Tarik Kousksou

A Ahmed

E Ben Ghoulam

Y Khattari

H El-Otmany

T El

E Ben

Physical models to evaluate the performance of impure phase change material dispersed in building materials

Keywords: PCM, Physical models, Building material, Latent storage, Hysteresis

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

1-Introduction

The building sector in Europe is one of the most energy consuming areas in the world due to its heating and cooling systems. As reported by the International Energy Agency (IEA), the sector produces about 1/3 of total greenhouse gas emissions [1-2]. It is therefore crucial to develop new approaches for saving energy and limiting energy use, without restricting the development of the building sector [START_REF] Brady | Assessment of energy consumption in existing buildings[END_REF][START_REF] Rezaei | A review of conventional, advanced, and mart glazing technologies and materials for improving indoor environment[END_REF]. In this context, an appropriate design of the building enclosure has a decisive role to ensure a reduction in the building's energy use and to preserve the thermal comfort of the residents [START_REF] Zinzi | Cool and green, an energy and comfort comparison between passive cooling and mitigation urban heat island techniques for residential buildings in the Mediterranean region[END_REF][START_REF] Omrany | Application of passive wall systems for improving the energy efficiency in buildings: A comprehensive review[END_REF]. Several passive strategies to improve the building's energy performance have recently been implemented [START_REF] Valladares-Rendon | Review on energy savings by solar control techniques and optimal building orientation for the strategic placement of façade shading systems[END_REF][START_REF] Albayyaa | Energy conservation in residential buildings by incorporating Passive Solar and Energy Efficiency Design Strategies and higher thermal mass[END_REF]. As a complement to these strategies, the integration of phase change materials (PCM) in construction materials is recently recognized as a popular technique for reducing interior temperature fluctuations and improving the energy efficiency of buildings [START_REF] Rao | PCM-mortar based construction materials for energy efficient buildings: A review on research trends[END_REF][START_REF] Bao | Development of high performance PCM cement composites for passive solar buildings[END_REF]. In building, the PCM not only was used in the surrounding envelopes [START_REF] Kuznik | In-situ study of thermal comfort enhancement in a renovated building equipped with phase change material wallboard[END_REF], but also in the ceiling [START_REF] Alqallaf | Concrete roof with cylindrical holes containing PCM to reduce the heat gain[END_REF], floor [START_REF] Royon | Thermal energy storage and release of a new component with PCM for integration in floors for thermal management of buildings[END_REF], and energy equipment [14 -15]. When the PCM is used in the buildings, the thermal stability should also be tested first. Some researchers have carried out nearly 4,000 cooling-heating thermal cycles to experimentally investigate it [START_REF] Mengjie | Thermal stability experimental study on three types of organic binary phase change materials applied in thermal energy storage system[END_REF][START_REF] Zhang | Experimental study on the thermal stability of a paraffin mixture with up to 10,000 thermal cycles[END_REF]. For this reason, physical models to describe heat transfers inside such materials are highly requested. However, the implementation and verification of such models is a challenging exercise due to the non-linearity of the solidliquid phase change [START_REF] Rhafiki | Numerical analysis of a micro-encapsulated PCM wallboard: Fluxmeter applications[END_REF].

Realistic simulation of heat transfer in a composite material incorporating PCM is an important challenge. However, due to the non-linearity of heat transfer during the solid-liquid phase change [START_REF] Zhang | Thermal storage and nonlinear heat-transfer characteristics of PCM wallboard[END_REF], a restricted number of analytical solutions are available, while numerical solutions are largely accessible. They can be consulted in the leading papers on heat transfer, such as Crank [START_REF] Crank | Free and moving boundary problems[END_REF], Hill [21], Voller [START_REF] Swaminathan | Towards a general numerical scheme for solidification systems[END_REF] and Alexiades and Solomon [START_REF] Alexiades | Mathematical modeling of melting and freezing processes[END_REF]. Additionally, it should be noted that the analytical solution for an ideal isothermal phase transition case may not be able to produce a complete representation of the composite material containing PCM.

Generally, PCMs used in the construction materials of the building are impure and act like binary mixtures [24-25], which mean that the phase change processes in these materials are not isothermal and often carried out within a range of temperature [START_REF] Egolf | Theory and modeling of phase change materials with and without mushy regions[END_REF][START_REF] Pomianowski | A new experimental method to determine specific heat capacity of inhomogeneous concrete material with incorporated microencapsulated-PCM[END_REF]. Other technical aspects like hysteresis phenomenon can also complicate the modelling of phase transition in building materials [START_REF] Biswas | Thermal characterization of full-scale PCM products and numerical simulations, including hysteresis, to evaluate energy impacts in an envelope application[END_REF][START_REF] Jin | Energy asymmetry in melting and solidifying processes of PCM[END_REF]. This phenomenon is typically marked by a total displacement of the enthalpy function during the freezing process of the PCM compared to the same one along the fusion process [START_REF] Zhang | Modified computational methods using effective heat capacity model for the thermal evaluation of PCM outfitted walls[END_REF][START_REF] Al-Saadi | Modeling phase change materials embedded in building enclosure : A review[END_REF]. In this context, some of the analytical and numerical solutions described earlier may give some useful insights, but may be not suitable for composite materials including PCMs [32-33].

A number of numerical methods are available in the literature for modeling PCMs, particularly the apparent heat capacity method (AHCM) [START_REF] Lamberg | Numerical and experimental investigation of melting and freezing processes in phase change material storage[END_REF][START_REF] Medved | Modeling of heat capacity peaks and enthalpy jumps of phase-change materials used for thermal energy storage[END_REF], the heat source method (HSM) [START_REF] Kousksou | Thermal behavior of building material containing microencapsulated PCM[END_REF][START_REF] Younsi | Numerical investigation of transient thermal behavior of a wallincorporating a phase change material via a hybrid scheme[END_REF], the explicit enthalpy method (EEM) [START_REF] Franquet | Experimental and theroretical analysis of a cement mortar containing microencapsulated PCM[END_REF] and the implicit enthalpy method (IEM) [START_REF] Zhou | Performance of shape-stabilized phase change material wallboard with periodical outside heat flux waves[END_REF][START_REF] Al-Saadi | Modeling phase change materials embedded in building enclosure : A review[END_REF]. However, the number of studies published in the literature that compare the results of these models with experimental ones and that outline the advantages and disadvantages of each approach is limited [START_REF] Al-Saadi | Systematic evaluation of mathematical methods and numerical schemes for modeling PCM-enhanced building enclosure[END_REF][START_REF] Jin | Comparison of two numerical heat transfer models for phase change material board[END_REF]. It is interesting to mention that there are few experimental studies that provide all the necessary information to validate physical models describing heat transfers in a composite PCM [START_REF] Franquet | Experimental and theroretical analysis of a cement mortar containing microencapsulated PCM[END_REF][START_REF] Joulin | Experimental investigation of thermal characteristics of a mortar with or without a micro-encapsulated phase change material[END_REF]. This includes both the accurate description of all the boundary conditions applied to the physical domain during the charging/discharging period, and precise determination of various thermophysical properties of the PCM-based materials adopted for the experiments.

A precise determination of the heat capacity and enthalpy functions of impure materials during the phase transition process is also essential for a correct mathematical modelling of heat transfer within the composite material. Whatever the physical model, if such functions are employed, they may be a potential source of imprecision [START_REF] Kuznik | Impact of the enthalpy function on the simulation of a building with phase change material wall[END_REF]. Usually, specific enthalpy and specific heat capacity of a PCM versus temperature are commonly determined using the DSC device. However, the precision of this apparatus relies on the accuracy of the protocol employed to describe the phase change characteristic of the PCM. When performing DSC experiments, particular consideration must be paid to the choice of the scan rates, as various heating rates provide various outputs for heat flux and phase transition temperatures. In this work, the apparent heat capacity function of an impure PCM is determined from an enthalpy function, which is deduced from an inverse method presented in detail in Ref. [START_REF] Franquet | Inverse method for the identification of the enthalpy of phase change materials from calorimetry experiments[END_REF].

To our best knowledge, a few numerical models are reported in the literature addressing the phase change process of impure PCMs dispersed in building material [START_REF] Franquet | Experimental and theroretical analysis of a cement mortar containing microencapsulated PCM[END_REF]. In this paper, four physical models are implemented to characterize heat transfers in a building component with an impure PCM. It particularly examines the feasibility of these methods for building applications. The experimental works of Joulin et al. [START_REF] Joulin | Experimental investigation of thermal characteristics of a mortar with or without a micro-encapsulated phase change material[END_REF] and Franquet et al. [START_REF] Franquet | Experimental and theroretical analysis of a cement mortar containing microencapsulated PCM[END_REF] were selected to verify these physical models. The merits and drawbacks of each physical model will be outlined and commented in the following sections of this work.

Fluxmeter Device

It is important to outline that phase transition characterization is a key point concerning both the thermal performance and the conception of composite PCMs. Storage density and melting temperatures are among the main design criteria of the composite material containing impure PCM. In addition, reliable mathematical models that accurately describe the heat transfer inside a composite PCM require accurate information on the heat capacity and enthalpy functions of these materials during the phase transition process.

Regardless of the physical model, if such functions are used, they could represent a possible source of inaccuracy [START_REF] Franquet | Experimental and theroretical analysis of a cement mortar containing microencapsulated PCM[END_REF][START_REF] Frazzica | Recent advancements in materials and systems for thermal energy storage: An introduction to experimental characterization methods[END_REF]. A number of researchers use the DSC device to measure the specific enthalpy and the heat capacity of the PCM as a function of temperature [START_REF] Rathgeber | Measurement of enthalpy curves of phase change materials via DSC and T-History: When are both methods needed to estimate the behaviour of the bulk material in applications?[END_REF].

However, the DSC's accuracy depend on the precision of the protocol adopted to describe the phase transition. The fluxmeter device is currently one of the instruments that used extensively to determine the thermophysical properties of composite PCM [START_REF] Rathgeber | Measurement of enthalpy curves of phase change materials via DSC and T-History: When are both methods needed to estimate the behaviour of the bulk material in applications?[END_REF][START_REF] Kheradmand | Experimental and numerical studies of hybrid PCM embedded in plastering mortar for enhanced thermal behaviour of buildings[END_REF]. It is interesting to note that this device (see Fig. 1) is unable to provide insight regarding the thermal gradients in the composite material during the phase transition process. The fluxmeter provides only temperature (Tp) and heat flux (∅) measurements at the material extremities. In this paper, the numerical models presented in section 3 are used to determine the temperature variations inside the composite PCM. In addition, these models are verified and validated using the experimental heat fluxes provided by the fluxmeter device [START_REF] Franquet | Experimental and theroretical analysis of a cement mortar containing microencapsulated PCM[END_REF]. In Ref.

[32], the mortar including 12.5% of microencapsulated PCM is disposed in a parallelepipedic form with dimension of 25×25×4 cm 3 [START_REF] Franquet | Experimental and theroretical analysis of a cement mortar containing microencapsulated PCM[END_REF]. A rectangular composite material containing microencapsulated PCM is used as a sample in this study, and each face of it is subjected to a linear plate temperature Tp (see Eq.1) which is dependent on time and ranging from 7 to 39°C over time by using different heating/cooling rates .

.

p o T t T β = + ( 1
)
where β is the heating/cooling rate and o T the temperature of the composite material at 0 t = .

Table 1 showed the thermophysical properties of the composite material [32].

Fig.1: Fluxmeter device [32]

Table 1: Thermophysical properties of composite phase change material

Mathematical models

The physical models that we will present in the succeeding paragraphs are based on the following hypotheses:

-The composite material consists of two elements: mortar and PCM.

-The PCM is impure and acts as a binary mixture.

-The thermal conduction is unidirectional in the x-axis.

Apparent heat capacity method (AHCM)

When the physical model is derived from the apparent calorific capacity approach, the heat transfer inside the composite PCM can be described by a single energy equation

[54], i. e. ( )
( ) 2 2
, , ( )

c app c T x t T x t c T k t x ρ ∂ ∂ = ∂ ∂ (2)
where c where h is the enthalpy of the construction material and may be obtained by considering the formula below:

( ) ( ) . 1 . pcm mortar h T h h ε ε = + - ( 4
)
where ε is the mass fraction of the PCM in the composite material.

Eq. ( 3) can be expressed as :

( ) ( ) ( ) . 1 . . ( ) 1 . pcm mortar app pcm mortar dh dh c T c T c dT dT ε ε ε ε = + - = + - (5)
In Eq.( 5), the mortar enthalpy is an usual sensible enthalpy, while the enthalpy of the PCM should be defined during both sensible and latent storage.

It can be noted that according to equations ( 2) and ( 5), the physical model can provide a clear description of the phase transition inside the composite material as long as the specific thermal capacity of the PCM is adequately defined.

In this work, the correlation developed by Franquet et al.

[32] is selected to determine the value of the apparent heat capacity of PCM behaving as a binary mixture:

( ) ( ) , , , 2 , ( )
A m A m s pcm L pcm S pcm f m A A pcm L pcm m T T T T c c c L if T T T T T T c T c if T T    - - + - × + ×     -   - =   ≥   p ( 6
)
where Tm represents the end of the non-isothermal melting of the PCM,TA is the melting temperature of the pure PCM and is the latent heat of fusion. The first two terms in Eq.6

reflect the sensible part and the last one describes the variation of the latent fusion throughout the phase transition of the PCM.

( ) ( ) ( )( ) ( ) 1 ln ( ) A m A S m L m A f S L A m m A A m L A m T T T T c T T c T T L c c T T if T T T T T T h T c T T if T T ε      - - -+ -- - + - -       - - =       - ≥   p (7)
where ( ) Fig. 2 illustrates the variation of the specific enthalpy versus temperature for two cases:

, . ( ) 1 .
Tm < TA and Tm = TA. During the heating process, the state of the composite material displaces from left to right across the curve, with increasing enthalpy and temperature. In a first step, the temperature of the PCM increases with the additional energy that is stored as sensible heat in the solid PCM. The latent heat of fusion is absorbed as the PCM passes from solid phase to liquid phase. When the melting process is concluded, additional energy input again results in a temperature increase (sensible heat in liquid phase). We note that in the case of Tm < TA, the PCM behaves like a binary mixture and the melting process is carried out over a range of temperatures. However, in the case of Tm = TA the PCM acts as a pure substance and the phase transition process is done at constant temperature. equations are represented by the following formulas:

1 1 1 1 1 1 1 n n n i i i i i i i a T a T a T b + + + + + -- = + + (8)
where:

1 1 c i i k a a x + - = = ∆ (9) 1 1 ( ) n c app i i i i c T a a a t ρ - + = + + ∆ (10) ( ) n c app i n i i c T b T t ρ = × ∆ (11)
As shown in Eqs (10) and (11), the apparent heat capacity of the composite material is calculated at the previous time (n) by using Eq.6.

In this paper, Eqs.(8) were solved iteratively by using a Tridiagonal Matrix Algorithm (TDMA) method [START_REF] Patankar | Numerical Heat Transfer and Fluid Flow[END_REF]. The computation procedure was carried out using Fortan. The specified iteration in each time interval was considered convergent when the maximum relative residual of T was less than 10 -4 .

Enthalpy method

The so-called enthalpy approach has been established to address phase change problems for such applications [START_REF] Swaminathan | Towards a general numerical scheme for solidification systems[END_REF]. Therefore, the enthalpy method can be adopted for the solution of phase change problems inducing both isothermal phase transition (i.e. the phase change taking place at a constant temperature) as well as non-isothermal phase transition (i.e. the phase change taking place over a range of temperatures) (see Fig. 2). We will now describe the application of the enthalpy method for the solution of one-dimensional fusion or solidification inside the composite phase change material using both explicit and implicit finite volume schemes.

For conduction-driven heat transfer, the energy equation can be rewritten into one equation where latent heat is integrated into the enthalpy term as shown below :

( ) ( ) 2 2
, ,

c c h x t T x t k t x ρ ∂ ∂ = ∂ ∂ (12)
which is assumed to be applicable to the overall solution domain, comprising the solid phase and the liquid phase as well as the solid-liquid interface. Eq. 12 can be resolved by two different techniques: the explicit enthalpic method or the implicit enthalpic method.

Explicit enthalpy method (EEM)

The finite volume approximation of Eq.( 12) with simple explicit enthalpy method is obtained as [32]:

1 1 1 1 1 n n n n n i i i i i i i i h h a T a T a T + -- + + = + + + (13)
where :

1 1 2
( )

c i i c k t a a x ρ + - ∆ = = ∆ (14) 2 2 ( ) c i c k t a x ρ ∆ = - ∆ (15)
As the Eq.13 is explicit, the following condition should be satisfied for stability:

2 1 ( ) 2 c c c k t c x ρ ∆ ∆ p (16)
The following algorithm can be used to solve explicit finite volume element equations for the enthalpy method.

We assume that the numerical solution has progressed as far as the time level and the numerical values of (ii) Compute the corresponding 1 n i T + from Eq.7 by using the value of 1

n i h + : 1 1 1 1 1 1 ( ) n n i i m n n i n i A i m L F h if h h T h T if h h c - + + + + +   =  + ≥   p (17)
where 1 1 ( )

n i F h - + is the inverse function of 1 n i h + .
To avoid the calculation of the inverse function of 1 n i h + , it is possible to approximate the enthalpy curve ( ) h T during the melting process by a smooth curve between two neighbouring points.

Implicit enthalpy method (IEM)

The finite volume approximation of Eq.( 12) with simple implicit enthalpy method is obtained as [41]:

1 1 1 1 1 1 1 1 n n n n n i i i i i i i i h h a T a T a T + + + + -- + + = + + + (18)
According to Eq.( 18), it is clear that the new value of the enthalpy function

1 n i h + at node i is dependent on the new value of temperatures 1 1 n i T + -, 1 n i T + and 1 1 n i T +
+ and therefore the enthalpy function is nonlinear. Eq.( 18) cannot be solved without using proper numerical techniques to handle this nonlinearity. A practical way to overcome this nonlinearity is to approximate the enthalpy curve (see Eq.( 7)) during the phase change transition process by a piecewise linear function. For example, we could use a linear approximation to describe the enthalpy curve during the melting process:

1 1 ,1 , 2
n n i i i i h b T b + + = + (19)
Where Using Eq.( 19), Eq.( 18) can be written as follows:

' 1 ' 1 1 1 1 1 1 n n n n i i i i i i i
a T aT a T h

+ + + -- + + + + = (20)
where:

' ,1 i i i a a b = -and ' , 2
n n i i i h b h = -
Eq.( 18) becomes linear equation (see Eq.( 20)) with one primary dependent variable « Temperature » that can be iteratively solved using a Tridiagonal Matrix Algorithm (TDMA)

method [START_REF] Patankar | Numerical Heat Transfer and Fluid Flow[END_REF]. The TDMA algorithm is faster because there are no restriction on the time step.

Heat source method (HSM)

The energy equation using the heat source approach can be expressed as follow [START_REF] Al-Saadi | Modeling phase change materials embedded in building enclosure : A review[END_REF][START_REF] Al-Saadi | Systematic evaluation of mathematical methods and numerical schemes for modeling PCM-enhanced building enclosure[END_REF]:

( ) ( ) 2 2
, ,

c c c pcm f T x t T x t f c k L t x t ρ ρ ∂ ∂ ∂ = - ∂ ∂ ∂ ( 21
)
Where f is the liquid fraction of the PCM.

The finite volume discretization of Eq.( 21), based on a fully implicit time integration has the following expression:

1 1 1 1 1 1 1 n n n i i i i i i i a T a T a T b + + + + + -- = + + (22)
where:

1 1 c i i k a a x + - = ∆ (23) 1 1 c c i i i c a a a x t ρ - + = + + ∆ ∆ (24) 1 n n n c c i i i i pcm f c f f b x T L x t t ρ ρ + - = ∆ × - ∆ ∆ ∆ (25)
For the isothermal phase change (i.e. m A T T = (see Fig. 2)), the liquid fraction can estimated at each time step, using the method reported in [22]:

1 n n n i i i i pcm f a T f f x L t ρ + = + ∆ ∆ (26)
The liquid fraction is updated at each node using the following corrections:

0 0 1 1 if f f if f ≤  =  ≥  (27)
For the phase change over a range of temperature from Tsol to Tliq, the liquid fraction can be estimated using the following expression:

1 1 n n i sol i liq sol T T f T T + + - = - (28)
In Eq.28, the enthalpy function can be approximated by a piecewise linear function (see Eq.19). Using Eq.( 19) and Eq.( 28), Eq.( 22) can be written as follows:

' 1 1 1 ' 1 1 1 1 n n n i i i i i i i aT a T a T b + + + + + -- = + + (29)
Where :

( )

,1 ' pcm f i i i liq sol L b x a a h h t ρ ∆ = + - ∆ and ( ) ,1 '
( )

pcm f i n i c c i liq sol L b x b c T t h h ρ ρ ∆ = + ∆ -
The liquid fraction is updated at each node using the following corrections:

0 1 sol liq if T T f if T T   =  >   p (30)
For both isothermal and non-isothermal phase change, Eqs. 22 and 29 can be solved iteratively using the TDMA algorithm.

It is important to mention that for the three physical models (AHCM, IEM and HSM), the space grid size of the composite PCM is 0.2 mm and the time step is 1 min. Further refinement of either space grids or time steps has no impact on the numerical results. The specified iteration in each time interval was considered convergent when the maximum relative residual of T was less than 10 -4 .

The main advantage of the EEM is its simplicity of programming. The drawback of the EEM is that the temperature of a grid point can only be calculated at specific times. In addition, as Eq.13 is explicit, the following condition should be satisfied for stability:

2 1 ( ) 2 c c c k t c x ρ ∆ ∆ p (31)
In all physical models, the computation procedure was carried out using Fortran.

The system of equations (8, 13, 18 and 29) needs to be closed by considering the following initial and boundary conditions:

( ,0) o T x T = (32)
Each face of the parallelepipedic material is exposed to a linear plate temperature Tp (see Fig. 3), this temperature changes with the time ranging between 7 and 39°C by using different heating/cooling rates .

( )

(0,t) , p o T T L t T t T β = = = + ( 33
)
where To is the initial temperature of the composite material.

The heat flux through the composite material can be calculated using the following formula:

Experimental validation and parametric study

In this paragraph, we will apply physical models described in section 3, to investigate and analyze two kinds of phase transition: non-isothermal phase transition (PCM with impurities i.e. (Tm<TA)) and isothermal phase transition (PCM without impurities (Tm = TA)).

Non-isothermal phase transition (Tm < TA)

The comparison between the experimental [32] and the numerical heat fluxes are reported in Figs. 4-a and4-b. These plots illustrate the variation of the heat flux at the extremities of the composite material versus time for two heating/cooling rates (

/

C h β = ° and the AHCM should be the same. However, since the enthalpy method and the AHCM method use different methods of resolution, the numerical results of these two approaches may be slightly different. Particularly during the phase transition, the computational error may be present. We can also notice that the three methods (EEM, IEM and HSM) produce practically the same numerical results. We can also mention that for the HSM, the two temperatures Tliquidus and Tsolidus have to be judiciously chosen in order to reproduce accurately the experimental results. It is interesting to note that EEM, IEM and HSM require more calculation time than AHCM.

Whatever the heating/cooling rate, the physical models reproduce with confidence the thermal behaviour of the composite material during the phase transition process. It has been noticed

that the solidification and melting processes are not symmetrical (see Figs. 7.8 / C h β = ° Fig. 5 shows the effect of the scan rate on the numerical heat flux produced by the IEM. We note that the numerical heat flux is highly dependent on the heating/cooling rate. The phase transition time reduces as the heating/cooling rate increases. We also observe a displacement of the heat flux to the left during the cooling process and to the right during the heating process. These results can be explained by the heating/cooling rate effect on the thermal gradients inside the composite material [START_REF] Rhafiki | Numerical analysis of a micro-encapsulated PCM wallboard: Fluxmeter applications[END_REF]. For slower heating/cooling rates, the thermal gradient inside the composite material decreases but the time duration of the phase transition increases.

It is interesting to notice that the HSM permits to estimate easily the evolution of the liquid fraction (see Eq.27) during the phase change process (see Fig. 6). The analysis of this figure confirms the asymmetrical nature of the melting and crystallization process due to the asymmetric form of the enthalpy function for non-pure PCMs. A significant hysteresis [START_REF] Klimeš | Computer modelling and experimental investigation of phase change hysteresis of PCMs: The state-of-the-art review[END_REF][START_REF] Buonomano | The impact of thermophysical properties and hysteresis effects on the energy performance simulation of PCM wallboards: Experimental studies, modelling, and validation[END_REF] in the liquid fraction is observed in Fig. 6. To verify if the hysteresis phenomenon is present or not within the impure PCM, the temperature and the specific enthalpy at the center of the composite material during heating and cooling modes for different scan rates β are presented on Fig. 7. The temperature is calculated using the apparent heat capacity method while the specific enthalpy is computed using the implicit enthalpy method. We remark that the temperature and the specific enthalpy function of the composite material integrating impure PCM are shifted towards the right (heating mode) and the left (cooling mode) respectively. We can note that the hysteresis phenomenon is amplified by increasing the rate of heating and cooling modes. This phenomenon is most probably due to the thermal gradients inside the composite material and to the non-symmetric enthalpy profile versus temperature. process in the composite material increases with increasingε. We can also note that during the heating or cooling process, the composite material without PCM will only store/release sensible heat. This curve shows clearly the benefits of incorporating PCMs into building materials to improve their thermal inertia. This discontinuity results from the numerical treatment that we used in the IEM method to avoid division by zero in equations s 6 and 7. -Correlations between specific enthalpy and temperature as well as apparent heat capacity and temperature are highly important for EM and AHCM.

-EM, AHCM and HSM based on the assumption of the binary mixture give very satisfying results.

-The appropriate choice of liquidus and solidus temperatures allows HSM to produce similar results to those obtained with EM.

-All four models describe perfectly the asymmetrical character of melting and crystallization of impure PCM in the composite material.

-Algorithms used in EEM, IEM and HSM require more computing time than the AHCM.

-AHCM is suitable for non-isothermal melting/freezing problems if the apparent heat capacity function is available during the phase transition process.

-HSM is relevant to describe heat transfer during isothermal melting/freezing of PCM inside composite material.

-EEM, IEM and AHCM have numerical difficulties to investigate isothermal melting/freezing inside the composite material. These difficulties can be explained by the numerical discontinuity of specific enthalpy and the apparent heat capacity during solid-liquid phase change.

Conclusion

In this work, we presented different models such as apparent heat capacity method, enthalpy method (explicit and implicit) and heat source method for the solution of 1D heat transfer problem applied to a composite building material (mortar) dispersed with encapsulated PCM.

The ability of the 1D models for analysing the thermal response of the composite binary material considered has been demonstrated by using the specific heat capacity and enthalpy functions already available in the open literature. The models have been investigated

considering the phase change at a constant temperature as well occurring over a short temperature range. The effect of the heating/cooling rate and the volume fraction of the PCM on the thermal behavior of the composite material is also analyzed. A significant hysteresis phenomenon is observed during the phase transition due to the thermal gradients within the composite material as well as the non-symmetric enthalpy profile as a function of temperature.

ρ and ck

  are the density [kg/m 3 ] and the thermal conductivity [W/(m.K] of the composite material including PCM respectively. T and t represent temperature (°C) and time (s) and ( ) app c T denotes the apparent heat capacity [kJ/(kg.K)].

  By using Eq.(6), one can analyze and explain the non-isothermal phase change in PCMs behaving as a binary solutions. By fixing the reference point ( ) 0 A h T = , an analogous expression can be deduced for the specific enthalpy of the composite material containing microencapsulated PCM [32]:

  either Solid or Liquid).

Fig. 2 :

 2 Fig.2: Specific enthalpy versus temperature

h

  are known. The relationship between enthalpy function and temperature can be derived from experimental data or standard physical tables. Generally, enthalpy is a non-linear function of temperature. The enthalpies and temperatures at the next time level can be determined as follows :

, 1 i b and , 2 ib

 12 are the constant coefficients.

Fig. 3 :

 3 Fig.3: Boundary conditions

  plate temperature Tp is also presented on these curves (see Figs.4) to indicate the variation of the recorded heat flux during the heating and cooling processes. We can remark that numerical results from different physical models are well aligned with experimental measurements. A slight difference has been noted between numerical results from the AHCM and experimental results [32]. As the calculation of the apparent heat capacity is based on the specific enthalpy function (see Eqs. 3, 6 and 7), the numerical results of the enthalpy method

Fig. 4 :

 4 Fig.4: Comparisons between numerical and experimental heat flux (a)

Fig. 5 :Fig. 6 :

 56 Fig.5: Numerical heat fluxes for various heating/cooling rates.

Fig. 7 :Fig. 8

 78 Fig.7: Temperature (a) and specific enthalpy (b) at the center of the sample versus TP

Fig. 8 : 4 . 2 Fig. 9 :In Fig. 9 ,

 84299 Fig.8: Numerical heat fluxes for various volume fraction of the PCM (AHCM)

Figs. 10 -Fig. 10 :

 1010 Figs.10-a and 10-b display the influence of the scan rate on the numerical heat flux produced by IEM and HSM. We show that for both methods the numerical heat flux is highly dependent on the heating/cooling rate. The isothermal phase transition time decreases as the heating/cooling rate increases.

technique [49-50]. Using this method, the material size is significantly larger and the effect of

	The selection of the scan rate should be done carefully during the DSC
	experiments, since different heating rates can afford different outputs for heat flux and phase
	transition temperatures [47-48]. This problem can be solved using a simplest and inexpensive
	technique to determine both latent heat and the melting point of PCMs namely T-history
	the non-homogeneity of the sample can be considered when carrying out the thermal
	characterization of the building material. However, despite the advantages of the T-history
	technique, it is not suitable to use this method to determine the enthalpy of large-scale of
	composite PCM [51]. The fluxmeter is commonly employed by several researchers to
	thermally characterize composite materials incorporating PCM [45]. The main advantage of
	this device is the ability of testing building material samples in cement blocks or in panel
	form, which helps to avoid the problems caused by the small mass of the sample [52].
	Furthermore, several studies are already used this apparatus in order to validate the physical
	models that describe the thermal behaviour of composites PCM [

32, 42].


S Bratos

J-Cl Leicknam

JITTER OF PUMP-PROBE TIME DELAYS IN XFEL EXPERIMENTS: HOW TO ELIMINATE IT?

Jitter of XFEL signals due to the disorder of pump-probe time delay is explored theoretically. Two basically different methods are applied: statistical mechanics and dimensional analysis. Although completely different, these two approaches suggest the same method to suppress jitter generated perturbations. The method which is proposed here is easily applicable and requires no computational effort.

(1) INTRODUCTION. Jitter of pump-probe time delays is one of the most severe limitations of the XFEL technology. A considerable experimental effort has thus been accepted to overcome this difficulty [START_REF] Meyer | Twocolor photoionization in xuv freeelectron andvisible laser fields[END_REF][START_REF] Fritz | Ultrafast Bond Softening in Bismuth: Mapping a Solid's Interatomic Potential with X-rays[END_REF][START_REF] Maltezopoulos | Single-shot timing measurement of extreme-ultraviolet freeelectron laser pulses[END_REF][START_REF] Azima | Time-resolved pump-probe experiments beyond the jitter limitations at FLASH[END_REF][START_REF] Glownia | Time-resolved pump-probe experiments at the LCLS[END_REF][START_REF] Löhl | Electron Bunch Timing with Femtosecond Precision in a Superconducting Free-Electron Laser[END_REF][START_REF] Bionta | Spectral encoding of x-ray/optical relative delay[END_REF][START_REF] Tavella | Few-femtosecond timing at fourthgeneration X-ray light sources[END_REF]. It culminated in the recently proposed "measure and sort" method [START_REF] Harmand | Achieving few-femtosecond timesorting at hard X-ray free-electron lasers[END_REF]. Theoretical literature on this problem is of a very recent date [START_REF] Bratos | XFEL experiments: jitter of pump-probe time delays and pulse intensities[END_REF]. To a general surprise, the theory proved to be much easier than the experiment: it was shown that the jitter can be eliminated employing standard mean square optimization techniques. However, this is not yet the end of surprises, further simplifications were in fact found possible. It will be shown below that the jitter correction is expressible in terms of a simple formula depending on two parameters: duration of the incident XFEL pulses and duration of the jitter. This problem can be solved without any computer.

Basically, the jitter problem of XFEL is closely related to those concerning motional narrowing processes of spectroscopy.

In a time-resolved X-ray experiment, the sample is pumped by an optical pulse and probed by an ultra-fast X-ray pulse (Fig. 1). The pump-probe time delay must be determined with great accuracy.

At the present time, while XFEL sources generate pulses down to 100 fs, there is a jitter on the pump-probe time delays of the same order. The experiment must thus be repeated a large number of times to make the results usable. Working methods have been proposed to accomplish this task and a specific terminology entered into use. Unfortunately, this averaging does not suffice to eliminate the jitter. An additional step is required to reach this goal. It is described in what follows.

(2) STATISTICAL MECHANICS. The starting point of the present statistical theory is the well known expression for the intensity, , , of diffracted X rays at time , the nominal pump-probe time delay, under the incident X ray intensity, IX :

, = < -> , (1)
averaged over a time bin. For detailed discussion of this approach, see Ref [START_REF] Bratos | XFEL experiments: jitter of pump-probe time delays and pulse intensities[END_REF], where this expression is deduced from rigorous statistical mechanics of non-equilibrium disordered systems. In what follows, the incident X ray intensity, IX is supposed to be Gaussian:

-- = - -- !" (2)
Here is the nominal pump-probe time delay, its ill controlled time increment and #1 ⁄ is the temporal width of the incident incident x-ray pulses. The distribution of pump-probe time delay increments was studied with great care by a number of excellent scientists [START_REF] Cavalieri | Clocking Femtosecond X Rays[END_REF], and was found to be Gaussian:

& = ' ( ⁄ ) ⁄ -'
where ' ) ⁄ defines the temporal extension of the jitter. Then, inserting (2) into (1) and integrating over results in

, = * + +,-. / 0 1 *- +-. +,-. - / , (3)
This equation plays an important role in the present study. To proceed further, a complementary information is required. Let the laser excitation promote the molecule from the ground state 0, where the length of given bond is2 3 , to an electronic state 1 where it is2 ) . According to the Franck-Condon principle,2 ) 0 = 2 3 . The simplest assumption to describe the bond length variation at latter

times consists in writing 2 ) = 2 ) -2 ) -2 3 -5
⁄ , where τr is the molecular reaction time.

The corresponding signal , , the non perturbed by the pump-probe time delay dispersion, can then be written:

Then, inserting Eq(4) into Eq(3) and integrating over t provides , . The integration can be performed exactly if2 ) -2 3 ≪ 2 3 . Note that this condition is not very restrictive. For example, when passing from a single C-C bond to a triple C-C bond, 2 3 = 1.5C and 2 ) -2 3 = 0.3C. One then finds:

, ≃ -2 ) -2 3 F ) 2 3 × H 2IJ K-L +-. +,-. M -2IJ N ) < = L +,-. +-. -L +-. +,-. O * ) P< = 1 +,-. +-. - < < = /Q (5)
This is the jitter perturbed signal predicted by the present statistical theory. Note that j1 is the Bessel function of the order 1. The normalized signal The jitter problem will now be reexamined using the new information provided by Eq [START_REF] Glownia | Time-resolved pump-probe experiments at the LCLS[END_REF] and Fig [START_REF] Meyer | Twocolor photoionization in xuv freeelectron andvisible laser fields[END_REF] for the non-normalized ad normalized signals, respectively. The following points merit attention.

= L* +,- + / ′ = UK1 + < VWXXY= 1 < .Z[\ 1 M ′ (6) 5 = L* +,- + / 5 ′ = UK1 + < VWXXY= 1 < .Z[\ 1 M 5 ′ (7)
where τjitter is the temporal width of the jitter, and τXFEL the temporal width of the incident XFEL pulses. Note that this correction depends exclusively on parameters ', characteristic of a given XFEL site. The jitter correction factor remains the same on a given machine, whatever the experiment.

These results are now briefly illustrated. Fig. 2 shows how the jitter manifests itself in fast and slow processes, respectively. If the jitter evolves on time scales comparable to those of the process under study, its effect may be large and can generally not be neglected. If these times are well separated, the jitter can be completely forgotten.

Fig. 3 illustrates XFEL signals in presence of very fast jitter. They provide information about processes generating the jitter, but no information about physics of the system under study. This being said, another central question arises: how large time corrections are? A look on Table 1 shows that they may be surprisingly large. In this Table, the temporal width of incident XFEL pulses is assumed to be 100 fs, the characteristic time of the jitter varying in wide limits between 300 fs and 10 fs. The system under consideration is supposed to evolve on the 300 fs time scale. What to say about the effect of shot-to-shot pulse intensity variations? They are essential if the absolute intensity of the diffracted XFEL signals are examined. On the contrary, they are not believed to intervene very much in pulse-probe experiments. Detailed experimental studies of shotto-shot intensity variations are needed to progress. For more details , see Ref. [START_REF] Bratos | XFEL experiments: jitter of pump-probe time delays and pulse intensities[END_REF].

(3). DIMENSIONAL ANALYSIS. Surprisingly enough, the above result may be reproduced quite simply applying methods of dimensional analysis. The latter are based on the postulate that all equations having a physical significance must be dimension-ally homogeneous. This requirement suggests the use of dimensionless variables and parameters. Methods have been proposed to find them. Dimensionless quantities entering in the present problem, denoted by the subscript d, are obvious: the dimensionless signal intensity ΔSd(τ) is ΔS(q, τ)/ΔS(q, τ = ∞), the dimensionless wave vector qd is qr, and the dimensionless time τd is #' ' + ⁄ . Note that the theory generated signal of fig. 1 is already written in this form. Then, according to the dimensional analysis, the dimensionless signal ΔSd(q,τ) = f(qd,τd), or

where f is an unknown function. This method does not permit to find it -laboratory channels are used to that purpose in practical engineering -but confirms that the jitter perturbed XFEL signal varies with #' ' + ⁄ rather than with √ . The very general dimensional theory thus predicts exactly the same time dependence of the XFEL signals as the detailed theoretical calculations.

(4) MOTIONAL NARROWING. The XFEL jitter problem is by no means a unique problem, having no analogue elsewhere in physics. In fact, it belongs to a large group of phenomena termed generally as "motional narrowing". Their common feature is that molecular motions appear slowed down, or even stopped completely, under insufficient instrumental resolution. Only the balancing of the signal intensities between those of the new and of the ancient molecule is seen in this case, but no signal shifts. This phenomenon was first studied by Anderson in his celebrated paper on collapsing multiplets in NMR [14]. Similar effects were observed with other spectroscopic techniques. The famous spectroscopic problem of finite slit width correction belongs to the same category of problems. This parenthood should be kept in mind when studying the jitter.

  is particularly appropriate for the present study of jitter induced time perturbations. It is illustrated on Fig.(1).

1 ,

 1 (i)If jitter is present, a process evolving on time τ, appears at time ′ = ' the main effect of the jitter is to contract the time scale by this factor. All physicochemical processes are thus slowed down in presence of jitter; they may then easily escape observation. Neglecting the jitter correction may lead to entirely erroneous conclusions. (ii) XFEL data can be corrected by simply multiply the XFEL times τ' by the factor # ' + ' ⁄ , thus:

  b c d e , = b c d e , = ∞ . I7 5 , #' ' + ⁄ >

( 5 ) 5 .

 55 CONCLUSIONS. It results from the present study that pump-probe time delay jitter generates a contraction of characteristic times. This contraction is very important at shortest times attainable by the actual XFEL machines; neglecting it may render the interpretation of measured signals entirely erroneous. It is safely absent only at times longer than those characterizing the jitter. A simple method is proposed to eliminate it. It is sufficient to average the signals in each time bin and replace bin averaged times τ or τr by theory imposed times L71 + ] 95 ^_` Eliminating jitter induced perturbations is unexpectedly easy. The present theory is believed to be an exact theory, and the jitter problem an exactly soluble XFEL problem.

Figure 1 :

 1 Figure 1: Schematic presentation of the experimental setting. Basic equation describing a jitter perturbed XFEL signal ΔS(10).

Figure 2 :

 2 Figure 2: Dependence of the XFEL signal on the reaction rate τr. This effect is important for fast processes (red) and slow processes (blue). β is equal to τ 2 XFEL.

Figure 3 :

 3 Figure 3: Dependence of the XFEL signal on the jitter variable.

TABLE 1

 1 The process under study evolves on a 300 fs time scale and the duration of the incident XFEL pulses, τXFEL, is of 100 fs

	τjitter (in fs)	Reduced reaction time (in fs)
	300	95
	200	134
	100	212
	80	234
	60	257
	10	298


Chau-Phi Phi Dinh

Alexia Ville

Konstantin Neukirch

Guillaume Viault

Veronika Temml

Andreas Koeberle

Oliver Werz

Daniela Schuster

Hermann Stuppner

Pascal Richomme

Jean-Jacques Helesbeux
email: jean-jacques.helesbeux@univ-angers.fr

Denis Séraphin

Structure-based design, semi-synthesis and anti-inflammatory activity of tocotrienolic amides as 5-lipoxygenase inhibitors

Keywords: Inflammation, 5-lipoxygenase, vitamin E, molecular docking, semi-synthesis, leukotrienes

I. Introduction

Inflammation is an adaptive response of the immune system triggered by exogenous harmful stimuli or damaged tissues to maintain homeostasis of the body [1]. This process is involved in the development of various pathologies, e.g. asthma, cardiovascular diseases, some types of cancer, and metabolic disorders [START_REF] Busse | Mechanisms of asthma[END_REF][START_REF] Hansson | Inflammation, Atherosclerosis, and coronary artery disease[END_REF][START_REF] Mantovani | Cancer-related inflammation[END_REF][START_REF] Hotamisligil | Inflammation and metabolic disorders[END_REF]. Inflammatory lipid mediators play a key role in the cascade response including the accumulation of leukocytes and the leakage of plasma from small vessels to inflamed tissues. 5-Lipoxygenase (5-LO)-derived leukotrienes (LTs) represent a class of pro-inflammatory lipid mediators derived from arachidonic acid (AA) [START_REF] Samuelsson | Leukotrienes and lipoxins: structures, biosynthesis, and biological effects[END_REF].

5-LO, a non heme iron-containing dioxygenase, is the key enzyme in LT biosynthesis which catalyses the oxidation of AA at C-5 position, yielding the intermediate (S)-5hydroperoxyeicosatetraenoic acid , and its dehydration to leukotriene A4 (LTA4) [START_REF] Rådmark | 5-Lipoxygenase, a key enzyme for leukotriene biosynthesis in health and disease[END_REF]. This derivative is rapidly transformed by LTA4 hydrolase to LTB4 or by microsomal glutathione-S-transferase to LTC4 and then further metabolized to the cysteinyl-LTs LTD4 and LTE4.

Due to the importance of LTs in the pathogenesis of inflammation-related diseases, 5-LO has been identified as a key target for the development of new therapeutics [8]. Despite intensive research over the past 30 years in order to find selective and potent 5-LO inhibitors, zileuton, which was approved by the FDA in 1996, is the only drug targeting this enzyme [START_REF] Carter | 5-lipoxygenase inhibitory activity of zileuton[END_REF][START_REF] Kaitin | The new drug approvals of 1996, 1997, and 1998: Drug development trends in the user fee era[END_REF].

Besides, numerous synthetic agents as well as naturally occurring compounds have been identified as 5-LO inhibitors, but most of them were neither sufficiently active nor selective against 5-LO, lacked in vivo efficiency, and/or were afflicted with severe side effects [START_REF] Pergola | 5-Lipoxygenase inhibitors: a review of recent developments and patents[END_REF].

In the frame of the Drugs from Nature Targeting Inflammation (DNTI) program, antiinflammatory vitamin E derivatives were identified [START_REF] Waltenberger | Drugs from nature targeting inflammation (DNTI): A successful Austrian interdisciplinary network project[END_REF][13][START_REF] Alsabil | Semisynthetic and natural garcinoic acid isoforms as new mPGES-1 inhibitors[END_REF]. Originally discovered in 1922 by Evans and Bishop, vitamin E is an essential fat-soluble vitamin encompassing 8 naturally occurring compounds classified in 2 subfamilies, namely tocopherols and tocotrienols [START_REF] Evans | On the existence of a hitherto unrecognized dietary factor essential for reproduction[END_REF][START_REF] Pennock | A reassessment of tocopherol chemistry[END_REF].

Endogenous metabolites of vitamin E selectively inhibited the biosynthesis of 5-LO-derived lipid mediators without impairing the production of 15-LO-derived leukotrienes, key mediators involved in the resolution phase of inflammation. Among them, natural δ-garcinoic acid (δ-GA, 1) (scheme 1), an ω-oxidized tocotrienol, inhibited human recombinant 5-LO and LTs biosynthesis by human primary polymorphonuclear leukocytes (PMNL) (IC50 = 57 ± 9 nM and 345 ± 73 nM, respectively) [START_REF] Pein | Endogenous metabolites of vitamin E limit inflammation by targeting 5-lipoxygenase[END_REF]. Recently, this acid was also identified as a selective agonist of pregnane X receptor [START_REF] Bartolini | Garcinoic acid is a natural and selective agonist of pregnane X receptor[END_REF].

Due to its potency at low nanomolar concentrations, δ-GA (1) was selected as a hit to develop further 5-LO inhibitors as well as to investigate the structure-activity relationships (SAR) of this class of compounds. First, the phenolic function of 1 was modified to give ester or ether derivatives, but a complete loss of inhibitory activity was observed (data not shown).

Therefore, this phenolic function is essential for 5-LO inhibition. Next, modulation of the acidic ω-function of 1 was investigated. On one hand, reduction of carboxylic acid to the corresponding primary alcohol led to a less active compound (IC50 = 147 ± 54 nM). On the other hand, pull-down experiment with immobilized-GA using Toyopearl AF Amino 650 allowed the fishing of 5-LO. Moreover, tocotrienols classically underwent side-chain degradation starting with ω-oxidation followed by a series of β-oxidation leading to shortchain metabolites excreted into urine [START_REF] Galli | Emerging aspects and new directions[END_REF]. Thus, chemical modification of terminal carboxylic acid might limit this process and enhance tocotrienol half-life. This prompted us to design a series of new garcinamides and to evaluate their 5-LO inhibitory activity.

In this paper, a molecular docking study, relying on the preliminary identification of a new allosteric binding site, was performed using an in-house database of vitamin E derivatives to build a semi-quantitative IC50 prediction workflow [START_REF] Pein | Endogenous metabolites of vitamin E limit inflammation by targeting 5-lipoxygenase[END_REF]. Then, a concise semi-synthesis of new garcinamides is described. Moreover, their inhibitory activity against 5-LO in cell-free and cell-based assays is evaluated, and SAR are discussed.

II. Results and discussion

Molecular docking

The combination of molecular docking simulations and site-directed mutagenesis studies reported previously showed the importance of Trp102 within the novel allosteric binding site of 5-LO [START_REF] Pein | Endogenous metabolites of vitamin E limit inflammation by targeting 5-lipoxygenase[END_REF]. Trp102 is located between the regulatory C2-like and the catalytic domains (Figure 1). Its indole ring is bulked in the cavity formed by these two domains and surrounded by other amino acids such as Gln15 and Asp170. The cavity is stretched toward Val110. Finally, it is defined by 11 residues from both domains of 5-LO. δ-GA 1 has been docked into this cavity using default parameters of GOLD [START_REF] Verdonk | Improved proteinligand docking using GOLD[END_REF]. Its best-ranked pose showed two intermolecular hydrogen bonds: one involved the ligand's phenolic oxygen and the NH of the indole of Trp102; the other linked the amide function of Val110's backbone and the ligand's carbonyl group. Additionally, the phytyl-like side chain and both methyl substituents of the chromanol formed hydrophobic interactions with Val110, His130, Lys133, Tyr383, and Arg401. Among the in-house tocotrienol library already evaluated against 5-LO (cell-free) assay, 17 derivatives, including δ-GA 1, exhibiting IC50 values ranging from 50 nM to 1722 nM were selected to build the training set (Supplementary data). These compounds were then docked into the allosteric binding site using the workflow previously used (see above) to optimize the in silico model of 5-LO. The output fitness scores calculated by the built-in CHEMPLP scoring function in GOLD -an empirical scoring function that takes into account the contribution of hydrogen bonds, non-polar interactions and metal chelation energy calculated from the distance of involved heavy atoms -did not significantly vary among the investigated compounds [START_REF] Korb | Empirical scoring functions for advanced proteinligand docking with PLANTS[END_REF]. Moreover, no linear correlation between these scores and the measured pIC50 values of these compounds could be established. Judging from the scoring function, a strong affinity for the allosteric binding site was predicted for all compounds. This in silico result was not in accordance with biological data that in general cannot often be directly translated to binding affinity, since other effects, like solubility or off-target interactions may prevent the molecule from reaching the intended binding site. However, aiming for a semi-quantitative structure-activity relationship, the workflow was refined, and the scoring function was modified to reflect the experimentally established importance of key hydrogen bonds.

In a detailed analysis of the docking results, we found that poses with H-bonds were calculated only for six compounds out of the 17 derivatives from the training set. The calculation run by this first model mainly took into account the hydrophobic interactions with residues Val110, Lys133 and Tyr383, leaving only a very limited contribution of hydrogen bonds to the fitness score. Besides, the lack of repulsion force observed in the best-ranked poses of all 17 compounds led to unexpectedly high fitness scores regarding to biological data. Thus, docking parameters were modified to increase the contribution of hydrogen bonds in the calculation. An advanced setting, "Protein HBond", from GOLD docking algorithm is dedicated to search solutions that featured intermolecular hydrogen bonds involving pre-defined protein atoms. The exhaustive analysis of docking poses of the training set allowed the identification of five structural moieties which formed hydrogen bonds with the ligands: the indole of Trp102, the carboxyl group of Glu134, the NH of Val110, the carboxyl group of Asp170 and the guanidine moiety of Arg401. Hence, the weight of each hydrogen bond contribution was tuned in order to emphasize the importance of each interaction leading to a correlation with R 2 = 0.86 (Figure 2) between the calculated and the measured pIC50 values (See experimental section IV.1). A first verification of this workflow with a test set of 20 vitamin E derivatives previously evaluated in cell-free 5-LO activity assay also yielded satisfactory correlation (R 2 = 0.65) (Supplementary Data). A second approach was developed with the distribution of the compounds from the test set into four groups depending on their pIC50 value: highly active (IC50 ≤ 100 nM), active (100 nM < IC50 ≤ 300 nM), moderately active (300 nM < IC50 ≤ 1000 nM), and inactive (IC50 > 1000 nM). Then, the compounds were also categorized into these groups based on the calculated pIC50 values, obtained from the compounds' fitness scores. A one-way ANOVA test showed that no significant difference between both distributions was observed (Supplementary Data). These two verifications validated the in silico workflow. It was thus applied to the design of 5-LO inhibitors based on the garcinoic acid scaffold. Despite their high anti-inflammatory activity through the inhibition of 5-LO, ω-oxidized vitamin E analogues, including δ-GA 1, undergo the classical oxidative metabolism of this class of derivatives [START_REF] Schmölz | Complexity of vitamin E metabolism[END_REF]. As a result, their bioavailability is questionable. Recently, the semi-synthesis and the anti-inflammatory activity of the benzylamide of δ-GA were reported [START_REF] Pein | Endogenous metabolites of vitamin E limit inflammation by targeting 5-lipoxygenase[END_REF]. This result prompted us to explore the pharmacological potential of other garcinamides. It can be assumed that these analogues could be less prone to the oxidative metabolism of the phytyllike side chain. Moreover, designing garcinamides opened the possibility to explore a chemical space with potentially new interactions with other amino acid residues from the 5-LO allosteric binding site. Therefore, the aforementioned docking procedure was used to predict the 5-LO inhibitory activity of in silico designed garcinamides. In accordance with the concentration ranges used in the cell-free 5-LO assay, the compounds from this virtual library were distributed to four groups of predicted activity: highly active (IC50 ≤ 100 nM), active (100 nM < IC50 ≤ 300 nM), moderately active (300 nM < IC50 ≤ 1000 nM), and inactive (IC50 > 1000 nM).

Among this virtual library of 117 garcinamides (Supplementary data), the docking results highlighted 24 promising compounds predicted as moderately to highly active. They were semi-synthesized and subjected to biological assays to validate the molecular model and to understand further the SARs (Table 1).

Semi-synthesis

δ-GA 1 was extracted from Garcinia kola nuts according to a previously described procedure [START_REF] Ville | Efficient semisynthesis of natural δ-(R)-tocotrienols from a renewable vegetal source[END_REF]. αand β-GA isoforms 2 and 3 were prepared in accordance with a previously established two-step method, with some optimizations giving 80 and 64% overall yield respectively [START_REF] Alsabil | Semisynthetic and natural garcinoic acid isoforms as new mPGES-1 inhibitors[END_REF]. It is worth mentioning that access to the β-isoform is a one-pot procedure and the reduction of intermediate is achieved at reflux in ethanol (Scheme 1).

Scheme 1: Semi-synthesis of αand β-garcinoic acids.

i/ (CH2O)n (20 eq), TMDA (20 eq), dioxane 140 °C, MW, 40 min; ii/ (CH2O)n (3 eq), TMDA (3 eq), EtOH 120 °C, MW,20 min;iii/ NaBH3CN (30 eq),EtOH,reflux,16 h;iv/ NaBH3CN (8 eq),EtOH,reflux,14 h. Amide synthesis involved the activation of the carboxylic function by an electron-withdrawing group and the attack of an amino group onto the activated form to give the expected function [START_REF] Sheehan | A new method of forming peptide bonds[END_REF][START_REF] Valeur | Amide bond formation: beyond the myth of coupling reagents[END_REF]. Various coupling agents were evaluated for the reaction of δ-GA (1) with 4methoxybenzylamine. Among them, O-(benzotriazol-1-yl)-1,1,3,3-tetramethyluronium hexafluorophosphate (HBTU) was chosen [START_REF] Knorr | New coupling reagents in peptide chemistry[END_REF]. The three isoforms of GA were coupled with 8 commercially available amines to afford, sometimes after tedious purification, 24 garcinamides 4 -27 (29 -88% yield) (Scheme 2).

Scheme 2: Synthesis of the garcinamide library.

Evaluation of 5-LO inhibitory activities in cell-free and cell-based assays

The effect of garcinamides on 5-LO was studied in a cell-free assay using the human recombinant enzyme and in a cell-based assay with activated human PMNL, which convert the supplemented substrate arachidonic acid into the 5-LO products LTB4, its isomers and 5-H(P)ETE. We expect substantial differences between the potency of garcinamides in cellfree and cell-based assays because SARs for 5-LO inhibition likely overlay with those for cellular uptake or retention, as recently shown for long-chain vitamin E metabolites [START_REF] Pein | Endogenous metabolites of vitamin E limit inflammation by targeting 5-lipoxygenase[END_REF].

Calculated and measured IC50 values of GA isoforms (1, 2, 3) and garcinamides 4 -27 are reported in Table 1, with zileuton as the reference [START_REF] Carter | 5-lipoxygenase inhibitory activity of zileuton[END_REF]. (11/24).

Fifteen out of these 24 compounds exhibited experimental IC50 values below 300 nM, which confirmed the importance of the carbonyl for 5-LO inhibition by GA analogues. This finding could be explained through an H-bond interaction between the carbonyl group and the amide function of Val110 (Figure 1 and3).

The docking results showed a π-π interaction between the phenyl moiety of 4 and the imidazole of His130 leading to a higher affinity of 4 in comparison to the corresponding cyclohexyl analogue 11 (Figure 3). 27) > 1000 nM -Table 1). creating a new favourable H-bond between the pyridyl nitrogen and the primary amine function of Lys133 (Figure 4). The substitution of the phenyl moiety with a methoxy group was then examined at ortho- [START_REF] Rådmark | 5-Lipoxygenase, a key enzyme for leukotriene biosynthesis in health and disease[END_REF][START_REF] Evans | On the existence of a hitherto unrecognized dietary factor essential for reproduction[END_REF][START_REF] Ville | Efficient semisynthesis of natural δ-(R)-tocotrienols from a renewable vegetal source[END_REF], meta- (8,[START_REF] Pennock | A reassessment of tocopherol chemistry[END_REF][START_REF] Sheehan | A new method of forming peptide bonds[END_REF], and para- [START_REF] Carter | 5-lipoxygenase inhibitory activity of zileuton[END_REF][START_REF] Pein | Endogenous metabolites of vitamin E limit inflammation by targeting 5-lipoxygenase[END_REF][START_REF] Valeur | Amide bond formation: beyond the myth of coupling reagents[END_REF] positions. Independent of the position of the alkoxyl group, the inhibitory activity remained close to that of the non-substituted phenyl derivatives in the α-and δ-series [START_REF] Mantovani | Cancer-related inflammation[END_REF][START_REF] Waltenberger | Drugs from nature targeting inflammation (DNTI): A successful Austrian interdisciplinary network project[END_REF], whereas the corresponding β-garcinamides 23, 24

and 25 were 4-fold more active than 20.

The H-bond interaction between the NH of garcinamides and Glu134 was regularly observed. In order to investigate the importance of this structural parameter, tertiary amides 5, 13 and 21 were docked, semi-synthesized and evaluated. The docked poses of these molecules showed a high variability of conformations in terms of position within the binding site and interactions with crucial residues. Consequently, the model led to predictions of IC50

values with a different level of confidence. Thus, despite a satisfactory correlation between in silico and biological results for amide 21, compound 5 was eventually more active than predicted. Nevertheless, biological results pointed out that these N,N-benzylethylamides 5

and 13 were as active as the corresponding benzylamides 4 and 12 while the IC50 of 21 was slightly lower than that of 20. Hence, the H-bond between the NH of garcinamides and Glu134 was not crucial for the inhibitory activity as its loss might be compensated by alternative hydrophobic interactions involving the N-ethyl group. This hypothesis could not be supported by docking studies because of the high variability of conformations previously mentioned. The same trend was observed also for the other set of tertiary amides 10, 18, and 26 that exhibited IC50 values ranging from 131 ± 17 to 265 ± 13 nM.

All garcinamides were additionally evaluated for inhibition of 5-LO in intact human PMNL, a cell-based assay which takes different cellular uptake/retention efficacies into account.

Benzylamide 12 (α-series) was 10-fold more active than α-GA while the other benzylamides 4 (δ-series) and 20 (β-series) were as active as δ-and β-GA, respectively. On the other hand, cyclohexyl analogues 11, 19 and 27 were all inactive (IC50 > 3000 nM). These results highlighted that the phenyl ring is not only favourable for 5-LO inhibition but also for providing access to the cellular target site. Replacing this ring with a 3-pyridyl did not improve the potency of the corresponding analogues (6, 14, and 22). The ortho-and meta-substitution of the phenyl ring with a methoxy group was detrimental as the resulting amides in all series ( δ, α, and β) were inactive. However, the presence of para-methoxy substituent was tolerated with amides 9 and 17, yielding 2-fold and 6-fold more active derivatives than the parent GA, respectively. Most of δ-garcinamides (4 -11) were comparably active (187 nM < IC50 < 561 nM) to the reference δ-GA 1 (IC50 = 345 ± 73 nM) in PMNL. Note that both reference 1 and compounds 4 -11 of the δ-series are substantially less potent in the cell-based as compared to the cell-free assay. This trend was not found with α-garcinamides (12 -19), as six out of eight compounds from this series exhibited comparable inhibitory activity in both assays. This suggests superior cellular uptake, retention, subcellular distribution to target sites (nuclear membranes), and/or stability of α-series derivatives.

Lipoxygenase isoenzymes are involved in the metabolism of AA and other polyunsaturated fatty acids leading not only to pro-but also anti-inflammatory lipid mediators (e.g., lipoxins and resolvins). In the current study, we analysed formation of 15-H(P)ETE, a 15-LO-derived precursor of specialized pro-resolving lipid mediators, which actively terminate the inflammatory reaction and promote pathogen clearance and tissue remodelling [START_REF] Serhan | Resolution phase of inflammation: novel endogenous anti-inflammatory and proresolving lipid mediators and pathways[END_REF].

Interestingly, most garcinamides led to an increased formation of 15-HETE (Figure 5) [START_REF] Serhan | Pro-resolving lipid mediators are leads for resolution physiology[END_REF].

Whether this effect resulted from a specific activation of 15-LO product biosynthesis or simply from substrate channelling from 5-LO to 15-LO needs further investigations. Such complementary study may also explore the consequences on in vivo levels of specialized pro-resolving lipid mediators during the resolving phase of inflammation.

III. Conclusion

Here, we developed a docking-based semi-quantitative predictive model to rationalize the design of vitamin E derivatives as 5-LO inhibitors. A training set of 17 compounds previously evaluated as 5-LO inhibitors was used to build the model exhibiting a satisfactory correlation between calculated and measured pIC50 with R 2 = 0.86. A virtual library of 117 garcinamides was screened. Among them, 24 derivatives were selected, semi-synthesized, and biologically evaluated. The comparison between calculated and measured pIC50 proved the accuracy of the model with a success rate of 46%. Hence, this study highlighted novel important structural features of an allosteric inhibitor binding site of 5-LO, involving e.g. Val110, His130, Glu134. It also allowed to explore further the chemical space for GA analogues and to identify three new active garcinamides [START_REF] Carter | 5-lipoxygenase inhibitory activity of zileuton[END_REF][START_REF] Waltenberger | Drugs from nature targeting inflammation (DNTI): A successful Austrian interdisciplinary network project[END_REF][START_REF] Pein | Endogenous metabolites of vitamin E limit inflammation by targeting 5-lipoxygenase[END_REF] from the α-and δseries bearing either a N-benzyl or a N-4-methoxybenzyl moiety. These amides exhibited a significant 5-LO inhibitory activity in both cell-free and cell-based assays. They are promising candidates for further pre-clinical development, with potentially superior stability and bioavailability as compared to the parent long-chain aliphatic acids. Moreover, the strategy reported here promises straightforward in silico design for other series of oxidized vitamin E analogues targeting 5-LO.

IV. Experimental section

Molecular docking

The molecular docking simulation was conducted with GOLD 5.6.3 (CCDC, Cambridge, UK) [START_REF] Verdonk | Improved proteinligand docking using GOLD[END_REF]. The built-in CHEMPLP scoring function was used to rescore the outputted poses ( 10best-scored poses were kept for each compound). The stable crystallographic tri-dimensional structure of 5-LO was downloaded from the Protein Data Bank (PDB entry 3O8Y) [29][30].

Four in silico mutations were inserted in order to return to the 5-LO wild-type sequence: E13W, H14F, G75W, and S76L. The residues were exchanged and the structure was energetically minimized in Discovery Studio 3.5 (Biovia,San Diego,CA) [START_REF] Guner | Pharmacophore Modeling and three dimensional database searching for drug design using catalyst: recent advances[END_REF]. Hydrogen atoms were added with GOLD, using default settings. The binding site was constituted by 11 amino acid residues: Gln15, Arg101, Tyr81, Tyr100, Arg101, Trp102, Val110, Glu134, Asp170, Arg401 and Glu622. Hydrogen-bond constraints were applied to Trp102-Hε1, Val110-HN, Glu134-Oε1, Asp170-Oδ1, Arg401-HH2, and Arg401-Hε with the constraint weight varying from 7 to 40 and the minimum H-bond geometry weight at 0.005 The ligands were allowed to detect internal H-bonds, flip pyramidal N, and flip amide bonds. The correlation as well as the linear regression equation between the calculated pIC50, converted from fitness score, and the measured pIC50 values was computed using Graphpad Prism 8.3.0. Protein-ligand interactions of docking poses were analyzed using LigandScout 4.3 (Inteligand,Vienna,AT) [START_REF] Wolber | LigandScout: 3-D Pharmacophores derived from protein-bound ligands and their use as virtual screening filters[END_REF].

Semi-synthesis

General experimental procedures: all solvents were dried and distilled before use. Reaction were performed in an inert nitrogen atmosphere. Unless otherwise stated, materials purchased from commercial suppliers were used without further purification. Ultrasoundassisted extraction was performed on hundred-gram scale with a PEX03 Sonifier (REUS, Contes, France). Reactions under microwave irradiation were performed in a Monowave 300 (Anton Paar), equipped with the MAS 24 autosampler, using borosilicate glass vials with snap caps. IR spectra were recorded on a Thermo Scientific Nicolet iS5 ATR-FTIR spectrometer and are reported in terms of frequency of absorption (cm -1 ). 1 H-NMR and 13 C-NMR spectra were recorded on a JEOL 400 MHz NMR spectrometer in deuterated solvents and calibrated using the residual undeuterated solvent resonance as internal reference.

Chemical shifts δ are given in ppm and coupling constants J in Hz. Mass spectrometry analyses were performed on a JMS-700 (JEOL) double-focusing mass spectrometer with reversed geometry, equipped with a pneumatically assisted ESI source. Column chromatography was performed by using silica gel 60 Å (particle size 40-63 μm) from Fisher Scientific. Flash chromatography purifications using prepacked columns (silica, 4 to 330 g) were carried out on a CombiFlash Rf-200 apparatus equipped with a gradient pump, a column station with a DASi introduction system, a multiwavelength UV detector, a fraction collector, and appropriate software to control the device. HPLC analyses were performed with a Waters Alliance HPLC system (Milford, CT, USA) equipped with a quaternary HPLC pump, degasser, autosampler, and UV detector.

Plant material: G. kola nuts were purchased from RIVEX SARL, Angers, France, in January 2016. Plant identification was verified by one of the authors (P.R.). A voucher specimen (GK201601) was deposited at the SONAS laboratory, University of Angers.

Extraction and purification of δ-GA (1):

The extraction, purification and identification of δ-GA were achieved following the procedure previously published [START_REF] Ville | Efficient semisynthesis of natural δ-(R)-tocotrienols from a renewable vegetal source[END_REF].

Semi-synthesis of α-GA (2): (2E,6E,10E)-13-((R)-6-hydroxy-2,5,7,8-tetramethylchroman-2-yl)-2,6,10-trimethyltrideca-2,6,10-trienoic acid ( 2): To a solution of δ-GA (1) (400 mg, 0.94 mmol, 1 eq) in dioxane ( 14mL), TMDA (2.56 mL, 18.80 mmol, 20 eq) and paraformaldehyde (569 mg, 18.80 mmol, 20 eq) were added. The reaction mixture was heated at 140 °C for 20 min under microwave irradiation. After cooling to room temperature, the solvent was evaporated to dryness. The crude product was dissolved in ethanol (14 mL), and treated with NaBH3CN (1772 mg, 28.20 mmol, 30 eq) . The reaction mixture was heated under reflux for 14 h. Then it was acidified to pH 1 by adding HCl 1N and was extracted with diethyl ether (3 x 100 mL). The combined organic layers were washed with water (2 x 100 mL), brine (100 mL) then dried over Na2SO4, and evaporated to dryness. The crude product was purified by flash column chromatography on silica gel, eluting with petroleum ether/acetone (9:1) mixture to afford the desired product as a light-yellow oil (343 mg, 80% yield); Rf = 0.45 (DCM/MeOH 9:1); 1 H NMR (400 MHz, CDCl3) δ 6.87 (td, J = 7.2, 1.0 Hz, 1H), 5.13 (t, J = 6.6 Hz, 2H), 2.61 (t, J = 6.8 Hz, 2H), 2.28 (dd, J = 14.9, 7.4 Hz, 2H), 2.16 -1.95 (m, 17H), 1.83 -1.73 (m, 5H), 1.67 -1.49 (m, 8H), 1.25 (s, 3H); 13 C NMR (100 MHz, CDCl3) δ 172. 7, 145.6, 145.0, 144.7, 135.0, 133.8, 126.9, 125.4, 124.7, 122.8, 121.2, 118.6, 117.5, 74.4, 39.7, 39.6, 38.2, 31.7, 27.7, 26.7, 23.9, 22.3, 20.9, 16.1, 16.0, 12.4, 12.2, 11.9, 11.4; HRMS (FAB) m/z calcd for C29H42O4 [M] +. 454.3078, found 454.3084; IR (neat) νmax 3489, 2965, 2851, 1680, 1452, 1240, 927 cm -1 .

Semi-synthesis of β-GA (3): (2E,6E,10E)-13-((R)-6-hydroxy-2,5,8-trimethylchroman-2-yl) -2,6,10-trimethyltrideca-2,6,10trienoic acid (3): To a solution of δ-GA (1) (396 mg, 0.93 mmol, 1 eq) in ethanol (12 mL), TMDA (0.38 mL, 2.79 mmol, 3 eq) and paraformaldehyde (84 mg, 2.79 mmol, 3 eq) were added. The reaction mixture was heated at 120 °C for 20 min under microwave irradiation.

Then NaBH3CN (468 mg, 7.44 mmol, 8 eq) was added and the reaction mixture was heated under reflux for 14 h. It was acidified to pH 1 with HCl 1N and was extracted with diethyl ether (3 x 100 mL). The combined organic layers were washed with water (2 x 100 mL), brine (100 mL) then dried over Na2SO4, and evaporated to dryness. The crude product was purified by flash chromatography column on silica gel, eluting with petroleum ether/acetone mixture to afford the desired product as a yellow oil (261 mg, 64% yield); Rf = 0.45 (DCM/MeOH 9:1); 1 H NMR (400 MHz, CDCl3) δ 6.88 (td, J = 7.2, 1.1 Hz, 1H), 6.48 (s,1H),5.13 (t,J = 6.7 Hz,2H),2.61 (t,J = 6.8 Hz,2H),2.28 (dd,J = 14.9,7.2 Hz,2H),14H),5H),8H),1.25 (s,3H); 13 C NMR (101 MHz, CDCl3) δ 173. 1,146.0,145.8,145.1,135.0,133.8,127.0,125.3,124.6,124.2,120.4,119.3,115.5,74.4,39.7,39.4,38.2,31.6,27.7,26.6,23.9,22.3,20.9,16.1,16.0 (2C),12.2,11.1;HRMS (FAB) m/z calcd for C28H40O4 [M] +. 440.2921, found 440.2917; IR (neat) νmax 3397, 2922, 2581, 1682, 1641, 1414, 1229, 915 cm -1 .

General procedure for amide synthesis from GA isoforms:

To a stirred solution of GA isoform (α, β or δ) (0.12 mmol) in DMF (3 mL) were added an appropriate amine derivative (0.18 mmol, 1.5 eq), diisopropylethylamine (0.36 mmol, 3 eq) and HBTU (0.18 mmol, 1.5 eq). The reaction mixture was stirred at room temperature for 18 h. Then the reaction was quenched with water (1 mL). The resulting mixture was extracted with diethyl ether (3 x 20 mL). The combined organic layers were washed with water (2 x 20 mL), brine (20 mL) then dried over Na2SO4, and evaporated to dryness. The crude product was purified either by reverse-phase flash column chromatography, eluting with water/MeOH 4): δ-GA 1 reacted with benzylamine to give product 4 (88% yield) as a brown oil; Rf = 0.26 (PE/acetone 8:2); 1 H NMR (400 MHz, CDCl3) δ 7.36 -7.28 (m, 5H), 6.50 (d, J = 2.6 Hz, 1H), 6.40 (d, J = 2.7 Hz, 1H), 6.36 (t, J = 7.2 Hz, 1H), 6.08 (t, J = 5.1 Hz, 1H, NH), 5.96 (s, 1H, OH), 5.09 (q, J = 6.2 Hz, 2H), 4.51 (d,J = 5.6 Hz,2H), 2.67 (t,J = 6.7 Hz,2H),2.19 (dd,J = 7.4,15.0 Hz,2H),11H),5H), (m, 8H), 1.27 (s, 3H); 13 C NMR (100 MHz, CDCl3) δ 169. [START_REF] Rådmark | 5-Lipoxygenase, a key enzyme for leukotriene biosynthesis in health and disease[END_REF]148.5,145.6,138.4,136.8,134.8,134.1,130.5,128.9 (2C),128.0 (2C),127.6,127.2,125.0,124.7,121.2,115.9,112.8,75.3,44.0,39.6,39.2,38.5,31.5,27.2,26.5,24.4,22.6,22.3,16.2,16.1,15.9,12.9;HRMS (FAB) m/z calcd for C34H45NO3 [M] +. 515.3399, found 515.3387; IR (neat) νmax 3328, 2924, 2850, 2360, 2342, 1659, 1617, 1528, 1469, 1219, 933, 698 cm -1 .

(2E,6E,10E)-N-benzyl-N-ethyl-13-((R)-6-hydroxy-2,8-dimethylchroman-2-yl)-2,6,10trimethyltrideca-2,6,10-trienamide (5): δ-GA 1 reacted with N-benzylethanamine to give product 5 (60% yield) as a brown oil; Rf = 0.34 (PE/acetone 8:2); 1 H NMR (400 MHz, CDCl3) δ 7.35 -7.22 (m, 5H), 6.48 (d, J = 2.9 Hz, 1H), 6.38 (d, J = 2.9 Hz, 1H), 5.53 (td, J = 7.2, 1.5 Hz, 1H), 5.06 (t, J = 6.8 Hz, 2H), 4.60 (s, 2H), 3.30 (s, 2H) 2852,1659,1619,1525,1427,1378,1253,1087,711 2, 157.7, 145.6, 144.8, 135.8, 135.0, 134.2, 130.9, 130.0, 128.9, 126.6, 125.0, 124.7, 122.7, 121.4, 120.9, 118.8, 117.4, 110.4, 74.4, 55.5, 39.8, 39.7, 39.5, 38.6, 31.7, 27.1, 26.7, 24.0, 22.4, 20.9, 16.1, 16.0, 12.8, 12.4, 11.9, 11.5 145.6, 144.7, 140.2, 136.2, 135.0, 134.2, 130.8, 129.9, 125.1, 124.7, 122.7, 121.3, 120.2, 118.8, 117.4, 113.6, 113.0, 74.4, 55.4, 43.9, 39.7, 38.6, 31.7, 27.1, 26.7, 23.9, 22.4, 20.9, 16.1, 16.0, 12.9, 12.4, 11.9, 11.5 4, 159.1, 145.5, 144.8, 136.1, 134.9, 134.1, 130.8, 130.7, 129.3 (2C), 125.1, 124.7, 122.7, 121.4, 118.8, 117.4, 114.2 (2C), 74.4, 55.4, 43.4, 39.7, 39.5, 38.6, 31.7, 27.1, 26.7, 23.9, 22.3, 20.9, 16.1, 16.0, 22.3, 20.9, 16.1, 16.0 (2C), 12.9, 11.2; HRMS (FAB) m/z calcd for C35H53NO3 [M] +. 535.4025 found 535.4018;IR (neat) νmax 3328, 2922IR (neat) νmax 3328, , 2851IR (neat) νmax 3328, , 1659IR (neat) νmax 3328, , 1619IR (neat) νmax 3328, , 1533IR (neat) νmax 3328, , 1414, 1230 cm -1 .

Biological assays

Determination of purified 5-LO activity

The plasmid pT3-5-LO was transformed into E. coli Bl21 (DE3) cells to express human

Determination of 5-LO product formation in activated PMNL

Leukocyte concentrates were provided by the Institute for Transfusion Medicine, University Hospital Jena (Germany). The protocols for experiments were approved by the ethical commission of the Friedrich-Schiller-University Jena. Blood was freshly collected from fasted (12 h) adult male and female healthy volunteer, with informed consent. These subjects donated blood every 8 -12 weeks, had no apparent infection, inflammatory conditions, or current allergic reactions (according to prior physical inspection by a clinician) and had not taken antibiotics or anti-inflammatory drugs for at least 10 days prior to blood donation.

Venous blood was centrifuged at 4,000 x g/20 min/20 °C in order to concentrate leukocytes,

Figure 1 :

 1 Figure 1 : Molecular docking pose of δ-GA 1 in the allosteric binding site of 5-LO. Hydrogen bonds are shown as red and green arrows, hydrophobic contacts as yellow spheres.

Figure 2 :

 2 Figure 2 : Linear regression between measured and calculated pIC50 values of both training and test sets.

  It was validated by biological data for 4 and 11 in the δseries (IC50 (4) = 50 ± 23 nM vs IC50 (11) = 129 ± 25 nM), and similarly for the analogues in the αand β-series (IC50 (12) = 595 ± 208 nM vs IC50 (19) = 998 ± 157 nM, and IC50 (20) = 538 ± 107 nM vs IC50 (

Figure 3 :

 3 Figure 3: The best-docked pose of compound 4 (above) and 11 (below). Hydrogen bonds are shown as red and green arrows, hydrophobic contacts as yellow spheres, and π-π interaction as blue circle.Interestingly, the pyridyl derivative 6 had a similar IC50 value than 4 (77 ± 6 and 50 ± 23 nM respectively) while the heterocyclic amides 14 and 22 of the α-and β-series were slightly more active than the respective carbocyclic amides 12 and 20. This discrepancy between different methyl substitution patterns of the chromanol could be explained by steric clashes of

Figure 4 :

 4 Figure 4: The best-docked pose of compound 14. Hydrogen bonds are shown as red and green arrows, hydrophobic contacts as yellow spheres.

Figure 5 :

 5 Figure 5: Percentage of 15-LO products formed by activated PMNL in the presence of garcinoic acid isoforms (1, 2 and 3) or garcinamides (4 -27), as compared to vehicle (DMSO) control (100%). Data were expressed as means ± SEM, n = 3 -4. P values vs vehicle lower than 0.0001 (Student's t-test) were obtained for all 27 compounds.

(

  50:50 to 0:100) mixture or by flash column chromatography eluting with PE/Acetone (80:20 to 60:40) mixture to afford the desired product. (2E,6E,10E)-N-benzyl-13-((R)-6-hydroxy-2,8-dimethylchroman-2-yl)-2,6,10-trimethyltrideca-2,6,10-trienamide (

recombinant 5 -

 5 LO, which was purified by affinity chromatography using an ATP-agarose column. In brief, E. coli was lysed by incubation in 50 mM triethanolamine/HCl at pH 8.0 with EDTA (5 mM), soybean trypsin inhibitor (60 µg/mL), 1 mM phenylmethylsulphonyl fluoride, and lysozyme (500 µg/mL). After homogenization by sonication (3 x 15 s) and centrifugation (10,000 x g) for 15 min, the supernatant was centrifuged again at 40,000 x g for 70 min at 4 °C. The supernatant was then applied into an ATP-agarose column and the column was washed first with PBS buffer (pH 7.4) plus 1 mM EDTA, then with 50 mM phosphate buffer (pH 7.4) 0.5 M NaCl, 1 mM EDTA, and finally with 50 mM phosphate buffer (pH 7.4). The 5-LO enzyme was eluted with 50 mM phosphate buffer (pH 7.4), 1 mM EDTA, and 20 mM ATP.Purified 5-LO (0.5 µg) in 1 mL of PBS buffer pH 7.4 containing EDTA (1 mM), and ATP (1 mM) was pre-incubated with test compounds or vehicle control (0.1% DMSO) for 10 min on ice and pre-warmed for 30 s at 37 °C. 5-LO production formation was started at 37 °C by adding 5 µL of AA (20 µM) and 5 µL of CaCl2 (2 mM). After 10 min of incubation, 1 mL of icecold methanol was added and formed 5-LO products (all-trans isomers of LTB4 and 5-H(P)ETE) were extracted using Milford, MA). 5-LO products were separated by RP-HPLC on a Nova-Pak C18 Radial-Pak column (5 × 100 mm, 4 µm, Waters) under isocratic conditions (73% methanol/27% water/0.007% trifluoroacetic acid) at a flow rate of 1.2 mL/min and detected at 235 and 280 nm. PGB1 was used as internal standard.

Table 1 :

 1

			Structures
						IC50 5-LO		IC50 PMNL
	Cpd				Predicted group*	[nM] (remaining activity (%)	Matched prediction	[nM] (remaining activity (%)
						at 1 µM)		at 3 µM)
		R1	R2	R3
	1	H	H	OH	I	57 ± 9		345 ± 73

Calculated and measured IC50 values. Data are expressed as means ± SEM,

were mainly assigned to group I. The corresponding α-isoforms 12 -19 belong to group II and III. Eventually, β-garcinamides

(20 -27)

were part of group II. Amides 4 -27 were evaluated for 5-LO inhibition (cell-free assay) and their measured IC50 values ranged from 50 ± 23 up to 1000 nM. Among these 24 compounds, the IC50 values were correctly predicted for 11 compounds homogeneously distributed over the groups I to III. This first predictive model built to categorize novel GA analogues into different 5-LO inhibitory activity ranges gave encouraging performances with a satisfactory prediction rate of 46%

  , 2.67(t, J = 6.8 Hz, 2H), 2.11 -(FAB) m/z calcd for C35H48N2O3 [M] +. 544.3665 found 544.3668; IR (neat) νmax 3297, 2921,

  cm -1 .

	(2E,6E,10E)-13-((R)-6-hydroxy-2,5,7,8-tetramethylchroman-2-yl)-N-(2-methoxybenzyl)-
	2,6,10-trimethyltrideca-2,6,10-trienamide	(15):	α-GA	2	reacted	with	(2-
	methoxyphenyl)methanamine to give product 15 (40% yield) as a yellow oil; Rf = 0.65
	(PE/acetone/DCM 7:2:1); 1 H NMR (400 MHz, CDCl3) δ 7.29 -7.24 (m, 3H), 6.94 -6.87 (m,
	2H), 6.29 (t, J = 6.7 Hz, 1H), 6.22 (t, J = 6.4 Hz, 1H), 5.11 (d, J = 2.6 Hz, 2H), 4.50 (d, J = 5.8
	Hz, 2H), 3.86 (s, 3H), 2.60 (t, J = 6.7 Hz, 2H), 2.21-1.93 (m, 19H), 1.82 -1.74 (m, 5H), 1.66
	-1.50 (m, 8H), 1.25 (s, 3H); 13 C NMR (100 MHz, CDCl3) δ 169.

V. Acknowledgements

The authors thank Ingrid Freuze for HRMS measurements of all molecules and Dimitri Bréard for semi-preparative HPLC assistance. C.P.D. received a PhD grant by the French Ministry of Higher Education, Research and Innovation (MESRI). J.J.H. was supported by MESRI and the French Ministry of Europe and Foreign Affairs through PHC fundings (AMADEUS 2017-18 N°38263PF, PROCOPE 2018-2019 N°40507RB). A.K. was supported by the German Research Council (GRK 1715, KO 4589/7-1) and the German Academic Exchange Service (57389523) paid from the German Federal Ministry of Education and Research. The work by O.W. was funded by the German Research Council (SFB 1278 Polytarget) and by the Free State of Thuringia and the European Social Fund (2016 FGR 0045).

VI. References

which were subjected to centrifugation on lymphocyte separation medium (LSM 1077, GE Healthcare, Freiburg, Germany). PMNL were recovered from the pellet after hypotonic lysis of erythrocytes.

Freshly isolated PMNL (5 x 10 6 cells) were resuspended in ice-cold PBS buffer plus glucose (1 mg/mL) at 4 °C, and CaCl2 (10 mM) was added. Suspensions were pre-incubated with test compounds or vehicle control (0.1% DMSO) for 10 min at 37 °C. 5-LO product formation was started by treatment with the Ca 2+ -ionophore A23187 (2.5 µM) and AA (20 µM). After 10 min of incubation, 1 mL of ice-cold methanol was added and formed 5-LO products (all-trans isomers of LTB4, 5-H(P)ETE and 12-HETE and 15-HETE) were extracted and analysed as described above.

Statistics

Data are expressed as mean ± S.E.M. IC50 values were graphically calculated from averaged measurements at 4 -5 different concentrations of the compound using GraphPad Prism


MD Andrada Chiron
email: andrada.chiron@aphp.fr

MD Hafida Gaouar

MD Jean-Eric Autegarden

MD Emmanuelle Amsler

MD, PhD Annick Barbaud

MD, PhD Angèle Soria

Allergy to third and second generation cephalosporins in confirmed penicillin allergic patients

Keywords: hypersensitivity reaction, penicillins, cephalosporins, cross-reactivity

Clinical implications box (35/40 words)

Clinically-relevant cross-reactivity between penicillins and third and second generation cephalosporins could be between 1% and 2%. In 234 confirmed penicillin-allergic subjects (180 immediate and 54 delayed-type hypersensitivity reactions) we found a cross-reactivity risk below 1%.

To the Editor: Beta-lactams (BLs) are a major cause of hypersensitivity reactions (HS) to drugs, both immediate (IHR) and delayed (DHR) [START_REF] Romano | Cross-Reactivity among Beta-Lactams[END_REF]. Historic risk of cross-reactivity to cephalosporins in penicillin-allergic patients (10-30%) was probably overestimated [START_REF] Liu | Cephalosporin and penicillin cross-reactivity in patients allergic to penicillins[END_REF][START_REF] Romano | Cross-Reactivity and Tolerability of Cephalosporins in Patients with IgE-Mediated Hypersensitivity to Penicillins[END_REF]. Cross-reactivity between penicillins and cephalosporins seems to be related mainly to side-chain similarities [START_REF] Romano | Cross-Reactivity among Beta-Lactams[END_REF], as administration of potential identical side-chain first (1GC) and second-generation cephalosporins (2GC) is associated with a HS risk exceeding 30% (1,2), whereas risk with dissimilar side-chain third generation cephalosporins (3GC) can be as low as 1% [START_REF] Liu | Cephalosporin and penicillin cross-reactivity in patients allergic to penicillins[END_REF].

However, skin testing (ST) followed by a drug provocation test (DPT) of negatively-tested compounds remains the gold standard [START_REF] Romano | Cross-Reactivity among Beta-Lactams[END_REF][START_REF] Liu | Cephalosporin and penicillin cross-reactivity in patients allergic to penicillins[END_REF].

Our objective was to assess allergy to 3GC and 2GC in penicillin-proven allergic patients.

We conducted a retrospective study including 234 adults with proven HS to penicillin, based on history according to EAACI criteria [START_REF] Demoly | Drug hypersensitivity: questionnaire. EAACI interest group on drug hypersensitivity[END_REF] and positive ST (immediate or delayed readings) to at least one penicillin, explored for 3GC and 2GC allergy (Online Repository, Tables E3 andE4).

The study group has a mean age of 52 years (range 17-93 years) and sex ratio F/M=1.7/1; respectively 180 patients (77%) and 54 patients (23%) with proven IHR and DHR to penicillin (Table 1). Six subjects among 240 evaluated were excluded because of lacking DPT at the time of the work-up (Figure 1).

The 234 patients reported 270 HS reactions (196 IHR and 74 DHR) : only one reaction for 203 (87%) and more than one for 31 (13%). Anaphylaxis [START_REF] Sampson | Second symposium on the definition and management of anaphylaxis: Summary report-Second National Institute of Allergy and Infectious Disease/Food Allergy and Anaphylaxis Network symposium[END_REF], acute or delayed urticaria and/or angioedema and cutaneous adverse drug reaction (CADR) were reported in respectively 118, 52 and 49 cases (Table 1). Although most DHR were benign maculopapular drug eruptions (56%), we report 5 severe CADR: two DRESS, two Acute Generalized Exanthematous Pustulosis and one Bullous drug reaction (Table 1).

All 234 patients had positive ST with amoxicillin (AX) and/or amoxicillin-clavulanic acid (AX-Clav), as follows: 84 (47%) on skin prick test (SPT) and 96 (53%) on intradermal ST (IDT) among IHR and 8 (15%) positive on patch test and 51 (95%) on delayed reading IDT among DHR respectively (5 positive for both) (Figure 1).

In 180 IHR penicillin patients, 409 negative ST were performed with 2GC cefuroxime (n=79) and 3GC (n=330) i.e ceftriaxone (n=154), cefpodoxime (n=172) and cefixime (n=4) (Figure 1). Only one patient among 80 (1.3%) IHR tested with cefuroxime (2GC) had positive immediate ST with cefuroxime and negative ST and DPT with cefpodoxime and ceftriaxone (3GC) (Figure 1 andTable E1).Among 54 patients with DHR to penicillin, 126 negative ST with 2GC (n=26) and 3GC (n=100) were performed i.e; ceftriaxone (n=48), cefpodoxime (n=50) and cefixime (n=2) (Figure 1). DPT were performed in all 234 patients: 18 had DPT only with 2GC cefuroxime 15 with one 3GC, 140 with two 3GC, 53 with one 2GC and one 3GC and 8 with two 3GC and one 2GC (Table E2). A total of 442 negative challenges were performed with 3GC i.e: ceftriaxone (n=159), cefpodoxime (n=198), cefixime (n=6) and with 2GC cefuroxime (n=79). Only 1/160 (0.6%) IHR to penicillin patient challenged with ceftriaxone had positive immediate DPT (with acute urticaria), tolerating subsequent DPT with cefpodoxime, another 3GC , whereas both ceftriaxone ST and post-DPT skin re-tests were negative (Figure 1 and Table E1) Negative predictive value for ceftriaxone ST was 99% for IHR and 100% for DHR.

Concerning IHR, we found a very low percentage of positive ST to 2GC (1/106 tested, 0.9%), no positive ST with 3GC (0/232 ST with at least one 3GC) and only one positive DPT to ceftriaxone (0/160 challenges), confirming data on a negligible risk of cross reactivity with C3G and some C2G [START_REF] Campagna | The use of cephalosporins in penicillin-allergic patients: a literature review[END_REF]. In line with this, the largest, prospective cohort of IHR to penicillins of Romano et al. reports positive ST with cefuroxime (2GC), or ceftriaxone (3GC) in 7/252 (2.8%) patients with positive responses in immediate-reading ST to at least one penicillin (mostly aminopenicillin) and negative DPT with afore mentioned molecules in all 244 patients, in a study group with a similar percentage of anaphylaxis (70%) as ours (66%) [START_REF] Romano | Cross-Reactivity and Tolerability of Cephalosporins in Patients with IgE-Mediated Hypersensitivity to Penicillins[END_REF].

Moreover results for ST to cephalosporins we tested (2/4: cefuroxime, ceftriaxone) and 7 other cephalosporins from group A (ceftazidime, cefotaxime, cefepime), group C (cefamandole) and group B aminocephalosporins (cephalexin, cefaclor, and cefadroxil) show the highest risk of cross-reactivity (38%) is related to similar side chain aminocephalosporins [START_REF] Romano | Cross-Reactivity and Tolerability of Cephalosporins in Patients with IgE-Mediated Hypersensitivity to Penicillins[END_REF].

As already published, none of the 54 patients with DHR to penicillins cross-reacted with 2GC and 3GC. All of the 97 patients with positive responses in late-reading ST to at least one penicillin evaluated by Buonomo et al. had negative DPT with cefixime and ceftriaxone, confirming a low cross-reactivity with penicillins [START_REF] Buonomo | Cross-reactivity and tolerability of cephalosporins in patients with cell-mediated allergy to penicillins[END_REF], whereas the rate of cross-reactivity upon ST and DPT with similar side-chain aminocephalosporins (cephalexin, cefaclor) was higher (11%).

All 4 cephalosporins we tested share the common methoxyimino group on the R1-side chain, belonging to group A cephalosporins based on chemical structure (Figure E1) and present no structural similarities with AX (no amino group) [START_REF] Romano | Cross-Reactivity among Beta-Lactams[END_REF]. Therefore, positive ST with dissimilar side-chain cephalosporins from group A could be related to coexisting sensitivities [START_REF] Romano | Cross-Reactivity among Beta-Lactams[END_REF] or, less likely, to cross-reactions due to sensitization to nuclear structures [START_REF] Romano | Cross-Reactivity and Tolerability of Cephalosporins in Patients with IgE-Mediated Hypersensitivity to Penicillins[END_REF].

First limitations of our study are the retrospective character and the limited type of cephalosporins tested, belonging exclusively to group A cephalosporins, possibly underestimating allergic risk for other cephalosporins, especially identical side chainaminocephalosporins. Second, lacking intravenous formulas for 2/4 cephalosporins (i.e cefpodoxime and cefixime) imposed testing by SPT only, possibly reducing sensitivity. Third, not all cephalosporins investigated are available in other countries, and, last, exclusion of sensitization to clavulanic acid by skin testing with AX was not systematic in AX-Clav STpositive patients

In conclusion, this series of 234 truly penicillin-allergic patients (aminopenicillins) confirms that cross-reactivity between penicillin and dissimilar side chain cephalosporins, like group A cefuroxime, ceftriaxone and cefpodoxime is very low (between 1 and 2%). Should urgent administration of different chemical structure cephalosporins be required, in both IHR or DHR confirmed penicillin allergic patients, it could be undertaken in hospitalized patients under close surveillance, after negative ST.

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Figure 1 .

 1 Figure 1. Results of 2GC and 3GC skin tests and drug provocation tests (DPT) in 234 penicillin-allergic patients

Acknowledgements:

We thank Dr Claude Ponvert (MD, PhD, Dept Paediatr, Pulmonol-Allergol Unit, Hôpital des Enfants Malades, Paris, France) for his help in proofreading this manuscript.