A Degiovanni

Yves Jannot

Christian Moyne

Electrical analogy associated with a multi-isotherms medium with internal heat source

Keywords: Conduction, electrical analogy, steady state, internal heat source. Nomenclature. A, B, C

The use of the electrical analogy in heat transfer allows to simply solve many problems in various fields such as building or electrothermics.

Nevertheless, it is limited to systems with two isotherms and a flux tube.

The fin approximation allows to introduce an exchange on the flux tube, but the electrical analogy does not work anymore if there is a heat source inside the fin.

In this paper, we will construct an electrical analogy for a system with:

-On its boundary, several isotherms surfaces, a surface that exchanges with the external medium and a zero flux region, -In the volume, a heat source with any distribution. This approach generalizes the notions of thermal resistance and partition coefficient of the internal heat source.

In the applications (here for a cylinder), the only approximation concerns the isotherms surfaces which in reality are not necessarily so (this approximation already exists in the elementary case, a thermal resistance is defined between two isotherms).

The application of resistance concepts to steady state problems is widely adopted in thermal science. Nonetheless, there are some difficulties when applying the foregoing concepts to problems with non-uniform internal source. Internal sources may be due to the passage of electric current through a solid or nuclear fission or to a chemical reaction taking place within the solid as in the problems of charging and discharging batteries [START_REF] Lui | Thermal issues about Li-ion batteries and recent progress in battery thermal management systems: a review[END_REF]. Two other difficulties make the use of the notion of resistance problematic: the systems with more than two isotherms and the numerous systems exchanging heat with the external medium. Indeed, the flow tube in heat transfers is in practice non-existent, it is particularly difficult to isolate a surface and there are always convective or radiative exchanges.

For the case of two isotherms with sources, we find a first approach in Bardon [2] for the particular case of sliding contact with friction, the author evaluated the heat transfer rate from both sides of the contact resistance using the notion of 'part of the generated heat that causes a spike in temperature at the interface' or 'heat generation factor'. Various authors used this representation to establish thermal models for sliding contacts with friction [START_REF] Chantrenne | A microscopic thermal model for dry sliding contact[END_REF][START_REF] Bauzin | Simultaneous estimation of frictional heat flux and two thermal contact parameters for sliding contacts[END_REF][START_REF] Laraqi | Contact temperature and flux partition-coefficient of heat generated by dry friction between 2 solids-new approach to flux generation[END_REF][START_REF] Guillot | Experimental study of thermal sliding contact with friction: application to high speed machining of metallic materials[END_REF][START_REF] Chantrenne | Study of a macroscopic sliding contact thermal model from microscopic models[END_REF].

Likewise, this representation was applied to various electrothermal applications [START_REF] Feulvarch | Resistance spot welding simulation: a general finite element formulation of electrothermal contact conditions[END_REF][START_REF] Rogeon | Characterization of electrical contact conditions in spot welding assemblies[END_REF][START_REF] Le Meur | Measurement of contact parameters at electrode/sheet interface during resistance spot welding process[END_REF][START_REF] Le Meur | Microscopic analysis of interfacial electrothermal phenomena--definition of a heat generation factor[END_REF]. For our part, we have demonstrated [START_REF] El Maakoul | A general approach to solve heat conduction problems with internal heat generations using resistance and quadrupole concepts[END_REF], in the general case of non-uniform internal sources, the validity of the partition coefficient and how to calculate it. The coefficient can be applied either to the source or to the resistance. This confirms that the resistance concepts can be used to solve steady-state heat problems with such internal (uniform or non-uniform) sources by introducing a resistance partition coefficient.

The main interest of electrical analogy is to solve complex problems that do not have exact analytical solutions. The electrical analogy allows to obtain an approximate solution very quickly and often very precisely as can be seen in [START_REF] El Maakoul | Modeling of thermal contact with heat generation: application to electrothermal problems[END_REF] for the calculation of the contact temperature in the case of spot welding.

In this paper we will show that in the general case of a medium whose surface is constituted by several isotherms and whose volume receives a uniform or non-uniform heat source, there is an exact electrical analogy for this type of medium, which generalizes the notion of thermal resistance in a medium with source.

The general problem of a multi-isotherms medium with internal heat source in steady state.

The approximate methods of fin type do not allow to obtain a representation by resistances in the presence of internal source. We will show that in a general way there is a representation in resistances and localized sources for a medium with several isotherms and internal heat source. This demonstration generalizes the concepts of resistances and partition coefficient demonstrated for a flow tube with two isotherms [START_REF] El Maakoul | A general approach to solve heat conduction problems with internal heat generations using resistance and quadrupole concepts[END_REF]. Figure [START_REF] Lui | Thermal issues about Li-ion batteries and recent progress in battery thermal management systems: a review[END_REF] shows the electrical analogy for this case, where two representations are possible (both representations are correct), either resistance partition (1-a) or source partition (1-b). Q is the total power released in the flux tube, R is the total resistance of the flux tube and α is the partition coefficient which depends only on the power distribution and the geometry of the flux tube. As an example, for a 1D problem, α is given by:

= ( ) ( ) ( )
Where: ( ) is the power distribution, ( ) is the section of the flux tube, ( ) is the

resistance distribution ( ( ) = ( )
), where s is a curvilinear coordinate.

For a cylinder of length e:

= ( )

If the power is evenly distributed, ( ) = ( ⁄ ) and = 1 2 ⁄

If the power is uniform between a and b, and zero elsewhere, = ( + ) 2 ⁄

As in many practical cases, one of the isotherms is the outside temperature, we will introduce, to generalize the problem, a surface exchanging by heat transfer coefficient with the outside. In V:

+ * = 0 (1)
On Si: = # On Se:

- %& %' = ℎ( -)
On Slat:

- %& %' = 0
The problem being linear we will solve it by superposition (the detailed demonstration is given in appendix).

Consider the following problems:

• n problems :

In V:

) # = 0 (2)
On Si:

) # = 1 On Sj (j ≠ i) ) # = 0
On Se:

- %* + %' = ℎ ) # On Slat: - %* + %' = 0 • 1 problem : In V: ) = 0 (3)
On Si:

) = 0 On Se: - %* , %' = ℎ() -1)
On Slat: -%* , %' = 0

• 1 problem :

In V: -+ * = 0 On Si: -= 0 On Se: - %. %' = ℎ - On Slat: - %. %' = 0
It is immediate to verify that:

/ ) # ' #0 + ) = 1 (4)
The solution of problem ( 1) is therefore given by:

= / 2 ' 20 ) 2 + ) + - (5)
Which can be written taking into account (4):

-# = /( 2 ' 20 -# )) 2 + ( -# )) + - ( 6
)
If n is the exterior normal to the volume V, the input fluxes 5 # are defined by:

5 # = 6 7 78 +
From the relation [START_REF] Guillot | Experimental study of thermal sliding contact with friction: application to high speed machining of metallic materials[END_REF], it comes immediately:

5 # = / 9 #2 ( # -2 ) 2:# + 9 # ( # -) -# (7) 5 = / 9 2 ( -2 ) - 2 (8)
By having posed:

9 #2 = 6 - 7) 2 78 + (9) 9 # = 6 - 7) 78 + ( 10
) 9 # = 6 - 7) # 78 , ( 11
) # = 6 - 7- 78 + (12)
Relationships ( 9) to ( 12) are used to calculate the admittances and partition coefficients. To complete the demonstration, it is necessary to show the symmetry of the admittances, i.e. that:

9 #2 = 9 2# > 9 # = 9 # . • 9 #2 = 9 2# ?
We start from (2) which we multiply by ) 2 :

0 = ) 2 ) # = . @) 2 ) # A -) 2 . ) # ( 13
)
The integration of ( 13) over the volume V of area = ∑ D D + + EFG leads to:

H ) 2 . ) # I = H . @) 2 ) # A I = 6 ) 2 ) # . 8 = 6 7) # 78 J + 6 ) 2 (- ℎ , ) # )
By swapping i and j we get:

H ) # . ) 2 I = 6 7) 2 78 + + 6 ) # (- ℎ , ) 2 )
And:

6 7) 2 78 + = 6 7) # 78 J > 9 #2 = 9 2# • 9 # = 9 # ?
Similarly, the relation (3

) becomes: 0 = ) # ) = . () # ) ) -) # . ) (14)
The integration of ( 14) over the volume V of area = ∑ D D + + EFG leads to:

H ) # . ) I = H . () # ) ) I = 6 ) # ) . 8 = 6 7) 78 + + 6 ) # (- ℎ , )() -1) (15)
By swapping i and e we get:

H ) . ) # I = H . () ) # ) I = 6 ) ) # . 8 = 6 ) (- ℎ , )) # (16)
Combining ( 15) and ( 16) we get:

6 7) 78 + + 6 ) # (- ℎ , )() -1) = 6 ) (- ℎ , )) # 6 7) 78 + = 6 ) # (- ℎ , ) = 6 7) # 78 , 8 >ℎK 9 # = 9 #
As an example, the analogical representation for a system with 3 isotherms is given in figure

(3). This representation is the exact solution of the problem, the only approximation is that the 3 surfaces are isothermal.

Figure (3):

Analogical representation of a system with three isotherms.

Application to a cylinder.

To illustrate the method we will treat the problem of the cylinder exchanging through its lateral surface and we will assume a uniform internal heat source.

Let be the system of figure (4), a cylinder of radius R, height e, thermal conductivity λ subjected to uniform boundary conditions (independent of r) in z, presenting exchanges on its lateral surface characterized by an heat transfer coefficient h and a volumic heat generation p0.

Figure (4):

A cylinder exchanging with three temperatures.

3.1. The system of equations:

7 7L + 1 7 7 + 7 7 + M = 0 (17) = 0 7 7 = 0 (18) = - 7 7 = ℎ( -N>) (19)
L = 0 > L = OPK8 Q RP8 S>SP8 S8 M 8 8> PT (20)

The analytical solution:

The solution of the problem is obtained by Hankel integral transformation on r, i.e.:

U = ( -N>) V ( ) W
With the eigenvalues given by:

X ' V (X ' ) = Y V (X ' ) PK X ' = ' > Y = ℎ / (21)
And the norm by

[ ' = V ( ' ) W = W \ (V ( ' ) + V ( ' )) ( 22
)
Where V (N) is a Bessel function of the first kind, order 1 and V (N) is a Bessel function of the first kind, order 0.

The relation (17) becomes after transformation:

7 U 7L -' U + n = 0 ( 23
)
Where

n = M V ( ) W = M W o V ( )
Whose solution is written in matrix form [START_REF] Maillet | Thermal Quadrupoles: Solving the Heat Equation through Integral Transforms[END_REF]:

p U 5 q = r s O t u v p U 5 q -w s -1 t x x y (
o • t = ' ℎ( ' ) > x = € o • ℎ( ' )
Where ch(x) is a hyperbolic cosine and sh(x) is a hyperbolic sine.

The return in the real space is done by the following expression: -Let us calculate the resistances, i.e. the inverse of the admittances 9 #2 :

= / 2 U ' V ( ' ) (V ( ' ) + V ( ' )) … '0 (25)

The electric analog solution:

1 = 9 = - 7) 7L W 2 † (26) 1 ‡ = 1 ‡ = 9 ‡ = - 7) 7 2 † L (27)
With the problem ) :

7 ) 7L + 1 7) 7 + 7 ) 7 = 0 (28) = 0 7) 7 = 0 (29) = - 7) 7 = ℎ ) (30) L = 0 ) = 1 (31) L = ) = 0 (32)
We get:

1 = † / 4 T ℎ(TX ' ) … '0 Y X ' (Y + X ' ) (33) 1 ‡ = 1 ‡ = 4 † / Rℎ(TX ' ) -1 ℎ(TX ' ) … '0 Y X ' (Y + X ' ) (34)
Where X ' solution of:

X ' V (X ' ) = Y V (X ' )
Where Y = ℎ / and the shape factor T = /

We deduce, the partition coefficients of the resistances:

ˆ = 1 † = / 4 T ℎ(TX ' ) … '0 Y X ' (Y + X ' ) ˆ ‡ = ˆ ‡ = 1 ‡ 1 4 † = 1 ‡ 1 4 † = / Rℎ(TX ' ) -1 ℎ(TX ' ) … '0 Y X ' (Y + X ' )
-Similarly for the partition coefficients :

= = - 7- 7L W 2 † ‡ = - 7- 7 2 † L
With the problem -:

7 - 7L + 1 7- 7 + 7 - 7 + 1 † = 0 (35) = 0 7- 7 = 0 (36) = - 7- 7 = ℎ - (37) L = 0 -= 0 (38) L = -= 0 ( 39
)
We get:

= = / Rℎ(TX ' ) -1 TX ' ℎ(TX ' ) … '0 4 Y X ' (Y + X ' ) (40) ‡ = /( 2@1 -Rℎ(TX ' )A TX ' ℎ(TX ' ) … '0 + 1) 4 Y X ' (Y + X ' ) (41)
The partition coefficients of the internal power and the partition coefficients of the resistances depend only on the Biot number (H) and the shape factor (f).

As an example, the variation of ˆ ‡ , ˆ and as a function of T for three values of H, is given in figures (5 to 7); figure (5) H=0.08, figure (6) H=0.64, figure (7) H=5.12.

Figure ( 5): Partition coefficients versus shape factor for H=0.08.

Figure [START_REF] Guillot | Experimental study of thermal sliding contact with friction: application to high speed machining of metallic materials[END_REF]: Partition coefficients versus shape factor for H=0.64. Figure [START_REF] Chantrenne | Study of a macroscopic sliding contact thermal model from microscopic models[END_REF]: Partition coefficients versus shape factor for H=5.12.

In particular, when the exchange coefficient tends to 0 (H → 0) or the shape factor tends to 0 (f → 0), the heat transfer becomes unidirectional along z, we find the results of [START_REF] El Maakoul | A general approach to solve heat conduction problems with internal heat generations using resistance and quadrupole concepts[END_REF], the resistances ‡ and ‡ tend to infinity (ˆ ‡ = ˆ ‡ → 0) and ˆ → 1 and = ‰W \ . For the partition coefficients of the internal power, we find = 0.5, which is normal since the internal power distribution in this problem is uniform.

Conversely, when the shape factor tends to infinity (f → ∞), the heat transfer becomes unidirectional in r (ˆ → 0), with a radial resistance that varies with the exchange coefficient H.

Case of several media:

This solution, allows to solve the problem of figure [START_REF] Feulvarch | Resistance spot welding simulation: a general finite element formulation of electrothermal contact conditions[END_REF], the analogical diagram is given in figure [START_REF] Rogeon | Characterization of electrical contact conditions in spot welding assemblies[END_REF].

This problem has no analytical solution, the electrical analogy allows to obtain an approximate solution. Indeed, for the analogy to be exact it would be necessary that the surface common to both media is isotherm, which is not the case. To this approximation (isotherms surfaces), another difficulty is the calculation of resistances and partition coefficients which requires the resolution of two or three dimensional problems and hence the search for eigenvalues not always easy, so we are going to look at the field of application of the first order approximation.

For the cylinder case, the first eigenvalue has been tabulated (see figure [START_REF] Le Meur | Measurement of contact parameters at electrode/sheet interface during resistance spot welding process[END_REF]):

Examples.

We present three examples:

-For the first one there is an analytical solution, the aim is to show the importance of the error when one of the surfaces is not isotherm (in z=0, the flux density is uniform, not the temperature).

-For the second one, there is also an analytical solution, the aim is to show that if the surfaces are isotherms the analogical solution is perfectly accurate even in the presence of an internal source.

-For the third, there is no analytical solution, the aim is to show that the analogical solution, although approximate, gives very good results. We calculate the average temperature at z=0 ( (0)) and the flux lost on the lateral surface (5 • ) as a function of the Biot number (H), the resistances are given by formulas (33) and ( 34)

: (0) = ‡ + ‡ ( † ‹ + ) 5 • = + ‡ ( † ‹ + + ‡ + ‡ ‡ )
Figure [START_REF] Le Meur | Microscopic analysis of interfacial electrothermal phenomena--definition of a heat generation factor[END_REF] shows the results for temperature and figure [START_REF] El Maakoul | A general approach to solve heat conduction problems with internal heat generations using resistance and quadrupole concepts[END_REF] for flux. The results are good, the first order model allows an approximate calculation of the loss flux and the full calculation is accurate for the fluxes as seen on example 1. We used the following values:

-Medium 1: e=0.1 m; R=0.05 m; λ=100 Wm -1 K -1 ; p0=10 5 Wm -3 -Medium 2: e=0.05 m; R=0.05 m; λ=20 Wm -1 K -1 ; p0=0 Wm -3 -Boundary conditions: T1=20 °C; T2=20 °C; T3=0 °C.

The mesh laws allow us to establish the following linear system:

-' = ‹ - ‡ = (‹ + -‹ ) ‡ -' = ‡ (‹ ‡ + ‡ + ‹ + -‹ ) ' -= " ‹ Ž ' - ‡ = Ž (‹ ‡ + ‡ + ‹ + + -‹ Ž ) ‡ -= " (‹ " + ‹ ‡ + ‡ + ‹ + + -‹ Ž )
Which is solved by formal calculation on Matlab to obtain Tx, the temperature at the interface of the two media. Figure [START_REF] Maillet | Thermal Quadrupoles: Solving the Heat Equation through Integral Transforms[END_REF] gives Tx as a function of the exchange coefficient h, for the complete calculation, the first order calculation and the results of a numerical calculation on the COMSOL software.

The figure (15) presents the mesh used on COMSOL, it is made of 4800 triangular elements, it was verified that the increase of the number of elements does not modify the value of the average temperature at the interface. The results are very good, for h=1000 Wm -2 K -1 , the difference is only 0.2 °C.

Conclusion.

It has been shown that the notion of thermal resistance could be generalized to a flow tube comprising several isotherms surfaces, a surface in exchange with an external temperature and an internal heat source, and that there was an analogical representation of the triangle type with sharing of the flows.

Regarding the first-order calculation:

-In the case without an internal source, an approximation was obtained for the temperatures when a surface is not isotherm (Neumann type boundary condition) not necessarily better than the fin hypothesis. On the other hand, the fluxes are obtained with a very good approximation.

-In the case of a system with an internal source the modeling is very efficient, while the fin approximation is not possible.

The generalization to a cylinder with any base is immediate.

The previous system is a steady state system connected to a single source T=1, the solution is obvious:

/ ) # ' #0 + ) = 1 (10)
The relation [START_REF] Feulvarch | Resistance spot welding simulation: a general finite element formulation of electrothermal contact conditions[END_REF] can then be written taking into account [START_REF] Le Meur | Measurement of contact parameters at electrode/sheet interface during resistance spot welding process[END_REF]:

-# = /( 2 ' 20 -# )) 2 + ( -# )) + - (11)

2 J0=

 2 Bessel function of the first kind, order 0 J1 = Bessel function of the first kind, order 1 p = power density (Wm -3 ) Q = total power (W) r = radial coordinate (m) R = thermal resistance (KW -1 ) or radius (m) S = section (m 2 ) T = temperature (K) Text = external temperature (K) V = volume (m 3 ) W = Hankel integral transform of p (Wm -1 ) z = axial coordinate (m) α = partition coefficient or eigenvalues (m -1 ) β = admittance (WK -1 ) γ = partition coefficient of the resistance θ = Hankel integral transform of (T-Text) (Km 2 ) λ = thermal conductivity (WK -1 m -1

Figure ( 1 Figure ( 1 )

 11 Figure (1-a) Figure (1-b) Figure (1): Analogical representation of a system with two isotherms: a) resistance partition, b) source partition.

Figure ( 2 )

 2 Figure (2): Diagram of a system with several isotherms.

U}}

  24)With U Laplace transform of the temperature in L = 0 Laplace transform of the temperature in L Laplace transform of the heat flux density in L Laplace transform of the heat flux density in L = s = u = Rℎ(

Figure ( 1 )

 1 Figure[START_REF] Lui | Thermal issues about Li-ion batteries and recent progress in battery thermal management systems: a review[END_REF] is the electrical analogy representation of this problem.

Figure ( 8 )

 8 Figure (8): Two media system exchanging with 3 temperatures.

Figure ( 9 )

 9 Figure (9): Analogical representation of the two media system.

Figure ( 10

 10 Figure (10): First eigenvalue () versus Biot number (H).

4. 1 .

 1 Example 1: a single medium without an internal source. With thickness e=0.1 m, radius R=0.05 m and conductivity λ=20 Wm -1 K -1 .

4. 3 .

 3 figure[START_REF] El Maakoul | Modeling of thermal contact with heat generation: application to electrothermal problems[END_REF].

Figure ( 13 )

 13 Figure (13): Analogical representation of the example 3.

Figure ( 16 )

 16 Figure (16) shows the temperature fields for the three values of the exchange coefficient (h=10, 100, 1000).It is particularly interesting to see that the electrical analogy gives very good values while the temperature fields are very different.

Figure ( 14 )

 14 Figure[START_REF] Maillet | Thermal Quadrupoles: Solving the Heat Equation through Integral Transforms[END_REF]: Temperature at the interface versus heat transfer coefficient.

  Figure (15): COMSOL mesh.

Figure ( 16

 16 Figure (16): Temperature fields (a : h = 10; b : h = 100; c : h = 1000).

Table (

 (

	1) summarizes the results:
		temperature	temperature	flux	flux
		Error of 0.1 °C	Error of 0.3 °C	Error of 1 %	Error of 10 %
	First
		H < 1.0	H < 3.4	H < 0.25	H < 1.6
	order
	complete	H < 0.36	H < 5.4	all H	all H
	Table (1): results example 1
	Figure (11): Temperature at z=0 versus Biot number.

Table ( 3

 ( ) summarizes the results:Tx (°C) h = 10 Wm -2 K -1 h = 100 Wm -2 K -1 h = 1000 Wm -2 K -1

	Numerical calculation	23.09	19.48	7.46
	Electrical analogy	23.09	19.47	7.25
	Electrical analogy first order	23.09	19.50	7.70

Table (3): results example 3. 21

Figure [START_REF] El Maakoul | A general approach to solve heat conduction problems with internal heat generations using resistance and quadrupole concepts[END_REF]: lateral heat flux versus Biot number.

For the full calculation, the error on the temperature comes from the fact that the lateral surface and the surface at z=0, are not isotherms. On the other hand, the flux calculation is correct. The partition coefficients are given by the relations (40) and (41).

In this problem:

APPENDIX:

The general problem is:

In V:

On Si: = # On Se:

On Slat:

The solution is obtained by superposition of the following problems:

-n problems:

In V:

On Si:

On Se:

On Si:

On Si:

It is immediate to verify that the sum of n problems (2), problem (3) and problem (4) gives problem (1):

Moreover, as each problem is a function of only one source, the problems (2) can be written:

In V:

On Si:

On Sj (j ≠ i):

On Se:

With:

The problem (3):

On Si:

On Slat:

The problem (4):

In V:

-+ * = 0

On Si: -= 0

On Se: -%.

%' = ℎ -

The solution of problem ( 1) is therefore given by:

On the other hand the sum of problems ( 5) and problem [START_REF] Guillot | Experimental study of thermal sliding contact with friction: application to high speed machining of metallic materials[END_REF] gives us:

In V:


Nicolas Kraupner

Chau Phi Dinh

Xiaoan Wen

Valérie Landry

Adrien Herledan

Florence Leroux

Damien Bosc

Julie Charton

Clara Maillard

Sandrine Warenghem

Wen ‡ Xiaoan

Isabelle Duplan

Catherine Piveteau

Nathalie Hennuyer

Bart Staels

Benoit Deprez

Rebecca Deprez- Poulain
email: rebecca.deprez@univ-lille.fr

Rebecca Deprez-Poulain

Identification of indole-based activators of insulin degrading enzyme

Keywords: Insulin-degrading enzyme, activators, screening, metalloenzymes AD, Alzheimer's disease, APP, amyloid precursor-peptide, EDTA, ethylene-diaminotetra-Acetate, IDE, insulin degrading enzyme, IGF-II, insulin growth factor -2, T2D, type-2 diabetes, T3P®, propylphosphonic anhydride, TGF-α, transforming growth factor α

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

Introduction

Insulin-Degrading Enzyme (IDE) is a Zinc endopeptidase of the M16 family involved in the degradation of many substrates. In particular, it is the main enzyme responsible for the intracellular hydrolysis of insulin, the most affine substrate for IDE [1]. Glucagon [2] and amylin [3], two other peptidic hormones secreted by the pancreas, are also substrates. IDE was subsequently proposed as one of the enzymes involved in the catabolism of the amyloid peptide (Aβ) [4]. Finally, the calcitonin gene-related peptide CGRP and many other peptides with various length and affinities like somatostatin, IGF-II, TGFα , β-endorphin, dynorphins, bradykinin, atrial natriuretic peptide (ANP) are substrates of IDE [5]. The reason underlying the ubiquitous expression of IDE is unknown. Still the diversity of the substrates and the non-proteolytic roles of IDE could explain this large distribution of IDE. For example, IDE is involved in the ubiquitin-proteasome pathway since the monomeric ubiquitin is degraded by IDE [6] and since IDE directly regulates the activity of the proteasome by protein-protein interaction [START_REF] Sbardella | The insulin-degrading enzyme is an allosteric modulator of the 20S proteasome and a potential competitor of the 19S[END_REF]. Interestingly, many substrates of IDE share a propensity to be amyloidogenic peptides [8] and IDE can be seen as a protein that prevents the formation of toxic peptide oligomers [9]. This possibly conserved function could explain the high level of sequence homology across distantly related species. Interestingly an enzymatically inactive variant of IDE conserves this function in vitro [10]. Moreover, the fission yeast IDE homologue named Iph1 was shown to modulate the sensitivity of cells to endoplasmic reticulum (ER) stress in a manner dependent on TORC1 and independent of its catalytic activity [START_REF] Beuzelin | Deletion of the fission yeast homologue of human insulinase reveals a TORC1-dependent pathway mediating resistance to proteotoxic stress[END_REF].

Along with the biochemical activity of peptide hydrolysis, genetic and epidemiological studies on populations associated a polymorphism within IDE gene loci to the risk of type 2 diabetes (T2D) [START_REF] Sladek | A genome-wide association study identifies novel risk loci for type 2 diabetes[END_REF].

The role of IDE in insulin levels and glucose tolerance has attracted a lot of attention in the past decade [START_REF] González-Casimiro | Modulation of insulin sensitivity by insulin-degrading enzyme[END_REF], [START_REF] Leissring | Targeting insulindegrading enzyme in insulin clearance[END_REF]. Using both cellular assays or animals with pan cellular genetic Ide deletion, tissue selective genetic Ide deletion [START_REF] Fernández-Díaz | Pancreatic β-cell-specific deletion of insulindegrading enzyme leads to dysregulated insulin secretion and β-cell functional immaturity[END_REF], [16], Ide overexpression or pharmacological inhibition [START_REF] Deprez-Poulain | Catalytic site inhibition of insulin-degrading enzyme by a small molecule induces glucose intolerance in mice[END_REF][START_REF] Maianti | Anti-diabetic activity of insulin-degrading enzyme inhibitors mediated by multiple hormones[END_REF][START_REF] Durham | Dual exosite-binding inhibitors of insulin-degrading enzyme challenge its role as the primary mediator of insulin clearance in vivo[END_REF] several teams including us have shown the complex role of IDE in glucose tolerance far beyond the hydrolysis of insulin, in particular in organs involved in the control glucose levels like pancreas and liver.

Variants of the ide gene and loci of the IDE gene on chromosome 10q have also been associated with plasma concentrations of Aβ1-42 and increased risk for Alzheimer's disease (AD) [START_REF] Bertram | Evidence for genetic linkage of Alzheimer's disease to chromosome 10q[END_REF], [21]. The role of clearance of Aβ by IDE has been demonstrated using IDE -/-mice, [START_REF] Farris | Insulin-degrading enzyme regulates the levels of insulin, amyloid betaprotein, and the beta-amyloid precursor protein intracellular domain in vivo[END_REF] or transgenic mice overexpressing both APP and IDE [START_REF] Leissring | Enhanced proteolysis of beta-amyloid in APP transgenic mice prevents plaque formation, secondary pathology, and premature death[END_REF].

IDE is a dynamic protein whose structure consists in an N-terminal part (IDE N), encompassing domains 1 and 2 (residues 43-285 and 286-515 respectively) and a C-terminal part (IDE C), consisting of domains 3 and 4 (residues 542-768 and 769-1016 respectively articulated around a flexible loop [START_REF] Shen | Structures of human insulin-degrading enzyme reveal a new substrate recognition mechanism[END_REF] (Fig. 1). It exists in solution in equilibrium between an open form and a closed form. Several biophysical studies have captured the displacement of a subdomain that creates an opening to the catalytic chamber for the substrates [START_REF] Mccord | Conformational states and recognition of amyloidogenic peptides of human insulin-degrading enzyme[END_REF]. The dynamics of the subdomain displacement has been shown to be disrupted by inhibitors thus impacting IDE's catalytic activity [START_REF] Zhang | Ensemble cryoEM elucidates the mechanism of insulin capture and degradation by human insulin degrading enzyme[END_REF]. In addition to the catalytic pocket containing the Zinc ion and HXXEH and GAMEN sequences, IDE displays an exosite located ∼30 Å away from the catalytic pocket, in the domain 2 (Fig. 1). This exosite has been shown to allow anchoring of the Nterminus of substrates causing a rearrangement of their secondary structure in order to facilitate binding and subsequent cleavages at the catalytic site [START_REF] Shen | Structures of human insulin-degrading enzyme reveal a new substrate recognition mechanism[END_REF]. The co-crystallizations of the IDE with ATP showed also an ATP pocket at domain 4 (IDE-C) of the protein [START_REF] Song | An extended polyanion activation surface in insulin degrading enzyme[END_REF] (Fig. 1).

Figure 1: Structure of IDE and key substrates a a (A) Structure of hIDE (from PDB 4NXO); IDE-N and IDE-C halves are colored in blue and gray respectively. Catalytic residues, exosite residues and ATP-binding residues are colored in red, magenta and yellow respectively. The "swinging door" and the loop are pointed with an arrow. (B) Main substrates of IDE and targeted organs. Underlined are peptides that can oligomerize.

Comforted by the disease implications of IDE, and in particular in T2D, several teams have in the past decade developed inhibitors of IDE via rational design [START_REF] Leissring | Designed inhibitors of insulin-degrading enzyme regulate the catabolism and activity of Insulin[END_REF], high-throughput screening [START_REF] Durham | Dual exosite-binding inhibitors of insulin-degrading enzyme challenge its role as the primary mediator of insulin clearance in vivo[END_REF][29][30], zinc-binding fragment screening [31], DNA-templated library screening [START_REF] Maianti | Anti-diabetic activity of insulin-degrading enzyme inhibitors mediated by multiple hormones[END_REF], drug repurposing [START_REF] Leroux | Identification of ebselen as a potent inhibitor of insulin degrading enzyme by a drug repurposing screening[END_REF] or kinetic target-guided synthesis [START_REF] Deprez-Poulain | Catalytic site inhibition of insulin-degrading enzyme by a small molecule induces glucose intolerance in mice[END_REF]. The inhibitors were shown to bind the catalytic site [START_REF] Deprez-Poulain | Catalytic site inhibition of insulin-degrading enzyme by a small molecule induces glucose intolerance in mice[END_REF][START_REF] Leissring | Designed inhibitors of insulin-degrading enzyme regulate the catabolism and activity of Insulin[END_REF][29] or exosites [29,[START_REF] Maianti | Anti-diabetic activity of insulin-degrading enzyme inhibitors mediated by multiple hormones[END_REF][START_REF] Durham | Dual exosite-binding inhibitors of insulin-degrading enzyme challenge its role as the primary mediator of insulin clearance in vivo[END_REF]. Some are pan-IDE inhibitors [START_REF] Deprez-Poulain | Catalytic site inhibition of insulin-degrading enzyme by a small molecule induces glucose intolerance in mice[END_REF][START_REF] Leissring | Designed inhibitors of insulin-degrading enzyme regulate the catabolism and activity of Insulin[END_REF], others are substrate selective inhibitors [START_REF] Maianti | Substrateselective inhibitors that reprogram the activity of insulin-degrading enzyme[END_REF] and some others are inhibitors of the hydrolysis of one substrate and activator of the hydrolysis of others [29,30].

Inhibitors have produced some controversial results regarding insulin clearance and their application as modulators of glucose tolerance is at stake. Still, they are highly useful tools to decipher the atypical roles of IDE.

Activators are also foreseen. First, there is a need for compounds that act as activators with respect to Aβ degradation, in order to decrease the levels of this toxic peptide in AD. Secondly, regarding insulin clearance and glucose homeostasis, recent studies have underlined the complex role of IDE in both pancreas and insulin sensitive tissues like liver [START_REF] Leissring | Targeting insulindegrading enzyme in insulin clearance[END_REF][START_REF] Fernández-Díaz | Pancreatic β-cell-specific deletion of insulindegrading enzyme leads to dysregulated insulin secretion and β-cell functional immaturity[END_REF]. As a consequence, activators could be worth exploring for glucose homeostasis too [START_REF] Merino | Hepatic insulin-degrading enzyme regulates glucose and insulin homeostasis in diet-induced obese mice[END_REF]. However, in constrast to inhibitors, only a handful of activators of this enzyme have been disclosed (Fig. 2). Suramin, was the first identified activator of the hydrolysis of the peptide Aβ by IDE [START_REF] Adessi | Activator for insulin degrading enzyme[END_REF] (Fig. 2). Unfortunately, suramin is non-permeable across the cell membrane, toxic and not suitable for in vivo studies. In 2009, activators Ia1 and Ia2were discovered by screening [START_REF] Cabrol | Small-molecule activators of insulin-degrading enzyme discovered through high-throughput compound screening[END_REF] (Fig. 2). A series of polyaromatic compounds D3, D4, D6 and D10 (Fig. 2) were identified through a virtual screening at the exosite. These compounds displayed IDE activation of insulin degradation over other substrates [START_REF] Cakir | Structure based discovery of small molecules to regulate the activity of human insulin degrading enzyme[END_REF]. Selective activators of rat IDE over human IDE, were discovered by high-throughput screening and displayed cellular activity (rat-7, Fig. 2) [START_REF] Kukday | Cell-permeable, small-molecule activators of the insulin-degrading enzyme[END_REF]. We also described a series of small molecules showing a dual modulation of IDE. By binding at two different sites, the catalytic site and the exosite, these compounds, like BDM43079 are inhibitors of amyloid degradation and activators of the hydrolysis of insulin and IGF-II [START_REF] Deprez-Poulain | Ligands of insulin degrading enzyme and their uses[END_REF] (Fig. 2). Here we describe the screening of a collection of more than 8 000 compounds and the discovery of indole-based activators of IDE. A set of 50 analogues allowed the establishment of structure-activity relationships and study of binding via docking. The best compound was shown to be activator of both Aβ and insulin hydrolysis by IDE and displayed cellular activity in a glucose-stimulated insulin secretion assay.

Suramin

Results and Discussion

1.1.

Screening of an 8500-member library.

With the aim of discovering new activators to explore the complex role of IDE, we screened at 30 µM a library of 8 500 drug-like compounds from in-house and commercial sources. Figure 3 summarizes the screening cascade. The compounds were screened in a fluorescence assay monitoring the hydrolysis by IDE of an Aβ substrate analogue (Supporting information Figure S1). Suramin at 10µM

was used as a positive control and displayed stable activity throughout the screening (Supporting information Figure S2). The screening allowed the identification of 12 activators (0.14% hit rate) that displayed enzyme activity of at least 1.3 times that observed in the presence of 10 µM suramin (Fig. 3 and Supplementary Table S1 and Figures S3-S4).

Dose-response curves were established and among the 6 confirmed hits, 2 displayed an EC50 below 10µM. Among them, indole derivative 1 with a potency (EC50) of 5.5 µM, an activation efficacy of 6 233% (2.33 fold) at 100µM and a promising lipophilic ligand efficiency LLE of 2.02, was selected for further pharmacomodulation (Fig. 4, Supplementary Figure S5).

Biological characterization of hit 1.

We first measured some in vitro ADME properties of hit 1. Hit 1 displays a medium LogD (2.7 at pH 7.4), a moderate aqueous solubility (8.9 µM) and a very good plasmatic stability (Half-life in rat plasma > 24 h) (Fig. 4). We then evaluated the behavior of 1 regarding the hydrolysis of a second substrate of IDE: insulin (Fig. 5 and Supplementary Table S2). EDTA was used as a control inhibitor. 1

behaves as an activator of full-length insulin hydrolysis by IDE. In an assay of insulin secretion induced by glucose by pancreatic β-cells (Fig. 6), 1 decreases insulin secretion significantly for medium and high glucose stimulation (Fig. 6A). In the meantime, insulin content is decreased in the presence of 1, compared to vehicle treatment (Fig. 6B).

Synthesis of analogues.

To explore structure-activity relationships around hit 1, we synthesized 47 analogues using

1.4.

Structure-activity relationships.

Table 1 summarises the impact of the N-substitution of the indole. Removal (2) or replacement by an alkyl group (3)(4), aryl ( 5) or benzyl (6)[START_REF] Sbardella | The insulin-degrading enzyme is an allosteric modulator of the 20S proteasome and a potential competitor of the 19S[END_REF] group of the sulfonylaryl group in 1 resulted in less potent or inactive compounds. Acylated analogue 8 retains some efficacy (2.40 activation fold at 100µM like 1)

but is less potent (pEC50 = 4.67 vs 5.30 for 1). The sulfonyl group was then maintained and diverse substituents were explored (9)(10)[START_REF] Beuzelin | Deletion of the fission yeast homologue of human insulinase reveals a TORC1-dependent pathway mediating resistance to proteotoxic stress[END_REF][START_REF] Sladek | A genome-wide association study identifies novel risk loci for type 2 diabetes[END_REF][START_REF] González-Casimiro | Modulation of insulin sensitivity by insulin-degrading enzyme[END_REF][START_REF] Leissring | Targeting insulindegrading enzyme in insulin clearance[END_REF][START_REF] Fernández-Díaz | Pancreatic β-cell-specific deletion of insulindegrading enzyme leads to dysregulated insulin secretion and β-cell functional immaturity[END_REF](16)[START_REF] Deprez-Poulain | Catalytic site inhibition of insulin-degrading enzyme by a small molecule induces glucose intolerance in mice[END_REF][START_REF] Maianti | Anti-diabetic activity of insulin-degrading enzyme inhibitors mediated by multiple hormones[END_REF][START_REF] Durham | Dual exosite-binding inhibitors of insulin-degrading enzyme challenge its role as the primary mediator of insulin clearance in vivo[END_REF][START_REF] Bertram | Evidence for genetic linkage of Alzheimer's disease to chromosome 10q[END_REF](21)[START_REF] Farris | Insulin-degrading enzyme regulates the levels of insulin, amyloid betaprotein, and the beta-amyloid precursor protein intracellular domain in vivo[END_REF][START_REF] Leissring | Enhanced proteolysis of beta-amyloid in APP transgenic mice prevents plaque formation, secondary pathology, and premature death[END_REF][START_REF] Shen | Structures of human insulin-degrading enzyme reveal a new substrate recognition mechanism[END_REF][START_REF] Mccord | Conformational states and recognition of amyloidogenic peptides of human insulin-degrading enzyme[END_REF]. Among N-sulfonylated indoles, replacement of the thiophene by a methyl ( 9) is tolerated. Fluorinated phenyl analogues [START_REF] Beuzelin | Deletion of the fission yeast homologue of human insulinase reveals a TORC1-dependent pathway mediating resistance to proteotoxic stress[END_REF][START_REF] Sladek | A genome-wide association study identifies novel risk loci for type 2 diabetes[END_REF][START_REF] González-Casimiro | Modulation of insulin sensitivity by insulin-degrading enzyme[END_REF] are more potent than phenyl analogue (10) but induce a lower activation fold. Substitution of the phenyl ring by chlorine [START_REF] Leissring | Targeting insulindegrading enzyme in insulin clearance[END_REF], bromine [START_REF] Fernández-Díaz | Pancreatic β-cell-specific deletion of insulindegrading enzyme leads to dysregulated insulin secretion and β-cell functional immaturity[END_REF], methyl (16)[START_REF] Deprez-Poulain | Catalytic site inhibition of insulin-degrading enzyme by a small molecule induces glucose intolerance in mice[END_REF] or methoxy [START_REF] Maianti | Anti-diabetic activity of insulin-degrading enzyme inhibitors mediated by multiple hormones[END_REF] groups led to inactive and/or insoluble compounds. Regioisomer 19 is slightly less potent than hit 1. Pyridyl analogue ( 22) is less potent than 1 but induces an activation fold of 3 at 100µM. Benzothiadiazolyl [START_REF] Leissring | Enhanced proteolysis of beta-amyloid in APP transgenic mice prevents plaque formation, secondary pathology, and premature death[END_REF], biphenyl [START_REF] Shen | Structures of human insulin-degrading enzyme reveal a new substrate recognition mechanism[END_REF] and naphthyl [START_REF] Mccord | Conformational states and recognition of amyloidogenic peptides of human insulin-degrading enzyme[END_REF] analogues are inactive. In comparison to 1, analogue 10 was found to be more soluble (15 µM) while having a similar LogD (2.7 at pH 7.4).

p-Chlorophenyl-SO2- _ a _ a p-Bromophenyl-SO2- _ a _ a p-Methylphenyl-SO2- _ a _ a o-Methylphenyl-SO2- _ a _ a p-Methoxyphenyl-SO2- _ a (1.08) Thiophen-3-yl-SO2- 4.86±0.14 1.97±0.25 1-Methylimidazol-4-yl-SO2- 4.54±0.12 1.99±0.19 3,5-Dimethylisoxazol-4-yl-SO2-_ a 1.50 3-Pyridyl-SO2- 4.57±0.23 2.75±0.28 2,1,3-Benzothiadiazol-SO2-4-yl-_ a (1.50) b p-Biphenyl-SO2- _ a (0.98) b 1-Naphthyl-SO2- _ a 1.0 a Not calculable; b Not soluble @100µM; n =4.
36 - H CH2 NH2 _ a 1.1 37S -(S)NHBoc CO OH _ a 1.23 37R -(R)NHBoc CO OH _ a 1.29 38S 3 (S)NHBoc CO NH _ a _ c 38R 3 (R)NHBoc CO NH _ a _ c 39S 3 (S)NH2 CO NH 4.84±0.11 2.28±0.12 39R 3 (R)NH2 CO NH _ a 1.54
a Not calculable; b Not soluble @100µM , c no dose-response effect; n=4.

In the phenylsulfonamide series, we explored the length, the branching and truncation of the linker and the amide function position (Table 2). Shortening of the linker by one, two or three methylene moieties (26-28 and 31) or elongation (29)(30) seems to be tolerated for the efficacy but without improvement of the potency. The substitution of the amide with methyl group [START_REF] Leroux | Identification of ebselen as a potent inhibitor of insulin degrading enzyme by a drug repurposing screening[END_REF] reduce the potency of the compound. Replacement of the amide with a retro-amide [START_REF] Maianti | Substrateselective inhibitors that reprogram the activity of insulin-degrading enzyme[END_REF] was detrimental for the activity. On the contrary, a urea linker [START_REF] Merino | Hepatic insulin-degrading enzyme regulates glucose and insulin homeostasis in diet-induced obese mice[END_REF] seems to be favourable for IDE activation activity but did not improve the potency (pEC50) compared to the amide (10). In the absence of imidazolyl moiety [START_REF] Adessi | Activator for insulin degrading enzyme[END_REF][START_REF] Cabrol | Small-molecule activators of insulin-degrading enzyme discovered through high-throughput compound screening[END_REF][START_REF] Cakir | Structure based discovery of small molecules to regulate the activity of human insulin degrading enzyme[END_REF], shortened basic [START_REF] Adessi | Activator for insulin degrading enzyme[END_REF], acid [START_REF] Cakir | Structure based discovery of small molecules to regulate the activity of human insulin degrading enzyme[END_REF] or neutral [START_REF] Cabrol | Small-molecule activators of insulin-degrading enzyme discovered through high-throughput compound screening[END_REF] compounds did not allow to activate IDE. In the n=2 series and in the presence of the imidazolyl moiety (28 and 38-39), bulky substituent, like a NHBoc group, onto the linker ( 38) decreased the activity while a primary amine substituent increased IDE activation, especially with the S-configuration (39S) compared to the R-configuration (39R) (Table 2).

Table 3: Impact of the replacement of the imidazole. Interestingly, only compound 1, bearing a 1-imidazolyl ring, was found to be an IDE activator.

Cpd

Modification of the imidazole ring by other basic rings like 4-imidazolyl ( 40) or 1-pyrrolidyl ( 41) led to a loss of activity (Table 3). Replacement of the indole core into oxindole [START_REF] Ivancic | Enzyme kinetics from circular dichroism of insulin reveals mechanistic insights into the regulation of insulin-degrading enzyme[END_REF], indazole (44) and aniline [START_REF]N-(3-imidazol-1-yl-propyl)-4-(2-oxo-2,3-dihydro-1H-indol-3-yl)-butyramide (42). To a solution of indole-3-butyric acid 42a in DMSO was added HCl 12N solution dropwise. The mixture was left to stir 30 min at room temperature. Water was added and the precipitate was collected with filter, washed with water and dried to afford the desired product 42b as brown yellow solid[END_REF] rings led to a decreased activity while the two 2 and 3-substituted (10,[START_REF] Berman | The Protein Data Bank[END_REF] indole regioisomers displayed equivalent activation fold (Table 4).

1.5. Docking of analogues 1, 10, 29-30.

In order to model the binding sites of compound 1, we first used the SiteFinder function of Molecular Operation Environment (MOE®, Chemical Computing Group, Montreal, Canada) within the crystallographic structure of the insulin-bound IDE (PDB code: 2WBY). We identified a putative binding pocket for 1 at the interface of the domains 2 and 4. This pocket happens to be the polyanion activation site of IDE [START_REF] Song | An extended polyanion activation surface in insulin degrading enzyme[END_REF], [40]. We thus further investigated the binding of 1 in this pocket using the 3D-structure of IDE bound to ATP (PDB Code 3TUV). In that structure, ATP forms potential hydrogen bonds with the side chains of Arg429 (domain 2), Lys898, Lys899 and Ser901 (domain 4), as shown in Supplementary

Figure S6. The best redocked pose of ATP into the polyanion-binding site deviated 0.86 Å from the true crystal pose deposited in the PDB, denoting that the docking procedure was able to correctly predict binding of ATP and could be employed for further investigation of the binding of compound 1 and its analogues (Supplementary Fig. S7). 1 was docked into the activation site using the aforementioned procedure. As depicted in the Figure 7, the carbonyl function of the amide is engaged in a hydrogen bond with the terminal amine function of Lys899, while the nitrogen of the imidazole ring makes another hydrogen bond with the terminal amine of Lys898. Finally, the sulfonamide function interacts with Ser901, via its oxygens. As the amide is playing a central role in the interaction of 1 with IDE, we decided to compare the binding of analogues 10, 29 and 30 that differ from 1 by the presence of a phenyl instead of a thiophene on the indole part, and that display various amide linker lengths (Fig. 8). Compounds were docked using the same method in the polyanion-binding site of IDE. Interestingly, 10 binds slightly differently from 1 as the imidazole ring makes a hydrogen bond with the NH of the backbone of Lys898 instead of the side chain of the same residue (Fig. 8A). Elongation by one methylene moiety of the aliphatic linker between the indole and the amide (29, Fig. 8B) or between the amide and the imidazole (30, Fig. 8C), restores the hydrogen bond between imidazole and the nitrogen of the side chain of Lys898. The extension of the linker on the indole side in 29, induces a new conformation that allows the carbonyl function of the amide to interact with side chain of Arg429 while Ser901 and Lys899 both make hydrogen bonds with the oxygens of the sulfonyl function (Fig. 8B). Interestingly, the analogue 30 is not able to make interactions with IDE via its amide function nor with Lys899 (Fig. 8C). 1.6. Discussion.

IDE was first described for its high affinity and hydrolytic properties towards insulin. Initially, the development of inhibitors to lift glucose intolerance by increasing insulin half-life was thought to be a therapeutic option. However, inhibitors tested both in vitro and in vivo displayed contradictory effects on this phenotype and the characterization of tissue-selective IDE-ko animals underlined the complex role of IDE in glucose homeostasis [START_REF] Leissring | Targeting insulindegrading enzyme in insulin clearance[END_REF], [START_REF] González-Casimiro | Modulation of insulin sensitivity by insulin-degrading enzyme[END_REF]. In particular some new non-proteolytic functions of IDE have been discovered [41]. In that context, and along with the need of activators of IDE regarding Aβ, activators of IDE regarding insulin could also be of interest.

Thanks to screening we identified an original chemical series of IDE activators of both Aβ and insulin hydrolysis. Here, activator 1 decreases glucose-stimulating insulin secretion in β-pancreatic cells as well as decreases insulin content. The latter can directly be linked to the catalytic activation of IDE by 1.

The decrease of GSIS in β-pancreatic cells treated with 1 could be linked to the extracellular activation of IDE. Still, it is surprising that activator 1 decreases GSIS like IDE inhibitors. As both activators and inhibitors are IDE ligands, they may act on this phenotype by modulating non-proteolytic functions of IDE.

Structure-activity relationships for this indole activators series highlighted the importance of the sulfonylation of the nitrogen of the indole (Table 1). Thiophene, fluoro-phenyl and phenyl analogues are the most potent (Table 1) while thiophene, phenyl and pyridine derivatives are the most efficacious regarding the fold of hydrolysis (up to 300%). Elongation of the linker between indole and imidazole is better tolerated than shortening (Table 2). Introduction of an amine function in the side chain is tolerated in shorter chains (Table 2) and specific configuration. Both a moderate pKa (10 > 40) and a right positioning of nitrogens (10 > 41) are essential for activity (Table 3). Other heterocycles than indole are also tolerated (Table 4).

IDE-C half is predominantly positively charged while IDE-N half is predominantly negatively charged. ATP, a substrate-dependent IDE activator, is thought to modify the IDE oligomer state or the open/close equilibrium of IDE by breaking the electrostatic forces between the two halves of IDE and consequently increasing the population of open form facilitating the uptake of peptide substrates [START_REF] Ivancic | Enzyme kinetics from circular dichroism of insulin reveals mechanistic insights into the regulation of insulin-degrading enzyme[END_REF].

X-ray structure of IDE co-crystallized with ATP revealed that the adenine ring of ATP was disordered.

Interactions of ATP with IDE are mediated through its triphosphate moiety. Lys898, Lys899 and Ser901 in domain 4 and Arg429 in domain2 make hydrogen bonds with this moiety via their side chain. Lys898 also interacts via its backbone to phosphate groups [START_REF] Song | An extended polyanion activation surface in insulin degrading enzyme[END_REF].

Docking is highly consistent with the structure-activity relationships as it shows that sulfonamide and imidazole are key for binding. All docked compounds are in the same activation range and it is not clear however how slightly different binding in the series affect potency or efficacy at this stage. Our docking study supports the idea that compounds in this series act through interaction with the polyanionbinding site. All compounds docked were shown to bind at least 3 of the 4 residues identified above.

This supports the possibility to target this site by compounds displaying HBA in place of ionisable groups like phosphates. Previously Ia1 and Ia2 have been shown to interact with a site partially overlapping with the ATP binding site [START_REF] Cabrol | Small-molecule activators of insulin-degrading enzyme discovered through high-throughput compound screening[END_REF]. Here we provide a new chemical series with extensive binding in the polyanion-binding site. Interestingly also, and as opposed to other chemical series of activators, this series acts as an activator of both a short Aβ analogue (10-mer) and full-length insulin hydrolysis.

Conclusion

Thanks to screening, we identified drug-like activators of IDE. Hit 1 (BDM35899) was shown to be an activator of both short Aβ-like peptide and full-length insulin hydrolysis by IDE. 1 was characterized in cells regarding glucose-stimulating insulin secretion. Structure-Activity Relationships highlighted the key role of the sulfonamide function and the imidazole ring in the activation of IDE. This role was confirmed by docking studies that showed an extended binding in the polyanion binding site of IDE, in an original, unprecedented mode. This series constitute an interesting starting point for future optimization of activators of IDE as tools to explore the multiple roles of IDE.

Experimental section

In vitro IDE activity assays

Recombinant IDE was a gift from Pr W.J. Tang, BenMay institute, University of Chicago, USA [START_REF] Shen | Structures of human insulin-degrading enzyme reveal a new substrate recognition mechanism[END_REF]. Ac-Cys-Lys-Leu-Val-Phe-Phe-Ala-Glu-Asp-Trp-NH2 was synthesized by NeoMPS. In vitro IDE activity was measured with a quenched substrate ATTO 655-Cys-Lys-Leu-Val-Phe-Phe-Ala-Glu-Asp-Trp (Km 100 µM) or with insulin (Actrapid®).

Screening assay with quenched susbtrate

Human IDE (0.05 µg/incubate) was incubated 10 min at room temperature with compound (final

concentration

Dose-Response Curves with quenched susbtrate

Percentage of activation at each concentration were obtained as for screening. All measurements were carried out as 8-point dose response curves (30 nM to 100 µM usually with constant 1% DMSO (v/v))

and reported as the average of at 4 independent repeats of duplicates.. Data analysis was performed using Xlfit® v 5.0 and GraphPad Prism® v 4.0. Nonlinear curve fitting and statistical analysis was done using built-in functions.

in vitro ADME

General information.

Chromatography was performed using a UPLC system, an Acquity I-Class (Waters). The separation was carried out on a Waters Acquity BEH C18 column (2.1 mm × 50 mm, 1.7 µm). The temperatures of the autosampler and column oven were 10°C and 40°C respectively and the sample injection volume was 1 µL. The mobile phase consisted of 0.1% formic acid in water as solvent A and 0.1% formic acid in acetonitrile as solvent B at a flow rate of 600 µL/min. The gradient was as follows: 0 -0.2 min (98% A and 2% B), 2 -2.5 min (2% A and 98% B), 2.6 min (98% A and 2% B), 4 min (98%

A and 2% B). The gradient step was linear.

Mass spectrometry was performed using a Xevo TQD mass spectrometer (Waters). Detection of the analytes was performed by electrospray ionization (ESI) in positive mode with the appropriate MRM transition. Capillary tension, cone tension and collision energy were optimized for each compound; the desolvation temperature was set at 600 °C, and the desolvation and cone gas flow rate respectively set at 1200 L / h and 50 L / h. The LC-MS/MS instrument was controlled by MassLynx software (Waters).

Solubility/LogD measurements.

Briefly, 10 μL of a 10 mM solution in DMSO of the compound are diluted either in 490μL of PBS

Stability in plasma

Incubations were performed in duplicate in Eppendorf tubes. The plasma (mouse plasma, lithium heparinated, from Sera Laboratories International Ltd) was pre-incubated 5 min at 37 °C before the addition of test compounds to a final concentration of 10µM (1% DMSO maximum). At the defined time points, 50 μL from each tube were removed to another tube containing 450 µL of cold CH3CN + internal standard (1µM). After centrifugation (10 min at 10000 rpm), supernatants are analyzed. The degradation half-life (t1/2) values were calculated using the following equation: t1/2 = 0.693/k where k is the firstorder degradation rate constant. The degradation rate constant (k) was estimated by one-phase exponential decay non-linear regression analysis of the degradation time course data using Xlfit software (version 2.1.2 or higher) from IDBS.Ltd.

Docking

A 3D structure of the ATP-bound IDE was downloaded from Protein Data Bank (PDB entry: 3TUV, rcsb.org) [START_REF] Berman | The Protein Data Bank[END_REF]. All implicit hydrogens (of the protein and the ligand) were added using MOE® 2020.09

(Chemical Computing Group ULC, 1010 Sherbrooke St. West, Suite #910, Montreal, QC, Canada, H3A 2R7). Water molecules that take part in at least three hydrogen bonds with the protein and/or the ligand, at least 2 of which are with the protein, were kept. Other water molecules were deleted. The protein structure was saved as a moe file. Hydrogen bonds were automatically detected by the programs MOE 2020.09 and PyMOL® (Delano, W. L. The PyMOL Molecular Graphics System. DeLano Scientific LLC:

San Carlos, CA, 2002). The 2D structures of ligands were constructed with Biovia Draw (Dassault Système, Vélizy-Villacoublay, France), and their energy minimization was carried out with the MMFF94 function implemented in MOE. All output ligands were saved in the mdb file format. A rigid molecular docking procedure was carried out using MOE 2020.09. The binding site was defined with "Ligand Atoms" mode in which the active ligand was ATP. A pharmacophore model consisting of 3 features denoted by the two aromatic rings and the oxygen bound to the two first phosphorus atoms of the ATP was applied (Supplementary Figure S7). The AMBER10 forcefield and the method Pharmacophore were used. A maximal number of 5 poses were retained for each ligand. Post-docking interactions of all ligands with the protein were analyzed with MOE 2020.09 and were rendered in PyMOL®.

Chemical synthesis 3.5.1. General information.

Solvents for synthesis, analysis and purification were purchased as analytical grade from commercial suppliers and used directly without further purification. Chemical reagents were purchased as reagent grade and used without further purification. LC-MS Waters system was equipped with a 2747 sample manager, a 2695 separations module, a 2996 photodiode array detector (200-400 nm) and a Micromass ZQ2000 detector (scan 100-800). XBridge C18 column (50 mm x 4.6 mm,3.5 µm,Waters) was used. The injection volume was 20 µL. A mixture of water and acetonitrile was used as mobile phase in gradient-elution. The pH of the mobile phase was adjusted with HCOOH and NH4OH to form a buffer solution at pH 3.8. The analysis time was 5 min (at a flow rate at 2 mL/min), 10 min (at a flow rate at 1 mL/min) or 30 min (at a flow rate at 1 mL/min). Purity (%) was determined by reversed phase HPLC, using UV detection (215 nm), and all isolated compounds showed purity greater than 95%.

HRMS analysis was performed on a LC-MS system equipped with a LCT Premier XE mass spectrometer (Waters), using a XBridge C18 column (50 mm x 4.6 mm, 3.5 µm, Waters). A gradient starting from 98% H2O 5 mM Ammonium Formate pH 3.8 and reaching 100% CH3CN 5 mM Ammonium The assignments were made using one-dimensional (1D) 1 H and 13 C spectra and two-dimensional (2D) HSQC-DEPT, COSY and HMBC spectra. NMR coupling constants (J) are reported in Hertz (Hz), and splitting patterns are indicated as follows: s for singlet, brs for broad singlet, d for doublet, t for triplet, q for quartet, quin for quintet, dd for doublet of doublet, ddd for doublet of doublet of doublet, dt for doublet of triplet, qd for quartet of doublet, m for multiplet, δ for chemical shift, J for coupling constant. Flash chromatography was performed using a Puriflash®430 with silica columns. UV and ELSD detection were used to collect the desired product. Reverse flash chromatography was performed using a CombiFlash® C18 Rf200 with C18 silica gel cartridges. UV detection (215 and 254 nm) was used to collect the desired product. Preparative HPLC was performed using a Varian PRoStar system with an OmniSphere 10 µm column C18 Dynamax (250 mm × 41.4 mm) from Agilent Technologies. A gradient starting from 20% MeCN / 80% H2O / 0.1% formic acid and reaching 100% MeCN / 0.1% formic acid at a flow rate of 80 mL/min was used. UV detection (215 and 254 nm) was used to collect the desired product. Purification yields were not optimized.

General procedure A.

To a solution of the specific commercial indole acid derivative (49a-49d) (1.0 eq.) in MeOH was added H2SO4 dropwise (3.3 eq.) with controlled temperature below 45 o C. The mixture was stirred at room temperature for 2h, then poured onto H2O, adjusted to pH ~ 8 with NaHCO3 and extracted twice with EtOAc. The combined organic layers were washed with H2O and brine, dried over MgSO4, filtered and concentrated to give the desired products (50a-50d). The crude product (50a-50d) and the aldehyde indole derivative (49e) were then solubilized in DCM of DMF and NaOH (3.0 eq.) and Bu4NHSO4 (0.05 eq.) were added and left to stir 10 min at room temperature before the halide or sulfonyl chloride derivative or the halogenated acyl (1.05 eq.) was added and left to stir overnight at room temperature.

The solid was filtered off. The filtrate was concentrated and dissolved in MeOH/THF (2/1 (v/v)). Aqueous solution of NaOH (3 mL) was added. The mixture was stirred at room temperature for 3h. It was diluted with H2O and adjusted to pH ~ 4 with 1M KSO4 solution. The precipitate was collected with filter, washed with H2O, and dried in a vacuum desiccator to afford the desired products (51a-51d). To the mixture of (51a-51e), HOBt (1.5 eq.) and EDCI (2.5 eq.) in DMF was added DIPEA (4.0 eq.). After stirred for 10 min at room temperature, the amine (1.5 eq.) was added and the mixture was left to stir overnight at room temperature. DMF was removed under reduced pressure and the residue was diluted with DCM, successively washed twice with aqueous saturated NaHCO3 solution, brine, dried over MgSO4, filtered and concentrated under reduced pressure. The residue was to afford the desired product (1-32 and 43-44).

General procedure B for the synthesis of analogues 41-42.

Tryptophan methyl ester hydrochloride (37a-37b) were suspended in DCM. To the suspension was added TEA (4.0 eq.), followed by di-tert-butyl dicarbonate (1.2 eq.) and left to stir at room temperature for 2h. It was diluted with DCM, washed twice with saturated NaHCO3 and brine, dried over (0.05 eq.) in DCM was stirred for 5 min at room temperature before benzenesulfonyl chloride (1.05 eq.)

was added and left to stir 2h at room temperature. DCM was removed under reduced pressure and to the residue were added NaOH (1.15 eq.), MeOH, H2O and THF. The mixture was stirred overnight at room temperature. It was adjusted to pH ~5 with acetic acid. Most of the organic solvents were removed under reduced pressure. The remained aqueous residue was extracted with DCM. The combined organic layer was washed with H2O and brine, dried over MgSO4, filtered and concentrated to afford the desired product (37-38) as off-white solid. To the mixture of (37-38), HOBt (1.5 eq.) and EDCI (2.0 eq.)

in DMF was added DIPEA (4.0 eq.). After stirred for 10 min at room temperature, 1-(3-aminopropyl)imidazole (1.5 eq.) was added. The mixture was stirred at room temperature over the week-end. DMF was removed under reduced pressure. The residue was diluted with DCM, successively washed twice with saturated NaHCO3 and brine, dried over MgSO4, filtered and concentrated by under reduced pressure. It was purified by flash column chromatography on silica gel (DCM/MeOH, 20/1) to afford the desired products [START_REF] Deprez-Poulain | Ligands of insulin degrading enzyme and their uses[END_REF](40) as white powders. The Boc-protected compound (39-40) was dissolved into HCl 4M in dioxane at 0°C and left to stir at room temperature overnight. Dioxane was removed under reduced pressure before the residue was dissolved in H2O, basified with NH4OH and extracted with DCM. The organic layer washed with brine, dried over MgSO4, filtered and concentrated under reduced pressure. The residues were purified by preparative LC-MS with pH 9 buffer solution as the eluent to give the desired products (41-42) as an oil.

3.5.4. Compounds 1-48.

4-[1-(thiophene-2-sulfonyl)-1H-indol-3-yl]-N-(3-imidazol-1-yl-propyl)-butyramide (1).

1 was synthesized according to the general procedure A from 4-(1H-indol-3-yl)-butyric acid and purified by flash column chromatography on silica gel (DCM/MeOH, 20/1) to afford the desired product as pale-yellow sticky oil (0.78 mmol, 29%). LC-MS: tr = 2.47 min, 100% purity (at 215 nm), m/z 454.9

[M-H] -, 500.9 [M-H+2Na] -, 456.9 [M+H] + . HRMS m/z calculated for C22H25N4O3S2 [M + H] + 457.1368, found 457,1366. 1 H NMR (300 MHz, CD3OD): δ 1.96 (4H, m), 2.25 (2H, t, J = 7.5 Hz), 2.73 (2H, t, J = 7.5 Hz), 3.16 (2H, t, J = 6.9 Hz), 4.04 (2H, t, J = 6.9 Hz), 6.97 (1H, s), 7.05 (1H, dd, J = 3.9, 5.1 Hz), 7.14 (1H, s), 7.27 (1H, t), 7.35 (1H, t), 7.39 (1H, s), 7.55 (1H, d, J = 7.5 Hz), 7.66 (1H, s), 7.73 (1H, m), 7.95 (1H, d, J = 8.1 Hz). 13 C NMR (75 MHz, CD3OD): δ 25.2, 26.3, 31.9, 36.4, 37.5, 45.6, 115.0, 120.6, 120.7, 124.1, 124.7, 125.0, 125.9, 128.6, 129.1, 132.5, 134.5, 135.3, 136.8, 138.5, 139.0, 175.8.

N-(3-imidazol-1-ylpropyl)-4-(1H-indol-3-yl)butanamide (2).

2 was synthesized according to the general procedure A from 4-(1H-indol-3-yl)-butyric acid and it was purified by flash column chromatography on silica gel (DCM/MeOH, 20/1) to afford the desired product as pale-yellow sticky oil (0.38 mmol, 37% 4, 26.3, 30.8, 35.4, 35.7, 44.0, 111.5, 114.2, 118.2, 118.4, 119.7, 121.0, 122.4, 127.3, 127.7, 136.4, 137.3, 172.5 3.5.4.3. 4

-(1-methyl-1H-indol-3-yl)-N-(3-imidazol-1-yl-propyl)-butyramide (3).

3 was synthesized according to the general procedure A from 4-(1H-indol-3-yl)-butyric acid and it was purified by flash column chromatography on silica gel (DCM/MeOH, 20/1) to afford the desired product as pale-yellow sticky oil 0.66 mmol, 33%). LC-MS: tr = 2.08 min, 99% purity (at 215 nm), m/z 323.2 [M-H] -, 369.1 [M-H+2Na] -, 325.0 [M+H] + . HRMS m/z calculated for C19H25N4O [M + H] + 325.2028, found 325,2020. 1 H NMR (300 MHz, CD3OD): δ 1.86 (2H, quint, J = 6.9 Hz), 1.98 (2H, quint, J = 7.5

Hz), 2.23 (2H, t, J = 7.5 Hz), 2.74 (2H, t, J = 7.5 Hz), 3.65 (3H, s), 3.91 (2H, t, J = 6.9 Hz), 6.88 (1H, s), 6.94 (1H, s), 7.01 (1H, t, J = 7.5 Hz), 7.04 (1H, s), 7.13 (1H, t, J = 7.5 Hz), 7.23 (1H, d, J = 8.1 Hz), 7.53 (1H, d, J = 7.8 Hz), 7.58 (1H, s). 13 C NMR (75 MHz, CD3OD): δ 24.3, 26.4, 30.5, 35.5, 36.0, 40.1, 44.1, 108.9, 113.9, 118.1, 118.5, 119.2, 120.9, 124.5, 127.7, 128.1, 136.2, 137.1, 174.9. 3.5.4.4. 4-(1-ethyl-1H-indol-3-yl)-N-(3-imidazol-1-yl-propyl)-butyramide (4).

4 was synthesized according to the general procedure A from 4-(1H-indol-3-yl)-butyric acid and it was purified by flash column chromatography on silica gel (DCM/MeOH, 20/1) to afford the desired chlorite (1.5 eq.). The mixture was stirred for 1 h at room temperature. Dioxane was removed under reduced pressure. The remained aqueous residue was adjusted to pH ~ 4 with saturated NaHCO3 solution and extracted three times with EtOAc. The combined organic layer was washed with H2O and brine, dried over MgSO4, filtered and concentrated. The residue was agitated to precipitate by addition of EtOAc/cyclohexane (5 ml / 30 ml). The precipitate was collected to give the crude product (50e) as pale solid (1.88 mmol, 89%), which was pure enough to be directly used in the next step. LC-MS: tr = eq.) and EDCI (2 eq.) in dry DMF was added DIPEA (4 eq.). After stirred for 10 min at room temperature, 4,36.9,45.4,113.6,117.8,119.8,122.5,124.5,125.7,127.3 (2C),128.3,128.3,129.9 (2C),134.8,135.1,137.4,.

27 was synthesized according to the general procedure A and it was purified by flash column chromatography on silica gel (DCM/MeOH, 18/1) to afford the desired product as white solid (0.58 mmol, 72% 1 H NMR (CDCl3, 300 MHz): δ 1.87 (2H, quint, J = 6.9 Hz), 3.16 (2H, q, J = 6.6 Hz), 3.62 (2H, s), 3.82 (2H, t, J = 6.9 Hz), 5.94 (1H, brs), 6.79 (1H, s), 7.00 (1H, s), 7.30 (2H,d,J = 8.4 Hz),7.35~7.57 (6H,m),7.89 (2H,d,J= 7.5 Hz),8.00 (1H,d,J = 8.4 Hz). 13 C NMR (CDCl3, 75 MHz): δ 30.8,33.1,36.6,44.4,113.6,116.5,118.9,119.7,123.5,124.7,125.2,126.7 (2C),129.0,129.3 (2C),130.3,134.0,135.1,136.9,- N-[3-imidazol-1-yl-propyl]-propionamide (28).

temperature for 3 h. It was diluted with H2O and adjusted to pH ~ 4 with 1M KHSO4 solution. The precipitate was collected with filter, washed with H2O, and dried in a vacuum desiccator to afford the desired product 3-(1-benzenesulfonyl-1H-indol-3-yl)-propionamide as white solid (98% yield). The carboxylic acid was treated with PyBOP (1.5 eq.), HOBt (1.5 eq.), DIPEA (4 eq.), NH4CI (2 eq.) in DMF and left to stir at room temperature overnight. DMF was removed under reduced pressure and the residue was diluted with DCM, successively washed twice with aqueous saturated NaHCO3 solution, brine, dried over MgSO4, filtered and concentrated under reduced pressure to give a brown oil.

Cyclohexane was added and evaporated off. 6, 35.8, 114.7, 120.5, 123.8, 124.4 (2C), 125.8, 127.8 (2C) 7, 31.7, 40.7, 113.5, 119.3, 122.8, 123.0, 123.5, 124.4, 126.4, 129.0, 131.1, 133.6, 135.5, 137.8 MHz): δ 2.02 (2H, quint, J = 6.9 Hz), 2.16 (2H, t, J = 6.9 Hz), 4.14 (2H, t, J = 6.9 Hz), 7.33 (1H, s), 7.40 (1H, s), 8.61 (1H, s). The data is identical to that in lit. J. Org. Chem., 2004, 69 (21): 7171. To the mixture of the acid 33b, HOBt (1.5 eq.) and EDCI (2.5 eq.) in DMF was added DIPEA (4.0 eq.). After being stirred for 10 min at room temperature, the amine 36 (1.05 eq.) was added and the mixture was left to [START_REF] Sbardella | The insulin-degrading enzyme is an allosteric modulator of the 20S proteasome and a potential competitor of the 19S[END_REF]26.8,28.3,32.1,38.6,46.0,113.5,119.2,119.3,112.9,123.1,124.5,126.5,127.8,129.0,131.0,133.7,135.4,137.1,137.8,-ethyl]- 3-(3-imidazol-1-yl-propyl)-urea (34).

A mixture of commercial N-Boc-tryptamine 34a, NaOH (3.0 eq.) and Bu4NHSO4 (0.05 eq.) in dry DCM was stirred for 5~10min before benzenesulfonyl chloride (1.05 eq.) was added. The mixture was stirred for 3h at room temperature. It was diluted with DCM, filtered and concentrated under reduced pressure.

The residue was dissolved in HCl 4M in dioxane and left to stir overnight at room temperature. Water was added adjusted to basic pH with NH4OH and extracted with EtOAc. The extracted organic layer was washed with brine, dried over MgSO4, and concentrated under reduced pressure to afford the desired product 34b as light brown oil, which became waxy residue (1.78 mmol, 96% ). 1 31.9, 33.2, 37.3, 45.5, 51.9, 117.2, 118.1, 120.6, 129.0, 130.2, 130.4 (2C), 134.7, 135.0, 135.1, 135.1, 138.5 (2C), 142.8, 174.8. 3.5.4.46. 4-(1-benzenesulfonyl-1H-indol-2-yl) 13 C NMR (75 MHz, CD2Cl2): δ 24.9, 28.5, 31.2, 35.7, 36.5, 44.7, 109.5, 114.7, 120.3, 123.7,124.0, 126.2, 129.3, 129.9, 133.8, 137.1, 138.6, 141.5, 172.5. 3.5.4.47. 4-(1-benzenesulfonyl-1H-indazol-3-yl)-N-(3-imidazol-1-yl-propyl)-butyramide (44).

A mixture of indazole 44a (0.5 g, 4.2 mmol), I2 (2.0 eq.) and KOH (3.8 eq.) in DMF and H2O ( 7 °C. To the mixture was added NiCl2(PPh3)2 (0.1 eq.) and ethyl 4-bromobutyrate (3.0 eq.). The mixture was left to stir overnight at 80 °C. The solvent was removed under reduced pressure. The residue was diluted with EtOAc, washed with saturated NH4Cl solution and brine, dried over MgSO4 and concentrated under reduced pressure to afford the desired ethyl ester compound. 1 H NMR (300 MHz, CD2Cl2): δ 1.23 (3H, t, J = 7.2 Hz), 1.76 (2H, q, J = 7.2 Hz), 2.44 (2H, t, J = 7.2 Hz), 3.66 (2H, t, J = 6.9

Hz), 4.07 (2H, q, J = 7.2 Hz), 7.06 (1H,d,J = 8.1 Hz),m),m),7.75 (1H,d,J = 7.5 Hz). 13 C NMR (75 MHz, CD2Cl2): δ 14. 0, 23.6, 30.7, 50.7, 60.4, 115.9, 116.5, 127.9, 129.0, 129.2, 129.5, 133.4, 133.5, 134.1, 137.6, 141.5, 172.5.LC-MS: tr = 2.77 min, m/z 370.9 [M-H]-, 372.8

[M+H]+, 326.9 [M-EtOH+H]+.To the above ester was added NaOH (3.0 eq.), MeOH and H2O (3/1 (v/v)).

The mixture was stirred overnight at room temperature. MeOH was removed under reduced pressure before the aqueous residue was diluted with H2O, adjusted to pH ~ 4 with HCl 1N and extracted three times with EtOAc. The combined organic layer was washed with brine, dried over MgSO4 and concentrated under reduced pressure. The residue was purified by flash column chromatography over silica gel (cyclohexane/EtOAc, 1/1) to afford the desired product 44c as white solid (0.36 mmol, 48% for 2 steps). 1H NMR (300 M, CD3OD): δ 1.69 (2H, quint, J = 7.2 Hz), 2.47 (2H, t, J = 7.2 Hz), 3.68 (2H, t, J = 6.6 Hz), 7.04 (1H, d, J = 8.1 Hz), m),m),7.81 (1H,d,J = 7.5 Hz). LC-MS: tr = 2.32 min, m/z 343.0 [M-H]-, 344.8 [M+H]+, 326.9 [M-H2O+H]+. To a mixture of 44c, HOBt (1.5 eq.) and EDCI (2.0 eq.) in DCM was added DIPEA (4.0 eq.). After being stirred for 10 min at room temperature, 1-(3-aminopropyl)-imidazole (1.5 eq.) was added and the mixture was stirred overnight at room temperature. It was diluted with DCM, successively washed twice with aqueous saturated NaHCO3 solution, brine, dried over MgSO4 and concentrated under reduced preffure. The residue was purified by flash column chromatography on silica gel (DCM/MeOH, 20/1) to afford the desired product 44 as colorless viscous oil (66% yield). LC-MS: tr = 1.97 min, 98% purity (at 215 nm), m/z 450.0 [M-H] -, 495.9

[M-H+2Na] -, 451.9 [M+H] + . HRMS m/z calculated for C23H26N5O3S [M + H] + 452,1756, found 452,1747. 1 H NMR (300 MHz, CD3OD): δ 1.71 (2H, quint, J = 6.9 Hz), 1.96 (2H, quint, J = 6.9 Hz), 2.39 (2H, t, J = 7.2 Hz), 3.16 (2H, t, J = 6.6 Hz), 3.67 (2H, t, J = 6.0 Hz), 4.05 (2H, t, J = 7.2 Hz), 6.96 (1H, s), 7.00 (1H, d, J = 8.1 Hz), 7.14 (1H,s),m),m),7.81 (1H,d,J = 7.5 Hz). 3.5.4.48. 6-(benzenesulfonyl-phenyl-amino)-hexanoic acid (3-imidazol-1-yl-propyl)-amide (45).

A mixture of iodobenzene Hz), 7.90 (2H, s). 13 C NMR (75 MHz, CDCl3): δ 24.6, 26.6, 29.1, 34.2, 44.2, 113.5, 117.9, 129.4, 148.0, 179.9. To the solution of 45b in DCM and pyridine (3/1 (v/v)) before benzenesulfonyl chloride was added 2, 29.7, 31.7, 37.7, 54.3, 131.5, 132.0, 132.67,

Figure 2 :

 2 Figure 2: Activators of IDE from the literature [35-39].

Figure 3 :

 3 Figure 3: Screening cascade a

Figure 4 :

 4 Figure 4: Structure of hit 1 and planned pharmacomodulation.

Figure 5 :

 5 Figure 5: Hydrolysis of insulin by IDE in the presence of cpd 1. a a Values are given as the mean of 3 experiments. [hIDE] = 7.5 µg/mL. [1] = 100 µM; [EDTA] = 50 mM. EDTA inhibits IDE by chelating the zinc, whereas 1 behaves as an activator of insulin hydrolysis by IDE. * p < 0.01.

Figure 6 :

 6 Figure 6: Effect of 1 on the glucose stimulation of insulin secretion (GSIS) on Min6 β-pancreatic cells. a a A) Insulin secretion induced by glucose stimulation in the presence of 1, overnight pretreatment before and during GSIS. B) Insulin content in the presence of increasing glucose concentrations, and in the presence of 1.* p<0.05, ** p <0.01, *** p <0.001. Values are given as the mean of 3 experiments.

8Scheme 1 .Scheme 2 .Scheme 3 .

 123 Scheme 1. Synthesis of indole derivatives 1-32 and 40-41. a a Reactants and conditions: a) H2SO4, MeOH, room temp., 2 h, 98%; b) NaOH, Bu4NHSO4 cat., DCM, halide, sulfonylchloride or acylhalide, room temp., 3 h or overnight; c) NaOH, MeOH/H2O, room temp., overnight, 27%quant (2-step yield); d) NaClO2, HOSO2NH2, dioxane/H2O, room temp., 1 h, 56% (2-step yield); e) HOBt/EDCi, DIPEA, DMF, room temp., overnight, 18-88%.

Scheme 4 .Scheme 5 .Scheme 6 .Scheme 7 .Scheme 8 .

 45678 Scheme 4. Synthesis of indole derivatives 37-39 from tryptophan. a a Reactants and conditions: a) Boc2O, Et3N, DCM, room temp., 2 h b) NaOH, Bu4NHSO4 cat., DCM, benzenesulfonyl chloride, room temp., 3 h c) NaOH, MeOH/H2O, room temp., overnight, 85-87% (3-step yield); d) 1-(3-aminopropyl)imidazole, HOBt/EDCi, DIPEA, DMF, room temp., overnight, 74-83%; e) HCl 4N in dioxane, 0 °C overnight, 60-63%.

  using PipelinePilot TM . b Not calculable; n=4. In the initial screening, several analogues of 1, displaying diverse alkyl groups, aromatic and heteroaromatic cycles, basic or not, in place of the N-(3-amino-propyl)imidazole moiety had been tested.

Figure 7 :

 7 Figure 7: Interactions of 1 with IDE polyanion-binding site. a

Figure 8 :

 8 Figure 8: Docking poses of the 3 analogues 10 (A), 29 (B) and 30 (C) in the polyanion binding site of IDE (PDB code: 3TUV). a a IDE N-terminus and the C-terminus of IDE were colored blue and gray, respectively. Oxygens, nitrogens, sulfur are in red, blue and orange respectively. Carbons are colored in cyan for IDE and in yellow for compounds. Polar

  30 µM, 1% (v/v) DMSO final) in Hepes sodium 50 mM, NaCl 100 mM, pH 7.4 and the enzymatic reaction is started by adding the quenched substrate (final concentration 5 µM). After 20 min at 37 °C, samples (1% (v/v) DMSO final) are excited at 635 nm and fluorescence emission at 750 nm is measured on a Victor3 V1420 Perkin Elmer spectrophotometer during 2 h every 2 minutes. Initial velocities were calculated on the linear phase of the enzymatic kinetic curve (usually 8 to 10 time points). Suramin was used as reference at 10 µM. Z and Z' factors were calculated according to J.-H. Zhang, T.D.Y. Chung, K.R. Oldenburg, A Simple Statistical Parameter for Use in Evaluation and Validation of High Throughput Screening Assays, J. Biomol. Screen., 4 (1999) 67-73. Data analysis was performed using Xlfit® v 5.0.

pH 7 .

 7 4 or in organic solvent MeOH in a 700 µL-microtube (in triplicate). The tubes are gently shaken 24h at room temperature, then centrifuged for 5 minutes at 4000 rpm. The mixtures are filtered over 0.45 μm filters (Millex-LH Millipore). 20 μL of sample are diluted in 180 μL of MeOH. The solubility is determined by the ratio of mass signal area PBS/ organic solvent. 40µL of a 10 mM solution in DMSO of the compound were diluted in 1.960 mL of a 1/1 octanol /PBS at pH 7.4 mixture. The mixture was gently shaken 2 h at room temperature. 20 µL of each phase was diluted in 480 µL of MeOH and analyzed by LC-MS. Each compound is tested in triplicate. Log D was determined as the logarithm of the ratio of concentration of product in octanol and PBS respectively, determined by mass signals.

Formate pH 3 .

 3 8 within 3 min at a flow rate of 1 mL/min was used. NMR spectra were recorded on a Bruker DRX-300 spectrometer. The results were calibrated to signals from the solvent as an internal reference [e.g. 2.50 (residual DMSO-d6) and 39.52 (DMSO-d6) ppm for ¹H and ¹³C NMR spectra respectively]. Chemical shifts (δ) are in parts per million (ppm) downfield from tetramethylsilane (TMS).

  MgSO4, filtered and concentrated to afford the desired product as white solid. LC-MS: tr = 2.97 min, m/z 317.0 [M-H] -, 319.0 [M+H] + .A mixture of N-Boc-tryptophan methyl ester, NaOH (3.0 eq.) and Bu4NHSO4

3 .

 3 02 min, m/z 284.1 [M-H] -, 286.0 [M+H] + .To the mixture of the carboxylic acid (1.12 mmol), HOBt(1.5

/ 1 ( 8 [

 18 v/v)) was stirred overnight at room temperature. The solution was poured into aqueous Na2S2O3 5% solution. The precipitate was collected by filter, washed with H2O and dried under reduced pressure to afford the 3-iodoindazole as off-white powder (73% yield). LCMS: tr = 2.43 min, m/z 242.8 [M-H]-, 244.M+H]+. A mixture of 3-iodoindazole, Bu4NHSO4 (0.05 eq.) and KOH (3.0 eq.) in DCM was stirred for 10 min. Benzenesulfonyl chloride (1.1 eq.) was added and left to stir for 3h at room temperature before the reaction mixture was diluted with DCM and filtered. The filtrate was washed with brine, dried over MgSO4 and concentrated under reduced pressure to afford the desired product 44b as white crystal(1.49 mmol, 99%). LC-MS: tr = 3.10 min, 100% purity (at 215 nm), m/z 382.8 [M-H]-, 384.7[M+H]+. A mixture of Zn dust (3.0 eq.) and I2 (3.0 eq.) in DMA under argon atmosphere was heated at 80°C for 5 min. To the mixture was added 44b dissolved in DMA. The mixture was stirred over the week-end at 80

  (4.1 g, 20 mmol), 6-aminocaproic acid 45a(3.95 g, 30 mmol), K3PO4•H2O(9.2 g, 40 mmol), CuI (380 mg, 2 mmol), deanol (6 ml) and H2O (20 ml) was heated for 48 h at 80 o C under argon atmosphere (LCMS showed the reaction was quite clean). After being cooled, it was diluted with H2O, adjusted to pH 4~5 and extracted with EtOAc (3 times). The combined organic layer was washed with brine, dried over MgSO4, filtered and concentrated by rotary evaporator in vacuo.The residue was purified by flash column chromatography on silica gel (cyclohexane/EtOAc, 1/1) to give 6-phenylamino-hexanoic acid 45b as pale white solid (2.40 mmol, 12% yield). LC-MS: tr = 2.22 min, m/z 206.4 [M-H] -, 208.5[M+H] + .1 H NMR (300 MHz, CDCl3): δ 1.53 (2H, m), 1.75 (4H, m), 2.44 (2H, t, J = 7.5 Hz), 3.18 (2H, t, J = 6.9 Hz),6.71 (2H, d, J = 7.5 Hz), 6.82 (1H, t, J = 7.2 Hz), 7.27 (2H, t, J = 7.5

( 1 .

 1 02 eq.) and left to stir overnight at room temperature. It was diluted with DCM, washed twice with 1M HCl solution and brine, dried over MgSO4, and concentrated under reduced pressure to afford the desired product 45c as light brown solid (1.45 mmol, 90%). LC-MS: tr = 2.70 min, m/z 346.0 [M-H]-, 348.0 [M+H]+.1H NMR (300 MHz, CDCl3 and CD3OD): δ 1.39 (4H, m), 1.58 (2H, quint, J = 7.2 Hz), 2.28 (2H, t, J = 7.2 Hz), 3.54 (2H, t, J = 6.3 Hz), 7.00 (2H, m), 7.27 (3H, m), 7.42 (2H, m), 7.55 (3H, m), 10.1 (1H, brs). 13C NMR (75 MHz, CDCl3 and CD3OD): δ 28.

Table 1 :

 1 Impact of the N-substitution of the indole

				Activation
	Cpd #	R1	pEC50	Factor @100 µM
				(30 µM)
	1	2-thiophenyl-SO2-	5.30±0.14	2.30±0.18
	2	H-	4.05±0.40	1.35±0.51
	3	Me-	_ a	1.49
	4	Et-	_ a	1.21
	5	Ph-	_ a	(0.93) b
	6	p-Chlorobenzyl-	_ a	(0.76) b
	7	p-Fluorobenzyl-	_ a	(0.71) b
	8	2-thiophenyl-CO-	4.67±0.27	2.40±0.05
	9	Me-SO2-	4.57±0.13	2.15±0.22
		Ph-SO2-	4.88±0.09	2.28±0.11
		o-Fluorophenyl-SO2-	5.10±0.16	(1.75±0.09) b
		m-Fluorophenyl-SO2-	4.99±0.06	(2.06±0.30) b
		p-Fluorophenyl-SO2-	5.17±0.27	(1.45±0.07) b

Table 2 :

 2 Impact of the linker.

							Activation
	Cpd #	n m	R1	X	Y	pEC50	Factor @100 µM
							(30 µM)
	10 3	-	CO	NH 4.88±0.09	2.28±0.11
	26 3	-	CO	NH _ a		(0.96) b
	27 3	-	CO	NH _ a		1.15
	28 3	-	CO	NH 4.81± 0.15	1.64±0.05
	29 3	-	CO	NH 5.14± 0.20	(1.71±0.07) b
	30 4	-	CO	NH 5.09±0.21	2.67±0.11
	31 2	-	CO	NH _ a		1.0
	32 3	-	CO NMe 4.85±0.13	1.53±0.13
	33 3	-	NH	CO _ a		0.78
	34 3	-	NHCO NH 4.99±0.05	2.41±0.40
	35 -	H	CO NH2 _ a		0.94

n 10,26-34 ( ) n 39-42 ( ) m 35-38 n ( ) m

Table 4 :

 4 Impact regioisomerism or bioisosterism on the indole

			Activation
	Cpd #	pEC50	Factor @100 µM
			(30 µM)
	2	4.05±0.40	1.35±0.51
	10	4.88±0.09	2.28±0.11
	42	4.41±0.07	1.31±0.02
	43	5.09±0.15	2.21±0.55
	44	4.91±0.56	1.52±0.11
	45	_ a	_ a

2: R=-H; X=C 10: R=-SO 2 -Ph; X=C 44: R=-SO 2 -Ph; X=N 43: R=-SO 2 -Ph 42 45: R=-SO 2 -Ph a Not calculable. n=4.

  The reaction was started with the addition of 40 μL of substrate at 4 μM. Final concentrations of IDE and insulin, were 7.51 μg/mL and 1 μM respectively. The reaction was quenched at a suitable time point with 20 µL of a solution of TFA/ACN 0.1%. Quantification of

	dimensions 0.3 * 100 mm from Interchim at 50 °C. A gradient starting from 75% H2O/0.1% TFA (v/v)
	and reaching 75% CH3CN /0.09% TFA (v/v) within 10 min at a flow rate of 0.3 µL/min was used and
	quantification was done at 215/254 nm.
	3.2. Cellular assays
	3.2.1. Cell culture
	Min 6 cells cells (provided by professor Jurgen Puenter (Sanofi Aventis, Germany)) were cultured in a
	humidified atmosphere containing 5% CO2 in DMEM glutamax medium (Gibco) (containing 25mmol/L
	glucose) supplemented with 10% heat-inactivated fetal bovine serum (FBS, Corning), β-mercapto-
	Ethanol 50 µM (Sigma), and gentamycin 1% (Invitrogen).
	3.2.2. Glucose Stimulated Insulin Secretion (GSIS):
	residual substrate was performed by HPLC analysis (UV 215 nm) using an UltiMate™ nano LC system
	apparatus, equipped with a Famos® autosampler and a Switchos™ precolumn switching device all from
	LC_packings (Dionex.Corp). 10µL of sample were loaded on a precolumn 5*0.3 mm equipped with a
	guard cartridge Q95961 10*1.0 mm from Interchim at a flowrate of 50 µL/min for preconcentration.
	Separation was performed using an Uptisphere UP5WTF-A10 C18wtf 5-µm particle size column,

3.1.3. Hydrolysis of unlabed insulin by IDE

Insulin (Actrapid®) was dissolved in Hepes 50 mM with 100 mM NaCl, pH 7.4. Then, 20 μL of IDE at 30 μg/mL were pre-incubated 1 or 10 minutes at 37 °C with 20 μL of vehicle, compound or inhibitor (EDTA) in microtiter plates (black, low-binding).

Min6 were seeded in 24 well plate (300 000 cells/well) and cultured for 7 days. The cells are pre-treated for 24h before or 1h during GSIS. Each compound is dissolved in DMSO. Before the GSIS experiment, the cells were washed and preincubated for 1 hour at 37 °C in glucose-free Krebs-Ringer bicarbonate HEPES buffer (KRBH) of the following composition: 115 mM NaCl, 4.7 mM KCl, 2.6 mM CaCl2, 1.2 mM KH2PO4, 1.2 mM MgSO4, 20 mM NaHCO3, 16mM HEPES adjusted pH 7.4, BSA free fatty acid 0.5% (w/v). Next the cells are stimulated in KRBH buffer containing 2.8 mM of glucose or 20 mM of glucose for 1 hour. Incubation was stopped by putting the plate on the ice, the supernatant was collected for insulin secretion. Insulin secretion was measured by ELISA (Mercodia).

  ). LC-MS: tr = 3.97 min, >99% purity (at 215 nm), m/z 311.1 [M+H] + . HRMS m/z calculated for C18H23N4O [M + H] + 311.1872, found 311,1874.

1

H NMR (300 MHz, DMSO-d6): δ: 1.76-1.92 (m, 4H), 2.14 (t, J = 7.5 Hz, 2H), 2.67 (t, J = 7.5 Hz, 2H), 3.00 (dd, J = 6.8 and 5.8 Hz, 2H), 3.95 (t, J = 6.8 Hz, 2H), 5.89 (s, 1H), 6.92-6.97 (m, 1H), 7.02-7.07 (m, 1H), 7.08-7.11

(m, 1H), 7.18 (s, 1H), 7.30-7.34 (m, 1H)

, 7.49 (br d, J = 7.7 Hz, 1H), 7.65 (s, 1H), 7.86 (t, J = 5.6 Hz, 1H), 10.77 (s, 1H); 13 C NMR (75 MHz, DMSO-d6): δ 24.

  1-(3-aminopropyl)imidazole (1.5 eq.) was added. The mixture was stirred overnight at room temperature.DMF was under reduced pressure. The residue was diluted with DCM, washed successively twice with saturated NaHCO3 aqueous solution, brine, dried over MgSO4, filtered and concentrated. The residue was purified by flash column chromatography over silica gel (DCM/MeOH, 15/1) and preparative LCMS to afford the desired product as a pale-yellow viscous oil(0.33 mmol, 30%). LCMS (10min): tr = 2.40 min, purity 98% (at 215 nm), m/z 407.0 [M-H] -, 453.0 [M+2Na-H] -, 408.9 [M+H] + . HRMS m/z calculated for C21H21N4O3S [M + H] + 409.1334, found 409,1336. 1 H NMR (CD2Cl2, 300 MHz): δ 2.14 (2H, quint, J

	= 6.6 Hz), 3.44 (2H, q, J = 6.0 Hz), 4.11 (2H, t, J = 6.6 Hz), 7.08 (2H, s), 7.29~7.59 (6H, m), 7.85 (1H,
	s), 7.90 (2H, d, J = 7.5 Hz), 7.96 (1H, d, J = 8.1 Hz), 8.14 (1H, d, J = 7.5 Hz), 8.26 (1H, s). 13 C NMR
	(CD2Cl2, 75 MHz): δ 31.

  . The acid 33b was obtained from ethyl 4-bromobutanate and imidazole in a 2-step reaction, first with NaH (1.0 eq.) in DMF at 80°C for 1h. DMF was removed by rotary evaporation in vacuo. The residue was diluted with EtOAc, washed with H2O dried over MgSO4, filtered and concentrated under reduced pressure. The residue was purified by flash column chromatography on silica gel (EtOAc/MeOH, 8/1) to afford the intermediate as a colorless oil (4.01mmol, 17%). The mixture of the intermediate methyl ester (4.18mmol), NaOH (1.2 eq.), H2O and EtOH was stirred at room temperature for 30 min. The mixture was adjusted to pH ~ 5 with HCl solution (1 M). The solvents were removed under reduced pressure. The residue was solubilized with hot EtOH and filtered. The filtrate was concentrated to afford the desired product 33b a colorless oil. (4.01 mmol, 96%).1 H NMR (D2O, 300

  stir overnight at room temperature. DMF was removed under reduced pressure and the residue was diluted with DCM, successively washed twice with aqueous saturated NaHCO3 solution, brine, dried over MgSO4, filtered and concentrated under reduced pressure. The residue was to afford the desired product 33. It was purified by flash column chromatography on silica gel (DCM/MeOH, 20/1) to afford the desired product 33 as a pale-yellow viscous oil (0.60 mmol, 52%). LC-MS: tr = 2.53 min, purity 100%

	3.99
	(2H, t, J = 7.2 Hz), 6.96 (1H, s), 7.08 (1H, s), 7.17 (1H, t, J = 7.2 Hz), 7.27 (1H, t, J = 7.2 Hz), 7.36 (2H,
	m), 7.44 (2H, m), 7.46 (1H, s), 7.62 (1H, s), 7.85 (2H, d, J = 7.2 Hz), 7.95 (1H, d, J = 8.4 Hz). 13 CNMR
	(CD3OD, 300 MHz): δ 21.

(at 215 nm), m/z 449.0 [M-H] -, 494.9 [M+2Na-H] -, 450.9

[M+H]

+ . HRMS m/z calculated for C24H27N4O3S

[M + H] + 451.1804, found 451,1797.

1

H NMR (CD3OD, 300 MHz): δ 1.83 (2H, quint, J = 7.5 Hz), 2.04 (2H, quint, J = 6.9 Hz), 2.16 (2H, t, J = 6.9 Hz), 2.65 (2H, t, J = 7.5 Hz), 3.19 (2H, t, J = 7.2 Hz),

  DIPEA (4.0 eq.). After being stirred for 10 min at room temperature, 1-(3aminopropyl)imidazole (1.5 eq.) was added. The mixture was stirred for 6h at room temperature. The solution was diluted with DCM, successively washed twice with aqueous saturated NaHCO3 solution, brine, dried over MgSO4, and concentrated under reduced pressure. The residue was purified by flash

	column chromatography on silica gel (DCM/MeOH, 8/1) to afford the desired product 42 as a colorless
	oil (0.14 mmol, 14%). LC-MS: tr = 1.58 min, 100% purity (at 215 nm), m/z 326.1 [M-H] -, 328.0 [M+H] + .
	HRMS m/z calculated for C18H23N4O2 [M + H] + 327.1821, found 327,1824. 1 H NMR (300 MHz, CD3OD):
	δ 1.60 (2H, m), 1.98 (4H, m), 2.20 (2H, t, J = 7.5 Hz), 3.15 (2H, t, J = 6.6 Hz), 4.04 (2H, t, J = 6.9 Hz),
	6.90 (1H, d, J = 7.8 Hz), 6.98 (1H, s), 7.00 (1H, t, J = 7.5 Hz), 7.14 (1H, s), 7.20 (1H, t, J = 7.5 Hz), 7.25
	(1H, d, J = 7.5 Hz), 7.69 (1H, s). 13 C NMR (CD3OD, 75 MHz): δ 25.1,

H NMR (CDCl3, 300 MHz): δ 1.88 (2H, brs), 2.76 (2H, t, J = 6.8 Hz), 2.94 (2H, t, J = 6.8 Hz), 7.16 (1H, t, J = 7.5 Hz), 7.21~7.

41 (5H, m), 7.46 (1H, d, J = 7.8 Hz), 7.82 (2H, d, J = 7.8 Hz), 7.97 (1H, d, J = 8.4 Hz)

. To 34b was added

Acknowledgements

We thank Pierre Boulens and Marion Gauriot for technical assistance and Pr W.J. Tang for recombinant IDE. The authors acknowledge financial support from INSERM, University of Lille, Institut Pasteur de Lille, Region Hauts-de-France, l'Agence Nationale de la Recherche ANR grants JCJC11-JS07-015-01, « European Genomic Institute for Diabetes » E.G.I.D, ANR-10-LABX-0046, under the frame program Investissements d'Avenir I-SITE ULNE / ANR-16-IDEX-0004 ULNE, INSERM PCSI grant (N°ASC20017ESA), Fondation pour la Recherche Médicale FRM grant (N°DCM20111223046), State

(0823007, 0823008, 07-CPER 009-01, 2007-0172-02-CPER/3), the European Union under the European Regional Fund (ERDF), by the Hauts-de-France Regional Council (N°17003781), the MEL (N°2016_ESR_05), and the French State (N°2017-R3-CTRL-Phase 1). The NMR facilities were funded by the Region Hauts-de-France, CNRS, Institut Pasteur de Lille, European Regional Fund (ERDF), Ministere de l'Enseignement superieur, de la Recherche et de l'Innovation (MESRI) and Lille University. N. K. is a recipient of a PhD fellowship from the University of Lille.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.