and C t ).

Let us notice that the maximum number of tuples that can be obtained in R su is na * nb * nc, i.e. the product of the numbers of labels appearing in the considered partitions. Thus, the "summarized" relation can be significantly smaller than the original relation R for large relations.

Computing the validity of a summary

Fuzzy cardinalities computed as explained in Section 3 can be used to evaluate the validity of fuzzy association rules. In this approach, we assume that the user indicates the attributes A , B or C that he/she is interested in. Two general forms of rules can be thought of. The first type of rule follows the pattern "the tuples of R are A r and B s ". This can be seen as a kind of degenerated rule with no attribute involved in the antecedent. The validity of such a rule corresponds to the extent to which the set of labels {A r , B s } is frequent. The second type of rule corresponds to the pattern "the tuples which are A r in R are also B s ". The computation of the validity of the rule (in terms of a fuzzy cardinality) is discussed in the following.

Computing fuzzy relative cardinalities

The two types of rules presented above relate to proportions. It will thus be necessary t o compute fuzzy relative cardinalities. Let us denote by F R Ar (resp. F R ArBs , F R ArBsCt ) the fuzzy proportion of the tuples of R which are "A r " (resp. "A r and B s ", "A r and B s and C t "). This fuzzy number is obtained by dividing each (more or less) possible cardinality appearing in F Ar (resp. F ArBs , F ArBsCt ) by the number of tuples in R.

For instance, the fuzzy relative cardinality F R ArBs representing the fuzzy proportion of elements in R which are both A r and B s is obtained by replacing F ArBs = 1/0 + ... + 1/n + ... + λ i /(n+i) +... by F R ArBs = 1/0 + ... + 1/(n/K)+ ... + λ i /((n+i)/K) +... where K denotes the number of tuples in R. This means that the proportion of elements which are A r and B s at level λ i is at least equal to (n+i)/K. Thus, the support of the fuzzy set F R ArBs is included in the unit interval.

Frequent sets of linguistic labels

Let us first consider the case where the user does not specify any fuzzy quantifier. From the tuples in R su , it is possible to produce summaries of the form (A r , B s , C t , F R ArBsCt ) or relative to projections of R such as (A r , B s , F R ArBs ). As in the nonfuzzy case, one produces the frequency, which is now a fuzzy number.

Of course, these summaries will be given t o the user in a linguistic form expressing the variability of the cardinality (the fuzzy cardinality is then described by some proportions obtained for different levels of possibility). Let us recall that these levels of possibility corresponds to the more or less "elastic" interpretations that can be associated with the linguistic labels involved in the summary.

Fuzzy association rules

Let us now consider a fuzzy association rule of the form: "the tuples in R which are A r are also B s ". We have available the fuzzy number of tuples in R which are A r and B s on the one hand, and the fuzzy number of tuples which are A r on the other hand. Several approaches can be thought of, for instance:

-by analogy with the nonfuzzy case and with the approach based on scalar cardinality of fuzzy sets, it is possible to compute the fuzzy quotient ρ = F ArBs / F Ar , enforcing the constraint that the fuzzy number F ArBs restricts a value which is less than or equal t o the value restricted by F Ar (see [START_REF] Dubois | Possibility Theory[END_REF]). However, this quotient of such two fuzzy numbers may lead to a too imprecise result.

-a more interesting approach consists in determining how the proportion of tuples which are (A r ) α and (B s ) α with respect t o those which are (A r ) α changes when α varies, i.e., depends or not a lot on the interpretation of the linguistic labels (according to whether they are reduced to their cores or extended to their supports). Then, the computation involves three steps:

1) for each α appearing in F Ar or F ArBs 1.1) determine |( A r ) α | and |( A r B s ) α | (which can be directly read on the fuzzy cardinalities computed as explained in section III.B);

1.2) compute c α = |(A r B s ) α | / |(A r ) α | corresponding to
the confidence value of the rule when the α-level cut is used to interpret the labels;

2) compute ρ' as the convex hull of the fuzzy number: ... + α/cα + ... + 1/c1.

Given a confidence threshold θ specified by the user, it is then possible to determine the highest degree α such that ρ' α ≥ θ. The association rule can then be expressed in a linguistic way, inasmuch as the α-cuts of A r and B s can be expressed in a linguistic way too. This approach in terms of α-level cuts of the cardinalities is in the spirit of [START_REF] Martin-Bautista | Measuring effectiveness in fuzzy information retrieval[END_REF] although these authors compute scalar cardinalities as weighted averages of cardinalities of α-cuts.

Case-based prediction

An order to determine meaningful clusters of values in the domain of the attribute involved in the conclusion part of the rules, a possibilistic case-based prediction method is used. Casebased reasoning, in general, assumes the following implicit principle: "similar situations may give similar outcomes". Thus, a similarity relation S between problem descriptions or situations, and a similarity measure T between outcomes are needed. This implicit CBRprinciple can be expressed in the framework of fuzzy rules as, "the more similar are the values of the situation attributes in the sense of S, the more possible the similarity of the values of the outcome attributes in the sense of T" [START_REF] Dubois | Flexible control of case-based prediction in the framework of possibility theory[END_REF]. Given a situation s 0 associated to an unknown outcome t 0 and a current case (s, t), this principle enables us to conclude on the possibility of t 0 being equal to a value similar to t. This acknowledges the fact that, often in practice, a database may contain cases which are rather similar with respect to the problem description attributes, but which may be distinct with respect to outcome attribute(s). This emphasizes that case-based reasoning can only lead to cautious conclusions.

This can be modelled in terms of the possibility rule [START_REF] Dubois | What are fuzzy rules and how to use them[END_REF] "the more similar s and s 0 , the more possible t and t 0 are similar". Then the fuzzy set F of possible values t' for t 0 with respect to case (s, t) is given by F t 0 (t') = min(S(s, s 0 ), T(t, t')).

However, here, we are interested in computing the set values which are close or equal to the value of attribute C for the tuples whose values of attributes A and B obey to some flexible requirements A r and B s . This means that S(s, s 0 ) is replaced by min(A r (a i ), B s (b j )) and T(t, t') by T(c k , c') where (a i , b j , c k ) is a tuple of the base. This contributes to make P smoother.

Experiment results

The experiment was carried out on the IRIT Platform for Experimentation and Research in the Treatment of Information (PRETI) accessible at http://www.irit.fr/PRETI. PRETI has a database containing the description of more than 600 houses which can be rent for vacations. They are described in terms of about 20 attributes. The results of the experiment are illustrated in two parts. Fuzzy ranges for July Week Fare (FF) taken from the distribution of Fig. 1 Cumulated number of houses with matching degree (600, 1000, 1200, 1500) First, we consider a query focusing on houses whose comfort is about 2 stars ('about' means that 2 stars has possibility 1, while 1 star and 3 stars have possibilty 1/2), and which are close to the sea ('close' means less than 5km with possibility 1, and a linearly decreasing possibility between 5km and 10km, possibility is 0 for distances greater or equal to 10km). Figure 1 exhibits the result of the possibilistic prediction for the July weekly fares (still in French Francs!) of the houses corresponding to this fuzzy query. The fuzzy similarity relation which is used for the fare has a peak corresponding to perfect identity and a support between -200 and +200 FF. Table 1 provides a complementary information by indicating the fuzzy cardinality of the fuzzy sets of houses close to the sea, with about a 2-star comfort, and having a price around one of the peaks of the distribution given in Figure 1. Note that if a peak is too large it may lead t o slice it into several ranges of prices. The fuzzy cardinality is presented by giving the cardinality followed after the '/' by the level of the corresponding level cut. When the cardinality remains unchanged for several level cuts, only the highest level cut appears. As expected the extreme prices correspond to very small numbers of houses. It can be also noticed that the cardinality number may have a substantial increase below .6, this mainly corresponds t o the impact of taking into consideration 1 star or 3 stars houses also with only a .5 possibility degree. Indeed, generally speaking, the interest of using fuzzy cardinality is to show the variations induced by the relaxation of flexible requirements.

Table 2 provides examples of fuzzy associations rules obtained by the method described in this paper. Here, for simplicity, we use a crisp 2-part partition for comfort, namely { { 1 star, 2 stars},{3 stars, 4 stars} }, and a 3-part fuzzy partition for the distance to the sea (close, not too far, far). 'Close', 'not too far', 'far' are represented by the following trapezoids (0, 0, 5, 10), (5, 10, 30, 35), (30, 35, 100, 100) respectively. We have only kept the rules corresponding to more than 10 hou-ses in the database. The fuzzy sets used for the July week fare are given under the form of trapezoids and are taken from fuzzy predictions like the one of Figure 1. These predictions are not given due to the lack of space. The cardinality of the data base which is used for computing the support is 444, which is the number of data for which we have a complete and precise information about the three considered attributes in the base. The number before the '/' is the support, or the confidence, and the corresponding level cutting is given after. Again it enables us to show if some rules are sensitive to changes of the scope of the fuzzy sets used in the partitioning of the attribute domains.

Conclusion

This paper has outlined a new approach to the linguistic summarization of data bases. The basic ideas are i) to use fuzzy partitions of attribute domains which are meaningful for the user (since fuzzy partitions are more compatible with a linguistic labelling), ii) to perform a "soft compression" of the data base and then to exploit it for evaluating potential summaries, iii) this evaluation is made by computing fuzzy cardinalities which account for the possible variations of the interpretation of the labels, and iv) to use a fuzzy prediction tool for selecting fuzzy sets of interest in the output domain. What is obtained are the (fuzzily known) proportions of elements satisfying fuzzy specifications.

  As it can be seen, what is obtained is the fuzzy set T(c k , . ) of values c' which are T-similar t o c k , whose possibility level is upper bounded by the global degree min(A(a i ), B(b j )). The maxbased aggregation of the various contributions, obtained from the evaluation of each tuple in the base, acknowledges the fact that each new comparison may suggest new possible values for C. Thus, we obtain the following fuzzy prediction set P of possible values c' : P(c') = max (ai, bj, ck) ∈ R min(min(A(a i ), B(b j )), T(c k , c')) P is the fuzzy set of possible values of attribute C for the items in the base for which the attributes values of A and B are restricted by A i and B j respectively. The similarity relation T on the domain of attribute C is used here for providing an understanding of the precise attribute values c k in the tuples of the base as interchangeable with any value close to them.

Figure 1 .

 1 Figure 1.

  Ar = 1/0 + ... + 1/n-1 + 1/n + λ 1 /(n+1) + ... + λ k /(n+k) + 0/(n+k+1) + ... be the current value of the fuzzy cardinality F Ar with 1 > λ 1 ≥ ... ≥ λ k > λ k+1 = 0 and n ≥ 0, k ≥ 0. Let us recall that this expression represents a cardinality that possibly equals at least n to degree 1 and possibly equals at least (n+k) to degree λ k[START_REF] Dubois | Fuzzy cardinality and the modeling of imprecise quantification[END_REF].

	Each cardinality is computed incrementally
	in the following way. At the beginning F Ar =
	1/0. Let:
	F Let us consider a new tuple whose A -value
	rewrites A r . Let x' be the degree attached t o
	A r in this tuple. F Ar must then be modified. If
	x' = 1, F Ar becomes:
	1/0 + ... + 1/n + 1/(n+1) + λ 1 /(n+2) + ... +
	λ k /(n+k+1) + 0/(n+k+2) + ... .
	All the tuples of the form (x/A r y/B s z/C t )
	which are identical with respect to the three
	labels are fused into one tuple (A r B s C t ) of R su .
	At the same time, we compute the cardinali-
	ties F Ar , F Bs , F Ct , F ArBs , F ArCt , F BsCt , F ArBsCt where
	F Ar (resp. F Bs , F Ct , F ArBs , F ArCt , F BsCt , F ArBsCt ) is a
	fuzzy set defined on the integers {0, 1, ...}
	which represents the fuzzy number of tuples
	which are somewhat A r (resp. B s , C t , A r and B s ,
	A r and C t , B s and C t , A r and B s and C t ) and
	which are fused into the considered tuple (for
	all the combinations of labels appearing in at
	least one tuple of R su ).

want to know how many tuples from R are A r , are B s , are C t , are A r and B s , ..., are A r and B s and C t , and this, for all the fuzzy labels. In order to have a more accurate representation of the relation, fuzzy cardinalities are used instead of scalar ones. It is then necessary to compute the different cardinalities related to each linguistic label and to the diverse conjunctive combinations of these labels. If x' < 1 , there are two cases. Either ∃ i, x' = λ

Table 1 .

 1

		1/1., 4/0.4
	(1400, 1600, 2000, 2300)	4/1., 13/0.4, 17/0.2, 18/0.

Table 2 .

 2

	Comfort Dist. to sea	July week fare	Support	Confidence
	{1,2}	close	(1400, 1500, 1900, 2000)	0.05/1., 0.06/0.8,	0.44/1., 0.46/0.6, 0.45/0.4, 0.5/0.2, 0.51/0.001
			(2200, 2300, 2900, 3100)	0.07/0.4	0.44/1., 0.40/0.8, 0.39/0.6, 0.38/0.4,
					0.34/0.2, 0.33/0.001
		not too far	(1000, 1200, 1900, 1900)	0.14/1., 0.16/0.8,	0.47/1., 0.49/0.8, 0.5/0.4, 0.51/0.2
			(1900, 1900, 2600, 2800)	0.17/0.6, 0.19/0.4,	0.36/1., 0.37/0.8, 0.38/0.6, 0.37/0.4
			(3000, 3100, 3300, 3500)	0.21/0.2	0.16/1., 0.14/0.8, 0.12/0.4, 0.11/0.2
		far	(1000, 1100, 2000, 2100)	0.39/1., 0.4/0.8,	0.66/1.
			(2000, 2100, 2900, 3000)	0.41/0.6, 0.42/0.4,	0.30/1.
				0.43/0.2
	{3,4}	close
		not too far	(1900, 2100, 2700, 2800)	0.07/1., 0.08/0.6,	0.32/1., 0.36/0.8, 0.35/0.6, 0.33/0.4, 0.34/0.2, 0.33/0.001
			(2700, 2800, 3500, 3600)	0.09/0.4,	0.20/1., 0.18/0.8, 0.24/0.6, 0.28/0.4, 0.27/0.2, 0.26/0.001
			(3500, 3600, 4100, 4200)	0.1/0.01	0.30/1., 0.27/0.8, 0.24/0.6, 0.25/0.4, 0.24/0.2
		far	1500, 1700, 2600, 2700	0.23/1., 0.24/0.4	0.39/1., 0.37/0.4, 0.38/0.2
			2600, 2700, 3400, 3500		0.40/1., 0.41/0.6, 0.42/0.4


Cédric Laguri

Alba Silipo

Alessandra M Martorana

Paul Schanda

Roberta Marchetti

Alessandra Polissi

Antonio Molinaro
email: molinaro@unina.it

Jean-Pierre Simorre
email: jean-pierre.simorre@ibs.fr

Cedric Laguri

Solid State NMR Studies of Intact Lipopolysaccharide Endotoxin

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Gram negative bacteria lipopolysaccharides (LPSs) are key microbial macromolecules involved in a plethora of functions in prokaryotes and in the elicitation of innate immune response in insects, animals and plants [START_REF] Brodsky | Targeting of immune signalling networks by bacterial pathogens[END_REF][START_REF] Silipo | Glycoconjugates as elicitors or suppressors of plant innate immunity[END_REF] . Gram negative microbes possess a double system of membranes (Figure 1) in which LPSs are only present on the outer leaflet of the external membrane but in great abundance. LPS is composed of a highly conserved hydrophobic lipid A moiety, a core oligosaccharide (core OS), and in many species a long-chain O-antigenic polysaccharide (Figure 1). Gram negative bacteria are more resistant to antibiotic treatment mainly due to their highly impermeable outer membrane where LPS is considered as the key actor in the membrane integrity [START_REF] Whitfield | Biosynthesis and Export of Bacterial Lipopolysaccharides[END_REF] . Indeed, the LPS layer is highly ordered and is stabilized by electrostatic interactions between divalent cations (as Ca 2+ and Mg 2+ ) and phosphate groups of the lipid A part. This low fluidity of the layer confers to the outer membrane a low permeability to hydrophobic compounds and to higher molecular weight hydrophilic compounds.

Only certain antibiotics directed against Gram-negative bacteria, such as polymyxin B or gentamicin, are able to destabilize the outer membrane leading to the disruption of the membrane integrity [START_REF] Delcour | Outer membrane permeability and antibiotic resistance[END_REF] .

LPS is also a bacterial hallmark, a microbe associated molecular pattern, which is specifically recognized by eukaryotic immunity cell line receptors as a microbial signature [START_REF] Brodsky | Targeting of immune signalling networks by bacterial pathogens[END_REF][START_REF] Silipo | Glycoconjugates as elicitors or suppressors of plant innate immunity[END_REF] . For these organisms, this preliminary step of the innate immunity process, serves to trigger the response in case of pathogenicity or to shut down the response itself in case of beneficial interactions, such as symbiosis. In animals/humans, LPS is extracellularly detected by its lipid A [START_REF] Molinaro | Chemistry of lipid a: At the heart of innate immunity[END_REF] at the level of immunity cell lines by a binary protein system (TLR4/MD2) which upon physical binding triggers the downstream reaction cascade 1 . Moreover, caspase-4/5 in humans and caspase-11 in mice detect intracellular LPS thus, likely being in direct binding and detection of intracellular pathogens 6 .

To understand these different biological processes at the molecular level, it is important to have methods to characterize macromolecular organization formed by LPSs in the membrane or in interaction with other proteins and/or ligands. However, because of their glycolipid nature they are generally neither soluble in water nor soluble in any organic solvents hampering the structural and functional characterization of LPSs in their intact state. The determination of the primary structure of a LPS is nowadays carried out separately on lipid A and O-antigen, chemically split in advance, by means of chemical analysis and biophysical methodologies (Gas Liquid Chromatography coupled to Mass spectrometry, GLC-MS; Mass Spectrometry, MS and solution-state Nuclear Magnetic Resonance, NMR) [START_REF] De Castro | Microbe-Associated Molecular Patterns in Innate Immunity: Extraction and Chemical Analysis of Gram-Negative Bacterial Lipopolysaccharides[END_REF][START_REF] Dilorenzo | Structure of the Lipopolysaccharide from the Bradyrhizobium sp. ORS285 rfaL Mutant Strain[END_REF] . Intact LPS molecules have been previously investigated, some of them also by NMR but no systematic approach has been adopted so far [START_REF] Renault | Cellular solid-state nuclear magnetic resonance spectroscopy[END_REF][START_REF] Ilg | HR-MAS NMR reveals a pH-dependent LPS alteration by de-O-acetylation at abequose in the O-antigen of Salmonella enterica serovar Typhimurium[END_REF][START_REF] Johnson | The antibacterial toxin colicin N binds to the inner core of lipopolysaccharide and close to its translocator protein[END_REF] . The most exhaustive NMR analysis of intact LPS molecules including 3D structure determination and dynamics were conducted with LPS solubilized in detergent micelles [START_REF] Wang | Structure and dynamics of 13C,15Nlabeled lipopolysaccharides in a membrane mimetic[END_REF][START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] . While these methods are efficient in attaining chemical structural studies of LPSs, there is a lack of alternative approaches able to study interaction of key molecules (receptors/antibiotics) with membrane surfaces formed by LPS. In fact, it is very important in this perspective to have a thorough view at molecular level at the whole intact molecule, at its overall supramolecular structure, at its delivery and at its atomic epitopes when bound and/or recognized by other ligands.

Atomic scale analysis of cell-surface glycoconjugates is particularly challenging. Magic Angle Spinning (MAS) solid state NMR (ssNMR) has provided in the last years interesting information on complex macromolecules alone or in complex with ligands (ions/proteins) [START_REF] Kern | Toward the characterization of peptidoglycan structure and protein-peptidoglycan interactions by solid-state NMR spectroscopy[END_REF][START_REF] Kern | Dynamics characterization of fully hydrated bacterial cell walls by solid-state NMR: Evidence for cooperative binding of metal ions[END_REF][START_REF] Schanda | Atomic model of a cell-wall cross-linking enzyme in complex with an intact bacterial peptidoglycan[END_REF][START_REF] Cegelski | Rotational-echo double resonance characterization of the effects of vancomycin on cell wall synthesis in Staphylococcus aureus[END_REF][START_REF] Warnet | In-Cell Solid-State NMR: An Emerging Technique for the Study of Biological Membranes[END_REF] .

Therefore, we have deemed that ssNMR could provide the missing information on the different supramolecular organizations adopted by these molecules and we have undertaken the study of intact LPS in an environment close to the bacterial membrane. To this aim, in the following work we studied LPS extracted from different bacterial strains and with the two different molecular arrangements, a rough type LPS (a lipooligosaccharide, R-LPS) from E. coli K-12 and a smooth-type LPS (S-LPS) from P. aeruginosa PAO1 strains (Figure 1). The analysis of LPSs by ssNMR indeed enabled to observe the main characteristics of both LPS molecules, i.e., comparable to the data obtained when LPS is chemically split and then analyzed by NMR. Moreover, in a proof of principle we also studied PAO1 LPS when bound to gentamicin; this latter approach revealed interesting molecular information confirming the involvement of the O-antigen in the intake of the antibiotic by bacteria.

On this ground, we estimate that ssNMR approach is a very useful and very informative technique to observe the behavior of different LPSs in their intact chemical form and when bound to prokaryotic or eukaryotic ligands.

RESULTS AND DISCUSSION

Characterization of lipid A and core oligosaccharide from rough-type E. coli K12 LPS. E. coli K12 cells were grown in media containing [START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] C as the sole carbon source and LPS molecules extracted and purified (see Methods). Freeze dried LPS molecules were re-suspended in water and, prior to conducting the NMR analysis, the macromolecular state of LPS was investigated by electron microscopy. Spontaneously E. coli R-LPS assembled into vesicles of 100-200 nm diameter with lipid bilayers of 26+/-4 nm that were protected from staining (Figure 2). 1). While the former experiment was able to dissect the rigid moiety of the molecule, the latter was more sensitive to flexible parts of LPS (Supplementary Figure 1). Proton LPS resonances are too broad to be observed at low spinning speed but could be detected at 34kHz MAS rotation in a [START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] C-1 H INEPT experiment. Resonances from most residues of E. coli LPS could be assigned and were in good agreement with those reported by liquid-state NMR (Supplementary Table 1). Signals for the two GlcN (glucosamine) of lipid A, straight assignments of the acyl parts of the molecules and parts of the core region including Kdo (keto-deoxyoctulosonate) and Hep (heptose) could be achieved (Figure 1). Lipid contaminants, probably tightly associated with LPS, were also identified, as cyclopropane modifications, normally present only on phospholipids. Insaturations, potentially occurring either on LPS fatty acids or on phospholipids acyl chains were assigned, as well as the two major phospholipids composing E. coli outer membrane inner leaflet, namely phosphatidyl ethanolamine and phosphatidyl glycerol. Peptidoglycan, another major component of the cell envelope, could also be detected, including GlcNAc and MurNAc (N-acetyl muramic acid) backbone sugars of the macromolecule, as well as characteristic Lactoyl signals (highlighted in yellow in figure 3). It is not unusual that peptidoglycan is associated with LPS preparation, presumably because of co-purification with Braun's lipoprotein that anchors PG in the outer membrane [START_REF] Vollmer | Peptidoglycan structure and architecture[END_REF] .

Characterization of core oligosaccharide and O-antigen from P. aeruginosa PAO1.

Since rough type K-12 R-LPS from common laboratory strains could be successfully analyzed by ssNMR, we investigated a wild-type S-LPS extracted from the pathogenic P. aeruginosa PAO1 strain. This microbe is responsible for severe infections in immunocompromised patients and in particular in cystic fibrosis, and possesses variable LPS O-antigens [START_REF] Knirel | Conserved and variable structural features in the lipopolysaccharide of <I>Pseudomonas aeruginosa</I&gt[END_REF] . Indeed, Pseudomonas LPS are composed of the same lipid A-core oligosaccharide skeleton but to which two different O-antigens are appended termed A and B bands [START_REF] Knirel | Conserved and variable structural features in the lipopolysaccharide of <I>Pseudomonas aeruginosa</I&gt[END_REF] (Supplementary Figure 1 and Figure 4

panel a). A-band O-

antigen is based on a D-rhamnose repeating unit while B-band is based on a complex trisaccharide unit with two N-acylated Mannuronic acids (ManNAc3NAcA or 3 AmA) and a FucNAc (Figure 4 panel a and Figure 5). These two O-antigen polysaccharides are simultaneously present at the surface of the bacteria. suggesting they belonged to rigid regions of the LPS. Similarly, one rhamnose spin system with chemical shifts matching those of the outer core 3-substituted -Rha could be identified as well as alanine residues, probably bound to galactose residues (Figure 4) [START_REF] Lorenzo | Persistent cystic fibrosis isolate Pseudomonas aeruginosa strain RP73 exhibits an under-acylated LPS structure responsible of its low inflammatory activity[END_REF] .

The ssNMR analysis of P. aeruginosa LPS showed also the signals of the major B-band O-antigen trisaccharide -FucNAc--ManNAc3NAmA--ManNAc3NAcA repeating unit for which most resonances were unambiguously assigned (Figure 4 and Supplementary Figure 2). The Oantigen was also observed in dipolar-coupling based experiments thus suggesting a significant degree of order in the O-antigen chains, possibly through lateral contacts between O-antigen chains. These last data are in agreement with what observed with gel forming glycan polymers such as maltodextrins that exhibit the same behavior with a degree of order that allows to efficiently transfer the NMR magnetization through dipolar couplings using Cross Polarization (CP) experiments [START_REF] Van Duynhoven | Solid-like components in carbohydrate gels probed by NMR spectroscopy[END_REF] . D-rhamnose A-band repeating unit could not be detected unambiguously at a first glance since rhamnose also composes the outer core oligosaccharide common to both O-antigens. However, one sugar spin system with a lowfield displaced C-2 chemical shift could be unambiguously assigned to a 2-substituted rhamnose residue and cross peaks were assignable up to the methyl group (Figure 4 and Table S2). Several resonances, probably corresponding to 3-substituted rhamnose could be identified in the spectra but only up to the C-2 / H-2 groups, because of severe signals overlapping.

Presence of A-Band polysaccharide could be confirmed by the presence of O-methylation ( 13 C/ 1 H resonances at 57.4ppm/3.75ppm) characteristic of O-methyl rhamnose residue found in A-Band Oantigen [START_REF] Arsenault | Structural studies on the polysaccharide portion of "A-band" lipopolysaccharide from a mutant (AK1401) of Pseudomonas aeruginosa strain PAO1[END_REF] . Nevertheless, this latter residue could not be assigned completely due to the lack of longrange distance correlations.

Interaction of P. aeruginosa LPS with gentamicin antibiotic.

LPS from PAO1 is a critical factor of virulence, which is particularly harmful in immunocompromised patients as those affected by cystic fibrosis. While A and B band O-antigens are found in patients at early onsets of the infection, only A band polysaccharide can be detected in chronic isolates of P. aeruginosa [START_REF] Rocchetta | Genetics of O-antigen biosynthesis in Pseudomonas aeruginosa[END_REF] . Furthermore engineered P. aeruginosa A + B -bacteria were found to be less sensitive to gentamicin antibiotic, because of a higher affinity of gentamicin for bacteria presenting B-band O-antigen. Nevertheless, the molecular basis of mechanism remains unknown [START_REF] Kadurugamuwa | Interaction of gentamicin with the A band and B band lipopolysaccharides of Pseudomonas aeruginosa and its possible lethal effect[END_REF][START_REF] Makin | Pseudomonas aeruginosa PAO1 ceases to express serotype-specific lipopolysaccharide at 45??[END_REF] .

Based on such previous studies, we decided to investigate the effect of gentamicin on isolated and intact PAO1 LPS. Gentamicin is a natural antibiotic from the aminoglycosides family produced by M. echinospora, a Gram-positive bacterium (Figure 5). In vitro gentamicin very efficiently binds to isolated PAO1 LPS and this can be easily observed by solution NMR. Addition of LPS to gentamicin in solution leads to total disappearance of its NMR signals (Supplementary Figure 4), showing that all free gentamicin in solution have bound to LPS. We then used electron microscopy to assess the influence of gentamicin binding on LPS supramolecular organization. Addition of 25mM final concentration of gentamicin PAO1 LPS did not significantly change the elongated micelles structures of isolated PAO1 LPS in solution (Figure 5 panel a).

Figure 5 P. aeruginosa LPS O-antigen is affected by interaction with gentamicin. a) EM pictures with negative staining of P. aeruginosa LPS in absence (up) or presence of 25mM Gentamicin (down). b) [START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] C-1 H INEPT ssNMR spectrum of LPS in absence or presence (green) of 25mM gentamicin. Spectra are normalized to the intensity of lipid CH3 peak. 1D slices of Lipid A CH3 and fucose CH3 peaks are shown above the spectrum. c) Ratio of peak intensities Igentamicin/I0 measured in the [START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] C-1 H INEPT experiment. d) Chemical structures of B-Band, A-Band trisaccharide repeats and of gentamicin.

In absence of supramolecular reorganization, ssNMR approach was used to investigate the gentamicin interaction with LPS at an atomic resolution. 25mM gentamicin was added to a 40mg/ml PAO1 LPS solution which was ultracentrifuged into the NMR rotor (see Methods). [START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] C-13 C Jcorrelation experiments as well as [START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] This specific decrease in intensity observed for the O-antigen, and more specifically for the saccharide present in the O-antigen B-Band can be interpreted as an interaction of gentamicin with some specific region of the LPS. To analyze in more detail the effect of gentamicin on the local flexibility of the LPS, we have also measured different relaxation parameters. However, only [START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] C T1 longitudinal relaxation constant time can be measured with a sufficient sensitivity and in a reasonable experimental time (Supplementary Figure 4). Unfortunately, these longitudinal relaxation rates do not show significant variations and cannot be used to refine the effect of the gentamicin on the Oantigen flexibility.

Though we have information on individual B-band trisaccharide resonances we could not isolate a unique residue or chemical group that was specifically affected by gentamicin interaction and we can conclude that the whole repeating unit is a determinant of the interaction. In agreement, we can speculate that the B-band possesses two negative charges (the two Mannuronic acids) per repeating unit which should bridge with the free amino groups of gentamicin, i.e., ammonium groups at physiological pH (Figure 5 panel d). Furthermore, additional contacts could be assumed by the several ester and amide carbonyl groups of the O-antigen with the same positively charged groups of gentamicin. Thus, the specific binding effect that we observed between gentamycin and the B-Band O-antigen explains why the PAO1 LPS B band positive strains are sensitive to gentamicin whereas A-band strains are not. Due to avidity phenomena, it can be certainly deemed that this binding process increases local concentration of gentamicin at outer membrane and increases gentamicin lethality on B band possessing strains.

CONCLUSION

The direct observation of LPS endotoxins in their natural environment constitutes an important step in the field of molecular microbiology and, in particular, toward the understanding of interactions of microbes with their eukaryotic hosts, either beneficial or harmful. Many studies have been published so far in which the double role and the action of the endotoxins has been elucidated, i.e., either as barriers to antibiotics or as elicitors/suppressors of innate immunity in eukaryotes [START_REF] Brodsky | Targeting of immune signalling networks by bacterial pathogens[END_REF][START_REF] Silipo | Glycoconjugates as elicitors or suppressors of plant innate immunity[END_REF][START_REF] Stokes | Pentamidine sensitizes Gramnegative pathogens to antibiotics and overcomes acquired colistin resistance[END_REF][START_REF] May | The Antibiotic Novobiocin Binds and Activates the ATPase That Powers Lipopolysaccharide Transport[END_REF] .

Beside this, however, very rarely it has been possible to understand the supramolecular behavior and their action as whole molecule, their delivery to the receptors or their action against antibiotics.

Nowadays, their study is still confined to a complex operation of bench organic and analytical bioorganic chemistry [START_REF] De Castro | Microbe-Associated Molecular Patterns in Innate Immunity: Extraction and Chemical Analysis of Gram-Negative Bacterial Lipopolysaccharides[END_REF] with no chances to comprehend how the primary structure affects the overall 3D structure. It is in fact pivotal to study LPS interactions with eukaryotic and prokaryotic lectins, immunity proteins (TLR4/MD2, caspases) and symbiosis proteins and get a perspective at molecular scale of the whole intact molecule when bound and/or recognized by other ligands.

In this work we have employed ssNMR for studying two different and archetypal LPS, with either long or short carbohydrate chain, in a membrane like structure without any alteration of the molecules, in the absence of detergents and in suitable conditions to study LPS interactions.

Furthermore, this study further confirmed the capacity of this approach to gain access to parts of the macromolecule that present different flexibilities (Figure 6). MAS ssNMR allowed to either record experiments on the most flexible segments of a molecule through experiments similar as those recorded in liquid-state, or on the most rigid parts by Cross-Polarization experiments. of the two types of experiments in Figure 6 point out an efficient CP transfer on R-LPS that shows mostly the relatively rigid lipid and core oligosaccharides while CP transfer is less efficient in S-LPS where the spectrum is dominated by flexible O-antigen. The versatility of the method will be particularly efficient in studying LPSs ligand binding, and especially binding to large ligands such as proteins which will significantly rigidify the LPS or when the rigid lipid A part is directly involved in the binding with a receptor (TLR4/MD2, CD14 or LBP protein binding). Further advances in ssNMR methods, in particular higher magic-angle spinning frequencies permit [START_REF] Brodsky | Targeting of immune signalling networks by bacterial pathogens[END_REF] H detection experiments with high resolution and increased sensitivity. High speed spinning (100-111kHz) allows to record 2D and 3D experiments through dipolar or J-couplings similar to liquid state experiments , and on complex [START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] C/ 15 N/( 2 H) labeled protein systems and on unlabeled molecules with together very low amounts of sample [START_REF] Quinn | Structural biology of supramolecular assemblies by magic-Angle spinning NMR spectroscopy[END_REF] and short experimental times. This should prove particularly useful for the study of LPS alone or in interaction with ligands and thus contribute to the elucidation of the fundamental properties of outer membrane permeability.

METHODS

Cell growths and LPS extraction

LPS [START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] C-labeling was performed by growing E. coli BL21(DE3) or P. aeruginosa PA01 in M9 minimal medium 31 supplemented with 0.1% (w/v) [START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] C glucose, as the sole carbon source. Cells were harvested from 1 liter of bacterial culture grown to OD600 of 0.8 and the bacterial pellet was lyophilized, washed with distilled water, ethanol and acetone followed by ultracentrifugation steps (45,000 rpm, 4 °C, 16 h). LPS were extracted by hot phenol/water extraction [START_REF] Galanos | A New Method for the Extraction of R Lipopolysaccharides[END_REF] . Both phases were dialyzed and lyophilized, followed by protease and nuclease digestions, then extensive dialysis against water and freeze-drying. Presence of LPS was assessed by SDS-PAGE all along the purification. Gentamicin was obtained from SIGMA(G1264).

Electron microscopy

Samples of LPS at 0.1 to 1mg/ml concentration in water for E. coli LPS or 50mM MES pH 6.0 for P. aeruginosa PAO1 LPS were used. LPS PAO1 with gentamicin was studied at 0.1 mg/ml in presence of 25mM gentamicin. Samples were absorbed to the clean side of a carbon film on mica, stained with Sodium Silico Tungstate and transferred to a 400-mesh copper grid. The images were taken under low dose conditions (<10 e -/Å 2 ) at a magnification of 23Kx and 49Kx times with defocus values between 1.2 and 2.5 μm on a Tecnai 12 LaB6 electron microscope at 120 kV accelerating voltage using CCD Camera Gatan Orius 1000.

Nuclear Magnetic Resonance

Lyophylised LPS sample was resuspended at ~50mg/ml final concentration in Milli Q water for E. coli at LOS or 50mM MES pH 6.0 for P. aeruginosa PAO1 LPS. E. coli LOS was sedimented into rotors by centrifugation (16-50.10 3 g) for 5 minutes. P. aeruginosa LPS was sedimented into rotors at 50000g for 16 hours. NMR experiments were recorded on Agilent 600MHz VNMRS spectrometer equipped with MAS 3.2 mm or 1.6 mm HCN probes. MAS frequencies used were 12.5 kHz when employing 3.2 mm probe and 34 kHz with the 1.6 mm probe. The sample temperature was set to ca. 25°C. For 2D [START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] C- [START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] C correlation experiments acquisition times were typically 14 -20ms for direct dimension and 5-7 ms in the indirect dimensions, interscan delay was set to 2-4 seconds. [START_REF] Brodsky | Targeting of immune signalling networks by bacterial pathogens[END_REF] H SPINAL-64 decoupling with a radio-frequency (rf) of 100-110 kHz was applied. In CP experiments, the 1 H radiofrequency field was between 55 and 60 kHz, and the [START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] C rf field adjusted to match the Hartmann-Hahn condition with n=1, and the CP time was set between 0.5 and 1.5ms. 1D [START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] C experiments with direct [START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] C excitation or 1 H-13 C CP-MAS were recorded with 12-19ms acquisition time and an interscan delay of 2-3 seconds. Typically, [START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] C- [START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] C DARR experiment on E. coli LPS in 3.2 mm rotor was acquired in 41 hours with a 100ms mixing time and 13 C- [START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] C Single Quantum J experiment in 16 hours. [START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] C-1 H INEPT experiments (Tinept=1ms) and 2D 13 C- [START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] C Single Quantum J experiment of PAO1 LPS in 1.6mm rotor were recorded in 6 and 24 hours respectively. A PAO1 LPS sample at 40mg/ml in 50mM MES pH 6.0 was split in two and gentamicin at 25mM final concentration was added to one of the sample and they were ultracentrifuged into NMR rotor as described above. [START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] C T1 longitudinal relaxation time constants were obtained with series of [START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] C-1 H INEPT experiments at 34kHz with inversion recovery periods and delays from 1ms to 1.3s in absence and presence of gentamicin. T1 values were fitted with CcpNmr software and presented with the fitting error provided by the software. NMR experiments were processed with NMRPipe 33 or Topspin 3.5 and analysed with CcpNmr 2.42 software [START_REF] Vranken | The CCPN data model for NMR spectroscopy: Development of a software pipeline[END_REF] . Comparison of 1D [START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] C Spectra of LPS with direct [START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] C excitation or through [START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] C-1 H Cross polarization experiment Spectra were recorded at 600 MHz and at a spinning rate of 12.5kHz with identical numbers of scans for each sample (PAO1-LPS 128, K12 LPS 64), and baseline was shifted for improved clarity.

Figure 1

 1 Figure 1 Localization and structure of lipopolysaccharides. LPSs constitute the major component of

Figure 2

 2 Figure 2 Characterization of E. coli R-LPS reconstituted in solution by a) Negative stain Electron

Figure

Figure 3 E

 3 Figure 3 E. coli LPS Lipid A and core oligosaccharide characterization. a) Chemical structure of E. coli K12 R-LPS with 13 C-13 C DARR spectra focused on the sugar region or lipid region respectively (b and c). Assignment of peptidoglycan is shown in orange. Cyclopropane and insaturations are

Figure 4

 4 Figure 4 MAS ssNMR O-antigen from P. aeruginosa PAO1. a) Chemical structure of P. aeruginosa PAO1 S-LPS. b) EM negative stain micrograph of PAO1 LPS. c) extract of a 13 C-13 C Single Quantum J correlation spectrum of P. aeruginosa LPS with the assigned resonances showing clearly the Oantigen repeat (labeled Fuc1-Man2-Man3) and several resonances from sugars of the extended core. * Artefacts

2

 2

  ) and only few resonances were unambiguously assigned to the inner core oligosaccharides, namely to Kdo and heptose. Residues from the core were particularly visible in dipolar coupling-based experiments,

  C-1 H INEPT experiments were thus recorded at 34kHz MAS in presence of gentamicin. Gentamicin bound LPS produced a similar spectrum as free PAO1 LPS, showing mostly the O-antigen repeats and the last 4 CH groups of the lipid A part. Small chemical shift variations are observed for the polysaccharides resonances (Supplementary Figure 5), but not for the resonances of the lipid A (Figure 5 panel b). Comparison of the peak intensities before and after addition of gentamicin also reveals that the lipid A resonances are not affected by the gentamicin interaction (Figure 5 panel b). However, polysaccharide resonances of the O-antigen are significantly decreased in intensity in presence of gentamicin. Interestingly, the presence of gentamicin has even a stronger effect on the resonance intensities corresponding to the B-band polysaccharides relative to the saccharides of the A-Band (Figure 5 panels b and c).

Figure 6

 6 Figure 6 ssNMR highlights regions of different flexibilities and regions of interactions in LPS. a) Comparison of 1D[START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] C Spectra of LPS with direct[START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] C excitation (red) or through[START_REF] Zähringer | NMR-based structural analysis of the complete rough-type lipopolysaccharide isolated from Capnocytophaga canimorsus[END_REF] C-1 H Cross polarization experiment(blue) shows that P. aeruginosa S-LPS, that assemble into micelles, displays mainly flexible signals (orange) belonging to O-antigens with less efficient CP transfer. These regions were identified as interacting with gentamicin antibiotic. b) E. coli R. LPS in vesicles CP spectrum shows rigid portions of the LPS (blue), mainly core oligosaccharides and lipids.

ACKNOWLEDGEMENTS

This work was supported by the Train2Target project granted from the European Union's Horizon 2020 framework program for research and innovation (Project #721484) and partly supported by the French National Research Agency in the framework of the " Investissements d'avenir" program Glyco@Alps (ANR-15-IDEX-02). This work used the platforms of the Grenoble Instruct centre (ISBG; UMS 3518 CNRS-CEA-UJF-EMBL) with support from FRISBI (ANR-10-INSB-05-02) and GRAL (ANR-10-LABX-49-01) within the Grenoble Partnership for Structural Biology (PSB). The electron microscope facility is supported by the Rhône-Alpes Region, the Fondation Recherche Medicale (FRM), the fonds FEDER, the Centre National de la Recherche Scientifique (CNRS), the CEA, the University of Grenoble, EMBL, and the GIS-Infrastrutures en Biologie Sante et Agronomie (IBISA). We thank D. Fenel and G. Schoehn, from the Electron Microscopy platform of the Integrated Structural Biology of Grenoble (ISBG, UMI3265). We gratefully thank M. Richerd for great assistance in spectra analysis and C. Bougault and B. Bersch for stimulating discussions.

ASSOCIATED CONTENT

Supporting information is available including NMR chemical shifts table and additional NMR spectra: This material is available free of charge via the Internet at http://pubs.acs.org.

The authors declare no competing financial interest.


T P Tuyen Dao

Lubomir Vezenkov

Gilles Subra

Vincent Ladmiral

Mona Semsarilar

Nano-assemblies with Core-Forming Hydrophobic Polypeptide via Polymerization-Induced Self-Assembly (PISA)

The aim of this study is to produce self-assembled structures with hydrophobic polypeptide cores via Reversible Addition-Fragmentation chain Transfer (RAFT) -mediated Polymerisation-Induced Self-Assembly (PISA). Hydrophilic poly(glycerol monomethacrylate) macromolecular chain transfer agents (PGMA mCTAs) were used to polymerize the selfassembling peptide monomers, resulting in the formation of diblock copolymer nano objects. Methacrylamide derivatives containing self-assembling tripeptide; MAm-GFF (MAm-Gly-Phe-Phe-NH 2 ) and MAm-FGD (MAm-Phe-Gly-Asp-NH 2 ) were used as hydrophobic monomers. The self-assembling behaviours of these monomers mainly derive from the interactions of the phenylalanine residues, however their difference in hydrophobicity required different polymerization conditions.

MAm-GFF was polymerized in the presence of organic solvent (ethanol or acetonitrile), under either dispersion or emulsion polymerization, while MAm-FGD was polymerized under aqueous dispersion conditions. PGMA-b-P(MAm-FGD) obtained from aqueous PISA typically formed fibrous structures while a range of morphologies such as fibre-, flake-, leaflike or spherical vesicles were obtained for PGMA-b-P(MAm-GFF) depending on the copolymer composition and solvent used. In all cases the peptides self-assembling core had a crucial influence on the final morphologies.

Mona SEMSARILAR, PhD CNRS Researcher Institut Européen des Membranes Université Montpellier 2 place E. Bataillon 34095 MONTPELLIER Cedex 5, France Mail : mona.semsarilar@umontpellier.fr Montpellier, 01/06/2020 Dear Editor, Please find attached our paper entitled "Nano-assemblies with Core-Forming Hydrophobic Polypeptide via Polymerization-Induced Self-Assembly (PISA)" for consideration for publication as a full article in Polymer Chemistry, Polymerization-Induced Self-Assembly (PISA) special issue.

In recent years polymerization-induced self-assembly (PISA) mediated by reversible addition-fragmentation chain transfer (RAFT) dispersion polymerization has changed the way synthetic chemists prepare and self-assemble block copolymers. PISA is indeed a powerful and versatile technique for the synthesis and self-assembly of a wide range of block copolymer nano-objects of controllable size, morphology, and surface functionality.

The polymers used in PISA have so far been for the vast majority unable to develop supramolecular interactions. Apart from the recent report of Rieger et al (https://doi.org/10.1002/anie.201809370), there are no other study on PISA and supramolecular interactions. In the present manuscript, we take a new approach to the established PISA procedure, and we prepare peptide-polymer hybrids. Two new monomers bearing short peptide sequences capable of self-assembling due to pi-pi stacking and Hbonding were synthesized. We demonstrate that insertion of only few units of these selfassembling peptide (SAP) monomers in the core-forming block of a typical PISA formulation (poly (glycerol monomethacrylate) (PGMA) stabilizing first block followed by dispersion polymerization of 2-hydroxypropyl methacrylate (HPMA)) completely changes the selfassembly regime of this diblock copolymers. New morphologies were observed thus underlining the decisive influence of the SAP monomers.

We believe that the special PISA issue in Polymer Chemistry is an ideal platform to report these exciting new results, which should be of considerable interest to polymer chemists as well as material scientists. We would thus be very grateful if you could consider our manuscript for publication.

On behalf of all the co-authors, Yours sincerely, Mona Semsarilar

Introduction

Self-assembled nanostructures based on polypeptide-polymer hybrid are interesting biomaterials with potential significant impacts in applied biology and medicine. Compared to pure polymeric nanoparticles, these structures could present increased biocompatibility and biofunctionality typical of the peptide sequences, [1][2][3] in addition to the robustness and functional diversity conferred by the polymer chains. Moreover, the range of selfassembled peptide-containing structures is more diverse than that of polymer nano-objects. [4][5][6] They can form more complex supramolecular assemblies such as nano-fibers, ribbons, tapes, tubes, wires or rods. [6][START_REF] Görbitz | Chemical communications[END_REF][START_REF] Marchesan | [END_REF][9][10][11][12][13][14][15] In particular, since the molecular selforganization of these structures is mainly attributed to weak interactions such as electrostatic forces, hydrophobic interactions, π -π stacking and hydrogen bonding, 16 these structures can largely vary in both shape and size depending on internal or external stimuli (pH, temperature, ionic strength, solvents…). [17][START_REF] Mendes | Wiley interdisciplinary reviews[END_REF][19] The diversity and versatility of peptide-based nanostructures allow them to be potentially used in different biomedical fields such as biosensors, tissue engineering, or drug delivery. 4,[20][21][22][23] Besides the conventional self-assembly strategies using purified and isolated amphiphilic block copolymers, polymerization-induced selfassembly (PISA) has been shown to be a powerful polymer selfassembly method over the last decade and as such has received considerable interest. 24,25 PISA strategy is fast, eliminating timeconsuming steps such as isolation/ purification and redispersion of the amphiphilic polymers since it proceeds via the simultaneous formation and self-assembly of the amphiphilic block copolymers. 26 While the conventional post-polymerization methods provide dilute suspensions of nanoparticles (ca. 1% w/w), PISA generates nanoparticles at much higher concentrations (up to 50% w/w as reported in recent studies). 27,28 Moreover, PISA works well under either dispersion [29][30][31][32][33] or emulsion polymerization conditions [START_REF] Boissé | Chemical communications[END_REF][START_REF] Chaduc | [END_REF][36][37] and in a wide range of solvents. [38][39][40][41][42][43][44][45] Although the use of PISA is drastically growing due to its advantages, most reports show relatively simple self-assembled morphologies (spheres, worms and vesicles). 25 Inspired by the properties of peptide-based nanostructures as well as PISA approach, we have recently reported the first example of PISA nano-objects derived from self-assembling peptide (SAP) containing polymer. 46 The SAP monomer used in this study (MAm-GFF), was a methacrylamide-functionalized GFF tripeptide (GFF = Glycine-Phenylalanine-Phenylalanine). The tripeptide moieties were incorporated along with glycerol monomethacrylate (GMA) in the stabilizing block which was successfully chain extended under PISA conditions with poly(2hydroxypropyl methacrylate) (PHPMA). The resulting P(GMA 65 -stat-(MAm-GFF) 7 )-b-PHPMA 28 diblock copolymer formed fibrous structures in water. Herein, the same peptide methacrylamide was used but as precursor of the core-forming block. PISA formulations with core-forming block composed of copolymer of this SAP Please do not adjust margins Please do not adjust margins methacrylamide and a solvophilic monomer (GMA or HPMA) were also examined. Moreover, a new tripeptide-containing methacrylamide, (MAm-FGD) based on the phenylalanine-glycineaspartic acid SAP sequence was also studied. As for MAm-GFF, the self-assembly property of MAm-FGD is also attributed to the phenylalanine residue. However MAm-FGD is slightly less hydrophobic than MAm-GFF at physiological pH, and thus allows the use of different PISA conditions. All the synthetic approaches of this work are summarized in Scheme 1.

ARTICLE

Experimental section

Materials

Synthesis of methacrylamide-functionalized peptide monomer MAm-FGD

MAm-FGD was synthesized on the resin using the same protocol employed to make MAm-GFF in our previous report 46 but with Fmoc-Phe-OH, Fmoc-Gly-OH and Fmoc-Asp(But)-OH) as the amino acids. At the end, the tripeptide was cleaved from the resin with a TFA/TIS/H 2 O (95/2.5/2.5) mixture for 2h at room temperature. It was recovered by precipitation in cold diethyl ether, taken up in water and freeze-dried. The obtained crude white powder was used for polymerisations without any further purification. Its purity and molecular structure were verified by LC-MS (Figure S2) and 1 H NMR spectroscopy (Figure S1).

RAFT Homopolymerization of GMA

A representative synthesis of the PGMA macromolecular chain transfer agents (mCTAs) proceeded as follows: a round bottom Schlenk flask equipped with a stirrer bar was charged with GMA (30 eq.), PETTC (1 eq.), ACVA initiator (0.1 eq.) and a volume of ethanol adjusted for the reaction to proceed at a solids content of 50% w/w. The flask was subsequently sealed with a rubber septum, placed in an ice-bath, degassed by bubbling nitrogen for 30 min and immersed in a preheated oil bath at 70°C. After 2h, the polymerization was quenched by immersing the flask in ice-cold water and opening the reaction to air. GMA conversion was determined by 1 H NMR in methanol-d4, from the ratio of the integral of the residual vinyl 1 H signals at 5.65 ppm (1H) or 6.15 ppm (1H) to the signals at 3.5-4.3 (5H). The mixture reaction was then dialyzed using a MWCO = 1kDa membrane against a 9/1 mixture of water and ethanol during two days and freeze-dried. The final product was a light yellow powder. The mean DP was determined by 1 H NMR and the molar mass distribution was determined using DMAc SEC. All the 1 H NMR spectra and SEC chromatograms of the PGMA mCTAs are provided in Figure S3-S6.

Preparation of diblock PGMA x -b-P(MAm-GFF) y via RAFT-PISA using PGMA x as mCTA PGMA x mCTA (1 eq.), MAm-GFF (y eq.), and ACVA (0.2 eq.) were charged into a 10-mL glass vial and stirred with the chosen polymerization solvent. The vial was sealed, submerged in an icebath, degassed for 30 minutes and put into an oil-bath set previously at 70°C. After 24h, reaction was cooled down, opened to the air and the MAm-GFF conversion was determined by 1 Please do not adjust margins

Please do not adjust margins

The procedure to prepare PGMA 18 -b-P((MAm-GFF) 9 -co-GMA 48 ) using PGMA 18 as mCTA was as follows: PGMA 18 mCTA (1 eq.), MA-GFF (10 eq.) GMA (48 eq.) and ACVA (0.2 eq.) were stirred with pure ethanol into a 10-mL glass vial. The vial was subsequently sealed with a rubber septum, submerged in an ice-bath, degassed by bubbling nitrogen for 30 min and immersed in a preheated oil bath at 70°C. After 24h, the reaction was quenched by cooling and exposing to air. MAm-GFF conversion was determined as described above while GMA conversion was always 100% (no remaining GMAvinyl signals). Other aliquots were also taken for SEC, DLS and TEM analyses. The procedures were as follow: PGMA 18 mCTA, MA-GFF, HPMA and ACVA at ratio 1 : 10 : 61 : 0.2 (to prepare PGMA 18 -b-P((MAm-GFF) 9co-HPMA 61 ) and 1 : 20 : 50 : 0.2 (to prepare PGMA 18 -b-P((MAm-GFF) 19 -co-HPMA 50 )) were stirred with ethanol into a 10-mL glass vial. The vial was subsequently sealed with a rubber septum, submerged in an ice-bath, degassed by bubbling nitrogen for 30 min and immersed in a preheated oil bath at 70°C. After 24h, the reaction was quenched by exposing to air. MAm-GFF conversion was determined as same as described above while HPMA conversion was always 100% (no remaining HPMA-vinyl signals). Other aliquots were also taken for SEC, DLS and TEM analyses.

Preparation of diblock

Preparation of diblock PGMA x -b-P(MAm-FGD) y via RAFT-PISA using PGMA x as mCTA

The typical procedure of RAFT-PISA to prepare diblock PGMA x -b-P(MAm-FGD) y using PGMA x as mCTA was carried out as described below. PGMA x mCTA (1 eq.), MAm-FGD (y eq.), ACVA (0.2 eq.) and water (to reach 10% w/w of solids content) were charged into a 10-mL glass vial. The vial was sealed, degassed for 30 minutes and put into an oil-bath set previously at 70°C. After 24h, reaction was cooled down, opened to the air and the MAm-FGD conversion was determined by 1

Proton nuclear magnetic resonance spectroscopy ( 1 H NMR):

1 H NMR spectra were recorded on a 300 MHz Bruker Avance-300 spectrometer, processed and analyzed with MestReNova 9.0.

Size exclusion Chromatography (SEC):

Polymer molar mass distributions were analysed using GPC Varian 390-LC system with PL1113-6300 ResiPore 300 x 7.5 columns connected with 390LC PL0390-0601 refractive index detector (RI). The mobile phase was DMAc with 0.1% w/w LiBr adjusted at a flow rate of 1mL min -1 while the columns were thermostated at 70°C. The calibration was done with near-monodisperse Poly(methyl methacrylate) (PMMA) standards ranging from 550 to 1 568 000 g mol -1 (EasiVial-Agilent).

Dynamic light scattering (DLS):

The hydrodynamic radii RH were analysed by dynamic light scattering at 90° using Litesizer TM 500 Anton Paar. All measurements were performed at 20°C and with samples diluted to 0.1% w/w. Transmission Electron Microscopy (TEM): TEM images were acquired using either JEOL 1200 EXII-120 kV or JEOL 1400 P+ -120 kV. To prepare the TEM grid, 10 µL of 100-fold diluted sample from PISA suspension (0.1% w/w) was deposited onto the grid for 60s and then blotted with filter paper to remove excess solution.

Afterward, the sample-loaded grid was stained with 7 µL of 1% ammonium molybdate solution for 20s and also removed the excess stain with filter paper. The grid was allowed to dry under the hood for 5 minutes.

Results and discussion

PGMA macromolecular chain transfer agents (PGMA mCTAs)

The homopolymerizations of GMA were performed in ethanol under solution polymerization conditions. Although almost full conversion could be reached in 5h as shown in previous studies, 47 in this work, the polymerizations of GMA were stopped at about 60% conversion to ensure good end-group fidelity. The DP of the resulting PGMA mCTAs (18, 40 and 83 for mCTAs 1, 2, and 3 respectively, Figure S3-5) were determined by 1 H NMR using the integrals of the signals of the backbone of PGMA (0.8-2 ppm, 5H) and of those of the PETTC end-group (7.2-7.4 ppm, 5H). All three mCTAs had narrow molar mass distributions (Đ = 1.16, 1.21 and 1.27) as judged by SEC in DMAc. SEC traces of these PGMA mCTAs are shown in Figure S6.

PISA using the GFF-functionalized methacrylamide (MAm-GFF)

The polymerizations of MAm-GFF using PGMA mCTAs to prepare self-assembled structures with P(MAm-GFF) as coreforming block were performed in different media containing organic solvents since MAm-GFF is only sparingly soluble in pure water. Common good solvents for hydrophobic peptides are DMF, DMSO, acetonitrile and ethanol. DMF and DMSO could not be used here, as they are both good solvent for P(MAm-GFF). Direct visual observation suggested that in ethanol, MAm-GFF was soluble up to 0.4% w/w at ambient temperature (ca. 20°C) and up to 5% w/w at 70°C. At higher concentrations (7% -10% w/w), it formed emulsion at both 20 and 70°C. Furthermore, a mixture of water/acetonitrile was also chosen to study as the reaction medium. It was found that in water/acetonitrile 1/2 v/v mixture, MAm-GFF is dispersed up to 10% w/w at both 20°C and 70°C, whereas in water/acetonitrile 1/1 v/v mixture, a 10% w/w MAm-GFF formed an emulsion at 20°C and a solution at 70°C. TEM images of MAm-GFF-derived structures prepared in the above media at low concentration (0.1% w/w) are presented in Figure 1. Please do not adjust margins Please do not adjust margins

In the water/acetonitrile 1/2 v/v mixture, only ill-defined aggregates were observed (Figure 1A), suggesting that MAm-GFF was completely solubilized. However, in mixture of water/acetonitrile 1/1 v/v or in ethanol, MAm-GFF selfassembled into relatively well-defined vesicular morphologies, (Figure 1B) and bundles of short fibers (Figure 1C). As discussed already in our previous work, 46 the self-assembly of MAm-GFF is attributed to the combination of hydrogen bonding and aromatic π-stacking interactions between the FF moieties. The final morphologies thus are not only determined by MAm-GFF molecular structure but also by the solvent quality (polarity and hydrogen bonding properties). This was indeed illustrated here: changing the solvent from ethanol to water/acetonitrile 1/1 v/v mixture provides two types of distinct structures: fibres and vesicles. These preliminary results on the solution properties of MAm-GFF allowed its use in PISA formulation as the core-forming building block (scheme 1).

PISA in ethanol

Solids content effect: A series of polymerisation carried out in ethanol using mCTA 1 (PGMA 18 ): an initial ratio of 1: MAm-GFF: ACVA of 1: 5: 0.2, for 24 h at 70 °C, at various solids content was performed. At 5% w/w, the reaction proceeded under dispersion polymerization, however above 10% w/w, the reaction became an emulsion polymerization. Surprisingly, only 45% MAm-GFF conversion could be attained at 5% w/w solids whereas at 11.2% w/w solids, MAm-GFF conversion reached 87%. This trend was confirmed by a third experiment carried out at 12.5% w/w solids (targeting a DP of P(MAm-GFF) of 10) which reached 92% MAm-GFF conversion. The DMAc SEC traces (Figure 2) of the resulting PGMA 18 -b-P(MAm-GFF) x diblock copolymers confirmed the relative good control of the RAFT polymerizations. However, a significant shoulder corresponding to the mCTA can be seen on the trace of the PGMA 18 -b-P(MAm-GFF) 9 block copolymer, suggesting a suboptimal blocking efficiency.

In all cases, at 70°C, the final reaction mixtures were turbid yellow suspensions. However, upon cooling, both suspensions were unstable. They became more turbid and yellow solids were observed on the wall of the vial at ambient temperature, even under continuous stirring, as shown in Figure S7.

Please do not adjust margins

Please do not adjust margins structures at the micrometric scale. The size distribution in this case was broad, probably due to its highly anisotropic morphology as seen with TEM. DLS data are presented in Figure S8. The significant change in both size and shape between the two diblocks (PGMA 18 -b-P(MAm-GFF) 4 and PGMA 18 -b-P(MAm-GFF) 9 ) indicated that the length of the hydrophobic SAP block P(MAm-GFF) effectively determines the final morphology of the PGMA-b-P(MAm-GFF) block copolymer. This result confirms the interplay and synergy between SAP and PISA in the formation of these morphologies.

Effect of the mCTA length

To overcome the instability, observed at 20°C for the previous diblock copolymer morphologies, stabilized by a relatively short PGMA 18 , longer hydrophilic mCTAs: PGMA 40 (2) and PGMA 83 (3) were used. All the PISA formulations were carried out at 12% w/w solids in ethanol. The polymerization led to yellow turbid suspensions after 24h. In these polymerizations, MAm-GFF conversions reached 90% or higher as judged by 1 HNMR and SEC analyses. However, the resulting diblock copolymers (PGMA 40 -b-P(MAm-GFF) 8 , PGMA 83 -b-P(MAm-GFF) 10 and PGMA 83 -b-P(MAm-GFF) 6 ) suspensions again lost their colloidal stability upon cooling from 70°C to 20 °C. Increasing the length of the PGMA block did not improve the stability of PGMA-b-P(MAm-GFF) self-assembled objects. Here, the balance between the hydrophobic and hydrophilic parts in the PGMA-b-P(MAm-GFF) system was not the dominant element in the self-assembly in contrast to the case of PGMA-b-PHPMA which have been thoroughly described. 48 The morphologies observed here were likely more affected by the selfassembling properties of the polypeptide part. The diblock copolymer morphologies were observed by TEM using 100-fold diluted samples. The dilution was carried out at 70°C. Welldefined morphologies were observed for all PISA formulations as shown in Figure 4. In all cases, despite the composition difference, the self-assembled morphologies were large (several μm) dendritic structures similar to the structures observed for PGMA 18 -b-P(MAm-GFF) 9 , and composed of fibrous elements (Figure 4). These fibrous substructures were better defined for the diblocks prepared from the longer PGMA 83 mCTA. Increasing the length of the P(MAm-GFF) block from 6 to 10 for these PGMA 83 -derived block copolymers led to even better defined fibrous substructures (Figure 4). When PGMA 40 was used as the stabilizing block, these substructures lost much of their fiber-like aspect.

Effect of the composition of the core-forming block

The effect of the composition of the solvophobic block was also examined by replacing the P(MAm-GFF) segment by a copolymer of HPMA (or GMA) and MAm-GFF. GMA and HPMA are highly soluble in ethanol. Three PISA formulations based on mCTA 1 were examined: 1: GMA: MAm-GFF = 1: 48: 10, 1: HPMA: MAm-GFF = 1: 61: 10, and 1: HPMA: MAm-GFF = 1: 50: 20. The addition of GMA or HPMA increased the solubility of MAm-GFF in the reaction medium, and thus the PISA could be carried out at higher solids contents (15% w/w) which led to higher monomer conversions. The SEC chromatograms of the resulting diblock copolymers shown in Figure 5 suggest that the PISA copolymerizations proceeded with relatively good control (the trace are monomodal and shifted towards higher Please do not adjust margins Please do not adjust margins molar masses). However, these chromatograms were also slightly broad suggesting a subpar blocking efficiency. As in the case of the previous formulations described above, the suspension of PGMA 18 -b-P((MAm-GFF) 9 -co-GMA 48 ) diblock copolymer was turbid and stable at 70°C but rapidly lost colloidal stability in a few minutes after cooling down (Figure S9). TEM images of the sample diluted at 70°C showed large clusters of fibrous structures. In contrast, the PGMA 18 -b-P((MAm-GFF) 9 -co-HPMA 61 ) and PGMA 18 -b-P((MAm-GFF) 19 -co-HPMA 50 ) diblock copolymers suspensions were colloidally stable at both 70°C and 20°C. The TEM images of these morphologies (samples prepared at 20°c) show that PGMA 18 -b-P((MAm-GFF) 19 -co-HPMA 50 ) selfassembled into vesicles while PGMA 18 -b-P((MA-GFF) 9 -co-HPMA 61 ) self-assembled into a mixture of short worms and vesicles (Figure 6). It is worth noticing here that these vesicles are undoubtedly the results of the self-assembling properties of MAm-GFF since PGMAb-PHPMA block copolymers are completely soluble in ethanol.

Solvent effect

The effect of the solvent on the PISA of PGMA-b-P(MAm-GFF) diblock copolymer was investigated, and ethanol was replaced by water/acetonitrile mixtures. The following PISA formulation based on mCTA 2 was examined: 2: MAm-GFF: ACVA = 1: 20: 0.2 in 1/1 v/v and 1/2 v/v water/acetonitrile mixtures. The polymerizations were carried out at 10 w/w solids under RAFT dispersion polymerization conditions at 70°C. The MAm-GFF conversions reached 69% and 72% in 1/1 v/v and 1/2 v/v water/acetonitrile mixtures respectively. Formation of the diblock copolymers via successful chain extension of the macro-CTA with P(MAm-GFF) was confirmed by SEC DMAc as shown in Figure S10. The resulting diblock copolymer morphologies were well-dispersed, giving rather clear colloidal suspensions that remained colloidaly stable even upon cooling to 20°C. TEM images (Figure 7) showed that PGMA 40 -b-(MAm-GFF) 15 formed monodisperse 220 nm spherical particles in water/acetonitrile 1/1 v/v. In water/acetonitrile 1/2 v/v the PISA of PGMA 40 -b-(MAm-GFF) 15 led to polydisperse vesicles with diameters ranging between 50 and 400 nm. In contrast to the PISA experiments carried out in ethanol which resulted in unstable dispersions and fibrous structures, no fibrous structures were observed for PGMA-b-P(MAm-GFF) in the two water/acetonitrile mixtures examined. It is however important to note that the diblock copolymers prepared in ethanol and in water/acetonitrile were not strictly identical. So the difference in their morphologies may not be ascribed only to the effect of solvent.

PISA using GFD-functionalized methacrylamide (MAm-FGD)

In order to perform PISA under aqueous dispersion conditions, a new peptide-functionalized methacrylamide, MAm-FGD, was designed. This monomer, reported for its self-assembling properties, similar to MAm-GFF contains a phenylalanine residue, however it is less hydrophobic as it also contains a polar aspartic

Please do not adjust margins

Please do not adjust margins acid unit instead of a second phenylalanine moiety. Indeed, MAm-FGD was soluble in water up to 10% w/w. The TEM images (Figure 8) of the MAm-FGD aqueous solution at 0.1% w/w revealed the presence of long (several μm) shard-like structures with width in the 100 -200 nm range that sometimes aggregated into bundles. These TEM images confirmed that a single phenylalanine unit can also drive self-assembly and lead to the formation of fibrous structures, as demonstrated by Gazit et al. 49 Polymerizations of MAm-FGD were performed using mCTAs 1, 2 and 3 at 10% w/w solids in water. In all cases, 100% MAm-FGD conversion were achieved and a yellow turbid suspension was obtained. Three diblock copolymers were thus prepared: PGMA 18b-P(MAm-FGD) 10 , PGMA 40 -b-P(MAm-FGD) 20 and PGMA 83 -b-P(MAm-FGD) 20 . All three samples formed colloidally stable suspensions at both 70°C and 20°C. TEM images of these suspensions revealed the formation of large dendritic and bow-tie shaped fibrous spherulitic structures (Figure 9). Although the overall shape is similar for all the compositions, indicating similar organization, a closer look at their internal structures reveals slight differences as seen in images at higher magnifications. From PGMA 18 -b-P(MAm-FGD) 10 , PGMA 40 -b-P(MAm-FGD) 20 to PGMA 83 -b-P(MAm-FGD) 20 , it seems that the fibers become shorter and the structures tend to be less packed.

Conclusions

Nanostructures constituted of a solvophilic PGMA corona and peptide-containing solvophobic cores were successfully prepared via RAFT-mediated Polymerization-Induced-Selfassembly using SAP-functionalized methacrylamide. The selfassembly of these polymer-polypeptide formulations proved to be much more diverse compared to the polymeric nanoobjects reported in previous PISA works. PISA formulations based on PGMA-b-P(MAm-GFF) or PGMA-b-P(MAm-FGD) formed large spherulitic bundles of fibrous structures in ethanol and water respectively. In contrast, only spherical particles and vesicles were observed for PGMA-b-P(MAm-GFF) synthesized via PISA in dispersion in water/acetonitrile mixtures. As observed in our previous work 46 the introduction of only few SAP residues was necessary to greatly influence the self-assembled morphology. This observation further strengthens our hypothesis that PISA and SAP motifs can synergistically contribute to the formation of nano-and micrometric morphologies.

Journal Name 2 |

 2 J. Name., 2012, 00, 1-3 This journal is © The Royal Society of Chemistry 20xx

Fmoc-amino acid

  derivatives (Fmoc-Phe-OH, Fmoc-Gly-OH, Fmoc-Asp(tBu)-OH), HATU (1-[bis(dimethylamino)methylene]-1H-1,2,3triazolo[4,5-b]pyridinium 3-oxide hexafluorophosphate) and polystyrene Fmoc Rink Amide resins (100-200 mesh) with a loading of 0.94 mmol/g were purchased from Iris Biotech GmbH. Methacrylic acid, piperidine, N,N-diisopropylethylamine (DIEA), trifluoroacetic acid (TFA), triisopropylsilane (TIS), glycerol monomethacrylate (GMA), 2-hydroxypropyl methacrylate (HPMA), 4,4'-azobis(4-cyanopentanoic acid) (ACVA) and all organic solvents were purchased from Sigma-Aldrich. The NMR deuterated solvents (DMSO-d6, methanol-d4 and D 2 O) were purchased from Eurisotop. The RAFT agent (4-cyano-4-(2-phenylethanesulfanylthiocarbonyl)-sulfanylpentanoic acid) (PETTC) and the peptide monomer MAm-GFF was prepared according to our previous report.46

1 .

 1 Scheme 1. Schematic representation of the synthesis of the monomers and block copolymers.

  PGMA 18 -b-P((MAm-GFF) 9 -co-HPMA 61 ) and PGMA 18 -b-P((MAm-GFF) 19 -co-HPMA 50 ) via RAFT-PISA using PGMA 18 as mCTA

4 |

 4 J. Name., 2012, 00, 1-3 This journal is © The Royal Society of Chemistry 20xx

  However, after dilution (100-fold) of the suspensions at 70 °C for TEM and DLS analyses, the samples remained stable at 20°C. TEM images of the PGMA 18 -b-P(MAm-GFF) 4 diblock copolymer revealed the formation of flake-like objects about 50 nm wide and 100-200 nm long. In comparison, the PGMA 18b-P(MAm-GFF) 9 diblock copolymer formed micrometric branched bundles of fibers (Figure3). In agreement with TEM results, DLS experiments indicated the presence of nanoobjects in PGMA 18 -b-P(MAm-GFF) 4 suspension with narrow size distribution (PDI = 0.187). Meanwhile, the DLS histogram of PGMA 18 -b-P(MAm-GFF) 9 showed the existence of large

Figure 1 .

 1 Figure 1. Representative TEM images of MAm-GFF-derived structures prepared from solutions at c = 0.1% w/w in: (A) water/acetonitrile 1/2 v/v; (B) water/acetonitrile 1/1 v/v and (C) ethanol.

Figure 2 .

 2 Figure 2. DMAc SEC chromatograms (refractive index detector) for mCTA 1 (PGMA 18 ) and the diblock copolymers PGMA 18 -b-P(MAm-GFF) 4 and PGMA 18 -b-P(MAm-GFF) 9 prepared via RAFT-mediated PISA at 70°C in ethanol at 11.2% w/w and 12.5% w/w respectively.

Figure 3 .

 3 Figure 3. Representative TEM images at different magnification of the PGMA 18 -b-P(MAm-GFF) 4 (top row) and PGMA 18 -b-P(MAm-GFF) 9 (bottom row) diblock copolymers morphologies prepared by RAFT-PISA in ethanol at 11.2% and 12.5% solids content respectively. Samples were diluted 100fold at 70°C.

Figure 4 .

 4 Figure 4. Representative TEM images of the PGMA 40 -b-P(MAm-GFF) 8 , PGMA 83 -b-P(MAm-GFF) 6 and PGMA 83 -b-P(MAm-GFF) 10 diblock copolymers morphologies prepared RAFT PISA in emulsion in ethanol at 12% solids. The samples were diluted to 0.1% w/w at 70°C.

Figure 5 .

 5 Figure 5. DMAc SEC chromatograms (refractive index detector) for mCTA 1 (PGMA 18 ) and the three diblock copolymers prepared by RAFT PISA in emulsion in ethanol.

6 |

 6 J. Name., 2012, 00, 1-3 This journal is © The Royal Society of Chemistry 20xx

Figure 6 .

 6 Figure 6. Representative TEM images of the PGMA 18 -b-P((MAm-GFF) 9 -co-HPMA 61 ) diblock copolymer morphology (top row) and of the PGMA 18 -b-P((MAm-GFF) 19 -co-HPMA 50 ) diblock copolymer morphology (bottom row) prepared by RAFT PISA in dispersion in ethanol at 15% w/w solids. The samples were diluted to 0.15% w/w at 20°C.

Figure 7 .

 7 Figure 7. Representative TEM images of the PGMA 40 -b-P(MAm-GFF) 15 diblock copolymer morphology in 1/1 v/v (top row) and (1/2 v/v) (bottom row) water/acetonitrile mixtures prepared by RAFT PISA in dispersion at 10% w/w solids at 70°C. The samples were diluted to 0.1% w/w.

Figure 8 .

 8 Figure 8. Representative TEM images of self-assembled structures of MAm-FGD in water at 0.1% w/w.

Figure 9 .

 9 Figure 9. Representative TEM images at different magnification of the PGMA 18 -b-P(MAm-FGD) 10 (top row), PGMA 40 -b-P(MAm-FGD) 20 , (medium row) and PGMA 83 -b-P(MAm-FGD) 20(bottom row) diblock copolymer morphologies prepared by RAFT PISA aqueous dispersion at 10% w/w solids. The samples were diluted to 0.1% w/w.

20 Figure S2 .Figure S4 .Figure S5 .

 20S2S4S5 Figure S2. HPLC profiles and ESI-MS of MAm-FGD (t R = 1.10 min, m/z 405.2 ([M+H] + ))

This journal is © The Royal Society of Chemistry 20xx J. Name., 2013, 00, 1-3 | 5

Acknowledgements

PDRA fellowship managed by the French national research agency (ANR): "investissement d'Avenir" LabEX CheMISyst, grant number ANR-10-LABX-05-01. The authors also thank CNRS for funding this work via the "Osez l'interdisciplinarité" programme awarded to MS.

Conflicts of interest

There are no conflicts to declare.

ARTICLE