Hui Guo
email: hui.guo@espci.fr

Nicolas Sanson

Alba Marcellan

Dominique Hourdet
email: dominique.hourdet@espci.fr

Thermo-Responsive Toughening in LCST-type Hydrogels: Comparison between Semi-Interpenetrated and Grafted Networks

Hydrophilic and LCST polymer chains, poly(N,N-dimethylacrylamide) (PDMA) and poly(Nisopropylacrylamide) (PNIPA), were combined in semi-interpenetrated architectures to investigate their responsive properties in swollen isochoric conditions comparatively to grafted network structures. Using equal weight fractions of PDMA and PNIPA, semi-IPN designed with opposite topologies have demonstrated a thermoresponsive behavior with very different structure/properties relationships as investigated by calorimetry, swelling experiments, tensile tests and 2D neutron scattering at rest and under deformation. In the case of the PDMA network interpenetrated by linear PNIPA chains, the phase transition of PNIPA gives rise to the formation of large microdomains, loosely percolating the PDMA network.

Above the transition, the enhancement of the mechanical properties remains low in terms of elastic modulus and fracture energy. Conversely, the opposite topology, with PDMA chains interpenetrating the crosslinked PNIPA network, brings a large improvement of the mechanical properties at high temperature with a 10-fold increase of the modulus and very high fracture energy. By comparison with grafted hydrogels of similar composition and different topologies, the impact of the primary structure over the phase-separated morphology and the resulting mechanical properties was clearly highlighted.

Introduction

Polymer hydrogels, that are three-dimensional networks swollen in water, have received considerable attention during the last decades due to their high potential as soft materials, water containers, texture modifiers or mechanical transducers with applications in various fields like food, agriculture, water treatment, cosmetics, oil recovery and microfluidics. They are actually used in many bioapplications [START_REF] Peppas | Hydrogels in medicine and pharmacy: properties and applications[END_REF][START_REF] Buchholz | Modern superabsorbent polymer technology[END_REF][START_REF] Hoare | Hydrogels in drug delivery: progress and challenges[END_REF][START_REF] Oh | The development of microgels/nanogels for drug delivery applications[END_REF] such as superabsorbents, contact lenses, dressings, drug delivery systems or scaffolds for tissue engineering, with a very special focus today on biomedicine due to their similarities with biological tissues. [START_REF] Drury | Hydrogels for tissue engineering: scaffold design variables and applications[END_REF] In this context many efforts have been made during the last 15 years to reinforce the mechanical properties of these soft and wet materials which were intrinsically weak. Today one can find two main strategies either with the idea to homogenize the stress distribution within the network with the development of slide-ring gels [START_REF] Okumura | The polyrotaxane gel: A topological gel by figure-of-eight cross-links[END_REF] and ideal tetra-PEG gels [START_REF] Matsunaga | SANS and SLS studies on tetra-arm PEG gels in as-prepared and swollen states[END_REF] or to develop dissipation mechanisms by introducing sacrificial bonds, either covalent or physical, [START_REF] Gong | Double-Network Hydrogels with Extremely High Mechanical Strength[END_REF][START_REF] Wu | Novel developed systems and techniques based on double-network principle[END_REF][START_REF] Sato | Phase-Separation-Induced Anomalous Stiffening, Toughening, and Self-Healing of Polyacrylamide Gels[END_REF] as in ionic, [START_REF] Sun | Highly stretchable and tough hydrogels[END_REF][START_REF] Sun | Physical hydrogels composed of polyampholytes demonstrate high toughness and viscoelasticity[END_REF] hydrophobic, [START_REF] Miquelard-Garnier | Synthesis and rheological behavior of new hydrophobically modified hydrogels with tunable properties[END_REF][START_REF] Abdurrahmanoglu | Design of high-toughness polyacrylamide hydrogels by hydrophobic modification[END_REF][START_REF] Hao | Viscoelastic and mechanical behavior of hydrophobically modified hydrogels[END_REF][START_REF] Yue | Lamellar hydrogels with high toughness and ternary tunable photonic stop-band[END_REF] nanocomposite and hybrid hydrogels. [START_REF] Haraguchi | Effects of clay content on the properties of nanocomposite hydrogels composed of poly (N-isopropylacrylamide) and clay[END_REF][START_REF] Carlsson | Nano-hybrid self-crosslinked PDMA/silica hydrogels[END_REF][START_REF] Rose | Time Dependence of Dissipative and Recovery Processes in Nanohybrid Hydrogels[END_REF] Although physical interactions are reversible in nature, they cannot be finely controlled and the synthesis of strongly interacting networks like polyampholytes [START_REF] Sun | Physical hydrogels composed of polyampholytes demonstrate high toughness and viscoelasticity[END_REF] or hydrogels containing large amount of hydrophobic groups require several step of synthesis and/or solvent exchange.

Recently, we propose to finely tune these secondary interactions within the hydrogel by playing with the thermodynamic properties of polymers in aqueous media and for that purpose we selected poly(N-isopropylacrylamide) (PNIPA) for its well-known LCST behavior. [START_REF] Guo | Thermoresponsive Toughening with Crack Bifurcation in Phase-Separated Hydrogels under Isochoric Conditions[END_REF] As the phase transition of PNIPA that occurs above 32 °C goes hand in hand with a large volume transition, [START_REF] Shibayama | Phase Separation Induced Mechanical Transition of Poly(N-isopropylacrylamide)/Water Isochore Gels[END_REF] we introduced a hydrophilic counterpart inside the hydrogel in order to maintain a high level of swelling in the segregated regime; i.e. well above the LCST of PNIPA. This has been successfully demonstrated with grafted architectures prepared with equal weight fractions of PNIPA and poly(N,N-dimethylacrylamide) (PDMA) and high amount of water, almost 85 wt% in the preparation state. By scanning the temperature from 20 to 60 °C, it was shown that grafted hydrogels were able to keep their high original swelling in the whole range of temperature and to develop in isochoric conditions a strong and reversible thermo-toughening behavior with a 10-fold increase of the elastic modulus above the phase transition of PNIPA. From the comparison between hydrogels designed with the same composition but opposite topologies, a crosslinked PNIPA grafted with PDMA sidechains and a crosslinked PDMA grafted with PNIPA side-chains (see GPN-D and GPD-N, respectively, in Fig. 1a), it was shown that the gel prepared with crosslinked PNIPA was much more resistant to fracture propagation even if initially the two hydrogels display a very similar thermo-toughening behavior at low deformation. [START_REF] Guo | Thermoresponsive Toughening with Crack Bifurcation in Phase-Separated Hydrogels under Isochoric Conditions[END_REF] From complementary experiments performed above the phase transition of PNIPA by small angle neutron scattering, the difference in mechanical reinforcement was attributed to the bicontinuous structure developed by the GPN-D hydrogel in the segregated regime compared to the micellar morphology of GPD-N. [START_REF] Guo | Thermoresponsive Toughening in LCST-Type Hydrogels with Opposite Topology: From Structure to Fracture Properties[END_REF] This responsive strategy allows not only to investigate how the phase separation will reversibly modify the bulk properties of the hydrogel, typically the mechanical behavior, but it is also an interesting way to reach in a controlled manner the strong segregation regime without additional steps of chemistry and/or solvent exchange.

Considering these results, the aim of the present work was to explore new topologies for thermo-toughening hydrogels and for that purpose we developed semi-interpenetrated networks (semi-IPN). With the idea to compare their properties with previous grafted hydrogels, we keep the same preparation conditions with the same weight fractions of PDMA, PNIPA and water and we also designed two semi-IPN architectures with opposite topologies in order to investigate the impact of the phase transition of linear PNIPA embedded into a crosslinked PDMA matrix or the opposite, i.e. a cross-linked PNIPA matrix swollen by PDMA linear chains (see GPD/PN and GPN/PD in Fig. 1b).

The structure and macroscopic properties of these new semi-IPN hydrogels have been investigated as a function of temperature by swelling experiments, differential scanning calorimetry, rheology, tensile tests and small angle neutron scattering at rest and under deformation. This comprehensive set of analyses will be compared with previous data obtained with grafted hydrogels in order to give a broader overview of the structure/properties relationships. Aldrich were used as received. All organic solvents were analytical grade and water was purified with a Millipore system combining inverse osmosis membrane (Milli RO) and ion exchange resins (Milli Q) for synthesis and purification.

Experimental section

Materials

Synthesis of linear polymers

Linear polymer chains were synthesized by radical polymerization using APS/SBS as initiators. In a three-necked flask, 100 mmol of monomers (NIPA or DMA) was dissolved in 100 mL of water and the solution was deoxygenated for 1 h with nitrogen bubbling. The The syntheses of PDMA and PNIPA macromonomers were performed as previously described [START_REF] Guo | Thermoresponsive Toughening in LCST-Type Hydrogels with Opposite Topology: From Structure to Fracture Properties[END_REF][START_REF] Guo | Influence of topology of LCST-based graft copolymers on responsive assembling in aqueous media[END_REF] using a telomerization process with cysteamine hydrochloride followed by modification of the amino end-group with acrylic acid in order to get the vinyl function. From previous works performed on similar systems, [START_REF] Petit | Synthesis of graft polyacrylamide with responsive self-assembling properties in aqueous media[END_REF]

Synthesis of hydrogels

Monomer, cross-linker (stock solution of MBA) and linear polymer chains (or macromonomers), were initially dissolved in a given amount of water under nitrogen bubbling; the temperature of the reactor being controlled with an ice bath. Stock solutions of KPS and TEMED were separately prepared under nitrogen atmosphere and after 30 min aliquots were added into the reaction medium. After fast mixing (2 min), the final formulation was rapidly transferred between glass plates of 2 mm width under nitrogen atmosphere and the reaction was left to proceed overnight in the fridge (4 °C). The resulting hydrogels were then cut with a die-cutter of rectangular or round shape and directly used for DSC and swelling experiments or stored into incompatible paraffin oil before mechanical testing in order to avoid any change in hydrogel composition induced by swelling or drying. For both topologies, the weight ratio "monomer/linear polymer/water" was kept constant to 1/1/10 (corresponding to an initial swelling ratio Q 0 =6), and the molar ratio "monomer/MBA/KPS/TEMED" was set equal to 100/0.1/1/1. The hydrogels are denoted GPN or GPD, according to the polymer used for the crosslinked matrix (N for PNIPA and D for PDMA), and the nomenclature GPN/PD and GPN-D (and vice versa) will be used for semi-IPN and grafted architectures, respectively. Two semi-IPN and three grafted networks have been used in the present study and the details of their formulation are reported in Table 1.

Gel composition and swelling experiments

The samples, originally in their preparation state (Q 0 ), were weighed and placed at a given temperature in a large excess of pure water. Water was changed twice every day during four days. The swollen gels were weighed over time (m t ) and the swelling ratio (Q) were calculated as Q = m t /m d , m d being the theoretical dry weight assuming 100% conversion.

Finally, after 4 days of equilibrium, the gels were dried at 80 °C and then weighed to calculate the loss of polymer material.

Differential Scanning Calorimetry (DSC)

The phase transition of PNIPA-based hydrogels was investigated by Differential Scanning Calorimetry using a DSC Q200 from TA instrument. Gel samples (ca. 80 mg), equilibrated with a reference filled with the same quantity of solvent, were submitted to temperature cycles between 10 and 70 °C. The heating and cooling rates were fixed at 2 °C/min.

Rheology

The viscoelastic properties of hydrogels in their preparation state (discs with 4 cm diameter and 2 mm thickness) were studied using a stress-controlled rheometer (AR 1000 from TA Instruments) equipped with a plate/plate geometry (diameter 40 mm). The experiments were performed in the linear regime and the temperature was controlled by a high power Peltier system. The experimental conditions were fixed at constant frequency (1 Hz) and shear stress (2 Pa) after applying a constant deformation of 20 % on the gel sample. A particular care was taken to avoid the drying of the sample by using a homemade cover which prevents from water evaporation during experiment. In these conditions, dynamic moduli (G ' and G '' ) were recorded between 20 and 70 °C by applying heating and cooling scans of 2 °C/min.

Large strain behavior in tension mode

Tensile tests were performed on a standard tensile Instron machine, model 5565, equipped with an environmental chamber allowing a precise control of the temperature. The device used a 10 N load cell (with a relative uncertainty of 0.16 % in the range from 0 to 0.1 N) and a video extensometer which follows the local displacement up to 120 mm (with a relative uncertainty of 0.1 % at full scale).

The gel samples used for mechanical tests were synthesized in home-made moulds consisting of two covered glass plates spaced by a stainless steel spacer of 2 mm thickness. The gels were then cut with a punch to their final dimensions: 30 mm x 4.9 mm x 2 mm. The gauge length was taken constant (L~20 mm) for all the tests and the gel strip was marked with two dots with a white marker, for their recognition by the video extensometer. For high temperatures or long-term experiments, tests were conducted in a temperature-controlled immersion cell consisting of a paraffin oil bath surrounding the sample in order to avoid water exchange with the environment. From swelling tests, carried out with dry PNIPA networks immersed during several days in paraffin oil at 60 °C, we have checked that this liquid is totally incompatible with PNIPA. Both monotonic tensile tests and fracture tests were performed in triplicate under controlled temperature applying a fixed strain rate of 0.06 s -1 .

During the test, the force (F) and the displacement (L) were recorded while the nominal stress (σ=F/S 0 ) and the stretch ratio  (=L/L 0 ) were calculated. Fracture tests were carried out using the single edge notch geometry. A notch of approximately 1 mm length was made in the middle of a gel strip, whose total width was 5 mm and the length L~20 mm. The fracture energy, G c has been calculated using the following expression: G c =(6•W•c)/√λ c with c the initial notch length, λ c the stretch ratio at break in single edge notch experiment and W the strain energy density calculated by integration of the stress-strain curve.

Small Angle Neutron Scattering (SANS)

SANS experiments were performed at Laboratoire Léon Brillouin (CEA-Saclay, France) on the PAXY spectrometer. The wavelength of the incident neutron beam was set at  0 = 12 Å with a corresponding sample-to-detector distance of 4.7 m. This configuration provides a scattering vector modulus q ranging between 0.003 and 0.05 Å -1 . For SANS experiments, gel plates of 2-mm thick were specially synthesized in D 2 O to enhance the scattering contrast between the polymer network and the solvent.

For isotropic analyses, the gel discs (diameter = 14 mm and thickness = 2 mm) punched from plate samples in their preparation state were fit inside a ring spacer hermetically sandwiched between two quartz slides. The gel samples were then placed in a temperature controlled autosampler and let to equilibrate at least during 30 min at a given temperature (between 20 and 50 °C) prior to scattering experiments.

For anisotropic measurements performed with hydrogels under uni-axial deformation, a special device has been developed as described in previous papers. [START_REF] Guo | Thermoresponsive Toughening with Crack Bifurcation in Phase-Separated Hydrogels under Isochoric Conditions[END_REF][START_REF] Rose | Structure investigation of nanohybrid PDMA/silica hydrogels at rest and under uniaxial deformation[END_REF] With this setup, the hydrogel strip, immersed into the thermostated chamber filled with perfluorodecalin, can be studied for hours without drying. In the following, all the anisotropic scattering experiments have been carried out during at least 1 hour for each sample in a given deformation state. For all the analyses, the efficiency of the detector cell was normalized by the intensity delivered by a pure water cell of 1-mm thickness and absolute measurements of the scattering intensity I(q) (cm -1 or 10 -8 Å -1 ) were obtained from the direct determination of the incident neutron flux and the cell solid angle. Finally, the coherent scattering intensity of the gel was obtained after subtracting the contribution of the solvent used, as well as the perfluorodecalin for samples studied in the oil environment. For 2D SANS experiments, the incident neutron flux recorded on a two dimensional detector built up with 15500 cells of 25 mm 2 , is directly transformed into a 2D image with a color code. After sector averaging, the data were quantitatively analyzed in terms of diffusion pattern.

Results and discussion

Transition temperature and swelling behavior

Independently of their macromolecular structure, all PNIPA based hydrogels display a clear endotherm upon heating that corresponds to the overall energy balance of hydrogen bonds disruption/re-formation between amide groups and water molecules. Nevertheless, as shown in Fig. 2a, where integral curves (cumulated enthalpy) have been plotted versus temperature, some differences can be pointed out as a function of the gel architecture. We can first underline that the phase transition of hydrogels prepared with the same cross-linked PNIPA frame (GPN/PD and GPN-D), starts at the same association temperature, T as , just above 30 °C. The transition enthalpy is nevertheless higher for the semi-IPN (4.3 kJ/mol NIPA) compared to the grafted PNIPA (2.9 kJ/mol NIPA) as the PDMA chains regularly grafted along the thermoresponsive backbone sterically hinder the aggregation process of NIPA units and their level of dehydration. By comparison, the two other hydrogels, tailored with a crosslinked PDMA frame, display much pronounced differences. As already described in previous papers, [START_REF] Guo | Thermoresponsive Toughening with Crack Bifurcation in Phase-Separated Hydrogels under Isochoric Conditions[END_REF][START_REF] Guo | Thermoresponsive Toughening in LCST-Type Hydrogels with Opposite Topology: From Structure to Fracture Properties[END_REF] the phase transition of short PNIPA chains anchored on the chemically crosslinked PDMA network starts at higher temperature (32-33 °C). This does not just have to do with the low molar mass of PNIPA grafts but it is also related to the penalty of selfassembling PNIPA chains covalently attached at one end to the PDMA network. On the other hand, long PNIPA chains of semi-IPN GPD/PN, which were embedded into the PDMA network, start to self associate at lower temperature (~28 °C). The lower transition temperature of linear polymer PNIPA chains compared to PNIPA gels has already been reported in the literature and attributed to the higher apparent diffusion coefficient of linear chains relative to polymer network. [START_REF] Otake | Thermal analysis of the volume phase transition with N-isopropylacrylamide gels[END_REF] Qualitatively, we may assume that the higher transition enthalpy observed with semi-IPN architectures is accounting for a higher extent of the phase separation process; the less constraint linear PNIPA demonstrating larger enthalpy than the cross-linked PNIPA of opposite topology. On the other hand, grafted architectures have to compromise at a lower scale with a greater proportion of hydrated interface due to chemical bounds between PNIPA and PDMA domains. As demonstrated in former studies, [START_REF] Guo | Thermoresponsive Toughening with Crack Bifurcation in Phase-Separated Hydrogels under Isochoric Conditions[END_REF][START_REF] Guo | Thermoresponsive Toughening in LCST-Type Hydrogels with Opposite Topology: From Structure to Fracture Properties[END_REF] the combination of thermo-responsive and hydrophilic polymers within the same network is crucial to control the level of swelling above the transition temperature. Indeed, as shown in Fig. 2b, grafted architectures prepared with equivalent weight fractions of PNIPA and PDMA are able to swell (Q e =10 for GPD-N) or at least to sustain their initial swelling (Q 0 =6 for GPN-D) when immersed at 60 °C in a large excess of water. Here the topology has a real impact on the volume transition as the crosslinked network mainly governs the swelling behavior. We effectively observe a higher shrinking ability of the gel when the thermoresponsive polymer is located in the cross-linked backbone (GPN-D) rather than in the side-chains (GPD-N). The situation is more complex in the case of semi-IPN networks as free linear chains, either PDMA or PNIPA, are able to diffuse inside and even outside the gel during long term swelling experiments. From analyses carried out after 4 days of equilibrium in water, the total polymer loss was about 5 wt% for GPD/PN and 20 wt% for GPN/PD. This means that when linear PNIPA chains phase separate within the hydrophilic network they are less prompt to diffuse out of the network (less than 10 % of PNIPA chains leave the gel during swelling). On the other hand, in the case of the GPN/PD network, about 40 % of hydrophilic PDMA chains can diffuse outside the shrinking network. Consequently, we observe slower kinetics for the two semi-IPN with a higher level of swelling for GPD/PN (Q e 20) and a much lower one for GPN/PD (Q e 4) after 4 days equilibrium at 60 °C. In the latter case, the deswelling from the preparation state is very progressive and for experiments performed on short time scale, typically below 4 hours, the collapse of the GPN/PD network remains low (< 15 %).

T (°C)

The main conclusion of these swelling experiments is that the mobility of linear chain in semi-IPN structures is responsible for polymer reorganization at larger scale above the transition temperature with the formation of PNIPA-rich domains alternating with the PDMA/water phase. The interesting feature is that, when gel samples are kept in their preparation state and isolated from water environment, they are able to retain their initial swelling (Q 0 =6) and consequently their initial volume over the whole range of temperatures, i.e. well below and above the phase transition. These isochoric conditions, which have been effectively verified for GPD-N, GPN-D and GPD/PN which do not deswell below Q 0 =6 at 60 °C, will be also assumed for GPN/PD that only slightly collapses on short time scales.

Phase-separated structure at rest and linear viscoelasticity response

SANS experiments were carried out with undeformed semi-IPN samples to investigate the phase transition taking place within the networks. As shown in Fig. 3, the phase separation of PNIPA starts at lower temperature (just above 28 °C) for GPD/PN compared to GPN/PD (T > 29-30 °C) as already described from DSC experiments. At high temperature, the scattered intensity of both hydrogels decays in the high-q regime with the same Porod law (I(q)~q -4 )

reporting the formation of a sharp interface between collapsed PNIPA domains and the PDMA/water phase. Contrary to grafted hydrogels, which display a clear correlation peak at high temperature (see Fig. 4), figuring fluctuation concentrations between rich-and poor-PNIPA phases with a characteristic distance (d c =2/q peak ) of about 500 Å, the scattered intensity of semi-IPN increases continuously from large q to low q values underlining larger distances between bigger phase separated domains. As regards the PNIPA network grafted with long PDMA side-chains (GPN-D long ), it shows an intermediate behavior between grafted and semi-IPN architectures with a scattering peak shifted at lower q values corresponding to a higher characteristic length of about 900 Å. Additional insights concerning the scale of the phase separation process can be obtained by calculating the total interface area of microdomains (S) in the scattering volume (V) using the asymptotic behavior obtained at high temperature (I(q) ~ q -4 ) and the experimental Invariant

   0 2 ) ( dq q I q Inv
, as follows :

) ( lim 4 1 2 q I q Inv V S S q spe        {1}
with  2 the volume fraction of PNIPA domains and

 1 =1- 2 .
As V 2 is the total volume of PNIPA microdomains and  1 is close to 0.9 for all the gels in the segregated regime, the left hand term in equation {1} can be identified with the specific surface of PNIPA microdomains (S spe ). These values reported in Table 2, quantitatively point out the large differences between the phase separated morphologies taking place within semi-IPN and grafted architectures; the latter showing a much larger interface corresponding to smaller spacing of the microphase separated structures. From previous works, it has been observed that the biphasic morphologies obtained at high temperature with weakly crosslinked ([MBA]/[monomers]=0.1 mol%) and uncrosslinked grafted copolymers were mainly fixed by the nature, the size and the distribution of grafts along the main chain. [START_REF] Guo | Thermoresponsive Toughening in LCST-Type Hydrogels with Opposite Topology: From Structure to Fracture Properties[END_REF][START_REF] Petit | Synthesis of graft polyacrylamide with responsive self-assembling properties in aqueous media[END_REF] Hydrophilic networks grafted with PNIPA side-chains (GPD-N) self-assemble at high temperature into a micellar morphology (see Figure 4), where the characteristic distance between hydrophobic domains is mainly controlled by the copolymer concentration, the solvent strength and the average molar mass of both hydrophilic spacers and thermoresponsive grafts. [START_REF] Borisov | Self-assembly of polysoaps[END_REF][START_REF] Hourdet | Smallangle neutron scattering study of microphase separation in thermoassociative copolymers[END_REF] For the opposite topology, i.e.

when the thermoresponsive backbone is grafted with hydrophilic side-chains (GPN-D networks), the macromolecular system self-assembles at high temperature into a bicontinuous morphology with a percolating cross-linked PNIPA phase (see Figure 4) which characteristics also depend on the primary structure of the copolymer [START_REF] Guo | Thermoresponsive Toughening with Crack Bifurcation in Phase-Separated Hydrogels under Isochoric Conditions[END_REF][START_REF] Guo | Thermoresponsive Toughening in LCST-Type Hydrogels with Opposite Topology: From Structure to Fracture Properties[END_REF] . Indeed, as theoretically described by Borisov and coworkers for hydrophobic backbones grafted with hydrophilic side-chains, [START_REF] Borisov | Amphiphilic graft copolymer in a selective solvent: Intramolecular structures and conformational transitions[END_REF][START_REF] Košovan | Amphiphilic graft copolymers in selective solvents: molecular dynamics simulations and scaling theory[END_REF] the axial dimension of macromolecular self-assemblies formed in dilute conditions is fixed 1) by the size of the hydrophobic core, which grows with the number of hydrophobic monomers within the spacer and the extent of the phase separation, and 2) by the span of crowded side-chains which increases with their molar mass. In the semidilute regime, as it is the case with GPN-D gels, the steric repulsions between PDMA coronas will also controls the characteristic length scale of the phase separation. Such behavior is highlighted with GPN-D networks in Figure 4 and Table 2, where the specific surface of PNIPA domains decreases, i.e. the thickness of the rich-PNIPA phase as well as the characteristic length scale of the phase separation (

1   spe S 
) increase, when the molar mass of PDMA side-chains and the average molar mass of PNIPA spacers increase (M PDMA M PNIPA ).

In the case of semi-IPN networks, the characteristic length of the phase separation will depend on the molar mass of free polymer chains, their level of entanglement within the cross-linked network as well as the overall dynamics of the phase separation process. For GPN/PD, designed with the cross-linked PNIPA frame, one can expect a similar bicontinuous morphology than the one reported for grafted GPN-D at high temperature. Nevertheless in this case, the specific surface of the rich-PNIPA phase is much smaller underlining the formation of thicker PNIPA domains and larger characteristic distances between these domains. For the opposite semi-IPN topology (GPD/PN), the free PNIPA chains embedded into the hydrophilic cross-linked network self-assemble into larger aggregates as suggested by the lower specific surface of the rich-PNIPA phase. SANS spectra plotted in Figure 3 do not really show great differences in this q-range between the biphasic morphologies adopted by the opposite semi-IPN networks. For this reason we will assume that GPD/PN adopt at high temperature an intermediate morphology with the formation of large and loosely connected PNIPA aggregates.

q I q Inv V S S q spe        GPD/PN 0.011 Å -1 GPN/PD 0.013 Å -1 GPN-D long 0.022 Å -1 GPN-D 0.027 Å -1 GPD-N 0.031 Å -1
Complementary experiments performed in the preparation state by dynamic rheology demonstrate that the combination of PNIPA and PDMA chains into semi-IPN architectures enables to trigger thermo-hardening properties under isochoric conditions (Figure 5).

Nevertheless, the mechanical hardening induced by the phase separation of PNIPA is much more efficient when PNIPA belongs to the network frame, that is the load bearing phase, rather than simply embedded as free chains that do not provide the same level of connectivity and dissipation above T as . As previously reported with graft copolymer networks, the variation of the viscoelastic properties are totally reversible with temperature but the transition temperature remains dependent on the thickness of the gel sample and the scanning rate. Indeed, the symmetric hysteresis observed between heating and cooling cycles can be highly reduced from T=30 °C to 5 °C by decreasing the scanning rate from 10 to 0.5 °C/min, respectively. [START_REF] Guo | Thermoresponsive Toughening in LCST-Type Hydrogels with Opposite Topology: From Structure to Fracture Properties[END_REF] T (°C) In this case the scale of the phase separation does not seem to matter on the viscoelastic properties at low deformation and the same conclusion holds for the comparison between GPN-D and GPN-D long prepared with short and long PDMA grafts (M n =39 and 89 kg/mol, respectively). If we assume that the volume fraction of PNIPA-rich domains ( 2 ) as well as the PNIPA weight fraction inside these domains are similar in all hydrogels prepared with a crosslinked PNIPA frame, this mechanical behavior can be interestingly compared with opencell polymer foams where the elastic modulus of the material varies only with the modulus of the wall and the square of their volume fraction. [START_REF] Ashby | The mechanical properties of cellular solids[END_REF] By comparison, the sharp phase separation that takes place within the GPD/PN hydrogel does not allow the formation of a PNIPA phase able to sustain the mechanical stress. Moreover, as there are no chemical connections between PNIPA and PDMA phases in GPD/PN, its properties are even much lower than GPD-N which micellar morphology formed at high temperature gives rise to an efficient coupling between the covalent crosslinks of the PDMA matrix and additional physical crosslinks formed by collapsed PNIPA microdomains.

Large strain behavior: structure and mechanical properties

The mechanical properties of GPD/PN and GPN/PD hydrogels reported in Fig. 7 have been carried out at 20 and 60 °C with a strain rate of 0.06 s -1 . For these mechanical tests, performed in an oil bath at 60 °C, we can reasonably assume that the gels keep their initial dimensions. This is obvious for GPD/PN, as PNIPA chains cannot diffuse in the oil phase which is totally incompatible and water molecules remain in the network because of the positive osmotic pressure. For GPN/PD, the same holds for linear PDMA chains which remain confined into the PDMA network. Only water can be expelled at the surface of the gel when heated at 60 °C but as the volume shrinkage is relatively slow compared to the duration of the mechanical test (10 minutes for thermal equilibrium and less than 2 minutes for the tensile test), this phenomenon will be considered as negligible in these conditions.

At 20 °C, when both PNIPA and PDMA chains are water-soluble, both gels exhibit a very similar mechanical behavior. On the other hand, working at 60 °C well above the critical temperature of PNIPA, the phase separated semi-IPN GPN/PD demonstrates a much larger mechanical reinforcement than GPD/PN with larger increase of both tensile modulus and extension at break. The work of extension, defined by the area under the tensile curve, is then more than 4 times higher for GPN/PD (190 kJ.m -3 ) compared to GPD/PN (42 kJ.m -3 ), confirming that the thermo-reinforcement of the mechanical properties is much more efficient when the responsive polymer is forming the crosslinked frame of the hydrogel.

As PNIPA-rich domains are forming quenched heterogeneities at high temperature, these scatterers can be used as probes to follow their average displacement under mechanical deformation and to investigate the local structure of thermo-responsive hydrogels. For that purpose, a series of SANS experiments have been carried out on GPN/PD and GPD/PN hydrogels, under incremental stretch ratio, from  = 1 to 2-3.5 at 60 °C, i.e. well above the phase transition temperature. The 2D SANS spectra, reported in Fig. 7, show that both undeformed samples ( = 1) display at 60 °C an isotropic pattern with a circular diffraction ring and a maximum of intensity localized close to the beam stop as already described with static experiments in Fig. 3. Under deformation, the 2D spectra are distorted into prolate ellipsoid with their major axis along the perpendicular direction due to the orientation and deformation of PNIPA-rich domains. Due to the nature of reciprocal space, this means that the frequency with which the neutron density difference is encountered is greater perpendicular to the direction of orientation than along the direction of orientation.

At the same stretch ratio, the distortion of the 2D pattern is much higher for GPN/PD highlighting larger local deformation of the PNIPA phase within this topology. Its behavior is very similar to the one reported for the grafted hydrogel GPN-D with the same PNIPA backbone where an elliptically shaped correlation band with a non-uniform azimuthal intensity distribution was observed with two diffraction spots in the perpendicular direction. [START_REF] Guo | Thermoresponsive Toughening in LCST-Type Hydrogels with Opposite Topology: From Structure to Fracture Properties[END_REF] The anisotropy induced upon stretching can be analyzed more quantitatively by plotting the parallel (I // (q)) and perpendicular (I  (q)) scattering intensities obtained after radially averaging the 2D data within a rectangular sector of axis, respectively, parallel (//) or perpendicular () to the deformation axis (Fig. 8). In the absence of characteristic distance observable in the q-range investigated the main characteristics of the two semi-IPNs at high temperature are the very weak and very strong dependences of the scattered intensity versus the deformation along the perpendicular and equatorial axes, respectively.

As suggested by Effler et al., [START_REF] Effler | Structural orientation functions for anisotropic small-angle scattering[END_REF] a simple characterization of the orientation undergone at the local scale by the sample would be to measure the ratio of Invariants determined along the stretching and transverse directions (Inv // /Inv  ). As shown in Fig. 9, the anisotropic ratio Inv // /Inv  strongly decreases with increasing strain. This means that the rich-PNIPA phase, which was initially randomly oriented within the network, becomes rapidly oriented in the direction of the deformation as schematically shown in Figures 9a and9b. For a given stretch ratio, the larger orientation of the semi-IPN GPN/PD compared to its opposite topology GPD/PN, can be attributed to a greater connectivity of the rich-PNIPA phase as already suggested from rheology and tensile tetts. While SANS and tensile tests clearly emphasize the large impact of the primary structure on both self-assembling and toughness above T as , the difference between the two gels becomes even more significant when comparing the fracture tests performed on notched samples. As shown in Fig. 10, the GPN/PD gel with PNIPA forming the cross-linked backbone can reach fracture energy as high as 1.5 kJ/m 2 at 60 °C with a systematic crack bifurcation. This energy is even much higher than the graft counterpart GPN-D long grafted with long pendant PDMA chains. As already emphasized with GPN-D samples designed with various grafting densities, [START_REF] Guo | Thermoresponsive Toughening with Crack Bifurcation in Phase-Separated Hydrogels under Isochoric Conditions[END_REF] the comparison with the semi-IPN GPN/PD confirms the close relationship between the cross-linked architecture, the scale of the phase separation and the mechanical properties. As pictured in Fig. 10, the thicker is the PNIPA phase and the higher will be the fracture resistance with original crack bifurcation specifically obtained in the case of GPN-D and GPN/PD networks. By contrast, the other semi-IPN GPD/PN can only achieved fracture resistance of one decade lower than GPN/PD; typically at the same level as the GPD-N hydrogel although they display different intrinsic morphology at high temperature. For the semi-IPN GPD/PN, we assume that the phase separation of linear PNIPA chains gives rise to weakly connected and uncrosslinked domains that cannot easily withstand the stress and prevent the crack propagation. The situation is different for the grafted GPD-N network where the selfassembling of PNIPA grafts at 60 °C into isolated micellar domains effectively contributes to the improvement of the elastic behavior (increase of the modulus and work of extension) but cannot prevent efficiently the crack propagation through the PDMA matrix.

Conclusion

Within the development of thermo-toughening hydrogels, the aim of this work was to combine hydrophilic chains (PDMA) and LCST polymers (PNIPA) in semi-interpenetrated architectures in order to investigate their responsive properties in swollen isochoric conditions comparatively to grafted network structures. By keeping constant and equal the weight fractions of PDMA and PNIPA in hydrogels, the new semi-IPN have both demonstrated thermoresponsive behavior with very different structure/properties relationships. In the case of the PDMA network interpenetrated by linear PNIPA chains (GPD/PN), the phase transition of PNIPA occurs at lower temperature comparatively to other hydrogels and gives rise to large microdomains with a very weak percolation through the PDMA network. The enhancement of the mechanical properties above the transition temperature is indeed very low with a 3-times increase of the elastic modulus and little improvement of the fracture energy;

the isolated PNIPA phase acting mainly like a filler in polymer materials.

Conversely, the interpenetration of PDMA chains within the PNIPA crosslinked network (GPN/PD) brings a large improvement of the mechanical properties at high temperature with a 10-fold increase of the modulus and a very high fracture energy. Nevertheless, the absence of connectivity between PNIPA and PDMA phase is responsible for the large scale of the phase separation which induces a small collapse of the network at 60 °C when starting from the preparation state.

From a general point of view, the comparison between semi-IPN and grafted networks clearly emphasizes the role of the primary structure over the phase-separated morphology and the resulting mechanical properties. It is obvious that the best reinforcement can be achieved by designing the gel with a PNIPA crosslinked frame and by implementing hydrophilic polymers in order to maintain a high level of swelling in the segregation regime. The comparison between GPN-D hydrogels brings highlights that the molar mass of PNIPA between hydrophilic side-chains is an important parameter for controlling the length scale of the phase separation; the larger being the best in the case of GPN-D versus GPN-D long . Nevertheless, in absence of chemical connection between PDMA and PNIPA, as in GPN/PD, the length scale of the phase separation becomes even larger leading at the same time to a very good mechanical reinforcement but to a lower control of the gel volume above the transition temperature. There is consequently an optimum in the structure/properties relationships that will depend on the required properties above the transition. This could be found by exploring different alternatives to control the level of the phase separation, playing with the chemistry of the precursors, with the environmental conditions (temperature, ionic strength, pH,…) and using various architectures like grafted, multiblock or even fully interpenetrated networks that will allow the percolation of the PNIPA phase and the control of the segregation length scale with the degree of network crosslinking.

Fig. 1 .

 1 Fig. 1. Schematic representation of thermo-responsive hydrogels with opposite PDMA and PNIPA topologies: (a) grafted networks (GPN-D and GPD-N) and (b) semi-IPN (GPN/PD and GPD/PN) architectures.

N

  -isopropylacrylamide (NIPA), N,N-dimethylacrylamide (DMA), potassium peroxodisulfate () and tetramethylethylenediamine (TEMED) obtained from

  redox initiator, APS (91.2 mg, 0.4 mmol) and SBS (38.0 mg, 0.2 mmol), were separately dissolved and deoxygenated in 10 mL of water prior addition into the monomer solution. The reaction was allowed to proceed in an ice bath and SEC was used to monitor the polymerization process. After stirring overnight, almost full conversion was achieved, and polymers were purified by dialysis against pure water (membrane cut-off=50 kDa) during one week and recovered by freeze-drying. The linear polymers were obtained with a yield of about 75 wt% for PNIPA and 71 wt% for PDMA. The absolute values of average molar mass and dispersity, characterized by SEC equipped with three detectors in line (refractometry, viscometry and light scattering), are M n =290 kg/mol (Ð=1.5) for PNIPA and 161 kg/mol (Ð=1.4) for PDMA.

Fig. 2 .

 2 Fig. 2. a) DSC analysis of hydrogels at preparation state (heating rate=2 o C.min -1 ); b) Swelling kinetics of the same hydrogels at 60 o C in pure water. GPD/PN (), GPN/PD (), GPD-N () and GPN-D ()

Fig. 3 .

 3 Fig. 3. Scattered intensity profiles of (a) GPN/PD and (b) GPD/PN semi-IPN hydrogels as a function of temperature. The solid lines indicate the Porod limit (Iq -4 ).

Fig. 4 .)

 4 Fig.4. Left: Log-log plot of the normalized* scattered intensity profiles of GPD/PN (),GPN/PD (),GPD-N (), GPN-D () and GPN-D long () at 51.5 °C. The lin-lin plot is given in inset. Right: Micellar (a) and bicontinuous (b) microphase-separated morphologies with PNIPA-rich domains (red), PDMA swollen phase (blue) and chemical cross-linkers (white dots). *SANS intensities were normalized by the Invariant ( 1 2

Fig. 5 .Fig. 6 .

 56 Fig.5. Temperature dependence (during heating) of viscoelastic properties at 1 Hz of GPN/PD (, ) and GPD/PN (, ) hydrogels at preparation state applying a heating rate of 2 °C/min (stars symbols stand for G' and triangle symbols for G''). The solid and short dash lines correspond, respectively, to G' and G" during subsequent cooling at 2 °C/min.

Fig. 7 .

 7 Fig. 7. Structure and properties of semi-IPN GPD/PN and GPN/PD under deformation. Primary structure of GPD/PN and GPN/PD hydrogels and their uniaxial tensile stress-strain curves at 20 and 60 °C. Iso-intensity SANS patterns were obtained after a step-by-step loading at 60 °C. The direction of the uniaxial deformation is along the horizontal axis.

Fig. 8 .

 8 Fig.8. Scattered intensity profiles at 60 °C of semi-IPN gels under uni-axial extension. (a, b) GPN/PD (from λ = 1 to λ = 3.5) and (c, d) GPD/PN (from λ = 1 to λ = 2). The data were obtained from 2D-SANS after sector averaging in the parallel (//) and perpendicular () directions of the deformation axis.

Fig. 9 .

 9 Fig. 9. Strain dependence of the Invariant ratio between parallel (Inv // ) and perpendicular (Inv  ) components for GPD/PN () and GPN/PD () hydrogels. (a) and (b) are schematic representations of the biphasic network (with rich-PNIPA phase in red) at rest and under uniaxial stretching, respectively.stretch ratio () 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.0

Fig. 10 .

 10 Fig. 10. Fracture energies obtained with PNIPA/PDMA hydrogels at 60 °C and schematic representation of the morphologies developed at high temperatures with PNIPArich domains (red), PDMA swollen phase (blue) and chemical cross-linkers (white dots).

  it was shown that the functionalization of telomers with amino end-group is almost quantitative, at least greater than 90 %, as well as the subsequent vinyl modification of amino-end groups due to the large excess of activated

	acrylic acid per amino end-groups ([COOH]/[NH 2 ]=15). The absolute characterization of
	macromonomers by size exclusion chromatography gives the following molar masses: M n =36
	kg/mol (Ð=1.4) for PNIPA, M n =39 kg/mol (Ð=1.3) for PDMA and M n =89 kg/mol (Ð=1.5) for
	PDMA long .

Table 1

 1 Formulation of thermo-responsive semi-IPN and grafted hydrogels

	Monomer g	MBA mg	Polymer g	M n kg/mol	Ð	KPS mg	TEMED mg	Water g
	GPN/PD GPD/PN GPN-D GPN-D long GPD-N a linear polymer and b macromonomer 1 1.36 1 1.56 1 1.36 1 1.36 1 1.56	1 a 1 a 1 b 1 b 1 b	161 a 290 a 39 b 89 b 36 b	1.4 23.9 1.5 27.3 1.3 23.9 1.5 23.9 1.4 27.3	10.3 11.7 10.3 10.3 11.7	10 10 10 10 10

Table 2 .

 2 Specific surface of PNIPA domains at 51.5 °C

	Hydrogel	lim 4	(	)
	2	1

Acknowledgements

We gratefully acknowledge the financial support of CNRS, ESPCI, and UPMC and the China Scholarship Council for the Ph.D. fellowship funding of H.G. The authors also thank Guylaine Ducouret from SIMM and Annie Brûlet from LLB (CEA, Saclay) for their assistance on rheology and small angle neutron scattering, respectively.


Guillaume Brogi
email: guillaume.brogi@akheros.com

Valérie Viet

Triem Tong

TerminAPTor: Highlighting Advanced Persistent Threats through Information Flow Tracking

Keywords: advanced persistent threat, chain of attacks, information flow tracking, intrusion detection

Long lived attack campaigns known as Advanced Persistent Threats (APTs) have emerged as a serious security risk. These attack campaigns are customised for their target and performed step by step during months on end. The major difficulty in detecting an APT is keeping track of the different steps logged over months of monitoring and linking them. In this article, we describe TerminAPTor, an APT detector which highlights links between the traces left by attackers in the monitored system during the different stages of an attack campaign. TerminAPTor tackles this challenge by resorting to Information Flow Tracking (IFT). Our main contribution is showing that IFT can be used to highlight APTs. Additionally, we describe a generic representation of APTs and validate our IFT-based APT detector.

I. Introduction

In recent years, Advanced Persistent Threats (APTs) have emerged as a new security risk for companies and governments. An APT is an attack campaign customised for its target and performed by highly skilled and highly motivated people. The attackers have precise goals and will do whatever it takes to achieve them, all the while avoiding detection. APTs have been recognised as a threat [START_REF] Hutchins | Intelligencedriven computer network defense informed by analysis of adversary campaigns and intrusion kill chains[END_REF]- [START_REF] Tankard | Advanced persistent threats and how to monitor and deter them[END_REF], but existing techniques are not able to detect them [START_REF] Kurucz | An independent test of apt attack detection appliances[END_REF]. Research has started focusing on this problem [START_REF]Assessing outbound traffic to uncover advanced persistent threat[END_REF], [START_REF] Bowers | Defending against the unknown enemy: Applying flipit to system security[END_REF] but no perfect solution has emerged yet.

Even though each APT is tailored for its target and, thus potentially unique [START_REF]Apt1: Exposing one of china's cyber espionage units[END_REF]- [START_REF]Safe: a target threat[END_REF], their evolution usually follows a pattern well summarised in [START_REF]Apt1: Exposing one of china's cyber espionage units[END_REF]. An APT starts with an initial reconnaissance step, followed by an initial compromise; once a foothold is established, the attacker will try to elevate their privileges and also move toward their target, which entails more internal reconnaissance and compromises; the final step, mission completion, is usually data exfiltration. We believe that this representation is flexible enough to represent every known APT and precise enough that it is the basis, in one form or another, of most of the research work on detecting APTs [START_REF] Bhatt | Towards a framework to detect multi-stage advanced persistent threats attacks[END_REF]- [START_REF] Virvilis | Trusted computing vs. advanced persistent threats: Can a defender win this game?[END_REF]. The hope is that by identifying the steps of an APT and by linking them together, then the APT itself can be detected. Most papers working on detecting APTs use the preceding observation of how an APT unfolds to base their approach on anomaly detection [START_REF] Chandran | An efficient classification model for detecting advanced persistent threat[END_REF]- [START_REF] Wang | A network genebased framework for detecting advanced persistent threats[END_REF]. Since APTs are potentially unique, it is impossible to predict their exact behaviour and we feel that the phases described earlier are merely a guideline and want to avoid any set of hard rules based on their anticipated development.

This article focuses on the detection of long term attack campaigns. APTs are represented here as a succession of elementary attacks. These elementary attacks are detected by a standard intrusion detection system (IDS). We claim that detecting an APT is equivalent to highlighting the links between elementary attacks. For highlighting these links, we propose to track the information flows between the elements of the system used by the elementary attacks. To verify this claim, we have simulated two realistic APTs scenarios. All these experiments are realised using our product TerminAPTor.

The rest of the article is divided in five sections. In Sec. II, we present existing research pertaining to the detection of APTs and the use of information flow tracking for security purposes. In Sec. III, we present our characterisation of the monitored system and the attacker. In Sec. IV, we present TerminAPTor, the APT detector module, in details. In Sec. V, we present examples to show how, using information flow tracking, TerminAPTor can highlight APTs and to validate our approach. We also check that it can operate in near real-time. Lastly, Sec. VI concludes the paper.

II. Related works

In the following, we present how previous works have modelled the different stages of APTs. We also present the main characteristics of works about information flow tracking for security purposes.

In [START_REF] Giura | A context-based detection framework for advanced persistent threats[END_REF], Giura and Wang first present the main stages of an APT, which is basically the same model as in [START_REF] Vries | Systems for detecting advanced persistent threats: A development roadmap using intelligent data analysis[END_REF], [START_REF] Sood | Targeted cyberattacks: a superset of advanced persistent threats[END_REF], [START_REF] Sexton | Attack chain detection[END_REF] or the one we present in this paper. Based on this model, they introduce the concept of attack pyramid, an extension of attack trees. An attack tree represents a threat, and is built recursively with the goal as the root of the tree and ways to reach that goal as children, who are then treated as new subgoals. A plane is the layer upon which a threat occurs, such as lockpicking in the physical plane or phishing on the user plane. The novelty of attack pyramids over attack trees is that paths can cross planes; this better reflects what happens during APTs where attacks unfold over several planes. A set of rules is then used to correlate events and detect security alerts. When the risk and confidence factors of events and alerts rise above a given threshold, an APT alarm is triggered. This work is interesting because it specifically addresses the detection of APTs and presents attack pyramids to represent them, which takes into account the fact that an APT can operate on several planes. However, it requires that the potential goals of an APT, the paths leading there and the sets of rules be defined beforehand and updated frequently. This is specifically something that our approach wants to avoid, because it involves a lot of work to set up and maintain.

In [START_REF] Sexton | Attack chain detection[END_REF], Sexton et al. decompose an APT into five phases, delivery, exploit, install, command and control (C&C), actions, which they call the attack chain. Contrary to the attack pyramid which starts from the goal and reconstructs possible attack paths, the attack chain is a model for APTs. This is more flexible in that there is no specified way to go from one phase to the next. Instead, each phase is associated with a number of event types indicative of this phase; events in different phases must then be combined before an APT can be detected. To combine them, each event is first assigned a score which is used to compute a score for each event type and then for each phase; an anomaly score is then computed for each host and each cluster of host where the same type of event is occurring. This work is interesting because it can highlight clusters being the target of an APTs. However, being based on anomaly detection, it requires that each possible event be listed and attributed to a phase of the APT model ahead of time.

Both of these approaches start from the same rough model of an APT in phases along its chain of attack and use it in different ways. This paper uses the same rough model to highlight APTs, but in a third way. However, both of these approaches require significant expert knowledge to set up and maintain. Our approach voluntarily distinguishes itself by eschewing the need for expert knowledge about the system and attacks. Instead, it requires tracking flows of information.

Information flow tracking refers to any method whose aim is to follow the evolution of pieces of information inside the observed system. For example, one application could be to follow sensitive information in the system in order to check that it isn't leaked on the network. To do this, an information flow tracking module has to be able to observe every flow of information and moreover to check if the flow involves a marked piece of information. This is usually done by adding a taint to the pieces of information to follow and then propagating that taint whenever a flow of information contains already tainted information. The main requirement of an information flow tracker is that every flow of information is indeed tracked.

There are two main kinds of approaches for information flow tracking. The first kind tracks the flows of information inside a single program while the second kind tracks all the flows inside a whole computer. Tracking the flows inside a single program is done either through binary instrumentation, like [START_REF] Qin | Lift: A low-overhead practical information flow tracking system for detecting security attacks[END_REF], or requires compilation of the source code with a special compiler, like [START_REF] Lam | A general dynamic information flow tracking framework for security applications[END_REF]. Tracking flows inside a whole computer is usually done at the hardware level, thus requiring custom hardware, like [START_REF] Dalton | Raksha: a flexible information flow architecture for software security[END_REF], [START_REF] Suh | Secure program execution via dynamic information flow tracking[END_REF]. Deploying either approach is not very practical, requiring either custom hardware or modifying all the binaries on a system. An approach with the benefits of system-wide monitoring but without the cost associated with custom hardware is [START_REF] Yin | Panorama: capturing system-wide information flow for malware detection and analysis[END_REF], where the authors modify qemu, a CPU emulator; this is an interesting compromise but cannot run on bare metal.

There is another option for system wide tracking without custom hardware or the need to modify every binary on the system: modify the OS to do the tracking. This is the approach adopted by [START_REF] Andriatsimandefitra | Capturing android malware behaviour using system flow graph[END_REF], [START_REF] Enck | Taintdroid: an information-flow tracking system for realtime privacy monitoring on smartphones[END_REF]. This way, the modification is software only and only needs to be done once. For example, in [START_REF] Enck | Taintdroid: an information-flow tracking system for realtime privacy monitoring on smartphones[END_REF], the authors modify the Android OS in order to check that applications do not leak private data, and call it TaintDroid. They leverage the fact Android applications run on the Java Virtual Machine (JVM) and modify it to track information flows, even when the JVM interacts with the OS and during interprocess communications. Additionally, TaintDroid can track multiple sources of taints to better pinpoint the source of the data.

In this paper, we use a mix of kernel space and user space probes to track information flows. The flows are collected and then centralised. Only then are taints associated and propagated.

III. Characterisation

In this part we characterise both the monitored system and the attacker. We also list the requirements for the information flow tracking and enumerate the phases of an APT used in our model.

We propose here to protect enterprise networks from APTs. These networks are a mix of computer systems used as servers and others used as workstations. Each one of these computer systems is monitored by an agent. This agent has two roles; first it detects security violations and raises alerts, which can be done by classical intrusion detection systems; and second, it records information flows in the system and associates them with security alerts when appropriate. TerminAPTor then uses the output of the agent to check if separate security alerts are related and part of the same attack campaign. In the rest of the paper, we assume that the agent does detect all security alerts and only security alerts.

The attacker has a very precise goal and follows the steps of an APT: reconnaissance, compromise, establish presence, any number of lateral movements composed of the previous three steps but on the internal network and then mission completion. Except for the reconnaissance part, we suppose here that the attacker has to exploit an existing tool or deploy their own in order to progress from one step to the next. For example, in the compromise part, the attacker will send a spearphishing email with a document containing a payload. When the document is opened, the payload installs a Remote Access Tool (RAT) which is then used in the establish presence phase. In any case, if TerminAPTor can show the links between the different steps all the way to the mission completion step at the end, then it will have highlighted the chain of attack used in this APT.

Thus, we assume that the attacker is capable of infiltrating any system they want to. To do so, they exploit existing tools or insert their own. Through the exploitation of these tools, the attacker goes from one step to the next; and these exploitations create flows of information that we track. One caveat is that the attacker does not want to be detected, so, for example, even though the attacker could become administrator and disable the monitoring agent, doing so would alert to their presence, thus, the attacker will not disable the monitoring agent or take any other actions leading to their being discovered.

In an attack campaign, each attack is part of a series of coordinated attacks. Thus, we define a chain of attacks as the list of attacks in an attack campaign, and we do not make a difference between an attack campaign and an APT. Each step in an attack campaign is an attack, and for a given attack, the attacks in the attack campaign which were used to set it up are called the direct ancestors and they are placed before the attack in the chain. More generally, ancestors of an attack are the attacks which precede it in the chain. Similarly, the direct descendants of an attack are the attacks which it sets up, and they are placed after it in the chain. We also generalise the concept of descendant to all the attacks after it in the chain.

IV. TerminAPTor, the APT detector

TerminAPTor acts over a supervision system composed of classical IDS which also record information flows. The IDS outputs data which are composed of events in chronological order, order which is assumed correct. The IDS also raises alerts whenever an attack is found. Each alert includes the list of events which triggered it. Thus, an attack is a list of events. Some event types can also be interpreted as flows of information. Every event interpreted as a flow of information is listed in Tab. I; each line in the table indicates that information is passed from the input objects to the output objects. For example, for the "Read file" event type, there is a flow of information from the file to the process reading it. As such, events are considered a tuple with four values: the event type, the timestamp, a list of references of input objects, and a list of references of output objects. If the lists of objects are empty, then the event cannot be interpreted as a flow of information. Objects are elements of the monitored system which either contain data (files and processes) or are communication channels (sockets). These flows are then processed in chronological order to perform information flow tracking.

Taking the list of events, whether they are part of an attack, and their associated information flows as our only known data, we aim to highlight chains of attacks. Our work is built on the intuition that if two attacks are consecutive steps in a chain of attacks, then there must be an information flow from the outputs of the events part of the first one to the inputs of events part of the second one. Since the first attack sets up the next, there should be an information flow from the first attack to the tools it uses and from these tools to the second attack. Let's take as example two attacks: the first attack installs a RAT, and the second uses that RAT to exfiltrate sensitive data. In this example, there is an information flow from the first attack to the RAT and then from the RAT to the second attack. Thus, if we want to link attacks in attack chains, we need to be able to differentiate the information flows depending on which attack they went through; the solution is to create a new tag to represent each newly detected attack. Tags are immutable and represent one and only one attack. They are attached to object through propagation. Whenever an object becomes tagged with a given tag, then it means that this object is part of an information flow coming from the attack represented by this tag.

The tags representing each attack are propagated through the monitored system by flows of information, and the attack chains are highlighted at the same time. Each flow of information is processed in chronological order. The propagation is done differently whether the inputs are tagged and whether the event is part of an attack:

1) The inputs are not tagged and the event is not part of an attack: the event is ignored; 2) The inputs are tagged and the event is not part of an attack: the tags on the inputs are propagated to the outputs (Propagate); 3) The inputs are not tagged and the event is part of an attack: a new chain of attacks containing only this attack is added to the list of chains of attacks (CreateChain) and the tag representing the attack is propagated to the outputs (Propagate); 4) The inputs are tagged and the event is part of an attack: the attack is appended to the appropriate chains of attacks (AppendAndMergeChains) and the tag representing the attack is propagated to the outputs (Propagate). The Propagate function merges the tags already present on the output with all the tags present on the inputs as in (1); let I be the set of inputs and O the set of outputs for a given event:

∀O ∈ O, Tags(O t n ) Tags(O t n-1 ) ∪ ∪ I∈I Tags(I t n-1 ) (1)
When a new attack is detected, its links to other attacks can show that previously unrelated attacks are in fact related. The AppendAndMergeChains function must take this into account. Let L CA be the list of chains of attacks [START_REF] Li | Evidence of advanced persistent threat: A case study of malware for political espionage[END_REF]. First, all the tags of the inputs of the new attack are put in a set, T (3). Then, each chain in L CA finishing with a tag in T is moved to L ne w , a new list (4). Then, each chain in L CA containing at least one tag of T is copied; each copy is truncated after the last tag of T in it; the truncated copies are put in L ne w [START_REF]Assessing outbound traffic to uncover advanced persistent threat[END_REF]. Then, all the chains in L ne w are merged by creating a new chain with all the attacks in chronological order [START_REF] Bowers | Defending against the unknown enemy: Applying flipit to system security[END_REF]; the new attack is appended to this chain [START_REF]Apt1: Exposing one of china's cyber espionage units[END_REF]; This new chain is added to L CA [START_REF]Apt30 and the mechanics of a long-running cyber espionage operation[END_REF].

L CA {A 1 -A 4 , A 2 -A 5 , A 3 } (2)
new attack:

A 6 , T {2, 4} (3)
L CA {A 2 -A 5 , A 3 } L ne w {A 1 -A 4 } (4)
L CA {A 2 -A 5 , A 3 } L ne w {A 1 -A 4 , A 2 } (5)
L CA {A 2 -A 5 , A 3 } L ne w {A 1 -A 2 -A 4 } (6)
L CA {A 2 -A 5 , A 3 } L ne w {A 1 -A 2 -A 4 -A 6 } (7)
L CA {A 1 -A 2 -A 4 -A 6 , A 2 -A 5 , A 3 } (8)
V. Examples of APT detections The aim of these examples is to show that TerminAPTor is capable of highlighting whole attack campaigns. All the tests used here are reproducible and available in [START_REF] Brogi | moirai[END_REF].

As a first example, we detail an APT targeted at a web server with a database. The attack campaign is composed of four attacks. Simultaneously, two other independent attacks also take place. For the duration of the scenario, standard web server usage is also simulated. In the attack campaign, the attacker starts by exploiting the shellshock vulnerability to install a Remote Access Tool (RAT) (Attack 1 ). Using the RAT, the attacker exploits a vulnerable application and starts a reverse shell with administration level rights (Attack 2 ). The attacker uses this shell to install a scheduled task which starts a second RAT also with administrator level rights (Attack 3 ). This second RAT is used to exfiltrate the website's database (Attack 4 ). While this is going on, two other attackers are active. The first one acts between Attack 1 and Attack 2 , using an SQL injection to exfiltrate the database (Attack 5 ). The last attacker acts between Attack 3 and Attack 4 , and uses the shellshock vulnerability to exfiltrate the list of users and passwords on the server (Attack 6 ). The logs produced by the IDS are collected at the end of the scenario. First, all the attacks are detected and the events that triggered their detection identified. Then, TerminAPTor is launched to highlight links between attacks and extract the chains. The results are shown in Fig. 1. The first chain of attack accurately links the attack campaign we wanted to detect. This shows that TerminAPTor is capable of properly linking attacks part of the same attack campaign. This is very encouraging since some steps are executed only indirectly by the previous attack, e.g. Attack 2 starts Attack 3 through a scheduled task, but they are still properly linked. The second highlighted chain of attack is a false positive. TerminAPTor detects an attack campaign because all three attacks use the same entry point even though they are unrelated. This is because our flow tracking cannot follow information flows inside processes. Thus, the module has to taint every output of a process with the taints of all the inputs, which causes false positives.

The second example showcases an attack campaign targeted at a workstation. The attack campaign is composed of four attacks. The monitored system is a single machine used as a workstation. The attack campaign starts when the attacker sends a phishing email to the user of the workstation. The email contains an infected pdf file which is not detected by the various antivirus software protecting the workstation. When the user opens the file, a simple RAT is launched (Attack 1 ). The attacker uses this RAT to install a larger, more feature complete RAT (Attack 2 ). The attacker uses the second RAT to inspect the system and find a mean to elevate their privilege (Attack 3 ). With elevated privileges, the attacker installs a third RAT and enables persistence (Attack 4 ), so that the third RAT restarts with the workstation.

Like in the first scenario, the logs are collected at the end of the scenario This time TerminAPTor finds one chain of attack as shown in Fig. 2. This scenario is simpler since each step directly launches the next and, as expected, TerminAPTor properly follows the flows of information and links the four attacks in a single attack campaign.

While the results are encouraging, we believe that they could be improved upon by a second phase to filter out false positives. In this regard, we are currently working on using our representation of APTs to create Markov models, based in part on the ideas in [START_REF] Ioannou | A markov multi-phase transferable belief model: an application for predicting data exfiltration apts[END_REF], [START_REF] Ye | Robustness of the markov-chain model for cyber-attack detection[END_REF]. Such models would be used to assess the quality of each link.

Additionally, our validation would benefit a lot from a public corpus of APT scenarios. Not only would this make validation more robust, but it enables comparing the results of different solutions. For example, it would have been very interesting to compare our results to those of the solutions presented in Sec.II.

Lastly, since the processing can be done on a separate machine, it has no impact on the monitored system. The only requirement is that it should be done in near real time. In order to test TerminAPTor on month long logs, we took the data from the APT against a server scenario and augmented it by mixing and mutating the original log as well as by inserting attacks. This produced a 67 day long log. In all, 3.2 billion events are processed, containing 500 attacks, over 67 days. This represents an average of 48 million events and 7.4 attacks per day. Processing the log on a single core took a bit less than 3 days and never exceeded 35MB in RAM usage. The aim of processing events in near real time is certainly met, especially since the code could certainly be optimised.

VI. Conclusion

This article proposes a new approach for detecting long lived attack campaign. The intuition leading to this work is that when an attacker constructs an APT step by step, each of these steps is a single attack. We claim that every single attack can be detected by a traditional intrusion detection system. Our main challenge was thus to be able to establish a link between these different attacks. In this article, we propose to retrace these links by observing information flows between traces left by the attacker during every single attack. We describe TerminAPTor, the tool being born from this idea. We present also some experiments as close as possible to real life APTs, using actual APT samples. These tests showed that our intuition is correct insofar that TerminAPTor accurately highlighted the chain of attacks targeting the monitored system.

2 Fig. 1 .Fig. 2 .

 212 Fig. 1. Results of the information flow tracking on the server

TABLE I

 I List of events and their information flows

	Type of event	Input objects	Output objects
	Create process	current process	new process
	Execute file	filename	current process
	Change permissions	current process	filename
	Change owner	current process	filename
	Create file	current process	filename
	Read file	filename	current process
	Write file	current process	filename
	Receive packet	remote socket	local socket
			current process
	Send packet	local socket	remote socket
		current process


Andrey S Andreev

A Kazakova

Arcady V Ishchenko

Alexander G Selyutin

Olga B Lapina

Vladimir L Kuznetsov

Jean-Baptiste D'espinose De

Magnetic and dielectric properties of carbon nanotubes with embedded cobalt nanoparticles

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


Thomas Hjelmgaard

Daniel Gardette

David Tanner

David J Aitken

Synthesis of (+)-coniceine via reductive photocyclization of dienamides : an entry to indolizidines

come   L'archive ouverte pluridisciplinaire


Vincent Savaux

Isabelle Siaud

Rodolphe Legouable

Optimal non-outage probability maximizing the outage rate in Rayleigh channel

In this paper, we derive an analytic closed-form of the optimal nonoutage probability value which maximizes the outage rate in a Rayleigh channel. Furthermore, asymptotic approximations of both the optimal non-outage probability and the maximum outage rate can be deduced from the proposed analysis.

Introduction:

The outage capacity is defined as the maximum data rate which is achieved for a specified outage probability [START_REF] Goldsmith | Wireless Communications[END_REF][START_REF] Choudhury | Ergodic capacity, outage capacity, and information transmission over Rayleigh fading channels[END_REF]. Thus, the outage capacity, unlike the ergodic capacity, takes into account the decoding errors due to the channel. From this definition of the capacity, the outage rate is expressed as

Co = PnoB log 2 (1 + γ min ), ( 1
)
where B is the bandwidth of the received signal, and

Pno = P(γ > γ min ), (2)
is the non-outage probability 1 , i.e. the probability that the transmitted signal is properly decoded, where γ is the signal-to-noise ratio (SNR), and γ min is a fixed threshold. In [START_REF] Choudhury | Ergodic capacity, outage capacity, and information transmission over Rayleigh fading channels[END_REF], the maximization of the outage rate in presence of Rayleigh channel is performed through simulations results only.

In this paper, we extend the work in [START_REF] Choudhury | Ergodic capacity, outage capacity, and information transmission over Rayleigh fading channels[END_REF], since we provide an analytical expression of the non-outage probability Pno which maximizes the outage rate in Rayleigh channel. Furthermore, we develop an asymptotic expansion of the obtained solution, which reveals that the optimal Pno value is bounded by 1 and 1/e. Next Section is devoted to the proposed analysis.

Optimal Non-Outage Probability: In this paper, the SNR, which is measured at a distance r from the transmit antenna, is defined by the log-distance path loss model as

γ = γ 0 r d 0 -α , (3)
where γ 0 is the SNR measured at distance d 0 from the transmit antenna, and obeys a given probability process according to the channel models, α is the path-loss exponent. In Rayleigh channel, γ 0 is a random variable, the probability density function (pdf) of which is given by the exponential distribution:

fγ 0 (γ 0 ) = 1 2γ 0 exp(- γ 0 2γ 0 ), (4)
where γ0 is the average SNR value. Other models as Nakagami (for the multipath fading), log-normal (for the shadowing), and a composite multipath/shadowing are provided in [START_REF] Simon | Digital Communication over Fading Channels[END_REF]. From (4) and ( 2), the nonoutage probability Pno can be expressed as

Pno = P(γ 0 ( r d 0 ) -α > γ min ) = P(γ 0 > γ min ( r d 0 ) α A ) = +∞ A γ 0 2γ 0 exp - γ 0 2γ 0 dγ 0 = exp - γ min ( r d 0 ) α 2γ 0 .
(5)

If a target non-outage probability, which is denoted by P t no , is set, then the threshold γ min can be written as a function of P t no . Thus, we have:

γ min = -2γ 0 ( r d 0 ) -α ln P t no . (6)
The non-outage rate can be rewritten by substituting (6) into (1):

Co = P t no B log 2 1 -2γ 0 ( r d 0 ) -α ln P t no . (7)
It can be noted that Co is a strictly decreasing function with the variable r, and a concave function with the variable P t no such that Co(P t no = 0) = Co(P t no = 1) = 0. Furthermore, it is straightforwardly shown in Appendix that, by solving the equation ∂Co ∂P t no = 0, the maximum outage rate is achieved for

P t no = exp 1 -exp(W (X)) X , (8)
where X = 2γ 0 ( r d 0

) -α , and W is the Lambert W function, which is defined as the solution of the equation a = xe x [START_REF] Corless | On the Lambert W Function[END_REF]. The substitution of (8) into (7) leads to the maximum outage rate:

Co = B ln(2) W (X) exp 1 -exp(W (X)) X . (9)
The asymptotic expansions of W (X) in 0 and +∞ (corresponding to cases where the SNR γ is weak and large, respectively) leads to the following limits (sea Appendix for more details):

lim X→0 P t no = e -1 , (10)
lim X→∞ P t no = 1. (11)
Result in (11) reveals that a very large γ value (similarly X value) leads to an optimal non-outage probability equal to 1, i.e. the signal can be perfectly decoded when the SNR tends to infinity. On the contrary, the asymptotic analysis in (10) reveals that the optimal non-outage probability is not 0 but e -1 when the SNR tends to zero. This reflects the fact that the term P t no B is dominating compared with the log 2 (.) in ( 7), and therefore a non-zero P t no value is mandatory in order to maximize the outage rate Co.

Numerical Results: In all the presented simulations results, the following parameters have been chosen: B = 20 MHz, d 0 = 5 m, γ0 = 30 dB, and α = 2. Fig. 1 depicts the outage rate as a function of P t no , considering a Rayleigh channel, and for r = 40 m and r = 100 m. It can be seen that, as expected, the outage rate is a concave function, which reaches 0 at P t no = 0 and P t no = 1. In the latter case when the non-outage probability tends to 1, only low rate signals (robust) can be transmitted in order to be properly decoded. Furthermore, one can observe that the lowest the distance r (namely the higher X), the largest the optimal P t no value. Fig. 2-(a) shows the maximum outage rate (9) and Fig. 2-(b) the optimal P t no value (8) versus X. The lowest X values correspond to cases where γ0 is weak or r is large, whereas the largest X values correspond to the opposite cases. From the asymptotic expansion given in Appendix, we can deduce that P t no ≈ exp 1-X/ ln(X) X and C 0 ≈ B ln(2) ln(X) when X tends to infinity. Furthermore, once again, it can be noticed that the optimal P t no is lower-bounded by 1/e.

Conclusion:

In this letter, we have proposed an analysis of the maximum achievable outage rate. To this end, we have derived the closedform expression of the corresponding optimal non-outage probability. Asymptotic expansions allow us to approximate these expressions in limit cases. The provided theoretical results have been illustrated through simulations.

Appendix:

Derivation of C 0

The derivative of C 0 with respect to P t no can be written as:

∂C 0 ∂P t no = B ln(1 -X ln(P t no )) - BX 1 -X ln(P t no ) , (12)
where X = 2γ 0 ( r d 0

) -α . By setting Y = 1 -X ln(P t no ), we deduce that the equality ∂C 0 ∂P t no = 0 leads to the following equation:

ln(Y )Y = X.
(13) Therefore, the solution of (13) maximizes the outage rate, since C 0 is a concave function. The above equation (13) can be rewritten as ln(Y )e ln(Y ) = X, and one can recognize the Lambert's transcendental equation, which is solved by: Y = exp(W (X)). Since P

t no = exp( 1-Y X ),
this proves the expression of P t no given in (8).

Asymptotic expansion of Pno

The series expansion of W Lambert function in 0 and +∞ are, respectively:

W (x) = +∞ n=1 (-n) n-1 n! x n , (14)
and

W (x) = ln(x) -ln(ln(x)) + o(ln(ln(x))). (15)
The substitution of ( 14) into the exponential function, and the series expansion of the exponential lead to:

exp +∞ n=1 (-n) n-1 n! X n = +∞ n=1 exp (-n) n-1 n! X n = +∞ n=1 +∞ k=0 (-n) k(n-1) n! k X nk = +∞ n=1 1 + +∞ k=1 (-n) k(n-1) n! k X nk = 1 + X + R n,k , (16)
with R n,k is the rest containing all the terms in X p , where p > 1.

Therefore, the limit of Pno in zero can be expressed as

which concludes the proof of (11).

V. Savaux, I. Siaud, R. Legouable (Network Interfaces Lab, b<>com, Rennes, France) E-mail: vincent.savaux@b-com.com

Fig. 1

 1 Fig. 1 Outage rate versus the non-outage probability Pno, in Rayleigh channels. ELECTRONICS LETTERS March 2016 Vol. 00 No. 00

Fig. 2

 2 Fig.2Maximum outage rate and optimal Pno value versus X, in Rayleigh channels.

1 - 1 -

 11 (1 + X + R n,k ) X = e -1 . (17)The limit of Pno in +∞ can be expressed by using (15) as lim exp ln(X) -ln(ln(X))

Note that, in this paper, we use the non-outage probability Pno instead of (1 -Po) in the definition[START_REF] Goldsmith | Wireless Communications[END_REF], where Po is the outage probability.


Microscopic Modelling of non-linear GJ channels

Anđela Davidović 1,2,3,4 , Yves Coudière 1, 2, 3, 4 , Thomas Desplantez 2,4 , Clair Poignard 1, 2, 3 1 INRIA Bordeaux Sud-Ouest, 2 University of Bordeaux, 3 Institut de Mathématiques de Bordeaux, 4 IHU-Liryc

On Gap Junctions

• What is a Gap Junction?

• Cluster of gap junction channels • Linking structure between neighbouring cells • Provides direct passage of molecules and ions • Where are they located in cardiac cells?

• Mostly on the longitudinal ends where they compose the intercalated disks • The behaviour of transversal GJ channels is not well understood

Macroscopic effects

• Primary cultures of Cx43 and Cx43KO ventricular myocytes.

• Macroscopic velocity calculated from the difference in activation times

Non linear GJ model -0D

• GJ current:

I j = G j (t, V j )V j ,
where:

• V j transjunctional voltage.

• Conductance: G j (t, V j ) = g j,0 g j (t, V j ).

• The amplitude of the junctional conductance: g j,0 = 68nS for Cx43 cells, i.e. g j,0 = 2nS for Cx43KO. • Gating variable:

g j = g j (t, V j ) dg j dt = g ∞ (V j ) -g j τ ∞ (V j )
• Fit experimental data to find normalised g ∞ (V j ).

Homotypic GJC made of mCx43 transfected in HeLa cells

Assumptions

• Use only homotypic Cx43 and Cx45 GJ channels.

• GJ channels are at the perimeters of the cells, on the membrane. • The rest of the membrane has only ionic channels. Use Beeler Reuter ionic model.

2D microscopic model

Ω e Γ gr Γ app Ω i Ω i Γ j Γ j Γ ion Ω e
Main problem:

σ i ∆u i =0, in Ω i , σ e ∆u e =0,
in Ω e .

Ionic model:

∂ t V m + I ion (V m , h) = -σ i ∇u i • n, ∂ t V m + I ion (V m , h) = -σ e ∇u e • n, ∂ t h = f ion (V j , h),                                    on Γ ion .
GJ model:

G j (V j , g j ) • V j = -σ i ∇u i • n, ∂ t g j = f j (V m , g j ),                      on Γ j .
Boundary conditions and stimulus: σ e ∇u e • n =0, on ∂Ω e \ Γ ion , u e =0, on Γ gr , for t ∈ [t 0 , t 0 + t stim ],

u e =U app , on Γ app .

• σ i , σ e intra and extracellular conductivities • h gating variables for ionic model

• V m = u i -u e transmembrane potential • V j = [u i ] transjunctional potential

Numerical analysis -2D test case

• Domain: 2 × 1 cells, cell size 100 × 20µm, distance 1µm. Mesh and time step: dx = 1µm, dt = 0.02ms.

• BR ionic model. Semi-implicit time scheme. FEM. Iterative method. Test: no gap junctions. On going work

• Current observations: without GJ there is no AP propagation from cell to cell. • To be tested: finer mesh, smaller cell distances.

• Include different types of GJCs on larger domains.

• Compare velocities with the experimental observations.

Future work:

• Move to homogenised model.

Figure :

 : Figure : Schematic diagrams of a standard connexin molecule and gap junction channel. (Del Corso et. al., 2006)

Figure :

 : Figure :Predicted configurations of connexons and gap junction channels for two different connexins.(Desplantez, 2004)

Figure :

 : Figure : Immunohistochemical analysis of Cx43. Left: Bar = 10µm. (Beauchamp, 2004) Right: top view(A), lateral view(B). Bar = 5µm. (Beauchamp, 2012)

Figure :

 : Figure : GJ currents in time, fixed V j . Left: Homotypic Cx43/Cx43 cell pairs. Right: Cx43KO/Cx43KO cell pairs.

Figure :

 : Figure : Left: A mixed patterned cell culture at low magnification. Right: Decrease in velocity of propagation w.r.t. presence of Cx43 cells.

•Figure :

 : Figure : Simulated GJ current per unit area w.r.t. the time for the fixed V j .

  (a) time: 0.0ms (b) time: 5.0ms (c) time: 15.0ms (d) time: 23.0ms (e) time: 27.0ms (f) time: 35.0ms


Effects of non-linear GJ channels on the AP propagation : a modelling insight Yves Coudière 1, 2, 3, 4 , Anđela Davidović 1, 2, 3, 4 , Thomas Desplantez 2, 4, 5 , Clair Poignard 1, 2, 3 1 INRIA Bordeaux Sud-Ouest, 2 University of Bordeaux, 3 Institut de Mathématiques de Bordeaux, 4 IHU-Liryc, 5 PTIB

On Gap Junctions

• What is a Gap Junction?

• Cluster of gap junction channels • Linking structure between neighbouring cells • Provides direct passage of molecules and ions • What are they made of?

• Proteins connexins.

• 6 connexins = 1 connexon (hemichannel)

• 2 connexons = 1 gap junction channel • Cardiac cell proteins: Cx43, Cx45 and Cx40. • Where are they located in cardiac cells?

• Mostly on the longitudinal ends where they compose the intercalated disks • The behaviour of transversal GJ channels is not well understood • Electrical behaviour?

• The dual voltage patch clamp • Non-linear behaviourgating of channels • Dependent on connexin arrangement.

Non linear GJ model -0D

• GJ current: I j = G j (t, V j )V j , where V j transjunctional voltage. • Conductance: G j (t, V j ) = g j,0 g j (t, V j ).

• The amplitude of the junctional conductance: g j,0 = 68nS for Cx43 cells, i.e. g j,0 = 2nS for Cx43KO. • Gating variable:

g j = g j (t, V j ) dg j dt = g ∞ (V j ) -g j τ ∞ (V j )
• Fit experimental data to find normalised g ∞ (V j ).

Homotypic GJC made of mCx43 transfected in HeLa cells

Assumptions

• Use only homotypic Cx43 and Cx45 GJ channels.

• GJ channels are at the perimeters of the cells, on the membrane.

• The rest of the membrane has only ionic channels. Use Beeler Reuter ionic model.

2D/3D mathematical microscopic model

• σ i , σ e intra and extracellular conductivities

• h gating variables for ionic model

• V m = u i -u e transmembrane potential, V j = [u i ] transjunctional potential. σ i ∆u i =0, in Ω i , σ e ∆u e =0,
in Ω e ,

σ e ∇u e • n =I app (t), on ∂Ω e ∂ t V m + I ion (V m , h) = σ i ∇u i • n, ∂ t V m + I ion (V m , h) = -σ e ∇u e • n, ∂ t h = f ion (V j , h),                                    on Γ ion . G j (V j , g j ) • V j = σ i ∇u i • n, ∂ t g j = f j (V m , g j ),                      on Γ j .
-

Numerical analysis -2D

• Tests on: 2 × 1, 4 × 1 and 10 × 1 cells, cell size 100 × 20µm. Mesh step: dx = 0.005mm.

• Time: T = 300ms, time step: dt = 0.001ms. Explicit FE time scheme. Iterative method.

• Execution time on 10 × 1 domain ≈ 10h. We need:

• Improve the model?

• Longer simulations. Larger domain.

• Try to observe dynamics of GJ channels by applying multiple stimuli.

• Move to HOMOGENISED model!

Figure :

 : Figure : Schematic diagrams of a standard connexin molecule and gap junction channel.(Del Corso et. al., 2006)

Figure :

 : Figure :Predicted configurations of connexons and gap junction channels for two different connexins.(Desplantez, 2004)

Figure :

 : Figure : Immunohistochemical analysis of Cx43. Left: Bar = 10µm. (Beauchamp, 2004) Right: top view(A), lateral view(B). Bar = 5µm. (Beauchamp, 2012)

Figure :

 : Figure : GJ currents in time, fixed V j . Left: Homotypic Cx43/Cx43 cell pairs. Right: Cx43KO/Cx43KO cell pairs.

  Dual voltage clamp recordings performed in stably transfected (single transfection) HeLa cells• Fit experimental data to find τ ∞ (V j ).

•

  Primary cultures of Cx43 WT and Cx43KO ventricular myocytes.• Macroscopic velocity was calculated from the difference in mean activation time within regions of interest.

Figure :

 : Figure : Left: A mixed patterned cell culture at low magnification. Right: Decrease in velocity of propagation w.r.t. presence of Cx43 cells.

Figure :

 : Figure : Up: domain of simulation and initial tansmembrane potential. Bottom: propagation of the potential.

•

  GJ facilitated the propagation in intracellular space.• Almost NO change in GJ gates -mostly open. Hard to observe dynamics. • Very small difference due to different GJ channels.


Clémence Chamard-Jovenin

Amand Chesnel

Emmanuel Bresso

Chloé Morel

Charlène Thiébaut

Malika Smail-Tabbone

El-Hadi Djermoune

Marie-Dominique Devignes

Taha Boukhobza

Hélène Dumond

Transgenerational effects of ERalpha36 over-expression on mammary gland development and molecular phenotype: clinical perspective for breast cancer risk and therapy

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

Transgenerational effects of ERalpha36 over-expression on mammary gland development and molecular phenotype: clinical perspective for breast cancer risk and therapy.

Clémence Chamard-Jovenin 1 , Amand Chesnel 1 , Emmanuel Bresso 2 , Chloé Morel 1 , Charlène Thiébaut 1 , Malika Smail-Tabbone 2 , El-Hadi Djermoune 1 , Marie-Dominique Devignes 2 , Taha Boukhobza 1 and Hélène Dumond 1 .

1 CNRS-Université de Lorraine, UMR 7039, Centre de Recherche en Automatique de Nancy, BP70239, Vandoeuvre-lès-Nancy, F-54506, France. 2 LORIA, CNRS UMR 7503, INRIA, Villers les Nancy, France. E-mail : clemence.jovenin@univ-lorraine.fr Growing source of evidence suggests that exposure to estrogen mimicking agents is a risk factor for breast cancer onset and progression. Long chain alkylphenols are man-made compounds still present in household products, industrial and agricultural processes, leading to a global environmental and human contamination. These molecules are known to exert estrogen-like activities through binding to classical estrogen receptors. Recently, we have demonstrated that a realistic mixture of 4-tert-octylphenol and 4-nonylphenol can stimulate proliferation and modulate epigenetic status of testicular cancer germ cells through a rapid, Estrogen Receptor alpha 36 (ERα36)dependent non genomic pathway (Ajj et al, 2013; doi: 10.1371/journal.pone.0061758). In a retrospective study of breast tumor samples, we also validated ERα36 expression as a reliable prognostic factor for cancer progression from an estrogen dependent proliferative tumor toward an estrogen dispensable metastatic disease (Chamard-Jovenin et al, 2015; doi: 10.1186/s12918-015-0178-7). Since high ERα36 expression enhances expression of migration/invasion markers in breast tumors, we addressed the question of its involvement in response to alkylphenol exposure in vitro (MCF-10A mammary epithelial cell line and MCF-7 estrogen-sensitive cancer cells) and in vivo (C57BL mice). A male inherited transgenerational model of exposure to environmentally relevant doses of an alkylphenol mix was set up in C57BL/6J mice to determine whether and how it impacts on mammary gland morphogenesis. Human mammary epithelial MCF-10A cells were exposed to similar doses to decipher the molecular mechanisms involved by a combination of transcriptomic study, cell phenotype analyses, functional and signaling network modeling. The relevance of mouse phenotype extrapolation to human risk is discussed. Mouse mammary gland exposed transgenerationally to the alkylphenol mix displayed a neoplastic-like histology. This phenotype was correlated with the enhanced proliferation, migration ability and apoptosis resistance observed in vitro on human mammary epithelial cells and mediated by the estrogen receptor variant ERα36. Since cellular phenotypes are similar in vivo and in vitro and involve the unique ERα36 human variant, such consequences of alkylphenol exposure could be extrapolated from mouse model to human. Low dose alkylphenol transgenerational exposure could promote abnormal mammary gland development and subsequently increase the risk of breast cancer at ageing. This work is supported by ANSES (n°2012-2-014) and INSERM/Plan Cancer (2013-2016).


Anđela Davidović

Yves Coudière

Clair Poignard

Modelling cardiac

come   L'archive ouverte pluridisciplinaire

Modelling cardiac electrophysiology with structural heterogeneities and dynamical gap junctions Anđela Davidović 1, 2, 3, 4 (andjela.davidovic@inria.fr), Yves Coudière 1, 2, 3, 4 , Clair Poignard 1, 2, 3 , Thomas Desplantez 2, 4, 5 1 INRIA Bordeaux Sud-Ouest, 2 University Bordeaux, 3 Institut de Mathématiques de Bordeaux (IMB), 4 IHU-Liryc, 5 PTIB -hospital Xavier Arnozan Why?

• > 17 000 000 people die every year • medical care -millions of EUR

Multiscale Modelling CELL SCALE -0D

dv m dt = -I ion (v m , h) -I stim dh dt = -g(v m , h) v m = u i -u e

TISSUE SCALE -2D or 3D

• Bidomain model (Neu-Krassowska, 1993)

∂ t h + g(v m , h) = 0 ∂ t v m + I ion (v m , h) = ∇ • (σ i ∇u i ) ∂ t v m + I ion (v m , h) = -∇ • (σ e ∇u e )
• generalised cable equation • derived from microscopic equations • anisotropic model

SCARS -BLACK BOXES

MAIN FACTORS

• Nonlinear ionic currents • MICROSTRUCTURE • Gap Junctions (resistors?)

Assumptions

• Periodic inclusions of size ε.

• Isotropic conductivity in the inclusions.

• No cells in the inclusionspassive conductors.

• Standard transmission conditions. Let ε → 0

MESOSCALE MODEL

∂ t h ε + g(v ε , h ε ) =0, in Ω B ε , ∂ t v ε + I ion (v ε , h ε ) =∇ • (σ i ε ∇u i ε ), in Ω B ε , ∂ t v ε + I ion (v ε , h ε ) = -∇ • (σ e ε ∇u e ε ), in Ω B ε . ∇ • (σ d ε ∇u d ε ) = 0, in Ω D ε . σ i ε ∇u i ε • n Σ ε = 0, σ e ε ∇u e ε • n Σ ε = σ d ε ∇u d ε • n Σ ε , u e ε = u d ε ,                                    on Σ ε . ε Ω Ω B ε Ω D ε Σ ε ∂Ω Y Y D Y B Γ 1 MODIFIED BIDOMAIN MODEL • Limit macroscale model ∂ t h 0 + g(v 0 , h 0 ) =0, |Y B |(∂ t v 0 + I ion (v 0 , h 0 )) =∇ • (σ i ∇u i 0 ), |Y B |(∂ t v 0 + I ion (v 0 , h 0 )) = -∇ • (σ e ∇u 0 ). σi = σ i |Y B | + A i (σ i , w i ), σe = σ e |Y B | + σ d |Y D | + A(σ e , σ d , w) • UPDATED CONDUCTIVITIES! • A i , A
L ε u ε = f → Lu = f • Formal asymptotic expansion u ε (t, x) = u 0 (t, x, x/ε) + εu 1 (t, x, x/ε) + • • •
=⇒ Cascade PDE systems • Cell problems for new variables w -define dependence of u 1 on u 0 -solved once.

Numerical results

• FreeFem++ and gnuplot • Mitchell Schaeffer ionic model • 2D simulations on rectangle, SBDF2 scheme • Circular and elliptical inclusions What about GAP JUNCTIONS? • Distributed around the cell perimeters.

• Expressed in ventricles: Cx43, Cx45 and Cx40.

• In recent models:

I j = g j V j
with g j = const and V j -transjunctional voltage.

NON LINEAR MODEL

• Gating variable: g j = g j (t, V j ) dg j dt = g ∞ (V j ) -g j τ ∞ (V j ) • Fit experimental data to find g ∞ /g 0 and τ ∞ .

Figure :

 : Figure :The infarct border zone.(Rutherford, 2012)

  matrices obtained by solving the cell problems on Y for w i and w.• volume fraction AND geometry A word on homogenisation..• Full problem depends on ε ⇒ very expensive • Averaging solution:

Figure :

 : Figure : Propagation of v m in heterogeneous tissue.

Figure :

 : Figure : Immunohistochemical analysis of Cx43. Left: Bar = 10µm. (Beauchamp, 2004) Right: top view(A), lateral view(B). Bar = 5µm. (Beauchamp, 2012)

Figure :

 : Figure : Fitting the non-linear model to the experimental data for the homomeric Cx43 gap junction in rodent.

  g j = g ∞ + (g 0 -g ∞ )e -t τ ∞ Work in progress... and beyond • Current work: including GJ model (i) as boundary condition (ii) rescaling propagation front • Future work:• SCAR modelling • Late enhancement MRI

Table :

 : Modified conductivities. C -cirles, E -elipses.

			e 22
	none	0.0	1.74 0.19 3.9 1.97
	C	0.18	1.29 0.18 3.28 2.45
	C	0.2	1.26 0.17 3.29 2.53
	C	0.4	1.07 0.15 3.42 3.53
	C	0.7	0.69 0.09 5.08 7.89
	E -long	0.18	0.31 0.19 0.75 2.61
	E -short	0.2	1.13 0.18 2.82 2.58
	E -medium	0.2	0.86 0.18 2.09 2.64
	E -short	0.4	0.81 0.16 2.53 3.70

Inclusions Vol. fraction σ * i 11 σ * i 22 σ * e 11 σ *