Davide Fabiani

Chuanyang Li

Guanjun Zhang

Giovanni Mazzanti

Gilbert Teyssedre

Jinliang He

High Voltage : Special Issue: Interface Charging Phenomena for Dielectric

Interface charge accumulation, leading to unpredictable insulation breakdown, restricts the development and industrialisation of high voltage direct current (HVDC) power equipment. Understanding the mechanism of interface charge transport and interface charge triggered dielectric breakdown is, therefore, of particularly high interest and vital importance. For example, the surface charging of aircraft in space brings damage to board electronic instruments as well as interference to sensing systems. Moreover, the randomly distributed charge clusters on the spacer surface, as shown in the cover page of this Special Issue, is considered as a potential threat to the surface flashover, while the accumulation of space charge within the insulating material poses a threat to the reliability of DC power cables. However, currently we still know very little about the development of charge dynamics in different interfaces, and the related breakdown mechanism of dielectrics induced by charge accumulation is also not very clear.

This Special Issue brings together recent studies of charging phenomena for dielectric interfaces including vacuum-solid interface, gas-solid interface, and solid-solid interface. Nine highquality papers are accepted for publication in this Special Issue: six papers focusing on gas-solid interface (including one review paper), two review papers focusing on vacuum-solid interface, and one paper focusing on solid-solid interface. A brief discussion of each paper is presented as follows.

Review papers

In 'Gas-solid interface charge characterisation techniques for HVDC GIS/GIL insulators' by Zhang et al., the paper reviews the current status, development needs and potential developing orientation of surface charge characterisation techniques. Different surface potential measurement methods and charge inversion algorithms are reviewed regarding the previous studies and future research needs. Drawbacks and outlooks of surface charge measurement techniques are also discussed with the background of laboratory experiment results and on-site measurements.

In 'Modelling vacuum flashover mitigation with complex surface microstructure: mechanism and application' by Zhang et al., the paper reviews the influence of surface microstructures on surface flashover in a vacuum. A particle simulation model is constructed to reveal multifactor development under various microstructure shape, size, and distribution. It is shown that anode current decays exponentially with the number of grooves, also trapezoid groove can effectively trap and deflect secondary electrons, thus improving strength of vacuum-insulator interface. Additionally, a theoretical model is proposed to link simulation results with surface charge distribution and flashover voltage. A saturation of groove depth is identified, and optimised groove parameters are given for practical insulator design.

In the paper 'Improvement of surface flashover in vacuum' by Li, the article reviews the research progress of surface flashover in vacuum regarding effective methods to improve the surface flashover performance in vacuum, including insulation system optimisation and material modification. The former is beneficial to reduce the electric field distortion, and the latter is able to adjust the surface trap parameters of the material through physical and chemical methods. Meanwhile, the ʻU-shaped' curve is proposed to reveal the relation between surface flashover voltage and surface trap level. Moreover, suggestions are made to build a unified surface flashover model which is suitable to the range from high vacuum to high pressure.

In 'Surface charge accumulation and pre-flashover characteristics induced by metal particles on the insulator surfaces of 1100 kV GILs under AC voltage' by Xing et al., the paper establishes a PD detection system with a sensitivity of 0.05 pC for 1100 kV insulators based on the cross-reference pulse current (PC) method. The PD development and flashover characteristics of 5 mm long metal particles on the surface of UHV insulators were studied. It is found that for 1100 kV AC insulators, although the discharges of millimeter-scale particles are low (usually lower than 2 pC), they will still result in charge accumulation on the insulator surface, leading to flashover along the surface. Meanwhile, the discharges with low amplitude is difficult to be detected by traditional PC and UHF methods.

In 'Influence of humidity on conduction processes in gasinsulated devices' by Tschentscher et al., the paper introduces a highly precise humidity control circuit to analyse the significance of humidity in the range from -25 to -5°C frost-point, which is fully applicable to operating gas-insulated devices. It is found that charge generation from micro discharges at the interfaces substantially increased with increasing humidity. For an electric field of 5 kV/mm, humidity strongly influences the charge provision from technically rough interfaces and potentially contributes to the surface charge accumulation at insulator surfaces. On the other hand, for low-field conduction phenomena, no increase in the ion currents from natural ionisation or electrophoretic conduction was observed.

In 'Dynamics of surface charge and electric field distributions on basin-type insulator in GIS/GIL due to voltage polarity reversal' by Luo et al., a simulation model is established to study the change of surface charge and electric field distributions under voltage polarity reversal. The surface charge and electric field distributions at different moments are calculated. The influence of reversal time on the transient and steady state is also discussed. The tangential and normal electric fields during the reversal process are analysed to describe the effect of the reversal on the flash characteristics.

The paper 'Charge accumulation characteristic on polymer insulator surface under AC voltage in air and C4F7N/CO2 mixtures' by Li et al., studies the charge transport characteristics on insulator surface in air and heptafluorobutyronitrile/carbon dioxide (C4F7N/CO2) mixtures under AC voltage. The results show that with the needle-plate electrode structure, charge distribution on the insulator surface presents a three-tier concentric circle structure both in air and C4F7N/CO2 gas mixtures, while the charge area range of charge distribution on insulator surface in C4F7N/CO2 mixtures is smaller than that in air. It is suggested that the charging property of insulators in C4F7N/CO2 mixtures is related to the larger electron attachment cross section of C4F7N gas in a wide range of electron energy distribution.

In 'Finite-element analysis for surface discharge on polyimide insulation in air at atmospheric pressure under pulsed electrical stress' by Dong et al., a surface discharge non-equilibrium plasma model of air-polyimide under pulsed electrical stress is established. The temporal and spatial evolution of the microparameters such as charge and electric field distribution during discharge are obtained. The results show that surface discharge develops from needle electrode to ground electrode under both repetitive pulses and single pulse stress. The relationship between the discharge propagation time under repetitive pulses and pulse repetition rate is a 'U-shaped' curve, and the inflection point moves to higher repetition rate region with the increase of voltage.

Solid-solid interface charging phenomena

In the paper 'Improved space charge transport model in bi-layer dielectrics-considering carrier dynamic equilibrium' by Liang et al., the authors propose an improved space charge transport model considering the carrier dynamic equilibrium process in solid dielectrics. The polarisation process of the LDEP/EPDM bi-layer dielectric was simulated by the Maxwell-Wagner model, the bipolar charge transport model and the carrier dynamic equilibrium model, respectively. Influences of parameters on the simulation results were investigated, and comparisons among the simulation results of different models were also made. Compared with the previous models, this improved model performs better in predicting the space charge distribution and the polarisation current.

Summary/conclusion

In summary, this Special Issue reports the most up-to-date researches in interface charging phenomena, and it will be of interest to a wide audience of both fundamental physicists and material scientists, with a background of high voltage engineering and microelectronics, focusing on interface charging problems. We do hope that this Special Issue will provide fruitful, educational and inspiring reading.

Acknowledgments

We would like to thank the authors for their contributions and the reviewers for their valuable time that contributed to the high quality and timely publication of this Special Issue. We would also like to acknowledge the support of the Editor-in-Chief of the High Voltage, Professor Weijiang Chen, during the entire process in preparing this Special Issue. Meanwhile, the Editorial Office of High Voltage should also be thanked for their kind assistance editing this Special Issue.


P Neige
email: pascal.neige@u-bourgogne.fr

MORPHOMETRICS OF HARD STRUCTURES IN CUTTLEFISH

Keywords: CUTTLEFISH, MORPHOMETRICS, TAXONOMY, DISPARITY, EVOLUTIONARY

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

INTRODUCTION

Morphometrics, as any other scientific field, has its own celebrities, who have greatly increased our knowledge. Among them is D'Arcy Thompson and his famous book On Growth and Form (1917). The basic idea of Thompson was to link numerical precision with biological science. Applied to the field of form comparison, he proposed to define the Science of Form as resulting from a two step process: "The study of form may be descriptive merely, or it may become analytical. We begin by describing the shape of an object in the simple words of common speech: we end by defining it in the precise language of mathematics; and the one method tends to follow the other in strict scientific order and historical continuity" [START_REF] Thompson | On Growth and Form[END_REF]. It is well known that D'Arcy Thompson was interested in cephalopods, as suggested by a famous photograph of him observing a shell section of a Nautilus. However, it is interesting to note that he used the words of common speech, and not the precise language of mathematics to discuss the shape of cuttlefishes. This was published in a short paper [START_REF] Thompson | How to catch cuttlefish[END_REF] devoted to explaining how to catch a cuttlefish, and included reports by classic authors (including Aristotle).

Morphometrics, a term that D'Arcy Thompson did not use, corresponds to the second step of his Science of Form. A modern and operational definition may be found in Rohlf & Marcus (1993, p. 129): "The field of morphometrics is concerned with methods for the description and statistical analysis of shape variation within and among samples of organisms and of the analysis of shape change as a result of growth, experimental treatment or evolution. Morphometric methods are needed whenever one needs to describe and to compare shapes of organisms or of particular structures. The samples may represent geographic localities, developmental stages, genetic effects, environmental effects, etc". Methods to describe and compare shapes are understood here as quantitative, based for example on dimensional measurements. Statistical analyses are mainly a multivariate exploration of data: the analysis at one time of many descriptors on many observations. In a broader sense, morphometrics may be applied to any biological shape. In practice, it is generally restricted to hard structures, mainly because these are not subject to deformations during analysis (e.g. storage, desiccation, dissection) but also because their shape represents a long process of growth and thus supposedly reflects some basic biological information (for example to explore taxonomy or phylogeny). However, we cannot exclude soft parts from the field of morphometry, although morphometric studies are then much more difficult to manage, when considering post-mortem shape deformation e.g.

During the last two decades, progress in morphometrics has greatly increased the field of the Science of Form (see [START_REF] Adams | Geometric morphometrics: ten years of progress following the 'revolution[END_REF],b u t progress in this field will convey nothing unless applied to some biological models, whatever the biological perspective covered: fundamental or applied. In this context, cuttlefishes have a special place within the cephalopods, largely due to their well-developed hard structures, and particularly when considering their inner shell.

This paper reviews what has been done and what could be done when using morphometrics to describe and quantify cuttlefish hard structures. It focuses primarily on Sepia officinalis, although it is not restricted to this species, since a discussion of such important fields as species comparisons and macroevolution is useful.

Hard structures in cuttlefish

In theory, four cuttlefish hard structures may be studied using morphometric techniques: (1) the inner shell (Fig. 1 A), or cuttlebone, whose function is to control buoyancy of the organism, (2) the statoliths (Fig. 1 B), which participate in the detection of gravity and linear acceleration, (3) the beaks (Fig. 1 C) and (4) the radula (Fig. 1 D), both being part of the digestive system. Although considered here as hard structures, their respective composition is quite different: aragonite for inner shells and statoliths, chitin for beaks and radula. To my knowledge, only three of the four have been extensively studied using morphometric tools: inner shell, beaks and statoliths.

A basic description of morphometric techniques

The following brief presentation of morphometric techniques is based in part on works of [START_REF] Rohlf | A revolution in morphometrics[END_REF] and [START_REF] Lestrel | Morphometrics for the Life Sciences[END_REF]. Only those who have been applied to cuttlefish hard structures are considered here. Complementary and up-to-date information of any kind about morphometrics may be found at the following reference web site: http: //life.bio.sunysb.edu/morph/index.html.

Traditional Morphometrics

Traditional Morphometrics uses quantitative features such as linear dimensions, perimeters, surfaces or angles as basic raw data (variables), and compares them using statistical approaches. In practice, variables usually correspond to distances measured on the organisms (Fig. 2). Therefore, statistical methods used can be mathematically very simple or more complex; examples vary from ratio calculations (i.e. the calculation of the proportion of a given character to total length of an organism or a given anatomical structure) to the calculation of new variables using multivariate statistics. The aim of these multivariate statistics is to reduce the number of variables under study. Traditional Morphometrics is now widely and routinely applied to cephalopod studies (e.g. [START_REF] Kassahn | Molecular and morphological analyses of the cuttlefish Sepia apama indicate a complex population structure[END_REF] for an application in Sepia apama,a n d Natsukari et al. 1991 in S. esculenta).

Coordinate Morphometrics

Coordinate Morphometrics emphasises the recognition of homologous landmarks (Fig. 2): points which have to convey a biological meaning, for example a point at the intersection of two structures. The basic idea is to compare and quantify geometrical differences between sets of landmark configurations (reflecting sets of organisms or species) rather than to quantify shape itself. This approach is relatively recent (starting in the eighties: [START_REF] Bookstein | Morphometrics in Evolutionary Biology[END_REF][START_REF] Bookstein | Morphometric Tools for Landmark Data[END_REF], thus applications on sepiids are still relatively sparse [START_REF] Neige | Morphometrics of the shell of three Sepia species (Mollusca: Cephalopoda): intra-and interspecific variation[END_REF][START_REF] Dommergues | Exploration of Morphospace using Procrustes Analysis in Statoliths of Cuttlefish and Squid (Cephalopoda: Decabrachia) -Evolutionary Aspects of Form Disparity[END_REF][START_REF] Neige | Disparity of beaks and statoliths of some coleoids: a morphometric approach to depict shape differentiation[END_REF], & Neige 2003a, 2003b). Coordinate Morphometrics offers interesting advantages [START_REF] Rohlf | A revolution in morphometrics[END_REF]: (1) movement of one structure relative to another one is easily located and quantified, (2) it is easy to separate affine shape changes from non-affine or local transforma- tion, (3) graphical outputs allow identification and location of shape modifications precisely from one shape to another one, using vector fields, for example.

Boundary Morphometrics

Boundary Morphometrics uses the general outline of an organism or a part of an organism as the shape proxy (Fig. 2). This technique is used when the biological information of interest is confined to the outline [START_REF] Lestrel | Morphometrics for the Life Sciences[END_REF]. The first step defines points located on the outline, and the second step uses Fourier analysis (or an equivalent technique) to transform spatial configuration (the position of the points on the outline) into frequency components (amplitude and phase). It is important to note that amplitudes may be used thereafter in multivariate statistical analysis. An important advantage of Boundary Morphometrics is that the frequency component transformation is reversible, allowing outlines to be geometrically reconstructed using frequency component information. Application of this approach is still very rare with cephalopods. Thus far, only one work has attempted such an analysis on sepiids [START_REF] Lombarte | Intraspecific shape variability in statoliths of three cephalopod species[END_REF], exploring intraspecific statolith variability in officinalis.

Usefulness of morphometrics for species identification and comparison

Morphometrics of the Cuttlebone

Scientists working on cuttlefish taxonomy have traditionally used cuttlebone features as a proxy for species identification. Many of them described the shape with basic terminology, while others attempted to characterise shape by measurements. Whatever the mode of description, quantitative or not, it has been noted, following [START_REF] Lu | Use of the sepion in the taxonomy of Sepiidae (Cephalopoda: Sepioidea) with an emphasis on the Australian fauna[END_REF], that utilising cuttlebone shape alone is certainly not significant when attempting to define a species. This is due in part to large cuttlebone shape variations, which occur in a species, due to growth, sexual dimorphism or geographical position. However, (1) several species were described based only on the cuttlebone (e.g. Sepia elegans and S. orbignaya), and (2) cuttlebone shape in turn (i.e. when species have been formally described, using soft and hard structures), is a good proxy when a species should be recognized from a specimen.

The first attempt to quantify cuttlebone shape is found in the work of Hoyle (1886, p. 123). He defined the locular index as the length occupied by the last loculus (the last septum) when compared to the cuttlebone length. The use of cuttlebone measurement ratios -i.e. ratios removing a part of size effects, another part (the allometric one) being still present -is now standard for taxonomic purposes (e.g. [START_REF] Roeleveld | A review of the Sepiidae (Cephalopoda) of Southern Africa[END_REF][START_REF] Reid | Australian cuttlefishes (Cephalopoda: Sepiidae): the 'doratosepion' species complex[END_REF]. For example, [START_REF] Guerra | Species differentiation of Sepia officinalis and Sepia hierredda (Cepahlopoda: Sepiidae) based on morphological and allozyme analyses[END_REF] used several cuttlebone shape parameters to compare S. officinalis and S. hierredda. Their results show some differences between the two species, which are congruent with genetic differences. Some workers have used a landmark based approach to explore cuttlebone shape at the species level [START_REF] Neige | Morphometrics of the shell of three Sepia species (Mollusca: Cephalopoda): intra-and interspecific variation[END_REF]. For S. officinalis, no sexual dimorphism and no ontogenetic growth allometry exist (for total cuttlebone sizes ranging from 62 to 256 mm). However, in the same analysis it is demonstrated that underfed individuals that were reared in the aquarium [START_REF] Boletzky | Effets de la sous-nutrition prolongée sur le développement de la coquille de Sepia officinalis L. (Mollusca, Cephalopoda)[END_REF]) are morphologically different from wild specimens, the former possessing a relatively broader anterior part. Note that the absence of sexual dimorphism and ontogenetic growth allometry are in contradiction with some other studies (e.g. [START_REF] Bello | Dimorphic growth in male and female cuttlefish Sepia orbignyana (Cephalopoda: Sepiidae) from the Adriatic Sea[END_REF]. These opposite results may be due to the relatively low number of specimens used for the landmark based approach.

Morphometrics of Statoliths

Many studies have focused on statoliths because of their ageing potential [START_REF] Bettencourt | Age studies based on daily growth increments in statoliths and growth lamellae in cuttlebone of cultured Sepia officinalis[END_REF] for a study on S. officinalis). Some others have considered the shape of statoliths for their taxonomic value and evolutionary significance. Among them, Clarke (see Clarke 2003 for a bibliographic list) explored this potential essentially using morphometric methods. Using Traditional Morphometrics, he demonstrates that the shape of statoliths is not only related to functional aspects, but shows much about relationships between genera and species.

Statolith shape analysis has benefited from various modes of quantification. In an exploratory analysis, [START_REF] Lombarte | Intraspecific shape variability in statoliths of three cephalopod species[END_REF] quantified statolith shapes with two methods. One method uses linear measurements of several parts of statoliths, the other uses their outline to define points on the shape and subsequently uses Fourier analysis to explore shape differences. [START_REF] Lombarte | Intraspecific shape variability in statoliths of three cephalopod species[END_REF] finally used a hierarchical classification based on 20 first Fourier parameters to evaluate shape variability for three species (including S. officinalis). Their final result is that statoliths show a high degree of intraspecific shape homogeneity (in the case of S. officinalis, for mantle lengths ranging from 40 to 210 mm). [START_REF] Dommergues | Exploration of Morphospace using Procrustes Analysis in Statoliths of Cuttlefish and Squid (Cephalopoda: Decabrachia) -Evolutionary Aspects of Form Disparity[END_REF] recognise 18 landmarks to depict statolith shape for several Mediterranean coleoid species including the three cuttlefishes S. officinalis, S. orbignyana and S. elegans. The different landmark topologies are compared and overall dissimilarities combined into phenetic trees. They conclude (1) that the three sepiid species have morphologically similar statolith shapes, compared to other coleoids (always with a distinctive lateral dome), and (2) that S. officinalis exhibits ontogenetic shape variations (mantle lengths ranging from 48 to 191 mm). Differences between the two results (intraspecific homogeneity vs ontogenetic variation) may essentially be due to the fact that the morphological aspects of statoliths under study are not identical depending on the morphometric technique used: the outline for Fourier based approach vs a part of the outline plus some points located at the connexion between the parts of the statolith for landmarks based approach.

Morphometrics of Beaks

In his handbook for identification of cephalopod beaks, [START_REF] Clarke | A handbook for the identification of cephalopod beaks[END_REF] defines some principal measurements to quantify and describe the beak (also see [START_REF] Clarke | The identification of cephalopod "beaks" and the relationship between beak size and total body weight[END_REF]. Most of them are linear measurements, one is an angle. Clarke's proposal is to calculate some ratios, which may serve for taxonomic identification (lower beaks only). Finally, qualitative and quantitative descriptions are gathered in a series of keys for the identification of families and genera. Quantitative description of beak shapes using landmarks (for upper and lower beaks), of different coleoids including S. officinalis, S. orbignyana and S. elegans, has been attempted by [START_REF] Neige | Disparity of beaks and statoliths of some coleoids: a morphometric approach to depict shape differentiation[END_REF]. They conclude that both the upper and lower beaks do not indicate the same interspecific pattern, shape differences being much more marked for upper beaks.

Usefulness of morphometrics to explore functional morphology of the shell

Based on ratio calculations (cuttlebone width/length and thickness/width ratios), [START_REF] Sherrard | Cuttlebone morphology limits habitat depth in eleven species of Sepia (Cephalopoda: Sepiidae)[END_REF] attempts to correlate the cuttlebone's general shape among various species with their actual maximum habitation or capture depths. It appears that relative cuttlebone width is larger in specimens of shallow water species, with relative thickness not differing significantly among species. [START_REF] Ward | Bathymetric ranges and morphological adaptations in the Sepiidae[END_REF] also reaches a quite similar conclusion. However, depth limits within cuttlefishes are in a large part a function of the microstructure of the shell (e.g. angle between septa and the dorsal shield, septal thickness and density and morphology of pillar structures, see [START_REF] Bandel | A comparative study of the structure, development and morphological relationships of chambered cephalopod shells[END_REF]). These must be extensively studied before one can identify anatomical factors that cause depth limits in cuttlefishes.

Morphometrics and macroevolutionary studies

During the last decade, macroevolutionary studies have seen some new developments thanks to the use of morphometric techniques. The general aim of these studies is to observe changes in biodiversity at large scales (in time and space) and then to establish which factors are responsible for these changes [START_REF] Jablonski | Micro-and macroevolution: scale and hierarchy in evolutionary biology and paleobiology[END_REF]. For example, a novel idea is that taxonomic diversity and morphological disparity can become complementary biodiversity indices. Although they share common data, it is generally considered that comparing the two offers an opportunity to infer macro-evolutionary processes [START_REF] Foote | Discordance and concordance between morphological and taxonomic diversity[END_REF].

The case of sepiids has been studied by Neige (2003aNeige ( , 2003b)). In this example, the number of species is used as a taxonomic diversity index whereas dissimilarities within cuttlebone shape are used as a morphological disparity index. Cuttlebone shape is characterised using 15 landmarks, then relative warp analysis method is used [START_REF] Bookstein | Morphometric Tools for Landmark Data[END_REF]) to explore dissimilarities between shapes. This method produces some new axes (the so-called relative warp axes: RW axes) that concentrate information contained within the initial matrix, and allows visualisation of deformation along an axis (Fig. 3). A morphospace is constructed using these relative warp axes (here RW1 vs. RW2). It concentrates a large amount of variance and illustrates the gross distribution pattern of cuttlebone shapes. It is possible to construct a morphospace for 17 chosen biogeographical units, because biogeographic distributions are known for the different sepiid species (see Fig. 4 for biogeographic limits). The total variance (the sum of variances for selected RW axes calculated on the points of the morphospace) is used here as a measure of morphological disparity for each of the 17 morphospaces (corresponding to the 17 biogeographical units). High values indicate that a given biogeographical unit comprises species with very different cuttlebones; low values indicate that cuttlebones are morphologically close to one another. Results in Figure 4 are plotted with one bar for taxonomic diversity (left light bar in Fig. 4), and one bar for morphological disparity (right dark bar in Fig. 4) for each of the 17 biogeographical units. The initial result is that the number of species does not predict morphological disparity (i.e. couples of bars on Fig. 4 display very distinctive patterns). This indicates that morphological disparity is a measurement of biodiversity that expresses complementary biological information to standard taxonomic diversity. A secondary result is the apparent contrast between the western diversity/disparity pattern (from Norway to the Gulf of Aden) and the eastern diversity/disparity pattern (Fig. 4). The western part associates few species with high disparity level (with one exception), while the eastern part associates an inverse pattern (with one exception). This intriguing geographical reverse pattern may have been, at least in part, a product of the history of the clade as a whole, and could reveal a complex biogeographical history (see Neige 2003a for details).

CONCLUSIONS

As reviewed here, the use of morphometrics on cuttlefish hard structures has allowed us to describe shape in a quantitative way. Several techniques have been employed, some traditional (i.e. Traditional Morphometrics), others more recently used for biological applications (i.e. Coordinate Morphometrics, Boundary Morphometrics). In the case of cuttlefishes, the main and traditional application of morphometrics is obviously concerned with taxonomic identification. But many other domains may also require morphometrics, for example functional morphology or biogeography, as demonstrated in the present paper. Some new techniques, such as Structural Morphometrics [START_REF] Lestrel | Morphometrics for the Life Sciences[END_REF], have not been attempted on sepiids yet, but it should be noted that their application for biological purposes is still very rare. These new techniques may open new perspectives to characterise texture or surface patterning, an interesting technique to quantify namely the shape of cuttlebone dorsal shield surfaces. These new morphometric tools have recently been explored for otolith characterisation [START_REF] Parisi-Baradad | Otolith shape contour analysis using affine transformation invariant wavelet transforms and curvature scale space representation[END_REF]. Fourier analysis has traditionally been used to represent otolith image. However, it is difficult to locate the contour's singularities from this spectrum. As an alternative, wavelet transform and curvature scale space representation allow to quantify the irregularities of the contour and to determine its precise position [START_REF] Parisi-Baradad | Otolith shape contour analysis using affine transformation invariant wavelet transforms and curvature scale space representation[END_REF].

Finally one might ask why cuttlefish should be a model within cephalopods, for the specific field of morphometric studies. This question may be answered if shape is seen not only as a static property but also as the result of a dynamic process of growth. In fact, description of shapes says nothing on the related processes that have generated them. T h e s ep r o c e s s e sh a v et ob ev i e w e da sac o m p l e x association of genetic and environmental factors. One very recent conceptual development that may be explored using morphometric tools is to affirm (or to reaffirm) that the shape of an organism and of its individual structures is a composite of many constituent parts: the so-called modules. Module partitioning and integration are genetically controlled [START_REF] Raff | Modularity and dissociation in the evolution of gene expression territories in development[END_REF][START_REF] Klingenberg | Developmental integration in a complex morphological structure: how distinct are the modules in the mouse mandible?[END_REF]. Their recognition can be based on partitions of configuration of landmarks. This emerging field of research is promising, because it opens the opportunity to understand shape in depth, and not only to mathematically characterise it. A consequence is that any scientific field that uses shape (e.g. taxonomy, phylogeny, biogeography) is potentially affected by these reinterpretations of morphology. For such studies, structures of organisms suspected to be arranged in modules are needed. Additionally specimens of different ontogenetic stages are needed in order to explore the variability at different taxonomic levels. Thus, cuttlebone is obviously the structure to be studied in this context. Existence of modules within the cuttlebone has already been pointed out by some authors, although they were not using this terminology, and did it in a qualitative way [START_REF] Adam | A review of the cephalopod family Sepiidae[END_REF][START_REF] Roeleveld | A review of the Sepiidae (Cephalopoda) of Southern Africa[END_REF][START_REF] Lu | Use of the sepion in the taxonomy of Sepiidae (Cephalopoda: Sepioidea) with an emphasis on the Australian fauna[END_REF]. Specimens are available from different species, at different ontogenetic stages, and possibly under different controlled conditions of growth if reared in the aquarium. Cuttlefish could therefore become a model even outside the study of cephalopods in this particular field of evolutionary biology.

Fig. 1 .

 1 Fig. 1. -Sepia officinalis and its main hard structures. A, cuttlebone. B, statoliths. C, beaks. D, radula. Only the first three structures have been studied using morphometric techniques.

Fig. 2 .

 2 Fig. 2. -The three main morphometric techniques applied to cuttlefish hard structures, exemplified here on a statolith. Note that they fundamentally differ by the nature of data they are based on (see text).

Fig. 3 .

 3 Fig. 3. -Overall morphospace (RW1 vs. RW2) of sepiid cuttlebones, and a plot of the first two relative warps shown as thin-plate splines, for positive and negative displacement along the axis. Mean shape is calculated from all shapes of the initial data matrix (covering all sepiid species known at present) (after Neige 2003a, modified).

Fig. 4 .

 4 Fig. 4. -Comparison of taxonomic diversity (left light bar) and morphological disparity (right dark bar) for each of the 17 biogeographical units for the complete cuttlefish clade. Note an intriguing geographical reverse pattern between West (few species with high disparity level) and East (many species with a relatively low disparity level).

ACKNOWLEDGMENTS. -This paper is a contribution to the Equipe "Forme, Evolution, Diversité" of the UMR CNRS 5561 Biogéosciences, and to the GDR 2474 "Morphométrie et evolution des formes". I thank the editors of this special volume for kindly inviting me to contribute this review. Thanks to the three reviewers for their constructive remarks, and to Aaron Hunter for his help with the English language.


Mingchao Ji

Jean-Philippe Champeaux
email: jean-philippe.champeaux@irsamc.ups-tlse.fr

Patrick Moretto-Capelle

Julie Renoud

Laurent Polizzi

Stéphane Faure

Martine Sence

Pierre Cafarelli

M.-C Ji

J.-P Champeaux

Absolute measurements of the double differential electronic emission cross-sections of isolated pyrene molecule (C16H10) in interaction with keV protons

Keywords: Molecular Physics, PAH, Cross Sections, Monte Carlo

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Introduction

The polycyclic aromatic hydrocarbon (PAH) molecules are widespread from the Earth to the interstellar medium (ISM). On Earth atmosphere, the PAHs are considered as environmental pollutants, thus the studies carried on PAHs in environmental science mainly focused on their pollution, degradation and bioremediation [START_REF] Sudip | Polycyclic aromatic hydrocarbons: environmental pollution and bioremediation[END_REF], [START_REF] Yu | Environmental carcinogenic polycyclic aromatic hydrocarbons: photochemistry and phototoxicity[END_REF]. In astrophysics, the PAHs are believed to be distributed ubiquitously in the ISM [START_REF] Puget | Identification of the 'unidentified' IR emission features of interstellar dust?[END_REF] [4] and were suggested to be possible carriers of the unidentified infrared bands (UIBs) from 3.3 -12.7 µm detected in many spectra of nebulae [START_REF] D'hendecourt | Are polycyclic aromatic hydrocarbons the carriers of the diffuse interstellar bands in the visible?[END_REF]. The PAHs were estimated to hold up to 20% of cosmic carbon based on the modeling of the absorption and emission power in a given radiation filed [START_REF] Joblin | Contribution of polycyclic aromatic hydrocarbon molecules to the interstellar extinction curve[END_REF]. These PAHs in astrophysical environments were expected to play important roles in the absorption of UV photons and heat input to the interstellar gas by photo-electric effects [START_REF] Tielens | The photoelectric heating mechanism for very small graphitic grains and polycyclic aromatic hydrocarbons[END_REF]. The stability of PAHs against degradation by radiation and high temperature may also have had functional and structural roles in the prebiotic chemistry [START_REF] Joost Groen | Polycyclic Aromatic Hydrocarbons as Plausible Prebiotic Membrane Components[END_REF]. Recent studies on the dissociation of PAHs induced by stellar wind particles and UV photon absorption both suggested that the PAHs could be the source of hydrogen molecule in some astrophysical environments [START_REF] Champeaux | Is the dissociation of coronene in stellar winds a source of molecular hydrogen? application to the HD 44179 nebula[END_REF] [10] [START_REF] Boschman | H2 formation on PAHs in photodissociation regions: a high-temperature pathway to molecular hydrogen[END_REF].

During the past three decades, the PAH hypothesis became widely accepted in astrophysics and initiated numerous theoretical and experimental studies on their physical and chemical properties, the and their interaction with photon and charged particles to clarify their evolution and role in the ISM [START_REF] Tielens | PAHs and the universe: a symposium to celebrate the 25th anniversary of the PAH hypothesis[END_REF]. Among all the studies, the infrared and electronic spectra are of great interest since they are directly related to the UIBs and the identification of PAHs in the ISM. The absorption/emission spectra of many PAHs have been extensively investigated from matrix-isolated to gas-phase environments [START_REF] Joblin | Infrared spectroscopy of gas-phase PAH molecules. II. Role of the temperature[END_REF] [START_REF] Salama | Polycyclic Aromatic Hydrocarbons and the Diffuse Interstellar Bands: A Survey[END_REF] [15] [START_REF] Malloci | Electronic absorption spectra of PAHs up to vacuum UV. Towards a detailed model of interstellar PAH photophysics[END_REF] [17] [START_REF] Junfeng Zhen | An optical spectrum of a large isolated gas-phase PAH cation: C78h26[END_REF].

The interaction with UV photons and cosmic particles are two dominant ways for the PAHs to gain energy in the ISM. Thus the energetic processing of PAHs after the interaction is crucial to determine the size and charge distribution, and the evolution of the PAHs in astrophysical environments. For this purpose, the ionization , dissociation and/or radiative cooling of a large number of PAHs after UV absorption or interaction with charged particles have been studied in detail [START_REF] Brandi | Photodissociation of Pyrene Cations: Structure and Energetics from C16h10+ to C14+ and Almost Everything in Between[END_REF] [START_REF] Junfeng Zhen | VUV Photo-processing of PAH Cations: Quantitative Study on the Ionization versus Fragmentation Processes[END_REF] [21] [START_REF] Martin | Fast Radiative Cooling of Anthracene Observed in a Compact Electrostatic Storage Ring[END_REF] [23] [START_REF] Holm | Dissociation and multiple ionization energies for five polycyclic aromatic hydrocarbon molecules[END_REF] [START_REF] Paris | Multiple ionization and hydrogen loss from neutral and positively-charged coronene[END_REF].

Although many works have been done on the PAHs, not even a single PAH species has been identified in the ISM up to now. The complex identification work requires not only the IR signatures but also the photophysics, interaction with cosmic particles or stellar winds particles, as well as possibles chemical reactivities of theses particular species to build up a clear picture of their role in the ISM [START_REF] Mulas | Interstellar polycylic aromatic hydrocarbons: from space to the laboratory[END_REF] [START_REF] Tielens | Diffuse Interstellar Bands: The Way Forward[END_REF].

In these context, we focus on one the pyrene smallest PAH : the pyrene molecule (C16H10) presented in figure 1 and, in particular, on its ionization cross section when interacting with stellar winds protons in close circum-stellar environement. A number of studies have been allready performed on pyrene molecules including (without been exhaustive) the optical spectra from infrared to UV range [START_REF] Joblin | Infrared spectroscopy of gas-phase PAH molecules. II. Role of the temperature[END_REF] [15] [START_REF] Malloci | Electronic absorption spectra of PAHs up to vacuum UV. Towards a detailed model of interstellar PAH photophysics[END_REF] and photon-induced dissociation and ionization processes [START_REF] Useli-Bacchitta | Visible photodissociation spectroscopy of PAH cations and derivatives in the PIRENEA experiment[END_REF] [21]. Up to date the studies on the collision-induced ionization and dissociation processes mainly carried concern the ionization energies, dissociation energies and pathways [28] [24]. No work on the collision-induced ionization cross-section was reported yet. In a recent paper [START_REF] Biswas | [END_REF], Biswas investigated both experimentally and theoretically differential electron emission cross-section for coronene and fluorene under 3.75 MeV/u O 8+ impact. Calculations were carried out with first-order approximation and good agreement with experimental results was obtained. A clear signature for the plasmon resonance was observed for coronene target.

In this paper, we report on the measurements of the double differential electronic emission cross-section (DDCS) 𝜕 2 𝜎(𝐸,𝜃) 𝜕𝜔𝜕𝐸 of isolated pyrene molecule, induced by protons with velocity of 1.4 to 2.2 atomic units corresponding to 50 to 125 keV.

A similar experimental method had been previously used to study the interaction of DNA/RNA bases with [30] and a detailed description of this method will be given in the coming section. These complete cross-section measurements were compared to the simulations of emitted electrons spectra obtained using a Semi-Classical Trajectory Monte-Carlo approach (SCTMC). The SCTMC method and the comparison with experimental results will be discussed.

Experimental Set-up

The experimental Set-up presented in figure 2 was developpe by the Interactions Ions-material team (I²M) of the LCAR laboratorie of Toulouse 3 University (UMR 5589).

A continuous ion beam produced in a high-frequency plasma ion source was accelerated to certain kinetic energies : 50, 75, 100 and 125 keV in this experiment series.

The proton beam current obtained after the mass over charge (m/q=1) selection through a 30° magnet was around 100 nA. The proton beam was then chopped at 25 kHz frequency by a pair of electrostatic deflectors in front of a 2 mm aperture to produce 500 ns width proton bunches. The temporal structure of the proton beam was used to discriminate signal from the constant background noise.

The obtain collimated protons bunches then entered the collision chamber and intercepted perpendicularly the continuous neutral pyrene molecular jet.

The pyrene molecular jet was obtained by sublimation of pyrene powder in an oven kept at 70±2 °C during the experiments. The pyrene powder was purchased from Sigma-Aldrich with 96% purity and was used without further purification.

The "collision"-induced electrons emitted at 35±1° from the proton beam axis were analyzed against their kinetic energy through a cylindrical mirror analyzer (CMA) and recorded by a SJUTS (KBL15RS) type channeltron. During the interaction between the incident protons and pyrene molecule, all the particules emitted at 90° with respect to the proton beam direction were collected by a micro-channel plates (MCP) detector associated to a drift tube, as shown in figure 2.

Doubly differential electronic emission crosssection measurements

Expression of the DDCS and experimental method

Experimentally, the absolute DDCS is linked to the number of electrons (Ne) detected by the CMA via the relation:

∂²σ 𝑖 ∂E ∂Ω e = 𝑁 𝑒 𝜂 𝑒 ∆E N ip [ρLΩ] 𝐶𝑀𝐴 eq. 1
Where [ρLΩ]CMA is a form factor homologous to a surface density. It regroups the absolute density profile of the molecular jet, the length of the interaction region (cross beam intersection of the two crossed beams) and the solid angle seen by the CMA channeltron detector at the emission point. ηe stands for the detection efficiency of the channeltron detector. E is the energy bandwidth of the CMA at electron energy E and Nip is the number of incoming protons.

Direct measurements of all parameters in eq.1 are experimentally very difficult to achieve with good accuracy and in particular, the absolute density of the molecular jet which appears in the surface density factor [ρLωe]. To overcome this problem, and get rid of the measurement of the molecular jet density, we have adopted the strategy of simultaneously records: the emitted electrons from pyrene, protons due to Rutherford scattering and particles (electrons and photons) emitted from K-shell ionization of the carbon atoms of the pyrene molecule. Cross sections of these three last processes are well known.

The protons from Rutherford scattering at around 90° from the proton beam axis were counted on the MCP detector, see Figure 2. These scattered protons were induced by low impact parameter collisions on the constituent atoms of the pyrene molecule i.e. mostly carbon atoms. The corresponding total cross-section is analytical and can be easily calculated by summing on the individual Rutherford cross-section of each atom of the molecule (P. Moretto-Capelle, 2006).

∂σ tot R ∂Ω 𝑝 = 𝑛 𝐶 ∂σ R (𝐻 + →𝐶) ∂Ω 𝑝 | 90° eq. 2
with nC=16 is the number of carbon atoms in pyrene.

Thus the number of protons scattered at 90° and detected on the MCP (𝑁 𝑝 𝑑𝑒𝑡𝑒𝑐𝑡𝑒𝑑 ) can be written as following according to eq. 2:

𝑁 𝑝 𝑑𝑒𝑡𝑒𝑐𝑡𝑒𝑑 = 𝜂 𝑝 ∂σ R ∂Ω 𝑝 [ρLΩ] 𝑀𝐶𝑃 N ip eq. 3
Considering their velocities (2 a.u), the 100 keV incident protons can also easily ionize the K-shell of the carbon atoms in the pyrene molecule. Then 277 eV K12 X-ray photons as well as electrons produced through the K-shell Auger cascades relaxations effect can be detected by the MCP detector.

According to NIST database, the most abundant primary Auger electrons following Carbon K-shell ionisation are emitted at around 260 eV. Then most of them are not stopped by the 200V polarized grid place in front of the MCP detector (see Figure 2.) and are recorded but others low energy electrons emitted by higher transition of the Auger cascade as well as electrons emitted by Hydrogen are stopped.

The collision induced Carbon-K Auger emission cross sections are very well documented. H. Paul et al. [31] have found between 8×10 3 barn at 35 keV collision energy to 5.6×10 5 barn at 200 keV with a maximum of 10 6 barn at 500-700 keV.

Moreover, for carbonated molecules such as pyrene, the total Auger emission cross section is directly proportional to the nC number of carbon atoms as shown by Biswas et al. [START_REF] Biswas | [END_REF].

Finally considering that the pyrene molecule was not experimentally oriented, the emitted Kphotons and Auger electrons are supposed to be emitted isotopically from the pyrene molecule after interaction.

Then, the corresponding differential emission crosssection can be written as the total one (noted σcK) divided by the total solid angle 4π and multiplied by the number of carbon atoms in pyrene:

∂σ K ∂Ω 𝑝 = 𝑛 𝐶 σ cK 4 eq. 4
The number of X-UV photons and Auger electrons detected on the MCP can be then expressed as:

𝑁 ℎ𝑣 𝑑𝑒𝑡𝑒𝑐𝑡𝑒𝑑 = 𝜂 ℎ𝑣 𝜔 𝐾 [ρLΩ] 𝑀𝐶𝑃 N ip ∂σ K ∂Ω 𝑝
eq. 5

𝑁 𝐴𝑢𝑔𝑒𝑟 𝑑𝑒𝑡𝑒𝑐𝑡𝑒𝑑 = 𝜂 𝑒𝐴 (1 -𝜔 𝐾 )[ρLΩ] 𝑀𝐶𝑃 N ip ∂σ K ∂Ω 𝑝 eq. 6
Where 𝑁 ℎ𝑣 𝑑𝑒𝑡𝑒𝑐𝑡𝑒𝑑 is the number of K X-ray photons detected by the MCP, 𝑁 𝐴𝑢𝑔𝑒𝑟 𝑑𝑒𝑡𝑒𝑐𝑡𝑒𝑑 detected is the number of detected Auger electrons, ηhυ is the MCP efficiency for X-UV photons at 277 eV and ηeA the MCP efficiency for 260 eV electrons.

The ωK factor is corresponding to the carbon fluorescence yield, which is very low for the photon emission following K-shell ionization : ωK=0.0035 10% [32]. Even if the main process of relaxation is therefore the Auger effect (i.e. 𝑁 𝐴𝑢𝑔𝑒𝑟 𝑑𝑒𝑡𝑒𝑐𝑡𝑒𝑑 > 𝑁 ℎ𝑣 𝑑𝑒𝑡𝑒𝑐𝑡𝑒𝑑 ), both processes were taken into account for the experimental DDCS estimation.

The particles from processes mentioned above (Rutherford scattered protons, Carbon K X-ray emission and Auger electrons) are detected by the MCP detector without any possible differentiation and the total number of counts detected by the MCP can be written as:

𝑁 𝑀𝐶𝑃 = 𝑁 𝑝 𝑑𝑒𝑡𝑒𝑐𝑡𝑒𝑑 + 𝑁 ℎ𝑣 𝑑𝑒𝑡𝑒𝑐𝑡𝑒𝑑 + 𝑁 𝐴𝑢𝑔𝑒𝑟 𝑑𝑒𝑡𝑒𝑐𝑡𝑒𝑑 eq. 7 𝑁 𝑀𝐶𝑃 = N ip [ρLΩ] 𝑀𝐶𝑃 (𝜂 𝑝 ∂σ R ∂Ω 𝑝 + 𝜂 𝑒𝐴 ∂σ K ∂Ω 𝑝 (( 𝜂 ℎ𝑣 𝜂 𝑒𝐴 -1) 𝜔 𝐾 + 1)) eq. 8
From the ratio between the number of recorded electrons (Ne) on the channeltron (eq. 1) and the number of particles (NMCP) detected on the MCP detector (eq. 8), we can then express the pyrene molecule's electronic emission DDCS as:

∂²σ 𝑖 ∂E ∂Ω e = 𝑁 𝑒 𝑁 𝑀𝐶𝑃 Γ 𝜂 𝑒 ∆E (𝜂 𝑝 ∂σ R ∂Ω 𝑝 + 𝜂 𝑒𝐴 ∂σ K ∂Ω 𝑝 (( 𝜂 ℎ𝑣 𝜂 𝑒𝐴 -1) 𝜔 𝐾 + 1)) eq. 9 Where Γ = [ρLΩ] 𝑀𝐶𝑃 [ρLΩ] 𝐶𝑀𝐴
only depends on the relative density profiles and the characteristics of the detectors in terms of solid angle seen by each detector, but no more depends on the absolute density of the pyrene molecular jet. Moreover, this DDCS formulation doesn't depend on the number of incident protons, which avoids precise measurement of the proton beam intensity.

In this serie of experiment, the proton energy range was 50 to 125 keV with 25 keV step. For such energies, the 90° Rutherford scattering cross-section is small comparing to the inner shell ionization cross-section. Thus, the main relaxation process will be the Auger electron emission and a coarse approximation of the DDCS can be expressed as:

∂²σ 𝑖 ∂E ∂Ω e ~ 𝑁 𝑒 𝑁 𝑀𝐶𝑃 Γ ∆E 𝜂 𝑒𝐴 𝜂 𝑒 ∂σ K ∂Ω 𝑝

eq. 10

Experimental determination of each parameter in eq. 10 will be described in the next paragraphs.

Experimental Evaluation of the 𝛤 factor

The evaluation of the Γ term requires the relative density profile of the gas-phase pyrene molecule jet. The relative density profile was estimated by measuring the deposit thickness profile on a glass surface which had been hold perpendicularly towards the molecule jet direction in the collision region with a deposit time of two hours under the same experimental conditions (oven temperature 70 °C and pressure 10 -7 Torr). Then the glass piece was scanned by a densitometer and a deposit thickness profile was obtained, as shown in figure 3. term was then estimated by Monte-Carlo simulation [30] which included the relative density profile measured above, the size of the projectile beam (2 mm diameter) and the geometrical characteristics i.e the relative positions, angles of detection, opening angle etc of the MCP and CMA spectrometers.

To achieve the simulation, 10 6 initials conditions have been randomly generated (positions according to intersection between beam and molecular beam profile as well as isotropic random direction for the velocity vectors). The Γ factor was then deduced from the ratio of the number of particles arriving on the MCP and the number of particles passing through the exit slit of CMA, we found : Γ=0.92 ± 0.02

Measument of the MCP yield ηp for 90° Rutherford scattered Protons

The MCPs used in these experiments are F4293-07 module manufactured by Hamamatsu. In order to measure the MCP yield ηp for Rutherford scattered protons, the MCP detector was mounted on a retractable manipulator in front of a Faraday cup and directly exposed to the incident proton beam. The proton beam energies were chosen from 40 to 105 keV which corresponds to the final kinetic energies of the 90° Rutherford scattered protons with initial kinetic energies from 50 to 125 keV. Two methods have been used for the absolute MCP yield measurement : one using a pulsed proton beam and the second using a continuous beam.

In the first method, the pulsed beam allows us to control the number N of ions per pulse, the probability to detect at least one ion at each pulse is then given by:

𝑃 = 1 -(1 -η p ) 𝑁 eq. 11
One has to achieve N<1 in order to have P~ηp. To obtain this, a continuous beam of intensity I0 = 100 pA pulsed with width t=1 ns gives average number N~0.6 per pulse.

Then the MCP detection efficiency can be express as :

η p = N c 𝑒 I 0 t eq. 12
where Nc is the count rate (in s -1 ) on the MCP and =30 kHz stands for the pulse frequency (e is the electronic charge). The MCP detection efficiency was measured to be constant over 30 -75 keV range and close to unity: ηp= 1 ± 0.05

In the second method, the MCP detector was exposed directly to a weak and stable continuous proton beam of intensity I0=20 fA, monitored by a Faraday cup and a Sub-Ampere multimeter (Keythley). The detection efficiency is then simply given by : η p = Ne I 0 T eq. 13

where N is the number of detected protons during the acquisition time T and I0 the intensity of the weak beam. With this direct method we obtained ηp =1.01 ± 0.05 in good agreement with the first method.

Such high detection efficiency near to unity is a consequence to the high kinetic energy of the protons which create secondary electrons on the MCP efficiently as well as the present a repeller grid (negative potential) placed in front of the MCP detector (B. Deconihout, 1996).

MCP yield ηeA for Carbon K photons

As mentioned before, we assumed that only UV photons from the ionization of the 1s 2 subshell of the carbon atoms can be detected on the MCP, the corresponding photon energy is 277 eV. The detection efficiency was extracted from the data for carbon K line efficiency given by Hamamatsu: a value ηeA=0.28 ± 0.08 was retained. The contribution of photons to the detected signal on the MCP is relatively small so a precise measurement of this efficiency is not critical for the absolute cross section measurement.

Channeltron yield ηe of the CMA

In order to calibrate the efficiency of the channeltron detector used inside the CMA electron spectrometer, a specific experimental setup was designed. Its principle is similar to that described by [33] and its schematics and CAO are illustrated in figure 4. This experimental setup consists of three spaced cylinders. The two external cylinders are 10 cm long and the middle one is 7 cm diameter. The middle cylinder was isolated from the two neighboring grounded cylinders and had a hole of 1 mm diameter on its sidewall.

A tungsten wire going through the center of the three tubes was heated up by a 1A DC current and floated to an adjustable negative potential U [0 -1000V]. Thus, inside the central cylinder, the thermal electrons emitted from the wire (cathode) penetrating into a uniform radial electric field and acquired well-defined kinetic energy with respect to the applied potential between the wire and the surface of the central tube. Electrons going through the hole on the central cylinder were counted by the channeltron mounted behind the hole (with the same montage as in the CMA). To stop the secondary electrons possibly produced on the inner wall of the hole, a polarized annular electrode was installed between the hole and the channeltron detector to allow only direct electrons to pass.

The middle cylinder was connected to a sub pico-ammeter (module 617 from Keythley) to measure the electronic current I_cylinder collected over its entire lateral surface. The surface ratio between the lateral surface and the hole was δ=2.4×10 4 . Thus the corresponding current through the hole can be calibrated as:

I hole = I cylinder δ eq. 14
By comparing the count rate of the channeltron detector and the calibrated current Ihole, detection efficiencies versus different incident electron kinetic energies were obtained.

The measured detection efficiencies was varying from ηe = 0.62 ± 0.02 to ηe = 0.75 ± 0.05 for incident electron energy from 100 eV to 1 keV respectively. An average efficiency of 0.7 ± 0.1 was retained for the cross section measurments.

The electron transmission inside the CMA spectrometer was also evaluated. For 25 eV electrons the total scattering cross-section is about 1.2×10 -15 cm 2 for N2 molecule [START_REF] Bennani | Measurement of the absolute electron detection efficiency of a channel multiplier (channeltron)[END_REF] and about 1.8×10 -15 cm 2 for H2O molecule [35]. The gas density under our experimental conditions (P ~10 -8 Torr) was about 10 9 cm -3 , therefore the mean free path was estimated to be about 8 km far longer than the trajectory length inside the CMA spectrometer (around 20 cm). We can then reasonably assume that the spectrometer transmission is 100% for measured electrons.

Noise reduction and 𝑁 𝑒 𝑑𝑒𝑡𝑒𝑐𝑡𝑒𝑑 , 𝑁 𝑀𝐶𝑃

𝑑𝑒𝑡𝑒𝑐𝑡𝑒𝑑

Measurments

In order to discriminate the N e detected and N MCP detected counts against the noise counts, a pulsed proton beam was used, so that the real signals were correlated temporally to the proton bunches. An example of raw histogram for 100 keV incident protons and 50 eV electrons detected on the CMA (36 h acquisition) is presented in figure 5. The temporal width of both peaks (counts on MCP and on CMA) was 500 ns corresponding to the temporal width of the incident proton bunches. If long enough to get suffisant statistic, such a temporal width was large comparing to the MCP arrival time differences between the Rutherford scattered protons, emitted Auger electrons and the X-UV photons coming from pyrene molecule, thus these three processes can't be temporally discriminated. The measured NMCP is then the one mentioned in eq. 7 and 8.

The long time scale background signal covering tens of microsecond corresponds to the asynchronous low velocity ions from the fragmentation of pyrene molecule. This cationic background signal was removed to evaluate NMCP.

The residual continuous background on the MCP coming from external noise is around 1 to 5 counts per channel over an integrating time of several days and can be then neglected.

SCTMC simulation methods for total and DDCS calculations

Classical Trajectory Monte-Carlo (CTMC) has been early [START_REF] Itikawa | Cross sections for electron collision with water molecules[END_REF] and intensively used and succeeded in the treatment of ion-atom collision [START_REF] Abrines | Proc. Phys. Soc[END_REF] [START_REF] Olson | [END_REF] and ion/molecule collision [39] [30]. In order to estimate the total and double differential electronic emission cross-sections of pyrene molecule as well as to compare with our experimental results, we have developed a fast optimized 3D Semi-Classical Trajectory Monte Carlo code. In these simulations, classical electrons and proton trajectories in the molecular potential derived from quantum calculations are performed. Typical keV proton-pyrene interaction and pyrene electronic emission (ionization) occurs at very short time scale (fs) comparing to nuclear motion, thus the pyrene molecule nuclei motions were not considered.

The numerical method implemented to integrate differential equations was a basic adaptative Runge Kutta method at the 4th-5th order (RKF45) with auto-adaptive relative step precision fixed from 10 -5 to 10 -8 to ensure satisfying total energy conservation over the calculated trajectory [40] and to achieve a reasonable calculation time per trajectory. Random numbers generation was done using Mersenne twister MT19937 algorithm [START_REF] Press | Numerical Recipies[END_REF].

SCTMC Initial Pyrene electron position and velocity

The initial position of the electron was randomly drawn following the distribution of the probability of presence deduced from the square of molecular orbitals (MO) wave function of pyrene molecule. The norm of the initial velocity of the electron was obtained through energy conservation knowing both binding energy of the MO and molecular potential Vm. The direction of the initial velocity is chosen randomly. Geometry of the MO, binding energy and Vm have been calculated using Gamess code [START_REF] Matsumoto | Mersenne twister: A 623dimensionally equidistributed uniform pseudorandom number generator[END_REF] using 6-31G(d,p) basis set at the Self Consistent Field (SCF) level of theory in D2h symmetry. An example of initial position distribution obtained for 50 103 electrons randomly picked up in the pyrene Homo orbital is shown in figure 6:

SCTMC Initial proton position, molecular orientation and reference surface

The molecular orientation was chosen randomly with uniform angle distribution, reproducing the experimental conditions.

The proton initial position was selected randomly in a reference surface Sref [30] perpendicular to the velocity vector of the incoming protons as shown in figure 7, at a distance of ten times the molecular radius (pyrene classical radius Rmol= 8.64627 a.u.) where the molecular potential and electron-proton force field is close to zero. The Sref is then:

𝑆 𝑟𝑒𝑓 = 4𝛼²(𝑅 𝑚𝑜𝑙 ) eq. 15
This reference surface was "empirically" chosen in a way that protons initially starting at the edge of this surface didn't induce any ionization of the molecule no matter where the initial position of the electron in the molecule was or what the molecular orientation was. The factor  was adjusted by iterative simulations increasing its value from 1 till no ionization event is detected for edge protons. In present CTMC simulations we found =1. 45.

The corresponding reference surface is then: 628.714 a.u² (176.058 10 -16 cm²). For this surface, 15 million trajectories with proton starting from its edge were performed showing no ionization event.

Then, the molecular orbital cross section can be writing as a function of Sref and ionization probability as:

𝜎 𝑀𝑜 = 𝑁 𝑘 𝑁 𝑡𝑟𝑎𝑗 . 𝑆 𝑟𝑒𝑓 eq. 16
Where Ntraj is the total number of generated trajectories and Nk is the number of trajectories conducting to the event of interest. The ionization process under interest will be characterized by the emission of the electron in the continuum of the molecule at an energy E and a θ angle relatively to the proton velocity vector.

SCTMC Potential

For theses simulations, the interacting potential are the coulombic interaction between electron and proton 𝑉 𝑐 𝑝,𝑒 - and the molecular potential Vm of the singly ionized pyrene molecule in its fixed neutral geometry. Individual atomic motions or molecular recoil are not take into account seen ionization occurs in very short time scale (fs) compare to any atomic motions (ps).

For numerical convenience, the molecular potential Vm was approximated by a sum over each atom of the molecule of a screened potential function and can be written as:

𝑉 𝑚 (𝑟 ⃗) = ∑ 𝑍 𝑖 𝑒 -𝑘 𝑖 |𝑟 ⃗ ⃗⃗-𝑅 ⃗⃗⃗ 𝑖 | |𝑟 ⃗-𝑅 ⃗⃗ 𝑖 | 𝑛 𝑖=0
eq. 17

Where r and Ri are the position of electron and atom i. The screen function coefficient (ki) and theeffective atomic charge (Zi) were adjusted to reproduce the molecular potential obtain with the Gamess code. Zi was found to be equal to 4 and 1 and ki=1.55 a.u -1 and 1.45 a.u -1 for carbon and hydrogen atoms respectively. Figure 8 presents an example of electron classical trajectory starting from HOMO orbital in the fitted Vm molecular potential without e -/proton interaction. The figure 8 shows a very good stability of the electron classical motion in the fitted molecular potential for a long integration time scale (typically >100 ps). Possible numerical "accidental" ionization linked, for example, to the discontinuity of the fitted potential near each atom and/or to the minimum pitch/precision couple set for the RKF45 method have been tested using energy conservation criteria (with respect to the virial theorem). Compromise between precision, stability and total duration of each trajectory was performed. A transient variation of less than 1% of the total initial energy was tolerated.

For the MO considered, the number of detected "accidental" ionization in the Vm potential (without proton interaction) were much lower than 1/1000 simulated trajectories. The ionization occurred essentially at very long integration time (10th of ps) comparing to the typical interaction time between the electron and the proton (At a 2 a.u velocity, the protons travels hundred times the pyrene molecular radius in ~20 fs).

CTMC: Simulated Cross Sections

For each MO, the partial ionization cross-section was evaluated over more than 10 million trajectories with typical simulations running over 100 random molecular orientations, 200 initial electron positions and 500 initials proton positions.

This large number of trajectories per orbital was sufficient to ensure full convergence of the total cross-section and to guaranty enough angular statics for DDCS calculation. The more bounded is the M.O. (electronic densities close to molecular atoms) the more trajectories simulations takes time (2 Weeks /orbitals) mostly due to the auto-adaptive stepper of the used numercical method. Then for Homo-36 "only" 2 million trajectories were evaluated and K-shell M.O. ionization cross-sections were not calculated. Missing orbitals partial ionization cross-sections will be interpolated (see paragraph 5).

We assume in our simulation that ionization of the electron was achieved when its distance from the molecule became greater than 1.5 time the molecular radius before proton reaches 10 time the molecular radius. The convergence of the electron kinetic energy was also checked as well as possible to determine if we observe a real ionization or a capture on the proton.

Trajectories of ionized electrons and outgoing proton were then extended (without molecular potential interaction i.e. only electron-proton interaction) at a long distance from the molecule (1000x Rmol) to guaranty a good proton/electron emission angle convergence. Final angles θ (referenced by the incoming proton axis), assymptotic velocities vectors and kinetic energy E of the ionized electrons were recorded.

The total ionization cross-section were derived from the eq. 14 for each MO including the MO multiplicity (closeshell i.e. 2 electrons per MO), so the total cross-section can be written as:

𝜎 𝑡𝑜𝑡𝑎𝑙 = 2 ∑ 𝜎 𝑀𝑜 𝑀𝑜 eq. 18
Similarly, the double differential cross-section was obtained from the NMO(E,θ) electron energy, angle 2D histogram with δE and δθ the binning resolution such as: For these simulations including the proton/electron interaction, the number of "false" ionization were higher than in the case of single electron/molecular potential interaction discussed in paragraph 4.3, especially for core-MO as shown in table 1 which presents the total number N of simulated trajectories per MO and number of rejected trajectories N*. This high number of bad trajectories for deeper shell orbitals is related to the less relevant sampling/interpolation of the wave function for core-MO. Indeed, the grid step covering the molecular volume extracted from the Gamess orbital calculation was not adaptive. Consequently, the regions with a high density of probability of presence or those having a strong gradient (which was the case for core-MO) may not be well sampled when determining the initial classical position of the electron. Then the electrons being potentially drawn at the same "places" can create redundancies in the initial conditions and the trajectories even for "good" trajectories (i.e. those respecting the 1% energetically criteria mentioned above (see 4.2)). This will result in an overestimation of the MO ionization cross-section of the core-MO, and a "fictive" increase of the convergence speed (in term of the number of simulated trajectories) of the total CTMC ionization crosssection simulations. This over-sampling of the core-MO may also induce a lower dispersion around the converged crosssection value which consequently conducted artificially to a drastic underestimation of the associated statistical uncertainty.

The CMTC cross-sections were finally calculated by removing the wrong trajectories. However, in order to include theses numerical biases we have chosen to take into account bad trajectories for cross-section uncertainties estimation.

Results and discussions

Total ionization cross-section

For each considered MO, the figure 9 presents the corresponding partial ionization cross-section as a function of the number of trajectories calculated, for 100keV/pyrene interaction. As we can see from Figure 9, the partial cross-section were well converged for every calculated orbitals after 8 Millions of trajectories. Then from the calculated HOMO-x, SCTMC cross-section simulation, intermediate HOMO orbitals ionization cross-sections were extrapolated.

Phenomenologically the total cross-section seems to follow a continuous exponential decay with the MO energies as shown in figure 10. The total uncertainty estimation takes into account statistical dispersion (95% of confidence) around the converged values evaluated over the last 1 Million trajectories, the uncertainty relative to the "bad" trajectories and the uncertainty of the exponential fitting curve.

Finally, summing over all MO partial cross section according to eq. 18, the total SCTMC single ionization crosssection of pyrene at 100 keV collision energy was estimated to: SCTMC= (47.59 ± 10.03) × 10 -16 cm² This value is in good agreement with the geometrical crosssection: 49.7 × 10 -16 cm².

In order to check once more this value, we have used Rudd's electron emission cross-section for 100 keV proton impact on molecules. Rudd et al obtained a cross-section of 7.4 × 10 -16 cm² and 2.26 × 10 -16 cm² for CH4 and H2 respectively [START_REF] Schmidt | General Atomic and Molecular Electronic Structure System[END_REF]. From those cross-sections and assuming that additivity rules apply, we can write (C16H10)=16(C)+10(H) with (C)= (CH4) -2(H2) and  (H)= (H2)/2, a total cross-section of 57.4 10-16 cm² was then obtained also in good agreement with the CTMC calculated one.

It must be noted that photoionization cross-section for pyrene or coronene is about 32 Mb per carbon [44] i.e. 51.2 × 10 -16 cm 2 for the pyrene molecule which is comparable to the total ionization cross-section by 100 keV proton found in this work. So the ionization via solar wind particles is as effective as UV photons (for comparable flux) in close circumstellar environment.

Results on Doubly Differential Cross Sections

From SCTMC trajectories the partial double differential ionization cross-sections for each considered molecular orbital and for 100 keV incident proton was evaluated using eq. 15.

To build the required NMo(E,θ) 2D histogram, steps of  and E = 0.1 a.u were used. Example of obtained results for Homo and Homo-36 orbitals are presented in figure 11.

The obtained partial DDCS peaked at low electrons energy and essentially in the forward direction ( from 0° to 20°) due to Post Collision Interaction (PCI) effect. One manifestation of this PCI effect is the Electron Capture in the Continuum (ECC) [45] corresponding to the peaks in figure 11 and obtained for all molecular orbitals at 0° and kinetic energy E2 a.u i.e. electron having the same velocity and direction as the 100 keV proton projectile but not bounded to it. In the SCTMC calculation, it was found that the electron energy distribution extended to higher energy when the electron emission came from more internal valence orbitals. The inner MO corresponds to higher binding energy and ionization potential and leads to higher energy in the energy distribution, this is qualitatively consistent with the empirical Rudd's formula (for single differential cross section, nevertheless) [START_REF] Crooks | Experimental Evidence for the Mechanism of Charge Transfer into Continuum States[END_REF]:

𝑑𝜎 𝑡𝑜𝑡 𝑑𝐸 = 5 𝑎 0 2 𝛼 3 𝐼 𝐻 2 ∑ 𝑁 𝑖 𝐼 𝑖 3 (𝑇/𝐼 𝑖 ) 𝛽-1/2 4+(𝑇/𝐼 𝑖 ) 2𝛽 𝑖 𝑒 - 𝛼𝐸 √𝐼 𝑖 𝑇 eq. 20
Where α and  are adjustable constants depending on target, Ii and Ni binding energy and occupation of level i, E the kinetic energy of the emitted electrons and T the energy of electron with the same velocity as the projectile. Experimental total electronic emission DDCS were measured at =35° for 25, 50, 100 and 150 eV, the corresponding partial SCTMC DDCS were extracted (θ = 35 ± 5°, E = E0 ± 0.05 eV). As for the case of partial MO ionization cross-section, non-calculated partial DDCS can be estimated by interpolation as show in figure 12. Experimental DDCS measured at 35° for 50, 75, 100 and 125 keV protons and simulated (35°, 100 keV proton) CTMC DDCS have been regrouped in table 2 and are presented in figure 13 as a function of emitted electron energies.

A reasonable agreement was obtained between CTMC simulations and the experimental DDCS at 100 keV collision energy even if the CTMC DDCS was always overestimated comparing to the measured one with a factor of 2.3 at low electron energy and a factor of 5.75 at 150 eV. This overestimation of the DDCS cannot be attributed to numerical problems or limited statistics since total crosssection was well converged and that CTMC overestimated uncertainties doesn't allow any overlap with experimental datas. But the Semi Classical model is as expected a coarse approach that gives only an order of magnitude of the DDCS.

Both experimentally measured and CTMC simulated DDCS in figure 13 highlights a strong population of low energy electrons which seems to be a general phenomenon in ion-atom collision [START_REF] Rudd | Ionization by low and intermediate energy ion and neutral beams[END_REF] or ion/molecule [START_REF] Rudd | Mechanisms of Electron Production in Ion-Atom Collisions[END_REF].

A strong increase of the cross-section with collision energy was experimentally observed from 50 to 125 keV and the maximum cross-section was reached at around 100-125 keV according to the quasi equivalent DDCS in this energy range. The DDCS obtained at 50 keV was quite low and might be underestimated. The experimental DDCS at 35° decrease almost exponentially with the energy of emitted electrons.

Conclusion

We have investigated the electron emission of a PAH molecule, the pyrene, submitted to solar wind particles, namely keV protons, both experimentally and theoretically through the Semi-Classical Trajectory Monte-Carlo method.

Absolute differential cross-sections were for the first time obtained and a reasonable agreement between experiment and semi-classical CTMC calculation achieve. The total cross-section of ionization process obtained from the CTMC method was comparable with the geometrical cross-section of the pyrene molecule.

The measurement of absolute quantities of such crosssection are important in astrophysics, has the reaction yields of such ion/molecule collision process are directly related to the cross-section. With the knowledge of the cross-section, the fragmentation patterns of the molecule can be quantified in an absolute way so that even the secondary molecular species generated by ionization process can be quantified. The ionization cross-sections obtained in the current work are comparable to the Photoionization cross-section. Therefore, such collision processes have to be taken into account for the PAHs physico-chemistry in Circumstellar environment especially in compact planetary nebulae.

Figure 1 .

 1 Figure 1. Neutral pyrene molecule geometry

Figure 2 .

 2 Figure 2. Schematic of the experimental setup

Figure 3 .

 3 Figure 3. Schematic of the experimental setup

Figure 4 .

 4 Figure 4. Experimental set-up for channeltron efficiency measurement

Figure 5 .

 5 Figure 5. Exemple of Raw Data histogram detected on the MCP and the CMA.

Figure 6 .

 6 Figure 6. Example of Homo random initial positions of the electron of pyrene molecule.

Figure 7 .

 7 Figure 7. Simulation geometries and reference surface definition (in atomic units).

Figure 8 .

 8 Figure 8. Classical trajectory, projected in the plane of the molecule, of an electron of the HOMO in the analytical molecular potential Vm. The green dots represent the positions of the atoms of the Pyrene molecule.

Figure 9 .

 9 Figure 9. Convergence of the MO total ionization cross-section as a function of the number of trajectories.

Figure 10 .

 10 Figure 10. MO SCMTC cross-sections (green dots), interpolated MO cross-sections from SCTMC cross-section (red squares).

Figure 11 .

 11 Figure 11. DDCS of pyrene electron emission for HOMO (upper part) and HOMO-36 (lower part) MO interacting with 100 keV protons. White dots correspond to the experimental conditions (35°, 25 -125 keV protons).

Figure 12 .

 12 Figure 12. partial SCTMC DDCS interpolation for pyrene electron emission from HOMO-x (x=0 to 36) and various electron emission energies : 25, 50, 100 and 150 eV

Figure 13 .

 13 Figure 13. Comparison of the DDCS between experiment and CTMC calculations

Table 1 .

 1 Number of rejected trajectories per MO

	M.O	N	N*	N*/N
	Homo	10 7	714354	7,14%
	Homo-1	10 7	749764	7,49%
	Homo-2	10 7	839546	8,39%
	Homo-5	10 7	1197211	11,97%
	Homo-10	10 7	1272417	12,72%
	Homo-15	10 7	1363274	13,63%
	Homo-36	2.10 6	676775	33,83%

Table 2 .

 2 Total DDCS from CMTC calculations for 100 keV protons and experimental DDCS at 35° dσ(35°,Ek)/dEdΩ (cm 2 sr -1 eV -1 ) x10-19

	Ek	50 keV	75 keV	100 keV	100 keV	125 keV
		Exp. (err)	Exp.(err)	CTMC(err)	Exp.(err)	Exp.(err)
	25 eV	4.26	20.23	100.7	43.81	51.85
		±1.70	±8.09	±21.5	±17.53	±20.74
	50 eV	1.04	5.51	36.5	11.37	14.86
		±4.16	±2.21	±7.8	±4.55	±5.94
	100 eV	0.08	0.78	11.9	2.16	3.08
		±0.04	±0.32	±2.6	±0.87	±1.24
	150 eV	0.007	0.12	2.82	0.49	0.86
		±0.003	±0.05	±0.59	±1.98	±0.35

Acknowledgements

We thank's the Labex Next (http://www.next-toulouse.fr/) for its financial support to these researches.


Virginie François

Arnaud F Klein

Cyriaque Beley

Arnaud Jollet

Camille Lemercier

Luis Garcia

Denis Furling
email: denis.furling@upmc.fr

Virginie Francois

Selective silencing of mutated mRNAs in DM1 by using modified hU7-snRNAs

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

We describe a novel function for modified human U7-snRNAs distinct from modification of pre-mRNA splicing events. Engineered hU7-snRNAs harboring a poly-CAG antisense sequence targeting the expanded CUG repeats of mutant DMPK transcripts in myotonic dystrophy cause specific degradation of pathogenic DMPK mRNAs without affecting wild-type DMPK allele products. Abolition of the RNA-gainof-function toxicity responsible for pathogenesis supports use of hU7-snRNAs for gene silencing in RNA-dominant disorders expressing expanded repeats.

Myotonic dystrophy type 1 (DM1), the most prevalent form of adult muscular dystrophy 1 is caused by expanded CTG repeats in the 3'untranslated region of the DM protein kinase (DMPK) gene 2 . This autosomal dominant genetic disease belongs to a group of RNA gain-offunction disorders 3 expressing pathogenic RNAs. Mutant DMPK transcripts containing up to thousands of expanded CUG repeats (CUG exp ) are entrapped in the nucleus 4 . Such an accumulation alters the regulation of alternative splicing, which subsequently leads to missplicing of several mRNA transcripts and neuromuscular dysfunction 5 . Indeed, CUG exp RNAs are folded in such a way that they aberrantly interact with proteins in the nucleus and bind muscleblind-like 1 (MBNL1) with high affinity to form stable ribonucleoprotein aggregates or foci 6 . Sequestration of MBNL1 in these complexes leads to a loss-of-function of this splicing regulator and alternative splicing defects 7 .

Strategies for phenotype rescue in DM1 using synthetic antisense oligonucleotides that target CUG expansions have been evaluated in mouse DM1 models 8, 9 . Local delivery of either morpholinos or 2'-O-methyl phosphorothioate oligonucleotides was performed with the aim to interfere and unfold CUG exp RNAs to release MBNL1 from foci, thus making it available for its overall splicing function. However the use of synthetic oligonucleotides requires repeated treatments to counteract continuous expression of toxic CUG exp RNAs. To circumvent this limitation and trigger a long lasting effect, we have developed an optimized human U7-snRNA harboring a poly-CAG antisense sequence to target the CUG exp RNAs (Fig. 1a). A fragment of about 0.5kb containing the human U7 gene was amplified from human genomic DNA and the U7-snRNA transcript was optimized 10 . First, its Sm binding domain was replaced by a canonical Sm sequence derived from the major snRNA (Sm-Opt) to bind appropriate Sm proteins that allow efficient snRNP assembly and increase its nuclear accumulation 11 . Subsequently, the natural histone pre-mRNA complementary sequence of U7-snRNA was replaced by a poly-CAG. The engineered human U7-snRNA-(CAG) n was kept under the control of its natural promoter and 3' downstream elements (Supplementary Fig. 1). This construct was further cloned into a lentiviral backbone for high efficiency gene transfer and long lasting expression in human cells.

To evaluate the potential of engineered hU7-snRNA-(CAG) n to target the CUG exp RNAs, skeletal muscle cells isolated from DM1 patients with various sizes of CTG expansions were transduced with lentiviral vectors expressing an optimized hU7-(CAG)15 (hU7-snRNA with 15 CAG repeats). In these cells, mutant alleles exhibited CTG expansions ranging from 800 to 2000 repeats while normal-sized alleles contained less than 37 repeats. Transduced cells were grown for several divisions before assessing DMPK mRNA stability. Northern blot analysis showed that the steady-state levels of CUG exp DMPK transcripts were significantly (P<0.001) reduced by 71 to 82% in DM1 cells expressing hU7-(CAG) 15 (Fig. 1b). Disappearance of expanded DMPK mRNAs occurred in a vector dose-dependent manner (Supplementary Fig. 2a), which correlated with hU7-(CAG) 15 expression in transduced DM1 cells (Supplementary Fig. 2b). The hU7-(CAG) 15 system allowed continuous and permanent targeted destruction of the deleterious transcripts over subsequent cell divisions (Supplementary Fig. 2c) as well as in non-mitotic muscle cells (Supplementary Fig. 2d,e).

Importantly, the normal-sized DMPK mRNA was preserved in treated DM1 cells (Fig. 1b).

This phenomenon was also confirmed in transduced wild-type myoblasts containing normalsized DMPK alleles (Supplementary Fig. 3). In addition, expression of a modified hU7control (without poly-CAG repeats) in DM1 cells did not induce degradation of CUG exp DMPK transcripts demonstrating the specificity of the poly-CAG antisense sequence (Supplementary Fig. 4). Furthermore, no specific occurrence of alternative modes of DMPK transcripts was induced by hU7-(CAG) 15 in DM1 cells (Supplementary Fig. 5a and data not shown). In particular, the alternative splicing event in the 3'DMPK region leading to the DMPK isoform exon14/exon16 (lacking both exon15 and CUG tract due to the presence of a putative 3'DMPK exon16) 12 was not promoted by hU7-(CAG) 15 , and no change in DMPK protein levels was observed in treated-DM1 cells (Supplementary Fig. 5b), establishing the selective silencing of CUG exp DMPK transcripts by engineered hU7-(CAG) 15 .

To further assess the disappearance of mutated DMPK mRNAs, we examined the CUG expribonucleoprotein complexes, which accumulate as foci in nuclei of DM1 cells. Fluorescence in situ hybridization (FISH) analysis showed a dramatic dose-dependent loss of these nuclear structures in treated DM1 myoblasts (Fig. 1c and Supplementary Fig. 6). Up to 60% of the hU7-(CAG) 15 treated DM1 myoblasts displayed no foci (P<0.001). In addition, 25% of them displayed only a single faint focus and no remaining foci were observed in the cytoplasmic compartment. Nuclear and cytoplasmic RNA fractionation of DM1 cells containing a transcripts are retained in the nucleus and are not exported to the cytoplasm (Fig. 1d). In the presence of hU7-(CAG) 15 , no transcripts from the expanded allele were detected in the cytoplasmic fraction suggesting a selective CUG exp DMPK mRNAs nuclear degradation mechanism. Strikingly, this mechanism did not affect DMPK pre-mRNAs, indicating that hU7-(CAG) 15 acted at mRNAs or foci levels rather than at the RNA genesis stage.

In order to evaluate the effect of the length of the CAG antisense sequence, we designed additional hU7-snRNA constructs harboring shortened CAG sequences (7 and 11 repeats). All hU7-(CAG) n targeted and silenced efficiently CUG exp DMPK mRNAs (P<0.001) in DM1 cells (Fig. 2a), when expressed at similar level in DM1 cells (Supplementary Fig. 7a).

However the shortened constructs also affected (P<0.01) the products of the normal-sized DMPK allele bearing 13 repeats. Such a loss of specificity prompted us to analyze six nonrelated human transcripts bearing CUG tracts ranging from 7 to 16 repeats (Supplementary Fig. 7b). Four of these gene products were unaffected in DM1 cells expressing hU7-(CAG) 7either11or15 . Nevertheless, altered expressions of CPA6(7CUG) and LRP8(11CUG) transcripts were observed in the presence of hU7-(CAG) 7or11 while the larger (CAG) 15 construct did not affect any of the selected transcripts.

To determine whether hU7-(CAG) 15 can reverse pathophysiological consequences of toxic CUG exp RNAs, we focused on DM1 hallmarks such as MBNL1 sequestration and abnormal regulation of alternative splicing. Even if MBNL1 distribution is not homogenous in primary DM1 cell cultures (Supplementary Fig. 8a,b), combined FISH-immunofluorescence analysis showed that silencing CUG exp mRNAs leads to the release of sequestered MBNL1 from the nuclear CUG exp -aggregates and a redistribution of MBNL1 in treated DM1 cells (Fig. 2b) as confirmed by the reduced number of DM1 cells containing MBNL1 foci (Supplementary Fig. 8c). The outcome on DM1 splicing misregulation was examined on DMD, BIN1 and LDB3 genes, which are abnormally spliced in differentiated DM1 muscle cells. Splicing profiles of these genes were significantly normalized (P<0.05) in the presence of hU7-(CAG) 15 , while hU7-(CAG) 15 did not affect the splicing of these genes in wild-type cells (Fig. 2c). In addition, hU7-(CAG) 15 did not induce a general shift in splicing since alternative splice modes that are unaltered in DM1 samples 7 were not affected (Supplementary Fig. 9). Moreover, because large CUG expansions altered the myogenic differentiation of DM1 muscle cells 14 , we also tested whether hU7-(CAG) 15 can overcome this deficiency. In the presence of hU7-(CAG) 15 , the fusion index of treated-DM1 myoblasts was appreciably restored (P<0.01) to a level similar to that of wild-type myoblasts (Fig. 2d).

In conclusion, our data show that the hU7-(CAG) n system allowed long-lasting selective destruction of deleterious CUG exp RNAs in DM1 cells. MBNL1 and possibly other mRNA binding factors are subsequently released from foci, thereby improving splicing abnormalities and differentiation defects. The length of the CAG antisense sequence seems critical because hU7-(CAG) n harboring less than 15 CAG repeats affects the normal-size DMPK allele products and perturbs the expression of some non-related transcripts bearing short (CUG) n tract. The precise mechanism by which the hU7-(CAG) 15 triggers selective and robust silencing of CUG exp RNAs is not fully determined but seems to require the association of multiple hU7-snRNA molecules. Engineered hU7-snRNA-(CAG) n described in this study as well as morpholinos 8 or 2'-O-methyl phosphorothioates 9 , which have been successfully applied in DM1 models, are not supposed to trigger RNase activities. On the contrary, these compounds are commonly used to force alternative splicing in both exon skipping and exon inclusion strategies 15 . It seems unlikely that the selective destruction of CUG exp DMPK mRNAs in the presence of these (CAG) n antisense molecules is based on canonical RNA interference mechanisms. Furthermore, small 19-22 nucleotides RNA fragments composed of CUG or CAG repeats were not detected in DM1 cells expressing or not hU7-(CAG) 15 (Supplementary Fig. 2b), strongly suggesting that the RNAi machinery is not involved in hU7-(CAG) 15 activity. Finally, specific hU7-(CAG) 15 -mediated silencing that appears to take place in the nuclear compartment, is not a splicing-related mechanism. Rather, disappearance or accelerated decay of CUG exp RNA/ hU7-(CAG) 15 heteroduplexes may be due to natural instability of the mutant DMPK mRNAs that is counteracted by MBNL1 binding in DM1 pathological context, or to a novel RNA degradation mechanism. Taken together, abolition of the RNA toxicity associated with DM1 pathogenesis supports the use of hU7-snRNAs for gene silencing in RNA-dominant disorders expressing expanded repeats.

Figure 1

 1 Figure 1 CUG exp RNAs silencing by hU7-(CAG) 15 . (a) Structure of the hU7-snRNA-(CAG) 15 indicating the loop, the Sm-Opt and the CAG antisense sequences. (b) Representative Northern blot and analysis (n=5) of DMPK mRNA expression in DM1 muscle cells (13/800CTG) transduced with hU7-(CAG) 15 lentiviral vector (4-8x10 6 vg ml -1 ). (c) FISH analysis (n=4) of the number of CUG exp -mRNA foci (red spots) into the nuclei (blue) of hU7-(CAG) 15 transduced (8x10 6 vg ml -1 ) DM1 cells (800CTG). (d) RT-PCR assay of normal and CUG exp -DMPK mRNA, GAPDH mRNA, U6 snRNA and DMPK pre-RNA in nuclear and cytoplasmic fractions of DM1 converted muscle cells (11/1300CTG). BpmI restriction site polymorphism located within exon 10 of expanded DMPK allele identifies normal and CUG exp allele products.

Figure 2

 2 Figure 2 Consequences of hU7-(CAG) n expression in DM1 muscle cells (a) Expression of normal and CUG exp -DMPK mRNAs in DM1 cells (13/800CTG) transduced with hU7-(CAG) n vectors (4x10 6 vg ml -1 ) harboring antisense sequences of 7, 11 or 15 CAG (Northern blot, n=3). (b) Localization of the splicing regulator MBNL1 in DM1 cells. (c) Correction of alternative splicing misregulation of BIN1, DMD and LDB3 transcripts in differentiated DM1 muscle cells (2000CTG) transduced with hU7-(CAG) 15 vectors (8x10 6 vg ml -1 )(RT-PCR, n=3). (d) Effect of hU7-(CAG) 15 expression on myogenic differentiation of DM1 muscle cells (2000CTG) quantified as fusion index (n=6).

ACKNOWLEDGMENTS

This work was supported by the Association Francaise contre les Myopathies (AFM). We thank D. Brook (Institute of Genetics, University of Nottingham, UK) for the DM1 Bpm1fibroblasts, I. Holt and G. Morris (CIND, RJAH Orthopeadic Hospital, UK) as well as "The Muscular Dystrophy Association Monoclonal Antibody Resource" for the MBNL1(MB1a) and DMPK(MANDM1) monoclonal antibodies, MyoBank-AFM for the muscle biopsies, O. Danos for viral production facility, S. Chaouch and V. Mouly for cell culture facility, and the French DM1 network, J. Puymirat, MSG, G. Butler-Browne and T. Voit for their helpful discussions.

AUTHOR CONTRIBUTIONS

V.F. and A.K. conducted most of the experiments. C.B. performed the constructs. A.J. produced the lentiviral vectors. C.L. supported some experiments. L.G. engineered the modified hU7-snRNA. D.F. supervised the entire project. L.G. and D.F wrote the manuscript.

§ L.G and § D.F should be considered as equal contributors.

COMPETING FINANCIAL INTERESTS

The method described in this paper is the subject of a patent application (inventors L.G, D.F, C.B and T.V)

Supplementary information

Selective silencing of mutated mRNAs in DM1 by using modified hU7-snRNAs Virginie Francois * , Arnaud F. Klein * , Cyriaque Beley, Arnaud Jollet, Camille Lemercier, Luis Garcia * & Denis Furling *

SUPPLEMENTARY METHODS

Cell culture

Human muscle cells were isolated from skeletal muscle biopsies or autopsies as described 1 , in accordance with French legislation on ethical rules. Wild-type (WT) and DM1 myoblasts were grown in HAM's F10 medium supplemented with 20 % FCS and 5 µg ml -1 gentamycin (Invitrogen), at 5% CO2 and 37°C. To trigger differentiation, growth medium was removed from subconfluent cultures and replaced by DMEM medium supplemented with 10 µg ml -1 insulin and 100 µg ml -1 transferrin (Sigma). To block cell division, the cultures were treated with 30µg ml -1 of mitomycin C (Sigma) for three days. DM1 fibroblasts containing a BpmI polymorphic restriction site on the expanded DMPK allele 2 were immortalized and converted into muscle cells using an inducible MyoD system as previously described 3 .

Lentivirus production and transduction

A self-inactivated HIV -1 -based lentiviral vector, pRRL-hU7-(CAG) n and pRRL-hU7-control (containing the GAAGTCTTATCTTTAATATG antisense sequence) were generated from the previously described pRRL-cPPT-hPGK-EGFP-WPRE vector 4 . VSV-G-pseudotyped vectors were produced by transient transfection of 293T cells 5 . The conditioned medium containing viral particles was collected and concentrated by ultracentrifugation. Vector titers (vector genome vg ml -1 ) were determined by quantitative PCR on genomic DNA of infected cells as described 5 .

1x10 6 to 1x10 7 vg ml -1 were used to transduce 1.5x10 5 human muscle cells. Vector transduction was performed overnight in the presence of 4 µg/ml of polybrene (Sigma) and the transduced cells were grown and amplified at least one week before analyses.

RNA isolation and Northern blot

Cells were lyzed in a proteinase K buffer (500 mM NaCl, 10 mM Tris-HCl, pH 7.2, 1.5 mM MgCl 2 , 10 mM EDTA, 2% SDS and 0.5 mg ml -1 of proteinase K) for 45 min at 55°C. Then, RNAs were isolated using TRIzol reagent (Invitrogen) according to the manufacturer's protocol.

RNAs were also isolated from nuclear and cytoplasmic fractions prepared as described previously 2 by hypotonic lysis in the presence of NP-40. For Northern blot analysis, 8-10 µg of RNA was separated on 1.3 % agarose MOPS-gels containing 0,66 M formaldehyde and transferred onto Hybond-N+ membrane (Amersham Pharmacia Biotech) by capillary transfer with 10x SSC. Blots were hybridized with random-primed 32 P-labeled (Bgl II-Sac I fragment of DMPK cDNA) probe in a hybridization buffer (2 % SDS, 10 % dextran sulfate, 1 x SSPE, 100 µg ml -1 salmon sperm DNA, 2 % Denhart's) at 68°C overnight. Signals were analyzed on a phosphoimager (Molecular Imager FX, Bio-Rad) and quantified using Quantity One (Bio-Rad). All values were normalized to 18S rRNA signal after hybridization with 5'-end 32 P-labeled 18S

rRNA-oligonucleotide probes. To detect the small hU7-snRNAs and miR-24, RNA was isolated using TRIzol reagent (Invitrogen). For Northern blot analysis, 15-20 µg of RNA was separated on 12 % polyacrylamide urea gels and transferred to Hybond-N+ membrane. Blots were hybridized with a hU7-snRNA 32 P-labeled probe (AGGGGCTTTCCGGTAAAA) or miR24 probe (TGTTCCTGCTGAACTGAGCCA) in hybridization buffer (6 X SSPE, 2 % Denhart's, 0,1 % SDS) at 42°C overnight.

RT-PCR analysis

1 µg of RNA was reverse transcribed using M-MLV first-strand synthesis system according to the manufacturer's instructions (Invitrogen) in a total volume of 20 µl. One µL of cDNA preparation was subsequently used in a semiquantitative PCR analysis according to standard procedures (ReddyMix, Thermo Scientific). PCR amplification was carried out for 20-35 cycles, within the linear range of amplification for each gene. The signal of GAPDH was used for normalization. PCR products were analyzed on 1-3% agarose gels, stained by ethidium bromide.

Quantification was done using the Quantity One software (Bio-Rad). For alternative splicing analysis, the genes and exons selected had been previously described as being altered in muscle from DM1 patients: exon 78 for DMD 6 (dystrophin), exon 7 for LDB3 7 (cypher) and exon 11 for BIN1 8 (bridging integrator1). The ratios of exon inclusion were quantified and expressed as percentage of inclusion relative to total intensities of isoform signals. For DMPK analysis, to distinguish the two alleles of DMPK, 6 µl of the PCR mixture was put into a 25 µl digestion mixture containing 2.5 units of BpmI (New England Biolabs) and incubated overnight at 37°C as described 2 . For hU7-snRNA analysis, addition of a poly(A) tail to 2 µg of total RNA was made using poly(A) plus polymerase tailing kit (Epicentre technologies, Madison, WI) according to manufacturer protocol. Then 1 µg of the resulting poly(A)-RNAs was reverse transcribed using a specific dT-UPR primer. hU7-snRNA-(CAG) n or endogenous hU7-snRNA were amplified using forward specific primers and reverse UPR primers.

The following primers were used:

FISH and immunofluorescence

Fluorescent in situ hybridization (FISH) was done as described 9 using a Cy3-labeled peptide nucleic acid (CAG) 7 probe. To determine the number of foci per nucleus, more than 500 DM1 cells were counted in at least three independent experiments. Combined FISHimmunofluorescence (IF) experiment was done as described 10 using a monoclonal MBNL1 antibody (MB1a developed by G. Morris 11 ) followed by a secondary Alexa 488-conjugated goat anti-mouse (Invitrogen) antibody. Pictures were captured using a Leica confocal microscope and software (Leica microsytems), and processed with Adobe Photoshop software (Adobe System Inc.). For fusion index analysis, IF was performed on differentiated muscle cell cultures as described 12 using a desmin (D33, DAKO) antibody and the nuclei were counterstained with Hoechst 33258 (Sigma). More than 1500 nuclei were counted and the fusion index was determined by the number of nuclei in differentiated myotubes (>2 myonuclei) as a percentage of the total number of nuclei in desmin-positive cells.

Western blotting

Western blotting was performed with standard methods using a DMPK antibody (MANDM1) as described previously 13 .

Statistical analyses

Group data are expressed as mean+/-SEM. Between group comparison was performed by unpaired Student's t test (Fig. 1b, 1c, S3, S4, S5 and S7) and Newman-Keuls test (Fig. 2a, 2b, 2c) using GraphPad Prism 4 software. Differences between groups were considered significant when P < 0.05 (*, P < 0.05; **, P < 0.01; ***, P < 0.001).