Dr Gireeshkumar Balakrishnan
email: gireeshkumar.balakrishnan_nair@univ-lemans.fr

Fabienne Lagarde

Christophe Chassenieux

Arnaud Martel

Elise Deniau

Taco Nicolai

Fate of polystyrene and polyethylene nanoplastics exposed to UV in water

Keywords: Nanoplastics, microplastics, nanoparticles, UV irradiation-induced degradation, polyethylene, polystyrene

The possible presence of plastic particles with a size smaller than 1 µm in the aquatic environment raises widespread concern over their environmental impact. Therefore, it is important to understand whether and to what extent nanoplastics dispersed in water degrade under UV irradiation. To address this issue, we studied the effect of UV irradiation on monodisperse polystyrene (PS) latex particles with hydrodynamic radii 0.10, 0.25, 0.52, and 2.5 µm as well as on polydisperse polyethylene (PE) particles with an average hydrodynamic radius of 0.35 µm. The degradation rate of both polymers was studied under high intensity UV irradiation, while only the degradation of PS was studied under simulated sunlight, as the degradation of PE was too slow in this case. The degradation was characterized with light scattering techniques, confocal laser scanning microscopy, UV visible spectroscopy, and total organic carbon (TOC) analysis. All particles were found to fully degrade, but the degradation rate of PS particles was much faster than that of PE particles. Aggregation of PS particles after the addition of sea salt did not inhibit their degradation under UV irradiation. TOC analysis showed that the large majority of the carbon of the polystyrene was converted into volatile products. Interestingly, both polymers, PS and PE, showed no change in the radius of the particles until their mass had decreased by more than 70%, implying that degradation mainly occurred within the particles through the release of organic molecules. The formation of hollow particles and their final fragmentation were confirmed by CLSM microscopy. It was estimated that complete degradation of nanoplastics dispersed in water and exposed to simulated sunlight takes about a month for PS and 2 years for PE, assuming that the effect of the radiation intensity was the same for PE as was determined for PS.

Introduction

There is growing concern over plastic waste in the marine environment. In the last 50 years, huge quantities of plastics entered the aquatic environment where they have been accumulating with unknown lifetimes [START_REF] Browne | Microplastic--an emerging contaminant of potential concern?[END_REF][START_REF] Eriksen | Plastic pollution in the world's oceans: more than 5 trillion plastic pieces weighing over 250,000 tons afloat at sea[END_REF] . Once in the marine environment, plastics undergo transformation, weathering and degradation and with possible fragmentation and/or erosion leading to the formation of microplastics and nanoplastics. Microplastics constitute a huge family of particles with sizes up to 5 mm displaying various shapes and chemical natures making it difficult to characterize their impact on marine life [START_REF] Andrady | The plastic in microplastics: A review[END_REF][START_REF] Barnes | Accumulation and fragmentation of plastic debris in global environments[END_REF] . Secondary nanoplastics with a size smaller than 1 µm can be released from macro and microplastics by strong mechanical abrasion of plastics such as milling [START_REF] Gardon | Cryogrinding and sieving techniques as challenges towards producing controlled size range microplastics for relevant ecotoxicological tests[END_REF] or rotational abrasion [START_REF] Song | Combined effects of UV exposure duration and mechanical abrasion on microplastic fragmentation by polymer type[END_REF] , but may also be the result of weathering 3,7, 8, 19, 9-11. In addition, primary micro-and nanoplastics are used in a range of industrial products and may be unintentionally released into the environment [START_REF] Müller | Disentangling biological effects of primary nanoplastics from dispersion paints' additional compounds[END_REF] . Ter Halle et al [START_REF] Ter Halle | Nanoplastic in the North Atlantic subtropical gyre[END_REF] reported for the first time their presence in the North Atlantic Gyre. Since then, nanoplastics have also become an increasing concern as their impact on organisms might be very important [START_REF] Tallec | Nanoplastics impaired oyster free living stages, gametes and embryos[END_REF][START_REF] Zaki | An overview of the effects of nanoplastics on marine organisms[END_REF] .

Whereas, the breakdown of macroplastics into micro and nanoplastics under environmentally relevant conditions has been investigated extensively in the last years [START_REF] Andrady | The plastic in microplastics: A review[END_REF][START_REF] Lambert | Characterisation of nanoplastics during the degradation of polystyrene[END_REF][START_REF] Julienne | From macroplastics to microplastics: Role of water in the fragmentation of polyethylene[END_REF][START_REF] Zhu | Photochemical dissolution of buoyant microplastics to dissolved organic carbon: rates and microbial impacts[END_REF][START_REF] Meides | Reconstructing the Environmental Degradation of Polystyrene by Accelerated Weathering[END_REF][START_REF] Menzel | Degradation of low-density polyethylene to nanoplastic particles by accelerated weathering[END_REF][START_REF] Qin | Liberation of plastic nanoparticles and organic compounds from three common plastics in water during weathering under UV radiation-free conditions[END_REF][START_REF] Ren | Elucidating the characteristic of leachates released from microplastics under different aging conditions: Perspectives of dissolved organic carbon fingerprints and nano-plastics[END_REF] , relatively few studies have reported on the ultimate fate of nanoplastics in the aquatic environment under UV-irradiation [START_REF] Pfohl | Environmental Degradation of Microplastics: How to Measure Fragmentation Rates to Secondary Micro-and Nanoplastic Fragments and Dissociation into Dissolved Organics[END_REF] . Concerning microplastics, very recently, Liu et al. [START_REF] Liu | Quantifying the dynamics of polystyrene microplastics UV-aging process[END_REF] reported a study of the degradation of polystyrene (PS) microparticles suspended in water during high intensity UV-irradiation in which they measured the size and number of the resulting particles. They observed that initially cavities were formed within the particles that subsequently break-up into smaller ones [START_REF] Liu | Quantifying the dynamics of polystyrene microplastics UV-aging process[END_REF] with the production of large amounts of nano/microsize fragments. Zhu et al [START_REF] Zhu | Photochemical dissolution of buoyant microplastics to dissolved organic carbon: rates and microbial impacts[END_REF] studied the degradation of several types of microplastics under sunlight and they showed that dissolved organic carbon (DOC) was the major by-product of sunlight-driven plastic photodegradation. Similarly, Ward et al [START_REF] Ward | Sunlight converts polystyrene to carbon dioxide and dissolved organic carbon[END_REF] showed that the complete oxidation of PS particles could occur within decades, producing CO 2 and dissolved organic carbon as the main products. Considering that nanoplastics are smaller than microplastics, it could be expected that their conversion into dissolved organic carbon should be quite fast. However, Paik et al [START_REF] Paik | Kinetics of thermal degradation and estimation of lifetime for polypropylene particles: Effects of particle size[END_REF] reported that the lifetime of thermodegraded polypropylene nanoparticles was moderately high compared to the polypropylene microparticles and other studies suggested that fragmentation process could be limited at small scales [START_REF] Brouzet | Laboratory model for plastic fragmentation in the turbulent ocean[END_REF] . Understanding the fate of nanoplastics is very important in view of their persistence and accumulation and their possible release of toxic plastic leachates and degradation products.

Therefore, the objective of the present study was to understand the fate of nanoplastics suspended in water under the influence of UV irradiation. Aqueous suspensions of commercial monodisperse PS latex particles with different well-defined sizes and polydisperse PE nanoparticles that were prepared as described elsewhere [START_REF] Balakrishnan | Towards more realistic reference microplastics and nanoplastics: preparation of polyethylene micro/nanoparticles with a biosurfactant[END_REF] , were irradiated using a high intensity UV lamp. Complete degradation under simulated sunlight could be studied for PS particles, but was too slow to achieve for PE particles. The molar mass and hydrodynamic radius were measured as a function of the irradiation time using static and dynamic light scattering techniques. As far as we know, this is the first investigation where both static and dynamic light scattering techniques were combined to understand the photodegradation mechanism of nanoplastics in water. We will show that measuring both the molar mass and the hydrodynamic radius during the degradation process is needed to fully describe the degradation mechanism. Moreover, the total organic carbon in the aqueous phase was monitored and allowed us to show the formation of volatile breakdown products.

PS is a major pollutant, but we are aware that understanding the degradation of PE is more relevant as it is far more common in the environment. Nevertheless, in this study PS particles were studied in more detail than PE particles, because they are commercially available in many well-defined sizes and degrade much faster. PS particle suspensions are therefore excellent model systems to study the effect of size on the degradation mechanisms and speed. The comparison of light scattering measurements on PS and PE particles during irradiation showed that the degradation process on the colloidal length scale is similar even though it occurs at different rates. As indicated above, PE degradation was found to be too slow under simulated solar irradiation for the study to be feasible. However, we were able to obtain realistic estimates of the degradation rate of PE nanoparticles in the natural environment by assuming that the effect of high-intensity UV irradiation and simulated solar irradiation on the degradation rate of PS nanoparticles was approximately the same for PE particles. To the best of our knowledge, this is the first study in which both the change of molar mass, size and structure of the small micro-and nanoplastics and the release of volatile organic carbon were monitored during photodegradation.

MATERIALS AND METHODS

Materials

Model polystyrene latex particles with 4 different hydrodynamic radii (R hz ) varying by more than one order of magnitude (R hz =0.10, 0.25, 0.52 and 2.5 µm) were purchased from Polysciences. According to the provider, the particles were negatively charged due to the presence of carboxylate groups on their surface which make them stable against aggregation. The 2.5 µm particles contain some divinylbenzene as the cross-linker. However, all other particles are free of any additives. The density of the polystyrene particles was 1.05 g/cm [START_REF] Andrady | The plastic in microplastics: A review[END_REF] .

Polyethylene particles were prepared without any surfactant using an emulsions of toluene in water with PE dissolved in the toluene phase as described in reference [START_REF] Balakrishnan | Towards more realistic reference microplastics and nanoplastics: preparation of polyethylene micro/nanoparticles with a biosurfactant[END_REF] . The toluene and water were removed by freeze-drying the emulsion which yields PE particles with R hz ranging between 0.2 to 0.8 µm. After freeze-drying, the PE powder was free of toluene which was confirmed with Raman spectroscopy and thermogravimetric analysis. It was shown that a small amount of PE particles could be dispersed in ultra-pure water without adding a surfactant forming a stable dilute suspension. It was speculated that the stability was in this case due to accumulation of charges onto the particles. The suspension of PE particles was filtered through 1 µm pore size filters. Light scattering measurements showed that after filtration, the R hz of the PE particles ranged between 0.1-0.5 µm with an z-average R hz = 0.35 µm.

Light scattering

Static and dynamic light scattering measurements were done using commercial equipment ALV/CGS3 (ALV-Langen, Germany) and quartz cells containing either PS or PE particles in ultrapure water. We verified that at the low concentration (5 mg/L) at which these measurements were done the effect of interaction between the particles was negligible. The light source was a He-Ne laser with wavelength λ = 632 nm. The temperature was controlled by a thermostat bath at 20 ± 0.2 °C. Measurements were made at angles of observation (θ) between 13 and 150 degrees which correspond to a scattering vector (q) range between 3×10 6 and 3×10 7 m -1 . We have used toluene as the standard.

In a static light scattering experiment, the time-averaged scattering intensity of the sample (suspended particles and solvent) was measured as a function of . The relative intensity of the suspended particles, Irel, was then calculated by subtracting the intensity of the solvent and dividing by that of a standard, for which we used toluene. I rel is related to the weight average molar mass (M w ) and the structure facture (S(q)) [START_REF] Berne | Dynamic light scattering: with applications to chemistry, biology, and physics[END_REF][START_REF] Brown | Dynamic light scattering: the method and some applications[END_REF][START_REF] Hulst | Light scattering by small particles[END_REF] of the particles according to:

I rel =KCM w S(q) ( 1
)
where K is an optical constant that depends on the setup and the specific refractive index increment of the solute. S(q) describes the dependence of the scattered intensity on the scattering vector q and for particles of any shape, the initial q-dependence of S(q) can be expressed as a series expansion in terms of the z-average radius of gyration (R g ).

(

) 2
In dilute solution, S(q) depends on the shape of the particles and is equal to 1 for q0. In order to measure the molar mass of particles with light scattering the condition q.R << 1 must be met. This cannot be done for particles with R = 2.5 µm where we can detect no plateau values for I rel at the lowest investigated q values by opposition to what is shown in fig. 1 and fig. S6.

In a dynamic light scattering experiment, fluctuations in the scattering intensity around the time-averaged value discussed above are measured to obtain the diffusion coefficient (D) and the z-average hydrodynamic radius (Rhz) of the particles. First, the autocorrelation functions of the intensity g 2 (t) are measured for different values of . Then, the autocorrelation functions of the electric field (g 1 (t)) are derived from g 2 (t) using the Siegert relation [START_REF] Berne | Dynamic light scattering: with applications to chemistry, biology, and physics[END_REF][START_REF] Brown | Dynamic light scattering: the method and some applications[END_REF][START_REF] Hulst | Light scattering by small particles[END_REF] . In this work, g 1 (t) was fitted with a monomodal relaxation time distribution (A()) according to :

  (3)
with

 (4)
where is a normalization constant,  gex is a characteristic relaxation time and p and s are parameters that characterized the different shape of the distribution. In dilute solutions the relaxation time is related to the diffusion coefficient of the particles:

 (5)
R hz can be calculated from D using the Stokes-Einstein relation. (6) where k is the Boltzman constant, T is the absolute temperature and  the viscosity of the solvent. In this manner A(, the relaxation time distribution obtained at q  0 can be transformed into a distribution of R hz . The z-average hydrodynamic radius (R hz ) was calculated from the average diffusion coefficient obtained at q  0.

Confocal laser scanning microscopy (CLSM)

Morphological changes of PS particles in suspension were investigated utilizing a Zeiss LSM 800 (Oberkochem, Germany). A water immersion objective lens was used (HCxPL APO 63× NA = 1.2) with a theoretical resolution of 0.1 μm in the x-y plane. The PS particles were fluorescently labelled by adding Nile red or Fluorescein isothiocyanate (FITC) that spontaneously adsorbed to the particles. The stock solutions of Nile red and FITC were prepared in ethanol and in water, respectively. The concentration of the fluorophore was 5 ppm in the particle suspension. FITC or Nile red was added after the UV irradiation because they bleach during irradiation. Initially, all the Nile red was bound to the PS particles. At longer irradiation times when most of the PS had degraded we observed the formation of dense and bright crystals of Nile red, which, however, could be easily distinguished from the PS particles. At longer UV irradiation time, we also used FITC to confirm the observations obtained with Nile red.

UV-visible spectroscopy

The UV-visible spectrum of PS particle suspensions at the different ageing times was recorded with a UV-visible spectrometer (Jasco PAC-743). The absorbance (A) was recorded between wavelengths 200-900 nm with a scan speed of 400 nm/minute at a temperature of 20°C. The path length of the light through the cell was 1 cm. With this setup, absorbance measurements are reliable up to 4.

Total organic carbon analysis (TOC)

TOC analysis was performed on PS latex particles with R hz = 2.5 and 0.25 µm and the samples (C = 100 mg/L) at different irradiation times were diluted by a factor of 4 before performing TOC measurements. The analysis was done, using a Multi N/C 3100 (Analytik Jena) TOC analyzer equipped with an autosampler. The TOC values are measured based on the integration signals of CO 2 by the infrared detector for total carbon (TC) and total inorganic carbon (TIC). The TOC value is calculated as TOC = TC-TIC. The vials used as containers for the TOC analyses were kept in an oven at 500°C for 8h to avoid any trace of organic matter and cooled down before further use. The conditions used in the method were as follows: from 5 to 8 measurements were performed with a coefficient of variation below 2%. The sample volume was 200 µL and the rinse volume was 1 mL. The integration time was 300 s and the stirring rate was fixed to 6. For TC measurements, the combustion temperature was set to 750°C. IC measurements were performed in the IC reactor with H 3 PO 4 10% wt. For TIC, three calibrations were performed between 0.1 and 100.0 mg/L corresponding to a limit of detection based on the lowest calibration curve equal to 33.7 µg/L.

For TC, three calibrations were also performed ranging from 1.0 up to 1000.0 mg/L leading to a limit of detection based on the lowest calibration curve of 112.1 µg/L. The average of three values differing by less than 2% was taken. We note that the measured values were always three times bigger than the detection limit and remained within the calibration range.

Irradiation

Two kinds of set-ups were used to UV irradiate the PE and PS suspensions. In order to simulate sunlight exposure, the samples were placed in a commercial solar exposure simulator (XLS+ chamber, Atlas), which is equipped with a xenon lamp, see figure S1a. Weathering was achieved with a daylight filter following the ISO 4892-2 standard at 40°C and a black standard temperature of 65°C. The irradiation intensity was 60 W/m², which corresponds to a solar radiation exposure of 216 kJ.m².h -1 . To accelerate the process further, the suspensions were also irradiated using a high intensity UV lamp. The high intensity UV lamp (HTC 400-241 SUPRATEC HTC/HTT, OSRAM GmbH) was used without any filter and was fixed inside a black box at a distance of 75 cm from the irradiated samples, see figure S1b of the supplementary information. The same lamp has been used earlier for the accelerated weathering of plastics [START_REF] Gewert | Identification of chain scission products released to water by plastic exposed to ultraviolet light[END_REF] . The temperature inside the quartz tubes was between 40 and 50°C due to the heat from the UV lamp. The intensity of the lamp near the sample was around 360 W/m², i.e. 6 times higher than with the solar chamber. We note that the spectra of the two UV light sources are not the same, see figure S2 For the analysis by light scattering techniques, PE or PS particle suspensions at C = 5 mg/L in ultrapure water (Millipore) were placed in capped quartz cells with an inner diameter of 8 mm. The tubes were placed at an angle so that the total path length of the light through the sample was 10 mm. These samples were transparent and the intensity of UV light was almost the same over the whole depth. The samples were regularly homogenized during irradiation and before the light scattering measurements by handshaking.

For TOC, CLSM, and UV-visible spectroscopy measurements on PS particles with radii of 2.5 µm and 0.25 µm, a quartz beaker containing 80 ml of the PS suspension at C=100 mg/L was placed under the high intensity UV lamp, while gently stirring with a magnetic stirrer to avoid sedimentation and ensure uninform UV exposure. 10 ml of the suspension was removed from the beaker at regular time intervals during the UV irradiation for the TOC analysis. During irradiation, the beaker was closed with a quartz cap and the sides of the cap were sealed with Teflon tape to avoid evaporation. These samples were only weakly turbid, which means that the UV-irradiation was on average less intense than for the dilute samples used for light scattering analysis. Therefore, ageing is expected to be somewhat slower.

However, this effect became progressively less important as more of the sample was removed so that the path length through the sample decreased from the initial 80 mm. A scheme of the experimental set-up is shown in figure S3.

Two different initial concentrations (c=5 mg/L and C=100 mg/L) of PS particles because for light scattering experiments the sample need to be transparent and therefore diluted whereas visually the breakdown is more easily seen at high concentration. It also allowed us to study the effect of concentration in terms of the penetration of the UV light in more turbid samples.

The reproducibility of the treatment was tested by irradiating at least two independent samples of the same systems. The results were combined in figs 3 and 5, which showed that the reproducibility is very good.

Results and Discussion

Degradation of PS particles during high intensity UV irradiation

The degradation of the PS particles with initial hydrodynamic radii R hz = 0.10, 0.25 and 0.52 µm was quantified by measuring their molar mass and radius after different UV irradiation times by light scattering techniques. Reliable light scattering measurements require that the suspension is transparent. Therefore, we did these measurements at a low concentration of PS particles (C = 5 mg/L), at which the suspensions were transparent and interaction between the particles was negligible. This means that all particles received the same irradiation. For comparison, the behaviour of the particle suspensions was also studied as a function of time in the dark. Figure S4 of the supplementary information shows the qdependence of the scattering intensity for samples kept at different times in the dark. It is characteristic for monodisperse spherical particles and no change was observed even after 120 hours indicating that the particles did not degrade when not irradiated. No aggregation upon time was detected either. Note that even weak aggregation is easily detected by light scattering as the scattered light intensity is proportional to the molar mass, see eq. 1.

Figure 1 displays the results that have been obtained for the PS particles with R hz = 0.10 µm and 0.25 µm after different UV irradiation times. A systematic decrease of the relative intensity (I rel ) was observed with increasing UV irradiation which means that the molar mass of the particles decreased assuming that their refractive index increment, and thus K, does not change significantly, see eq. 1. Interestingly, up to 48 h irradiation no significant change of the q-dependence was observed, which means that the form and size of the particles remained unchanged. After 72 h irradiation, particles could still be detected. However, the qdependence of I rel showed that the particles were no longer spherical and monodisperse. After 96 h, the scattering intensity was not significantly higher than that of Millipore water, see figure S5 of the supplementary information, and no particles were detected, which shows that the particles had fully degraded. Similar results were obtained for particles with R hz = 0.52 µm as shown in figure S6 of the supplementary information. Analysis of the autocorrelation functions determined with DLS on the same samples showed narrow relaxation time distributions from which R hz could be determined, as described in section 2.2. The dependence of R hz on the irradiation time is shown in Figure 2b.

R hz remained the same up to 40 h for particles with initial R hz = 0.10 and 0.25 µm and decreased weakly at longer times. The size of particles with initial R hz = 0.52 µm had already decreased significantly after 40 hours of UV irradiation. Interestingly, when comparing fig 2a

and b, it appears that the degradation of the particles induced by UV-radiation did not cause a change in their size until their mass had decreased very substantially. The implication is that the material was not preferentially removed from the surface, but rather from the interior of the particles. This degradation phenomenon was induced by UV radiation, as no degradation was observed for particles kept in the dark, see figure S4. UV light can easily penetrate relatively small particles, which explains why degradation occurred everywhere and not specifically on the surface.

We also investigated the effect of the initial concentration of PS particles with R hz = 0.25 µm by increasing the concentration from 5 to 100 mg/L. At C = 100 mg/L the suspension was initially turbid, see figure 3. The suspension was irradiated at different UV irradiation times under gentle stirring to avoid uneven exposure to UV. Figure 3 shows the evolution of the visual appearance of a PS particle suspension at different UV irradiation times. The turbidity of the particle suspension decreased with increasing UV irradiation and after 72 hours it became transparent. M w and R hz of the PS particles at different UV irradiation times were determined after dilution to C = 5 mg/L. In Figure S7(a) we compare the relative decrease of I rel (t) at q  0 with respect to the initial value as a function of the irradiation time for particles aged at C=5 mg/L and aged at C=100 mg/L. The corresponding comparison for R hz is shown in figure S7(b). As expected, the degradation rate was slower for the turbid suspensions due to the lower average irradiation intensity received by the particles. However, in both cases the degradation mechanism was the same, i.e. material was preferentially removed from within the particles. In order to observe the morphological changes during UV irradiation with CLSM we studied a suspension of larger PS particles with R h = 2.5 µm at C=100 mg/L. The particles were stirred gently during irradiation. After the UV irradiation, the particles were labelled with Nile red. We note that no fluorescence was detected without adding a fluorophore.

Figure 4 shows images of the PS particle suspensions at different ageing times. Up to 40

24 h 48 h 72 h

hours of irradiation the fluorophore rapidly distributed homogeneously throughout the particles. However, after 60 h irradiation, the fluorescence was no longer homogenously distributed within the particles but appeared to be localized, which suggests the removal of material from the interior of the particles. After 72 h most particles showed a strong fluorescent shell with almost no fluorescence from the inside. After 96 h UV irradiation, smaller particles were formed, probably due to the break-up of larger ones. Finally, no particles were detected after 120 h of UV irradiation. It is clear that all particles were broken down at approximately the same rate, which justifies the assumption that the decrease of the scattering intensity corresponds to a decrease of the molar mass of the particles. These results are in agreement with those reported by Liu et al [START_REF] Liu | Quantifying the dynamics of polystyrene microplastics UV-aging process[END_REF] . mentioned in the Introduction. The results from light scattering and confocal microscopy are in agreement and show that the degradation of PS particles upon irradiation was not restricted to their surface.

Material was mostly removed from the interior of the particles, which explains why the breakdown occurred at approximately the same rate for particles of different sizes, see figure 2a. Here we used spherical particles, whereas nanoplastics formed by weathering or abrasion are not expected to be spherical. However, since the material is mostly removed from the

µm 0 h 40 h 60h 72h 96h

interior of the particles, we don't expect the shape to play a major role in the degradation rate as long as the UV-light can penetrate to the core of the particles. However, if the particles are so large that a significant fraction of the UV light cannot penetrate them, the shape of the particles will become an important parameter to take into account.

When the particles sediment or cream and form a thick dense layer, the UV light cannot penetrate all particles. This is what happened when PS particles with R hz = 2.5 µm at C=100 mg/L, were exposed to UV without stirring, leading to the formation of a thick particle layer at the bottom of the quartz beaker due to sedimentation. It explains why we found that the degradation rate of sedimented particles was slower than when sedimentation was avoided by stirring, see figure S8 and figure S9 of the supplementary information for CLSM images of the particles labelled with Nile red and FITC, respectively. We noticed that FITC adsorbed to the particles only after more than 24 h UV irradiation. The reason is most likely that UV irradiation chemically modified the particles. From figure S8 and figure S9 it is clear that without stirring, only a few particles were degraded from the inside at t = 72 h, but most of the particles were affected between t = 96 and 120 h. After 178 h UV irradiation, smaller particles were also formed. No particles were detected by confocal microscopy after 216 hours of UV irradiation. This indicates that the degradation rate was slower without stirring, but in both cases, degradation started from the inside.

Figure 5 shows the absorbance spectra of PS particles with R hz =0.25 µm at C= 100 mg/L after different durations of irradiation while stirring gently. The spectra are in agreement with the UV visible spectrum of polystyrene earlier reported in the literature [START_REF] Ward | Sunlight converts polystyrene to carbon dioxide and dissolved organic carbon[END_REF][START_REF] Li | UV absorption spectra of polystyrene[END_REF] .

Before irradiation, the spectrum showed an absorbance peak at 250 nm together with the effect of turbidity that decreased with increasing wavelengths. The absorbance peak at 250 is due to the aromatic ring of the polystyrene as was reported elsewhere [START_REF] Ward | Sunlight converts polystyrene to carbon dioxide and dissolved organic carbon[END_REF][START_REF] Li | UV absorption spectra of polystyrene[END_REF] . After 24 h irradiation, the turbidity of the suspension had decreased, but the amplitude of the absorbance at 250 nm showed a weak increase. However, after 48 h irradiation, the absorbance peak at 250 nm had completely disappeared and was replaced by a strong increase of the absorbance at lower wavelengths, whereas the effect of the turbidity continued to decrease. At longer times the absorbance at low wavelengths decreased also and after 120 h irradiation, it had become negligible. The disappearance of the peak at 250 nm suggests that PS was chemically modified within the first 48 h and that breakdown products were formed that strongly absorbed UV light at lower wavelengths. These products were subsequently degraded by further irradiation.

(nm)

Similar results were obtained for PS particles with R hz = 2.5 µm at C= 100 mg/L during irradiation while gently stirring, see figure S10 of the supplementary information. Here a strong increase in the absorbance appeared at lower wavelengths that disappeared after longer irradiation times. However, these larger PS particles showed a broad absorbance peak centred at 650 nm of which we do not know the origin. This peak also disappeared during irradiation and after 120 h the absorbance had become negligible.

It has been reported that photodegradation of PS leads to the formation of short polymer chains or other small molecules [START_REF] Gewert | Identification of chain scission products released to water by plastic exposed to ultraviolet light[END_REF][START_REF] Domínguez-Jaimes | Degradation of primary nanoplastics by photocatalysis using different anodized TiO2 structures[END_REF][START_REF] Luo | Environmental behaviors of microplastics in aquatic systems: A systematic review on degradation, adsorption, toxicity and biofilm under aging conditions[END_REF][START_REF] Nabi | Complete photocatalytic mineralization of microplastic on TiO2 nanoparticle film[END_REF][START_REF] Tian | A carbon-14 radiotracer-based study on the phototransformation of polystyrene nanoplastics in water versus in air[END_REF] or even carbon dioxide [START_REF] Ward | Sunlight converts polystyrene to carbon dioxide and dissolved organic carbon[END_REF] . Here we investigated the total organic carbon content (TOC) of the suspensions of PS particles with R h = 2.5 and 0.25 µm at different irradiation times, see figure 6. A weak decrease of the TOC was observed until approximately 40 h irradiation followed by a strong decrease. The rate of decrease of the TOC was independent of particle radius up to 120 h of irradiation in agreement with the light scattering results shown above. The decrease shows that PS was broken down into volatile molecules, probably carbon dioxide [START_REF] Ward | Sunlight converts polystyrene to carbon dioxide and dissolved organic carbon[END_REF] . After 219 h irradiation, the TOC in the solution was reduced from 30 mg/L to 2.5 and 6 mg/L for the particles with R hz = 2.5 and 0.25 µm, respectively, see figure 6. As mentioned in the introduction, Ward et al [START_REF] Ward | Sunlight converts polystyrene to carbon dioxide and dissolved organic carbon[END_REF] showed that photodegradation of PS leads to complete degradation into CO 2 for samples with a thickness below 200 μm. The authors estimated that in natural sunlight this process takes a few decades assuming that CO 2 production increases linearly with UV irradiation times. However, here we observed that in the case of PS the rate of mass loss during UV irradiation is not linear with time but accelerates after some time, see figure 2a. This implies that the time required for the complete degradation of PS in the natural sunlight is much shorter than that estimated by Ward et al [START_REF] Ward | Sunlight converts polystyrene to carbon dioxide and dissolved organic carbon[END_REF] .

Time (hours

Degradation of PS particles in simulated sea water

The stability of nanoplastics in the sea may be different from that in salt-free water.

Therefore, we studied the degradation of PS particles with R hz = 0.25 µm in simulated seawater produced by adding 35 g/L sea salt to Millipore water, i.e. approximately the same concentration as in natural seawater. Weak aggregation of the particles occurred as soon as the salt was added to the particle suspension, caused by the screening of electrostatic repulsion between the particles by the salt. During the first 24 h of UV irradiation, the aggregates grew in size and became visible to the eye, but subsequently, they disappeared gradually with increasing irradiation time, see figure S11. A transparent solution was formed after 168 h irradiation. UV induced aggregation of nanoplastics in salty water was reported by various authors [START_REF] Duan | ROS-mediated photoaging pathways of nano-and micro-plastic particles under UV irradiation[END_REF][START_REF] Li | UV/ozone induced physicochemical transformations of polystyrene nanoparticles and their aggregation tendency and kinetics with natural organic matter in aqueous systems[END_REF][START_REF] Liu | Aggregation kinetics of UV irradiated nanoplastics in aquatic environments[END_REF][START_REF] Wang | UV-induced aggregation of polystyrene nanoplastics: effects of radicals, surface functional groups and electrolyte[END_REF] but their complete degradation has been rarely discussed in the literature.

No significant visual changes were observed in the dark for up to at least 7 days. This observation shows that even if the particles are in the aggregated state, they can be degraded by UV irradiation, albeit at a slower rate.

Degradation of PS particles during simulated solar irradiation

Figure S12 of the supplementary information shows the evolution of the q-dependent relative scattering intensity of a suspension of PS particles with initial R h = 0.25 µm after different times of simulated solar irradiation. Three independent measurements were performed for the same particle suspension and a good reproducibility is observed in all cases.

The behaviour was similar to that observed during high intensity irradiation, but much slower.

In figure 8 the evolution of I rel at q0 and R hz during simulated solar irradiation is compared with that during irradiation with a high intensity UV lamp. The comparison shows that the breakdown under simulated solar light was about 12 times slower than during irradiation with a high intensity UV lamp. The difference in degradation rate was larger than the difference in UV intensity (6 times), which can be explained by the different wavelength distribution of the two UV sources, see fig. S2 of the supplementary information. Even though the rate is slower the degradation process appears to be the same with a decrease of the R hz starting only after I rel had already strongly decreased.

Degradation of PE particles during high intensity UV irradiation

The scattering intensity of PE particles at C = 5 mg/L in the dark and during irradiation with the high intensity UV lamp is plotted in Figure S13a and S13b of the supplementary information, respectively. The suspension of PE particles was observed to be stable in the dark for at least one month. No creaming was observed despite the density of the PE particles, which can be explained by the low creaming speed given the size of the particles (approximately 0.003 µm/s for a radius of 0.35 µm and a density of 0.9 g/ml). However, during irradiation, a systematic decrease in Irel was observed. In figure 9a the dependence of I rel at q0 on the irradiation time is shown. I rel decreased relatively sharply after about 4 days of irradiation by about 60% after which the decrease became more gradual. R hz remained approximately constant for about 25 days after which it decreased weakly, see figure 9b. The crystalline fraction of the PE used in the investigation was 32% [START_REF] Balakrishnan | Towards more realistic reference microplastics and nanoplastics: preparation of polyethylene micro/nanoparticles with a biosurfactant[END_REF] . We speculate that the initial fast decay is due to the degradation of PE in the amorphous region whereas the slow decay corresponds to the crystalline PE. The degradation rate of PE particles was found to be much slower than that of PS particles. The time required to reduce 90% of the relative scattering intensity with a high intensity UV irradiation was around 38 days for PE compared to 2 days for PS particles, see fig. 9a. Considering that I rel  M w 2 , a 90% reduction of the intensity corresponds to a mass loss of 70%. As for PS particles, the time needed to decrease by half the amount of PE in the particles can be estimated from the decrease of the molar mass and was approximately 20 days.

Interestingly, a similar degradation behaviour was observed for PE as that of PS, i.e.

the M w of the particles was decreased substantially without changing the radius see figure 2 and figure 9. However, the degradation rate was much slower for PE, which implies that the chemical reactions leading to the break-down of PE are very different than for PS. However, for both polymers the break-down is caused by UV radiation, which can easily penetrate both the small PS and PE particles studied, which explains why it is much faster using a high intensity lamp than in simulated sunlight. Therefore, it is reasonable to assume that the effect of the UV source on the degradation rate is approximately the same for PS and PE. For PS particles we found that it was13 times slower under sunlight than under the high intensity UV lamp. Assuming that the degradation rate of PE particles is also 13 times slower under simulated sunlight we find that it will take more than a year to decrease by 70% the molar mass of PE particles suspended in water under simulated solar irradiation.

The stronger resistance to UV irradiation of PE compared to PS was also noted in a study by Zhu et al [START_REF] Zhu | Photochemical dissolution of buoyant microplastics to dissolved organic carbon: rates and microbial impacts[END_REF] . These authors investigated the photochemical dissolution of buoyant microplastics of PE, PP and expanded PS by monitoring the formation of dissolved organic content (DOC) under natural sunlight exposure. The authors reported that the highest DOC production was for PS followed by PP and then PE. The faster degradation rate of PS is related to its chemical structure which renders it more prone to photo oxidation than polyolefins. Another difference between the PS and PE particles is that the latter was not necessarily spherical. However, given that the degradation rate is independent of the particle size for small particles and starts from the inside, the shape is unlikely to have an influence on the degradation rate except perhaps in the final stage where the particles break-up.

The results reported in the current study show that nanoplastics in aqueous suspension degrade more or less slowly under solar radiation depending on their chemical nature.

Degradation does not occur in the dark and therefore requires that the particles are near the surface where the intensity of UV irradiation is still significant. If the particles are larger or aggregate into larger flocs they will sink or float depending on their density. Only when they float they will be subjected to irradiation leading to their degradation. In that case, their rate of degradation is expected to be similar to that found here for small particles as long as the UV light can penetrate them, as was shown here for aggregated PS particles. For instance, at least 50% of UV light penetrates pure PS to a depth of 100 µm [START_REF] Kadhim | Study of some optical properties of polystyrene-Copper nanocomposite films[END_REF] . Notice, however, that here we studied pristine PS and PE particles, but in practice, additives that protect against UV or oxygenation can be present. Their presence may lead to a slow-down of the degradation process.

Conclusion

Nanoplastics made from polystyrene (R hz = 0.1 -2.5 µm) and polyethylene (R hz = 0.1 -0.5 µm) in aqueous suspension fully degrade during irradiation with UV light. Light scattering and CLSM measurements show that initially, mass loss occurs from the interior of the particles rendering the particles increasingly less dense without changing their size.

Fragmentation occurs only after the large majority of the mass is lost and the particles have become fragile. The degradation rate was found to be similar for PS particles with radii up to at least 2.5 µm. TOC analysis showed that degradation of PS particles leads to the removal of carbon from the suspension in the form of volatile carbon. The degradation process of PE particles induced by UV irradiation was similar to that of PS particles, but approximately 20 times slower than for PS particles. Under simulated sunlight irradiation it takes about one month for PS and 2 years for PE to fully degrade.

In more realistic situations it is likely that nanoplastics aggregate. Here we showed for PS particles that the degradation occurs also in the aggregated state. Of course, it is necessary that UV light can penetrate the aggregates, which is easier when they are small and have an open structure. Other issues that will need to be considered in future research are the effect of additives and contaminants that may influence the degradation rate.

Figure 1 .Figure 2 .

 12 Figure 1. Double logarithmic plot of the relative scattering intensity as a function of q for PS

Figure 3 .

 3 Figure 3. Effect of high intensity UV irradiation time on the turbidity of a suspension of PS

Figure 4

 4 Figure 4 CLSM images of a PS particle suspension (R hz = 2.5 µm) at high intensity UV

Figure 5 .

 5 Figure 5. Absorbance spectra of a suspension of PS particles with R hz = 0.25 µm at 100mg/L

Figure 6 .Figure 7 .

 67 Figure 6. The decrease of total organic carbon content for a suspension of PS particles with

Figure 8 .

 8 Figure 8. (a) The decrease of I rel with respect to the initial value and of (b) the hydrodynamic

Figure 9 .

 9 Figure 9. (a)The decrease of I rel with respect to the initial value (b) and the average

Acknowledgements

The French National Research Agency (ANR) is acknowledged for the financial support of this project (ANR POEM ANR-21-CE06-0019).

Conflicts of interest

There are no conflicts of interest to declare


Eugenio Azpeitia
email: eazpeitia@matmor.unam.mx

François Parcy
email: francois.parcy@cea.fr

Christophe Godin
email: christophe.godin@inria.fr

Cauliflowers or how the perseverance of a plant to make flowers produces an amazing fractal structure Le chou-fleur ou comment la persévérance d'une plante à vouloir faire des fleurs produit une étonnante structure fractale

Keywords: Biological fractals, Plant development, Multiscale modelling, Cauliflower curds, Flower, Meristems, Plant shapes Fractales biologiques, Développement des plantes, Modélisation multi-échelle, Pommes de chou-fleur, Fleurs, Méristèmes, Formes végétales

Biological organisms have an immense diversity of forms. Some of them exhibit conspicuous and fascinating fractal structures that present self-similar patterns at all scales. How such structures are produced by biological processes is intriguing. In a recent publication, we used a multi-scale modelling approach to understand how gene activity can produce macroscopic cauliflower curds. Our work provides a plausible explanation for the appearance of fractal-like structures in plants, linking gene activity with development.

Résumé. Les organismes biologiques possèdent une immense diversité de formes. Certains d'entre eux arborent des structures fractales remarquables et fascinantes présentant des motifs similaires à toutes les échelles. La manière dont ces structures sont produites par des processus biologiques est intrigante. Dans une publication récente, nous avons utilisé une approche de modélisation multiéchelle pour comprendre comment l'activité de certains gènes peut engendrer des pommes de choufleur macroscopiques. Notre travail fournit une explication plausible quant à l'apparition de structures de type fractal chez les plantes, en reliant l'activité des gènes au développement.

Introduction

Fractals are intriguing by their mathematical and geometric beauty [START_REF] Mandelbrot | Is nature fractal?[END_REF]. Their intricate shapes are made up by the repetition of a similar pattern at every scale. Despite their complexity, they can be easily simulated using intensive recursive computation on standard computers (see e.g. [2]). Biology provides a wealth of illustrations of fractal-like shapes. However, none of the computational algorithms used to generate fractals consider the complex chemical and physical processes responsible for the development of biological shapes, therefore giving little insight into their origins in nature, which thus remains largely unknown.

Cauliflower curds provide a unique opportunity to address this question. Their fractal-like shape derives from a modification of the flower development process. Strikingly, a cauliflower-like severe change of morphology is produced by mutations of the APETALA1 (AP1) and CAULIFLOWER (CAL) genes in Arabidopsis thaliana [START_REF] Kempin | Molecular basis of the cauliflower phenotype in Arabidopsis[END_REF][START_REF] Ferrándiz | Redundant regulation of meristem identity and plant architecture by FRUITFULL, APETALA1 and CAULIFLOWER[END_REF], a brassicaceae from the same family as the cauliflower and broccoli (Figure 1a,b). In a recent work [START_REF] Azpeitia | Cauliflower fractal forms arise from perturbations of floral gene networks[END_REF], we provided a mechanistic explanation of how these mutations alter flower development, by recursively triggering lateral meristem development, which results in the fractal-like shape of the curds. Moreover, our work showed how different cauliflower morphologies can be caused by changes in the regulation of plant growth dynamics. In the following, we explain the main results and contributions of our work. In the first section, we describe how some mutations of the gene regulatory network (GRN) involved in flower development can open the way to the development of iterative structures necessary to produce fractals. Then, we explain how this GRN regulates the growth dynamics of plant axes and induces a chain reaction of growing axes leading to the emergence of fractal curds. We then describe how a simple model of plant architecture development was used to show that the changes in plant growth dynamics can be at the origin of the remarkable Romanesco cauliflower. Finally, we briefly discuss the relevance of our findings in the context of plant domestication.

The gene regulatory network

Aerial plant meristems are structures composed of undifferentiated cells that are located at the most apical part of shoots. These meristems produce lateral meristems that can take different identities (e.g. leaf, inflorescence (IM) or flower meristems (FM)) depending on the regulatory genes they express (Figure 1c). The gene expression in meristems is regulated by interactions between master regulatory genes. In particular, in A. thaliana, shoot meristems express TERMINAL FLOWER1 (TFL1), a shoot identity gene that prevents meristems from differentiation by repressing flower identity genes, such as APETALA1 (AP1), CAULIFLOWER (CAL) and LEAFY (LFY ) [START_REF] Bowman | Control of flower development in Arabidopsis thaliana by APETALA1 and interacting genes[END_REF][START_REF] Ratcliffe | Separation of shoot and floral identity in Arabidopsis[END_REF][START_REF] Liljegren | Interactions among APETALA1, LEAFY, and TERMINAL FLOWER1 specify meristem fate[END_REF][START_REF] Winter | LEAFY target genes reveal floral regulatory logic, cis motifs, and a link to biotic stimulus response[END_REF][START_REF] Kaufmann | Orchestration of floral initiation by APETALA1[END_REF][START_REF] Liu | A conserved genetic pathway determines inflorescence architecture in Arabidopsis and rice[END_REF] (Figure 2a). During the vegetative phase of plant development, flower identity genes are inactive and lateral meristems take shoot and leaf identity. However, as plant ages, flowering signals induce the expression of AP1, CAL and LFY in new lateral meristems (Figure 2b), which turns them into flowers. AP1 inhibits shoot identity by repressing TFL1 in FM [START_REF] Ratcliffe | Separation of shoot and floral identity in Arabidopsis[END_REF][START_REF] Ratcliffe | A common mechanism controls the life cycle and architecture of plants[END_REF][START_REF] Goretti | TERMINAL FLOWER1 functions as a mobile transcriptional cofactor in the shoot apical meristem[END_REF] and stabilises the expression of floral regulators by forming a positive feedback loop with LFY (Figure 2a) [START_REF] Bowman | Control of flower development in Arabidopsis thaliana by APETALA1 and interacting genes[END_REF][START_REF] Ratcliffe | Separation of shoot and floral identity in Arabidopsis[END_REF][START_REF] Liljegren | Interactions among APETALA1, LEAFY, and TERMINAL FLOWER1 specify meristem fate[END_REF][START_REF] Winter | LEAFY target genes reveal floral regulatory logic, cis motifs, and a link to biotic stimulus response[END_REF][START_REF] Kaufmann | Orchestration of floral initiation by APETALA1[END_REF][START_REF] Grandi | Uncovering genetic and molecular interactions among floral meristem identity genes in Arabidopsis thaliana[END_REF][START_REF] Moyroud | Prediction of regulatory interactions from genome sequences using a biophysical model for the Arabidopsis LEAFY transcription factor[END_REF][START_REF] Goslin | Transcription factor interplay between LEAFY and APETALA1/CAULIFLOWER during floral Initiation[END_REF][START_REF] Parcy | A genetic framework for floral patterning[END_REF]. In A. thaliana, the double mutant of ap1 cal, produces cauliflower-like structures instead of flowers [START_REF] Kempin | Molecular basis of the cauliflower phenotype in Arabidopsis[END_REF][START_REF] Ferrándiz | Redundant regulation of meristem identity and plant architecture by FRUITFULL, APETALA1 and CAULIFLOWER[END_REF][START_REF] Bowman | Control of flower development in Arabidopsis thaliana by APETALA1 and interacting genes[END_REF]. Those structures correspond to meristems initiated as floral (with LFY expression) but that revert to shoot (with TFL1 expression) because the AP1/CAL-LFY positive feedback is missing (Figure 2c).

The first attempts to model the floral GRN only based on TFL1, AP1/CAL (AP1 and CAL were included as a single variable because they are homologous genes with redundant functions) and LFY, led us to realise that there were missing elements in the network. In particular, those inducing the expression of TFL1 were lacking. We therefore looked for possible candidate genes and identified additional genes intricately linked to the original master regulators. These genes are the MADS-box genes SUP-PRESSOR OF OVEREXPRESSION OF CONSTANS1, AGAMOUS-LIKE24 and XAANTAL2 (collectively renamed the "SAX" genes). Interestingly, on the one hand, SAX proteins promote the expression of the flowering genes AP1 and LFY [START_REF] Grandi | Uncovering genetic and molecular interactions among floral meristem identity genes in Arabidopsis thaliana[END_REF][START_REF] Liu | Direct interaction of AGL24 and SOC1 integrates flowering signals in Arabidopsis[END_REF][START_REF] Lee | SOC1 translocated to the nucleus by interaction with AGL24 directly regulates leafy[END_REF][START_REF] Pérez-Ruiz | XAANTAL2 (AGL14) is an important component of the complex gene regulatory network that underlies Arabidopsis shoot apical meristem transitions[END_REF] and repress TFL1 forming a complex with AP1 [START_REF] Liu | A conserved genetic pathway determines inflorescence architecture in Arabidopsis and rice[END_REF]. On the other hand, work from our collaborators showed that SAX proteins are also able to activate TFL1 expression. We updated the GRN with this information (Figure 3), formalised these interactions in a model of ordinary differential equations and analysed both its transitory and stationary properties. These analyses showed that the GRN was sufficient to produce the expected patterns of gene expression in a wild-type (WT) plant, in an ap1 cal mutant, and in the other single mutants of the different genes present in the network. In addition, the model predicted a high level of SAX expression in ap1 cal meristems that is not observed in WT plants and we experimentally confirmed this prediction with the SOC1 gene [START_REF] Azpeitia | Cauliflower fractal forms arise from perturbations of floral gene networks[END_REF].

Having found a minimal GRN able to recapitulate the different gene expression states and explain the shoot identity of new lateral meristems in the ap1 cal mutant, we wondered whether it was sufficient to explain the cauliflower inflorescence morphology.

To address this question, we first took into account that the plant architecture does not solely depend on the fate of its meristems, but also on additional developmental factors such as phyllotaxis of the shoots, the growth rate of the internodes, the time it takes for newly created meristems to produce new lateral organs, etc. Moreover, we also noticed that the GRN final states for lfy and ap1 cal mutant simulations are identical with a high level of TFL1 and SAX and a low level of AP1/CAL and LFY, indicating that the architecture of the plant cannot be solely explained by the GRN stationary states. To understand the origin of curd morphology, we were thus led to analyse in greater depth the dynamics of the different actors in the growing branching structure. For this, we designed a 3D computational model simulating the growth of a plant whose development dynamics was regulated by the state of GRNs computed in each meristem. We call this model, the architectural model.

The architectural model

More precisely, our architectural model comprises two main components, meristems and internodes. Each meristem has its own identity based on the state of its GRN (Figure 4a). The identity of a meristem determines its behaviour. Vegetative and inflorescence meristems produce internodes and new lateral primordia (meristems) at each plastochron. Flower meristems turn into flowers, thus ending the axis growth. Vegetative meristems have low TFL1, AP1 and LFY expression. Inflorescence meristems have high TFL1 expression and low AP1 and LFY expression. Finally, flower meristems have low TFL1 expression and high AP1 and LFY expression. At each step, the model inputs a level of flower inducing signal (that was assumed to increase in each meristem with aging) and a level of auxin that was set maximal in each new meristem and then exponentially decay. The state of the GRN was thus reevaluated in each meristem at each time step and was used to determine the identity of the meristem. In addition, since most meristems of order 3 remained inactive in A. thaliana, we added a rule to the model, specifying that meristems of order 3 should be kept dormant, irrespective of their identity (Figure 4b). This model, calibrated for WT plant development, was able to recapitulate morphologies of mutated plants with the expected architecture (Figure 4b). For example, tfl1 mutants terminate with the production of a few flowers due to AP1 and LFY expression in the shoot apical meristem [START_REF] Shannon | A mutation in the arabidopsis TFL1 gene affects inflorescence meristem development[END_REF], lfy mutant produced mostly secondary branches [START_REF] Weigel | LEAFY controls floral meristem identity in Arabidopsis[END_REF]. However, the model could not reproduce the ap1 cal morphology. First the ap1 cal inflorescence, contrary to lfy, is mostly devoid of leaves and no element was accounting for this in the model. Second, the cauliflower phenotype arises from the accumulation of meristems on the top of each other, reaching orders higher than 3 while we had imposed a limitation to the growing orders to model the wild-type plant properly (Figure 4c).

We then realised that, despite the fact that the lfy mutant and the ap1 cal mutant have identical stationary states in the inflorescence lateral meristems, a critical difference between the two mutants lies in the dynamics to reach that state. While in the lfy mutant, LFY expression never rises up, a transient peak of LFY expression is produced in lateral meristems of ap1 cal mutants before they finally take a shoot identity. This key difference was enough to explain both previous issues. Indeed, it was already well documented that the presence of LFY is responsible for repressing bracts in primordia [START_REF] Weigel | LEAFY controls floral meristem identity in Arabidopsis[END_REF]. Second, previous work from our group [START_REF] Chahtane | A variant of LEAFY reveals its capacity to stimulate meristem development by inducing RAX1[END_REF] had shown that ectopic expression of LFY was able to allow high order meristems to grow. The transient rise of LFY in ap1 cal was thus essential to free meristem outgrowth at all orders and induce a chain reaction.

In conclusion, our work showed that the cauliflower phenotype is mainly due to the fact that in the ap1 cal mutant there is an unsuccessful flower development that produces undifferentiated meristems instead of flowers. The transient peak of In the middle, a photograph showing an ap1 cal plant with a meristem order higher than 3. On the right panel, a simulation assuming that LFY expression releases the production of meristems of orders higher than 3.

LFY expression in the ap1 cal mutant is responsible for the activation of all meristems and causes the recursive production of new meristems at all orders. In other words, the fractal-like cauliflower morphology is the result of an alteration of two fundamental processes shaping plant architecture, namely meristem differentiation and meristem outgrowth repression.

The Romanesco hypothesis

Brassicas curds have different fractal morphologies. Cauliflowers exhibit a curd with a round dome. Their fractal nature can be observed with a curd morphology observable at many scales, each curd being formed of smaller curds with similar round domes. This fractal pattern is reinforced by the typical spiral arrangement of smaller curds forming each larger one. The fractal structure of the Romanesco in nested spiralling curds is similar, but the conic shape of curds dramatically highlights its fractal geometry (Figure 5a,b).

We thought of taking advantage of our architectural model to better understand what regulates the development of the different curd morphologies. A previous comparison between cauliflower and Romanesco curds identified several features that are constantly increasing during development in Romanesco curds, but that are constant in cauliflowers [START_REF] Kieffer | Explaining curd and spear geometry in broccoli, cauliflower and 'romanesco': quantitative variation in activity of primary meristems[END_REF]. These properties are: (1) the production rate of new lateral meristems; (2) the number of phyllotaxis spirals in clockwise and counter-clockwise directions; (3) the number of lateral primordia produced by a meristem before the first one starts producing its own lateral primordial (meristem onset delay); and (4) the size of the meristems. Whether some of these parameters are causal to the Romanesco phenotype had remained elusive. However, we reasoned that according to phyllotaxis studies [START_REF] Richards | Phyllotaxis: its quantitative expression and relation to growth in the apex[END_REF][START_REF] Douady | Phyllotaxis as a dynamical self organizing process Part I: The spiral modes resulting from timeperiodic iterations[END_REF][START_REF] Douady | Phyllotaxis as a dynamical self organizing process Part II: The spontaneous formation of a periodicity and the coexistence of spiral and whorled patterns[END_REF][START_REF] Douady | Phyllotaxis as a dynamical self organizing process Part III: The simulation of the transient regimes of ontogeny[END_REF], these properties must be linked to each other. Consequently, we wondered if the morphological curd variations could also be explained by the difference in any parameter controlling these properties. To check this, we constructed a simplified version of our architectural model, making it possible to test the consequences of changing these parameters on the final curd morphology. Strikingly, we found that an increase in the meristem production rate was sufficient to produce conspicuous Romanesco-like shape whereas constant values of this parameter produce a normal cauliflower morphology (Figure 5c,d). This acceleration in the meristem production rate induces the insertion of more internodes in the meristem's axis. Assuming that this process does not affect the elongation law of the internodes (internode elongation was kept unchanged in the simple model), this acceleration of the meristem production rate indirectly induces an acceleration of overall stem elongation relative to its lateral axes, which results in conspicuous conical structures with very visible spirals themselves made of cones and so on.

According to our model, increasing the production rate of lateral meristems should transform a cauliflower into a Romanesco curd. To test this hypothesis in planta, we used the fact that, according to phyllotaxis models, meristem production rate may in principle be augmented by an increase in the size of the central zone. In A. thaliana, the clavata (clv) mutants (e.g. clv1 and clv3) are known to produce bigger meristems [START_REF] Fletcher | Signaling of cell fate decisions by CLAVATA3 in Arabidopsis shoot meristems[END_REF][START_REF] Kitagawa | Control of meristem size[END_REF]. Thus, we crossed a clv3 mutant with the ap1 cal double mutant. Indeed, the clv3 ap1 cal triple mutant has a modified curd shape, with a morphology being more pyramidal than for ap1 cal curds (Figure 5e,f). This result suggests that the meristem production rate is a fundamental regulator of the final curd morphology. Interestingly, CLV3 and a couple of other related genes seem to have a lower expression in Romanesco curds than in cauliflowers [START_REF] Azpeitia | Cauliflower fractal forms arise from perturbations of floral gene networks[END_REF], but the causal link between this observation and the curd phenotype needs to be studied.

This mechanism provides a first evidence that the strikingly different morphologies observed in curds could be due to simple change in a single parameter, such as the size of the meristem central zone. This changes meristem production rate, which is then propagated throughout the whole plant as a change in the relative elongation rates of the different axes, resulting in a dramatic change of the curd global morphology.

Altogether, our results provide a plausible explanation for the appearance of fractal-like structures in plants and for the possibility to significantly modify their geometry based on variations of only a limited number of growth regulation factors.

Discussion

The pervasive presence of fractal-like structures in biology is intriguing. Until now, the developmental origin of most biological fractal-like structures was still unknown. However, deciphering their origins is a non-trivial task due to the high interconnectivity and non-linearity of developmental processes, which take place at multiple scales. In our work, we used modelling and experimental tools to study the origin of fractal-like cauliflower structures. Our results showed that the fractal structure of curds is very likely the consequence of three main mechanisms. First, the mutation in the ap1 cal genes produces an unsuccessful flowering transition. As a consequence, all meristems take a vegetative or inflorescence identity. The ap1 cal mutation also releases the production of lateral meristems at all orders. This is due to the transitory expression of LFY in the mutant. Finally, a Romanesco-like form of the curds can be induced when extra mutations induce an accelerated production of new lateral meristems. Our work provides a first plausible explanation of how fractal-like structures develop linking gene activity with macroscopic structures.

Our work also provides a framework to better understand fundamental aspects of plant development and plant domestication. The unexpected discovery that a transient exposure to LFY can have a profound effect on how the meristem responds to general cues such as those limiting the growth of high-order structures is not understood at the molecular level and it would be interesting to identify which LFY target genes exert this function.

Moreover, even if our work pointed towards flower and inflorescence regulators that can be responsible for the development of curds, the mutations that were selected during the long process of cabbage, broccoli, cauliflower and Romanesco domestication still need to be identified [START_REF] Cai | Evidence for two domestication lineages supporting a middle-eastern origin for Brassica oleracea crops from diversified kale populations[END_REF] and validated using genetic and functional analyses. Genome comparisons are a powerful tool, but yield many possible candidates that until now, except for mutations affecting the CAL gene, have not yet been validated [START_REF] Guo | Genome sequencing sheds light on the contribution of structural variants to Brassica oleracea diversification[END_REF]. We believe that our models can provide a very useful framework for their identification.

Figure 1 .

 1 Figure 1. WT vs ap1 cal morphology. (a) WT plant with an inflorescence meristem producing flower meristems. (b) The cauliflower morphology produced by the overproduction of lateral meristems in the ap1 cal mutant. (c) A microscopy image of an inflorescence meristem (IM), surrounded by flower meristems (FM). Photographs credits: Jan Trass (c) and Marie Le Masson (a and b).

Figure 2 .

 2 Figure 2. Gene regulatory network and gene expression profiles involved in the flowering transition. (a) Interactions between the major floral regulators. Gene expression during late development in the shoot and lateral meristems of wild-type (WT) (b) and ap1 cal mutant (c) plants. SAM = shoot apical meristem. FM = Floral meristem (lateral meristem). In green and red, TFL1 and LFY expression, respectively.

Figure 3 .

 3 Figure 3. Gene regulatory network of the main genes involved in early floral development (Image from [5]. Arrows represent positive regulations, flat head arrows represent negative regulations and the merging arrows from SAX and AP1 towards TFL1 represent the formation of the SAX-AP1 complex. F and Auxin are inputs of the model. The equations of the model are available in [5].

Figure 4 .

 4 Figure 4. The architectural plant model. (a) Schematic description of the architectural plant model. Green circles represent inflorescence/vegetative meristems. Red circles represent flower meristems. Red lines represent internodes. The simulation starts with a vegetative meristem. Vegetative and inflorescence meristems were able to produce lateral meristem and internode, therefore driving plant growth with time. Each meristem contains its own GRN. The state of the GRN determines its identity. (b) WT morphology produced by the model vs a photograph of a WT A. thaliana. The arrows indicate the meristems order. In (c) the left panel shows that the original model produced cauliflowers with meristems of maximal order 3.In the middle, a photograph showing an ap1 cal plant with a meristem order higher than 3. On the right panel, a simulation assuming that LFY expression releases the production of meristems of orders higher than 3.

Figure 5 .

 5 Figure 5. Cauliflower and Romanesco morphologies produced by the model and experimentally. (a) Cauliflower and (b) Romanesco morphologies. Curd morphologies produced by the model with (c) constant plastochron vs (d) accelerating plastochron. (e) ap1 cal curd morphology vs (f ) clv3 ap1 cal curd morphology. Photograph credits: Marie Le Masson.

Conflicts of interest

Authors have no conflict of interest to declare.


Irene Reginato

John Tolan

Davide Scotto

Maurizio Busca

published or not. The documents may come   L'archive ouverte pluridisciplinaire

INTRODUCTION *

European Visions of the Qur'an in the Middle Ages Florence Ninitte and Irene Reginato

NANTES UNIVERSITÉ

From its first translation into Latin in 1143 up to its first vernacular (Italian) translation in 1547, the sacred book of Islam elicited passionate and contrasting reactions in Europe, ranging from vehement attacks concerning its content or composition to an acknowledgement of the aesthetics of its stylistic features and the quality of its message. Moreover, since the publication of Thomas Burman's pioneering study, Reading the Qur'ān in Latin Christendom, 1 the question of the Western perception of the holy book of Islam has become even more complexand nuancedthan previously imagined. Reading the Qur'ān has brought to light a plurality of attitudes on the part of the West towards the Qur'an that many of the studies that have emerged in its wake continue to confirm.

The conviction that the Qur'an has played an important role in medieval and early modern European culture was the inspiring principle of the European research project EuQu -The European Qur'ān: Islamic Scripture in European Culture and Religion 1150-1850 (European Research Council [ERC], Synergy Grant agreement [SyG] n°810141). Established in 2019, this ambitious project seeks to study how the Qur'an was interpreted, adapted, and used in Christian European contexts over the course of the Middle Ages and early modern period. Relying on a multidisciplinary team of researchers, the objective of the EuQu project is thus to write the first history of the 'European Qur'an'or, rather, of the 'European Qur'an(s)'through academic research and publications, but also by means of public engagement 2 that aim to throw new light on the multiple ways of copying, reading, translating, interpreting, and exploiting the Qur'an in European culture from its first Latin translation in 1143 to the middle of the nineteenth century. [START_REF] Tolan | Le Coran européen'. 4 Loop[END_REF] It is within this context that the workshop 'European Visions of the Qur'ān in the Middle Ages' that led to the genesis of this special issue was conceived. The aim of the workshop, which was held on 20-21 May 2021, was to investigate the different perspectives from which the Qur'an was addressed in medieval times by a wide range of actors that encompassed translators, polemicists, and commentators who had accessdirectly or indirectlyto the Qur'an, or parts of it, and to identify the various attitudes they adopted: the mechanisms of reading they elaborated; the texts through which they became acquainted with it; the hermeneutic filters they applied; and, finally, the ideas and perceptions they developed. The contributions, from scholars working in different fields and from different backgrounds, went far beyond the original scope we had planned for the workshop, leading us to propose this special issue, so that the richness of the research presented could be fully expressed in longer and more complex essays. The Journal of Qur'anic Studies immediately came to mind as an ideal venue, in continuity with a previous issue edited by Jan Loop which first presented the premises of the EuQu project in 2018. 4 This special issue gathers eight essays that are varied in their approaches and themes, but which nevertheless share many points of contact that are proving to be fundamental in the attempt to define some key aspects of the medieval reception of the Qur'an in Europe. A first key aspect is the importance of 'intermediary texts' in almost any medieval approach to the Qur'an. By 'intermediary texts' is intended all those writings through which, in an indirect manner, the West came into contact with the contentsif not with the actual textof the Qur'an. It is, of course, a label derived from our modern critical view: medieval authors did not perceive those writings as 'intermediary', but rather as sources of knowledge equivalent, even from a theological point of view, to the Qur'an itself.

These intermediary texts are represented, first of all, by the Latin translations of the Qur'an by Robert of Ketton ( 1143) and Mark of Toledo (1210). As is well known, the former was produced to be included in the Corpus Islamolatinum, a collection of translations and writings on Islam conceived by Abbot Peter the Venerable of Cluny as a powerful cultural weapon to be used against the 'Saracens' in the wake of the Second Crusade. As for the latter, this was produced during the Spanish Crusade against the Almohad caliphate, at the behest of the Archbishop of Toledo, Rodrigo Jiménez de Rada. The two translators take essentially different approaches to transferring the text into Latin. [START_REF]Among the extensive bibliography on these two translations, see Burman, Religious polemic and, Reading the Qur'an; Cecini, Alcoranus Latinus; Martínez Gázquez, 'Trois traductions médiévales'; Grévin, 'Les traductions médiévales'; Petrus Pons, 'The Latin Qur'an'. For a more detailed analysis of the context of these translations, see also Scotto[END_REF] Focusing primarily on their different lexical choices, Olivier Hanne's article demonstrates the different attitudes adopted by Robert and Mark towards the Arabic terms used by the Qur'an to refer to itself: kitāb, Qurʾān, dhikr, ḥ ikma, etc. The author points out, on the one hand, the translator's shared definition of the Qur'an as a 'book' and, on the other hand, their difficulties and choices in rendering the terms and concepts from which the doctrine of inimitability will arise. This issue crystallises around the term tanzīl, which both translators are reluctant to translate literally.

In addition to Qur'an translations, medieval readers also came to know the Qur'an through a rather limited number of fundamental texts that combined reliable information, Qur'anic quotations and, most of all, polemical arguments presented in a 'ready to use' form. These texts proved essential in terms of spreading knowledge, but also prejudices and polemical tools, thanks to their huge success and their continuous reuse and incorporation into both medieval bestsellers and lesser-known works.

Eloquent examples of this are offered by the seven works contained in the previously mentioned Corpus Islamolatinum, whose importance to our special issue, as well as to the medieval reception of Islam, is worth a brief digression.

In It was perhaps through these channels that the redactor of the Codice Cassinese borrowed the Islamic professio fidei, as noted by Vera Ribaudo in her article on the presence of the Qur'an in the commentaries of Dante's Comedy. Ribaudo also reminds us that only focusing on the direct filiation of a text can sometimes be of less use than investigating the multiple forms of reception of widespread ideas. In the complex case of possible Islamic sources in Dante's Comedy, she suggests that the intertextual influence 'should be discarded in favour of an interdiscursive influence' (p. 93), and undertakes to reconstruct the image of the Qur'an and Muḥ ammad in the commentaries of Dante's Comedy, which had generally access to the ESRC through the Speculum Historiale and the Legenda Aurea.

Derivative texts should therefore be granted as much attention as original ones, since their unique mixing of inherited motifs and newly conceived ones can be extremely relevant, not just to throw light on new particular reception contexts, but even to offer a better understanding of European encounter(s) with the Qur'an. In fact, through his analysis of Petrus de Pennis' Tractatus contra Alchoranum and the Epitome Bellorum Sacrorum, Langeloh identifies two main stages in the Western reception of the Qur'an: an initial one (coinciding with the missionary activity of mendicant orders) that was mainly directed 'towards the outside' (that is, aimed at converting infidels) and a later one (1350-1420), which was marked by intra-Christian controversies and was mainly directed 'towards the inside' (p. 203).

A similar line of research is proposed by Tristan Vigliano, in his study of the role of intermediary texts such as the Liber Scalae Mahumeti and the Liber Denudationis (or Contrarietas Alfolica), in terms of the European importation and use of the Arabic motifs of Muḥ ammad's night journey (isrāʾ) and ascent (miʿrāj). Vigliano isolates the different conceptual mechanisms that underlie the exploitation of such motifs according to different cultural contexts, thus demonstrating that a variety of different narratives can be generated from the same central motif.

In all its multiple receptions, the Qur'an was hardly ever read in a neutral way in the context of medieval Europe. Instead, it was most often approached through a number of hermeneutic and epistemological 'filters' of different natures. Thinking again about the first two Latin alcorani, Olivier Hanne corroborates Burman's observations while offering further evidence that Robert of Ketton attempted to convey his Latin Qur'an with the same stylistic elegance he found in Classical works, while Mark of Toledo chose a more literalist approach for his Latin rendition. 10 Hanne shows how the translational filters applied by Robert and Mark deeply influenced their respective renderings of Qur'anic self-referentiality, but also the image of the Qur'an that they would offer to their future readership.

The articles collected in this special issue offer further meaningful examples of hermeneutic filters through which the Qur'an was perceived. The first of these relates to the conventions and features of literary genres, especially travel and pilgrimage accounts. In addition to the Italian Itinerario al Santo Sepolcro by Antonio da Crema mentioned above, Burgio and Simion also analyse the Latin Itinerarium Terrae Sanctae by Anselmo and Giovanni Adorno, two Genoese brothers who were established in Flanders, where they were involved in commercial activities but also held political and diplomatic positions. Although they were certainly influenced by Burgundy's interest in the Crusade, their travel account was mainly conceived as a testimonial to their religious devotion ('volontà testimoniale di referto dell'atto devoto', p. 145), and this led them to discard standard medieval polemical tones and adopt instead a moderate and more objective attitude towards Islam. While Adorno's text never quotes the Qur'an directly, faithful Qur'anic quotations can be identified in another little-known travel account: the Itinerarium by Symon Semeonis, a Franciscan friar who travelled from Ireland to Jerusalem in 1323-1324. Here, the main filter consists in a contrast between the author's first-hand comments, drawn from his own personal experience or autonomous reflection, and the influence of deeply-rooted stereotypes and ideas about Islam. As a matter of fact, in his article about Semeonis, Agustín Justicia Lara notices that, when the Irish traveller temporarily departs from his valuable copy of Ketton's Latin Qur'an, he falls back on well-established topoi that reflect Christian polemical views of the Qur'an, heedless of the subsequent contradictions. This is revealing of the importance of conceptual frameworks when perceiving other religious systems: the traveller's eye can be blinded by his long-term preconceptions, which can even prevent him from grasping the most innovative aspects of the valuable sources he is drawing on, or from confronting his assumptions with the on-the-ground reality he witnesses.

A second interpretative filter eloquently highlighted by the articles in the present dossier stems from authors' 'literary attitude', that is either the influence exerted on them by their literary models or their aesthetic criteria. Burgio and Simion notice that Antonio da Crema's account is filtered through his erudite and literary tastes, and that he reverted to literature in order to fill in the gaps in his personal experience. In another case, a literature-inspired reading also sparked off stylistic criticism of the Qur'an: in her article, Sara Fani analyses a bifolium contained within codex Ricc. 217 (best known for the presence of the valuable Mozarabic glossary Vocabulista in Arabico) which is generally known as Fragmentum Disputationis de Alcorani Eloquentia. Through a detailed study of the codicological, linguistic, and contextual aspects of the volume's production and circulation, Fani proposes an innovative reading of the text in question.

Taking her observation of the imprecision of the Qur'anic quotations contained in this text as her starting point, the author considers the Fragmentum as a text which is, despite its brevity, autonomous, and whose purpose was to refute, through the artificial creation of a 'Qur'an-like style', the Islamic idea that only God could have produced the precious eloquence of the Qur'anic text. In similar vein, in his chronological review of the evolution and use of the motifs of the isrāʾ and the miʿrāj, Tristan Vigliano notices that, in contrast to its first appearances in works like the Liber Denudationis and the Liber Scalae, whose inclusion in the Corpus Islamolatinum (in one manuscript only in the case of the Liber Scalae) determined a purely polemical use of the two motifs (specifically in the debates around the authenticity of Muḥ ammad's prophecy), later works from the sixteenth century onwards inaugurated a new and more 'literary' approach. The starting point for this coincides, according to Vigliano, with a work by Juan Andrés dating to 1515 (Confusiόn o Confutaciόn de la Secta Mahomética y del Alcorán), which proposes a reading of the isrāʾ and the miʿrāj that goes beyond the strictly polemical, to reveal an aesthetic pleasure in the narrative itself that, however, coexists with a view on topics related to Islam that remains negative: the night journey and the ascent, although considered to be pleasant stories, are nevertheless a sham.

A third, and very specific, filter is identified in Michelina di Cesare's article. Di Cesare focuses on the connections among the various texts that constitute the Corpus Islamolatinum, questioning the way they help to interpret the Qur'an. Taking further hypotheses that have already been put forward by James Kritzeck,[START_REF]He argued that the Corpus was formed around the Risāla: Kritzeck, Peter the Venerable[END_REF] she provides new clues for understanding the collection of the Corpus Islamolatinum, showing that the surrounding context of the Latin translation of the Qur'an produces a sort of 'Judaising filter' through which the sacred book of Islam is read. To be more precise, this filter emerges from a remark made in the ESRC, which mentions the major intervention of three Jews in the editing process of the Qur'an. Through consideration of the other texts of the Corpus, Di Cesare brings out a network of correspondence with these Jewish figures that reveals an anti-Judaising perception underlying the objectives pursued by Peter the Venerable, whose vision has deep roots in Cluniac thought. [START_REF]For Peter the Venerable's attitude towards Judaism and Islam in the light of his soteriological conceptions, see Scotto, 'I Invite You to Salvation[END_REF] The presence of this allusion to a genetic relationship between Judaism and Islam can therefore be traced back to the first Cluniac (or Cluny-affiliated) works that mention Islam. Di Cesare's article leads us to a final feature of this special issue that is worthy of mention: its contribution in throwing new light on some crucial aspects of the Corpus Islamolatinum and, in particular, its origin and fate. Considering the evolution of Peter the Venerable's thinking, Di Cesare reconsiders his role in the genesis of the project and suggests that the Abbot might also not have been the actual designer behind the Corpus collection: [START_REF]See the different descriptions of the manuscripts in the critical editions of each text of the Corpus: González Muñoz, Exposición; Cecini[END_REF] It is possible that Peter gained a deeper understanding of the collection of texts translated from Arabic into Latin after Bernard of Clairvaux declined to write a refutation of Islam […]. This would lead to the conclusion that the texts to be translated in order to contextualise the Qur'an in the Corpus islamolatinum, namely the Fabulae Sarracenorum and Epistola Saraceni et Rescriptum Christiani, were selected by a concepteur who developed the anti-Jewish arguments contained in nuce in the Rescriptum. If this hypothesis is right, this concepteur could not be Peter the Venerable but someone who had read the Rescriptum in advance. European Visions of the Qur'an

The profoundly malleable character of the Corpus can also be seen in the other contributions, which show how easily works could be added to and deleted from it. 14 These fluctuations contribute to a more precise consideration of the ways in which certain texts have been evaluated, thought through, and received. For example, Vigliano shows that the inclusion of the Liber Scalae Mahometi in a manuscript of the Corpus Islamolatinum illustrates a stage in the history of the reception of the text which, through indisputable material evidence, testifies to the authority that was assigned to this literary text.

The case of the Itinerarium of Symon Semeonis, which exploits Ketton's translation of the Qur'an, as well as the Liber de Doctrina Mahumet, to describe Islamic rites and laws is also significant. 15 Focusing on the use of glosses in the Itinerarium, Justicia Lara shows that Semeonis uses both Ketton's translation and some 'reading aids', especially the apparatus of glosses that accompany some of Ketton's copies of the Qur'an, as well as the De Doctrina Mahumeti, shifting from the desire to produce a theological refutation to a more neutral use, which is mainly descriptive and integrated into the rhetorical codes of the itinerarium genre. Even if it remains difficult to identify the manuscript Semeonis used (the variants in his quotations do not correspond with any of the existing codices, even if they share primitive glosses with most of the more ancient and important manuscripts), Justicia Lara proves it belonged to family α in Martínez Gázquez and González Muñoz's edition of Ketton's Alcoranus Latinus, 16 offering new elements with which to map the possible circulation of the manuscripts of the Corpus.

It is also clear that research on derivative texts can greatly profit from new discoveries about the manuscript and textual diffusion of the Corpus Islamolatinum. An understanding of how and where copies of the Corpus travelled, as well as the texts they contained (either in terms of the whole sylloge or part of it), can provide valuable help in reconstructing which sources were or were not available in certain contexts, historical periods and cultural milieux. In the same vein, this could help identify discrepancies between the primary objectives of the Corpus, as conceived by Peter the Venerable and its assembler, and the ways in which this collection was exploited by its subsequent users.

With their expertise in different disciplines, the contributions of the nine authors gathered here provide a plurality of answers to the questions asked in this issue. They offer a clearer picture of the different channels through which knowledge about the Qur'an was transmitted and filtered, highlighting the importance of intermediary texts, and the tight correlation between their different receptions and the cultural context and aims of each of the authors of the texts studied. They also throw light on the reasons for the success of certain texts at the expense of others, suggesting important questions that we can ask in order to improve and refine our understanding of the dissemination of Qur'anic material in the West. For example, why would a reader with a copy of the Corpus Islamolatinum in his hands choose a text other than the Qur'an to engage with Islam? Why would he choose to focus on Riccoldo's works? Not only did the degree of importance attributed to each work differ from our modern criteria, but it varied greatly according to the personality, background and causae scribendi of each author and work.

Albeit fundamental, this is just one of the many possible textual interrogations and lines of research deployed by the essays collected in this special issue. Many of the ideas presented in it, as well as the authors and works mentioned, are currently the focus of monographic studies conducted by EuQu project researchers. 17 The richness and variety of the ongoing results, but above all, the constant emergence of new lines of investigation, demonstrate the productivity of the research topic identified by the EuQu project, to whose academic depthbut also implicit cultural and social valuethis dossier hopes to make a worthy contribution.

  This contains the letter of a Muslim called al-Hāshimī, who invites his Christian friend to convert to Islam; the Christian correspondent, named al-Kindī, replies point by point to the statements of his interlocutor.6 Incredibly rich in valuable information about Islam, faithful Qur'anic quotations, and effective polemical arguments, this text was among the most exploited sources on Islam from the tenth to the fifteenth century.The essays collected in this issue also highlight the remarkable influence exerted by another fundamental intermediary text: Riccoldo da Monte Croce's Contra Legem Sarracenorum (henceforth CLS; c. 1300). Similarly to the ESRC, the overall success of Riccoldo's writingsboth the CLS and his Liber Peregrinationislargely depends on his own exploitation of first-hand information and valuable sources on Islam filtered through an argumentative and polemical frame which proved accessible and effective to Western readers interested in religious polemics. However, even if they draw on extant sources, Riccoldo's works are not translations of existing texts detailing previous Eastern religious debates, like the ESRC, but original texts expressing a viewpoint which was, albeit exceptional and extremely learned, totally internal to medieval Western culture. Furthermore, the list is preceded by a biography of Muḥ ammad which contains two scarcely known episodes which have no correspondence in Riccoldo, and whose circulation is not yet well defined. The authors explain that Antonio followed the preaching of the Augustinian Mariano da Genazzano (1412-1498), and suggest that his Itinerario did not directly follow Riccoldo's text, but rather a Latin intermediary text in which the CLS had already been reduced into a sort of handbook or cento circulating in the Holy Land among Mendicant friars. These remarks are valuable, since they lead us to consider the importance of orality, and also of compilations and florilegia, in the reception of Riccoldo and other intermediary texts about Islam in the Middle Ages.

	its most ancient form (embodied by the twelfth-century manuscript Paris,
	Bibliothèque de l'Arsenal 1162, for which see D'Alverny, 'Deux traductions'), the
	Corpus Islamolatinum consists of seven texts: (1) Peter the Venerable's Summa Totius
	Haeresis ac Diabolice Secte Sarracenorum; (2) Peter the Venerable's letter to Bernard

of Clairvaux, which was an invitation (that remained unanswered) to write a refutation of Islam on the basis of the Corpus; (3) Robert of Ketton's Chronica Mendosa et Ridicula Sarracenorum, a Latin translation of an Arabic chronicle that related the history of the world from its creation to the rule of the second Umayyad caliph Yazīd I (d. 61/683), which also contains a biography of Muḥ ammad; (4)-(

5

) two translations by Hermann of Carinthia: the Liber de Generatione Mahumet, in which Muḥ ammad is described as the recipient of prophetic light, and prodigious episodes from his childhood are recounted; and the De Doctrina Mahumeti, which relates a dialogue between the Jew Abdias (ʿAbd Allāh b. Salām) and Muḥ ammad in which, by answering the various questions and riddles of the former, the latter reveals himself to be an authentic prophet; (6) Ketton's Latin rendition of the Qur'an, entitled Alchoran siue lex Sarracenorum; (7) a translation of an Arab-Christian apologetic work known as the Apology of al-Kindī (Epistula Sarraceni et Rescriptum Christiani; henceforth ESRC), translated by Peter of Toledo and the Abbot's secretary, Peter of Poitiers.

[START_REF]For the Latin ESRC, see Bottini[END_REF]

Many later works relied on it, such as Petrus Alfonsi's Dialogi contra Iudaeos, Vincent of Beauvais's Speculum Historiale, James of Voragine's Legenda Aurea, but also, on the vernacular side, the Trésor des Simples (or Débat du Chrétien et du Sarrasin), a long fifteenth century treatise by the Burgundian bishop Jean Germain.

8 9

While stressing the erudite nature of Riccoldo's CLS, which combines direct and indirect reference to Islamic scripture with Christian auctoritates, in his article Jacob Langeloh studies its use in two lesser-known texts: Petrus de Pennis's Tractatus contra Alchoranum (1370-1440) and the anonymous Epitome Bellorum Sacrorum. Langeloh analyses the similarities and differences in their reception of Riccoldo's text, seeking to explain and account for these in light of their historical and cultural context. While Petrus de Pennis combines the CLS with the Legenda Aurea, rearranging Riccoldo's text into a more assertive and impersonal account (a 'doctrinalisation of Riccoldo's work

', p. 202)

, the Epitome transforms it into a stringent synthesis adapted to a Christian audience and a more purely educational intent.

A further proof of Riccoldo's influence comes from Eugenio Burgio and Samuela Simion's article. The authors dwell on a little-known text, the Itinerario al Santo Sepolcro by the Italian podestà ( jurist) Antonio da Crema. Highly indebted to the CLS, the Itinerario draws from it a list of 'thirty errors of the Qur'an', thus representing the first known Italian translation of a fragment of Riccoldo's treatise (especially chapters I and IX).

The topic has been previously discussed in another contribution. See Justicia Lara, 'Context and Use'.

The family α is composed of fourteen manuscripts, dating from the thirteenth to the fifteenth century. All of them share several disjunctive variants with respect to the Arsenal manuscript and manuscripts of family β, which are in some cases copy mistakes but above all deliberate innovations intended to improve and clarify the text. This group of manuscripts could therefore be thought of as the result of an older and revised version of A 1 , which is itself the revision of the archetypal version of the Arsenal manuscript. See the introduction in Martínez Gázquez and González Múñoz (eds), Alchoran siue lex Saracenorum.