Ariane Peyret

Emmanuel Ibarboure

Arnaud Tron

Dr Louis Beauté

Ruben Rust

Prof. Dr Olivier Sandre

Nathan D Mcclenaghan
email: nathan.mcclenaghan@u-bordeaux.fr

Sébastien Lecommandoux
email: lecommandoux@enscbp.fr

Sebastien Lecommandoux

S Lecommandoux

Dr R A Tron

Dr N D Rust

Mcclenaghan

Polymersome Popping by Light-Induced Osmotic Shock under Temporal, Spatial, and Spectral Control

Keywords: polymersomes, photochemistry, photorelease, fluorescence, self-assembly

  L'archive ouverte pluridisciplinaire

Polymersomes are mechanically robust self-assembled vesicular structures that are widely studied and are proving central in increasing research and application areas ranging from nanomedicine to artificial cell design. [1] Control over their membrane diffusion properties and structural integrity is crucial for the development of new complex systems, such as artificial cells. Compartmentalization is central in biological cells. Indeed, physical separation of biochemical species allows metabolic reactions to take place independently and simultaneously in a confined and crowded space. [2][3][4][5][6][7][8][9][10] For decades, different methods have been proposed to construct elaborate structures that have been developed in the field of lipid and polymer chemistry. [11][12][13][14] Amongst others, double emulsion techniques [15- 17] , phase transfer of emulsion droplets over an interface [18][19][20] , layer-by-layer assembly [21] or microfluidics [22] have proved efficient in affording micron-sized vesicles, allowing the encapsulation of distinct biochemical species in different compartments and the ability to control simple biomimetic enzymatic reactions in a confined space. [13,[23][24][25] One additional major characteristic of natural cells is their ability to initiate metabolic reactions at a specific time and at a desired location, independently and repeatedly. In this regard, temporal control is crucial in artificial cell systems. However, most of the designed synthetic systems to date lack some control over the initiation of the reactions, which are generally induced by passive diffusion of species across semi-permeable membranes, either as a result of intrinsic membrane permeability [23] or by the incorporation of channels or pores into the membrane, resulting in a slow release of reactants. [26][27][28] As a result, a remaining major challenge concerns the ability to trigger specific reactions by selectively and rapidly inducing the release of species from independent compartments, while controlling their concentration. [29,30] Herein, we introduce a tunable protocol for light-driven specific polymersome rupture in time and space, which combines the advantages of utilizing light as a trigger and the fast release of components from bursting vesicles. Our system is based on laser excitation of hydrophilic dyes encapsulated in the lumen of distinct giant poly(butadiene)-b-poly(ethylene oxide) (PBut-b-PEO) polymersomes, across the whole visible spectrum gamut. Upon excitation the dye is degraded, either through photofragmentation or reactive oxygen species (ROS)-mediated degradation, leading to an increase of the internal osmotic pressure until subsequent polymersome rupture. This process allows for a precise and fast release of entrapped species from different compartments. Additionally, such a selective mechanism allows discrimination between two types of polymersomes within a group of many and to successively trigger the release of their content without altering the remaining vesicles. This system offers great potential for the development of cell mimics where different species encapsulated in distinct organelle-like compartments have to be released independently, in a controlled manner, but also for the release of other (bio)active compounds. Poly(butadiene)-b-poly(ethylene oxide) (PBut2.5-b-PEO1.3) giant unilamellar vesicles (GUVs) were prepared by a previously reported emulsion-centrifugation method. [31] As suggested in Scheme 1. a), due to the limited water permeability of the polymersome membrane, compared to liposomes, we initially hypothesized that a sudden increase in the internal osmotic pressure of the vesicles would lead to efficient rupture of the membrane. Indeed, water would be unable to diffuse into the cavity fast enough to compensate for the pressure difference between the lumen and the external medium. The outcome is that the membrane is exposed to a large lateral tension and ruptures irreversibly to release pressure. On the other hand, liposomes exhibit a tenfold larger permeability towards water compared to polymersomes (Supplementary Information (SI) p. 14,15), and whenever a pore opens up, the lateral stress on the membrane can be relaxed by hydrodynamic flow from inner to outer solutions through transient pores reported by many groups on large or giant liposomes irrespective of the means used to stress their bilayer: osmotic pressure [32] , applied electric field [33] , lipid photo-oxidation [34] or membrane dye illumination [START_REF] Sandre | Proc. Natl. Acad. Sci[END_REF] (Scheme 1. b). Osmotic pressure was also shown to induce shell rupture of layer-by-layer coated gel beads releasing microcapsules. [START_REF] De Geest | [END_REF] To test our hypothesis, a photodegradation experiment was performed to confirm that fast in situ molecule fragmentation and subsequent osmotic pressure increase in the lumen of giant polymersomes could indeed cause vesicle rupture. In this context, N-diethyl, O-({7-[bis(carboxymethyl)amino]coumarin-4-yl}methyl carbamate (coumarin derivative (11), SI, p. 5-7) was synthesized, inspired by a previously described procedure. [37] It has been established that coumarin derivatives undergo heterolytic C-O bond cleavage under UV irradiation. This cleavage results in the formation of a carbamate ion. After decarboxylation of the carbamate, carbon dioxide and diethylamine are released (Φreaction = 0.003 on irradiating at 405 nm) (figure 1. a). [38] Cleavage of the molecule was confirmed by a decrease and a shift of the absorption band after 30 min UV irradiation (365 nm, 200 W Hg-Xe lamp) (figure 1. b). This photoinduced coumarin cleavage feature was used as a way to increase the osmotic pressure inside the polymersomes. The molecule was encapsulated inside the PBut2.5-b-PEO1.3 GUVs. The vesicles were then irradiated under confocal observation (405 nm, 50 mW, 25%) resulting in a fast (few milliseconds) explosion (figure 1. c). As a control, dye-free (sucrose-loaded) polymersomes were irradiated at 405 nm and coumarin-loaded polymersomes were irradiated at 488 nm and 561 nm. In all cases, no rupture was observed, confirming that the explosion results from coumarin selective irradiation. In order to broaden the scope and versatility of the release process, we reasoned that as increased osmolarity is a colligative process, any molecule able to degrade/cleave following illumination would potentially provide a complementary alternative release pathway. In this context, we chose two hydrophilic fluorescent dyes, calcein and methylene blue (MB), that are known to be effective photosensitizers. [39,40] Upon irradiation in the visible region, they generate reactive oxygen species (ROS) including singlet oxygen ( 1 O2) via energy transfer from the excited triplet state of the dye to the triplet ground state of molecular oxygen ( 3 O2). [41] We hypothesized that the fast generation of reactive species upon irradiation would result in increasing the osmotic pressure inside the lumen of the polymersomes and would lead to vesicle bursting. As shown in the confocal images of Figure 2. a), and b), irradiation of GUVs loaded with either 15 mM calcein (λexc=488 nm,) or 10 mM MB (λexc=633 nm,) led to a rapid (t <10 s) rupture of the membrane and content release (SI, videos S1, S2). For both dye-loaded vesicles, no bursting occurred on illuminating at wavelengths outside the dye absorption bands, nor for dye-free vesicles (sucrose-loaded only) at any available wavelength (SI, video S3), confirming that the mechanism is not related to direct local heating or any other disturbance of the membrane due to the laser excitation. Further investigation on the exact role of ROS in the overall process showed that ROS are responsible for dye degradation and osmotic pressure increase (SI, p. 8-12). This auto-degradation was evidenced by a decrease of the absorbance of both calcein and MB after 30 min irradiation (Figure 2. c, d) and is considered as the origin of polymersome bursting.

In order to demonstrate the role and versatility of compartmentalization and polymersome explosion in vesiclebased chemical factories or proto-cell design, further series of experiments were conducted. In a first series (Figure 4. a), calcein-loaded PBut2.5-b-PEO1.3 polymersomes were observed with a confocal microscope in bright field (transmission) and in the green channel (emission range of calcein). Regions of interest (ROIs) in the form of circles were defined over several distinct polymersomes. At a defined time, these ROIs and consequently the chosen vesicles were subjected to intense irradiation (488 nm, 40 mW, 30%) corresponding to calcein absorption. The fluorescence intensity inside the ROIs could be followed during excitation. As shown in a series of snapshot images taken from the videos of the confocal observations, the chosen polymersomes rupture shortly (≈3 s) after being excited. The rupture is associated with the appearance of a peak (arrows) during the fluorescence intensity decay inside the ROIs. This decay corresponds to the bleaching of the dye. Because of and 633 nm (10 mW, 10%, red channel). Then, vesicles are irradiated at 633 nm (high laser intensity), resulting in a rupture of red vesicles followed by an irradiation at 488 nm (high laser intensity), provoking rupture of green vesicles. Empty vesicles remain intact as can be seen in the transmission channel. (The movies corresponding to these two series of experiments are presented in SI, video S4 and video S5). its high concentration, calcein fluorescence that was initially quenched inside the polymersomes is rapidly recovered when diluted in the external medium due to vesicle rupture (see arrows on Figure 3. a). This method allows fast release of loaded species with high precision in space and time. In another series of experiments, calcein-, methylene blue -loaded and dyefree (sucrose-loaded) giant polymersomes were prepared, mixed together and visualized using confocal microscopy (Figure 3. b). MB-loaded vesicles were visualized in the red channel, calcein-loaded vesicles in the green channel and the native vesicles were only visible in bright field. First, the whole solution was illuminated in the absorption range of MB. As expected, only the red polymersome ruptured while the green and empty ones remained stable. Then, we excited calcein (λex=488 nm) and selectively-induced rupture of the green polymersome. The sucrose-loaded vesicles remained stable through the whole process. This method of wavelength selectivity for explosion allows targeting of one or more types of vesicles within a group of many, and to specifically address them.

To illustrate and generalize this last example of controlled species release, an experiment was designed where nanopolymersomes and nano-liposomes (100 nm diameter) were encapsulated separately in PBut2. 4. Then, the sample was irradiated (λex=633 nm) to induce the DPPC "red" liposomes release after MB-loaded GUV explosion. This is, to the best of our knowledge, the first reported example of selective triggered release of nano-vesicles (liposomes or polymersomes) loaded in giant polymersomes.

To summarize, photoirradation of vesicles (both polymersomes and liposomes) loaded with photofragmenting dyes (either via the intermediacy of ROS activity or direct photodecaging) is proposed as an efficient external trigger to modulate their membrane properties and structural integrity. Considering much more permeable phospholipid vesicles, the direct consequence of this dye photo-degradation process is vesicle swelling, which renders their membrane more taut (see SI). The ability to tune membrane surface tension of these micron-sized capsules can offer scope in studies of surface tension effect on motility in aqueous solution. Concerning polymersomes, which are much less capable of exchanging water with external bulk solution through passive permeability and cannot open up transiently (due to lower line energy, see SI), an increase in osmolarity accompanying photo-irradiation provokes bursting of their membrane, which is shown to release any cargo initially sequestered within the lumen (such as internalized molecules or nano-polymersomes and liposomes). We anticipate that such behavior can be generalized to any other kind of polymersomes or membranes with low water permeability. Additionally, this process is subject to spatial and temporal control based on the appropriate choice of the illumination source and of the irradiation wavelength, depending on the selected photosensitizer, making this phenomenon a universal and versatile approach. Envisioned applications range from directed delivery in nanomedicine, as well as controlled dosing of nutrients and cofactors locally, which may prove decisive in decrypting biochemical interplays in cascade reactions and enzyme function.

COMMUNICATION

An original and versatile protocol is described for the controlled light-triggered rupture of giant polymersomes. This method allows precise and selective delivery of a range of loaded species with full control in time, space and excitation wavelength. minutes. 60 µL of the above emulsion was slowly poured over the interface and the sample was immediately centrifuged (3 min, 500 g, ambient temperature). The resulting polymersomes were recovered in the lower phase. In the case of calcein or methylene blue (MB)-loaded polymersomes, the dye was dissolved in a sucrose solution to reach the desired concentration and 5 µL of this solution was used to form the emulsion. The concentration of glucose was adjusted to the same osmotic pressure as the dye in sucrose solution. For the ROS quenching experiment with sodium azide (NaN 3 ), the desired concentration of NaN 3 was added to the calcein in sucrose solution and 5 µL of this solution was used to form the emulsion. The concentration of glucose was adjusted to the same osmotic pressure (sucrose and dye-containing solution).

Confocal microcopy observations: Laser scanning confocal microscopy images were acquired on an inverted Leica TCS SP5 microscope equipped with an HCX PL APO 63×, NA 1.4 oil immersion objective in fluorescence mode. Samples (≈20 μL) were injected in a homemade chamber that was sealed to prevent evaporation. The laser outputs were controlled via the Acousto-Optical Tunable filter (AOTF) and the two collection windows using the Acousto-Optical Beam Splitter (AOBS) and photomultipliers (PMT) as follows: Alexa Fluor 405 was excited with a diode laser at 405 nm and measured with emission settings at 415-455 nm, calcein was excited with an argon laser at 488 nm (3-20 %) using a 418-423 nm window, rhodamine was excited at 561 nm using a 575-600 nm window and MB was excited at 633 nm with emission settings at 650-700 nm (90%). The Helium-Neon laser at 633 nm (10 %) was also used in transmission mode. Images were collected in simultaneous mode using a resonant scanner at 8000 Hz in bidirectional mode at a resolution of either 512×512, 1024×1024 or 1024×256 pixels. For the pore opening measurements, a lower resolution was used (128×128) to acquire 1frame/10ms. The FRAP wizard using the fly mode for faster time resolution was used to define regions of interest (ROIs) around chosen vesicles. Processing of fluorescence confocal acquisitions was performed with the ImageJ freeware.

Gel assisted giant unilamellar vesicle (GUV) formation: Giant liposomes were prepared by spin-coating and film rehydration on polyvinyl alcohol (PVA, Mw=143 000 g⋅mol -1 , 100 % hydrolyzed, Merck S6585 194 247) gel. [1] A few drops of 30 mM calcein in 5 % PVA solution in water (pH adjusted to 7.4) were spin coated on a microscope coverslip (2500 rpm, 3 minutes). 1-Palmitoyl-2-oleoyl-sn-glycero-3phosphocholine (POPC) lipids (1 mg/mL) tagged with rhod PE and dissolved in chloroform were spread out on the dried calcein-PVA film. After solvent evaporation, small chambers were formed and filled with 1 mL sucrose solution (0.35 M). GUV formation was followed under the confocal microscope (bright field). Glass micropipettes used to aspire the GUVs were prepared using a pipette puller (from Sutter Instrument: Model P97) followed by micro-forge treatment of the tip to adjust the inner diameter of the capillary around 5-10 µm. A micromanipulator (Eppendorf PatchMan NP2) connected to a water reservoir was used to move the micropipette. A micrometer allowed both to move the water reservoir with precision and to measure the low pressures applied to the aspired GUVs.

Photocapture of singlet oxygen: Photocapture of singlet oxygen was determined upon excitation at 488 nm (calcein) or 633 nm (methylene blue) on an optical bench equipped with a 150 W Hg-Xe lamp and a monochromator. Samples (ratio fluorescent dye/oxygen trap : 10 µM / 40 µM in sucrose 0.35 M) were stirred during the irradiation and the amount of converted material was determined by UV-visible spectroscopy following the disappearance of the absorption band of the oxygen trap at 425 nm.

Small unilamellar liposome/polymersome preparation and incorporation in giant polymersomes:

Liposomes were prepared by the thin film rehydration method, followed by extrusion. 1,2-Dipalmitoylsn-glycero-3-phosphocholine (DPPC) lipids (6 mg/mL) and L-α-phosphatidylethanolamine-N-(lissamine rhodamine B sulfonyl) (rhod PE) (0.1 mg/mL) were solubilized in chloroform. 1 mL of the above solution was evaporated on a rotary evaporator and rehydrated under magnetic stirring with 1.5 mL milliQ water (50 °C, overnight). The resulting suspension was extruded (Avanti Mini-Extruder, Avanti Polar Lipids) through a 400 nm poly-carbonate filter. For the encapsulation in the giant polymersomes, the vesicle preparation protocol was followed. 15 µL of the liposomes suspension was added to 15 µL of 30 mM calcein in sucrose 0.35 M and 5 µL of this solution was used to form the emulsion. The concentration of the glucose solution for the interface was adjusted to the same osmotic pressure as the liposomes in calcein-sucrose solution. The same procedure was applied to form PBut-b-PEO (Mn x 10 3 : 1.2-b-0.6) polymersomes with ≈ 3 wt. % PBut (Mn=1700 g⋅mol -1 ) tagged with Alexa Fluor 405. [2] Di-tert-butyl 2,2'-((4-(hydroxymethyl)-2-oxo-2H-chromen-7-yl)azanediyl)diacetate (9): Compound 8 (4.8 mmol, 1 eq) was dissolved in a mixture of methanol (50 mL) and THF (50 mL) and the solution was cooled on ice. NaBH 4 (7.2 mmol, 1.5 eq) was added in small portions and the reaction mixture was stirred for 3 h. After this time, the reaction was quenched by addition of 1 N aqueous HCl (20 mL) and the mixture was extracted twice with EtOAc. The combined organic layers were washed with brine and dried (MgSO 4 ). The product was purified by column chromatography over silica gel (cyclohexane:AcOEt; 1:1 v/v) and resulted in a green solid (40% yield). 10): Diethylcarbamoyl chloride (0.5 mL, excess) was added to a solution of compound 9 (0.24 mmol, 1 eq) in pyridine (3 mL) at ambient temperature. Then the mixture was heated to 90°C for 48 hours under a nitrogen atmosphere. After the reaction mixture was cooled to ambient temperature, 1N HCl was added and the mixture was extracted with EtOAc. The combined organic layers were washed with saturated NaHCO 3 solution and concentrated. Then the crude product was purified by silica column chromatography, eluting with cyclohexane:EtOAc (5:1, v/v) yielding the product (40% yield) upon solvent removal.

2,2'-((4-(((diethylcarbamoyl)oxy)methyl)-2-oxo-2H-chromen-7-yl)azanediyl)diacetic acid (11) :

Compound 10 (0.058 mmol, 1eq) was dissolved in THF (0.5 mL). Then 0.13 mL of a water solution containing 100 mg of KOH in 1 mL of water was added (KOH = 4eq). The mixture was stirred at room temperature overnight. Water and THF were removed and the product was dissolved in water and precipitated on adding a small amount of HCl until precipitate formation was complete. The product, which was a red powder, was filtered off and dried in vacuo (50% yield). 1 H NMR (DMSO, 600 MHz, 60°C) δ (ppm): 7.53 (d, 1H), 6.64 (dd, 1H), 6.5 (d, 1H), 6.01 (s, 1H), 5.28 (s, 2H), 4.22 (s, 4H), 3.31 (q, 4H), 1.12 (t, 6H). Solution osmolarity was found to significantly increase (up to 80 mOsm/kg) with increasing sucrose concentration (Figure S 2). For a solution of 0.35 M sucrose and 15 mM calcein, there was an increase of 18 mOsm/kg after irradiation, whereas no increase was observed when irradiating pure sucrose solutions. Irradiation of calcein in the absence of sucrose led to the same increase of osmotic pressure, thus proving the non-interference of sucrose in the process. Then, we observed that increasing viscosity was correlated with a higher osmolarity difference after irradiation. Indeed, for 0.7 M sucrose, the osmolarity increase was about 40 mOsm/kg and it doubled for 1.4 M sucrose. We propose the interpretation that the viscosity of the solution has an impact on the diffusion of ROS and promotes degradation of the dye by lowering their diffusion away from the dye molecule. 1 H NMR analysis of calcein in D 2 O during irradiation (Figure S 3) proved that the changes in osmolarity were most certainly due to its degradation. Indeed, a decrease of the intensity of the resonance of the CH 2 proton adjacent to the carboxylic moiety (a, δ=3.93 ppm, -CH 2 -COOH) was observed as a function of irradiation time. Moreover, the apparition of a peak at 8.46 ppm after irradiation was consistent with the presence of formic acid, one of the probable degradation products. [8] The control experiment, which consisted of irradiating solutions without calcein, did not show any Based on these results, as well as previous studies of ROS-mediated oxidation [8] , the suggested mechanism is based on a radical-mediated oxidation of calcein, leading to an increase of the internal osmotic pressure of the vesicle caused by the degradation products, arising through bond cleavage at the position labeled a on After irradiation of methylene blue the ESI spectrum shows an increase of the peak at 270.1 m/z that corresponds to dye degradation. The same peak is present in a smaller proportion in the spectrum before irradiation because the sample was left unprotected from light a few hours before the analysis. If the limited diffusion of water across the membrane is responsible for the explosion, using a much more permeable membrane should prevent it. In order to test this hypothesis, we formed 1-palmitoyl-2oleoyl-sn-glycero-3-phosphocholine (POPC) GUVs [1] , as lipidic membranes are known to exhibit tenfold higher permeability towards water than polymersomes. [9] Figure S 10 represents confocal images of a POPC GUV loaded with 30 mM calcein before and after irradiation. For visualization in the red channel, the membrane was tagged with rhodamine. The images clearly show a floppy membrane before irradiation. After being excited (λ exc = 488 nm; 5 % laser intensity; 20 s), the vesicle swelled without rupturing, even if higher laser intensity and/or illumination times were applied. These observations confirmed that water indeed diffused into the interior of such permeable lipidic vesicles to compensate for the osmotic imbalance, inducing its swelling, but without a rupture of the membrane.

Vesicle swelling upon irradiation

This scenario was confirmed by an additional experiment where a POPC GUV was partially aspired through a micropipette to evaluate its internal volume increase and hence the initial osmotic pressure In the initial state (a), the vesicle has not been irradiated at 488 nm and the floppy membrane is rendered tauter by aspiration inside the capillary. When the vesicle is irradiated at 488 nm (b), calcein generates ROS that degrade the dye and induce an increase of the osmotic pressure. As the lipid membrane is permeable, water is able to enter the GUV to compensate for the osmotic imbalance. This results in a swelling of the vesicle and a retraction of the membrane tongue from the capillary by a length ∆𝐿 P ≈ -4 µm. Using an equation introduced by Olbrich et al. for osmotically-swollen giant liposomes under micropipette aspiration, [10] we can estimate the volume increase of liposomes caused by irradiation and ROS production: ∆𝑉 = -𝜋𝐷 P (𝐷 V -𝐷 P )∆𝐿 P 4 ⁄ = 91 µm 3 for a vesicle of diameter 𝐷 V = 10.8 µm (initial volume 𝑉 i = 660 µm 3 ) aspired in a pipette of diameter 𝐷 P = 5 µm. The ratio ∆𝑉 𝑉 i ≈ 0.14 ⁄ can give an estimate of the osmotic pressure variation under illumination ∆𝐶 𝐶 i ≈ 0.14 ⁄

where the initial osmolarity is 𝐶 i = 380 mOsm • kg -1 . Therefore we can estimate the osmolarity increase build up by light-induced ROS production and dye degradation at ∆𝐶 ≈ 52 mOsm • kg -1 .

When the pressure inside the capillary (c) was adjusted to pull the vesicle tether end back to its initial position, the lateral tension was raised up to 𝜎 = 1.3 mN.m -1 , a value still below the maximum lateral tension that a phospholipic GUV can withstand σ lys ∼10 mN⋅m -1 . [10] The effective diffusion coefficient D eff is given by:

𝐷 eff = 2𝑟 𝑐 𝑆 0 (𝜂 𝑙𝑙) ⁄ = 2𝜋𝜅 (𝑒𝜂𝑙𝑙) ⁄ = 4π𝜏 (𝜂𝑙𝑙) ≈ 5𝜏 2𝜂 ⁄ ⁄ Eq. (2)
where η represents the viscosity of the solution in which the membrane curls (the outside glucose solution in our case) and ln is a logarithmic term arising from the drag coefficient of a cylinder that is considered as constant: [11] 𝑙𝑙 = ln(2𝜋 𝑟 𝐿 ⁄ ) + 1 2 ⁄ ≈ 5, and 4𝜋 𝑙𝑙 ⁄ ≈ 5 2 ⁄ (hence the simplified right term on Eq. ( 2).)

To compare our system with the aforementioned one, we prepared three different batches of giant vesicles with the emulsion-centrifugation technique (see experimental methods) with varying glucose concentrations. In each experiment, the concentration of the inner sucrose solution was adjusted to reach an osmotic equilibrium with the outer glucose solution. Calcein (15 mM) was encapsulated within the vesicles to enable bursting under laser irradiation (488 nm, 5-10 % laser intensity). Movies of pore bursting were obtained at the highest achievable speed of the Leica SP5 resonant scanner (100 frames/s).

The extracted frames of the explosions were processed with ImageJ freeware to track and measure membrane pore growth. For each glucose concentration, the experiment was repeated on an average of ten vesicles of equivalent sizes, and the results were plotted on a master curve (horizontal error bars From the fits derived from the experimental data (Eq. ( 1)), the effective diffusion coefficients Deff could be calculated by fixing the value of the critical radius rc to 0.38 μm for each viscosity. In agreement with the model proposed by Mabrouk et al., the diffusion coefficient is roughly inversely proportional to the viscosity of the solution into which the membrane curling rim advances (which determines the viscous losses) as in Eq. ( 2). The slight deviation from the perfect ~1 𝜂 ⁄ dependency might be ascribed to a weak variation also of the line tension of the PBut 2.5 -b-PEO 1.3 membrane with the sucrose and glucose concentrations, as with the reported modification of the mechanical properties (𝜅 and thus 𝜏) for phospholipid bilayers exposed to high sugar concentrations. [13] Regarding quantification, we can estimate the structural (hydrophobic thickness e) and mechanical (bending modulus κ) properties of the PBut 2.5 -b-PEO 1.3 membrane from their reported experimental values: 𝑒 = 9.6 nm and 𝜅 = 24.7 ± 11.1𝑘 B 𝑇 , according respectively to cryo-TEM image analysis and micropipette measurements. [14] Scaling laws versus the molar mass M h of the hydrophobic block were proposed by Bermudez et al.: [15] 𝑒~𝑀 h for PBut-b-PEO copolymers, [11] and are significantly lower than those measured on DPPC large liposomes at 46°C by Taupin et al. through the leakage of parametric probes under various hypotonic shocks (from 𝜏 = 6.5 pN for irreversible pores to 𝜏 = 5.5 -8 pN on sub-critical resealing pores) [16] , on DOPC giant liposomes by Karatekin et al. [17] through the closure dynamics of transient pores (from 𝜏 = 6.9 ± 0.4 pN to 𝜏 = 20.7 ± 3.5 pN depending on the supplier, and thus of purity, of DOPC), or by Levadny et al. [18] by statistical analysis of the pore induction rate under micropipette pulling ( 𝜏 = 10.5 ± 0.5 pN ). Although the pore dynamics here are qualitatively equivalent to the experiment of Mabrouk et al. with photo-isomerizable liquid crystalline copolymers, in our case with PBut 2.5 -b-PEO 1.3 the critical radius 𝑟 𝑐 = 0.38 µ𝑚 is much lower, which implies that the initial elastic tension is higher: 𝑆 0 = 8.8 • 10 -2 mN. m -1 . From the expression of the initial elastic tension 𝑆 0 = 1 2 𝜅(𝑐 0 ) 2 , we get an estimate of the spontaneous curvature 𝑐 0 of the membrane, from which we deduce the spontaneous radius of curvature (𝑐 0 ) -1 ≈ 24 nm. Interestingly, this value is typically comparable to the smallest radius that large unilamellar vesicles (LUV) of a given copolymer can withstand from the rule-of-thumb 𝑒 𝑅 min ⁄ ≈ 0.25 as shown by Salva et al. after LUV rupture by hypertonic shocks, [19] thus here 𝑅 min ≈ 38 nm for PBut 2.5 -b-PEO 1.3 polymersomes.

To interpret the different fates between liposomes and polymersomes exposed to increased internal osmotic pressure through dye irradiation at its maximum absorption wavelength, we propose a kinetic control of the membrane pore induction in these two different types of vesicles as opposed to a mere thermodynamic control sometimes put forward by several authors. [20,21] To give quantitative values, the water permeability of monounsaturated phospholipids like POPC measured by the Evans micropipette aspiration method is P∼30 µm⋅s -1 and their lysis tension is σ lys ∼10 mN⋅m -1 , [10] whereas values for PBut 2.5b-PEO 1.3 polymersomes are respectively P∼3.1±1.6 µm⋅s -1 from osmotic inflation experiments [22] and σ lys ∼16 mN⋅m -1 from micropipette aspiration measurements [23] . In brief, polymersomes resist larger applied lateral stresses than fluid-phase liposomes and exhibit a higher toughness (i.e. a larger surface area below the curve of lateral tension versus membrane expansion coefficient), but they are 10 times less permeable to water, which is mainly ascribed to their thicker hydrophobic membrane (∼6-10 nm as compared to ∼3-5 nm). The lateral tension arising from the increased osmotic pressure relative to the external solution after dye photo-degradation can be estimated by the Laplace law of fluid interfaces ∆𝜋 = 2𝜎 0 𝑅 0 ⁄ where R 0 is the initial vesicle radius and σ 0 is the lateral tension just before pore aperture.

Converting the estimated osmolarity difference ∆𝜋 ≈ 18 mOsm • kg -1 into an osmotic pressure through the perfect gas law ∆𝜋 = ∆𝑐𝑅𝑇 = 4.5 • 10 4 Pa and using the Laplace law, we obtain a lateral tension σ 0 ∼225 mN⋅m -1 with R 0 =10 µm, well above the rupture tension σ lys .

In the case of liposomes, the lateral tension on the membrane built up by the increase of solute concentration inside the vesicles can relax by internal volume reduction through outwards flow across "sub-critical" pores, i.e. holes in the bilayer that have a size insufficient to expand (below the critical radius 𝑟 𝑐 ) but nevertheless contribute to increase permeability. Their existence has been evidenced more than four decades ago by the pioneering work of Taupin et al. [16] using electron paramagnetic resonance (EPR) probes. These authors also demonstrated that the frequency of vesicle leakage (i.e. inverse of mean leakage time) through transient pores for a given solute over-concentration inside the vesicles is inversely proportional to 𝜏 2 , the square of line tension. This mechanism of transient or "pulsatile" pore formation relaxing the pressure in response to an osmotic shock, classical for liposomes, [24] can S19 certainly not work in the case of polymersomes due to their too low line energy 𝜏 compared to liposomes, not sufficient to reseal the membrane once a pore is nucleated. This is why for the same osmotic pressure imposed (same solutes encapsulated and same conditions of illumination), polymersomes leak much more slowly than liposomes, and thus they stay longer in a taut state without relaxing their lateral tension, until they eventually burst irreversibly. The osmotically driven vesicle rupture triggered by illumination described in this article corresponds to a kinetic control of rupture, the lower permeability of polymersomes letting them for longer in a tense state and maximizing their probability to undergo rupture with less possibility of resealing (since the driving force for pore closure is 𝜏).

Figure 2 .

 2 Figure 2. a) Photocleavage of N-diethyl, O-({7-[bis(carboxymethyl)amino]coumarin-4-yl}methyl carbamate (coumarin derivative) under irradiation. b) Electronic absorption spectrum of a 80 μM coumarin derivative in aqueous solution before and after (dashed line) 30 min irradiation at 365 nm with a 200 W Hg-Xe lamp. c) Confocal observation of a 10 mM coumarin-loaded GUV (green channel, emission range of coumarin, 485 nm). The vesicle undergo fast (few milliseconds) rupture upon irradiation at 405 nm (50 mW, 25%). Scale bar = 10 μm.

Figure 1 .

 1 Figure 1. a) Chemical structure of calcein and confocal images of a 15 mM calcein-loaded polymersome irradiated at 488 nm, with laser intensity 40 mW, 5% (green channel, emission range of calcein, 520 nm). b) Chemical structure of methylene blue (MB) and confocal images of a 10 mM MBloaded polymersome irradiated at 633 nm with laser intensity 10 mW, 90% (red channel, emission range of MB, 660 nm). c) Electronic absorption spectrum of a 30 μM calcein photosensitizer in aqueous solution before and after (dashed line) 30 min irradiation in the 400 -550 nm range with a 200 W Hg-Xe lamp equipped with a bypass filter, showing photoinduced degradation. d) Electronic absorption spectrum of a 30 μM methylene blue in water solution before and after (dashed line) 30 min irradiation in the 240 -550 nm range with a 200 W Hg-Xe lamp

Figure 3 .

 3 Figure 3. Selective rupture of vesicles. a) Time and space. Confocal microscopy observation of 15 mM calcein-loaded PBut2.5-b-PEO1.3 vesicles. Regions of interest (ROIs) are defined around chosen vesicles (circles) and allow specific irradiation of those vesicles. The fluorescence intensity inside the ROIs is monitored over time. At t=0 s, 5 vesicles (circled) are subjected to high irradiation intensity at 488 nm. Rapid vesicle rupture (t=3.1, 3.6, 4.3, 4.7 and 5.3 s) is indicated by a sudden burst in fluorescence intensity (arrows) in the 5 defined ROIs. The global decay of fluorescence intensity corresponds to the bleaching of the dye upon irradiation. b) Time and wavelength. Confocal observation of PBut2.5-b-PEO1.3 vesicles loaded with methylene blue (10 mM; red), calcein (15 mM; green) or sucrose (0.35 M; arrow). The first column of pictures shows vesicles subjected to low laser intensity irradiation at 488 nm (40 mW, 2%, green channel) and 633 nm (10 mW, 10%, red channel). Then, vesicles are irradiated at 633 nm (high laser intensity), resulting in a rupture of red vesicles followed by an irradiation at 488 nm (high laser intensity), provoking rupture of green vesicles. Empty vesicles remain intact as can be seen in the transmission channel. (The movies corresponding to these two series of experiments are presented in SI, video S4 and video S5).

  5-b-PEO1.3 GUVs (Figures S13, S14). The PBut1.2-b-PEO0.6 nano-polymersomes tagged with Alexa fluor 405 were encapsulated with calcein in PBut2.5-b-PEO1.3 GUVs and the rhodamine tagged 1,2-dipalmitoyl-snglycero-3-phosphocholine (DPPC) nano-liposomes were loaded with MB in another batch of PBut2.5-b-PEO1.3 GUVs. Figure 4 shows confocal images of two neighboring GUVs. Visualization in the emission range of Alexa fluor and L-α-Phosphatidylethanolamine-N-(lissamine rhodamine B sulfonyl) (blue and red channel respectively) confirmed the effective encapsulation of the nano-vesicles (polymersomes and liposomes) in the cavity of the GUVs. A first irradiation (λex=488 nm) triggered selective rupture of calcein-loaded GUVs and a consequent release of PBut1.2-b-PEO0.6 "blue" nanopolymersomes, as schematically represented in Figure

Figure 4 .

 4 Figure 4. Controlled release of internalized cargo by selective vesicle rupture. Confocal observation of two neighbouring PBut2.5-b-PEO1.3 GUVs loaded with 15 mM calcein (green) or 10 mM methylene blue (red). Nano-PBut1.2-b-PEO0.6 polymersomes tagged with Alexa Fluor 405 (blue) dye are loaded in the green GUV and nano-DPPC liposomes doped with fluorescent L-α-Phosphatidylethanolamine-N-(lissamine rhodamine B sulfonyl) dye (red) are loaded in the red GUV. After a) irradiation at 488 nm (high laser intensity) the green vesicle ruptures and releases the nano-polymersomes. Then, b) irradiation at 633 nm (high laser intensity) caused rupture of the red vesicle and subsequent release of the nano-DPPC liposomes. (Movies corresponding to these two series of experiments are presented in SI, video S6).

  A. Peyret, E. Ibarboure, A. Tron, L. Beauté, R. Rust, O. Sandre, N. D. McClenaghan*, S. Lecommandoux* Page No. -Page No. Polymersome popping by lightinduced osmotic shock under temporal, spatial and spectral control. Materials: Poly(butadiene)-b-poly(ethylene oxide) PBut 46 -b-PEO 30 and PBut 23 -b-PEO 14 (Mn x 10 3 PBut-b-PEO: 2.5-b-1.3 and 1.2-b-0.6; Mw/Mn 1.04 and 1.09) were ordered from Polymer Source (P18422-BdEO and 10191-BdEO batches respectively, both comprising 89% 1,2-addition of butadiene). 1-Palmitoyl-2oleoyl-sn-glycero-3-phosphocholine (POPC), 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) and L-α-phosphatidylethanolamine-N-(lissamine rhodamine B sulfonyl) (rhod-PE) were purchased from Avanti Polar Lipids (reference numbers: 850457, 850355 and 810146 respectively). Sodium azide (NaN 3 ), sucrose, glucose, calcein, methylene blue and rhodamine were purchased from Sigma Aldrich and used as received. Hydrosoluble caged coumarin and a dibenzofuran-based singlet oxygen trap were synthesized using standard protocols. Methods: NMR experiments were performed at 25 °C on a Bruker Advance 400 spectrometer operating at 400 MHz calibrated to the solvent peak in reference to the tetramethylsilane standard. Electronic absorption experiments were carried out on a Varian Cary 5000 UV-vis-NIR spectrophotometer. Mass spectrometry was performed by the CESAMO analytical centre (University of Bordeaux, France) on a QStar Elite mass spectrometer (Applied Biosystems). The instrument is equipped with an ESI source and spectra were recorded in the positive mode. The electrospray needle was maintained at 5000 V and operated at room temperature. Samples were introduced by injection through a 10 μL sample loop into a 200 μL/min flow of methanol from the LC pump. Dynamic Light Scattering (DLS) was used to determine the average size of extruded liposomes and polymersomes in solution. The measurements were performed on a Malvern ZetaSizer Nano ZS instrument with detection at 90°. Samples were analyzed at room temperature. Osmolarity measurements were performed with a freezing point Type-15M automatic osmometer (Löser, Berlin, Germany). Irradiation experiments were carried with a Mercury-Xenon 200 W lamp. A filter was used to cut UV light below 400 nm. The wavelength range was 400-550 nm. Samples (≈1-2 mL) were placed 1 cm from the light guide output end and irradiated in the dark under magnetic stirring for a defined time. Osmolarities were measured before and after irradiation. Viscosities were determined with a DMA generation M density meter equipped with a Lovis 2000 M/ME rolling ball micro-viscometer from Anton Paar at 20°C. Vesicle preparation: Poly(butadiene)-b-poly(ethylene oxide) (PBut 2.5 -b-PEO 1.3 ) giant polymersomes were prepared by a previously reported emulsion-centrifugation method. Briefly, 5 µL of sucrose 0.38 M was poured into 3 mg/mL PBut 2.5 -b-PEO 1.3 in 500 µL toluene. The solution was vigorously handshaken for 30 seconds to create a water-in-oil emulsion. An interface was prepared by pouring 30 µL of PBut 2.5 -b-PEO 1.3 (3 mg/mL) in toluene over 30 µL glucose 0.38 M and allowed to stabilize for 30

1 H

 1 NMR (DMSO, 300 MHz) δ (ppm): 7.50 (d, 1H), 6.55 (dd, 1H), 6.45 (d, 1H), 6.16 (s, 1H), 5.56 (t, 1H), 4.70 (d, 2H), 4.19 (s, 4H), 1.43 (s, 18H).

13 CFigure S 2 .

 132 Figure S 2.Evolution of osmolarity increase upon irradiation correlated with the relative viscosity of 15 mM calcein in increasing sucrose concentrations. Calcein solutions (15 mM) with different sucrose concentrations were irradiated for 30 min in the 400 -550 nm range with a 200 W Hg-Xe lamp equipped with a filter. Osmolarites were measured before and after irradiation. The difference in osmolarity after irradiation increases with the sucrose concentration, which determines the relative viscosity of the solution (ratio compared to pure water).

Figure S 3 . 1 H

 31 Figure S 3. 1 H NMR in D 2 O of calcein before and during irradiation (t=30 and 90 min). Integration of proton a resonance (-CH 2 -COOH, δ=3.9 ppm) decreases with irradiation time indicating a probable cleavage of the -CH 2 -COOH arm mediated by ROS. Reference resonance for integration: aromatic proton e (H, δ=7.9 ppm).

change (Figure S 4

 4 and Figure S 5). Additional control 1 H NMR experiments were performed in order to verify the non-interference of ROS with the membrane of the polymersomes (Figure S 6 and Figure S 7).

Figure S 3

 3 (and also most likely at the two quasi-equivalent methylene groups adjacent to the carboxylate moiety). The same experiments were performed with MB and showed that the dye underwent auto-degradation through the same process (Figure S 8 and Figure S 9).

Figure S 4 . 1 H

 41 Figure S 4. 1 H NMR of sucrose. (400 MHz, D 2 O), δ (ppm): 5.42 (d, J=3.8 Hz, 1H), 4.22 (d, J=8.6 Hz, 1H), 4.06 (t, J=8.6 Hz, 1H), 3.91 -3.86 (m, 1H), 3.84 (m, 1H), 3.81 -3.78 (m, 4H), 3.77 (t, J=10.1 Hz, 1H,), 3.69 (s, 2H), 3.57 (dd, J=13.1 Hz, J=3.8 Hz, 1H), 3.48 (t, J=9.1 Hz, 1H).

Figure S 5 .

 5 Figure S 5. 1 H NMR of sucrose after 30 min irradiation between 400 and 550 nm. (400 MHz, D 2 O), δ (ppm): 5.40 (d, J=4 Hz, 1H), 4.21 (d, J= 8.6 Hz, 1H), 4.03 (t, J=8.5 Hz, 1H), 3.89 -3.86 (m, 1H), 3.84 (m, 1H), 3.81 -3.78 (m, 4H), 3.74 (t, J=9.9 Hz, 1H), 3.66 (s, 2H), 3.55 (dd, J=9.9 Hz, J=3.8 Hz, 1H), 3.45 (t, J=9.3 Hz, 1H).

Figure S 6 . 1 H

 61 Figure S 6. 1 H NMR spectrum of PBut 1.2 -b-PEO 0.6. (400 MHz, CDCl 3 ), δ (ppm): 5.65 -5.30 (m, 1H), 5.0 -4.75 (m, 2H), 3.64 (s, 4H), 1.25 (s, 2H).

Figure S 7 . 1 HFigure S 8 .

 718 Figure S 7. 1 H NMR spectrum of PBut 1.2 -b-PEO 0.6 after irradiation at 488nm in presence of calcein. (400 MHz, CDCl 3 ), δ (ppm): 5.65 -5.30 (m, 1H), 5.0 -4.75 (m, 2H), 3.64 (s, 4H), 1.25 (s, 2H).

Figure S 9 .

 9 Figure S 9. ESI mass spectrum of methylene blue before and after overnight irradiation. A solution of 5 mM methylene blue in D 2 O was irradiated overnight at 633 nm and ESI analyses were performed a) before and b) after irradiation.

Figure S 10 .

 10 Figure S 10. Confocal observations of POPC GUVs loaded with 30 mM calcein before and after irradiation at 488 nm. The membrane is doped with L-α-Phosphatidylethanolamine-N-(lissamine rhodamine B sulfonyl) to allow observation in the red channel. Upon irradiation, the vesicle membrane tightens without rupturing.

  increase upon calcein irradiation (Figure S 11).

Figure S 11 .

 11 Figure S 11. Controlled membrane deformation of a phospholipid GUV by pressure adjustments through aspiration in a capillary. Confocal images of a 30 mM calcein-loaded POPC GUV aspired inside a micropipette. The membrane is tagged with rhodamine for visualization in the red channel. Image a) shows the vesicle before irradiation. In image b), the vesicle is irradiated at 488 nm (calcein) and then (image c)) the pressure is adjusted (i.e. the level of the tank is decreased by a 55 mm height, corresponding to a negative pressure of 540 Pa) to aspire the vesicle portion within the capillary back to its initial position 𝑳 P = 𝟓 µm.

  represent standard deviations from different vesicles and horizontal error bars correspond to ± 5 ms, i.e. half of the interval between successive frames) (Figure S 12).

Figure S 12 .

 12 Figure S 12. Variations of pore opening dynamics in PBut 2.5 -b-PEO 1.3 vesicles containing sucrose and calcein 15 mM depending on viscosity of the external glucose solution. Pore radius as a function of time for three different glucose viscosities as averaged on several pore dynamics: (•) η=1.33 mPa⋅s, (▲) η=2.46 mPa⋅s, (■) η=4.19 mPa⋅s. Equation (1) was used to fit the experimental data with two parameters: the critical pore radius (r c ) and the effective diffusion constant (D eff ). The external glucose concentrations were chosen to balance osmolarity of the internal sucrose/calcein mixtures: (•) sucrose 20% in glucose 10% (0.6 M), (▲) sucrose 50% in glucose 26% (1.475M), (■) sucrose 70% in glucose 36% (2.06 M). Negative points on the time scale arise from the uncertainty about the initial time of pore nucleation (on the order of 10 ms, i.e. the interval between successive frames).

1 2 ⁄

 12 and 𝜅~𝐾 a 𝑒 2 ~𝑀h since the area expansion elastic modulus was shown to be constant material property 𝐾 a = 102 ± 11 mN/m for all the PBut-b-PEO copolymer series. Therefore we deduce 𝑒 = 6.7 nm and 𝜅 = 11.9 ± 5.3𝑘 B 𝑇 for the less commonly used PBut 1.2 -b-PEO 0.6 copolymer. From these values, we can obtain an estimate of the pore line tension: 𝜏 = 𝜅 2𝑒 ⁄ = 3.7 ± 1.7 pN and 5.3 ± 2.4 pN for PBut 1.2 -b-PEO 0.6 and PBut 2.5 -b-PEO 1.3 , respectively. Such line energies compare well to the value 𝜏 = 4 pN estimated by Mabrouk et al.

1 H NMR (CDCl 3 , 300 MHz) δ (ppm):

	7.40 (d, 1H), 6.54 (m, 2H), 6.24 (s, 1H), 5.29 (d, 2H), 4.09 (s,
	4H), 3.38 (q, 4H), 1.52 (s, 18H), 1.2 (t, 6H).

13 C

NMR (CDCl 3 , 400 MHz) δ (ppm): 167

  .9, 160.7, 154.6, 153.8, 150.2, 149.5, 123.5, 108.1, 107.3, 106.8, 98.2, 81.5, 61.1, 53.3, 41.2, 40.4, 28.7, 27.1, 13.1, 13.4. MS-TOF: m/z = 541.2520 calculated for C 27 H 38 N 2 O 8 Na; m/z = 541.2504 [M+Na] +

Table S 1

 S . Variation of the apparent diffusion coefficient with external glucose solution viscosity (measured independently by rolling ball viscosimetry) as obtained by fitting the pore dynamics (FigureS1) with Eq. (1) with a constant critical radius 𝒓 𝒄 = 𝟎. 𝟑𝟑 µ𝒎. The calcein concentration is maintained at 15 mM.

	Glucose concentration	Glucose viscosity η	Apparent diffusion
	(M)	(mPa⋅s)	coefficient Deff, (μm 2 ⋅s -1 )
	0.6	1.33	1111
	1.475	2.46	612
	2.060	4.19	522

Acknowledgements

This work was funded by the French Ministry of Research and Education (fellow A.P. and A.T.) and the Agence Nationale de la Recherche (ANR program NO-SynthCell N° ANR-14-CE16-0015).

Table of contents Page

Supplementary movies S1

Supplementary materials and methods S2-S4

Synthesis of the coumarin derivative (11) S5-S6 Supplementary discussion on the role of ROS S7-S12

Vesicle swelling and membrane tension rise upon irradiation S13-S14 Supplementary discussion on membrane pore opening dynamics S15-S19

Supplementary figures S20

List of Supplementary Movies:

Video S1: bursting of calcein-loaded PBut The synthesis protocol was adapted from literature procedures for a structurally-related photoactive conjugate. [3,4] The mixture was heated at reflux for 3 days. Then the mixture was concentrated in vacuo and the residue was dissolved in EtOAc (100 mL) and washed with water (100 mL) and brine (100 mL) and dried over MgSO 4 . Following purification by column chromatography on silica gel (cyclohexane/EtOAc, 5:1) and solvent removal, an orange solid was obtained (25% yield). To further understand the mechanism of vesicle bursting at the molecular level, we investigated the role of ROS production in the overall phenomenon. We first evaluated the generation of ROS using a scavenger for singlet oxygen ( 1 O 2 ), known to be predominantly generated by excited calcein in the presence of oxygen. [5] The scavenger is a hydrophilic derivative of 1,3-diphenylisobenzofuran (DPBF), used for the detection of 1 O 2 in vitro. [6] A mixture of calcein in sucrose was prepared with a four-fold excess of the scavenger. The evolution of the absorption band of the scavenger was followed spectrophotometrically during excitation of the solution at 488 nm on an optical bench (Figure S 1. a).

The disappearance of the main emission band at 425 nm (arrow) as a function of illumination time, which is directly correlated with the consumption of 1 O 2 , confirmed that ROS were effectively generated by calcein upon irradiation. If ROS generation is part of the process leading to membrane rupture, then the use of a scavenger should prevent vesicles from bursting, as confirmed in Figure S 1. b using sodium azide (NaN 3 ) as a 1 O 2 quencher. [7] Under the same irradiation conditions, explosion was inhibited by the presence of the oxygen scavenger, meaning that the scavenger efficiently trapped the generated singlet oxygen. In order to evaluate the consequence of singlet oxygen generation on the osmotic pressure change, a solution of calcein in sucrose (at varying concentration) was prepared at the same concentration as that used in polymersome formation (15 mM). The solution was irradiated at wavelengths ranging between 400 nm and 550 nm for 30 min using a mercury-xenon (Hg-Xe) lamp equipped with a broadband filter, and the osmolarity of the solutions was measured before and after the irradiation by the freezing point determination method.

Supplementary discussion: membrane pore opening dynamics

The dynamics of pore opening were experimentally monitored and fitted with a theoretical model proposed by Mabrouk et al. in which they describe the curling of polymersome membranes induced by nucleation of a pore as a result of creation of an excess area on one of the two leaflets of the membrane through photo-isomerization of azobenzene moieties. [11] We show that our system exhibits the same trends in pore opening dynamics although the initial constraint needed to induce membrane rupture is different in the two cases.

According to their model, the opening of a pore in the membrane can be compared with the curling rim instability of a bimetallic spring or an asymmetric elastic sheet. The dynamics of pore growth is governed by a transfer of the membrane surface elastic energy S into viscous dissipation of the curling rim within the solution (either the inside solution of the polymersome if the rim curls inward, or the outside solution if the rim curls outwards, depending on whether the photoisomerizable groups are located on the outer or inner leaflet of the asymmetric block copolymer bilayer, respectively). In our case, Fig. 2a clearly shows the calcein outward flow through the pore (the fluorescence bursts arising from a suddenly unquenched signal by dye dilution), whereas the still quenched solution pocket trapped inside the rim is moving into the external medium. Our experiments are thus consistent with their model: the vesicles might also experience a change of spontaneous curvature due to the photo-osmotic phenomenon described to occur in the inner compartment. The pore opening dynamics has two regimes: [11] constant velocity at the early stages, followed by a quasi-diffusive regime at longer times.

More precisely, the effective diffusion constant of the rim (governing the rate of pore opening at long times) is expected to have a bulk (external) solution viscosity dependence when the rim is directed outwards (provoked by azobenzene groups in the inner leaflet in the previous case or internal osmotic pressure in the current case). In their initial publication, [11] Mabrouk et al. gave an oversimplified form 𝑟 2 + 2 𝑟 𝑟 𝑐 = 𝐷 eff 𝑡 that simply reduces to linear regime 𝑟~(𝐷 eff 2𝑟 𝑐 ⁄ ) 𝑡 at early stages and to pure diffusive regime 𝑟~�𝐷 eff 𝑡 at long stages. Subsequently, they considered a slightly modified form of the growth dynamics of a pore of radius r at time t as given by Equation (1) [12] :

where Deff is the effective diffusion coefficient and rc is defined as the critical pore radius,


Guillaume Metzler
email: guillaume.metzer@univ-st-etienne.fr

Xavier Badiche
email: xbadiche@blitzbs.com

Brahim Belkasmi
email: bbelkasmi@blitzbs.com

Elisa Fromont
email: efromont@irisa.fr

Amaury Habrard
email: amaury.habrard@univ-st-etienne.fr

Marc Sebban
email: marc.sebban@univ-st-etienne.fr

Tree-based Cost Sensitive Methods for Fraud Detection in Imbalanced Data

Keywords: Cost Sensitive Learning, Imbalance Learning, Binary Classification

Bank fraud detection is a difficult classification problem where the number of frauds is much smaller than the number of genuine transactions. In this paper, we present cost sensitive tree-based learning strategies applied in this context of highly imbalanced data. We first propose a cost sensitive splitting criterion for decision trees that takes into account the cost of each transaction and we extend it with a decision rule for classification with tree ensembles. We then propose a new cost-sensitive loss for gradient boosting. Both methods have been shown to be particularly relevant in the context of imbalanced data. Experiments on a proprietary dataset of bank fraud detection in retail transactions show that our cost sensitive algorithms allow to increase the retailer's benefits by 1,43% compared to non cost-sensitive ones and that the gradient boosting approach outperforms all its competitors.

Introduction and Related Work

Imbalanced data are ubiquitous in many real world applications, e.g. in medical domains [START_REF] Ling | Test strategies for cost-sensitive decision trees[END_REF], bank transactions [START_REF] Bahnsen | Fraud detection by stacking cost-sensitive decision trees[END_REF][START_REF] Sahin | A cost-sensitive decision tree approach for fraud detection[END_REF] or industrial processes [START_REF] Aggarwal | Outlier Analysis[END_REF]. Supervised machine learning tasks are challenging in this context because algorithms struggle to focus on the important class (e.g. fraud, disease, failure, etc.) which is under-represented in the data. Classical approaches tend to tackle the problem by rebalancing the data [START_REF] Chawla | Smote: Synthetic minority over-sampling technique[END_REF] or optimizing different performance measures than the classical accuracy [START_REF] Puthiya Parambath | Optimizing f-measures by cost-sensitive classification[END_REF] which would otherwise lead to predict all instances in the over-represented classes. Ensemble methods such as random forests [START_REF] Breiman | Random forests[END_REF] or boosting algorithms [START_REF] Freund | A short introduction to boosting[END_REF][START_REF] Sun | Cost-sensitive boosting for classification of imbalanced data[END_REF] have been shown to be particularly successful in this context because they can combine local decisions taken in areas where the imbalance is (made) less prominent.

In some application domains such as fraud/anomaly detection, additional precise information can be given to favor one class from other ones in the learning process. This can for example be done by cost-sensitive learning approaches [START_REF] Elkan | The foundations of cost-sensitive learning[END_REF] which can take into account user preferences (in terms of the importance of the classes or of the attributes). For example, [START_REF] Bahnsen | Fraud detection by stacking cost-sensitive decision trees[END_REF] proposes a cost-sensitive decision tree stacking algorithm to tackle a fraud detection task in a banking context. The authors provide a cost matrix that assigns costs to each decision made by the model and define an optimization function that takes this matrix into account. In Decision Tree learning the splitting criterion is made according to these costs method and not according to the usual impurity measures (such as entropy or Gini). This allows them to better target the rare classes. [START_REF] Sun | Cost-sensitive boosting for classification of imbalanced data[END_REF] presents a cost-sensitive version of the Adaboost boosting algorithm [START_REF] Freund | A short introduction to boosting[END_REF] and also shows its relevance in this imbalanced scenario. [START_REF] Thai-Nghe | Cost-sensitive learning methods for imbalanced data[END_REF] gives a general study of the costsensitive learning methods in the context of imbalanced data. They categorise the methods into two sets: those which fix the error costs in each class and apply it a posteriori to make a decision, and those which tune a priori the cost matrix depending on the local distribution of the data (this category seems more successful). [START_REF] Sahin | A cost-sensitive decision tree approach for fraud detection[END_REF] tackles the problem of credit card fraud detection. The approach, similar to [START_REF] Bahnsen | Fraud detection by stacking cost-sensitive decision trees[END_REF] and to the first one we present in this paper, proposes to induce decision trees by splitting each node according to a cost matrix associated to each example. However, as in [START_REF] Sahin | A cost-sensitive decision tree approach for fraud detection[END_REF], they focus on the actual money losses losses but not on possible benefits of better classifications and they apply their method to ranking problems. Other methods like [START_REF] Ling | Test strategies for cost-sensitive decision trees[END_REF] have focused on the cost of the attributes (here in the context of medical data). They consider that acquiring the exact value of a given attribute is costly and try to find a good compromise between the classification errors and the total feature acquisition costs.

In this paper, we also propose different cost sensitive tree-based learning approaches in the highly imbalanced context of bank fraud detection. The first approach, similar to [START_REF] Bahnsen | Fraud detection by stacking cost-sensitive decision trees[END_REF] and [START_REF] Sahin | A cost-sensitive decision tree approach for fraud detection[END_REF] and presented in Section 3, uses a cost sensitive splitting criterion for decision trees that takes into account the costs (as well as the benefits) of each transaction. But it differs from [START_REF] Bahnsen | Fraud detection by stacking cost-sensitive decision trees[END_REF] and [START_REF] Sahin | A cost-sensitive decision tree approach for fraud detection[END_REF] in the combinaison strategy for building an ensemble method. The second one presented in Section 4 is a new cost-sensitive proper loss [START_REF] Buja | Loss functions for binary class probability estimation and classification: Structure and applications[END_REF] for gradient boosting. Section 2 presents our notations, the gain/cost matrix we are working with and the associated weighted miss-classification loss we want to optimize. The experiments and results are presented in Section 5. We illustrate the different methods using both the retailer margin and the F-Measure (F 1 ) as performance measures. The experiments are made on a proprietary dataset of the Blitz company. We finally conclude in Section 6.

Notations and Problem Formulation

Notations

We focus in this paper on binary supervised classification problems. Let S = (X, Y) = ((x 1 , y 1 ), ...(x m , y m )) be a set of m training instances where x i ∈ R d and y i ∈ {0, 1} m are their corresponding labels. The notation x j i is used to denote the value of the j th variable of the instance i. The label 0 will be used for the negative or majority class (i.e. the genuine transactions) and the label 1 will be used for the positive or rare class (i.e. the fraudulent transactions). We will further denote by S + the set of m + positive examples and S -the set of m - negative examples (here m ->> m + ). We will also note ŷi the label predicted by our learned model for the instance i. We use the notation p for the predicted probability that an example belongs to the minority class, F will be used to design the learned model, i.e. p i = F (x i ) is the probability that the transaction is fraudulent. A threshold is then used to get its label.

Problem Formulation

Our goal is to maximize the profits of the retailers by predicting, online, with decision trees [START_REF] Breiman | Classification and Regression Trees[END_REF] which transactions, made by a customer are genuine or not. While training the trees offline, the company might like to introduce some costs assigned to the training examples, according to the adequacy between the actual label of the transaction and the predicted one (see Table 1). For instance, the retailers will gain money by accepting a genuine transaction, i.e. c T Ni > 0, where T N stands for True Negative or genuine transactions correctly classified. However, if the retailers accept a fraudulent one, they will loose the amount of the transaction c F Ni < 0, where F N stands for False Negative or fraudulent transaction predicted as a genuine one. In this paper, we use a similar approach as the one presented in [START_REF] Bahnsen | Fraud detection by stacking cost-sensitive decision trees[END_REF]. However, instead of only minimizing the money loss due to an acceptation of a fraudulent transaction, we rather focus on maximizing the retailers profits, i.e. we aim at maximizing the loss function L defined as follows:

L(y | ŷ) = m i=1 [y i (ŷ i c T Pi + (1 -ŷi )c F Ni ) + (1 -y i )(ŷ i c F Pi + (1 -ŷi )c T Ni )] .
(1) Talking about profits instead of classical "costs" is more meaningful for the retailers. Furthermore, if we simply focus on the error made by the algorithm, a correctly classified instance will have no influence on the learned model.

In the next section, we show how this loss function can be optimized while learning decision trees.

Cost Sensitive Decision Trees

A classic decision tree induction algorithm proceeds in a top-down recursive divide-and-conquer manner. At each step, the best (according to a given criterion) attribute A is chosen as a new test (internal node) in the tree and the set of examples is splitted according to the outcome of the attribute for each of the instance (there is one child node v per possible outcomes for a given attribute). Then, the same procedure is applied recursively to each new created subset of examples S v until reaching a given stopping criterion. Classification trees (e.g. [START_REF] Breiman | Classification and Regression Trees[END_REF]) usually split the nodes according to an "impurity" measure. One such measure is the Gini index of a set of m instances (x i , y i ) defined as follows:

Gini = 1 - C k=1 p 2
k , where p k denotes the probability to belong to the class k and C is the number of classes (C = 2 in our case). In this paper, the splitting criterion is based on the cost matrix defined above. We do not want to minimize an impurity but to maximize the retailer profits according to the cost matrix.

Splitting criterion and label assignment

Our splitting criterion Γ S on a given set of training instances S of size m (as defined in Section 2) is:

Γ S = 1 m   i∈S- m + m c F Pi (x i ) + m - m c T Ni (x i ) + i∈S+ m + m c T Pi (x i ) + m - m c F Ni (x i )   , (2)
where the first term corresponds to the profits due to genuine transactions and the second to the fraudulent transactions.

Note that this quantity depends on the amount of the transaction of each example in S through the costs c. The best attribute A is the one which maximizes the quantity:

v∈Children(A) Γ Sv -Γ S .
Note that this quantity is very similar to the splitting criterion used to minimize to minimize the Gini impurity up to the number of examples in the parent node. We simply take the opposite of the classical gain and divide it by the number of instances in the parent node, so that this criterion becomes convex.

The values Γ Sv are computed using equation (2) on each set S v . It differs from the splitting criterion used in [START_REF] Bahnsen | Fraud detection by stacking cost-sensitive decision trees[END_REF] where the splits minimize the cost of wrongly accepting or blocking the transactions.

Once the induction tree stopping criterion is reached (ours is defined in Section 5), a class label is associated to each leaf of the tree. For the sake of clarity we introduce the following notations:

• γ 0 (l): the average profit associated to the leaf l if all the instances are predicted as genuine:

γ 0 (l) = 1 |l|   i:xi∈l∩S- c T Ni + i:xi∈l∩S+ c F Ni   ,
• γ 1 (t): the average profit associated to the leaf l if all instances are predicted as frauds:

γ 1 (l) = 1 |l|   i:xi∈l∩S- c F Pi + i:xi∈l∩S- c T Pi   ,
where |l| denotes the number of examples in the leaf l and i : x i ∈ l ∩ S denotes the index i of the example x i both in leaf l and in the set S.

A leaf is assigned the label 1 if γ 1 > γ 0 , i.e. all the transactions in a given leaf are predicted fraudulent if the associated average profit is greater than one associated when all instances are predicted genuine.

Note that this strategy can be easily extended to ensembles of trees [START_REF] Breiman | Random forests[END_REF]. In this case, a standard decision rule consists in applying a majority vote over the whole set of the T learned decision trees. However, this decision rule does not take into account the probability score that can be associated to each tree prediction using the class distribution of the examples in the leaf l(x i ) (as in [START_REF] Sahin | A cost-sensitive decision tree approach for fraud detection[END_REF]). Following this idea, we suggest here to label an instance as positive if the average γ1 (x) of the average profits γ 1 (l j (x i )) over the T trees is greater than γ0 (x), where l j (x i ) is the leaf of the j th tree containing x i :

γ1 (x) = 1 T T j=1 γ 1 (l(x)) ≥ 1 T T j=1 γ 0 (l(x)) = γ0 (x).

Cost Sensitive Gradient Boosting

In this section, we briefly present the gradient boosting framework introduced in [START_REF] Friedman | Greedy function approximation: A gradient boosting machine[END_REF]. Then we present a proper cost-sensitive loss function in order to implement it in a gradient boosting algorithm in an efficient way.

Generalities about Gradient Boosting

Gradient boosting has been shown to be very efficient to deal with classification problems, and a very good candidate to address issues due to imbalance data [START_REF] Beygelzimer | Online gradient boosting[END_REF][START_REF] Li | Mcrank: Learning to rank using multiple classification and gradient boosting[END_REF]. Unlike the well known Adaboost algorithm [START_REF] Freund | A short introduction to boosting[END_REF], gradient boosting performs an optimization in the function space rather than in the parameter space. At each iteration, a weak learner f t is learned using the residuals (or the errors) obtained by the linear combination of the previous models. The linear combination F t at time t is defined as follows:

F t = F t-1 + α t f t , (3)
where F t-1 is the linear combination of the first t-1 models and α t is the weight given to the t th weak learner. The weak learners are trained on the residuals r i = y i -F t-1 (x i ) of the current model. These residuals are given by the negative gradient, -g t , of the used loss function L with respect to the current prediction F t-1 (x i ):

r i = g t = - ∂L(y, F t-1 (x i )) ∂F t-1 (x i ) .
Once the residuals r i are computed, the following optimization problem is solved:

(f t , α t ) = argmin α,f m i=1 (r i -αf (x i )) 2 .
Finally, the update rule (3) is applied.

Cost sensitive loss for gradient boosting

In this section we aim to use the framework presented in [START_REF] Buja | Loss functions for binary class probability estimation and classification: Structure and applications[END_REF] to give a proper formulation of our loss function of Eq (1) in the context of a boosting algorithm, using the gain matrix presented in Table 1.

Using a Bayes rule for classification [START_REF] Elkan | The foundations of cost-sensitive learning[END_REF], an instance i is predicted fraudulent if γ 1 > γ 0 , i.e:

p i c T Pi + (1 -p i )c F Pi -p i c F Ni -(1 -p i )c T Ni > 0,
where p i denotes the probability of the instance to be a genuine transaction. It gives us a threshold over which the transaction is declined (or predicted fraudulent):

p i > c T Ni -c F Pi c T Pi -c F Ni + c T Ni -c F Pi = s i
Using the threshold s i , our cost-weighted miss-classification loss can be rewritten as:

L(y | p) = - 1 m m i=1 (y i c T Pi + (1 -y i )c F Pi ) 1 pi>si +(y i c F Ni +(1-y i )c T Ni )1 pi≤si .
(4) Then, following the framework presented in [START_REF] Buja | Loss functions for binary class probability estimation and classification: Structure and applications[END_REF], L(y | p) can be rewritten as follows:

L(y | p) = 1 m m i=1 ξ i [y i (1 -s i )1 pi≤si + (1 -y i )s i 1 pi>si ] - 1 m m i=1 (y i c T Pi + (1 -y i )c T Ni ), ( 5
)
where 1 is an indicator function and where we use the fact that s = s1 p>s + s1 p≤s and set ξ i = c T Ni -c F Pi + c T Pi -c F Ni which is positive in our context. In fact, c T N > c F P , we earn more if we correctly classify a genuine transaction. Furthermore, if we accept a fraudulent transaction then we loose money and we earn nothing if we declined it, i.e. 0 = c T P > c F N . The first part of equation ( 5), which we will note L si corresponds to the costsensitive loss introduced in [START_REF] Buja | Loss functions for binary class probability estimation and classification: Structure and applications[END_REF] with s i ∈ [0, 1]. Each term of the sum is multiplied by a constant ξ i which depends on the data. The second term represents the maximum that our loss can reach if the predictions were perfect. Note that this second term does not depend on p i . Therefore, we want to minimize:

argmin p∈[0,1] E y [L(y | p)] = argmin p∈[0,1] E y 1 m m i=1 ξ i L si (y i | p i ) .
However it has been shown that in the context of Boosting, it is more convenient to use an exponential approximation [START_REF] Friedman | Greedy function approximation: A gradient boosting machine[END_REF]. We adapt it to consider the output of a prediction model F directly in our approach as follows4 : :

si = (1 -s i )y i e -F (xi) + s i (1 -y i )e F (xi) . Solving ∂E Y [ si ] ∂F (x i )
= 0, we obtain the link function ψ i between p i and Fi = F (x i ):

p i = ψ i ( Fi ) = 1 1 + 1 -s i s i e -2 Fi
, and its inverse ψ -1 i is given by:

e Fi = 1 -s i s i 1/2 p i 1 -p i 1/2 . ( 6
)
The way to transform the output of a boosting model into a probability (the calibration process) plays a key role in the performance of the predictive algorithm. It has been shown that we can achieve at least the same performance with well calibrated boosting model than with one which is cost sensitive [START_REF] Nikolaou | Cost-sensitive boosting algorithms: Do we really need them?[END_REF]. However, we think that our cost sensitive approach gives us a good transformation of the output of the model into a probability.

It is worth noticing that we can make use of equation ( 6) to provide a smooth approximation of the indicator function, such that:

1 pi>si ≤ 1 -s i s i 1/2 p i 1 -p i 1/2 = e Fi .
Note that: p i > s i ⇐⇒ ψ i ( Fi ) > s i ⇐⇒ e Fi > 1 ⇐⇒ Fi > 0. So it is enough to check the sign of the score to predict the label of each transaction. Finally we are minimizing an upper bound L of L:

L(y | p) ≤ L(y | F ) = 1 m m i=1 (1 -s i )y i e -Fi + s i (1 -y i )e Fi .
To use it in a gradient boosting algorithm, it remains to compute the first and second order derivative of L for each instance i with respect to Fi . They are given by:

∂ L ∂ Fi = ξ i -(1 -s i )y i e -Fi + s i (1 -y i )e Fi ,
and

∂ 2 L ∂ F 2 i = ξ i (1 -s i )y i e -Fi + s i (1 -y i )e Fi .

Experiments

In this section, we evaluate the decision rule presented in Section 3 and the loss function presented in Section 4. We compare the results of our method on the retailer profits compared to using a classic Random Forest (RF) algorithm based on the Gini impurity criterion (baseline). The experiments are performed on a private dataset own by the Blitz company which can not be entirely described and made available for privacy reasons.

Dataset and experiments

The Blitz dataset consists of 10 months of bank transactions of a retailer. The first six months are used as the training set (1, 663, 009 transactions) and the four remaining ones as test set (1, 012, 380 transactions). The data are described by 17 features and are labeled as fraud or genuine. The Imbalance Ratio (IR) of the dataset is equal to 0.33%.

The first series of experiments compares the random forest baseline (RF) to the tree ensemble algorithm which uses the decision rule presented in Section 3 (RF X ). We made different variants of the decision rule:

1. RF maj : each leaf is labeled according to the majority class of the examples that fall into the leaf, thus the output of each tree is in {0,1}. The voting criterion is detailed below. 2. RF maj-mar : each leaf is labeled to maximize the profit (also called margin) over the set of all examples in the leaf (the label is 0 if γ 0 > γ 1 and 1 otherwise). We then use a majority vote to predict the label of each transaction. 3. RF mean-mar : this model is the one described in Section 3

For each tree ensemble algorithm, we have used 24 trees with the same maximum depth. Furthermore, for the models RF, RF maj and RF maj-mar , the ensemble classifies a transaction as "fraud" if at least 9 trees agree on this positive class (this threshold is coherent with the one currently used in the Blitz company).

The second series of experiments is dedicated to the analysis of the gradient boosting approaches. We compare our approach GB margin , presented in Section 4.2, with three gradient boosting algorithms which aim to minimize the logistic loss:

1. GB tune-Pre : the threshold has been chosen so that we have the same precision on the validation set as the model RF in the training phase. 2. GB tune-mar : the threshold has been chosen to maximize the margin on the validation dataset. 3. GB tune-F1 : the threshold has been chosen to maximize the F-Measure F 1 on the validation dataset.

For each of these three experiments we needed a validation data set to choose the optimal threshold over which a transaction is predicted as fraudulent. For this purpose, the training set is splitted in two sets, the first one is used to train the model and the other as a validation set, to find the best threshold for the given criterium we want to optimize. To do so, the first four months of transactions constitute the training set, the two remaining months are used as the validation set. Finally these three experiments have been conducted on the same training/validation set and the R software 5 . For privacy reasons, the explicit expressions of c T Pi , c F Pi , c T Ni , c F Ni of the cost matrix can not be given. Note that they are simple functions of the amount M of the transaction. For example, we define c F Pi as follows c F Pi = h(M ) -ζ, where ζ is a parameter used to translate in financial terms, the dissatisfaction of the customer whose transaction has been declined.

Results

To measure the performance of each algorithm, we measure the gap between the maximum profits, i.e. the profits obtained if no errors are made, and the profits given by the algorithms. We use classic performance measures that are often used in an imbalanced setting such as the Precision, Recall and F 1 -Measure defined as follows:

P recision = T P T P + F P , Recall = T P T P + F N F 1 = 2 P recision × Recall P recision + Recall .

All the experiments have been conducted with the same cost matrix where ζ = 5. The results are presented in Table 2. We first notice that we get a reduction of the gap of profits of 1.43%, with the gradient boosting model GB margin compared to the baseline RF. To give an idea to the reader, having a gap of 1% to the maximum profits represents a loss of 43, 000 euros. So, by reducing the gap of 1.43% we increase the profits of the retailer by 60, 000 euros.

Regarding the Random Forest models, we note that the proposed approaches are able to improve the profits of the retailer compared to the model RF. However, we note that RF maj , which uses the number of examples and their label to predict the class of the examples in the leaf, gives similar performance as RF even if it is built differently. This means that the way to label the leaves has, at least, the same importance as the way to build the trees. The models RF maj-mar and RF mean-mar which directly use the notion of average profits in each leaf are the two models that give the best results, in terms of both profits, recall and F-Measure even if the precision is reduced. This is explained by the fact that refusing a genuine transaction will have small impact on the margin of the retailers while accepting a fraudulent transaction will represent a loss for the retailers that is close to the amount of the transaction. Using only our proposed method of Random Forest algorithm, we are able to reduce the gap of 1.18.

If we focus now on gradient boosting models, we first note that the model GB tune-Pre is the one with the highest precision. On the other hand, the other models have a significantly smaller precision but exhibits a higher recall: by maximizing the margin they actually try to find the most fraudulent transactions. As mentioned previously, our cost-sensitive approach GB margin is the one that achieves the best results in terms of margin. But it has also the worst precision (18.8%) for the reason given in the previous paragraph. This model provides also better results than GB tune-mar which emphasizes the interest of a costsensitive approach compared to a simple classification model. However, we note that the model GB tune-F1 is not the one achieving the best F-Measure at test time. Let us also note that F 1 score remains low for each presented algorithms. We think that low values are observed because of the complexity of the data and the problem. Frauds are rare and spread in the all data set.

In a second part, we want to analyze the effect of the parameter ζ. Indeed, some retailers, for marketing reasons, do not want to refuse the transaction of good customers, i.e. they prefer to have a higher precision on their predictions.

A simple way to take this into account in our model is to artificially increase the value of ζ. Figure 1 shows the impact of the parameter ζ on the P recision, Recall and F 1 , while the Gap Margin is still evaluated with ζ = 5. Recall that some retailers do not want to refuse the payment of the good customers, however, the model which maximized is the one with the lowest precision (16.6%). So, it can be interesting to propose to the retailers several models using different values of ζ and give them the choice of the compromise between profits and precision. We first notice that the higher the value of ζ, the higher the precision and the smaller the recall. However, we see that it possible to reach a precision which is twice superior than the GB margin one by setting ζ = 20 and the gap will still be low with a value of 1.94%.

Conclusion

We have presented different cost sensitive tree-based learning strategies to detect frauds in imbalanced retail transaction data. The first strategy is a tree ensemble algorithm which uses a new decision rule which tries to directly optimize the retailer profit. The second one is a gradient boosting algorithm which optimizes a new cost-sensitive loss function. Experiments show that our cost sensitive algorithms allow to increase the retailer's benefits by 1,43% compared to non cost-sensitive ones and that the gradient boosting approach outperforms all its competitors. We plan to focus on how to combine different types of models that may capture different modalities of the data. Furthermore, due to our industrial context, we also want to work on the notion of concept drift and study how the distribution of frauds is evolving in order to take it into account in our models. This opens the door to the development of new domain adaptation methods.

Fig. 1 .

 1 Fig. 1. Study of the influence of the parameter ζ in the definition of the gain of false positive CF P i . We illustrate the behaviour of the Precision, Recall and F1 according to ζ. We also represent the gap to the maximum margin with respect to ζ, but we set ζ = 5 to compute the gap.

Table 1 .

 1 Cost Matrix associated to each example of the training set.

		Predicted Positive (fraud)	Predicted Negative (genuine)
	Actual Positive (fraud)	cT P i	cF N i
	Actual Negative (genuine)	cF P i	cT N i

Table 2 .

 2 Gap to the maximal margin of each algorithm. In this table, the value of ζ was set to 5. The results are separated into two groups: Random Forest models and Gradient Boosting models.

	Experiments	Gap max	Precision	Recall	F1
		profits
	RF	2.99%	68.1%	5.66%	10.5%
	RF maj	2.88%	73.8%	4.71%	8.86%
	RF maj-mar	1.81%	30.2%	10.6%	15.7%
	RF mean-margin	1.87%	30.3%	9.52%	14.5%
	GB tune-Pre	3.01%	61.0%	6.49%	11.7%
	GBtune-mar	2.26%	19.1%	16.6%	17.8%
	GB tune-F1	2.70%	45.4%	9.24%	15.4%
	GB margin	1.56%	18.8%	13.3%	15.6%

note that it exists a direct link between a predicted probability and the output of a model (see Section 3 of[START_REF] Friedman | Additive logistic regression: a statistical view of boosting[END_REF] and Section 4 of[START_REF] Buja | Loss functions for binary class probability estimation and classification: Structure and applications[END_REF] for further details

https://www.r-project.org/ and using the package XGBoost.