Frédéric Bimbot

Emmanuel Deruty

Gabriel Sargent

Emmanuel Vincent

Equipe Metiss

"Semiotic structure labeling of music pieces : concepts, methods and annotation conventions" (Proceedings ISMIR 2012)

Keywords: music structure, form, semiotics, semiology, relational graph, music analysis, music signal processing, music information retrieval, musicology, system contrast ___________ structure musicale, forme, sémiotique, sémiologie, graphe relationnel, analyse musicale, traitement du signal musical, recherche d'information musicale, musicologie, système contraste

At a low timescale (i.e. typically below 1 s) a music piece can be viewed as a combination of musical elements drawn from a limited inventory of predetermined conventional unitary items such as notes, duration values or chords. However, above a certain timescale, the organization of music is more relevantly described in terms of complex piece-specific objects linked to each other by a compact set of local self-deducible relationships, thus forming structured musical segments.

The present report proposes a model called "system & contrast" (S&C), which aims at describing the inner organization of structural segments in terms of a carrier system (i.e. a set of elements forming a simple network of logical relationships) and a contrast, namely a substitutive element (usually the last one) which partly deviates from the logical sequence induced by the carrier system.

We show that the S&C model is polymorphous in the sense that it applies to any type of musical information layer (melody, harmony, rhythm, rhymes, effects, etc…) in a very versatile way, therefore offering a powerful meta-description of musical content.

The model has been designed for specifying a methodology for music structure annotation [5], but we briefly mention also its potential implications in other domains of music analysis and music information retrieval (MIR).

INTRODUCTION

The description of the organization of music pieces at a high timescale, i.e. the task usually called structural segmentation and labeling, constitutes an open problem.

Several recent studies [START_REF] Bimbot | Decomposition into Autonomous and Comparable Blocks : A Structural Description of Music Pieces[END_REF][START_REF] Bimbot | Methodology and Resources for The Structural Segmentation of Music Pieces into Autonomous and Comparable Blocks[END_REF][START_REF] Peeters | Deruty : Is Music Structure Annotation Multi-Dimensional ? LSAS[END_REF][START_REF] Smith | Design and Creation of a Large-Scale Database of Structural Annotations[END_REF] in the context of MIR have been aiming at characterizing structural segments and producing annotated resources accordingly, but they all have been facing difficulties in formulating general properties which would qualify objectively and (almost) unambiguously the segmental units, independently of a given music genre, style or musical property.

Our research group has been investigating this question both from fundamental and experimental viewpoints. The annotation, discussion and adjudication of several hundreds of pieces, and the experience thus acquired, has gradually led us to the conclusion that the key features that create the perception of autonomous structural segments in music are not primarily some properties of their intrinsic substance but patterns of their inner organization.

In this report, we are therefore considering the "intermediate" level of music organization, which corresponds to timescales typically ranging between 1 and 16 snaps (analogous to down-beats), which we call the morpho-syntagmatic bandwidth [START_REF] Bimbot | Methodology and Resources for The Structural Segmentation of Music Pieces into Autonomous and Comparable Blocks[END_REF] and which lies below the level at which the structure of the entire piece is usually described.

This report presents what we consider as the core of the inner organization of structural segments in conventional music : 1) a small set of self-deducible relations between musical properties forming a logical carrier system and 2) an (optional) deviation of the last element, called contrast, and which acts as both a modulation and a punctuation of the system. We call this model system & contrast (S&C).

An S&C can be described as a simple network of relationships between a small number of morphological elements and it can be used to characterize structural segments both in terms of boundaries (segmentation) and distinctive properties (labels), independently of their actual substance.

The present article starts, in section 2, by presenting the principles of the S&C model in a completely intuitive and metaphoric manner, so that the reader can easily grasp the basic concept. Section 3 formalizes the S&C model in the case of square systems, without any reference to music, up to this point. It is only in section 4 that we instantiate the S&C model in connection with music information layers and we show how the model is able to describe a considerable variety of familiar (and less familiar) patterns, governing the organization of structural segments.

Section 5 extends the model to non-square configurations. Section 6 concludes on how the model has been used in the context of structural annotation and on its potential in other domains of MIR, Computer-Aided Music and music education. Analyses of S&Cs occurring in actual musical examples are provided at the end of the report. This report focuses on the principles of the S&C, whereas [START_REF] Bimbot | Semiotic Structure Labeling of Music Pieces : Concepts, Methods and Annotation Conventions, to appear[END_REF] presents extensively how the S&C model has actually been used for annotating the semiotic structure of a set of approximately 500 songs.

If you wish to cite this report in one of your publications, please be kind to contact the first author for updated pointers towards potentially more accessible, extended and peer-reviewed versions of this work.

INTUITIVE PRESENTATION

The square system

These 4 elements form a system based on the combination of two binary oppositions, in terms of shape and colour. We will call this system a square system.

Figure 1 gives a few examples of square systems, for which it is easy to deduce which are the properties used as oppositions, and therefore to explain easily the system.

The contrast

A fundamental property of a square system is its redundancy. Indeed, figure 2 depicts a few incomplete square systems, i.e. systems for which the 4 th element is missing (and replaced by a question mark). As can be easily experienced by the reader, some properties of the 4 th element are predictable and can be logically inferred from the knowledge of the first 3 elements.

As a consequence, it is easy to determine, on the basis of the exposition of 3 elements and the presentation of a fourth one, whether this 4 th element matches or deviates from the system, and in what respect.

The 4 elements beside form a system & contrast (S&C). The shape and colour properties of the 4 th element both contradict the combination expected in 4 th position, from the first three elements. The 4 th element creates a logical contrast.

Carrier system and contrasting properties

The characterization of a system and its contrast requires the determination of the set of properties which form the system and the identification of those which take part in the contrast. It is important to note that the contrastive properties act as a logical modulation of the information conveyed by the carrier system.

Analyzing a S&C

Let's now consider the following quadruplet of elements :

. A close study of this set leads to the following analysis : shape, size progression, colour, homogeneity and halo are properties of the carrier system. Among them, only shape, size progression and homogeneity participate to the contrast. Texture varies erratically and is therefore an off-system property. The status of orientation is not decidable.

In summary, the carrier system is based on 5 properties and the contrast comes from the deviation of the fourth element, from 3 of these 5 properties. Indeed, the 4 th element is a large heterogeneous cross instead of being a very-large homogeneous square, which can be visually depicted as :

FORMALIZATION

Specification of the carrier system

A square system (in its carrier form) can be denoted as :

S 0 =
As S 0 forms a square system, a network of relationships exists between its elements :

 horizontal relationship :  vertical relationship :  diagonal relationship : ( )
This can also be stated as a logical proposition :

is to what is to and is to what is to
This is nothing else than the generalization of the well-known "rule of three", i.e. the relationship between 4 numbers forming a system of proportions.

Note that and may apply only to a subset of the properties of the elements of S 0 (which we will call structuring properties of the system).

Altogether, the carrier system boils down to a seed element ( ) and a redundant network of relationships ( , and ).

Formulation of the contrast

Following similar notations as in the previous subsection, the system & contrast can be noted :

S =
Whereas the horizontal and vertical relationships (f, g) remain identical to that of the carrier system, we now have a specific diagonal relationship : , with .

A contrast results from the disparity between and and this disparity can itself be viewed as a function which relates the actual element to the (virtual) expected one , i.e :

As a result of the presence of the contrast, we have now the following situation :

is not to what is to and/or is not to what is to

Element is breaking the "natural" flow of events and creates a logical rupture. Function thus appears to create a discordance in the system, which incidentally conveys some additional information which can be decoded by first deducing and then factoring out the properties of the (aforesaid) carrier square system S 0 .

Visualization of the S&C model

Figure 4 below depicts a square S&C as a diagram representing elements and z together with the network of relations f, g and . The black line with double arrows represents the order in which the elements occur if the S&C is unfolded in time as :

.

Figure 4 : a schematic view of the S&C model components for an unfolded square system

THE S&C MODEL FOR MUSIC

In this section we discuss how the S&C model applies to music, and in particular how it is suited to describe the inner organization of structural segments.

We consider S&Cs whose elements are musical fragments with typical size of a few seconds and which relate through simple-to-detect syntagmatic relations.

From now on, we represent square systems in an unfolded way rather than as a matrix.

Musical information layers

As mentioned in the introduction, by musical information layer, we mean any property of the musical content which evolves in an organized manner at the snap scale, in the sense that it can be accurately described and tracked at that scale by a sequence of levels, values or states which samples its behavior over time and range.

A non-limitative list of these properties is :

-Melody / melodic contour -Harmony / harmonic progressions -Rhythm / rhythmic cells -Energy distribution and flow -Drum sequences and loops -Chant (phonetic flow) -Rhymes in lyrics -Arrangements and supports -Special effect schemes -etc…

Musical information layers must be distinguished from musical sources (i.e. the actual vehicles of the musical substance).

It is also worth noting that macroscopic musical properties, such as tonality, modality, tempo, timbre, etc... which usually vary at a slow rate, can acquire the status of musical information layer (within the morpho-syntagmatic bandwidth), if they happen to create patterns in a passage.

The identification of musical information layers is a key step in the analysis of the inner organization of structural units. However, the S&C model indifferently applies to any combination of musical information layers, i.e. independently of the actual musical substance of the structural segments.

Morphological elements

We assume that the typical basic elements of the system (namely the ) are musical fragments whose typical span is 4 snaps (i.e. 2 bars). However, they can occasionally be twice smaller, twice larger or irregular (variable number of downbeats).

Syntagmatic relationships

As the carrier system must be easily self-deducible, syntagmatic relationships f and g, are prone to be rather simple. For instance : identity, translation (shift on the scale), inversion, complementation, transposition, quasi-repetition, hold, suppress, augment, decrease, … Of course, not all morphological elements show obvious relationships on all musical layers. It is sometimes impossible to formulate a simple correspondence, and the syntagmatic relations must be understood as a de facto mapping function from one element to the other, which we will denote new.

However, it is generally the case that, within a structural segment, one or several layer(s) form(s) an obvious syntagmatic network of relations which thus ensures (and signals) the overall cohesion of the segment. It must also be noted that comparable lower scales systems usually develop simultaneously within the segment).

Concerning the contrast, "low-complexity" functions are frequently used, and the special case when (no contrast) leads to the (flat) realization of the carrier system.

Morpho-syntagmatic patterns

In this section, we denote as a the seed element (previously ), to simplify the notations.

Given the network of syntagmatic relationship f, g and , the unfolded sequence of morphological elements can now be written :

The use of the identity function (id) for f and/or g on some layers is rather frequent and leads to typical patterns. Let's therefore consider the special (id-or-new) case when one of the relations f or g within the system is either id or new, and let's denote as b, c (and later d), distinct elements from a (and from one another).

Generating all S&C based on a id-or-new network of functions yields the following 8 patterns (two of which being particular cases of the others, where c = a) : The patterns listed in table I indeed correspond to configurations frequently observed in music pieces, especially in pop music, at typical scales between 8-10 seconds up to 25-30 seconds.

f
These particular patterns turn out to be very easy to detect, as identity (or "close-to-id") is undoubtedly the most easily deducible function within a S&C, whichever musical information layer is involved.

Seven other patterns can be obtained as the combination of 2 to 4 distinct elements (see Table II). Three of them are analyzable as contrastive S&Cs, whereas the other four may happen to be constrastive or non-contrastive, depending on the actual relationship of the last element with the other ones : for instance, in abbc, it depends on whether there exist a simple function which relates c to b in the same way as b is related to a.

Patterns of tables I and II can easily be generalized to "close-to-id" (quasi repetition) or to "begins-like", which are very frequent relations between morphological elements, such as aaa'b, aba'c, aa'bc, etc…

Constrastive or non-contrastive Contrastive

new a  b new a  b abbc (abba) abbb new a  b new a  c abcd (abca) abcb, abcc
Table II : list of secondary morpho-syntagmatic patterns obtained as combinations of 2 to 4 distinct elements Note also that in the particular case when , the sequence of carrier morphological elements forms a regular progression :

which can be inflected in the last position by applying the function new as a contrast to , thus yielding a 1 a 2 a 3 b.

It therefore becomes clear at this stage that the S&C model is able to encompass a wide variety of well-know morphosyntagmatic patterns under a unifying (and simple) framework.

Correspondence with musicological concepts

Clearly, there is a direct conceptual connection between the S&C model and the carrure as mentioned by Fetis [START_REF] Fetis | La musique mise à portée de tout le monde[END_REF] and used extensively by Mozart. Also, the contrast (as defined here within the S&C model) can be viewed as an element that punctuates and concludes the flow of a musical segment, thus constituting some sort of morpho-syntagmatic cadence. Furthermore, Schoenberg [START_REF] Schoenberg | Fundamentals of Music Composition[END_REF], and after him Caplin [START_REF] Caplin | Classical Form : A Theory of Formal Functions for the Instrumental Music of Haydn, Mozart, and Beethoven[END_REF], define two types of structural segments, referred to (by Caplin) as formal types : the period and the sentence. Both types are normatively 8-bar segments, even though they may last 16 or even 32 bars. They begin with what Schoenberg calls a "two-measure phrase" (Caplin, a "two-measure idea", or a "basic idea"), which occupies the first quarter of the segment (typically our morphological element).

The difference between the period and the sentence lies in the way the repetition of the basic idea is handled.

 In sentences, the basic idea is repeated immediately so it is presented twice in a row, forming what Caplin calls the presentation. The second part of the sentence, the continuation, can either be the result of transformations (or formal processes)1 of the presentation, or the presentation of new ideas (cf. function new).

 The period differs from the sentence in the postponement of the repetition. This is done using the introduction of what Caplin calls a "contrasting idea2 " between the two occurrences of the basic idea, which normatively lasts a quarter of a period. The first half of the period is called the antecedent, and the second half the consequent.

A period may therefore normatively be written as abac, with c being unspecified. As for the sentence, it may be written as aabc, with both b and c being unspecified.

It is altogether extremely positive to note that the S&C model encompasses, under a single framework, the two major formal types of musical segment constructions identified by expert musicologists and musicians and extends them further.

Figure 6 illustrates a variety of S&Cs analyzed on 3 passages of pieces from different music genres.

EXTENSIONS TO NON-SQUARE SYSTEMS

Up to this point, focus has been put on systems composed of 4 elements, which constitute some sort of canonical configuration (which we will codify, by rendering its matrix shape, as .

However, the principles behind the square S&C model can be extended to non-square configurations so as to enable the analysis of configurations of fewer (2, 3) or more (5, 6, …) morphological elements. This is what we discuss in this section.

Dyadic systems

Even if we consider a timescale where structural blocks are typically composed of 4 morphological elements, there happens to be, at that timescale, segments with systems consisting of 2 elements, which we call dyadic (and codify as ). They usually appear either as a repetition aa or a difference ab and they can be analysed as a square S&C at the immediately lower half-scale.

The immediate repetition of a dyadic system forms naturally a non-constrastive square system : aaaa or abab and this situation is frequent in some types of pop music. Such situations can be codified as a shape.

Triadic systems

Triadic systems can be viewed as a singular class of square systems where function g (and the corresponding morphological element ) is missing. The typical triadic carrier system can be written as : and its contrastive form is

, where z = . Its shape can be codified as .

In particular z can be close-to-identity variants of a or (i.e, or ), yielding aba or abb triadic patterns. Note also that, if (but is not), one obtains the pattern aab.

Truncated square systems

Some triadic segments can also be analyzed as particular cases of square systems. Those correspond to situations where the segment can be understood as the realization of a square system for which the contrastive function is the "delete" function.

This yields a sequence of morphological elements which can be denoted as :

, where denotes the total absence of musical substance (i.e. not even "silence", but "what comes next in the piece", i.e. typically, the beginning of a new system). The inner organization of truncated square systems can be codified as .

Pentadic systems

Pentadic systems (i.e. systems formed of 5 morphological elements) are, in practice, very common in music. However, this is not in contradiction with the use of a square model. Indeed, pentadic systems can be reduced to a square system (stem) enriched by the insertion of an additional element (which we call affix). The affix can be either the (near-)repetition of one element of the system, or the importation (usually in 4 th position) of a completely new element, before the actual contrast.

Hexadic systems

In their general form, hexadic systems are defined on the basis of 3 syntagmatic functions f, g and h, and they can be viewed as rectangular rather than square. Two categories of rectangular carrier systems must be distinguished depending on which way they decompose, but some other hexadic forms are better explained as a square S&C in which a double infix is nested, itself forming an independent dyadic system ( (see table IV).

Formalization Shape ( ) ( ) ( ) ( ) ( )
Table IV : S&C formalization of hexadic carrier systems

Larger systems

Heptadic segments can be analyzed as various affixed versions of square or rectangular systems : , , …

Quite naturally, octadic (cubic) and nonadic systems usually shape as and respectively, the former being quite common, while the latter, very rare.

CONCLUSIONS

The S&C model offers a powerful formalism for defining and characterizing structural segments. It accommodates the diversity of musical substance with versatility and shows polymorphism by being able to explain a wide variety of morphological forms under a unified framework.

The S&C model is used as one of the key concepts to produce structural annotations of a database of 500 music pieces (segment boundaries and labels) [9] : in [START_REF] Bimbot | Semiotic Structure Labeling of Music Pieces : Concepts, Methods and Annotation Conventions, to appear[END_REF], we illustrate how the detection of a multi-layer network of syntagmatic functions constitutes a decisive cue for identifying segment boundaries, and how the distinctive properties of two S&C offer a relevant criterion for the determination of segment labels.

In automatic MIR, the S&C model is expected to lead to new algorithms for automatic structure extraction. It is also bound to be a base for the design of new music language models, which would model separately the morphological elements and the syntagmatic networks, thus providing powerful generalization capabilities.

Beyond MIR, the S&C model may also exhibit great potential in computer-assisted musical creation and composition, as well as in music education and teaching.

Figure 1 :

 1 Figure 1 : Four examples of square systems

Figure 2 :

 2 Figure 2 : Four incomplete square systems

Figure 3 :

 3 Figure 3 : examples of various contrasts, based on the same carrier system Figure 3 illustrates several configurations where the contrastive property varies over the same baseline square system, which we call carrier system.

Figure 5 :

 5 Figure 5 : diagram illustrating the S&C network corresponding to the most frequent pentadic systems

Table

  III inventories the typologies of pentadic systems and figure5illustrates S&C networks for a few of them.

	Configuration	Contrastive form	Shape codification
	Prefix
	Suffix
	Delayed contrast
	Redundant infix
	Extraneous infix

Table III :

 III inventory of contrastive configurations of pentadic system (derived from square stems)

This resonates well with our concept of syntagmatic function.

In the present report, the "contrasting idea" does not strictly correspond to a contrast, but to an opposition.

Acknowledgements

Part of this work was achieved in the context of the QUAERO project, funded by OSEO.

MUSICAL EXAMPLES

EXAMPLE II Nirvana, Smells like Teen Spirit ("Nevermind", Mobile Fidelity Sound Lab 1991), first verse (00:33-00:50) EXAMPLE III Sean Kingston, Take you there ("Sean Kingston", Epic International 2007), first verse (00:16-00:33) In these examples, various systems co-exist on several musical layers at a time and they participate to the morpho-syntagmatic consistency of the segment. Ex. 1 mainly exhibits an abac system on the melodic and harmonic layers. Ex. 2 is based on the superposition of three carrier systems aabb (rhymes), abab (vocal line) and aaaa (chords), while the drum loops forms the sole contrastive system : aaab. Ex. 3 illustrates a case where the contrast is produced by the vocal layout (schematically represented on the right-hand side of the contrast table) while all other musical layers (melodic line, harmony, etc…) are non-contrastive at that timescale. Note however that the lyrics (left-hand side of the contrast table) form an abcb pattern which can be viewed as a secondary form of S&C.


Mathieu Laurencin

Baptiste Legrand

Emilie Duval

Joël L Henry

Michèle Baudy-Floc'h
email: <michele.baudyfloch@univ-rennes1.fr

Céline Zatylny-Gaudin

Arnaud Bondon

Mich Le Baudy-Floc

' , C Line Zatylny-Gaudin

From a marine neuropeptide to antimicrobial pseudopeptides containing

Keywords: Amino Acids, chemical synthesis, chemistry, pharmacology, Animals, Anti-Bacterial Agents, chemical synthesis, chemistry, pharmacology, Antimicrobial Cationic Peptides, chemistry, Aza Compounds, chemical synthesis, chemistry, pharmacology, CHO Cells, Circular Dichroism, Cricetinae, Cricetulus, Gram-Negative Bacteria, drug effects, Gram-Positive Bacteria, drug effects, Hemolysis, Magnetic Resonance Spectroscopy, Microbial Sensitivity Tests, Models, Molecular, Molecular Conformation, Neuropeptides, chemical synthesis, chemistry, pharmacology, Oligopeptides, chemical synthesis, chemistry, pharmacology, Rabbits, Stereoisomerism, Structure-Activity Relationship

Introduction

Antimicrobial -peptides (AMPs) are natural occurring peptides that play essential roles in the host innate defense of wide array of α organisms and represent one of the major anti-infectious agents against bacterial pathogens. 1 5 At this time, databases report over 1000 [ -] sequences for natural AMPs ( ), whereas several thousand others have been designed http://www.bbcm.units.it/~tossi/amsdb.html de novo and produced synthetically. [START_REF] Shai | Mode of action of membrane active antimicrobial peptides[END_REF] Although they differ widely in sequence, AMPs are usually short (12 50 residues) with hydrophobic and [ ] cationic residues, spatially segregated in amphipathic structures. Many AMPs kill microorganisms by permeabilization of the cytoplasmic membrane whereas others penetrate into the cell and target additional anionic intracytoplasmic constituents (e.g., DNA, RNA, proteins, or cell wall components). [START_REF] Brogden | Antimicrobial peptides: pore formers or metabolic inhibitors in bacteria?[END_REF] These mechanisms of action require an interaction with the cell membrane and numerous interaction models have

[ ]
been proposed, including the barrel-stave pore, 2 the toroidal pore, 8 the carpet like, 2 the aggregate 9 and the detergent like models. 10,11

[ ] [ ] [ ] [ ] [

] Due to the low degree of selectivity between microbial and host cells, and the vulnerability of peptides to the rapid degradation, in vivo

AMPs have yet to see widespread clinical use. [START_REF] Hancock | Antimicrobial and host-defense peptides as new anti-infective therapeutic strategies[END_REF] Therefore, a strategy to improve the activity, selectivity and bioavailability of natural peptides is to design pseudopeptides. Recently, numerous peptidomimetics have been developed in this field of biological application including -peptides, 12 14 peptoids, 15 17 -peptoids, 18,19 oligoureas 20 and in this work antimicrobial properties of aza--amino

β [ -] [ -]β [ ] [ ] β 3
acids-containing pseudopeptides are investigated.

We try to improve the biological activity of a natural occurring AMP using aza--amino acids which are known to enhance the

β 3
bioavailability of biological active peptides, notably for immunological applications. [START_REF] Dali | Heteroclitic properties of mixed alpha-and aza-beta3-peptides mimicking a supradominant CD4 T cell epitope presented by nucleosome[END_REF] These monomers are aza analogs of

[ ] β 3
-aminoacids in which the CH is replaced by a nitrogen stereocenter atom. This confers a better flexibility to the pseudopeptide due to the β side chain attached to a chiral nitrogen atom with non-fixed configuration. [START_REF] Cheguillaume | Solution synthesis and characterization of hydrazinopeptoidic oligomers[END_REF] The nonnatural oligomers have an extended conformational

[ ]
space and are supposed to adopt non-canonical secondary structures. To date, no structures of peptides containing aza--amino acids in

β 3
solution have been determined. The X-ray crystal structures of linear and macrocyclic aza--peptides have been solved and exhibit an

β 3
internal hydrogen-bond network leading to bifidic eight-membered ring pseudocycles, called N-N turn or hydrazino turn. [START_REF] Grel | Aza-beta3-cyclohexapeptides: pseudopeptidic macrocycles with interesting conformational and configurational properties slow pyramidal nitrogen inversion in 24-membered rings ![END_REF] 25 Recently, [ -] it was demonstrated that the nitrogen configuration inversion could be fixed, by incorporating chiral monomers among heteromacrocyles. [START_REF] Mocquet | Aza-beta3-cyclopeptides: a new way of controlling nitrogen chirality[END_REF] Seawater contain many invading microorganisms (up to 10 bacteria/mL and 10 virus/mL) and marine invertebrates have a large 6 9 number of AMPs. [START_REF] Henry | Peptidergic control of egg-laying in the cephalopod Sepia officinalis: involvement of FMRFamide and FMRFamide-related peptides[END_REF] . It was reported that some neuropeptides or peptidic hormones display structural similarities with antimicrobial [ ] peptides and exhibit antimicrobial activities. [START_REF] Brogden | The nervous system and innate immunity: the neuropeptide connection[END_REF] First, we identified a short neuropeptide, H-ALSGDAFLRF-NH (AD) of the cuttlefish [ ]

2

, belonging to the FMRF-amide-related peptides (FaRPs), involved in control of chromatophores and reproductive Sepia officinalis functions in cuttlefish. [START_REF] Henry | Peptidergic control of egg-laying in the cephalopod Sepia officinalis: involvement of FMRFamide and FMRFamide-related peptides[END_REF] The decapeptide AD has a weak antimicrobial activity and a very low cytotoxicity on mammalian cells and [ ] constitutes a suitable template to study the impact of the incorporation of aza--amino acids on the antimicrobial activity of an AMP.

β 3
Then, a large range of -Fmoc-aza--amino acids with proteinogenic and non-proteinogenic side chains have been synthesized to be N

β 3
incorporated into peptide sequences via solid-phase peptide synthesis (SPPS). [START_REF] Busnel | Preparation of new monomers aza-beta 3-amino acids for solid-phase syntheses of aza-beta 3-peptides[END_REF] 32 Finally, all synthesized peptides and pseudopeptides [ -] are tested on various Gram-positive and Gram-negative bacteria including marine bacteria classically encountered by the cuttlefish and typical human pathogens and their structures are determined by NMR.

Substitutions of -amino acids by aza--amino acids induce a strong improvement or, in contrast a complete loss of the antimicrobial

α β 3
activity of this marine neuropeptide. We found that the AD or AK (H-ALSGKAFLRF-NH ) C-terminal amphiphilic helical moiety in 2 SDS micelles is destabilized by the aza-residues incorporation and can tentatively rationalize the structure-activity relationship of the

β 3
studied peptides and pseudopeptides.

Results and Discussion

Design of antimicrobial analogs

The neuropeptide AD possesses a net charge of 1 at physiological pH. Antimicrobial activity can often be improved upon increasing + the peptide positive net charge as a result of enhancing the electrostatic interactions with the negatively charged bacterial membranes.

Consequently, we chose first to replace the aspartic acid residue in position 5 by a lysine residue. This AD analog, noted AK, keeps the same hydrophobic ratio of 50 but possesses a net charge of 3, at physiological pH, and an isoelectric point (pI) of 14, instead of 11 for The first pseudopeptide A K (H-ALSG-aza--K-AFLRF-NH ) is designed based on the AK, replacing a lysine in position 5 by an

β 3 β 3 2
aza--lysine. Then, one phenylalanine residue of the AK peptidic sequence is substituted by an aza--2-naphthylalanine (K-2Nal7:

β 3 β 3
H-ALSGKA-aza--2-Nal-LRF-NH ), which displays good antimicrobial activities (Table 1). As a result, this led us to synthesize two phenylalanine by aza--naphthylalanine residues has already been reported to improve antimicrobial activities with a therapeutic containing naphthylalanine amino acid are classically more hemolytic with regard to the parent peptides. Indeed, this residue is already known to enhance the interaction of antimicrobial peptides with the lipid bilayers, 36 as their aromatic nucleus structurally close to the [ ] hydrophobic indole nucleus, can promote the AMPs burying within the hydrophobic core of the lipid bilayer.

Antibacterial activities

In screening experiment, antibacterial activity was assayed against a representative set of Gram-positive and Gram-negative bacteria (Table 1). The results allow us to compare the antibacterial activities of these analogs with the endogenous peptide AD. Ampicillin, a common antibiotic, serves as a positive control. The neuropeptide AD possesses a narrow-spectrum antibacterial activity and acts more particularly on marine bacteria of the genus with relatively high MICs (> 320 g.mL ). Indeed, its MICs are widely superior to Vibrio μ 1 other marine antimicrobial peptides so it is unlikely that this marine neuropeptide is responsible for the cuttlefish s innate immunity. properties may result from the close structural resemblance between short neuropeptides and AMPs.

As expected, the simple D5>K substitution considerably improves the antibacterial activity of the natural peptide. The peptide AK possesses a larger antibacterial spectrum than native AD. AK is active on all Gram-negative bacteria tested and becomes active on S.

V. splendidus.

Our first attempt to design AMPs with aza--amino acids is unsuccessful since the pseudopeptide A K is inactive on all bacteria

β 3 β 3
except on These results demonstrate that the incorporation of aza--amino acid can switch off the biological activity. V. splendidus.

β 3
Interestingly, the side chains being similar for AK and A K, the loss of activity is exclusively related with the backbone atom variation Fortunately, in contrast to A K, the three other synthesized pseudopeptides, K-2Nal7, K-1Nal and K-2Nal, exhibit very broad and 40 g.mL against . Surprisingly, K-2Nal, which contains also two aza--naphthylalanine residues in position 7 and aureus,

μ 1 - E. coli β 3
10, but aza--2-naphthylalanine instead of aza--1-naphthylalanine, exhibits large variations in antimicrobial activities when compared

β 3 β 3
to K1-Nal, as the MICs of K-2Nal are always superior or equal to that of K-1Nal when considering the same bacterial strain. This result points out the possible fine tuning of the activity related to the macrocycle interaction with the bacterial walls. Concerning K-2Nal7, MICs are close to those of the K-1Nal and are better than those of K-2Nal. Finally, considering the four studied marine bacteria, we observe this time that K-1Nal and K2-Nal antimicrobial activities are globally similar but not better than AD and AK while K-2Nal7 exhibits the lowest MICs for all the tested marine bacteria. Interestingly, whereas no antimicrobial activities improvement has been measured for K-1Nal and K2-Nal when compared to AK, K-2Nal7 has MICs much lower than AK. These good activities are encountered for all the four marine bacteria and are even better than those of ampicilline against and .

V. harveyi V. alginolyticus

Hemolytic activity and cytotoxicity of analogs in vitro

The hemolytic activities are measured on rabbit erythrocytes (Figure 1) and the peptide cytotoxicities are determined on Chinese Hamster Ovary ( -) cell (Figure 2). No significant hemolytic activity (<1,5 ) of AK is observed for concentrations up to 320 CHO K1 line % μ g.mL and very low cytotoxicity is measured up to 640 g.mL with 87 of viability indicating a good selectivity for bacterial cells over

1 - μ 1 - %
mammalian cells. The pseudopeptide K-1Nal is hemolytic with a 50 hemolytic dose (HD ) close to 200 g.mL . This concentration is

% 50 μ 1 -
lower than some MICs but is ten times higher than MIC observed on the pathogen K-2Nal is less hemolytic than K-1Nal with S. aureus. only 14 of hemolysis at 320 g.mL . Concerning the cytotoxicity, at 640 g.mL of K-2Nal, we find 47 of cell viability while the

% μ 1 - μ 1 - %
K-1Nal appears to be highly toxic. For K-1Nal, the smallest doses (up to 40 g.mL ) are not cytotoxic to CHO-K1 cells, slightly μ 1 cytotoxic (78 of viability) at 160 g.mL and toxic at 640 g.mL , but this later concentration is 8 times higher than its MICs against

% μ 1 - μ 1 -
human pathogens and and 32 times higher than its MICs against As often observed, the L. monocytogenes S. typhimurium S. aureus.

improvement of the antimicrobial activity is associated with a decline of the selectivity between prokaryotic and eukaryotic cells. The presence of non proteinogenic naphthylalanine side chains seems to decrease the peptide selectivity 35 and notable differences appear

[ ]
between K-1Nal and K-2Nal demonstrating that physico-chemical parameters such as the orientation of the aromatic naphthylalanine moieties have a great influence on the biological activities and selectivity. It has also been pointed out that K-2Nal7 which contains one naphthylalanine side chain displays only very weak hemolytic (5 at 320 g.mL ) or cytotoxic (87 of viability at 640 g.mL ). These

% μ 1 - % μ 1 -
behaviors, very similar to those of the a-peptide AK, support the idea that naphthylalanine residue do not induced a systematic cell selectivity decrease.

Circular dichroism analysis

The CD spectra of the endogenous peptide AD and its analog AK are similar, in agreement with an identical structural behavior in several media (Figure 3A). They present a random coil CD profile in phosphate buffer (10 mM KP, pH 7.4) and a typical helical signature in hydrophobic environments. Indeed, in 50 TFE or in the presence of SDS micelles, the CD spectra exhibit a maximum at 190 nm and % two minima towards 208 and 222 nm showing that AD and AK adopt to some extent a well-defined helical character in these two lipid membranes mimicking media. Nevertheless, we notice that these short peptides (10 residues) cannot form more than one to two helix turns (3.6 residues per turn).

Interestingly the A K displays a random profile in phosphate buffer, but an atypical CD profile in the presence of micelles of SDS

β 3
with a thin minimum at 202 nm (Figure 3B), which may be attributed to the presence of turns within the peptidic backbone. The extinction of the activity of A K may be caused by the loss of helicity in membrane mimicking media due to the incorporation of the aza--K in

β 3 β 3
position 5. K-2Nal7 exhibits a similar profile to that of A K and no helical conformation can be detected (Figure 3B). In the case of

β 3
pseudopeptides K-1Nal and K-2Nal (Figures 3C and3D), interpretation of the CD spectra is difficult due to the strong absorbance of the aromatic nuclei of aza--naphthylalanine residues that perturbs their CD profiles. Nevertheless, the pseudopeptides K-1Nal and K-2Nal wavelength around 225 nm is related with the B transition of a naphthalene group in presence of SDS micelles. Two other residues along 1 b its long axis separate the aromatic nuclei of the aza--naphthylalanine residues. This CD spectrum suggests a distance between the

β 3
aromatic residues that is short enough to allow dipole-dipole interaction. This interpretation is further supported by a similar spectrum when studying the K-2Nal pseudopeptide in the presence of SDS micelles. Dathe and coworkers obtained the same type of CD profiles with cyclic antimicrobial hexapeptide RNal ( -R-R-1Nal-1Nal-R-F-) in contact with SDS micelles or POPG Small Unilamellar cyclo[ ] Vesicles (SUVs). [START_REF] Dathe | Cyclization increases the antimicrobial activity and selectivity of arginine-and tryptophan-containing hexapeptides[END_REF] This cyclopeptide contains two -L-naphthylalanine residues and exhibits, in membrane like environment (micelles

[ ] α
or SUVs), a CD spectrum displaying a couplet centered at 227 nm with a maximum of positive ellipticity at 222 nm and a maximum of negative ellipticity at 232 nm. [START_REF] Dathe | Cyclization increases the antimicrobial activity and selectivity of arginine-and tryptophan-containing hexapeptides[END_REF] It is important to notice that this type of couplet is inverted in the case of an antimicrobial D-peptide

NMR experiments and structure calculations

Since the CD spectra revealed that the five peptides AD, AK, A K, K-2Nal7 and K-2Nal could adopt particular conformations in

β 3
presence of SDS micelles, NMR structural studies are performed in aqueous solution with SDS detergent. In the case of A K, K-2Nal7

β 3
and K-2Nal, as the aza--amino acids side chain attached to an unprotonated nitrogen atom no classical spin systems through

β 3
magnetization transfer from the amidic proton can be seen in the TOCSY spectra. However, starting from the typical amide proton singlet near 9 ppm of the aza--residue, we can easily identify the side chain proton resonance of the aza-residues on the NOESY spectra.

β 3 β 3
Then the strong NOEs between H of the aza-residues and the amide proton of the previous amino acid allow us to perform the α β 3 sequential assignment. The peptide resonances are reported in the supplementary Table S1.

Where possible, NOEs are assigned based on unambiguous chemical shift assignments, but due to chemical shift overlap, ambiguous NOEs are also incorporated and used by ARIA. In the final ARIA run, the AD structure is calculated using 147 distance restraints and 5 dihedral restraints for the Leu2, Asp5, Ala6, Leu8 and Arg9 residues. At the last iteration, 60 structures are refined in a shell of water, the 20 lowest energy conformers with no distance violations > 0.3 and a good stereochemical quality are represented in Figure 4. The global Å fold of AD in SDS micelles displays a disordered N-terminal domain and a well-defined helical encompassing residues 5 to10. Indeed, the backbone RMSD on the whole structure is 1.312 and fall to 0.163 if the poorly defined N-terminal moiety is ignored (see

Å Å
supplementary Table S2). This peculiarity is similar to structural features of other short neuropeptides belonging to the tachykinin family.[ 40 In addition, the AD structure is amphipathic, displayed in Figure 4A, which shows the polar residues Asp5 and Arg9 aligned on the ] same side of the helix turn and at the opposite side, a large hydrophobic surface composed of the Ala6, Phe7, Leu8 and Phe10. Then, to solve the AK structure, 170 distance restraints and 5 dihedral restraints (Lys5, Leu6, Phe7, Leu8, Arg9) are used in the final iteration of ARIA. The proton chemical shifts of AK are very close to those of AD and, as expected, the global fold of AK (Figure 4B) is similar to the AD structure with a disordered N-terminal moiety and a well-defined helical turn from Lys5 to Phe10 (Figure 5). Consequently, the effect of the mutation D5K on the neuropeptide structure is very slight and do not alter its amphipathic property.

NMR solution structure of A K is clearly different than AD and AK peptides. The stereochemistry of the nitrogen bearing the side

β 3
chain of the aza-residue is not fixed, thus the configuration of the stereocenter of the aza--Lys5 is not fixed in our dedicated CNS

β 3 β 3
topology and parameter files. The final restraint file of A K comprises a set of 213 distance restraints and 3 dihedral restraints. Despite a

β 3
unique set of signals, we notice in the 20 lowest energy selected structures, two conformations according to the configuration R or S of the stereocenter of the aza--Lys5. Respectively, 15 and 5 structures are composed with a R-and a S-aza--Lys5. The A K NOESY N

β 3 β 3 β 3
spectrum exhibits 20 more NOE peaks and as opposed to the AD and AK structures, the backbone of the A K peptide is quite

% β 3
well-defined all along the sequence (Figures 4 and5). Moreover, its global fold is very different and does not exhibit a helical character in contrast to the two a-peptides AD and AK. We observe, in Figure 6, that the introduction of the aza--Lys induces a hydrazino turn or (Supplementary material, Table S3). Interestingly, this particular turn is surrounded by two -turns composed of the residues 2-5 and 5-8

β
on each side of the hydrazino turn (Figure 6). They are stabilized by hydrogen bonds between the carbonyl of Leu2 and amide protons of To our knowledge, this work describes the first NMR three-dimensional structure of pseudopeptides including aza--residue in an β 3 aqueous medium. The presence of two sets of structure with the R and S configuration of the aza--lysine does not necessary mean that

β 3
the two populations can be found in solution but reflect the fact that the distance restraints used in the NMR structure calculations can be satisfied by the R and S configuration.

The AD and AK well-ordered helix moieties are dramatically modified by the incorporation of only one aza--residue which induces

β 3
a loss of the amphipathic properties. This amphipathic character can be associated with the antimicrobial peptide activities of AD and AK.

For the peptides K-2Nal7 and K-2Nal, only their C-terminal moieties are ordered forming -turn in contrast with the helical structure of β the -peptides AD and AK (Figures 4D,4E). They share a similar turn, which slightly approaches the two hydrophobic aromatic residues α in position 7 and 10. Nevertheless, the aromatic rings are too far to affect each other (~9 ) in agreement with the absence of NOEs Å between the residues 7 and 10 aromatic protons. NMR 2D-NOESY spectra of the pseudopeptides K-2Nal7 and K-2Nal in SDS micelles display less NOEs comparing to the three other peptides pointing out the relative flexibility of these pseudopeptides. Surprisingly, the hydrazino turn NOE markers previously noticed on the A K NOESY spectrum cannot be detected for these pseudopeptides and the

β 3
K-2Nal7 and K-2Nal structures do not exhibit a hydrazino turn.

Overall, structural characterization of the -peptides and the pseudopeptides permits us to study the influence of the aza-residue.

α β 3
The D5K substitution does not cause any loss of the helix encountered with the native neuropeptide, for both peptides the amphipathic character is conserved. All the introductions of aza-residue induce drastic structural modification, especially in the case of A K with a

β 3 β 3
well-defined structure along all the sequence. This rigidity has to be related with the disappearance of any antibacterial activity. In the case of aza--naphthylalanine derivatives only the C-terminal moieties are well-defined adopting a -turn but the remaining of the peptides

Conclusion

This article reports the first observation of antibacterial activity for a modified marine invertebrate neuropeptide. CD and NMR data show that this peptide adopts an amphiphilic -helical conformation in a hydrophobic medium as seen for the majority of natural α antimicrobial peptides. The importance of the cationic net charge is demonstrated by the improvement of the antibacterial activity due to a simple substitution of aspartic acid to lysine without affecting the secondary structure. On the other hand, the incorporation of only one aza--amino acid can lead to a drastic rearrangement of the peptidic backbone resulting in a rigid structure and the loss of antibacterial

β 3
activity. However the first three-dimensional structure of a pseudopeptide with a heterogeneous backbone containing an aza--amino acid

β 3
was solved in aqueous micellar environment and this structure provided essential information on the impact of aza--residues

β 3
incorporation in peptidic sequences. Interestingly, the two more biologically active pseudopeptides do not display helical character in contrast to AD/AK peptides and appear to be less structurally defined than the A K pseudopeptide.

β 3
Finally, as it was recently reported for heterogenous helical urea/amide backbones, 42 mixed pseudopeptides containing -and aza-

[ ]" " α β
-amino acids appear as a promising therapeutic tool to fight multiresistant bacteria. The present work demonstrates that aza--amino

Experimental Section

Peptides and Pseudopeptides Synthesis

Peptides (AD and AK) and the pseudopeptide A K were synthesized on an Advanced Chem Tech 440 Mos synthesizer .

β 3 ®
Pseudopeptides K-2Nal7, K-1Nal and K-2Nal were synthesized on a Pioneer Peptide Synthesis System . Synthesis was accomplished ® using commercially available -Fmoc-amino acid, -Fmoc-aza--amino acid 29 32 and a Rink Amide resin. Peptides were synthesized N N

β 3 [ -]
via Fmoc solid phase synthesis methods using a 4-fold excess of amino acid, TBTU, and HOBt in the presence of a 8-fold excess of DIPEA for 1 h for standard residues and 2 h for aza-residues. The Fmoc group was removed with 20 piperidine in DMF for 10 min.

β 3 %
At the end of the synthesis, the resin was washed with CH Cl and dried. Side chain deprotection and cleavage of peptides from the resin 2 2

were performed simultaneously by treatment with TFA/ H O/TIS (95/2.5/2.5, v/v/v) for 3h. After filtration of the resin, the TFA solutions 2 were concentrated in vacuo and peptides were precipitated by addition of cold diethyl ether. Peptides were purified by RP-HPLC on a C18

XTerra semi-preparative column (10 m, 19 mm 300 mm, Waters) with a linear gradient of water, 0.08 TFA (A)/acetonitrile, 1

® μ × % % TFA (B) (5

Antibacterial assays

The antibacterial activity of peptides was measured by liquid growth inhibition assay, performed in 96-wells microtiter plates.

% % %

The experiments were set in triplicate.

Hemolytic activity

The hemolytic activity of analogs was determined with freshly isolated rabbit erythrocytes as already describe. [START_REF] Duval | KKKKPLFGLFFGLF: a cationic peptide designed to exert antibacterial activity[END_REF] Erythrocytes measuring the optical density of the supernatant at 415 nm. Zero hemolysis (blank) and 100 hemolysis were determined in PBS buffer % and 1 Triton X-100, respectively. For each concentration and control, the experiments were set in triplicate.

%

Circular dichroism

CD experiments were carried out using a JASCO J-815 spectropolarimeter (Easton, USA) equipped with Peltier devices for temperature control. All of the spectra were obtained with a quartz cell of 0.2 mm path length. Spectra were recorded at a peptide concentration of 100 mM in different environments: water, phosphate buffer 10 mM, in 50 TFE, in presence of SDS detergent (30 mM).

%

The baseline-corrected spectra were smoothed, ellipticities were converted to mean residue molar ellipticities in degree cm . assess the stereochemical quality of the structures. The calculations were initiated using the default parameters of ARIA and a nearly complete set of manually assigned NOE. The CNS 52 and ARIA topology and parameter files were modified to define the aza-residues N inversion, the stereochemistry of the nitrogen bearing the side chain of the aza-residues is not fixed. The torsion angle was restrained

β 3 ϕ
to 60 40 for < 6 Hz. At the end of each run, violations and assignment proposed by ARIA were checked before starting a new -± °3 J HN-HA run. This process was repeated until all the NOE were correctly assigned and no restraints were rejected. A last run of 60 structures was performed and refined in water, a set of 20 structures of lowest energies with no violation > 0.3 were considered as representative of the Å peptide structure. configurations of the aza--lysine and the aza--naphtylalanine, respectively. The superposition was performed using the backbone atoms

β 3 β 3
of residues 5 10. For clarity, the side chains of residues 1 4 are not drawn. The backbone of all structures is shown in black while the side -chains of the Phe residues are displayed in red, the Asp or Lys residues in green, the Ala residues in orange, the Leu residues in purple, and the Arg residues in blue.

Figure 5

The best structures (with the lowest energies) of AD (green), AK (cyan), A K (yellow), K-2Nal7 (pink) and K-2Nal (grey). The side chains

β 3
of the polar and hydrophobic residues are respectively in blue and orange. Aza-residues snapshots are available for the A K and K-2Nal7

β 3 β 3
peptides (see also Table S2).

3 synthesized .

 3. , based on the AK sequence, four pseudopeptides containing standard -amino acids and aza--residues are α β Substitution of -amino acids by aza--amino acids prevents stereochemical constraints and may contribute to enhance

β 3 2

 3 new pseudopeptides (K-1Nal: H-ALSGKA-aza--1-Nal-LR-aza -1-Nal-NH and K-2Nal: H-ALSGKA-aza--2-Nal-LR-aza-Nal-NH ) based on the template where both phenylalanine residues are replaced by aza--naphthylalanine. Substitution of 2 β 3

  For

'

  example, the defensin MGD-1 of exhibit MICs that are inferior by 25 to 100 times. 37 The AD antibacterial Mytilus galloprovincialis [ ]

  -naphthylalanine residues. D-Nal-Pac-525 ( -k-nal-r-r-nal-v-r-nal-i-) in the presence of phospholipids or micelles β Ac NH displays the same type of couplet centered towards 225 nm but with opposite sign for the maxima (a positive ellipticity maximum at 229 nm and a negative maximum at 220 nm). 35 In the case of our pseudopeptides, the aromatic side chains are carried by chiral nitrogen [ ]atoms with a non-fixed configuration. Thus, CD spectra of pseudopeptides in SDS micelles seem to indicate that the side chains are preferentially positioned in an orientation similar to -naphthylalanine with L configuration (absolute configuration S). Moreover, K-2Nal α CD spectra, in the presence of SDS micelles (reported in Figure3D), show a strong temperature dependence. An increase in temperature results in a strong decrease in the intensities of the CD ellipticity maxima, possibly related to a fluctuation of the distance between the aromatic rings due to the thermal motion or rapid inversion of the nitrogen stereochemistry.

β 3 N

 3 -N turn which has been previously shown in CDCl and described in aza--peptide crystal structures.[START_REF] Grel | Aza-beta3-cyclohexapeptides: pseudopeptidic macrocycles with interesting conformational and configurational properties slow pyramidal nitrogen inversion in 24-membered rings ![END_REF][START_REF] Salaun | Crystal structures of aza-beta3-peptides, a new class of foldamers relying on a framework of hydrazinoturns[END_REF][START_REF] Salaun | Aza-beta3-cyclotetrapeptides[END_REF] The amide proton of Leu6 3 β 3 [ ] is H-bonded with both the lone pair of the sp nitrogen atom of the aza--Lys5 (6.HN-5.N 2.33 ) and the carbonyl of Gly4 3 β 3 α = Å (6.HN-4.CO 1.81 ). We have also measured four characteristic torsional angles , , and for the R-and the S-hydrazino turn = Å ω ϕ θ ψ

Gly4 (2.O- 4 .

 4 HN 1.83 ) and aza--Lys5 (2.O-5.HN 2.31 ), and the carbonyl of aza--Lys5 and amide protons of Phe7 (5.O-7.HN and Leu8 (5.O-8.HN 2.33 ). This specific folding feature is particularly stable and strong NOEs peaks can be detected on the = Å = Å NOESY spectrum between the amide protons 2.HN-3.HN, 4.HN-5.HN, 7.HN-8.HN, 9.HN-10.HN.

β 3 β

 3 display large flexibility. This flexibility, along with the properties of the naphthylalanine side chains, is related to the increase in the antimicrobial activities. Such an observation is consistent with the hypothesis that peptide structural flexibility improves ntimicrobial activity. 41 [ ]

3 β 3 acid

 33 can modify pseudopeptide structures and modulate the biological activities depending on the number and the position of the substitutions.

43

 43

1 -

 1 Microbial growth was assessed by measurement of the optical density at after the 20 h incubation at 30 C or 18 C for . The D °°Vibrios minimal inhibitory concentration (MIC) is defined as the lowest concentration required to inhibite growth (100 inhibition). The bacteria % species tested were the Gram-positive , tests, distilled water is used to dissolve peptides. Briefly, 10 aestuarianus V. alginolyticus V. harveyi V. splendidus) l of water or 10 l of peptide solution at a final concentration ranging from 20 to 640 g.mL , were incubated with 100 l of a growth phase culture of bacteria at a starting optical density of 0.001. Poor-broth nutrient medium (PB: 1 peptone, D = % 0.5 NaCl, w/v, pH 7.5) was used for standard bacterial culture. Pathogenic bacteria were grown in PB with 0.3 of beef extract (BD) or % % in brain heart infusion for and were grown in Saline PB (SPB: 1 peptone, 1.5 NaCl, w/v, pH 7.2). Enterococcus Listeria. Vibrios % % Cytotoxicity assay Cytotoxicity of peptides on CHO-K1 cells were determined by the colorimetric MTT (3-4,5-dimethylthiozol-2-yl [ ] -2,5-diphenyltetrazolium bromide) dye reduction assay. Briefly, 1.34 10 cells/well in Ham F12 supplemented with L-glutamine (Gibco) × 4 and 10 foetal calf serum (Eurobio) were placed into 96-well plates. After incubation for 6h under a fully humidified atmosphere of 95 % % room air and 5 CO at 37 C, analogs dissolved in phosphate buffered saline (PBS) were added to cell cultures at a final concentration % 2 °ranging from 20 to 640 g.mL . After 36-hours incubation, toxicity was evaluated by measuring the optical density of the culture at 570 μ nm using the cell growth determination kit (Sigma) based on conversion of the yellow tetrazolium salt MTT into purple formazan crystals by metabolically active cells. 100 of Viability and 0 of viability were determined in PBS buffer and 1 Triton X-100, respectively.

  incubated for 1 hour at 37 C with peptide dissolved in PBS to reach 20 at 320 g.mL . Hemolysis was determined by °μ 1 -

  characteristic angles and distances in the previously published crystalline structures.[START_REF] Grel | Aza-beta3-cyclohexapeptides: pseudopeptidic macrocycles with interesting conformational and configurational properties slow pyramidal nitrogen inversion in 24-membered rings ![END_REF] 25 According to the pyramidal[ -]

Figure 1

 1 Figure 1Hemolytic activity of analogs on rabbit erythrocytes.

Figure 2

 2 Figure 2 Cytotoxic activity of analogs on Chinese Hamster Ovarian cells (CHO-K1 cell line).

Figure 3

 3 Figure 3 CD spectra of peptides AD and AK (A), and pseudopeptides A K, K2-Nal7 (B), K-1Nal (C), temperature dependence of K-2Nal (D).

β 3 Buffer: 10

 310 mM Phosphate buffer, SDS: 30 mM SDS in buffer

Figure 4

 4 Figure 4The 20 lowest energy structures with no violations > 0.3 from the 60 structures calculated in the final iteration of ARIA for neuropeptide Å analogs in SDS micelles. (A) AD, (B) AK, the two set of structures of (C) A K, (D) K-2nal7 and (E) K-2Nal for the two possibleβ 3

Figure 6 (

 6 Figure 6 (A) The structural features of the A K. The carbon atoms of the R-hydrazino turn are displayed in green and the two -turn carbon atoms β 3 β involving the residue 2-5 and 5-8, surrounding this N-N turn, are respectively shown in cyan and in magenta, side chains have been removed for clarity. Hydrogen bonds are represented with dashed lines. (B) Distances and torsion angles in the hydrazino turn.

  calculated as the TFA salt (assuming association of one molecule of TFA per cationic residue, determined by C NMR). /mol. LC-ESI-MS/MS mass: found m/z 1095.27 M H , C H N O (without TFA) requires.1095.59. TFA 1286.0 g/mol. LC-ESI-MS/MS mass: found m/z 1173.70 M H ; C H N O .(without TFA) requires 1173.69.

	purified peptides by RP-HPLC analyses were performed on a C18 XTerra (4.6x250 mm, 5 m) column using water 0.08 TFA ® μ %
	(A)/acetonitrile, 1 TFA (B) linear gradient (5 60 B in 20 min, 1 ml/min, 30 C, 215nm). Peptide concentrations for all experiments % -% °were
						13
		H-ALSGDAFLRF-NH (AD): Yield after purification 26 ; white powder; RP-HPLC : 17.30 min; MWt C H N O .TFA 2 % t 51 79 14 13
	1208.6 g[ + + ] 51 79 14 13
		H-ALSGKAFLRF-NH (AK): Yield after purification 40 ; white powder; RP-HPLC : 16.93 min; MWt C H N O .TFA 2 % t 53 85 15 11
	1222.0 g/mol. LC-ESI-MS/MS mass: found m/z 1108.60 M H , C H N O (without TFA) requires 1108.66. [ + + ] 53 85 15 11
		H-ALSG-	aza--K β 3	-AFLRF-NH (A K): Yield after purification 18 ; white powder; RP-HPLC : 15.17 min; MWt C H N O 2 β 3 % t 53 86 16
	11	.TFA 1237.0g/mol. LC-ESI-MS/MS mass: found m/z 1123.65 M H ; C H N O (without TFA) requires 1123.67. [ + + ] 53 86 16 11
		H-ALSGKA-	aza--2Nal β 3	-LRF-NH (K2-Nal7): Yield after purification 58 ; white powder; RP-HPLC : 14.85 min; MWt C H 2 % t 57 88
	N O .16 11				[ + + ] 57 88 16 11
		H-ALSGKA-	aza--1Nal β 3	-LR-	aza--1Nal β 3	-NH (K1-Nal): Yield after purification 21 ; white powder; RP-HPLC : 19.13 min; 2 % t
	MWt C H N O .TFA 1352.1 g/mol. LC-ESI-MS/MS mass: found m/z 1238.65 M H ; C H N O (without TFA) requires 61 91 17 11 [ + + ] 61 91 17 11
	1238.71.
		H-ALSGKA-	aza--2Nal β 3	-LR-	aza--2Nal β 3	-NH (K2-Nal): Yield after purification 55 ; white powder; RP-HPLC : 20.56 min; 2 % t
	MWt C H N O .TFA 1352.1 g/mol. LC-ESI-MS/MS mass: found m/z 1238.65 M H ; C H N O (without TFA) requires 61 91 17 11 [ + + ] 61 91 17 11
	1238.71.
		-%			-	%	≥ %

60 B in 40 min and 60 100 B in 20 min, 8 ml/min, 215nm) to a final purity of 95 and lyophilized. Characterization of

  All spectra were recorded on a Bruker Avance 500 spectrometer equipped with a 5 mm triple-resonance cryoprobe (PRISM, Rennes).1D spectra were first recorded at concentration around 1 mM for each peptide, dissolved in aqueous (90 H O, 10 D O) increasing Euriso-top) concentrations, the pH was adjusted to 5.0 (until 200 mM SDS). Up to 50 mM SDS, variations in chemical shifts and line width narrowing could be observed, and then no change occurred at higher concentrations for all the peptides. The detergent concentrations were subsequently set at 50 mM for the further experiments. Homonuclear 2-D spectra DQF-COSY, TOCSY (MLEV) and NOESY were recorded in the phase-sensitive mode using the States-TPPI method as data matrices of 256 real (t ) 2048 (t ) complex HMBC were acquired to help to fully assign the naphthylalanyl side chains. Spectra were processed with Topspin (Bruker Biospin) or the NMRpipe/NMRdraw software package 46 and visualized with Topspin or NMRview 47 on a Linux station. The matrices were NMRView software. 47 Structure calculations were performed with ARIA 2.2.[START_REF] Linge | Automated assignment of ambiguous nuclear overhauser effects with ARIA[END_REF] Representation and quantitative analysis of the

			2	d.mol , and 1 -
	the helical content was estimated as previously described 45 [ ]
	NMR experiments
			% 2	% 2
	SDS d-25 (1 ×	2
	data points; 64 scans per t increment with 1.5 s recovery delay and spectral width of 5341 Hz in both dimensions were used. The mixing 1
	times were 100 ms for TOCSY and 200 ms for the NOESY experiments. In addition, 2D heteronuclear spectra C-HSQC and 13	13
	C-[ ]	[ ]
	zero-filled to 1024 (t ) 2048 (t ) points after apodization by shifted sine-square multiplication and linear prediction in the F1 domain. 1 × 2
	Chemical shifts were referenced to the solvent chemical shifts.
	Structure calculations
	1	H chemical shifts were assigned according to classical procedures. 48 NOE cross-peaks were integrated and assigned within the [ ]
		[ ]	[ ]
	calculated structures were performed using MOLMOL 50 and PyMOL (Delano Scientific). The PROCHECK program 51 was used to [ ] [ ]

Table 1

 1 Antibacterial Activities of peptides and pseudopeptides minimal inhibitory concentration (MIC) expressed in g.mL .

	μ	-	1

[START_REF] Porter | Mimicry of host-defense peptides by unnatural oligomers: antimicrobial beta -peptides[END_REF]

[START_REF] Porter | Mimicry of host-defense peptides by unnatural oligomers: antimicrobial beta -peptides[END_REF]

[START_REF] Porter | Mimicry of host-defense peptides by unnatural oligomers: antimicrobial beta -peptides[END_REF]

[START_REF] Porter | Mimicry of host-defense peptides by unnatural oligomers: antimicrobial beta -peptides[END_REF]

[START_REF] Porter | Mimicry of host-defense peptides by unnatural oligomers: antimicrobial beta -peptides[END_REF]

[START_REF] Porter | Mimicry of host-defense peptides by unnatural oligomers: antimicrobial beta -peptides[END_REF]

[START_REF] Porter | Mimicry of host-defense peptides by unnatural oligomers: antimicrobial beta -peptides[END_REF]

[START_REF] Porter | Mimicry of host-defense peptides by unnatural oligomers: antimicrobial beta -peptides[END_REF]

[START_REF] Porter | Mimicry of host-defense peptides by unnatural oligomers: antimicrobial beta -peptides[END_REF]

Acknowledgements:

We thank SERB Laboratories and Region Bretagne for their financial support and IFR 140 and Biogenouest for access to PRISM and Spectroscopies facilities. We are grateful to Pr. Fran oise Vovelle for her helpful participation in the aza-residues description in CNS/ARIA ç β 3 parameter files. We thank Dr Helena Wee for post-editing the English style.

Footnotes:

Chemical shift of AD, AK, A K and K-Nal in presence of 50 mM SDS (Table S1); Structural statistics Supporting Information Available:

for the 20 models of AD, AK, A K, K-2Nal7 and K-2Nal bound to SDS micelles (Table S2) and (A) Average torsion angles of the (R)-and

(S)-Hydrazino turn and (B) of the -turn 2-5 and 5-8 for the A K peptide (Table S3) are available free of charge.


José V Manjón
email: jmanjon@fis.upv.es

Pierrick Coupé

Antonio Buades

D Louis Collins

Montserrat Robles

author. José V Manjón

MRI Superresolution Using Self Similarity and Image Priors

In Magnetic Resonance Imaging low-resolution images are routinely interpolated to decrease voxel size and improve apparent resolution. However, classical interpolation techniques are not able to recover the high frequency information lost during the acquisition process. In the present paper a new superresolution method is proposed to recover such information using coplanar high resolution images. The proposed methodology takes benefit from the fact that in typical clinical settings both high and low-resolution images of different types are taken from the same subject. These available high resolution images can be used to improve effectively the resolution of other coplanar lower resolution images. Experiments on synthetic and real data are supplied to show the effectiveness of the proposed approach. A comparison with classical interpolation techniques is presented to demonstrate the improved performance of the proposed methodology over previous State-of-the-art methods.

Introduction

In Magnetic Resonance Imaging (MRI), data is acquired with a finite resolution that is limited by several factors like the SNR, hardware, time limitations or patient´s comfort. In typical clinical settings several types of images are obtained with different voxel resolutions. Traditionally, in-plane resolution has been higher than resolution in the slice direction yielding non isotropic voxel sizes.

In many applications such as segmentation or registration, data has to be upsampled to decrease its voxel size to make it compatible with a higher resolution dataset. In such cases, interpolation techniques [START_REF] Thévenaz | Interpolation Revisited[END_REF][START_REF] Lehmann | Survey: Interpolation Methods in Medical Image Processing[END_REF] have been traditionally applied. Techniques like linear interpolation or spline-based methods have been used extensively in the past to decrease voxel size and increase apparent data resolution. However, such techniques invent new points assuming that the existing ones (in the low resolution (LR) image) have the same value in the high resolution (HR) images which is only valid within homogeneous regions. As a result interpolated images are typically blurred versions of the corresponding high frequency reference images.

A better approach to increase effectively the resolution of the reconstructed data is to use SuperResolution (SR) techniques [START_REF] Carmi | Resolution enhancement in MRI[END_REF]. In MRI, superresolution techniques have been previously applied to increase image resolution in functional MRI (fMRI) [START_REF] Kornprobst | A Superresolution Framework for fMRI Sequences and Its Impact on Resulting Activation Maps[END_REF] and Diffusion Tensor Imaging (DTI) studies [START_REF] Peled | Superresolution in MRI: Application to Human White Matter Fiber Tract Visualization by Diffusion Tensor Imaging[END_REF]. Unfortunately, most of such techniques are based on the acquisition of multiple low-resolution images with small shifts; a process which is time consuming and therefore not adequate for typical clinical settings.

Fortunately, if HR images of the same subject within the same or other image modality are available, it is possible to recover some of the lost high frequency information within the LR image. This idea was recently applied in a method proposed by [START_REF] Rousseau | Brain Hallucination. European Conference on Computer Vision (ECCV)[END_REF] where a low-resolution volume is reconstructed using information of a HR reference volume while taking into account an expected degradation model. In Rousseau´s method the HR data is used to regularize a deconvolution based reconstruction using a Non-Local Means denoising method [START_REF] Buades | A non local algorithm for image denoising[END_REF]. The method proposed in this paper is related to Rousseau´s work in the sense that we also use HR data to constrain the reconstruction process but our method is based on a totally different strategy to compute the image reconstruction.

Material and methods

Image voxels in LR data y can be related to the corresponding underlying HR voxels x through a simple degradation model.

(

) 1
where D is a decimation operator (defined as taking each Lth value starting from zero in each dimension), H is the convolution matrix , x is the underlying HR data and n is a random Gaussian noise. In MRI H can be roughly approximated by a 3D boxcar function since the values on LR data can be well modeled as an average of the corresponding HR voxel values. Therefore, the value yj of any voxel in the LR image can be expressed as follows:

(2) where the value of the LR voxel yj is the average of the corresponding N xi voxels in the HR image plus some additive noise from the measurement process. While noise in MRI is Rician, the noise here can be approximated as Gaussian distributed in the imaged object for typical clinical SNR values.

Therefore, the aim of any superresolution method is to find the xi values from the yj values, a very ill posed problem as there are infinite xi values that meet such a condition. A common approach to solve this problem is to minimize a merit function such as:

(3) Due to the non-uniqueness of the solution for this problem, some extra information is needed to constrain the possible solutions of equation 3 to obtain plausible results. This has been traditionally done using smoothness constrains which are based on the assumption of smoothness of the reconstructed data.

(4) where R(x) is a regularization term and λ is a weight that balances the contribution of smoothness and data fidelity terms. However, such smoothness assumption penalizes high frequency content of the reconstructed image that is precisely what we want to obtain.

In contrast to this optimization approaches, we propose to estimate using a direct iterative method using coplanar HR data to control the reconstruction process.

Proposed method

The proposed method in this paper is not based on the smoothness assumption but on the assumption that if a registered HR image/volume of the same subject from the same or other modality is available then anatomical information from this HR data can be used to recover additional structure in the superresolution reconstructed LR data. Furthermore, if noise present in the LR data is minimized by applying a specific filter, we can impose as an additional constraint the fact that the down-sampled version of the reconstructed data has to be exactly the same as the original LR data. This constraint has been previously applied in the SR context and referred as sub-sampling consistency (Banerjee and Jawahar, 2008).

(5)

To apply the proposed method, two preprocessing steps have to be accomplished:

• Data registration: In order to extrapolate voxel local similarities from the HR reference data to the LR reconstructed data both reference and LR data have to be in the same geometrical space.

• Image denoising: Due to the presence of noise, equation 5 cannot be used directly. To simplify the problem, the HR and LR data are first denoised using a recently proposed robust denoising method for 3D MR images [START_REF] Coupé | An Optimized Blockwise Non Local Means Denoising Filter for 3D Magnetic Resonance Images[END_REF] based in the well-known Non-local Means filter early proposed by [START_REF] Buades | A non local algorithm for image denoising[END_REF]. It has been demonstrated

that such filter (i.e., the BNLM3D filter) is able to remove noise effectively while minimally affecting the image structure.

The proposed method uses as input data a HR reference data and a preinterpolated version of the LR data. It is an iterative procedure based on two steps that corresponds to the two assumptions used which are:

1) Regularization: Locally, similar voxels in the HR data tends to be similar in the reconstructed LR data. Therefore, regularizing an interpolated version of the LR data using the reference HR data similarities will enforce this condition. This is the key contribution of the proposed procedure. First, the LR data is interpolated in order to obtain a volume with the same voxel size as the HR reference data. To Regularize the interpolated data a 3D Neighborhood filter [START_REF] Yaroslavsky | Digital Picture Processing. An Introduction[END_REF] can be used, however the weights are calculated using the reference HR data information instead of the LR data.

(

) 6
where z is the HR reference data, p and q are data indexes, x t is the current reconstructed data at iteration t, h controls the intensity similarity and Cp is the normalization factor.

This approach gives very good results if LR and HR data are in perfect geometric match but it is very sensible to misregistration between LR and HR data. A more robust approach can be used if using also information from the LR data to constrain the process.

(

) 7
here, is a 3D window surrounding voxel i at iteration t and k is parameter controlling the influence of the LR data in the reconstruction process.

2) Mean correction: Since the down-sampled version of the reconstructed LR data must be equal to the original LR data, the mean value of the reconstructed HR voxels need to be corrected to fit the value of the original LR voxel. This is accomplished by adding a corresponding offset to each reconstructed voxel.

(

) 8
where NN is the Nearest neighbor interpolation operation.

These two steps are iteratively repeated, using the current reconstructed data in the next regularization step (instead of the initial interpolated data) until no significant difference is found between two consecutive iterations (mean absolute difference between two iterations is inferior to a given tolerance, tol). A block diagram of the proposed method can be observed in figure 1.

Experiments and results

Experimental data

To validate the proposed method a synthetic dataset was used. High resolution T1 and T2 data with both normal and pathology (multiple sclerosis) from the publicly available Brainweb database was used [START_REF] Cocosco | BrainWeb: Online Interface to a 3D MRI Simulated Brain Database[END_REF]. The HR T1 and T2 volumes had 181x217x180 voxels with a resolution of 1 mm 3 ). The Peak Signal to Noise Ratio (PSNR) measure was used to compare the reconstructed data and the original HR data. All the experiments were performed using Matlab 7.4 (Mathwork inc.). The source code of the proposed method can be downloaded from http:/site/webpage.html to ease the reproducibility of this work.

Implementation details

As the proposed methodology can be implemented in a number of different manners we will discuss here how these different alternatives were selected prior the comparison of the proposed methodology with other reconstruction methods.

Initial interpolation

To find out how the initial interpolation affects the reconstruction results of the proposed method, different interpolation methods (Nearest Neighbor, Trilinear, Cubic and B-spline interpolation) were compared for the initial step. Results can be seen in left of Fig. 2. As can be noted, the proposed method obtained nearly the same stable solution in all the cases independently of the initial interpolation method used in approximately the same number of iterations. The only differences found were starting PSNR values, as expected. Thus, a Nearest

Neighbor interpolation seems to be the better option because it is the simpler and it hast the fastest implementation.

Size of search area

The proposed methodology was applied with different search area sizes and the results were analyzed (see Fig. 2). From this experiment, we found that a good option for the size of the search area Ω was 7x7x7 voxels (3D window radius=3). Increasing the search area beyond this size provides only a slight improvement while considerably increasing the computation time.

Value of h and k parameters

Finally, the value of h parameter plays a major role in the reconstruction process, so its correct adjustment is very important. In the present method, an iterative decremental assignment of its value is proposed. This approach enables a stable coarse to fine reconstruction in a similar manner as done for Non local demosaicing (Buades et al, 2007). In this approach, the use of high values of h produces the averaging of different parts of the image while small values directly copy similar values. For 8 bit quantization input data, decreasing values of h (32,16,8,4 and 2) were used in all experiments. Each value is used once and then decreased until the last h value (2 in our case) and then the process is iterated with h=2 until the mean absolute value of the difference between two consecutive reconstructions falls below a given tolerance. For other quantization levels h values can be linearly adjusted.

Regarding the k parameter, if this parameter is too small the method will be very robust to misregistration but few improvement in the reconstruction will be achieved since almost not information from HR data will be used. In contrast, if k is too high only HR information will be used which will lead in a good reconstruction when data is perfectly registered but the robustness of the method can be seriously affected when LR and HR data is geometrically incoherent. We have found experimentally that a factor k=256 allows to obtain good reconstructions while maintaining the robustness of the method. As can be noted the no significant improvement is found beyond that using a radius equal to 3.

Computational complexity

Since the proposed approach is an iterative process, the computational burden of the method is high (being the filtering step the heaviest part). To reduce the processing time, we have implemented the proposed method using symmetric weight computation on the filtering step which reduces the computational burden a factor 2. Besides, a multithreading implementation was used which allowed to reduce the processing time another factor 4 in the Quad Core 2.4

GHz Pentium machine used in the experiments. This lets an average time of around 8 minutes per iteration. This makes the required time for reconstructing a typical MR volume to be approximately 1 hour. Further time reduction can be achieved by processing only object voxels avoiding useless computations at background voxels.

To summarize, in all the experiments the search area Ω in the HR volume was set to have a radius equal to 3 (i.e. a 3D region of 7x7x7 voxels) and h = [32,16,8,4,2]. The parameter k was set to 256 and the tolerance was set to 0.01 (0.005% of the range).

Comparison on Normal Brain anatomy

The first comparison consisted in reconstructing downsampled versions of the Brainweb HR T2 volume. This HR volume was downsampled in the z direction to have different slice thickness (2, 3, 5, 7 and 9 mm). The proposed method used T1 data (1 mm 3 ) as HR reference data. The resulting reconstructed data was compared to the standard NN and B-Spline interpolation as implemented on MATLAB 7.4. In addition, the authors of the method recently proposed in [START_REF] Rousseau | Brain Hallucination. European Conference on Computer Vision (ECCV)[END_REF] provided results for the 3 mm case for comparison. In these experiments, no noise was added to simplify the analysis of the results. It has to be also noted that the proposed method is always applied after a denoising step so zero noise condition can be nearly met. The results can be observed in Table 1 and Fig. 3. As can be noticed the proposed method drastically improved the results in all the cases.

Comparison on Pathological Brain anatomy (Multiple Sclerosis)

In this case, the same experiment was repeated as above, but this time using the MS T2 HR and MS T1 HR phantoms also available from the Brainweb website. The proposed method was also compared to the standard NN and B-Spline interpolation. Again, Rousseau´s method results for 3 mm slice thickness were supplied by the authors. The results can be observed in Table 2. In Fig. 4, a visual comparison of the results for 3 mm slice thickness can be done. Again, the proposed method drastically improved the results in all the cases. We were curious about the effect of the proposed method in the MS lesions, since lesions appearing as T2 hyperintensities are not often clearly visible in T1.

We observed that MS lesions were well reconstructed, even though the T1 regularization information did not help much to recover such structures. The appearance of the lesions in the reconstructed images is due to the mean correction step which ensures that the reconstructed data maintains correct intensity levels in the reconstructed data. In Fig. 5, a transverse slice with MS lesions is displayed for the original and reconstructed volumes. The differences of the different reconstruction methods are clearly visible.

Noise sensitivity

It is clear that the zero noise case is an idealization of the real MR image conditions. To address this issue, another experiment was performed on the Brainweb data, but this time adding noise. A LR T2 volume of voxel resolution 1x1x5 mm was reconstructed to 1 mm 3 . Both HR reference T1 and LR T2 data were corrupted with several levels of Gaussian noise (0, 1, 2, and 4% of the maximum intensity). In this case, the reconstruction was performed after denoising the noisy data using the BNLM3D filter. To assure a fair comparison, NN and B-Spline interpolation methods used also the denoised data to compute the HR T2 volume. Qualitative results are shown in Fig. 6. Quantitative results are displayed in Table 3. Again, the proposed method outperformed the other methods in all noise levels.

One can notice that performance of the proposed method decreases with the noise amplitude as the denoising process inevitably erases some high frequency information in the images. It is also important note that in this experiment we have added the same level of noise to LR and HR data as it is supposed to be machine dependent, but in many cases HR data are acquired with 3D acquisitions and therefore can be less noisy than a LR multislice acquisition (for example a typical T1 volume compared to DWI). In such cases, the reconstruction of the LR data is highly improved due to the fact that the HR data does maintains its high frequency information.

Registration sensitivity

As it has been pointed out previously, the accuracy of the proposed method highly depends on the correct registration of the LR and HR images. To evaluate how the misalignment affects the accuracy of the proposed method, the HR T1-w reference volume was shifted in the 3 directions (x, y and z). In this experiment, a 1x1x5 mm voxel resolution LR T2-w volume was reconstructed to 1 mm 3 voxel resolution using as reference a shifted HR T1 volume. Results are showed on table 4. Differences in the results of x and y axis compared to z axis are due the axial acquisition of the images. From this results, it can be concluded that the proposed method is able to tolerate a small misregistration (up to 1 or 2 mm) while maintaining an improved performance over the reference B-Spline interpolation mainly due to the inclusion of information of LR data during reconstruction. This is important since in real world conditions small misalignments can be present after registration.

However, most of current linear registration methods are able to obtain a submillimeter accuracy which enables the application of the proposed methodology [START_REF] Hajnal | Medical Image Registration[END_REF]Vandermeulen et al,1999).

Real clinical data

To evaluate quantitatively and qualitatively the proposed approach on real clinical data, three real datasets were used. In the three cases, the 3D search region was set to 7x7x7 voxels, the h values used were consecutively (12%, 6%, 3%, 1.5 % and 0.7% of the image range) of the HR image range and the tolerance was set to the 0.0005% of the same range. The second dataset consisted in a HR T1-w (170x256x256 voxels) and a LR T2-w (85x256x256 voxels) images acquired on a 3T Siemens TimeTrio (Erlangen, Germany) machine. The resolution of the T1-w data was 1 mm 3 while the resolution of the T2-w data was 2x1x1 mm 3 . In this case, the LR data was upsampled to 1 mm 3 using the B-Spline and the proposed method. Fig. 8 shows the reconstruction results using the compared methods. As in this case, we had not HR to compare the results were judged visually. Such qualitative analysis showed that the reconstruction using the proposed approach was less blurry than B-Spline interpolation. To apply the proposed method the LR and HR were first filtered using the BMNLM3D filter and then the LR T2-w data was registered to the HR T1-w data using SPM5 software (Friston et al., 1999) with a 3D rigid transformation. Finally, the third dataset consisted of a pathological dataset containing a brain tumor. In this case, a HR T1-w volume (224x256x174 voxels) and a LR FLAIRw volume (224x256x29 voxels) were used. The resolution of the T1-w data was 1 mm 3 while the resolution of the FLAIR data was 1x1x6 mm 3 . This dataset (named CEREBRIX) was downloaded from a public MR DICOM data repository (http://pubimage.hcuge.ch:8080/). Again, the LR data was upsampled to 1 mm 3 using the B-Spline interpolation and the proposed method and the results were qualitatively evaluated. In Fig. 9, the reconstruction results are compared to B-Spline reconstruction. Again, the visual inspection of the results showed a less blurry reconstruction when using our proposed approach showing consistent anatomical information. To apply the proposed method, the data was filtered using the BNLM3D filter and the LR FLAIR data was registered to the HR T1 data using also the SPM5 software with a 3D rigid transformation.

Conclusion

We have presented a new superresolution method that enables recovery of HR data information from LR data when a coplanar HR data volume of the same subject from the same or other modality is available. The proposed method has been validated, using synthetic and real data. Our experiments demonstrated that the proposed method outperforms classical interpolation methods.

Experiments presented here show how images with highly anisotropic voxels can be reconstructed to have isotropic voxels (e.g. 1x1x9 mm 3 to 1 mm 3 ) when HR data of such resolution is available. However, it is worth to note here that the reconstruction can be performed in any dimension when suitable data is available (e.g. 3x3x3 mm 3 to 1x1x1 mm 3 ).

The iterative approach here described relies on a correct registration of LR and HR data to assure that HR similarities can be extrapolated to the reconstruction of LR data. Moreover, a proper denoising step is mandatory prior to the reconstruction process. In this sense, we have used a BNLM3D method that performed very well in all cases.

The use of a 3D boxcar function as convolution matrix is supported by the concept of partial volume on MRI where voxel intensity can be modeled as a linear combination of the voxel intensities of the adjacent HR data. Our experiments on real data seems to confirm this assumption yielding plausible results when using this model.

It is important to note that no special hardware nor specific imaging sequences are needed to apply the proposed approach. The proposed methodology can be applied to increase the resolution of multimodal studies after data registration.

Other specially interesting field could be the application of the proposed technique to artificially increase the resolution of fMRI studies where typically a HR reference volume is acquired with LR EPI data.

Further work has to be addressed to assess the value of the proposed methodology on clinical and research frameworks.

Figure 1 .

 1 Figure 1. Block diagram of the proposed method.

Figure 2 .

 2 Figure 2. Left: Effect of initial interpolation method in the proposed method (All methods compared reached a similar stable result after 11 iterations). Right: PSNR values of the proposed method as a function of the radius of the search area. As can be noted the no

Figure 3 .

 3 Figure 3. A parasagittal slice for the normal anatomy case. From top to bottom, results with different slice thicknesses (2,3,5,7,9 mm) and from left to right, the original HR T2 data, the NN reconstruction, the B-Spline reconstruction and the proposed method.

Figure 4 .

 4 Figure 4. From top to bottom: Original Axial, Saggital and Coronal sections of the HR T2 data, NN interpolation, B-Spline interpolation, Rousseau's method and proposed reconstruction.Results for 3 mm slice thickness reconstruction. Note that MS lesions are better reconstructed using the proposed method.

Figure 5 .

 5 Figure 5. Example of reconstruction of a transverse slice with MS lesions. Top-left: Original HR data, Top-right: B-Spline interpolation. Bottom-left: Rousseau´s reconstruction. Bottom-right: Proposed reconstruction.

Figure 6 .

 6 Figure 6. From Top to Bottom, 0 ,1, 2 and 4% noise case. From left to right, HR T2 data, LR noisy T2 data, LR denoised T2 data, B-spline interpolation and proposed reconstruction.

Figure 7 .

 7 Figure 7. Comparison of real clinical data experiment. Top-Left: HR T2 volume. Top-Right: downsampled version of the HR T2 volume. Bottom-Left: B-spline reconstruction. Bottom-right: Reconstruction using the proposed method. Note that the proposed methodology yields a significantly less blurred reconstruction than other methods compared. A close up of the cerebellum area clearly shows the improved reconstruction.

Figure 8 .

 8 Figure 8. Comparison of real clinical data experiment. Top-Left: HR T1 volume. Top-Right: LR T2 volume. Bottom-left: B-Spline reconstruction. Bottom-right: Reconstruction using the

Figure 9 .

 9 Figure 9. Comparison of real clinical data experiment. Top-Left: HR T1 data. Top-Right: LR FLAIR volume. Bottom-left: B-Spline reconstruction. Bottom-right: Reconstruction using the proposed method. In the each case a close-up of the coronal slice is presented to better show how the proposed method provides a less blurry reconstruction.

Table 1 .

 1 PSNR values (larger values are better) of the different methods compared for several slices thicknesses for the normal brain anatomy case.

	Slice Thickness (mm)	2	3	5	7	9
	NN	25.13	21.91	19.04	17.68	16.70
	B-Spline	28.09	23.77	20.20	18.44	17.18
	Rousseau	-	26.71	-	-	-
	Proposed	40.65	37.64	34.37	32.24	30.64

Table 2 .

 2 PSNR values of the different methods compared for several slices thicknesses for the multiple sclerosis anatomy case.

	Slice Thickness (mm)	2	3	5	7	9
	NN	26.21	22.99	20.09	18.72	17.73
	B-Spline	29.33	24.99	21.29	19.59	18.33
	Rousseau	-	27.33	-	-	-
	Proposed	41.04	38.08	34.81	32.64	30.96

Table 3 .

 3 PSNR values of the different methods compared for several noise levels.

	Noise (%)	0	1	2	4
	NN	19.04	18.94	18.79	18.59
	B-Spline	20.20	20.04	19.84	19.57
	Proposed	34.37	29.76	26.82	24.25

Table 4 .

 4 PSNR enhancement values of the proposed referred to B-Spline method in function of misregistration.

	Shift (mm)	0	1	2	3
	x-axis	13.92	5.35	1.61	0.47
	y-axis	13.92	5.61	1.83	0.37
	z-axis	13.92	2.98	-0.42	-1.67

Acknowledgments

The authors want to thank Dr. Vladimir Fonov for supplying some of the MR images used in this paper. We are also grateful to Dr. Rousseau for providing the results of his method for the comparisons and for his useful comments. This work has been partially supported by the Spanish Health Institute Carlos III through the RETICS Combiomed RD07/0067/2001, the Ministerio de Ciencia e Innovación though the grant TIN2008-04752 and by the Canadian grant Industry Cda (CECR)-Gevas-OE016.

The first case consisted in a dual PD-w/T2-w study. In this way, we were sure that PD-w and T2-w data were perfectly registered as they are acquired at the same time. This dataset was obtained with a PD-w/T2-w volumetric sequence (256x256x56 voxels with a voxels resolution of 0.94x0.94x3 mm) in a Philips Gyroscan 1.5 Tesla scanner (The Netherlands). In this case, the T2 weighted volume was downsampled to a voxel resolution of 0.94x0.94x6 mm (i.e. a reduction factor 2 in z direction). Both, reference PD-w and T2-w volumes were filtered using the BNLM3D method and PSNR values were computed using as reference the denoised version of the HR T2-w volume. The NN interpolation method obtained a PSNR equal to 27.68 dB, the B-Spline method 28.90 dB and the proposed method 32.51 dB. In Fig. 7, the different results can be visually compared. One can see that the reconstruction using the proposed approach not only obtained a better PSNR value than the other methods but also showed a better anatomical content.