Thibault Hilaire

LOW PARAMETRIC SENSITIVITY REALIZATIONS WITH RELAXED L 2 -DYNAMIC-RANGE-SCALING CONSTRAINTS

Keywords: Digital filter implementation, coefficient sensitivity, scaling, fixed-point implementation implémentation de filtre, sensibilité des coefficient, implémentation virgule fixe, mise à l'échelle

This paper presents a new dynamic-range scaling for the implementation of filters/controllers in state-space form. Relaxing the classical L 2 -scaling constraints by specific fixed-point considerations allows for a higher degree of freedom for the optimal L 2 -parametric sensitivity problem. However, overflows in the implementation are still prevented. The underlying constrained problem is converted into an unconstrained problem for which a solution can be provided. This leads to realizations which are still scaled but less sensitive.

I R I S A 1 Introduction

The majority of control (or signal processing) systems is implemented in digital general purpose processors, DSPs 1 , FPGAs 2 , etc. Since these devices cannot compute with infinite precision and approximate real-number parameters with a finite binary representation, the numerical implementation of controllers (filters) leads to deterioration in characteristics and performance. This has two separate origins, corresponding to the quantization of the embedded coefficients and the roundoff errors occurring during the computations. They can be formalized as parametric errors and numerical noises, respectively. The focus of this paper are parametric errors, but one can refer to [START_REF] Gevers | Parametrizations in Control, Estimation and Filtering Probems[END_REF][START_REF] Hilaire | Bit accurate roundoff noise analysis of fixedpoint linear controllers[END_REF][START_REF] Hwang | Minimum uncorrelated unit noise in state-space digital filtering[END_REF][START_REF] Mullis | Synthesis of minimum roundoff noise fixed point digital filters[END_REF] for roundoff noises.

It is also well known that these Finite Word Length (FWL) effects depend on the structure of the realization. This motivates to investigate the coefficient sensitivity minimization problem. It has been widely studied since Thiele published [START_REF] Tavşanoglu | Optimal design of state-space digital filters by simultaneous minimization of sensibility and roundoff noise[END_REF][START_REF] Thiele | Design of sensitivity and round-off noise optimal state-space discrete systems[END_REF] and the definition of a tractable input-output sensitivity norm (the L 1 /L 2 -sensitivity). This work has been extended with a more natural and reasonable measure, the L 2 -sensitivity ( [START_REF] Gevers | Parametrizations in Control, Estimation and Filtering Probems[END_REF][START_REF] Hinamoto | L2-sensitivity analysis and minimization of 2-d separabledenominator state-space digital filters[END_REF]).

The dynamic-range-scaling constraints have been introduced in [START_REF] Jackson | Roundoff-noise analysis for fixed-point digital filters realized in cascade or parallel form. Audio and Electroacoustics[END_REF] and [START_REF] Hwang | Dynamic range constraint in state-space digital filtering[END_REF] to prevent overflow and underflow during the evaluation of the state-vector, and as well as the state and criteria normalization. These constraints have to be considered in the L 2 -sensitivity minimization problem, for which [START_REF] Hinamoto | Minimization of l2 sensitivity of one-and two dimensional state-space digital filters subject to l2-dynamic-range-scaling constraints[END_REF] proposes an efficient quasi-Newton algorithm to solve it. This paper investigates the L 2 -dynamic-range-scaling problem by considering concrete fixed-point implementation of state-space realizations. It reveals that the classical L 2 -scaling is only a sufficient condition to prevent overflows and thus it can be slightly relaxed in order to extend the degrees of freedom for the optimization process. New relaxed -L 2 -dynamic-rangescalings are then presented with respect to the described computational scheme. Finally, the L 2 -sensitivity minimization problem with relaxed L 2 -scaling constraints is solved. A numerical example illustrates that the proposed constraints can offer reduced L 2 -sensitivity with overflow protection.

L -sensitivity analysis

Let (A, b, c, d) be a stable, controllable and observable linear discrete time SISO 3 state-space system, i.e.

x(k

+ 1) = Ax(k) + bu(k) y(k) = cx(k) + du(k) (1)
where

A ∈ R n×n , b ∈ R n×1 , c ∈ R 1×n and d ∈ R. u(k) is the scalar input, y(k)
is the scalar output and x(k) ∈ R n×1 is the state vector. Its input-output relationship is given by the scalar transfer function h : C → C defined by:

h : z → c(zI n -A) -1 b + d. ( 2
)
1 Digital Signal Processors

T. Hilaire

The quantization of the coefficients introduces some uncertainly to A, b, c and d leading to A + ∆A, b + ∆b, c + ∆c and d + ∆d respectively. It is of interest to consider the sensitivity of the transfer function with respect to the coefficients, based on the following definitions.

Definition 1 (Transfer function sensitivity) Consider X ∈ R m×n a matrix and f : R m×n → C a scalar complex function, differentiable with respect to all the entries of X. The sensitivity of f with respect to X is defined by the matrix S X ∈ R m×n :

∂f ∂X S X with (S X ) i,j ∂f ∂X i,j (3)
Definition 2 (L p -Norm) Let H : C → C k×l be a function of the scalar complex variable z. H p is the L p -norm of H, defined by:

H p 1 2π 2π 0 H e jω p F dω 1 p (4)
where . F is the Froebenius norm.

Gevers and Li [START_REF] Gevers | Parametrizations in Control, Estimation and Filtering Probems[END_REF] have proposed the L 2 -sensitivity measure to evaluate the coefficient roundoff errors. It is defined by

M L2 ∂h ∂A 2 2 + ∂h ∂b 2 2 + ∂h ∂c 2 2 + ∂h ∂d 2 2 (5)
and can be computed by ∂h ∂A (z) = G (z)F (z), ∂h ∂b (z) = G (z), ∂h ∂c (z) = F (z) and ∂h ∂d (z) = 1, with

F (z) (zI n -A) -1 b, G(z) c(zI n -A) -1 . ( 6
)
This measure is an extension of the more tractable but less natural L 1 /L 2 sensitivity measure proposed by V. ( Ã,B,C,D) with

à A bc 0 A , B 0 b I n 0 , C I n 0 0 c , D 0 0 0 1 . ( 8
)
4 Multiple Inputs Multiple Outputs

Irisa

See [START_REF] Gevers | Parametrizations in Control, Estimation and Filtering Probems[END_REF] and [START_REF] Hilaire | On the compact formulation of the derivation of a transfer matrix with respect to another matrix[END_REF] for more details.

The following proposition allows to compute M L2 .

Proposition 1 Let us consider H the MIMO state-space system (K, L, M , N ). Its L 2norm can be computed by

H 2 2 = tr(NN + M W c M ) ( 9 )
= tr(N N + L W o L) [START_REF] Hwang | Minimum uncorrelated unit noise in state-space digital filtering[END_REF] where W c and W o are the controllability and observability Gramians, respectively. They are solutions of the Lyapunov equations

W c = KW c K + LL , W o = K W o K + M M . ( 11
)
Applying a coordinate transformation, defined by x(k) T -1 x(k) to the state-space system (A, b, c, d), leads to a new equivalent realization (T -1 AT , T -1 b, cT , d).

Since these two realizations are equivalent in infinite precision but are no more equivalent in finite precision (fixed point arithmetic, floating-point arithmetic, etc.), the L 2 -sensitivity then depends on T , and is denoted M L2 (T ). In this case, it is natural to define the following problem: Problem 1 (optimal L 2 -sensitivity problem) Considering a state-space realization (A, b, c, d), the optimal L 2 -sensitivity problem consists of finding the coordinate transformation T opt that minimizes M L2 :

T opt = arg min T invertible M L2 (T ). (12)
[3] shows that the problem has one unique solution. Hence, for example, a gradient method can be used to solve it.

L p -dynamic-range scaling

The L p -dynamic-range-scaling constraints have been introduced by Jackson in [START_REF] Jackson | Roundoff-noise analysis for fixed-point digital filters realized in cascade or parallel form. Audio and Electroacoustics[END_REF] and Hwang in [START_REF] Hwang | Dynamic range constraint in state-space digital filtering[END_REF]. It consists in scaling the state-variable vector such that overflows or underflows during its evaluation are prevented. (A,b,c,d) is said to be L p -scaled if the L p -norms of the transfer functions from the input to each state are set to 1, i.e.:

Definition 3 (L p -scaling) A state-space realization

e i (zI n -A) -1 b) p = 1, ∀1 i n ( 13
)
where e i is the column vector of appropriate dimension and with all elements being 0 except from the i th element which is 1.

PI n˚1924

T. Hilaire Let max u denote the maximum value of the input u:

max u max k∈N |u(k)| ( 14
)
The L 1 -scaling guarantees that the dynamic of each state x i is lower than max u , whereas the L 2 -scaling guarantees that the variance of each state is unitary for a unit-variance centered white noise input. L 2 -scaling doesn't completely prevent overflow as does L 1 , but it is less conservative and more realistic, so it is widely used [START_REF] Parhi | VLSI Digital Signal Processing Systems: Design and Implementation of Digital Controllers[END_REF].

With proposition 1 applied to the system (A, b, e i , 0), the L 2 -scaling constraints (13) can be expressed as:

(W c ) i,i = 1, ∀1 i n ( 15
)
where W c is the controllability Gramian of the state-space system (A, b, c, d).

Problem 2 (sensitivity problem with L 2 -scaling constraints) The optimal L 2 -sensitivity problem with L 2 -scaling constraints can be formulated as the optimization problem 1, subject to the constraints in [START_REF] Parhi | VLSI Digital Signal Processing Systems: Design and Implementation of Digital Controllers[END_REF].

Moreover, it is possible to L 2 -scale a realization with the following proposition.

Proposition 2 (a posteriori L 2 -scaling) Considering a state-space realization (A, b, c, d), it is also possible to a posteriori L 2 -scale it with a diagonal coordinate transformation T such that:

T i,i = (W c ) i,i , ∀1 i n (16)
Then, there exist infinite transformation matrices T (not necessary diagonal) that produces L 2 -scaled realizations: Let us consider the invertible matrix U ∈ R n×n , then also the transformation matrix T = UV produces L 2 -scaling with V diagonal such that:

V i,i = (U -1 W c U -) i,i , ∀1 i n ( 17
)
Proof:

A transformation matrix T that transforms (A, b, c, d) into (T -1 AT , T -1 b, cT , d) changes the controllability Gramian W c into T -1 W c T -. Since T is diagonal, the constraints (W c ) i,i = 1 imply T i,i = (W c ) i,i .
Moreover, it is also possible to successively apply two transformation matrices U and V on ( A,b,c,d). If V is composed according to [START_REF] Thiele | Design of sensitivity and round-off noise optimal state-space discrete systems[END_REF], then the transformation T = UV performs the L 2 -scaling. This proposition can be used to transform the constrained problem 2 into an unconstrained problem. Then an optimization algorithm, like quasi-Newton, can be used to solve it. Other analytical algorithms for this problem can be found in [START_REF] Hinamoto | Minimization of l2 sensitivity of one-and two dimensional state-space digital filters subject to l2-dynamic-range-scaling constraints[END_REF] and [START_REF] Hwang | Minimum uncorrelated unit noise in state-space digital filtering[END_REF].

Irisa 4 Fixed-point implementation

Fixed-point representation

In this paper, the notation (β, γ) is used for the fixed-point representation of a variable or coefficient (2's complement scheme), according to Figure 1. β is the total wordlength of the representation in bits, whereas γ is the wordlength of the fractional part (it determines the position of the binary-point). They are fixed for each variable (input, states, output) and each coefficient, and implicit (unlike the floating-point representation). β and γ will be suffixed by the variable/coefficient they refer to.

± 2 1 2 0 2 -1 ... ... 2 β-γ-2 β -γ -1 β γ 2 -γ
β x -γ x -1 log 2 |x| + 1 (18)
where the a operation rounds a to the nearest integer less or equal to a (for positive numbers a is the integer part). An important fixed-point issue is to find a valid fixed-point representation, such that (18) is satisfied for all values which x can assume during the execution of the algorithm.

State-overflow

Definition 4 (State-overflow) The overflow of the state variables (x i ) 1 i n can be strictly avoided iff (

1 i n) ∀k, -2 βx i -γx i -1 x i (k) < 2 βx i -γx i -1 . ( 19
)
The overflows are avoided if the binary-point position of each state is carefully chosen, such that

γ x i = β x i -2 -log 2 max x i , ( 20
)
where

max
x i is the maximum magnitude for the i th state:

max x i max k∈N |x i (k)| . ( 21
) PI n˚1924
T. Hilaire

However only upper bounds can be computed. A first upper bound up x i can be obtained by an L 1 -norm:

up x i = (zI n -A) -1 b i 1 max u , ( 22
)
and a second one can be estimated by an L 2 -norm [START_REF] Parhi | VLSI Digital Signal Processing Systems: Design and Implementation of Digital Controllers[END_REF]:

up x i δ (zI n -A) -1 b i 2 max u . ( 23
)
Here, the parameter δ can be interpreted as a representation of the number of standard deviations of x i , if the input is unit-variance white centered noise (δ 1). Since the L 2 -norm in (23) doesn't give a strict bound (contrary to (22)), δ can be seen as a safety parameter [START_REF] Parhi | VLSI Digital Signal Processing Systems: Design and Implementation of Digital Controllers[END_REF]. Finally, these upper bounds are used to define the binary-point positions:

γ x i = β x i -2 -log 2 up x i . ( 24
)
In general, the L 1 and L 2 estimations of up x i approximately leads to the same binary-point position, with 1 or 2 bits deviation. However, since the L 2 -norm is more tractable (with proposition 1) and the L 1 -norm too conservative ( 23) is used, with δ = 1. After implementation, a simulation-based estimation like in [START_REF] Belanovic | Automated floating-point to fixed-point conversion with the fixify environment[END_REF] or [START_REF] Kim | Fixed-point optimization utility for C and C++ based digital signal processing programs[END_REF] can also be used to verify in situ the peak values and the binary point positions, according to the inputs.

max x i up x i ), in practice (

Computational scheme

In order to implement a realization without overflows, two equivalent choices are possible:

• set the binary-point position for each state, according to (24), to make sure that the fixed-point representation of the states avoids state-overflows;

• or define a binary-point position for each state, and apply a scaling to them in order to adapt the peak values of each state to the chosen binary-point position.

Here, we here focus on the 2 nd choice, referring to dynamic-range-scaling constraints. Let us consider in detail the fixed-point implementation of the system given in [START_REF] Belanovic | Automated floating-point to fixed-point conversion with the fixify environment[END_REF]. It leads to (n + 1) scalar products to be evaluated, of the form:

S = N i=1 p i q i ( 25
)
where the (p i ) are given coefficients and (q i ) are bounded variables.

To avoid bit-shift operations between each addition in the evaluation of eq. ( 25), the binarypoint positions of each partial product of the sum should be equal. Then, two computational schemes are possible: the Roundoff After Multiplication scheme,

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where shifts are added after each product to align the operands of the sum (p i q i is implemented as (p i * q i ) >> d i ) and the Roundoff Before Multiplication scheme, where the required shifts are reported into the coefficients (p i q i is implemented as (p i >> d i ) * q i ).

The main idea of the scaling is to scale each variable (q i ) such that the shifts (d i = 0, ∀i) are prevented. In fixed-point representation, the scaling only implies that all the (q i ) have a common format, and so have the (p i ). See [START_REF] Constantinides | Synthesis And Optimization Of DSP Algorithms[END_REF][START_REF] Hilaire | Bit accurate roundoff noise analysis of fixedpoint linear controllers[END_REF] for more details on implementation schemes.

Applied to the state-space realization (1), this yields that all the states must have the same binary-point position as the input and the coefficients A, b, c and d. Besides, since they have the same fractional part, their quantization's errors ∆A, ∆b, ∆c and ∆d have the same magnitude 2 -γZ -1 , and the L 2 -sensitivity measure represents a meaningful bound on the transfer function error ∆h:

∆h 2 2 ∂h ∂A × ∆A 2 2 + ∂h ∂b × ∆b 2 2 + ∂h ∂c × ∆c 2 2 + ∂h ∂d × ∆d 2 2 (26) 2 -2(γZ+1) M L2 (27)

New L 2 -scaling constraints

Taken this into consideration, the overflows will be avoided by setting the same binary-point position for the states and the input, and by applying an appropriate scaling on the states such that the constraints (20) are satisfied.

Compared to strict L 2 -scaling where the states must satisfy max x i = max u , here, the constraints are relaxed (but still restrictive enough to guarantee the protection against overflow) and replaced by γ x i = γ u . Proposition 3 (relaxed -L 2 -scaling constraints) Since the input and the states may have the same binary-point position, the L 2 -scaling constraints [START_REF] Parhi | VLSI Digital Signal Processing Systems: Design and Implementation of Digital Controllers[END_REF] are now transformed into

2 2αi δ 2 (W c ) i,i < 4 2 2αi δ 2 , ∀1 i n ( 28
)
where

α i β xi -β u -F 2 max u ( 29
)
and F 2 (x) is defined as the fractional value of log 2 (x):

F 2 (x) log 2 (x) -log 2 (x) (30)
For microcontroller or DSP implementations (contrary to FPGA or some ASIC implementations), the wordlength of all variables is equal, i.e.

β u = β x i (1 i n). Also max u could PI n˚1924 10
T. Hilaire be set to a power of 2. Then, if δ is set to unity (as for classical L 2 -scaling constraints), the relaxed-L 2 -scaling constraints (28) become:

1 (W c ) i,i < 4, ∀1 i n (31) Proof:
The binary-point position of the input is set to γ u = β u -2log 2 max u . Hence, with (24), the constraints γ u = γ x i lead to

β u -log 2 max u = β x i -log 2 δ (zI n -A) -1 b i 2 max u and log 2 δ (W c ) i,i + F 2 max u = β x i -β u (32)
And finally

2 αi δ (W c ) i,i < 2 αi+1 (33)
It is important to remark that these new constraints allow more freedom for the scaling and introduce a new degree of freedom for the search for optimal realizations. Even though not considered in this paper, moreover it could give more freedom for the minimization of the roundoff noise power.

Optimal L 2 -sensitivity realization with relaxed L 2 -norm dynamic-range-scaling constraints

Then, these relaxed constraints can be applied to a new sensitivity problem:

Problem 3 (relaxed sensitivity problem) The optimal L 2 -sensitivity problem with relaxed L 2 -norm dynamic-range-scaling constraints can be expressed in the form of the constrained problem 2 subject to constraints in (28).

This constrained problem can be solved by two different means. First, in addition to the n 2 free parameters of the transformation matrix U applied to the system, n extra parameters (γ i ) 1 i n can be considered. These (γ i ) represent the desired L 2 -scaling and will be constrained by

2 2αi δ 2 γ i < 4 2 2αi δ 2 , ∀1 i n. ( 34
)
Then a diagonal transformation matrix V γ is applied, with

(V γ ) i,i = (W c ) i,i γ i . ( 35
)

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In this case, a constrained optimization algorithm (like quasi-Newton one, implemented in fmincon with Matlab) can then be used to solve the following problem:

(U opt , γ opt ) = arg min U invertible γ satisfying (34) M L2 (U V γ ) (36)
The optimal realization satisfying the relaxed-L 2 constraints is then obtained by applying the transformation matrix

T opt = U opt V γ opt .
The other approach is to scale the system after each transformation to ensure that the constraints are met: Proposition 4 (a posteriori relaxed scaling) Considering a state-space realization, it is possible to a posteriori scale it with a diagonal transformation matrix T given by

T i,i = δ (W c ) i,i 2 -F2(δ √ (Wc) i,i )-αi , ( 37
)
such that the constraints (28) are satisfied. Moreover, it is possible to build all the transformation matrices that meet the constraints (28): Let us consider an invertible matrix U ∈ R n×n , then the transformation matrix T = UV with V diagonal such that:

V i,i = δ (U -1 W c U -) i,i 2 -F2(δ √ (U -1 WcU -) i,i )-αi (38)
produces the relaxed-L 2 -scaling. Proof: F 2 acts as a modulo operator. For x ∈ R, x 2 F2(x)+a is such that 2 a x < 2 a+1 . Since the constraints (28) are equal to

2 α i δ (W c ) i,i < 2 α i +1 (39)
and T transforms (W c ) i,i into T -2 i,i (W c ) i,i , then T i,i has to be of the form:

δT -1 i,i (W c ) i,i = 2 F2(δ √ (Wc) i,i )+αi (40)
Thus, the optimization problem is given by

U opt = arg min U invertible V defined by (38) M L2 (UV ). (41)
These two ways of solving problem 3 are implemented in the FWR toolbox 5 for Matlab, with fminsearch, fmincon and fminunc functions, and they both give same results with similar numbers of iterations. Of course, the use of matrices V γ and V, that are merely used to eliminate the constraints and solve an unconstrained minimization problem, increases the degree of non-linearity for the objective function to minimize. However, this seems not to be a problem, since in our tests, the optimal realizations found seem to be global optima. and its multiple equivalent (in infinite precision) realizations:

• R 1 is the original realization given by (42)

• R 2 is the optimal L 2 -scaled realization (solution of problem 2). It is obtained with proposition 2 and a quasi-newton algorithm. The numerical values are given by (43).

• R 3 is the optimal relaxed-L 2 -scaled realization (problem 3), with max u a power of 2, and δ = 1. It is obtained with proposition 4. The numerical values are given by (44).

The following table gives the M L2 sensitivities of these different realizations:

realization M L 2 sensitivity R 1 6355.5 R 2 530.0964 R 3
528.2532

In this example, the relaxed L 2 -scaled realization R 3 achieves lower sensitivity than the strict L 2 -scaled optimal realization R 2 while protecting implementation from overflows. But it is not always the case : if we consider the example in [START_REF] Hinamoto | Minimization of l2 sensitivity of one-and two dimensional state-space digital filters subject to l2-dynamic-range-scaling constraints[END_REF], the optimal relaxed-L 2scaled realization satisfies (W c ) i,i = 1 and is then also a strict L 2 -scaled realization. This depends on the diagonal terms of the controllability Gramians of the (non scaled) optimal realization. It is also interesting to notice that a good estimation of max u (if it is not a power of 2) can allow to achieve lower sensitivity by moving the constraints (it could also be the case for the example in [START_REF] Hinamoto | Minimization of l2 sensitivity of one-and two dimensional state-space digital filters subject to l2-dynamic-range-scaling constraints[END_REF]).

Conclusion

This paper has presented the L 2 -sensitivity minimization problem and the associated L 2scaling constraints. These constraints that prevent from overflows have been considered with concrete fixed-point implementation schemes. Novel L 2 -dynamic-range constraints have been exhibited. Even if the goal of this paper is not a detailed optimization algorithm like in [START_REF] Hinamoto | Minimization of l2 sensitivity of one-and two dimensional state-space digital filters subject to l2-dynamic-range-scaling constraints[END_REF], two different means to solve the constrained optimization problem have been exhibited and applied on a numerical example.

These relaxed constraints could also be very important for some other realizations, like δ-operator state-space or the ρ-Direct Form II transposed [START_REF] Li | On the generalized DFIIt structure and its state-space realization in digital filter implementation[END_REF]. For these realizations where a parameter ∆ should be used to achieve the L 2 -scaling, a relaxed-L 2 -scaling permits to fix this parameter as a power of 2, in order to decrease the amount of computations. To apply this work to other classical structures, it will be soon extended to the Specialized Implicit Framework [START_REF] Hilaire | A unifying framework for finite wordlength realizations[END_REF] that allows to encompass existing structures in an implicit state-space form.

  A T O I R E S P U B L I C A T I O N I N T E R N E N o

Figure 1 :

 1 Figure 1: Fixed-point representation

12 T. Hilaire 6 Example

 126 Let us consider the following state-space digital controller, given in modal form 6 :

sources available at http://fwrtoolbox.gforge.inria.fr/ PI n˚1924

Due to a lack of space, only 4 digits are given, but more may be required to completely define the system. Irisa


Yih Valentin Buchter

Ching Ong

François Mouvet

Abdallah Ladaycia

Elise Lepeltier

Ursula Rothlisberger
email: ursula.roethlisberger@epfl.ch

Jennifer Keiser
email: jennifer.keiser@unibas.ch

Gilles Gasser
email: gilles.gasser@chimeparistech.psl.eu

# Yih

Abdallah Ladaycia

Yih Ching Ong

Abdallay Ladaycia

Multidisciplinary Preclinical Investigations on Three Oxamniquine Analogues as Novel Treatment Options for Schistosomiasis

Keywords: Bioorganometallic Chemistry, Molecular Dynamics, Medicinal Organometallic Chemistry, Metabolic Stability, Schistosomiasis

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

Introduction

S. mansoni, S. haematobium and S. japonicum account for over 90% of the cases of schistosomiasis, an acute and chronic parasitic disease that affects over 200 million people worldwide [START_REF] Colley | Human schistosomiasis[END_REF][START_REF] Rotger | Increasing incidence of imported schistosomiasis in Mallorca, Spain[END_REF][START_REF] Berry | Schistosomiasis Haematobium, Corsica, France[END_REF] and threatens more than 700 million people the risk of infection. [START_REF] Steinmann | Schistosomiasis and water resources development: systematic review, meta-analysis, and estimates of people at risk[END_REF] In children, schistosomiasis stunts physical growth and ability to learn, while in adults, the disease affects the ability to work, and can cause organ failure and ultimately death, a situation that causes an enormous socioeconomic burden for developing communities. [START_REF] Bergquist | Elimination of schistosomiasis: the tools required[END_REF] Praziquantel (PZQ) is the only drug being used for periodic mass drug administration to control the disease. Considering the threatening and real possibility of resistance [START_REF] Geerts | Drug resistance in human helminths: current situation and lessons from livestock[END_REF] and that PZQ presents drawbacks, our efforts are oriented to identify and develop a new molecule with the potential to become an alternative therapeutic option in the treatment of this disease.

Oxamniquine (OXA, Figure 1) is an anthelmintic drug developed in the 1960s [START_REF] Lago | Antischistosomal agents: state of art and perspectives[END_REF] that showed high activity and a very convenient drug profile in terms of safety and ease of administration. It became the cornerstone of the schistosomiasis eradication program in Brazil in the past and beginning of the 21st centuries but fell into disuse because of two main reasons: it was only active against adult S. mansoni [START_REF] Lago | Antischistosomal agents: state of art and perspectives[END_REF][START_REF] Pica-Mattoccia | Enzymatic basis for the lack of oxamniquine activity in Schistosoma haematobium infections[END_REF][START_REF] Sabah | Schistosoma mansoni: Chemotherapy of infections of different ages[END_REF] and resistance was clinically confirmed. The drug was therefore no longer commercialized after 2010 and replaced by PZQ. [START_REF] Lago | Antischistosomal agents: state of art and perspectives[END_REF] OXA is a prodrug that needs to be activated by the sulfotransferase of S. mansoni (SmULT) to an alkylating molecule that binds proteins and DNA, consequently killing the parasite. [START_REF] Pica-Mattoccia | The schistosome enzyme that activates oxamniquine has the characteristics of a sulfotransferase[END_REF] Different enzyme orthologues are present in all Schistosoma species, but only the active site of the sulfotransferase of S. mansoni can activate OXA. [START_REF] Valentim | Genetic and molecular basis of drug resistance and speciesspecific drug action in Schistosome parasites[END_REF] OXA was administered as a 1:1 racemate mixture, with both enantiomers having anti-parasitic activity, although the S-OXA contributes the most. Crystal structures of R-OXA and S-OXA complexes with SmSULT target show similarities in the modes of OXA binding, but only the S-OXA enantiomer is observed in the structure of the enzyme exposed to racemic OXA [START_REF] Taylor | Structural and functional characterization of the enantiomers of the antischistosomal drug oxamniquine[END_REF] .

The mechanism of resistance and lack of activity in the remaining species has been well studied.

Resistance is based in one or more point mutations in the enzyme's active site that prevent the molecule to be sulfonated. [START_REF] Chevalier | Independent origins of loss-of-function mutations conferring oxamniquine resistance in a Brazilian schistosome population[END_REF] Taking into account that there is a 70% homology between the amino acid sequences of the sulfotransferases of S. mansoni and S. haematobium, [START_REF] Valentim | Genetic and molecular basis of drug resistance and speciesspecific drug action in Schistosome parasites[END_REF] we derivatized OXA based on the hypothesis that modification of OXA could overcome the species and stage specificity. [START_REF] Rugel | Design, synthesis, and characterization of novel small molecules as broad range antischistosomal agents[END_REF] Previous studies by Jaouen and co-workers on the anticancer drug candidate ferrocifen [START_REF] Hillard | Ferrocene functionalized endocrine modulators as anticancer agents[END_REF][START_REF] Biot | Bioorganometallic Chemistry and Malaria[END_REF][START_REF] Gasser | The potential of organometallic complexes in medicinal chemistry[END_REF] and Brocard, Biot and co-workers on the anti-malarial drug candidate ferroquine showed that the ferrocenyl analogues of tamoxifen and chloroquine, respectively have improved bioactivity compared to the original organic drug compounds. [START_REF] Patra | The medicinal chemistry of ferrocene and its derivatives[END_REF][START_REF] Ong | Metal compounds against neglected tropical diseases[END_REF] This was due to several factors: the ferrocenyl component acted as a producer of reactive oxygen species (ROS), increased the lipophilic character of the molecule and provided a mechanism of action different to that of the original drug. [START_REF] Dubar | The antimalarial ferroquine: role of the metal and intramolecular hydrogen bond in activity and resistance[END_REF][START_REF] Keiser | In vitro and in vivo antischistosomal activity of ferroquine derivatives[END_REF][START_REF] Biot | Insights into the mechanism of action of ferroquine. Relationship between physicochemical properties and antiplasmodial activity[END_REF] With this concept in mind, we developed several metal-containing derivatives of OXA, which were studied in vitro and in vivo against Schistosoma spp. [START_REF] Hess | Ferrocenyl, ruthenocenyl, and benzyl oxamniquine derivatives with cross-species activity against Schistosoma mansoni and Schistosoma haematobium[END_REF][START_REF] Hess | Toward organometallic antischistosomal drug candidates[END_REF][START_REF] Buchter | Assessment of tegumental damage to Schistosoma mansoni and S. haematobium after in vitro exposure to ferrocenyl, ruthenocenyl and benzyl derivatives of oxamniquine using scanning electron microscopy[END_REF] Among others, we demonstrated that the three derivatives of OXA, namely a ferrocene-(Fc-CH2-OXA), ruthenocene-(Rc-CH2-OXA) and benzene-containing (Ph-CH2-OXA) derivative (Figure 1), showed promising in vitro results, where all three OXA derivatives caused death of S. mansoni and S. haematobium adult worms [START_REF] Buchter | Assessment of tegumental damage to Schistosoma mansoni and S. haematobium after in vitro exposure to ferrocenyl, ruthenocenyl and benzyl derivatives of oxamniquine using scanning electron microscopy[END_REF] and worm burden reductions of 76 to 93% against adult S. mansoni in vivo. [START_REF] Hess | Ferrocenyl, ruthenocenyl, and benzyl oxamniquine derivatives with cross-species activity against Schistosoma mansoni and Schistosoma haematobium[END_REF] Encouraged by our promising preliminary results, we decided to go further in the development and to fully characterize these three OXA analogues. In vitro studies were conducted against S. mansoni juvenile worms, and S. japonicum and S. haematobium adult worms. In vivo studies were carried out against adult S. haematobium and juvenile S. mansoni including studies with Ph-CH2-OXA encapsulated in Lipid NanoCapsules (LNC). Only racemic mixtures were tested as we focused on determining the presence of activity for the OXA derivatives in vivo with S. mansoni and S. haematobium, rather than spending time on isolating the enantiomers if these compounds were not active. Stability in acidic conditions are also determined as the final goal to develop these derivatives as orally administered compounds which pass through the stomach's acidic environment. Our work was complemented by computational models and molecular dynamics simulations as well as microsomal stability and albumin binding studies.

Results and Discussion

In vitro studies

Fc-CH2-OXA, Rc-CH2-OXA and Ph-CH2-OXA previously demonstrated promising activity as drug candidates in vitro against adult S. mansoni and S. haematobium and first stage of the larval development (NTS: newly transformed schistosomula) and in vivo in adult S. mansoni infected mice. [START_REF] Hess | Ferrocenyl, ruthenocenyl, and benzyl oxamniquine derivatives with cross-species activity against Schistosoma mansoni and Schistosoma haematobium[END_REF][START_REF] Buchter | Assessment of tegumental damage to Schistosoma mansoni and S. haematobium after in vitro exposure to ferrocenyl, ruthenocenyl and benzyl derivatives of oxamniquine using scanning electron microscopy[END_REF] In order to test the full potential of our compounds, we first elucidated the in vitro activity of the OXA derivatives against 28-day-old juvenile S. mansoni worms since one of the important drawbacks of PZQ is its low activity against this developmental stage. All three compounds killed all the worms within 24 h of incubation at a concentration of 100 μM (Table 1).

Against juvenile S. mansoni, Fc-CH2-OXA had the lowest IC50 (0.5 µM) while Ph-CH2-OXA was the drug with the highest IC50 value (26.7 µM), the one with the lowest activity. Interestingly, in the case of Ph-CH2-OXA, the effect of the molecules on the juveniles was faster than against the adults: while on adult S. mansoni, Ph-CH2-OXA needed 72 h to exert its maximal activity; against juvenile stages, we observed a total lethal effect within 24 h of incubation at a dose of 100 μM. For comparison, by the same incubation time, juvenile S. mansoni exposed to OXA showed an IC50 of >100 μM, confirming previous studies of OXA being only slightly active in vitro and against juvenile stages of the parasite. [START_REF] Sabah | Schistosoma mansoni: Chemotherapy of infections of different ages[END_REF][START_REF] Buchter | Assessment of tegumental damage to Schistosoma mansoni and S. haematobium after in vitro exposure to ferrocenyl, ruthenocenyl and benzyl derivatives of oxamniquine using scanning electron microscopy[END_REF] Only by 72 h of incubation at 100 μM, where the derivatives had long exerted their activity, we found a 48% reduction of the viability of OXA respect to the control worms (Table S2).

Against S. japonicum adult worms, we observed the same behavior: while OXA was not active even by 100 μM after 3 days (Table 1 and Table S2), our derivatives showed considerable activity. Of the three derivatives tested, Fc-CH2-OXA proved to be the most active of all three derivatives, killing all the parasites within 24 h at a concentration of 100 μM and having the lowest IC50 value (22.6 μM). On S. haematobium instead, the most active compound was Rc-CH2-OXA, also killing all parasites at a concentration of 100 μM and revealing the lowest IC50 value (15.5 μM).

Moreover, we incubated adult S. mansoni in medium containing albumin and compared the activity determined to our standard assay. A lower activity of the three drugs was observed in the enriched medium, with Fc-CH2-OXA showing the least loss of activity of the three derivatives (Table 1). The albumin binding experiment was also performed for adult S. haematobium. Also in this case, the three compounds showed a reduction of the activity. These results are comparable with those obtained by Pasche et al, [START_REF] Pasche | Screening a repurposing library, the Medicines for Malaria Venture Stasis Box, against Schistosoma mansoni[END_REF] who also identified a significant decrease in drug activity incubating antischistosomal drug candidates in vitro in the presence of albumin. Also, PZQ presents a high percentage (around 80%) of drug bound to protein [START_REF] Olliaro | The little we know about the pharmacokinetics and pharmacodynamics of praziquantel (racemate and R-enantiomer)[END_REF] and this might be one of the reasons for the high doses needed to reach a significant effect. Protein binding is a major issue in drug development, since only the free fraction of the drug is able to interact with the target. 28

Studies on juvenile S. mansoni in the mouse model

In terms of activity against juvenile parasites in vivo, we identified a lower activity of all three compounds in respect to the results on adult parasites. [START_REF] Hess | Ferrocenyl, ruthenocenyl, and benzyl oxamniquine derivatives with cross-species activity against Schistosoma mansoni and Schistosoma haematobium[END_REF] Though the drug showed moderate activity, as shown by their shift to the liver due to the loss of vein attachment (data not shown), worm burden reductions were low ranging from 39 to 47% (Table 2).When considering the gender of the surviving worms we evidence that there is no gender difference in susceptibility (binomial test, p > 0.77).

In vivo studies on adult S. haematobium

Table 3 shows the worm burden reduction of the three compounds against S. haematobium: none of the compounds affected S. haematobium in vivo, contradicting the findings observed in vitro.

Computational studies

In order to understand the interaction between OXA analogues and the sulfotransferase proteins from S. mansoni (SmSULT) and S. haematobium (ShSULT), we performed classical molecular dynamics simulations of OXA, Fc-CH2-OXA, Ph-CH2-OXA and Fc-CO-OXA to determine their binding poses within the active site of the two sulfotransferases at body temperature. Fc-CO-OXA was added to the comparison to include the case of a derivative that was shown to be less active against S. mansoni in vitro than the other compounds considered in the present study. [START_REF] Hess | Ferrocenyl, ruthenocenyl, and benzyl oxamniquine derivatives with cross-species activity against Schistosoma mansoni and Schistosoma haematobium[END_REF] We did not consider Rc-CH2-OXA explicitly since both from a geometrical and electrostatic point of view, the force field models for ferrocenyl and ruthenocenyl compounds are very similar and would likely yield comparable behavior at this simplified level of theory.

The free energy difference between bound and unbound states of a receptor-ligand complex is a direct measure of the binding affinity. To estimate this quantity from our trajectories, we used the MM/PBSA (Table 4) and MM/GBSA methods (Table S1). All binding free energies are negative, meaning that the bound state is energetically favorable for all compounds. No systematic difference can be noted between the two proteins and all modified OXA compounds show a higher binding affinity than OXA itself. This is probably due to their larger size, forcing a tighter fit inside the protein and increasing the number of interactions with the binding pocket. Consequently, all analogues are strongly bound to their target proteins. Since the drugs are supposed to react with PAPS within the target protein, the distance between the closest oxygen of the sulfate group of PAPS and the hydrogen in the hydroxyl group of each drug was measured every 40 ps. These distances are represented as histograms in Figure 2 and their average is shown in Table 5. The near-attack configurations (NAC), i.e., the ones with shorter distances between the reactive groups are more likely to result in the activation of the compounds. For OXA in SmSULT, the sulfate-hydroxyl distance is short and stable for both enantiomers, with an average slightly above 3 Å. The relative orientation of the reactive groups is fixed through their mutual interaction with ASN230, thus promoting the interaction (Figure S2). The chain of residues 19 to 23 also binds to PAPS and OXA at different places, stabilizing the configuration. For OXA, the difference between Rand S-enantiomers is very small, which is consistent with previous experimental works that already reported that both enantiomers bind in a similar fashion and that the activity difference originates from their binding kinetics. [START_REF] Taylor | Structural and functional characterization of the enantiomers of the antischistosomal drug oxamniquine[END_REF] Both enantiomers of Ph-CH2-OXA and Fc-CH2-OXA show a very strong interaction with PAPS within SmSULT. Residues 18 to 21 bind both ligands in several places, highly stabilizing their binding (Figures S4 andS6). Moreover, the residue ASN230 also binds to PAPS and to the chain of residues 18-21, further increasing the stability. This may explain the high activity of these compounds in vitro. On the other hand, the R-enantiomer of Fc-CH2-OXA seems to drift slowly away from PAPS and a proper equilibrium is never reached within our simulation time. The distance increases over time, which suggests that the final configuration will not be active. Strikingly, Ph-CH2-OXA does not seem to be impacted by the enantiomer selectivity observed for all other derivatives.

Fc-CH2-OXA, that was the most active against S. mansoni according to the in vitro experimental studies, shows short average distance to PAPS. In S. haematobium instead, the shortest distance to PAPS is held by the S-enantiomer of Ph-CH2-OXA, which also shows a lower IC50 against this species when compared to Fc-CH2-OXA. Furthermore, our simulations of Fc-CO-OXA in SmSULT

show NAC distributions where the reactants are about 3 times more distant than in OXA, with averages above 10 Å. These configurations are very unlikely to activate the drug, which is again consistent with experimental results.

In practice, OXA is not active on S. haematobium. In simulations where OXA is docked into ShSULT, we observe that the distance between the reactive groups is much larger than in SmSULT, by more than 6 Å on average. Furthermore, we observe a large difference between enantiomers, where the R-enantiomer shows a broad distribution of NAC distances with an average of 9.5 Å. This strong enantiomer dependence is present for all compounds and is more pronounced than in SmSULT with all R-enantiomers adopting less reactive configurations. The residue ASP80 seems to have a negative impact, forming a stable bond with the drug's hydroxyl group (Figures S3, S5, S7). This bond is far from PAPS, leading to unreactive geometries shown by a widening of the distance distributions between the compounds and PAPS. This residue is conserved in SmSULT, but stays at larger distances (more than 4.5 Å from the hydroxyl group of all considered compounds).

In ShSULT, the S-enantiomer of Ph-CH2-OXA shows the most promising results. Our in vitro experiments showed that this compound was active against S. haematobium and our structures show significant improvements over OXA. The distances between reactant groups are significantly smaller, at about 4.3 Å on average and only slightly larger than for OXA in SmSULT, indicating that the compound could be activated. We also noticed that the difference between enantiomers is much larger in ShSULT than in SmSULT, suggesting that using enantiopure samples of Ph-CH2-OXA instead of a racemic mixture may significantly improve the drug's efficacy against S. haematobium.

However, given the overall low activity of the racemate in vivo, this specific point was not further evaluated.

Stability of OXA Analogues in Acidic Environments and in the Presence of Microsomes

We further investigated if the limited in vivo activity on juvenile S. mansoni and adult S.

haematobium could be explained by physiological stability issues. We therefore evaluated two different conditions: an acidic environment and the co-incubation in the presence of liver microsomes, to simulate the environments within the stomach and the liver, respectively.

Simple HPLC methods with a short run time were used to visually check the elution of the fragments before and after exposure to 1 M HCl (Figure S8). Since all compounds after 24 h incubation with 1 M HCl produce completely different elution peaks after incubation, all three compounds have little stability in acidic media.

We conducted the metabolic stability assays using commercially available human liver microsomes, which are specific for Phase I processes catalyzed by cytochrome P450 (CYP) monooxygenases and flavin containing monooxygenases (FMO). We selected human instead of murine microsomes because the human is the final species of interest and the results of these metabolic studies can give us an inference of the behavior in our mouse experiments.

The metabolic stability results are summarized in From the values of intrinsic clearance in Table 6, according to McNaney et al., Fc-CH2-OXA could be categorized as "low" clearance, while Rc-CH2-OXA, Ph-CH2-OXA and OXA would be categorized as "intermediate". [START_REF] Mcnaney | An automated liquid chromatography-mass spectrometry process to determine metabolic stability half-life and intrinsic clearance of drug candidates by substrate depletion[END_REF][START_REF] Krzyżak | Metabolic stability and its role in the discovery of new chemical entities[END_REF] The elution peaks showed (Figure S9, S10 and S11) for Fc-CH2-OXA, Rc-CH2-OXA and Ph-CH2-OXA that only the Ph-CH2-OXA derivative remained unchanged in an acceptable 56 % after 24 h of incubation in the presence of microsomes, what indicates that the Ph-CH2-OXA derivative was more resistant to microsomal oxidation, hydroxylation and reduction compared to its metallocenyl analogues, Fc-CH2-OXA and Rc-CH2-OXA.

We previously reported [START_REF] Hess | Ferrocenyl, ruthenocenyl, and benzyl oxamniquine derivatives with cross-species activity against Schistosoma mansoni and Schistosoma haematobium[END_REF] excellent in vivo efficacy in the S. mansoni murine model at 100 mg/kg.

At that time, the stability of the compounds was yet unknown. Based on the stability results we obtained, it is entirely possible to attribute some activity of the derivatives to OXA itself, in addition to the derivatives' own bioactivity. Furthermore, we could infer that the factors of poor metabolic stability, solubility and permeability of the compound to the membrane contributed to the poor in vivo results. In order to have a better idea of the permeability of Ph-CH2-OXA (deemed the most stable candidate via stability testing), we proceeded to calculate the MW, logP value, number of Hydrogen bonds donors and Hydrogen bonds acceptors, using the software Molinspiration 32 to estimate its theoretical solubility and membrane permeability. These values gave us a rational basis for selecting a compound for formulation studies aimed at improving bioavailability.

Traditionally, therapeutics have been small molecules that fall within the Lipinski's rule of five [START_REF] Lipinski | Experimental and computational approaches to estimate solubility and permeability in drug discovery and development settings[END_REF] (i.e., a molecule with a molecular mass ≤ 500 Da, ≤ 5 hydrogen bond donors, ≤ 10 hydrogen bond acceptors, and an octanol-water partition coefficient log P ≤ 5). Molecules violating more than one of these rules may experiment limited bioavailability. Ph-CH2-OXA has a molecular mass of 369 Da, 6 H-bond acceptors, 2 H-bond donors, and a calculated logP value of 4.26 with 7 rotatable bonds, which were well within the parameters of being an ideally permeable small molecule (Table S2).

It is important to note that it is solubility, permeability and metabolic stability, collectively that have a bearing on the bioavailability of oral drugs. Ph-CH2-OXA was active in vitro, and the in silico studies predicted as well a very promising interaction with the parasite's active site on both evaluated species. Additionally, since Ph-CH2-OXA was metabolically the most stable compound and with predicted acceptable permeability according to the Lipinski's criteria, we proceeded with Ph-CH2-OXA for further nanoencapsulation formulation studies on the hypothesis that the nanoencapsulated compound would have increased overall solubility and reduced degradation within the acidic environment of the stomach, a new panorama, which would allow better delivery of the compound to its parasitic target.

Lipid Nanocapsules loaded with Ph-CH2-OXA

Lipid nanocapsules (LNC) are the vector of choice to encapsulate lipophilic molecules. [START_REF] Huynh | Lipid nanocapsules: a new platform for nanomedicine[END_REF] Indeed, LNC present an oily core formed of medium-chain triglycerides covered by a membrane made from a mixture of lecithin and a PEGylated surfactant [START_REF] Huynh | Lipid nanocapsules: a new platform for nanomedicine[END_REF] (Figure 3): this core is able to encapsulate various lipophilic compounds and LNC have already been intensively used for in vivo administration of ferrocifens. The in vivo activity of the drug loaded nanocapsules was evaluated in mice harboring a 21-day S.

mansoni infection but this improvement in formulation was not translated into a raise of the activity, as summarized in Table 2. The low activity could be the result of a slow or even an absence of drug release, and/or a limited pathogen LNC internalization. In a study instigating the release of different dyes from LNC to a lipophilic compartment mimicking the cells lipid membrane, lipophilic indocarbocyanine dyes were reported to stay entrapped in the surfactant shell of the LNC and no transfer was observed. [START_REF] Bastiat | A new tool to ensure the fluorescent dye labeling stability of nanocarriers: a real challenge for fluorescence imaging[END_REF] In a similar paper, studying the transfer in vivo of different dyes from LNC to different lipophilic acceptors, the absence of release of lipophilic indocarbocyanine from LNC was confirmed. [START_REF] Simonsson | Internanocarrier and nanocarrier-to-cell transfer assays demonstrate the risk of an immediate unloading of dye from labeled lipid nanocapsules[END_REF] The Ph-CH2-OXA being similar in terms of hydrophobicity, the same behavior could be hypothesized and explain the lack of increase of activity of the LNC in comparison to the pure compound.

Conclusion

In this study, we followed up on three OXA analogues that had shown promising antischistosomal activity. The computational models forecast that the ferrocene-and benzene-containing analogues sample far more near attack configurations with the target sulfotransferase than the parent compound (OXA) for S. mansoni. On the contrary, in S. haematobium, only the Senantiomer of Ph-CH2-OXA shows the most significant improvement over OXA and could be active against this species. In vitro, the derivatives showed improved activity compared to OXA, against adult worms of all three species evaluated (S. mansoni, S. haematobium and S. japonicum) and against juvenile S. mansoni. When considering the in vivo studies instead, we evidenced a lack of activity for all three derivatives against juvenile S. mansoni and adult S. haematobium. We found that all three compounds were only slightly cleared in the in vitro liver model but were poorly stable within an acidic environment. This is likely the reason as to why the promising in vitro results

did not translate to in vivo activity. We further evaluated if the lipid nanoencapsulation of the lead compound (Ph-CH2-OXA) could overcome this limitation, but unfortunately the formulated compound was also inactive. Since the stability and not the activity on the target seems to be the main limitation of these molecules, further steps should include additional strategies for improved drug formulation, to find out if an enhanced bioavailability can overcome the loss of in vivo activity.

EXPERIMENTAL SECTION 1 H and 13 C NMR spectra

All chemicals were either commercially available or were prepared following standard literature procedures. Solvents were used as received or distilled using standard procedures. All preparations were carried out using standard Schlenk techniques.

1 H and [START_REF] Chevalier | Independent origins of loss-of-function mutations conferring oxamniquine resistance in a Brazilian schistosome population[END_REF] C NMR spectra were recorded in deuterated solvents on Bruker 400 or 500 MHz spectrometer at room temperature. The chemical shifts, δ, are reported in ppm (parts per million).

The residual solvent peaks have been used as internal references. The abbreviations for the peak multiplicities are as follows: s (singlet), d (doublet), t (triplet), m (multiplet). ESI mass spectrometry was performed using a LTQ-Orbitrap XL from Thermo Scientific. Elemental analysis was performed at Science Centre, London Metropolitan University using Thermo Fisher (Carlo Erba) Flash 2000

Elemental Analyser, configured for % CHN. The scanned spectra of the compounds are available in the SI.

OXA-Derivatives preparation

The OXA derivatives were prepared starting from the parent compound oxamniquine (Pfizer) as described previously. [START_REF] Hess | Ferrocenyl, ruthenocenyl, and benzyl oxamniquine derivatives with cross-species activity against Schistosoma mansoni and Schistosoma haematobium[END_REF] The analytical data matched that previously reported and is available in the SI for further reference. 23 The animals were kept in the animal facility with humidity and light control (50 % -12/12) for three months.

Animals and parasites

Swiss Webster mice infected with S. japonicum (Philippine strain) were also obtained from NIH NIAID SRC for our in vitro studies.

In vitro studies

Adult S. mansoni, S. haematobium and S. japonicum worms were collected by dissection from the mesenteric veins. Until use (within 24 h after dissection) and during the experiments, the worms were kept in the incubator by 37°C and 5% CO2 and the culture medium consisted of RPMI 1640 (Gibco -Thermofisher, Waltham, MA USA) supplemented with 1% penicillin/streptomycin (BioConcept, Allschwil, Switzerland) and 5% Fetal Calf Serum (FCS) (BioConcept). The control groups consisted of culture medium spiked with dimethyl sulfoxide (DMSO) at a concentration of 1% or 0.5%, equivalent to the content of DMSO present in the wells of worms treated with the highest drug concentration for that assay. The concentrations evaluated were 100, 50, 25, 12.5 and 6.25 μM. The studies on S. mansoni and S. japonicum were performed as duplicates and repeated once, while the studies on S. haematobium were performed in duplicates. Every study condition included at least three worms.

We further evaluated the effect of the addition of albumin (AlbuMAX II, Gibco) to the culture medium to investigate if the activity of the derivatives was different. For this we set the same assay design as described before and added 45 g/l albumin to the culture medium, corresponding to the content of albumin within the range of human plasma. 42 We performed the study with medium containing albumin on adult S. mansoni (duplicate and repeated once), and on adult S. haematobium (on duplicate). To assign a score to the viability, we used a previously described method [START_REF] Keiser | In vitro and in vivo trematode models for chemotherapeutic studies[END_REF] scoring motility, viability, and morphological alterations using a bright field inverted microscope (Carl Zeiss Oberkochen, Germany, magnification ×4 and ×10).

S. mansoni juvenile worms for in vitro studies

28 days after infection, mice were euthanized and juvenile worms were obtained by blood perfusion. The perfusion solution consisted of 8.5 g/L NaCl, 7.5 g/L Na-citrate in distilled water.

Parasites were in different stages of development, as reported somewhere else. [START_REF] Faust | Life history of manson's blood fluke (Schistosoma mansoni). III. The Blood Picture in Schistosomiasis Mansoni[END_REF] All juvenile worms were kept in culture medium as described before for adult S. mansoni until use within 24 h. To test the activity of the derivatives against the juvenile stages, we incubated the worms with a 100 μM concentration of each of the derivatives in duplicates and at least two worms per well.

Duplicates of 100 μM OXA and 1 % DMSO served as control conditions.

Calculation of IC50 values

Statistical analysis

All statistics were performed using RStudio version 3.5.1 [START_REF] Team | Integrated Development for R. 3.5.1[END_REF] . For evaluating significance in the in vivo studies we applied the non-parametric Kruskall Wallis test for multiple comparisons, and the Dunn test with Bonferronni correction for individual differences. Significance was defined as an adjusted p value < 0.05. To evaluate if there was difference in gender susceptibility we applied the binomial test.

Drug suspension for oral administration

The derivatives were administered to the animals in form of an oral suspension. The compounds were first dissolved in DMSO (Sigma-Aldrich, Buchs, Switzerland) corresponding to 10% of the total volume, and then a mixture of Tween 80 and ethanol in a proportion of 70:30 was added, also corresponding to 10% of the final volume. The remaining 80% of the volume consisted of distilled water, which was added under stirring by small aliquots.

In vivo activity on juvenile S. mansoni

21 days after infection, mice were treated orally with each of the derivatives and the nanocapsules loaded with Ph-CH2-OXA at a concentration of 200 mg/kg. The control group consisted of four mice which were infected on the same day and under the same conditions as the treatment arm, but

were not treated avoiding additional stress, in accordance to animal welfare regulations. Four weeks after treatment (seven weeks after infection), when the worms reached the adult stage of development, the mice were euthanized with CO2, dissected and the remaining alive worms were picked out from the mesenteric veins and liver, sexed and counted.

In vivo activity on adult S. haematobium

The hamsters harboring an adult infection were treated with a dose of 200 mg/kg of the compounds. Three weeks after treatment, the hamsters were euthanized with CO2, dissected and the worms were picked out from the mesenteric veins and liver, sexed and counted. The control group consisted of four untreated hamsters.

Computational studies

Classical molecular dynamics simulations were performed of the target proteins, i.e. the sulfotransferase of S. mansoni (SmSULT) and of S. haematobium (ShSULT), in complex with OXA, Fc-CH2-OXA and Ph-CH2-OXA. Since the two enantiomers of OXA show different activities against schistosomes, [START_REF] Taylor | Structural and functional characterization of the enantiomers of the antischistosomal drug oxamniquine[END_REF][START_REF] Taylor | Structural and enzymatic insights into species-specific resistance to schistosome parasite drug therapy[END_REF] we performed separate simulations for both enantiomeric forms of all molecules.

To develop force field parameters for the drugs, the geometry of all compounds was optimized in the gas phase with the Gaussian 16 software package, [START_REF] Frisch | Gaussian 16 Rev. B.01[END_REF] using DFT with B3LYP functional and a 6-31+G* basis set for non-metallic atoms and LANL2DZ pseudopotential for the iron atom. The initial geometries were taken from crystallized S-OXA complexed to SmSULT (PDB: 4MUB [START_REF] Valentim | Genetic and molecular basis of drug resistance and speciesspecific drug action in Schistosome parasites[END_REF] ). Hess et al.

crystallized in 2017 the R-enantiomer of Fc-CO-OXA [START_REF] Hess | Ferrocenyl, ruthenocenyl, and benzyl oxamniquine derivatives with cross-species activity against Schistosoma mansoni and Schistosoma haematobium[END_REF] and we used this structure as a starting point for all R-isomers. The electrostatic potential was computed with the same functional and basis set in order to estimate the effective atomic point charges through RESP fitting. [START_REF] Bayly | A well-behaved electrostatic potential based method using charge restraints for deriving atomic charges: the RESP model[END_REF] Classical molecular dynamics simulations were performed using Amber16. 49 The protein was modelled using the FF14SB force field and the Generalized Amber Force Field 2 (gaff2) was used as a base for the ligands. The ferrocenyl group was modelled using the force field published by Doman et al. [START_REF] Doman | Molecular mechanics force fields for linear metallocenes[END_REF] To estimate the missing dihedral parameters between the ferrocenyl group and the rest of the molecule, we scanned the angles of interest and performed DFT single point energy calculations for all angles, using the same functional, basis set and pseudopotential as for the geometry optimization. We then used the software paramfit from AmberTools16 49 to estimate the parameters. To prevent clashes between nuclei during the rotation, we performed these computations on subsystems containing solely atoms that are relevant for these parameters (e.g.

Fc-CH2-NH2, Fc-CH2-N-(CH3)2, Fc-CO-NH2 and Fc-CO-N-(CH3)2). All parameters determined in this way accurately reproduce the corresponding ab initio energy profiles (Figure S5).

The crystallographic structures of SmSULT and ShSULT with OXA and the cofactor 3′phosphoadenosine-5′-phosphate (PAP) served as a starting point for our simulations (PDB: 4MUB and 5TIY, 46 respectively). OXA was replaced by its derivatives through alignment of their shared atomic groups. 3′-phosphoadenosine-5′-phosphosulfate (PAPS), the active version of PAP, was inserted in the same way by minimizing the distance between shared PAP atoms. Missing loops of the protein were added using the ModLoop web server. [START_REF] Fiser | Modeling of loops in protein structures[END_REF] Using tleap, the resulting system was put in an 84 x 84 x 84 Å 3 periodic box filled with explicit TIP3P water molecules. Finally, the total charge was neutralized by adding Na + counter-ions. The resulting systems consisted of about 50,000 atoms.

Classical trajectories were computed using Amber's CUDA version of the PMEMD program. After minimization, the SHAKE algorithm [START_REF] Ryckaert | Numerical integration of the cartesian equations of motion of a system with constraints: molecular dynamics of n-alkanes[END_REF] was used to constrain covalent bonds involving hydrogen atoms and the system was heated to body temperature (T = 310 K) in two steps using a Langevin thermostat. First, the water molecules were heated to the target temperature while restraining the positions of the ligand and protein during 50 ps with a time step of 1 fs. Then, the restraints were released and the whole system was thermalized in the NPT ensemble for 400 ps, with a time step of 1 fs and a pressure relaxation time of 3 ps. We then performed NPT simulations for 40 ns with a time step of 2 fs to reach an equilibrium state of the system. We finally performed 80 ns NPT production runs that were used for analysis.

The binding free energy of the ligands inside the protein was estimated based on the MD trajectories using two methods available in Amber16: Generalized Born Surface Area (MM/GBSA) The metabolic stability of the three OXA derivatives was studied by in vitro co-incubation with human liver microsomes. All three compounds were incubated in the presence of NADPH at 37 °C.

The protocol was adapted from previous studies: [START_REF] Patra | In vitro metabolic profile and in vivo antischistosomal activity studies of (η6-Praziquantel)Cr(CO)3 derivatives[END_REF][START_REF] Keller | A tutorial for the assessment of the stability of organometallic complexes in biological media[END_REF] By comparing the differences in respective m/z values in MS spectra, m/z values for the parent compound and OXA could be identified. Semi-quantitative analysis of the ratio of parent compound and different metabolites present in the mixture after incubation with human liver microsomes was achieved by comparing the areas under the respective peaks of different compounds visible in the UV traces of the LC analysis at 245 nm. To determine the in vitro half-life (t1/2), the following process was derived from Tan et al. [START_REF] Tan | Gold(I) bis(N-heterocyclic carbene) complexes: metabolic stability, in vitro inhibition, and genotoxicity[END_REF] The peak areas of the compounds at different time points are expressed first as a percentage of the internal standard, caffeine.

Ratio at timepoint = Area under curve of compound Area under curve of internal standard Following this, normalized ratios were calculated using the ratio of peak area of the test compounds to caffeine at t = 0 h. Normalised ratios were calculated at each assessed timepoint of t = 1 h, 4 h and 24 h.

Normalised ratio =

Ratio at timepoint ≠ 0 Ratio at timepoint = 0

The normalized ratio values are then plotted against incubation time. The t1/2 values calculated via analyses methods in GraphPad Prism 8 (nonlinear regression, exponential one phase decay). The degradation rate constant, k was then calculated using the t1/2 values (converted from hours to minutes).

The predicted in vitro intrinsic clearance values (expressed as µL/min/mg protein) were then calculated as a ratio of the degradation rate constant k (expressed as min -1 ) and the microsomal protein concentration (mg/µL).

in vitro intrinsic clearance values CLint = k microsomal protein content (0.4 mg/mL protein)

Ph-CH2-OXA loaded lipid nanocapsules

Lipid nanocapsules (LNC) were formulated by the phase inversion phase method. [START_REF] Heurtault | A novel phase inversion-based process for the preparation of lipid nanocarriers[END_REF] Briefly, to prepare blank LNC, Labrafac® (Gattefossé SAS, France, 20.6 % w/w), Lipoid® S 100 (Ludwigshafen, Germany 1.5 % w/w), Kolliphor HS 15 (Florham Park, USA 17 % w/w), NaCl (Sigma-Aldrich, USA 1.3 % w/w) and water (59.6 % w/w) were mixed and homogenized under magnetic stirring at 80 °C. Three cycles of progressive heating and cooling between 90 °C and 50 °C were then performed.

During the last cooling cycle, the mixture was diluted by adding 2 °C purified water (28.7 % v/v) in order to induce an irreversible shock and formulate LNC. In order to encapsulate Ph-CH2-OXA inside the LNC, some slight changes to this protocol have been applied. The Ph-CH2-OXA (4.35 % w/w) was mixed with Labrafac®, Lipoid® S 100 and ethanol (Fisher, USA) to help solubilization of the molecule in the lipid phase. This mixture was put under agitation at 50 °C until total solubilization of the Ph-CH2-OXA. The ethanol was then evaporated under argon. Once the ethanol evaporated, Kolliphor HS 15, NaCl and water were added and three heating and cooling cycles were performed as prescribed for formulating blank LNC. During the last cooling cycle, the mixture was diluted by adding 2 °C purified water. Empty LNC and Ph-CH2-OXA loaded LNC were characterized using Dynamic Light Scattering (DLS) to determine their size, polydispersity index (pdi) and zeta potential. S2. Molecular properties calculated using Molinspiration (http://molinspiration.com).

Figure 1 .

 1 Figure 1. Structures of the compounds investigated in this study.

Figure 2 .

 2 Figure 2. Distance between the closest oxygen of PAPS and the hydroxyl group of the analogues. R-enantiomers in blue and S-enantiomers in orange.

  All animal experiments were conducted at the Swiss Tropical and Public Health Institute (Swiss TPH) and authorized by the animal welfare office Kanton Basel Stadt, Switzerland (Authorization no. 2070).NMRI female mice were purchased from Charles River (Sulzfeld, Germany) at the age of three weeks and were left without intervention for one week of acclimatization. Mice were infected with a subcutaneous infection of around 100 cercariae in the back of the neck, following the procedure described by Lombardo et al.[START_REF] Lombardo | Life cycle maintenance and drugsensitivity assays for early drug discovery in Schistosoma mansoni[END_REF] For the S. haematobium chronic infection, one-month old LVG hamsters (Charles River, NY) were provided by the National Institutes of Health (NIH)-National Institute of Allergy and Infectious Diseases (NIAID) Schistosomiasis Resource Center (SRC) for distribution by the Biomedical Research Institute in Rockville, USA, which were pre-infected with 350 S. haematobium cercariae.

CompuSyn 1 .

 1 0 (ComboSyn Inc, 2007) was used to calculate the IC50 values of each of the derivatives after an incubation period of 72 h. The following equation was used to normalize the scores of the treated worms to the controls: Effect = 1 -average score treatment average score control

2 . 5

 25 µL of 5 mM caffeine (TCI Chemicals) in HPLC MeCN as internal standard were added during the quenching process. The mixture was shaken for 10 min to ensure complete extraction. The DCM layer was carefully removed and then evaporated to provide residues that were analyzed by LC-MS (HPLC Waters 2525/Mass Spectrometry Waters ZQ 2000) using a pure acetonitrile-water system with the same column as above. The residues were dissolved in 100 µL HPLC grade acetonitrile. 20 µL from each MeCN residue sample was injected manually using the following run parameters: 3 min 5 % MeCN 95 % H2O; 13 min 40 % MeCN 60 % H2O; 14 min 100 % MeCN 0 % H2O; 20 min 100 % MeCN 0 % H2O; 23 min 5 % MeCN 95 % H2O. UV spectra were analyzed and compared at different time points.

Figure S10 .Figure S11 .

 S10S11 Figure S10. Comparison of LCMS trace for Rc-CH2-OXA before and after incubation for 24 h in liver microsomes

Table 1 .

 1 In vitro activity of Fc-CH2-OXA, Rc-CH2-OXA and Ph-CH2-OXA versus OXA against S. mansoni, S. haematobium and S. japonicum.

S

. mansoni S. haematobium S. japonicum Compound IC50 adults 72 h (µM) IC50 adults in medium 45 g/L albumin. 72 h (µM) Onset of action on juveniles 100 µM (h) IC50 28 day juveniles 72 h (µM) IC50 adults 72 h (µM) IC50 adults in medium with albumin. 72 h (µM) IC50 adults 72 h (µM)

	Fc-CH2-OXA	9.0	28.1	< 24	0.5	52.3	55.7	22.7
	Rc-CH2-OXA	6.0	NC	< 24	1.3	15.5	25	30.9
	Ph-CH2-OXA	13.5	90.7	< 24	26.7	32.6	70.6	39.8
	OXA	>100	>100	72	>100	>100 *	ND	>100
	* Hess et al. 23 , NC: no correlation, ND: not done.

Table 2 :

 2 Reduction of the juvenile worm burden in S. mansoni infected mice after treatment with 200 mg/kg of the OXA derivatives and after treatment with the nano encapsulated Ph-CH2-OXA.

Compound No. of mice Worm burden (SD) WBR % pure drug (SD) WBR % nanocapsule Females

				Total	Females	Total	Females Total
	Control group	8	6.5 (1.6) 12.3 (2.5)	-	-
	Fc-CH2-OXA	4	3.8 (0.96) 7.5 (2.65)	42.3 (14.7)	38.8 (21.6)	ND	ND
	Rc-CH2-OXA	4	3 (2.45)	6.5 (4.43) 53.8 (7.7) 46.9 (36.2)	ND	ND
	Ph-CH2-OXA	4	4.3 (0.5) 7.5 (0.58)* 34.6 (7.7) 38.8 (4.7)*	0	0
	ND: Not done; WBR: worm burden reduction. *Statistically different from control on p<0.05

Table 3 :

 3 Change in the worm burden of S. haematobium infected hamsters after treatment with 200 mg/kg of the OXA derivatives.

	Compound	No. of mice	Worm burden (SD) Females Total	WBR %
	Control group	4	18.5 (8.3) 40 (13.6)	-
	Fc-CH2-OXA	4	25.8 (7.5) 54 (16.2)	0
	Rc-CH2-OXA	3*	55 (16.1) 108 (28.9)	0
	Ph-CH2-OXA	4	19 (3.7)	51 (18.9)	0
	*One animal died during the experiment.

Table 4 .

 4 Estimated binding free energies computed by the MM/PBSA method (kcal/mol).

	Compound	S. mansoni R S	S. haematobium R S
	Fc-CH2-OXA	-39.3	-41.9	-36.3	-39.9
	Fc-CO-OXA	-36.3	-29.9	-26.4	-32
	Ph-CH2-OXA	-30.3	-35	-36.6	-18.3
	OXA	-12.5	-8	-17.1	-22.8

Table 5 .

 5 Average O-H distance with standard deviation (Å)

	Compound	S. mansoni R	S	S. haematobium R	S
	Fc-CH2-OXA	5.1 ± 1.1	1.8 ± 0.1	11.8 ± 0.7	6.1 ± 0.8
	Fc-CO-OXA	12.2 ± 1.2	10.0 ± 0.9	12.8 ± 1.9	6.2 ± 0.7
	Ph-CH2-OXA	2.2 ± 0.7	2.0 ± 0.7	14.5 ± 1.1	4.3 ± 0.5
	OXA	3.3 ± 0.4	3.5 ± 0.3	9.5 ± 1.6	6.1 ± 0.8

Table 6 .

 6 The stability of the compounds decreased exponentially with > 40 % compound remaining after 24 h, with similar half-life values ranging from 2.2 -3.8 h. The intrinsic clearance of the compounds was low and intermediate ranging from 7.5 to 13.3 µL/min/mg.[START_REF]Measurement of in vitro intrinsic clearance using microsomes[END_REF]

Table 6 .

 6 Metabolic stability in human microsomes

	Compound	t1/2 (h)	k (min -

1 ) CL int (µL min -1 mg -1 )

	Fc-CH2-OXA	3.8	0.003	7.5
	Rc-CH2-OXA	2.2	0.0053	13.3
	Ph-CH2-OXA	2.4	0.0048	12
	OXA	3.1	0.0037	9.3

Table 7 .

 7 Physico-chemical parameters characterized by DLS of empty LNC (blank) and Ph-CH2-OXA loaded LNC

	Ph-CH2-OXA was encapsulated at a concentration of 32.35 mg per mL of LNC, representing a drug
	loading of 4.35 % w/w. The physico-chemical parameters (characterized by Dynamic Light
	Scattering), of blank LNC and Ph-CH2-OXA loaded LNC were the same: diameters of approximately
	50 nm, a pdi value below 0.2, which demonstrates a monodispersed population of nanoobjects,
	and a zeta potential close to neutrality as shown in Table 7.
	Sample	Diameter (nm)	pdi	Zeta potential (mV)
	Blank LNC	57.4 ± 0.9 0.07 ± 0.02	-3.9 ± 0.7
	Ph-CH2-OXA LNC 53.0 ± 0.5 0.04 ± 0.02	-3.1 ± 0.1
	pdi: Polydispersity index

[START_REF] Laine | Brain tumour targeting strategies via coated ferrociphenol lipid nanocapsules[END_REF][START_REF] Allard | Local delivery of ferrociphenol lipid nanocapsules followed by external radiotherapy as a synergistic treatment against intracranial 9L glioma xenograft[END_REF][START_REF] Karim | Enhanced and preferential internalization of lipid nanocapsules into human glioblastoma cells: effect of a surface-functionalizing NFL peptide[END_REF][START_REF] Laine | The in vivo performance of ferrocenyl tamoxifen lipid nanocapsules in xenografted triple negative breast cancer[END_REF]

Figure 3. Schematic representation of LNC.

  10 µL of 20 mg/mL microsomes (GIBCO, 50 pooled), 463 µL of PBS (GIBCO, 1x PBS) and 2 µL of 40 mM NADPH (Sigma) were added to 1.5 mL Eppendorf tubes and incubated at 37 °C for 10 min to prime the microsomes. Following this, 10 µL of 50 mM test compound and an additional 15 µL of NADPH were added (1 mM final concentration of test compound in 500 µL total volume). The samples were incubated at 37 °C, and quenched at the desired time points of 1, 4 and 24 h by adding 2 mL of dichloromethane (DCM) or any other organic solvent.

Acknowledgements

This work was financially supported by the Swiss National Science Foundation (Grant Sinergia CRSII5_173718) and has received support under the program «Investissements d'Avenir» launched by the French Government and implemented by the ANR with the reference ANR-10-IDEX-0001-02 PSL (G.G.). We are grateful for the loan of analytical instruments by Agilent Technologies and CEA Saclay to Chimie ParisTech. V.B. is grateful to the Swiss excellence scholarships for financial support, scholarship number 2017.0801.

Ancillary information

Supporting information

Figure S1. Rigid dihedral scan energy profiles for representative subsystems Table S1. Estimated binding free energies computed with the MM/GBSA method (kcal/mol).

Conflict of interest

Authors have no competing interests to declare.


Luisa De Sordi
email: luisa.de_sordi@sorbonne-universite.fr

Gut bacteriophages and the pinball challenge

Five years ago, my first study on the mechanisms that govern the coexistence of intestinal bacteria and bacteriophages was published in Cell Host & Microbe. In this commentary, I use the following evolutionary steps of my career to discuss the larger frame of bacteriophage biology in gut health and disease.

Introduction: the microbiota, between -omics and -ology

Mankind has long sought the answer to what defines a human being through philosophy, social sciences, evolutionary biology, and multiple other disciplines. The Human Genome Project, conceived in the '80s as one of the most ambitious scientific projects of all time, opened the path to exploration of the genetic determinants of human physiology and launched a revolution in sequencing technology.

It was at approximately the same time as its conclusion, in the early '00s, that a new awareness started to pervade the scientific community: man is also made of microbes, and this should not be ignored when considering who we are. In 2008, I started my Ph. D. studies and watched from afar as the Human Microbiome Project was launched and a worldwide effort made towards defining the composition of the microbiota and its importance for human health. Since then, progress in gene barcoding and metagenomics has unveiled an unprecedented diversity of microbes and additional "'omics" approaches have followed to complement the global genomic information with that of proteins, transcripts, and metabolites. Although this picture is far from being completed, it has started to outline the biological functions of the microbiota and correlate perturbations of such functions with genomic signatures of microbial abundance and diversity found in patients affected by several diseases and disorders. Most efforts have been towards defining the densest microbial niche, the intestinal tract, and its most numerous inhabitants, bacteria. More recently, relatively neglected microbes, such as fungi, archaea, and viruses, have also been acknowledged to be important components of intestinal and human health, which sparked my research interest in bacterial viruses, or bacteriophages (phages), the most abundant of intestinal viruses.

Certain phage biological features, such as the range of hosts, can be extrapolated by metagenomics data or combinational approaches of phage isolation and sequencing and comparison with metagenomic databases [START_REF] Camarillo-Guerrero | Massive expansion of human gut bacteriophage diversity[END_REF][START_REF] Hryckowian | Bacteroides thetaiotaomicron-Infecting Bacteriophage Isolates Inform Sequence-Based Host Range Predictions[END_REF]. However, for the most part, our understanding of gut phages, and the microbiota in general, is still descriptive and the search for the biological mechanisms governing these communities cannot keep pace with the petabytes of sequence data deposited. As a microbiologist, I find it frustrating that most of these organisms never enter the laboratory as pure cultures for study. Here, I claim that there is still a place for biology in studying the microbiota, and that it is important to do so.

The microbiota as a phage pinball machine

Many metaphors have been used to describe the nature and functions of gut phages, the nanoorganisms of the intestine. Russian dolls have repeatedly been used as a proxy for nested relationships between phage, bacteria, and the human host. In addition, "ripple" and "domino" effects describe well the chain of events that may start from the infection of bacteria by phages to regulation of the microbial community, ending with a potential effect on human health. Indeed, a strong case can be made for these points of view, but I find them somehow too linear and organised for our actual understanding of the topic. Here, I propose my personal vision, in which the microbiota is like a pinball machine, and I ask the reader to bear with me while I use this commentary to explain what I mean. In such a game of pinball, phages can be likened to little balls bouncing off various targets that are much bigger than they are in an apparently chaotic manner. The levels of interaction include, naturally, bacteria, but also possibly other viruses, the intestinal barrier, the immune system, and, more vaguely, other cellular compartments, with a resulting variable impact on human health, the pinball score (Figure 1). In the following sections, I will retrace some steps of my career during which I have attempted to obtain a better understanding of the biology of intestinal phages through these interactions and propose a number of future challenges faced by phage biologists, the pinball players.

Phage interactions with other microbes

Five years ago, while I was a postdoctoral researcher at the Institut Pasteur of Paris in the laboratory of Laurent Debarbieux, we published an article in Cell Host & Microbe showing that gut phages can perform successive passages of infection in multiple intestinal bacteria and select for structural mutations that allow adaptation to infect previously non permissive hosts [START_REF] De Sordi | The Gut Microbiota Facilitates Drifts in the Genetic Diversity and Infectivity of Bacterial Viruses[END_REF]. These viral "host jumps" were not new to virologists and epidemiologists studying zoonoses and it was hard to imagine that, a few years later, viral mutations would become a common topic of conversation at a family dinner during a Coronavirus pandemic. However, at the time we started this project, few studies had experimentally examined these mechanisms in complex microbial communities, but a solid basis had already been established, starting from the 70s and 80s, on how individual phagebacteria couples can coevolve with each other. In our article, we studied a simple community composed of one virulent phage that could infect an E. coli host strain but that was unable to bind to and lyse a second E. coli strain, even after weeks of patient coincubation in vitro and in the gut of axenic mice colonised with our three-partner community. All changed when this community was added to the microbiota of conventional mice, and it behaved differently. The phage was then able to infect both E. coli strains and selected genomic mutations that did not appear in the other experimental conditions. The microbiota changed what our phage could do, but how? We reasoned that the phage could have replicated on other bacterial hosts on the basis that E. coli is nearly omnipresent in the mammalian gut. Although this hypothesis appeared to be reasonable, proving it turned out to almost as hard as finding the proverbial needle in a haystack. With a mix of method, patience, resistance, and luck, the haystack of the mouse microbiota yielded what we were looking for: an E. coli strain that our phage was able to infect and that allowed the host-jump towards the noninfectable host. Changes in the viral host-range can be extrapolated from studies of phage-bacteria infection networks, but it was exciting to see them happen before our eyes.

Determining the microbiota as a promoting factor supported the idea that this ecosystem is continuously shaped and expanded by parasitic and predatory mechanisms driven by gut phages.

Their study will bring us to the next challenge: how do these mechanisms interconnect with other microbial ecological dynamics? Bacterial resistance, persistence, and abortive infections are also among the factors expected to affect the community structure, together with phage-associated fitness advantages driven by prophages carrying useful features, such as superinfection exclusion, immuneevasion, or even the expression of virulence factors.

In addition, virus-virus interactions have been little studied in the intestinal environment but cooperation between phages has been recently shown in vitro [START_REF] Chevallereau | Exploitation of the Cooperative Behaviors of Anti-CRISPR Phages[END_REF]. As the concept of sociovirology is firmly taking hold, it only seems predictable that it could be key to the coexistence of densely associated mixed phage subpopulations in the intestinal tract. Improving our understanding of their diversity may cast light on new roles for virus-virus interactions, similarly to when we became aware of bacterial community behaviours a few decades ago.

Phage-bacteria interactions in the intestinal environment

The microbiota lives and evolves in a defined environment, the intestinal tract, with mutual effects on microbial and intestinal physiology. While in the Debarbieux lab at the Institut Pasteur, I had the luck to also work with a then Ph. D. candidate, Marta Lourenço. Marta set up a model to study phagebacterial interactions in mice hosting a defined microbiota of 12 bacteria. We chose this model to work in a controlled setting in which we could follow changes in the entire microbial community. We separately challenged two E. coli strains with different phages, but the density of the colonising E. coli was only slightly affected [START_REF] Lourenço | The Spatial Heterogeneity of the Gut Limits Predation and Fosters Coexistence of Bacteria and Bacteriophages[END_REF]. The phages, however, were actively replicating, as shown by their high titres. This might seem puzzling, but is not surprising per se, as the gut is colonised by a stable density of bacteria and their predators and parasites. But how do they coexist? Decades of research have revealed several models of phage-bacteria coevolution based on the emergence of bacterial resistance to phage predation and the corresponding mechanisms of phage counterresistance. The hypothesis that coevolution is key to maintaining stable bacterial and viral intestinal populations is appealing. However, although we previously characterised coevolution in in-vivo experimental settings [START_REF] De Sordi | I will survive": A tale of bacteriophage-bacteria coevolution in the gut[END_REF], in this study, hours of plaque assays did not reward us with the isolation of resistant bacterial clones. We reasoned that we did not know how the spatial heterogeneity of the intestinal tract could affect phage-bacteria interactions and decided to investigate where in the intestine phage infections were more likely to take place. We found that the phage-to-bacteria ratio was much lower in the mucus layer than in the luminal compartment of different gut sections. We proposed that actively mobile bacteria can become better established in the micro compartment of the outer mucus, thus finding refuge from phage predation, more prominent in the gut lumen [START_REF] Lourenço | The Spatial Heterogeneity of the Gut Limits Predation and Fosters Coexistence of Bacteria and Bacteriophages[END_REF]. If trivially compared to the predator-prey dynamics of higher organisms, this may function like a rabbit-hole, providing a haven for rabbit reproduction and protection from a chasing falcon. We published this work in 2020 in Cell Host & Microbe and contributed to conveying the message that the spatial organisation of the microbiota may have an influence on the community structure and interactions with the host.

However, in our study, we only tested a handful of phages, and it would be presumptuous to believe that their interactions with their hosts can be generalisable to the billions of particles present in an intestine. Indeed, a few months after we showed that our phages were weak mucus colonisers, Green et al. published the characterisation of phages with a strong affinity for mucin and intestinal glycan and capable of targeting pathogenic E. coli embedded in the mucus layer [START_REF] Green | Targeting of Mammalian Glycans Enhances Phage Predation in the Gastrointestinal Tract[END_REF]. On the one hand, this is a reminder of how phage-specific these mechanisms can be and that an unprecedented diversity of such mechanisms could be hidden in the microbiota community. On the other hand, it should motivate the continuing isolation of more intestinal viruses if we are to characterise their biological role. This is easier said than done, as four years have elapsed from the first computational identification of the universally abundant Crass-like phages and the in vitro cultivation of their first representative, but definitively worth the effort [START_REF] Shkoporov | PhiCrAss001 represents the most abundant bacteriophage family in the human gut and infects Bacteroides intestinalis[END_REF] Another aspect that was highlighted in our study of the intestinal spatial heterogeneity is that bacterial resistance to phages is not required for this model to work, and we thought that other resistanceindependent mechanisms could be involved in the coexistence of intestinal phages and bacteria.

Indeed, in a recent study, we reported the intestinal-specific transcriptional profile of E. coli, showing downregulation of phage membrane receptors. The consequence is bacterial phenotypic resistance to phage infection that relies on the physiological response of the bacteria to the gut environment rather than irreversible genomic mutations, thus explaining the return to susceptibility of the bacteria in vitro [START_REF] Lourenço | The gut environment regulates bacterial gene expression which modulates susceptibility to bacteriophage infection[END_REF].

Interestingly, resistance seems to minimally impact the bacterial ability to colonise different eukaryotic hosts under virulent phage predation, as shown by recent studies using Pseudomonas syringae infecting tomato leaves, and bobtail squid symbiont Vibrio fischeri [START_REF] Hernandez | Phage resistance evolution in vitro is not reflective of in vivo outcome in a plant-bacteria-phage system[END_REF][START_REF] Lynch | Independent host-and bacterium-based determinants protect a model symbiosis from phage predation[END_REF]. Yet, all these studies share the rapid evolution of bacterial resistance during free, planktonic, lifestyle. This confirms that protecting host factors favour bacterial colonisation in different host-microbe associations, leaving us with a lot to be done to understand the biology of phage-bacteria interactions in vivo.

The pinball challenge

After four years of postdoctoral studies on gut phage research, I started an academic position at Sorbonne University in Paris in 2018, bringing my phage experience with me and the determination to use it to understand gut diseases. This gave rise to a new group, ready to take on new challenges in the context of intestinal inflammation. Indications that phages may play a role in intestinal conditions have come from several viral metagenomics studies showing that the abundance and diversity of gut phages is altered in patients relative to that of healthy subjects. In Crohn's disease, an expansion of free temperate phages at the expense of virulent phages has been observed [START_REF] Clooney | Whole-Virome Analysis Sheds Light on Viral Dark Matter in Inflammatory Bowel Disease[END_REF].

What is the biological basis for this observation and what does it mean for the development of the disease? An elegant in vivo experimental study using a P2-like phage of Salmonella spp. showed that intestinal inflammation can act as a potent inducer of the lytic cycle of temperate phages [START_REF] Diard | Inflammation boosts bacteriophage transfer between Salmonella spp[END_REF]. The outcome of interactions between this new pool of phages and the intestinal environment is still largely unexplored. For example, whether phages activate the immune system is still debated. However, certain evidence suggests a role for unbalanced phage communities in aggravating inflammatory symptoms, as shown by faecal phages from ulcerative colitis patients during flare-ups, specifically inducing IFN-γ by CD4 + T [START_REF] Gogokhia | Expansion of Bacteriophages Is Linked to Aggravated Intestinal Inflammation and Colitis[END_REF]. If more functional studies manage to complete the metagenomic characterisation of disease-associated phage communities, we may begin to appreciate their possible involvement in intestinal conditions.

Interesting biological questions to be tackled go back to the bouncing pinball analogy introduced before and include interactions with the unbalanced microbial community, the mucus, the epithelial barrier function, and the above-mentioned immune cells. This brings me to the next question: can we, as scientists and clinicians, control the flippers? That is, can we use our knowledge of phage biology to improve the health score linked to the microbiota by adding specific microbiota components? Attempts to engineer the microbiota have long been based on the use of pre-/probiotics or faecal material transplant (FMT) to modulate bacterial communities, with variable outcomes. Little has been done using phages. A traditional way of looking at the problem is the use of phages as therapeutic weapons against targeted bacteria (aka phage therapy). Although phage therapy has consistently proven its value in treating various bacterial infections, results are still largely missing for the selective targeting of intestinal pathogens or the outgrowth of intestinal commensals or pathobionts. While the pioneering treatment of Shigella infections by Felix d'Herelle launched the fame and diffusion of phage therapy worldwide in the early 20 th century, more recent data proved that therapeutic phages may fail to replicate in the desired host, leading to phage loss, like a pinball inexorably hitting the bottom of the machine without hitting the flippers or any target. On the one hand, this observation strengthens the argument for more detailed biological characterisation of phage replication in the intestinal tract. On the other, it suggests that we may need a broader approach towards gut engineering and that to hit a single bacterial microbiota member, we may need to act on the coexisting community associated with its expansion, and thus on multiple targets. This approach is routinely used to treat recurrent infections from Clostridioides difficile with FMT, and a number of results suggest a role for the gut virome in its therapeutic success. In addition, filtered, bacteria-depleted, viral transplants (FVT) have been shown to be effective in several experimental in vivo models of disorders.

As for its bacterial counterpart, active components in this mysterious mixture are unknown: do phages from healthy individuals act as master regulators of the community and, directly or indirectly, intestinal physiology or do a few key phages restore bacterial diversity and evenness by targeting the out growers? Finally, external intervention may include bacterial lysogens carrying prophages of clinical interest.

With Laurent Debarbieux, we were recently involved in a study from the group of Laurence Zitwogel in which it was shown that specific microbiota components can improve the efficacy of cancer immunotherapy. In particular, one epitope of a prophage protein from Enterococcus hirae triggered cytotoxic T-cell responses that cross-reacted with tumour-associated antigens. As a result, the immunogenic reaction was restricted to bacterial strains carrying the prophage, whereas the nonlysogenic form of the same species failed to show therapeutic efficacy [START_REF] Fluckiger | Cross-reactivity between tumor MHC class I-restricted antigens and an enterococcal bacteriophage[END_REF]. In this perspective, pools of temperate gut phages could represent an arsenal of molecular mimics with immunogenic potential against tumour antigens and could be used as personalised microbiota modulators via the administration of bacterial lysogens.

Conclusions

The network of biological interactions between phages, the microbiota, and their human host can shed light on the fundamentals of gut health and disease, represented in this commentary as a pinball machine. As phage biologists, we, the pinball players, can diversely contribute to resolving this network via structural, molecular, genomic, evolutionary, and mathematical studies. A fundamental understanding of the microbial alterations highlighted by metagenomic studies in clinical settings well support the hypothesis of translational engineering of intestinal ecosystems using various features of the versatile nature of phages. This spans the spectrum from their therapeutic applications against pathogenic bacteria to being regulators of microbial populations via FVT through the modulation of innate and adaptive immunity, among other possible mechanisms (Figure 1). The outcome is targeted intervention for acute and chronic conditions aimed at improving the clinical symptoms, the disease score.

Figure 1 :

 1 Figure 1: The pinball challenge of gut phages

Acknowledgements

I would like to thank Laurent Debarbieux for the opportunity to work in his laboratory and set the basis of my career as an independent PI and the members of the group at the time. I am also grateful to all the present and past members and collaborators of my group. Research in my group is founded by the Agence Nationale de la Recerche (ANR) and the Societé Nationale Française de Gastro-Entérologie (SNFGE). The figure was created with Biorender.com.