Ihab Haidar
email: haidar@supagro.inra.fr

Frédéric Gérard
email: gerard@supagro.inra.fr

Alain Rapaport
email: rapaport@supagro.inra.fr

Comparison of numerical simulations of reactive transport and chemostat-like models

Keywords: reactive transport models, chemostat model, microbial growth, numerical simulation

published or not. The documents may come

Introduction

The chemostat is a popular apparatus, invented simultaneously by Monod [START_REF] Monod | La technique de la culture continue: thorie et applications[END_REF] and Novick and Szilard [START_REF] Novick | Description of the chemostat[END_REF], that allows the continuous culture of micro-organisms in a controlled medium. The chemostat has the advantage to study bacteria growth at steady state, in contrast to batch cultivation. The chemostat model serves also as a representation of aquatic natural ecosystems such as lakes. In the classical experiments involving chemostats, the medium is assumed to be perfectly mixed, that justifies mathematical models described by systems of ordinary differential equations [START_REF] Smith | The theory of the chemostat: dynamics of microbial competition[END_REF]. In natural ecosystems, ground-waters or industrial applications that use large reservoirs, the assumption of perfectly mixed medium is questionable, leading to spatialized models such as systems of nonlinear partial differential equations [START_REF] Steefel | Reactive transport modeling: An essential tool and a new research approach for the Earth sciences[END_REF]. However, nonlinear partial differential equations are difficult mathematical objects to understand, analyze and simulate. Even numerical schemes pose significant difficulties, particularly when solving coupled systems involving stiff reactions [START_REF] Carrayrou | Comparison of numerical methods for simulating strongly nonlinear and heterogeneous reactive transport problems-the MoMas benchmark case[END_REF][START_REF] Nowack | Verification and intercomparison of reactive transport codes to describe root-uptake[END_REF][START_REF] Yeh | Numerical modeling of coupled variably saturated fluid flow and reactive transport with fast and slow chemical reactions[END_REF]. Spatial considerations can be introduced in the "classical" model of the chemostat in simpler ways, as it is done in the gradostat model [START_REF] Lovitt | The gradostat: a bidirectional compound chemostat and its applications in microbial research[END_REF] that mimics a series of interconnected chemostats of identical volumes. Other kinds of interconnection can be considered in order to cope with heterogeneity of porous media, considering stagnant water with small diffusion, mixing due to porosity [START_REF] Haidar | Effects of spatial structure and diffusion on the performances of the chemostat[END_REF][START_REF] Nakaoka | Competition in chemostat-type equations with two habitats[END_REF]. If course, such representations are still oversimplified with regard to the complexity of natural porous media.

Over the past three decades, numerous reactive transport codes have been developed to study complex interactions between geochemical and transport processes in porous media. A number of reactive transport computer codes exist. Let us mention for instance the models COMEDIE-2D [START_REF] Cochepin | Approaches to modelling coupled flow and reaction in a 2D cementation experiment[END_REF], CRUNCH [START_REF] Steefel | Crunch-users guide[END_REF], PHREEQC [START_REF] Parkhust | User's guide to PHREEQC (version2). A computer program fo speciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations. Water resources investigations report[END_REF], ECOSAT [START_REF] Keizer | ECOSAT, a computer program for the calculation of chemical speciation and transport in soil-water systems[END_REF], ORCHESTRA [START_REF] Meeussen | ORCHESTRA: an object-oriented framework for implementing chemical equilibrium models[END_REF] , RAFT [START_REF] Chilakapati | Groundwater flow, multicomponent transport and biogeochemistry, Development and application of a coupled process model[END_REF], RT3D [START_REF] Clement | RT3D-A modular computer code for simulating reactive multi-species transport in 3-dimensional groundwater aquifers[END_REF], HYTEC [START_REF] Van Der Lee | Module-oriented modelling of reactive transport with HYTEC[END_REF], HP1 [START_REF] Jacques | Modelling coupled water flow, solute transport and geochemical reactions affecting heavy metal migration in a podzol soil[END_REF] and MIN3P [START_REF] Mayer | Multicomponent reactive transport modeling in variably saturated porous media using a generalised formulation for kinetically controlled reactions[END_REF]. To our knowledge, some of these numerical tools, such as COMEDIE-2D and PHREEQC, are not suitable for unsaturated porous media and thus cannot be readily applied to soils (excepted in the special case of wetland soils). A range of other limitations can be found as well. For example, RT3D does not include equilibrium-controlled reactions, while ECOSAT neglects kinetically-controlled reactions and is limited to a single spatial dimension.

The standard approach for evaluating the computational accuracy of a reactive transport code is to compare its numerical results to those obtained from an analytical or a semi-analytical solution [START_REF] Gérard | Introduction of transport phenomena into the thermo-kinetic code KINDIS: The code KIRMAT[END_REF][START_REF] Nowack | Verification and intercomparison of reactive transport codes to describe root-uptake[END_REF][START_REF] Sun | Analytical solutions for mutiple species reactive transport in multiple dimensions[END_REF][START_REF] Van Genuchten | Analytical solutions for chemical transport with simultaneous adsorption, zero-order production and first-order decay[END_REF]. Unfortunately, analytical solutions are only available for simplified systems, such as the reactive transport of a single solute in 1-D homogeneous systems at steady state, which is well behind the actual capabilities of the models. To remediate to this, inter-comparison of numerical codes has been largely employed. This intercomparison involves the independent solution of the same problem using a variety of numerical techniques [START_REF] Carrayrou | Comparison of numerical methods for simulating strongly nonlinear and heterogeneous reactive transport problems-the MoMas benchmark case[END_REF][START_REF] De Dieuleveult | Aglobal approach to reactive transport, application to the MoMas benchmark[END_REF][START_REF] Gérard | Numerical validation of an Eulerian hydrochemical code using a 1-D multisolute mass transport system involving heterogeneous kinetically-controlled reactions[END_REF][START_REF] Mayer | Solution of the MoMas reactive transport benchmark with MIN3P-model formulation and simulation results[END_REF][START_REF] Cochepin | Approaches to modelling coupled flow and reaction in a 2D cementation experiment[END_REF].

This study aims at comparing the accuracy of a reactive transport model with other kinds of models such as the mathematical model of the chemostat. This confrontation takes place in the framework of microbial ecology, for which concepts of competition and coexistence are crucial [START_REF] Aris | Dynamics of a chemostat in which two organisms compete for a common substrate[END_REF][START_REF] Butler | A mathematical model of the chemostat with a general class of functions describing nutrient uptake[END_REF][START_REF] El Hajji | Practical coexistence of two species in the chemostat-A slow-fast characterization[END_REF][START_REF] Rapaport | Coexistence in the design of a series of two chemostats[END_REF][START_REF] Stephanopoulos | A stochastic analysis of the growth of competing microbial populations in a continuous biochemical reactor[END_REF][START_REF] Stephanopoulos | Effect of inhomogeneities on the coexistence of competing microbial populations[END_REF]. We have chosen the reactive transport code MIN3P [START_REF] Mayer | Multicomponent reactive transport modeling in variably saturated porous media using a generalised formulation for kinetically controlled reactions[END_REF] for this study. This reactive transport model is notably recognized for its numerical robustness [START_REF] Carrayrou | Comparison of numerical methods for simulating strongly nonlinear and heterogeneous reactive transport problems-the MoMas benchmark case[END_REF][START_REF] Mayer | Solution of the MoMas reactive transport benchmark with MIN3P-model formulation and simulation results[END_REF]. In addition, the model MIN3P can simulate general reactive transport problems in variably saturated media for 1D to 3D systems. The flow solution is based on Richard's equation [START_REF] Neuman | Saturated-Unsaturated seepage by finite elements[END_REF], and solute transport is simulated by means of the advection-dispersion equation. Gas transport can be taken into account as well, either by considering advection and Fick diffusion or the Dusty Gas Model [START_REF] Molins | Coupling between geochemical reactions and multicomponent gas diffusion and advection-a reactive transport modelling study[END_REF][START_REF] Molins | Transport and reaction processes affecting the attenuation of landfill gas in cover soils[END_REF]. A range of bio-geochemical processes are included in MIN3P (aqueous speciation, mineral dissolution-precipitation, gas dissolution/exsolution, ion exchange, and competitive or non competitive sorption). A generalized kinetic expression for dissolution-precipitation and intra-aqueous reactions allows the consideration of fractional order or Monod-type rate expressions, and parallel reaction pathways. This code has been used for a number of applications in different fields of environmental science, ranging from inorganic and organic contaminant transport and groundwater remediation [START_REF] Masue-Slowey | Transport Implications Resulting from Internal Redistribution of Arsenic and Iron within Constructed Soil Aggregates[END_REF][START_REF] Mayer | Reactive transport modeling of processes controlling the distribution and natural attenuation of phenolic compounds in a deep sandstone aquifer[END_REF][START_REF] Mayer | Process-based reactive transport modelling of a permeable reactive barrier for the treatment of mine drainage[END_REF][START_REF] Molins | Vadose zone attenuation of organic compounds at a crude oil spill site -Interactions between biogeochemical reactions and multicomponent gas transport[END_REF] to soil hydrology and bio-geochemical cycles in terrestrial ecosystems [START_REF] Gérard | Preferential flow revealed by hydrologic modeling based on predicted hydraulic properties[END_REF][START_REF] Gérard | Modelling the biogeochemical cycle of silicon in soils: application to a temperate forest ecosystem[END_REF][START_REF] Maier | Calibration of hydraulic parameters for large-scale vertical flow constructed wetlands[END_REF].

The chemostat model is the simplest mathematical model for describing the dynamics of microbial growth under a constant flow of substrate, and its theory is well understood [START_REF] Steefel | Reactive transport modeling: An essential tool and a new research approach for the Earth sciences[END_REF]. In this work, we consider a series of interconnected chemostats for the simulation a one-dimensional heterogeneity, that we compare with the solutions provided by reactive transport models considering the same spatial structure.

Material and method

In practice, a chemostat in laboratory is an apparatus that consists of three connected vessels as shown in Fig. 1. The leftmost vessel is called the feed bottle and contains all of the nutrients needed for the growth of a microorganism. The central vessel is called the culture vessel, while the last is the overflow or collection vessel. The content of the feed bottle is pumped at a constant rate into the culture vessel, while the content of the culture vessel is pumped at the same constant rate into the collection vessel. We denote by S in [mol/l] the constant concentration of nutrient pumped with a volumetric flow rate that we denote by Q[l.s -1 ]. The dilution rate [s -1 ] is defined as D = Q/V, where V is the volume of the culture vessel. We shall also denote by µ(.)[s -1 ] the specific growth rate of micro-organisms and k the yield factor of the bio-conversion. The dynamical model of the chemostat can then been written in the following way.

       dS dt = - µ(S) k B + D(S in -S) dB dt = (µ(S) -D)B (1)
Because of the boundary conditions (i.e. input of nutrients in the culture vessel and output of contents from the culture vessel), numerical implementations of reactive transport models such as MIN3P are not able to simulate straightforwardly a single ecosystem such as the one in the culture vessel. Indeed, the use of the logarithm of the concentrations in the numerical code prevents to having a null concentration of biomass at the input of the culture vessel. In order to simulate an ecosystem in a single tank, one has to consider three control volumes. Moreover, for intrinsic reasons, three control volumes is the minimum number for a one dimensional discretization in numerical implementations of reactive transport models, such as the MIN3P code that we have chosen to simulate our ecosystem. In this way, the numerical implementation is closer from the true laboratory experiment with three vessels, that we described above. Nevertheless, we shall refer in the following to the chemostat for the culture vessel only. 0000000 1111111

P P N C O Figure 1: A schematic view of the chemostat experiment
With MIN3P we began by simulating a simple example of three chemostats in series having the same volume, in presence of a single biomass B and a single substrate S with the same initial conditions in the three control volumes. The dynamical model representing n chemostats connected in series is given by the equations:

       dS i dt = - µ(S i ) k B i + D i (S i-1 -S i ) dB i dt = (µ(S i ) -D i )B i + D i B i-1 ,
where D i = Q/V i , S i (respB i ) represents the substrate concentration (resp biomass concentration) in the ith bioreactor (i = 1, , n). S 0 = S in and B 0 = 0 and V i = V n . We consider that the qualitative behavior of this system of ordinary differential equations (ODE) is today well understood (see the Appendix), and we used different robust numerical schemes for solving this system of ODE (Runge-Kutta, LSODA ...) that were all thoroughly consistent with the analytic analysis of the steady states and their stability. That amounts to assume that we can trust the numerical solutions obtained by the numerical integration of ODEs for this model.

For the simulation of the chemostat model with reactive transport models, we consider a boundary domain in three dimensions. The boundary conditions for the liquid flow are of first type with a value of 0 in the output face, and of second type specifying a flux of Q[l.s -1 ] in the input and output faces. A specific choice of flow condition gave us a fully water saturated medium at any time . The boundary conditions for the reactive part are of second type in the output face and of third type in the input face with a value of the substrate concentration equal to S in .

To simulate several chemostats connected in series without diffusion, we have chosen the free diffusion coefficient in water and air, as well as the specific storage coefficient equal to zero. The porosity of the Finally, we have introduced a simple theoretical irreversible reaction expressing the bio-conversion of moles of substrate into one mole of biomass. The specific growth rate of biomass considered here is of Monod's type:

S out Q S in Q Third C.V.
µ(S) = µ max S k s + S ,
where µ max [s -1 ] represents the maximum of the intra-aqueous kinetic reaction and k s [mol/l] the half saturation constant.

In a second stage, we consider the same spatial considerations but with two species instead of one, assuming that each species has a growth function that follows a Monod law, as described above. We assume that their interaction is due only to a common limiting resource, that is the species compete for the same substrate. We focus on the case of a "true" competition, in the sense that we assume that a species is the most efficient one when the resource is very rare, while the other species is better when the resource is less rare.

Results and discussion

Denote by S * M (resp. S * C ) the value of the substrate concentration computed by MIN3P (resp. by the chemostat model) at the steady state, and by B * M the value of the biomass concentration at steady state given by MIN3P. Let δ be the absolute value of the difference between S * M and S * C , that serves as an indicator of divergence between simulations of both models.

For the comparison of the two models, we first represent the indicator δ as a function of Q. For the study of the effect of a spatial discretization, we shall then consider δ as a function of the number of cells.

For convenience, we shall omit the units of the numerical values that we give below (concentrations are assumed to be measured in mol.l -1 , volumes in l, flux in l.s -1 and growth rates in s -1 .

The single species case

Choosing µ max = 4.10 -5 , we have studied the variation of δ with respect to Q in the first and third control volumes. Each volume has been chosen equal to 1. On the graphs of δ that correspond to the first (resp. third) control volume (see Figure 3, Output (resp. Input)), we notice that for 10 -6 ≤ Q ≤ 10 -5 , one faces a significant difference between simulations of both models in the input control volume, and that is even greater in the output control volume. But for 10 -5 ≤ Q ≤ 15.10 -6 , one has almost no difference in the input control volume, and one can observe a jump of δ about Q = 10 -5 in the output control volume. For the simulations, we have chosen S in = 3, k s = 1, B(0) = 2 and S(0) = 5.

We know from the theory of the chemostat (see Appendix, Proposition 4.4), that for a "perfectly mixed" tank, with a single species growing on a single limiting substrate, the condition µ(Sin) D > 1 ensures that the biomass B is not wash-out. This result is surprisingly not observed in simulations with MIN3P. To show that, we studied the variation of the biomass concentration B with respect to Q in the input control volume. We notice that the biomass is washed out for Q ≥ 8.10 -6 (see Figure 3,B * M in dashed line). But when 8.10 -6 ≤ Q < 10 -5 , we have µ(Sin) D1 = 10 -5 Q > 1, and one can observe on the graph of δ and the difference between MIN3P and the chemostat simulations in the input control volume.

For the case of three chemostats connected in series with the same volume and traversed by the same flow rate Q, the removal of the biomass in the input control volume has to lead theoretically to its removal in the output control volume. But this is not the case with MIN3P and we can notice on Fig. 3 (Output), that for 8.10 -6 ≤ Q ≤ 15.10 -6 , we obtain the wash-out of biomass in the input control volume, the biomass in the output control volume being not yet washed out. In other words, under certain conditions, the microbial growths predicted by both simulations are radically different. For the study of the effect of a spatial discretization on the difference between numerical reactive transport and chemostat models at steady state, we took the same conditions as before, with a maximal kinetic rate equal to µ max = 5.10 -4 and a flow Q = 10 -5 . We did vary the number of discretization steps between n = 3 and n = 50 and studied the variation of δ with respect to n (the total number of cells) in the input and output control volumes. Denote by D n the dilution rate in each control volume for a discretization in n cells. On the graphs of δ that corresponds to the input (resp. output) control volume (see Fig. 4, Input (resp. Output)), we notice for 3 ≤ n ≤ 37 (that theoretically corresponds to the survival of biomass, because one has µ(Sin) Dn = 75 2n > 1) that we have the same behavior of δ as before. Similarly, for 39 ≤ n ≤ 50 (values that correspond to µ(Sin) Dn < 1), we have no difference between MIN3P and the chemostat model in the input and output control volumes. But for n = 38, we observe the same jump of δ in the output control volume as previously observed.

We have observed on this example a significant difference between reactive transport and chemostat models when passing from a steady state of survival of the biomass to the wash out steady state. this corresponds to a bifurcation passing from two equilibriums (wash-out and biomass survival) to a single equilibrium (wash-out). The limiting case corresponds to a non-hyperbolic equilibrium (see the Appendix for the definition of hyperbolic equilibriums). Because of the use of the logarithm in the MIN3P code, we expect the internal solution to take very large values when the concentration of biomass tends to zero. One can also detect this phenomenon on the simulations when noticing a "time lag" between MIN3P and chemostat trajectories about the steady state.

The two species case

To emphasize the problem that occurs about non-hyperbolic equilibrium in the case of one species, we present in this part a more subtle situation, considering two species that compete for the same substrate.

The extension of the model ( 1) is given by the following equations:

                 dS dt = - µ 1 (S) k 1 B 1 - µ 2 (S) k 2 B 2 + D(S in -S) dB 1 dt = (µ 1 (S) -D)B 1 dB 2 dt = (µ 2 (S) -D)B 2 (2)
where functions µ 1 (.) and µ 2 (.) denote the kinetics of species B 1 and B 2 respectively. For this system, the Proposition 4.5 given in the Appendix shows that non-hyperbolic equilibrium points could exists away from the wash-out equilibrium. For the one species case, a non-hyperbolic equilibrium could exists but on the boundary of the positive domain only. For the two species case, many non-hyperbolic equilibriums could exists on the interior of the positive domain.

Let λ i be the positive solution, when it exists, of µ i (S) = D for i = 1, 2. Under the condition S in ≥ max(λ 1 , λ 2 ), the system (2) admits generically three equilibrium points, given by E 0 (S in , 0, 0), E 1 (λ 1 , k 1 (S inλ 1 ), 0) and E 2 (λ 2 , 0, k 2 (S in -λ 2 )). We distinguish now two different cases. If for some i = 1, 2 one has λ i = S in , then the equilibrium E 0 is non-hyperbolic as before (see Proposition 4.4 in the Appendix). Moreover if one has λ 1 = λ 2 < S in , then E 1 = E 2 is also a non hyperbolic equilibrium (Proposition 4.5 in the Appendix). Starting from our observations in the case of one species, we have built suitable examples to study the behavior of MIN3P about those non-hyperbolic equilibriums.

To understand the comparison, we first recall that the mathematical theory of the model (2) predicts the competitive exclusion in the generic case, that is at most one competitor avoids the extinction (see the Appendix). This property refers to the well-known Competitive Exclusion Principle in ecology, that has been widely studied in the literature (see for instance [START_REF] Aris | Dynamics of a chemostat in which two organisms compete for a common substrate[END_REF][START_REF] Butler | A mathematical model of the chemostat with a general class of functions describing nutrient uptake[END_REF][START_REF] El Hajji | Practical coexistence of two species in the chemostat-A slow-fast characterization[END_REF][START_REF] Stephanopoulos | A stochastic analysis of the growth of competing microbial populations in a continuous biochemical reactor[END_REF]). For the chemostat model, the Principle can be stated as follows.

Considering two increasing growth rates µ 1 (.) and µ 2 (.) such that both λ 1 and λ 2 are smaller than S in (for a sufficiently large S in ). Then, one has the following issue of the competition for large times -when λ 1 < λ 2 , the species B 1 avoids the extinction, -when λ 1 > λ 2 , the species B 2 avoids the extinction.

For the non generic case λ 1 = λ 2 , it is possible to predict the coexistence of the two species, invalidating the Principle (on this single chemostat case).

In the simulations, we have considered two species B 1 and B 2 with a specific growth rate given by µ 1 (S) = 1.10 -3 S 5 + S and µ 2 (S) = 3.10 -3 S 30 + S .

One can notice on Fig. 5 (left) that the graphs of these two functions intersect away from zero. This implies that depending on the dilution rate D, the corresponding value of λ 1 can be less or greater than λ 2 .

The input concentration S in has been chosen equal to 20 and the initial state vector has been kept equal to (S(0), B 1 (0), B 2 (0)) = [START_REF] Clement | RT3D-A modular computer code for simulating reactive multi-species transport in 3-dimensional groundwater aquifers[END_REF][START_REF] Butler | A mathematical model of the chemostat with a general class of functions describing nutrient uptake[END_REF][START_REF] Carrayrou | Comparison of numerical methods for simulating strongly nonlinear and heterogeneous reactive transport problems-the MoMas benchmark case[END_REF]. A simple calculation shows that for Q = 2.10 -4 , one has λ 1 = λ 2 = 15 2 < S in . Then for this choice of µ 1 , µ 2 and Q the dynamical system (2) admits positive non-hyperbolic equilibriums. We aim to study the numerical evolution of the species concentrations about those equilibriums in both models, depending on the choice of the flow Q. For this purpose, we have plotted the graphs of the species concentrations at steady state given by MIN3P and the chemostat model in the input control volume (see Fig. 5, right), denoting by B * M,i (resp. B * C,i ) for species i = 1, 2. We observe that for Q ≤ 10 -5 , both simulations present almost the same solutions. When Q increases a difference between the models begins to appear until we detect a wrong prediction of the species that avoids the extinction. This happens for 15.10 -5 ≤ Q ≤ 4.10 -4 . For Q ≥ 4.10 -4 , both simulations show again almost the same solutions. So we have observed another significant difference between simulations of reactive transport and chemostat models about a bifurcation point, where the species that avoid extinction switches. To study the effect of a spatial discretization in the case of two species, we have chosen a specific example of twenty perfectly-mixed tanks that are interconnected in series. The volumes V i (i = 1, ..., 20), the input concentration S in , the flux Q and the specific growth rates µ 1 (.) and µ 2 (.) are chosen as follows, in such a way that the species B 1 passes from the wash-out state (in V 1 , V 2 and V 3 ) to a coexistence state (in Under MIN3P we have discretized the domain into twenty control volumes, and have compared the solutions of both models in each control volume at steady state.

V i , i = 4, ..., 20). V 1 = 10.10 -2 V 2 = 9.10 -2 V 3 = 1.10 -2 V 4 = 11.10 -2 V 5 = 9.10 -2 V 6 = • • • = V 20 = 4.
On Figure 6 (right), one can observe that the substrate concentrations computed at steady state with both models are almost identical in the first control volumes, up to the third one where the solutions are different, and become radically divergent in further control volumes. Here, the solution computed by MIN3P does not predict the coexistence of two species... Let us underline that the species coexistence is no longer a pathological case when chemostats of different volumes are connected in series (see for instance [START_REF] Stephanopoulos | Effect of inhomogeneities on the coexistence of competing microbial populations[END_REF][START_REF] Rapaport | Coexistence in the design of a series of two chemostats[END_REF]).

To summarize, we have shown that under certain circumstances the issue of the winner of the competition between the two species are predicted radically different by the simulations of both models.

Conclusion

Our results show a possible inaccuracy of numerical reactive transport models in the simulation of the dynamics of simple ecosystem of chemostat type. Our objective was not to challenge the model MIN3P for its ability to simulate complex problems involving mass flow and multicomponents reaction networks, but we raise the fact that the numerical accuracy of the model MIN3P depended on the evolution of microbial species. When the hydrodynamic conditions make the system close to a washing-out of one or several microbial species, or to the coexistence of species, we observe numerical bias in the computation of the solution that leads to radically different predictions. Consequently one may wonder if the numerical issue found here in simple systems (a single substrate and one or two microbial species, advective transport) prevails in more complex systems, when a network of kinetically-controlled reactions is considered to simulate for instance remediation problems in ground-waters. We believe that a study of the eigenvalues of the linearized dynamics about steady states is important, for detecting possible numerical inaccuracy. Thus E 0 is unstable. At E 1 , the eigenvalues are v 1 (E 1 ) = -D < 0, v 2 (E 1 ) = -µ 1 (λ 1 ) k 1 k 1 (S in -λ 1 ) < 0, v 3 (E 1 ) = µ 2 (λ 1 ) -D , and symmetrically for E 2 :

v 1 (E 2 ) = -D < 0, v 2 (E 2 ) = - µ 2 (λ 2 ) k 2 k 2 (S in -λ 2 ) < 0, v 3 (E 2 ) = µ 1 (λ 2 ) -D .
One can notice that λ i < λ j ⇔ v 3 (E i) < 0 and conclude that when λ i < λ j , E i is locally exponentially stable and E j is unstable.

For the particular case of λ 1 = λ 2 we find that v 3 (E 1 ) = v 3 (E 2 ) = 0. Therefore in this case E 1 (that coincides with E 2 ) is a non-hyperbolic equilibrium point.

Figure 2 :

 2 Figure 2: Configuration of three control volumes

Figure 3 :

 3 Figure 3: Comparison for three control volumes

Figure 4 :

 4 Figure 4: Comparison with several control volumes

B M, 1 B M, 2 B C, 1 BFigure 5 :

 1215 Figure 5: Two species in competition in a single chemostat

10

 10

- 2 µ 1 5 S

 215 (S) = 4.629.10 -5 S 6 + S µ 2 (S) = 6.944.10 -5 S 18 + S Q = 0.3587.10 -in = 19.25

1 B C, 2 NFigure 6 :

 126 Figure 6: Two species in competition in a series of chemostats

Appendix

For the study of the behavior of autonomous dynamical systems in R n , dX dt = F (X),

with F ∈ C 1 (R n ), one usually determine first its equilibrium points (denoted X ) as solutions of f (X) = 0, and then study the eigenvalues of the linear dynamics dX dt = J(X )X, called the linearization of (3) about X , where J(X ) is the Jacobian matrix of F at X . If all the eigenvalues v i (i = 1, ...n ) of J(X ) have nonzero real parts, then we said that X is hyperbolic. When at least one of its eigenvalues has a zero real part, then we said that X is non-hyperbolic (see for instance the reference [START_REF] Perko | Differential Equations and Dynamical Systems[END_REF]).

We recall now the usual definitions of stability and a main result allowing to conclude about the nature of an equilibrium (see the reference [START_REF] Perko | Differential Equations and Dynamical Systems[END_REF] for more details). Definition 4.1 The equilibrium X is said to be stable if for every > 0 there exists δ > 0 such that

If this condition its not satisfied, the equilibrium is unstable. Definition 4.2 The equilibrium X is said to be (locally) exponentially stable if for every > 0 there exists three real numbers a > 0, b > 0 and δ > 0 such that

• If all the eigenvalues of J(X ) have negative real parts then the equilibrium point X is exponentially stable.

• If one of the eigenvalues of J(X ) has a positive real part then the equilibrium point X is unstable.

Remark. If the Jacobian matrix J(X ) has at least one eigenvalue with zero real part, then we need to use other results to conclude about the behavior of the trajectory of the system (3).

For the chemostat model ( 1), one has the following result. • If D < µ(S in ), the system (1) admits two equilibrium points given by E 1 (S in , 0), which is unstable and E 2 (λ, k(S in -λ)), which is locally exponentially stable.

• If D ≥ µ(S in ), the only non-negative equilibrium point it is E 1 which is locally exponentially stable, excepted for the case D = µ(S in ) for which it is non-hyperbolic.

Proof. We can easily verify that for any t ≥ 0, the trajectories of (1) remains in the first positive orthant, and are bounded: one can straightforwardly write

from which one deduces that t → B(t) + kS(t) is bounded that the trajectories of the system are bounded.

Determining the equilibrium points of the system (1) amounts to solve the following system

The wash-out equilibrium point E 1 (S in , 0) is always solution, and there is a possibility of another equilibrium point E 2 (S , k(S in -S )) with S = λ, when S < S in . To study the stability of these equilibrium points, we write the Jacobian matrix of the system (1):

At E 1 , one has v 2 (E 1 ) = µ(S in ) -D and at the non-trivial equilibrium E 2 (when it exists), one has v 2 (E 2 ) = -µ (S ) k B < 0. So, when µ(S in ) < D, we conclude that the non-trivial equilibrium does not exist and we obtain that E 1 is locally exponentially stable. When µ(S in ) > D, E 1 is unstable and E 2 is locally exponentially stable. For the particular case µ(S in ) = D, the non-trivial equilibrium does not exist and E 1 is a non-hyperbolic equilibrium.

For the chemostat model [START_REF] Butler | A mathematical model of the chemostat with a general class of functions describing nutrient uptake[END_REF] with two species, one has the following result.

Proposition 4.5 Denote by λ i the solution (when it exists) of µ i (λ i ) = D. Under the condition that S in > max(λ 1 , λ 2 ), the system (2) admits three equilibrium points given by E 0 (S in , 0, 0),

). Furthermore, one has

• when λ i < λ j , E i is locally exponentially stable and E 0 and E j are both unstable.

• when λ 1 = λ 2 then E 1 = E 2 is a non-hyperbolic equilibrium point.

Proof. As before, the equilibrium points are given by the following system

One can find that there exist at most three equilibrium points E 0 (S in , 0, 0), E 1 (λ 1 , k 1 (S in -λ 1 ), 0) and

For the study of their stability, we write for convenience the dynamics in variables (Z, B 1 , B 2 ) with

In these coordinates, the Jacobian matrix takes the following form:

.

At E 0 , we can check that J(E 0 ) admits three eigenvalues:


Fei Li

Andrew D Patterson
email: andrewpatterson@mail.nih.gov

Constance C Höfer
email: c.hoefer@dmpkore.com

Kristopher W Krausz
email: krauszk@intra.nci.nih.gov

Frank J Gonzalez

Jeffrey R Idle
email: idlejr@mail.nih.gov.

Comparative Metabolism of Cyclophosphamide and Ifosfamide in the Mouse Using UPLC-ESI-QTOFMS-Based Metabolomics

Keywords: Ifosfamide, Cyclophosphamide, Metabolomics, Ultra-performance liquid chromatography, Time-of-flight mass spectrometry, Tandem mass spectrometry

Ifosfamide (IF) and cyclophosphamide (CP) are common chemotherapeutic agents. Interestingly, while the two drugs are isomers, only IF treatment is known to cause nephrotoxicity and neurotoxicity. Therefore, it was anticipated that a comparison of IF and CP drug metabolites in the mouse would reveal reasons for this selective toxicity. Drug metabolites were profiled by ultra-performance liquid chromatography-linked electrospray ionization quadrupole time-of-flight mass spectrometry (UPLC-ESI-QTOFMS), and the results analyzed by multivariate data analysis. Of the total 23 drug metabolites identified by UPLC-ESI-QTOFMS for both IF and CP, five were found to be novel. Ifosfamide preferentially underwent N-dechloroethylation, the pathway yielding 2-chloroacetaldehyde, while cyclophosphamide preferentially underwent ring-opening, the pathway yielding acrolein (AC). Additionally, S-carboxymethylcysteine and thiodiglycolic acid, two downstream IF and CP metabolites, were produced similarly in both IF-and CP-treated mice.

This may suggest that other metabolites, perhaps precursors of thiodiglycolic acid, may be responsible for IF encephalopathy and nephropathy.

Cyclophosphamide (CP) and ifosfamide (IF) are isomeric oxazaphosphorine cytostatic drugs used widely in the chemotherapy of various cancers. CP was developed over 50 years ago as a innovative example of a pro-drug that might be transported to the tumor and then activated by tumor-specific enzymes, a strategy that had proven valuable for the treatment of prostate carcinoma with stilbestrol diphosphate [START_REF] Druckrey | Specific chemotherapy of carcinoma of the prostate[END_REF]. High tumor expression and activity of phosphoramidase was the rational design principle [START_REF] Arnold | Chemotherapeutic action of a cyclic nitrogen mustard phosphamide ester (B 518-ASTA) in experimental tumours of the rat[END_REF] that lead to the incorporation of the highly cytotoxic nornitrogen mustard (NNM) into a stable and apparently inert oxazaphosphorine ring (Fig. 1A). It soon transpired that NNM was generated only in trace amounts but rather CP was converted in the liver into a transported metabolite that could be readily taken up by tumors [START_REF] Brock | Metabolism of cyclophosphamide[END_REF]. A somewhat complex hepatic metabolic scheme gradually unfolded with CP converted to 4-hydroxycyclophosphamide (4OHCP) [START_REF] Sladek | Evidence for an aldehyde possessing alkylating activity as the primary metabolite of cyclophosphamide[END_REF], which in turn taumomerized to aldophosphamide (AP) [START_REF] Hill | Enzymatic metabolism of cyclophosphamide and nicotine and production of a toxic cyclophosphamide metabolite[END_REF] that β-eliminated AC [START_REF] Alarcon | Formation of the cytotoxic aldehyde acrolein during In vitro degradation of cyclophosphamide[END_REF][START_REF] Connors | Some studies of the active intermediates formed in the microsomal metabolism of cyclophosphamide and isophosphamide[END_REF] to yield phosphoramide mustard (PM) [START_REF] Connors | Some studies of the active intermediates formed in the microsomal metabolism of cyclophosphamide and isophosphamide[END_REF][START_REF] Colvin | A biologically active metabolite of cyclophosphamide[END_REF]. This pathway can readily be reconciled with other observed metabolites of CP, such as 4-oxocyclophosphamide (4-ketocyclophosphamide; 4OCP) [START_REF] Struck | Urinary metabolites of the antitumor agent cyclophosphamide[END_REF], iminocyclophosphamide (ICP) [START_REF] Fenselau | Iminocyclophosphamide as a chemically reactive metabolite of cyclophosphamide[END_REF], and carboxyphosphamide (CXP) [START_REF] Struck | Isolation and mass spectral identification of blood metabolites of cyclophosphamide: evidence for phosphoramide mustard as the biologically active metabolite[END_REF] (Fig. 1A). Both AP [START_REF] Connors | Some studies of the active intermediates formed in the microsomal metabolism of cyclophosphamide and isophosphamide[END_REF] and PM [START_REF] Struck | Isolation and mass spectral identification of blood metabolites of cyclophosphamide: evidence for phosphoramide mustard as the biologically active metabolite[END_REF] were postulated as transport forms of CP. Ifosfamide (IF) was developed a decade after CP [START_REF] Brock | New nitrogen mustard phosphamide esters and their cytostatic activity[END_REF] and its metabolic transformation was reported to bear similarities to its isomer CP (Fig. 1B). Specifically, phenobarbital-induced rat liver microsomes converted IF to AC [START_REF] Connors | Some studies of the active intermediates formed in the microsomal metabolism of cyclophosphamide and isophosphamide[END_REF][START_REF] Alarcon | Isophosphamide as a new acrolein-producing antineoplastic isomer of cyclophosphamide[END_REF] after the prior formation of 4-hydroxyifosfamide (4OHIF) [START_REF] Connors | Some studies of the active intermediates formed in the microsomal metabolism of cyclophosphamide and isophosphamide[END_REF], which was later reported to be in equilibrium with its tautomer aldoifosfamide (AIF) [14]. However, a major metabolic pathway for IF was side-chain dealkylation to yield A c c e p t e d M a n u s c r i p t 4 2-and 3-dechloroethylifosfamide (2-DCIF and 3-DCIF), both in vitro [START_REF] Connors | Some studies of the active intermediates formed in the microsomal metabolism of cyclophosphamide and isophosphamide[END_REF] and in vivo [START_REF] Norpoth | Studies on the metabolism of isophosphamide (NSC-109724) in man[END_REF], together with 2-chloroacetaldehyde (CAL) [START_REF] Goren | Dechloroethylation of ifosfamide and neurotoxicity[END_REF] and 2-chloroethylamine (CEA) [17][START_REF] Norpoth | Side chain oxidation of ifosfamide in man[END_REF].

These two-carbon metabolites had been reported at only low levels in CP-treated rodents [START_REF] Struck | Isolation and mass spectral identification of blood metabolites of cyclophosphamide: evidence for phosphoramide mustard as the biologically active metabolite[END_REF][START_REF] Shaw | 2-Chloroacetaldehyde: a metabolite of cyclophosphamide in the rat[END_REF][START_REF] Shaw | 2-Chloroacetaldehyde, a metabolite of cyclophosphamide in the rat[END_REF]. Later reports demonstrated side-chain dealkylation yielding 2-DCIF and 3-DCIF as a major pathway of IF metabolism in both pediatric [START_REF] Boddy | Pharmacokinetics and metabolism of ifosfamide administered as a continuous infusion in children[END_REF][START_REF] Boddy | Comparison of continuous infusion and bolus administration of ifosfamide in children[END_REF][START_REF] Boddy | Intrasubject variation in children of ifosfamide pharmacokinetics and metabolism during repeated administration[END_REF] and adult patients [START_REF] Boddy | The kinetics of the auto-induction of ifosfamide metabolism during continuous infusion[END_REF][25][START_REF] Martino | A new approach to the study of ifosfamide metabolism by the analysis of human body fluids with 31P nuclear magnetic resonance spectroscopy[END_REF]. While the systemic toxicity of the aldehyde product of CP and IF metabolism AC had been mitigated by the introduction of mesna [START_REF] Brock | Detoxification of urotoxic oxazaphosphorines by sulfhydryl compounds[END_REF][START_REF] Brock | Acrolein, the causative factor of urotoxic side-effects of cyclophosphamide, ifosfamide, trofosfamide and sufosfamide[END_REF], the issue of host toxicity due to CAL was not immediately addressed [START_REF] Goren | Dechloroethylation of ifosfamide and neurotoxicity[END_REF].

The differential metabolism of CP and IF most likely plays a central role in the differing toxicity profiles of these isomeric drugs. While the general pattern of intact oxazaphosphorine metabolites is similar for CP and IF, a key difference is the number and abundance of two-carbon metabolites that derive from side-chain dealkylation. It was proposed that CAL underlies both the neurotoxicity [START_REF] Goren | Dechloroethylation of ifosfamide and neurotoxicity[END_REF][START_REF] Aeschlimann | Inhibition of (mono)amine oxidase activity and prevention of ifosfamide encephalopathy by methylene blue[END_REF][START_REF] Kupfer | Methylene blue and the neurotoxic mechanisms of ifosfamide encephalopathy[END_REF] and nephrotoxicity [START_REF] Dubourg | Human kidney tubules detoxify chloroacetaldehyde, a presumed nephrotoxic metabolite of ifosfamide[END_REF] of IF.

Additionally, CEA was proposed as a toxic metabolite [START_REF] Aeschlimann | Inhibition of (mono)amine oxidase activity and prevention of ifosfamide encephalopathy by methylene blue[END_REF][START_REF] Kupfer | Methylene blue and the neurotoxic mechanisms of ifosfamide encephalopathy[END_REF] and has been reported to derive directly from IF by chemical hydrolysis and also reacting with bicarbonate to form 1,3-oxazolidin-2-one [17]. CAL has been reported to be converted to 2-chloroacetic acid (CAA) by human kidney [START_REF] Dubourg | Human kidney tubules detoxify chloroacetaldehyde, a presumed nephrotoxic metabolite of ifosfamide[END_REF] and rabbit heart [START_REF] Loqueviel | A 13C NMR study of 2-(13)Cchloroacetaldehyde, a metabolite of ifosfamide and cyclophosphamide, in the isolated perfused rabbit heart model. Initial observations on its cardiotoxicity and cardiac metabolism[END_REF]. In turn, CAA may react with cellular thiols to yield S-carboxymethylcysteine (SCMC) and its metabolite thiodiglycolic acid (TDGA) [START_REF] Norpoth | Studies on the metabolism of isophosphamide (NSC-109724) in man[END_REF] (Fig. 1B). Other cysteine derived metabolites have also been observed [START_REF] Loqueviel | A 13C NMR study of 2-(13)Cchloroacetaldehyde, a metabolite of ifosfamide and cyclophosphamide, in the isolated perfused rabbit heart model. Initial observations on its cardiotoxicity and cardiac metabolism[END_REF].

What role this panoply of small IF metabolites plays in the selective toxicity and efficacy of IF is poorly understood.

A c c e p t e d M a n u s c r i p t

What is clear is that CP and IF are two potent drugs which are inactive per se and whose effects on both the tumor and the host are determined by metabolism. Despite the large number of published studies on the metabolism of CP and IF both in vitro and in vivo and in a variety of species including Man (Table 1), a comprehensive comparative analysis of their metabolism is indicated. We have chosen to do this in the mouse for the sole reason that such a study lends itself to further investigation in animals humanized for various metabolic enzymes and the nuclear receptors that regulate their tissue expression [START_REF] Cheung | Humanized mouse lines and their application for prediction of human drug metabolism and toxicological risk assessment[END_REF]. We have also employed ultra-performance chromatography-linked electrospray ionization quadrupole timeof-flight mass spectrometry (UPLC-ESI-QTOFMS), which has proven successful in studies involving metabolomic protocols to uncover unforeseen drug metabolites of PhIP [START_REF] Chen | A comprehensive investigation of 2-amino-1-methyl-6-phenylimidazo[4,5-b]pyridine (PhIP) metabolism in the mouse using a multivariate data analysis approach[END_REF], melatonin [START_REF] Ma | A metabolomic perspective of melatonin metabolism in the mouse[END_REF], aminoflavone [START_REF] Chen | Urinary metabolite profiling reveals CYP1A2-mediated metabolism of NSC686288 (aminoflavone)[END_REF], acetaminophen [START_REF] Chen | Identification of novel toxicity-associated metabolites by metabolomics and mass isotopomer analysis of acetaminophen metabolism in wild-type and Cyp2e1-null mice[END_REF], and the areca alkaloids [START_REF] Giri | A metabolomic approach to the metabolism of the areca nut alkaloids arecoline and arecaidine in the mouse[END_REF][START_REF] Giri | The metabolomics of (+/-)-arecoline 1oxide in the mouse and its formation by human flavin-containing monooxygenases[END_REF].

A c c e p t e d M a n u s c r i p t 6

Materials and Methods

Materials

IF (ifosfamide), CP (cyclophosphamide), SCMC (S-carboxymethylcysteine), TDGA (thiodiglycolic acid), and 4-nitrobenzoic acid were purchased from Sigma-Aldrich (St. Louis, MO). Solvents and other chemicals were of the highest grade commercially available.

Animals and treatments

Male C57BL/6 mice were obtained from the NCI-Frederick Animal Production Program.

Mice were maintained under standard 12 h light/12 h dark cycle with water and chow provided ad libitum. Handling and treatment was in accordance with an animal study protocol approved by the National Cancer Institute Animal Care and Use Committee. IF (50 mg/kg) and CP (50 mg/kg) were dissolved in saline solution and administered by intraperitoneal injection. Control mice were treated with saline alone. Urine (24 h) samples were collected from mice housed individually in glass metabolic chambers (Jencons, Leighton Buzzard, UK).

UPLC-ESI-QTOFMS profiling of urinary metabolites

Urine samples were prepared by mixing 10 μl of urine with 90 μl of 50% aqueous acetonitrile and centrifuging at 18,000  g for 10 min to remove protein and particulates. A 5 μl aliquot of supernatant was injected into a Waters UPLC-ESI-QTOFMS system (Milford, MA). An Acquity UPLC BEH C18 column (Waters) was used to separate chemical components, including IF, CP and their metabolites. The mobile phase was comprised of A c c e p t e d M a n u s c r i p t 7 0.1% formic acid (A) and acetonitrile containing 0.1% formic acid (B). A 0.5 ml/min flow rate was maintained during a 10 min run. The QTOF Premier mass spectrometer was operated in electrospray positive ionization mode (ESI+). Capillary voltage and cone voltage were maintained at 3 kV and 20 V, respectively. Source temperature and desolvation temperature were set at 120 °C and 350 °C, respectively. Nitrogen was used as both cone gas (50 l/h) and desolvation gas (600 l/h), and argon was used as collision gas. Sulfadimethoxine was used as the lock mass (m/z 311.0814 + ) for accurate mass calibration in real time. As for MS/MS fragmentation of target ions, collision energy ranging from 10 to 40 eV was applied.

Mass chromatograms and mass spectral data were acquired using MassLynx software (Waters) in centroid format. IF, CP and their urinary metabolites were identified through accurate mass measurement and the analysis of the MS/MS fragmentation patterns. Since IF and CP each have two chlorines, IF and CP metabolites could be identified and distinguished from endogenous metabolites based on the chlorine isotope ratio. For example, metabolites containing a single chlorine would be expected to exhibit a chlorine isotope ratio of 3:1.

Metabolites containing two chlorines would be expected to have a chlorine isotope ratio of 9:6:1.

Data processing and multivariate data analysis (MDA)

The mass chromatographic data were deconvoluted using MarkerLynx software (Waters), and a data matrix was generated for MDA. The ion intensity was calculated as the percentage of total ion counts (TIC) in the whole chromatogram. The data matrix was exported into SIMCA-P software (Umetrics, Kinnelon, NJ) for MDA. In order to separate drug metabolites A c c e p t e d M a n u s c r i p t from endogenous metabolites in urine, the integrated ions in vehicle group and treatment group were analyzed using an orthogonal projection to latent structures (OPLS) model. OPLS analysis was conducted to represent the major latent variables in the data matrix and was described in a scores scatter plot after data were Pareto scaled. Identification of IF, CP and their metabolites was performed by analyzing the loadings plot and contribution table, as previously described [START_REF] Chen | A comprehensive investigation of 2-amino-1-methyl-6-phenylimidazo[4,5-b]pyridine (PhIP) metabolism in the mouse using a multivariate data analysis approach[END_REF][START_REF] Ma | A metabolomic perspective of melatonin metabolism in the mouse[END_REF][START_REF] Chen | Urinary metabolite profiling reveals CYP1A2-mediated metabolism of NSC686288 (aminoflavone)[END_REF][START_REF] Chen | Identification of novel toxicity-associated metabolites by metabolomics and mass isotopomer analysis of acetaminophen metabolism in wild-type and Cyp2e1-null mice[END_REF][START_REF] Giri | A metabolomic approach to the metabolism of the areca nut alkaloids arecoline and arecaidine in the mouse[END_REF][START_REF] Giri | The metabolomics of (+/-)-arecoline 1oxide in the mouse and its formation by human flavin-containing monooxygenases[END_REF]. The general protocol for the identification of xenobiotic metabolites using metabolomics has recently been reviewed [START_REF] Patterson | Xenobiotic metabolism: A view through the metabolometer[END_REF].

Tandem LC-MS quantitation of SCMC and TDGA

Samples from IF-or CP-treated mice were prepared by mixing 20 μl of urine with 80 μl of 50% aqueous acetonitrile and centrifuging at 18,000  g for 10 min. 10 μl was injected for LC-MS/MS analysis. LC-MS/MS analysis was performed on an Applied Biosystems API 2000 ESI triple quadrupole mass spectrometer (Applied Biosystems, Foster City, CA). A Luna 3-μm C18 50 mm  46 mm internal diameter column (Phenomenex, Torrance, CA) was used to separate SCMC, TDGA, and 4-nitrobenzoic acid (internal standard). The flow rate was 0.2 ml/min with 95% aqueous acetonitrile containing 0.1% formic acid. The mass spectrometer was operated in negative ion (ESI-) mode. The turbo ion spray temperature was maintained at 350 °C, and a voltage of 5 kV was applied to the sprayer needle. Nitrogen was used as the turbo ionspray and nebulizing gas. The detection and quantitation of SCMC, TDGA and 4-nitrobenzoic acid (internal standard) were accomplished by multiple reaction monitoring with the transitions m/z 178.0/77.9 (SCMC), 149.0/92.7 (TDGA) and 165.9/109.6 (

4-nitrobenzoic acid).

A c c e p t e d M a n u s c r i p t 9

Relative quantitation of the metabolites of IF and CP

Although the authentic standards of metabolites were unavailable, it was possible to determine their approximate abundance in the urine. Using several assumptions [START_REF] Giri | A metabolomic approach to the metabolism of the areca nut alkaloids arecoline and arecaidine in the mouse[END_REF][START_REF] Giri | The metabolomics of (+/-)-arecoline 1oxide in the mouse and its formation by human flavin-containing monooxygenases[END_REF],

including that the metabolites were equivalently eluted and ionized (ESI+) over the entire chromatographic range, with equivalent degrees of ion suppression, it was possible to approximate the relative excretion of IF, CP, and their metabolites in the urine. These assumptions have been validated in a metabolomics study of the metabolism of (±)-arecoline 1-oxide in the mouse [START_REF] Giri | The metabolomics of (+/-)-arecoline 1oxide in the mouse and its formation by human flavin-containing monooxygenases[END_REF]. However, it is accepted that such estimates of relative concentration may be error-prone.

Statistical analysis

Experimental values are expressed as mean ± standard deviation (S.D.). Statistical analysis was performed using independent Student's t tests or ANOVA. P-values less than 0.05 were considered significant.

Metabolomic analysis of mouse urine after IF and CP administration

After urine samples from the treated and control groups were analyzed by UPLC-ESI-QTOFMS, data were deconvoluted, and analyzed using OPLS. The advantage of OPLS is that the model is rotated so that class (treated and control) separation is found in the first predictive component, tp, also referred to as the correlated variation [START_REF] Wiklund | Visualization of GC/TOF-MS-based metabolomics data for identification of biochemically interesting compounds using OPLS class models[END_REF]. This multivariate model was built to determine the relationship between the treated and control groups, and the contribution of each detected urinary ion to the model. As shown in the scores scatter plot (Fig. 2A-B), urine samples from IF and CP treatment were clearly separated from the control in the first component (t [START_REF] Druckrey | Specific chemotherapy of carcinoma of the prostate[END_REF]), driven predominantly by the presence of drug and drug-related metabolites (Fig. 2C-D). The trend plots of ions from putative drug-related metabolites were used to display graphically the absence of those ions in vehicle-treated animals (Fig. 3A-E).

The increased ions were further determined as drug-related or endogenous metabolites based on the mass defect shifts [START_REF] Zhang | Mass defect filter technique and its applications to drug metabolite identification by high-resolution mass spectrometry[END_REF]. In general, the mass defects of phase I and II drug metabolites were over the range of -50 mDa and +50 mDa compared with the parent drug. After drug metabolites were determined, their chemical structures could be elucidated through MS/MS.

Identification and structural elucidation of the urinary metabolites of IF and CP

After the metabolites were screened using OPLS and accurate mass measurement, their chemical structures were identified on the basis of the MS/MS fragmentation. Overall, IF (F1), CP (P1) and their 23 metabolites were identified in the urine samples from mice (Tables 2 and3). Eighteen of them (F2, F3, F4, F6, F7, F8, F9, F10, F12, F13, P2, P3, P4, P5, P6, P7,

Estimation of relative concentrations of IF and CP metabolites by chromatographic analysis

Based on their exact masses, peaks were extracted from the UPLC chromatograms, and areas integrated (Tables 2 and3). The metabolites of IF and CP were grouped by metabolic transformation,as follows: dechloroethylation, hydroxylation, ketonization, dehydroxylation, A c c e p t e d M a n u s c r i p t 14 alkylation, ring-opening, and conjugation reactions (Table 4). As shown in Fig. 5, the excretion of the unchanged IF in mouse urine was similar to the excretion of CP. The dechloroethylated metabolites of IF were present in higher concentrations than CP (2-fold).

The ring-opened and ketonization metabolites of CP were present at higher concentrations than IF (5-fold and 3-fold, respectively). In addition, although the hydroxylated, dehydroxylated, alkylated, and conjugated metabolites were different between IF and CP, their relative abundance in the urine was very low following treatment with either IF or CP.

Urinary excretion of SCMC and TDGA

After the treatment of mice with either IF or CP, SCMC (F12) and TDGA (F13) excretion was increased above endogenous levels. Because of their low molecular weight and weak acidity, SCMC and TDGA could be detected in negative ion mode of using UPLC-ESI-QTOF-MS. However, their concentration was determined by triple quadrupole mass spectrometry. From Fig. 6A, it can be seen that SCMC excretion was increased 32-fold and 44-fold in urine above endogenous levels, respectively, after treatment with IF and CP.

TDGA excretion was also increased in urine by 14-fold and 17-fold following IF and CP treatment, respectively. Therefore, both isomeric drugs show surprisingly similar profiles with respect to these metabolites.

A c c e p t e d M a n u s c r i p t

Discussion

Metabolomics is an invaluable tool for profiling biological fluids for small molecules, and with respect to pharmacology, metabolomics has provided substantial insight into drug metabolism pathways. For example, the metabolic map of acetaminophen (which had been studied for over 40 years) was recently expanded by three metabolites [START_REF] Chen | Identification of novel toxicity-associated metabolites by metabolomics and mass isotopomer analysis of acetaminophen metabolism in wild-type and Cyp2e1-null mice[END_REF]. Similarly, the metabolic maps of IF and CP were expanded (two IF and three CP new metabolites) and 18 known metabolites that otherwise had taken over 40 years to identify (Table 1) are also reported here. This demonstrates the power of UPLC-ESI-QTOFMS-based metabolomics applied to the study of drug metabolism.

IF and CP are prodrugs that are converted to their active forms during metabolic biotransformation [START_REF] Zhang | Metabolism and transport of oxazaphosphorines and the clinical implications[END_REF]. Their biological activity is mediated through their active metabolites, including 4-hydroxyifosfamide and 4-hydroxycyclophosphamide, both of which were detected in this study. Because of their respective equilibrium with aldoifosfamide and aldophosphamide, a minor amount of 4-hydroxyifosfamide and 4-hydroxyclophosphamide were excreted in the urine. Aldoifosfamide was both reduced and oxidized to alcoifosfamide and carboxyifosfamide, respectively, presumably by the action of alcohol dehydrogenase and aldehyde dehydrogenase [START_REF] Martino | A new approach to the study of ifosfamide metabolism by the analysis of human body fluids with 31P nuclear magnetic resonance spectroscopy[END_REF]. In a similar manner, aldophosphamide was both reduced and oxidized to alcophosphamide and carboxyphosphamide, respectively [START_REF] Joqueviel | Urinary excretion of cyclophosphamide in humans, determined by phosphorus-31 nuclear magnetic resonance spectroscopy[END_REF]. It can be seen from Fig. 5 that ring-opened metabolites were produced to a greater extent from CP than from IF, and this was the major difference between the two drugs. However, in compensation, the dechloroethylated metabolites of IF were excreted to a greater extent than from CP. SCMC and TDGA, both normal products of endogenous metabolism, were found at A c c e p t e d M a n u s c r i p t low concentrations in control urine. Following treatment with IF and CP, SCMC and TDGA were significantly elevated in vivo (Fig. 6). It is known that CAA can lead to the formation of SCMC through conjugation with cysteine or glutathione, and SCMC is further transformed to TDGA [START_REF] Steventon | Diurnal variation in the metabolism of S-carboxymethyl-L-cysteine in humans[END_REF]. SCMC has been reported to activate the α-amino-3-hydroxy-5-methyl-4isoxazolepropionic acid (AMPA)/kainite receptor and induce cellular acidification which may be responsible for the reported encephalopathy [START_REF] Chatton | Insights into the mechanisms of ifosfamide encephalopathy: drug metabolites have agonistic effects on alpha-amino-3hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA)/kainate receptors and induce cellular acidification in mouse cortical neurons[END_REF][START_REF] Lerch | Cerebral formation in situ of Scarboxymethylcysteine after ifosfamide administration to mice: a further clue to the mechanism of ifosfamide encephalopathy[END_REF]. In addition, TDGA can cause mitochondrial dysfunction which may also contribute to the side-effects associated with IF treatment [START_REF] Visarius | Thiodiglycolic acid is excreted by humans receiving ifosfamide and inhibits mitochondrial function in rats[END_REF]. However, there have been no reports that SCMC and TDGA resulting from the treatment by CP lead to toxicity. Here, SCMC and TDGA were detected in urine from the CP-treated mice. The generation of CAA from IF was greater than from CP, according to the significantly higher rate of N-dechloroethylation of IF (Fig. 5) Surprisingly therefore, there were no significant differences in SCMC and TDGA production in IF-and CP-treated mice (Fig. 6B andD). However, it was previously reported that TDGA is the major urinary metabolite in cancer patients treated with IF and this was suggested as the causative IF metabolite of encephalopathy [START_REF] Visarius | Thiodiglycolic acid is excreted by humans receiving ifosfamide and inhibits mitochondrial function in rats[END_REF]. Apparently, TDGA is an inconsequential urinary metabolite of CP (A. Küpfer, unpublished observation). However, TDGA was determined in these human studies by lyophilization and derivatization of urines with BF 3 /methanol at 60 ºC, in contrast to the studies described here where diluted urines were injected directly into the tandem mass spectrometer. It is therefore possible that TDGA is formed during the heating process, either by spontaneous decarboxylation of the α-keto acid of SCMC (Scarboxymethyl-3-thiopyruvic acid; SCMTPA) [START_REF] Chatton | Insights into the mechanisms of ifosfamide encephalopathy: drug metabolites have agonistic effects on alpha-amino-3hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA)/kainate receptors and induce cellular acidification in mouse cortical neurons[END_REF][START_REF] Lerch | Cerebral formation in situ of Scarboxymethylcysteine after ifosfamide administration to mice: a further clue to the mechanism of ifosfamide encephalopathy[END_REF] or from an acid-or heat-labile ester, such as the carnitine ester of TDGA.

A c c e p t e d M a n u s c r i p t

Previous studies suggested that IF treatment resulted in changes in the excretion patterns of low molecular weight endogenous metabolites (hippuric acid, trimethylamine N-oxide, glycine, lactate, histidine and glucose), which were regarded as biomarkers of IF nephrotoxicity and encephalopathy [START_REF] Foxall | Urinary proton magnetic resonance studies of early ifosfamide-induced nephrotoxicity and encephalopathy[END_REF]. The current findings suggest that IF-induced sideeffects may result directly from CAA rather than from SCMC and TDGA. Studies have reported that CAA can result in neurotoxicity and nephrotoxicity [START_REF] Springate | Ifosfamide metabolite chloroacetaldehyde causes renal dysfunction in vivo[END_REF][START_REF] Woodland | Evidence of renal metabolism of ifosfamide to nephrotoxic metabolites[END_REF]. This observation may offer one potential mechanism to explain IF-related neurotoxicity and nephrotoxicity.

Despite the large number of published in vitro and in vivo CP and IFO metabolism studies, five novel metabolites (F5, F11, P9, P11 and P12) were found by metabolomic analysis in this study. Iminoifosfamide from IF corresponded to iminocyclophosphamide (F6) from CP. Previous studies reported some conjugated metabolites with GSH from IF and CP, such as ifosforamide mustard and cyclophosphamide [14,52]. However, there was no GSH conjugation detected in either urine and serum. Here, two minor glucuronide conjugate metabolites (F11 and P9) were found from IF-and CP-treated mice. Furthermore, two new Ndechloroethylated (P11 and P12) metabolites from CP were found in the urine (Fig. 8).

Inspection of the loadings S-plot in Fig. 2D suggests that P11 has a similar abundance to the principal N-dechloroethylated metabolite P3, while P12 is a much more minor metabolite.

The metabolomic studies described here were carried out in the mouse. As shown in Table 1, rat and human have been the principal species studied historically for CP and IF metabolism. There are relatively few data in the mouse. Nevertheless, the value of the mouse is that future studies may be conducted in genetically modified mice, that permit direct questions to be asked about the role of discrete enzymes and the nuclear receptors that control their expression in the liver and other tissues [START_REF] Cheung | Humanized mouse lines and their application for prediction of human drug metabolism and toxicological risk assessment[END_REF]. It may be envisaged that data from mice humanized for CP and IF metabolizing enzyme genes could be compared with actual clinical data for these drugs, thus refining and improving animal modeling of caner chemotherapy.

In conclusion, the present study investigated IF and CP in mice using a metabolomic approach, which gave a comprehensive understanding of their metabolism in vivo. Twenty three urinary metabolites, including five novel drug metabolites, were identified and structurally elucidated by mass fragmentography. Their metabolic pathways in vivo were presented. Although they went through similar metabolic processes, the amount of metabolites in urine was significantly different between IF and CP, in particular, the Ndechloroethylated and ring-opened metabolites. SCMC and TDGA, that have been regarded as the toxic metabolites, specifically of IF [START_REF] Chatton | Insights into the mechanisms of ifosfamide encephalopathy: drug metabolites have agonistic effects on alpha-amino-3hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA)/kainate receptors and induce cellular acidification in mouse cortical neurons[END_REF][START_REF] Lerch | Cerebral formation in situ of Scarboxymethylcysteine after ifosfamide administration to mice: a further clue to the mechanism of ifosfamide encephalopathy[END_REF][START_REF] Visarius | Thiodiglycolic acid is excreted by humans receiving ifosfamide and inhibits mitochondrial function in rats[END_REF], were also found in similar amounts in the A c c e p t e d M a n u s c r i p t

  A c c e p t e d M a n u s c r i p t P8 and P10) are known metabolites, and five of them (F5, F11, P9, P11 and P12) were novel metabolites. MS/MS spectra of the five novel metabolites (F5, F11, P9, P11 and P12) are presented in Fig. 4. The empirical formula of F5 (iminoifosfamide), a new metabolite of IF, was calculated as C 7 H 13 Cl 2 N 2 O 2 P (0.4 ppm mass error) based on the accurate mass measurement, m/z 259.0171 + . Compared with the chemical composition of IF (C 7 H 15 Cl 2 N 2 O 2 P), it was concluded that F5 was a dehydrogenated form of IF. As seen from Fig. 4A, its molecular ion peak showed three chlorine isotope peaks m/z 259.012 + , 261.012 + and 263.138 + with the ratio of ion intensity 9:6:1, showing that F5 contained two chlorines. Tandem mass spectrometry (MS/MS) revealed four major fragment ions at m/z 230.986 + , 182.013 + , 153.982 + (base peak), 118.042 + . The fragment ion at m/z 182.013 + was generated by the cleavage of the exo P-N bond to eliminate one chloroethylamine. The ion at m/z 118.042 + was formed by the elimination of another chloroethyl group. It suggested that the double bond occurred in the oxazaphosphorine ring. The parent ions produced the peak at m/z 230.986 + through the loss of ethylene at the C5-C6 bond of the oxazaphosphorine ring. The base peak at m/z 153.982 + occurred from the ion at m/z 182.013 + by the same cleavage pattern. It was more stable for the double bond between the C4 and C5 than that between the C3 and C4, which was consistent with the base peak. Therefore, F5 was identified as iminoifosfamide. F11 (4-hydroxyifosfamide glucuronide), a new metabolite of IF, was calculated as C 13 H 23 Cl 2 N 2 O 9 P (2.6 ppm mass error) based on the accurate mass measurement, m/z 453.0584 + . As seen from Fig. 4B, its molecular ion peak showed three chlorine isotope peaks m/z 453.056, 455.060 + and 457.069 + with the ratio of ion intensity 9:6:1, indicating that F11 A c c e p t e d M a n u s c r i p t contained two chlorines. It was clear that the base peak at m/z 277.028 + was produced from its [M+H] + ion (m/z 453.056 + ) by the loss of 176 Da. It was concluded that F11 was the glucuronide conjugate of an hydroxylated metabolite of IF. MS/MS revealed major fragment ions at m/z 232.996 + , 136.018 + , and 92.023 + . The fragment pattern was similar to the metabolite 4-hydroxyifosfamide (F10). Therefore, F11 was identified as 4-hydroxyifosfamide glucuronide. P9 (alcophosphamide glucuronide), a new metabolite of CP, was calculated as C 13 H 25 Cl 2 N 2 O 9 P (2.6 ppm mass error) based on the accurate mass measurement, m/z 455.0765 + . As seen from Fig.4E, its molecular ion showed three chlorine isotope peaks m/z 455.074 + , 457.076 + and 459.069 + with the ratio of ion intensity 9:6:1, demonstrating that P9 contained two chlorines. In its MS/MS spectrum, the base peak at m/z 279.043 + was generated from its [M+H] + ion (m/z 455.074 + ) by the elimination of 176 Da. It was concluded that P9 was the glucuronide conjugate. MS/MS revealed its major fragments at m/z 262.017 + , 221.000 + , and 138.032 + , which was similar to fragments of the metabolite alcophosphamide (P5). Therefore, P9 was identified as alcophosphamide glucuronide. P11 (dechloroethylketocyclophosphamide), a novel metabolite of CP, was calculated as C 5 H 10 ClN 2 O 3 P (0.9 ppm mass error) based on the accurate mass measurement, m/z 213.0198 + . Compared with the [M+H] + ion (m/z 275.010 + ) of 4-ketocyclophosphamide, P11 was lower by 62 Da than 4-ketocyclophosphamide. N-dechloroethylation was the common pattern in the metabolism of CP through the loss of 62 Da. It was concluded, therefore, that P11 was generated from alcophosphamide through the elimination of the chloroethyl group. As seen from Fig. 4C, its molecular ion peak showed two chlorine isotope peaks m/z A c c e p t e d M a n u s c r i p t 13 213.019 + and 215.025 + with the ratio of ion intensity 3:1, showing that P11 contained one chlorine. MS/MS revealed its major fragments at m/z 159.011 + , 141.983 + and 112.077 + , which was similar to the major fragments of 4-ketocyclophosphamide. Therefore, P11 was identified as dechloroethylketocyclophosphamide. P12 (dechloroethylalcophosphamide), a novel metabolite of CP, was calculated as C 5 H 14 ClN 2 O 3 P (0.9 ppm mass error) based on the accurate mass measurement, m/z 217.0511 + . The [M+H] + ion of P12 was lower by 62 Da than that of alcophosphamide (m/z 279.0437 + ). Compared with the metabolite P11, P12 was supposed to be the Ndechloroethylated product of alcophosphamide. As seen in Fig. 4D, its molecular ion showed two chlorine isotope peaks, m/z 217.052 + and 219.054 + with the ratio of ion intensity 3:1, demonstrating that P12 contained only one chlorine. MS/MS revealed its major fragments at m/z 200.022 + , 159.008 + , and 138.031 + . The base peaks at m/z 159.008 + was produced by the cleavage of the -CH 2 CH 2 OH group at the C-O bond. The fragment at m/z 200.022 + was generated from the loss of the hydroxyl group. The fragment at m/z 138.031 + was produced from the hydroxylation and chloroethylation of P12. The cleavage pattern was similar to the alcophosphamide. Therefore, P12 was identified as dechloroethylalcophosphamide.

  urine of IF-and CP-treated mice. Future studies are needed to examine the potential of CAA, SCMTPA or TDGA carnitine ester to be the causative factors in IF-associated neuro-and nephrotoxicity.

Figure Legends:Fig. 1 .

 1 Figure Legends:

Fig. 2 .

 2 Fig. 2. Identification of urinary IF and CP metabolites through LC-MS-based metabolomics.

Fig. 3 .

 3 Fig. 3. Trend plots of ions from novel metabolites in the treatment groups. (A) Novel IF

Fig. 4 .

 4 Fig. 4. Tandem MS and chemical structures of novel CP and IF metabolites. (A)

A c c e p t e d M a n u s c r i p tFig. 5 .

 5 Fig. 5. Relative quantitation of urinary metabolites from different groups of metabolic

Fig. 6 .

 6 Fig. 6. The amount (μmol/24h) and % dose excreted for SCMC and TDGA in 0-24 h mouse

Fig. 7 .

 7 Fig. 7. Major in vivo IF metabolic pathways showing the enzyme systems that are believed to

Fig. 8 .

 8 Fig. 8. Major in vivo CP metabolic pathways showing the enzyme systems that are believed

A c c e p t e d M a n u s c r i p t

A c c e p t e d M a n u s c r i p t

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Table 1

 1 Reported metabolites of IF and CP in vivo and in vitro.

	Year	Drug	Metabolite	Species	Reference
		CP	Nornitrogen mustard	Rat (iv)	[3]
			2-Chloroethylaziridine
			(decomposition products of unknown
			primary metabolite)
		CP	Hydracrylic acid	PB-induced rats (ip)	[53]
		CP	Carboxycyclophosphamide	Dog (iv), Human (iv)	[9]
			4-Oxocyclophosphamide
		CP	Acrolein	Liver microsomes	[9]
		IF	Acrolein	PB-induced rat liver	[13]
				microsomes
		CP	Aldophosphamide	Uninduced mouse liver	[5]
				microsomes
		CP	4-Hydroxycyclophosphamide	PB-induced rat liver	[4]
			[tautomer of aldophosphamide]	microsomes
		CP	Phosphoramide mustard	PB-induced mouse liver	[8]
				microsomes
		IF	2-Dechloroethylifosfamide	PB-induced rat liver	[7]
			3-Dechloroethylifosfamide	microsomes
			4-Hydroxyifosfamide
		IF	2-Chloroethylamine	Rat (iv), Human (iv)	[54]
		CP	3-(2-Chloroethyl)oxazolidone	Human (iv)	[55]
			(from nornitrogen mustard + CO 2 )
			1,4-Di(2-chloroethyl)piperazine
		CP	4-Oxocyclophosphamide	Mice (ip)	[11]
			Alcophosphamide
			2-Dechloroethylcyclophosphamide
			Carboxyphosphamide
			Phosphoramide mustard
			Nornitrogen mustard
		CP	3-Hydroxypropylmercapturic acid	Rat	[56]
		IF	[metabolite of acrolein]
		IF	Carboxyifosfamide (1.4%)	Human (iv)	[15]
			2-Dechloroethylifosfamide (6.2%)
			3-Dechloroethylifosfamide (12.5%)
			S-Carboxymethylcysteine (10.4%)
			Thiodiglycolic acid (4.7%)
		CP	4-Hydroxycyclophosphamide	Rat (ip), Mouse (ip)	[57]
			Aldophosphamide
			Phosphoramide mustard
			4-Oxocyclophosphamide
		CP	Phosphoramide mustard	Human (iv)	[58]
			Nornitrogen mustard (?artifact)
		CP	Iminocyclophosphamide	Immobilized rabbit liver P450	[10]
		CP	2-Chloroacetaldehyde	Rat (iv)	[20]
		CP	3-(2-chloroethyl)-l,3-oxazolidin-2-one	Rat (iv)	[59]
			3-(2-chloroethyl)-4-hydroxy-1,3-
			oxazolidin-2-one
			3-(2-hydroxyethyl)-l,3-oxazolidin-2-one
		IF	2-Chloroacetaldehyde	Human (iv)	[16]
		CP	4-Oxocyclophosphamide	Human (iv)	[60-61]
			Carboxyphosphamide

Table 1 (

 1 Continued)

	Year	Drug	Metabolite	Species	Reference
	1992	CP	Dechloroethylcyclophosphamide
			4-Oxocyclophosphamide
			Carboxyphosphamide
			Phosphoramide mustard

Table 2

 2 IF metabolites ions identified in the LC-MS-based metabolomic analysis of urine samples from IF-treated mice.

	Symbol	Rt (min)	m/z ( ESI+)	Formula	Mass Error (ppm)	Identity	Peak area (Mean ± SD)
	F1	4.36	261.0322	C 7 H 15 Cl 2 N 2 O 2 P	-1.5	Ifosfamide	836.0 ± 357.0
	F2	2.42	199.0405	C 5 H 12 ClN 2 O 2 P	1.0	2-Dechloroethylifosfamide	529.0 ± 272.5
	F3	2.14	199.0403	C 5 H 12 ClN 2 O 2 P	0.0	3-Dechloroethylifosfamide	472.2 ± 238.7
	F4	3.33	293.0221	C 7 H 15 Cl 2 N 2 O 4 P	-1.4	Carboxylifosfamide	370.8 ± 107.9
	F5	3.20	259.0171	C 7 H 13 Cl 2 N 2 O 2 P	0.4	Iminoifosfamide	113.4 ± 43.9
	F6	3.51	279.0377	C 7 H 17 Cl 2 N 2 O 3 P	-19.7	Alcoifosfamide	92.6 ± 53.4
	F7	3.32	275.0170	C 7 H 13 Cl 2 N 2 O 3 P	18.5	4-Ketoifosfamide	74.6 ± 18.4
	F8	3.16	277.0272	C 7 H 15 Cl 2 N 2 O 3 P	-1.4	Aldoifosfamide	11.2 ± 2.2
	F9	1.69	221.0014	C 4 H 11 Cl 2 N 2 O 2 P	0.5	Ifosforamide mustard	17.4 ± 8.2
	F10	2.78	277.0270	C 7 H 15 Cl 2 N 2 O 3 P	-2.2	4-Hydroxyifosfamide	37.4 ± 12.3
	F11	3.47	453.0584	C 13 H

23 Cl 2 N 2 O 9 P -2.

Table 3

 3 CP metabolite ions identified in the LC-MS-based metabolomic analysis of urine samples from CP-treated mice.

	Symbol	Rt (min)	m/z ( ESI+)	Formula	Mass Error (ppm)	Identity	Peak area (Mean ± SD)
	P1	4.53	261.0333	C 7 H 15 Cl 2 N 2 O 2 P	2.7	Cyclophosphamide	1047.2 ± 311.5
	P2	3.57	293.0227	C 7 H 15 Cl 2 N 2 O 4 P	0.7	Carboxyphosphamide	2105.4 ± 416.9
	P3	2.42	199.0405	C 5 H 12 ClN 2 O 2 P	1.0	Dechloroethylcyclophosphamide	333.6 ± 68.3
	P4	3.81	277.0267	C 7 H 15 Cl 2 N 2 O 3 P	-3.2	Aldophosphamide	7.6 ± 3.2
	P5	3.73	279.0437	C 7 H 17 Cl 2 N 2 O 3 P	1.8	Alcophosphamide	251.8 ± 27.8
	P6	3.20	259.0171	C 7 H 13 Cl 2 N 2 O 2 P	0.4	Iminocyclophosphamide	31.8 ± 7.7
	P7	3.32	221.0019	C 4 H 11 Cl 2 N 2 O 2 P	2.7	Phosphamide mustard	7.6 ± 4.4
	P8	3.01	277.0279	C 7 H 15 Cl 2 N 2 O 3 P	1.1	4-Hydroxycyclophosphamide	7.6 ± 2.4
	P9	3.19	455.0781	C 13 H 25 Cl 2 N 2 O 9 P	2.6	Alcophosphamide glucuronide	5.8 ± 1.5
	P10	3.58	275.0100	C 7 H 13 Cl 2 N 2 O 3 P	-6.9	4-Ketocyclophosphamide	455.8 ± 69.3
	P11	1.83	213.0198	C 5 H 10 ClN 2 O 3 P	0.9	Dechloroethylketocyclophosphamide	117.2 ± 24.3
	P12	1.86	217.0511	C 5 H 14 ClN 2 O 3 P	0.9	Dechloroethylalcophosphamide	23.2 ± 3.8

Acknowledgements

This work was supported in part by the Intramural Research Program of the Center for Cancer Research, National Cancer Institute, National Institutes of Health. JRI is grateful to the U.S. Smokeless Tobacco Company for a grant for collaborative research. The authors thank Professor Adrian Küpfer, University of Bern, for helpful discussions.


Mhammed Touinssi

Martine Reynaud-Gaubert

Carine Gomez

Pascal Thomas

Bertrand Dussol

Yvon Berland

Agnes Basire

Christophe Picard

Jean François Cantaloube

Philippe De Micco

Philippe François De Micco

Dr Philippe ; Biagini
email: philippe.biagini@efs.sante.fr

Parvovirus 4 in French in-patients: a study of haemodialysis and lung transplant cohorts

Keywords: PARV4, Parvoviridae, hemodialysis, lung transplant, epidemiology haemodialysis, lung transplant, epidemiology, 46 genetic diversity

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

samples (n=289) were tested for PARV4 by real-time PCR assay (ORF2), and 32 amplification products selected at random were sequenced. Analysis of available 33 serological and biological markers was also undertaken. Fifty-seven samples out of 34 185 (30.8%) were positive for PARV4 DNA in the cohort of haemodialysis patients. A 35 higher prevalence of the virus was identified in patients with markers of HBV 36 infection. PARV4 was also identified in 14 out of 104 samples (13.5%) from lung 37 transplant recipients, with no clear-cut association with available clinical markers. 38

Point mutations located on the zone of real-time detection were identified for some 39 amplification products. This study describes the detection of PARV4 in the blood of 40 haemodialysis and lung transplanted patients with significant difference in prevalence 41 in these two cohorts. Further studies will be needed in order to understand better 42 both the potential implication in host health and the natural history of this virus. showing two large non-overlapping ORFs [START_REF] Simmonds | A third genotype of the human parvovirus PARV4 in sub-Saharan Africa[END_REF]. First studies 55 revealed that the virus was present in the blood from intravenous drug users and 56 individuals positive for HCV or HIV at prevalence ranging from 6% to 30%, and in 57 cohorts of kidney transplant patients as well [START_REF] Biagini | Human parvovirus 4 246 in kidney transplant patients, France[END_REF][START_REF] Fryer | Novel parvovirus and 254 related variant in human plasma[END_REF]58 Fryer et al., 2007;[START_REF] Lurcharchaiwong | Parvovirus 4 (PARV4) in serum of intravenous drug users 267 and blood donors[END_REF][START_REF] Vallerini | Parvoviruses in blood donors and transplant patients, Italy[END_REF]. PARV4 had 59 been also identified in individuals without apparent pathology like blood donors (1%-60 24%), and in blood products negative for parvovirus B19 DNA [START_REF] Fryer | 256 Frequent detection of the parvoviruses, PARV4 and PARV5, in plasma from 257 blood donors and symptomatic individuals[END_REF]61 Lurcharchaiwong et al., 2008;[START_REF] Touinssi | Detection of human bocavirus in respiratory, fecal, and blood samples by 284 real-time PCR[END_REF][START_REF] Vallerini | Parvoviruses in blood donors and transplant patients, Italy[END_REF]. Genetic 62 diversity of the virus is poorly known, but was extended recently to highly divergent 63 animal variants identified in domestic (cow, pig) and wild (baboon, chimpanzee) 64 species [START_REF] Adlhoch | High prevalence of porcine 2005. Cloning of a human parvovirus by molecular screening of respiratory tract 241 samples[END_REF][START_REF] Lau | Identification of novel porcine and bovine parvoviruses 264 closely related to human parvovirus 4[END_REF][START_REF] Sharp | Widespread 274 infection of chimpanzees and gorillas with homologues of human parvoviruses 275 B19, PARV4 and human bocavirus in the wild[END_REF]. Interestingly, 65 these studies demonstrated high prevalence values (up to 40%) for these PARV4-66 related animal viruses. 67

Another member of Parvoviridae family identified recently, human Bocavirus (HBoV) 68 [Allander et al., 2005], had been more investigated and is suspected to be associated 69 with wheezing and respiratory disease, mainly in young children [START_REF] Brown | The expanding range of parvoviruses which infect humans[END_REF]. 70 Despite these advances, the natural history and the clinical role of these new viruses, 71 and more particularly that of PARV4, remain unknown to a large extent. 72 prior to DNA extraction. Total nucleic acids were extracted from 1 ml of plasma by 98 using the MagNA Pure LC instrument (Roche Diagnostics, Meylan, France), as 99 described previously [START_REF] Biagini | Human parvovirus 4 246 in kidney transplant patients, France[END_REF][START_REF] Touinssi | Detection of human bocavirus in respiratory, fecal, and blood samples by 284 real-time PCR[END_REF]. 100 101

PARV4 PCR assay 102

Samples were screened for the presence of PARV4 DNA by real-time PCR 103 (StepOne Plus, Applied Biosystems, Courtaboeuf, France) using a TaqMan detection 104 system located on the ORF2 of the viral genome. Primers used were PARV4Fwd (5'-105 CTAAGGAAACTGTTGGTGATATTGCT-3') and PARV4Rev

(5'-106 GGCTCTCCTGCGGAATAAGC-3'), in combination with fluorogenic probe PARV4-N 107

(5'-FAM-TCCTACYGCCCSCTCCTCCTTCTT-TAMRA-3') [START_REF] Touinssi | Detection of human bocavirus in respiratory, fecal, and blood samples by 284 real-time PCR[END_REF]. 108 Amplification reactions were performed using 5 µl of extracted nucleic acids in 109 a 20 µl reaction volume (TaqMan Fast Universal PCR kit, Applied Biosystems) 110 according to manufacturer's instructions. The amplification conditions were 95°C for 111 20 seconds, followed by 50 cycles of 95°C for 1 second and 60°C for 20 seconds. 112

The sensitivity of the TaqMan assay was estimated at 10 copies of PARV4 113 DNA per reaction using dilutions of a synthetic template corresponding to the target 114 sequence (103 nt) [START_REF] Biagini | Human parvovirus 4 246 in kidney transplant patients, France[END_REF][START_REF] Touinssi | Detection of human bocavirus in respiratory, fecal, and blood samples by 284 real-time PCR[END_REF]. TAMRA-3') [Tozer et al., 2009]. 123 Amplification conditions were identical as those adopted for PARV4 detection. 124

The detection limit of the real-time PCR assay was 10 copies of HBoV DNA per 125 reaction [Tozer et al., 2009]

Haemodialysis patients 143

Among the 185 samples tested, 30.8% (n=57) were positive for PARV4 DNA 144 using the real-time approach described. Analysis of serological markers revealed that 145 PARV4 DNA was detectable in 27.3% (6/22) and 38.7% (29/75) of patients positive 146

Genetic variability 175

Positive real-time PARV4 amplification products selected at random (n=15 and 176 n=14 for haemodialysis patients and lung transplant recipients cohorts, respectively) 177 were confirmed by analysis on agarose gel electrophoresis, whereas negative 178 samples did not shown any amplification pattern. Amplification products confirmed 179 their PARV4 origin following cloning and sequencing. Most of them exhibited 100% 180 nucleotide identity with the PARV4 prototype isolate (GenBank accession no. 181 AY622943) in this region, while three samples exhibited a point mutation (Fig. 1). 182

Absence of amplification was confirmed for each of the negative real-time 183

HBoV amplification products analyzed. 10 Such findings would be in accordance with the lower prevalence (13.5%) identified 197 here in the cohort of lung transplanted patients, in which HCV, HBV and HIV markers 198 were hardly absent due to the preliminary selection of patients undergoing lung 199 allograft. However, the fact that this prevalence value was largely lower than that 200 identified in the normal population was unexpected and possibly due to undiscovered 201 aspects of PARV4 infection with respect to the immunosuppressive treatment of 202

patients. 203

HBoV DNA was not identified in the cohort of adult lung transplant recipients. 204

This would confirm its preferential implication in respiratory diseases of young 205 children, even if many aspects of its natural history remain to be clarified [Schildgen 206 et al., 2008].

207

A low titre of PARV4 viral particles (<500 copies/ml) was identified in all 208 positive samples identified in both cohorts. This is an agreement with previous 209 studies relating generally mild PARV4 levels in blood samples, although values 210 reaching up to 10 6 copies/ml were reported as well [START_REF] Fryer | Novel parvovirus and 254 related variant in human plasma[END_REF]Fryer et al., 211 2007;[START_REF] Biagini | Human parvovirus 4 246 in kidney transplant patients, France[END_REF][START_REF] Touinssi | Detection of human bocavirus in respiratory, fecal, and blood samples by 284 real-time PCR[END_REF]. In addition, the presence of 212 serological markers of HCV or HBV did not modify significantly the titre of viral 213 particles of the positive samples in the study. It is conceivable, however, that 214 fluctuations in viraemia would occur according to the immune status of the host, and 215 that additional serial samples tested negative here in the case of lung transplant 216 patients may represent periods of lowest replication of the virus, leading to 217 undetectable levels in blood. 218

It was also shown that point mutations may be identifiable in the short genomic 219 zone dedicated to PARV4 detection. This is in agreement with a recent study 220 demonstrating notable differences in the detection of the virus, even if two slightly 221 This study demonstrates that haemodialysis and lung transplant patients could 227 be infected by PARV4, extending the spectrum of viral infections identifiable in these 228 cohorts [START_REF] Alpers | Emerging paradigms in the renal pathology of viral 243 diseases[END_REF][START_REF] Fischer | Emerging viruses in transplantation: there is more to infection after 252 transplant than CMV and EBV[END_REF]. Many aspects characterizing 229 PARV4 are still largely unknown: both natural history and implication in host health, 230 along with its genetic diversity and real dispersion in human and animal species need 231 to be address in a near future. Interestingly, some aspects of this virus would be 232 close to those identified in another viral family identified thirteen years ago, 233

Anelloviridae [START_REF] Biagini | Classification of TTV and related viruses (anelloviruses)[END_REF], which biology remains largely misunderstood.

  PARV4) is a virus discovered recently belonging to the family 51 Parvoviridae [Jones et al., 2005]. Identified initially in the blood of a patient 52 harbouring acute viral syndrome, this virus had limited sequence homology with 53 parvovirus B19 (<30% aa similarity) despite a conserved genomic organization 54

  Aim of this study consisted in the evaluation of PARV4 DNA prevalence in two 73 different cohorts of haemodialysis patients and lung transplant recipients, combined 74 with the analysis of available serological and biological markers. An additional 75 investigation of HBoV DNA in lung transplant patients was also performed.Two hundred and eighty-nine plasma samples originating from two cohorts of 82 in-patients from south-eastern France were analyzed retrospectively: 83 i) 185 haemodialysis patients (mean age 64 years; sex ratio 1.37 (men:women), 84 mean duration of dialysis 30±28 months) from the Nephrology and Renal Transplant 85 Centre, Conception Hospital (Marseille) (date of sampling: 2007); 86 ii) 104 adult lung transplant recipients (mean age 42 years, sex ratio 0.73) 87 transplanted between October 2005 and August 2008, and followed at the Lung 88 Transplant Centre of the University Hospital of Marseille (date of sampling: from 89 June 2007 to December 2008); blood samples were not available before 90 transplantation. 91 Information relating to the presence of specific antibodies to HCV, HBV, HIV, and 92 HBs antigen in the plasma samples tested was collected. Of the 185 haemodialysis 93 patients, 22 tested positive for HCV, 75 for HBV, 4 for HIV, and 5 for HBsAg. Of the 94 104 lung transplant recipients, only 2 tested positive for a serological marker of HCV. 95 Blood samples were collected in vacuum tubes (Vacutainer, SST, Becton 96 Dickinson, Meylan, France), centrifuged, and plasma aliquots were stored at -80°C 97

  time PCR assay for HBoV DNA located on the non-structural protein 118 (NP-1) gene was further applied to samples belonging to the lung transplant cohort. 119Primers used were STBoNP-1f (5'-AGCATCGCTCCTACAAAAGAAAAG-3') and 120 STBoNP-1r (5'-TCTTCATCACTTGGTCTGAGGTCT-3'), in combination with 121

  HBV, respectively. PARV4 DNA was further identified in 60% (3/5) of 147 patients positive for HBsAg, but not in any of the samples positive for HIV (n=4). The 148 titre of PARV4 DNA in the positive samples was low (<500 copies/ml of plasma). 149No specific correlation was found between PARV4 viraemia and duration of dialysis 150 or other available biological/clinical markers. 151 152Lung transplant patients 153PARV4 DNA was detected in 13.5% plasma samples (14/104), including one 154 of the two patients with HCV positive pretransplant viraemia who received 24 weeks 155 treatment with pegylated interferon alfa plus ribavirin, with a rapid virological 156 response and a negative viraemia before transplantation. A low titre of PARV4 DNA 157 (<500 copies/ml) was also noted. Patients with positive sera for PARV4 DNA were 158 transplanted for cystic fibrosis (n= 8), emphysema (n=1), alpha 1 antitrypsin 159 deficiency (n=1), pulmonary fibrosis (n= 3), sarcoidosis (n=1). 160Dating of positive samples ranged from 1 (day of transplant procedure) to 1097 days 161 after the allograft with a median of 206 days. No other serological marker was 162 identified in the cohort studied. No difference in clinical outcome and survival was 163 noted between recipients positive for PARV4 and those who were negative. 164In order to analyse tentatively the time-course of infection in relation to patients 165 positive for PARV4 DNA, additional serial plasma samples obtained at ±6 months, 166 with respect to the date of initial positive detection, were investigated when available. 167In each case (n=3, on average), attempts to detect PARV4 DNA in these samples 168 remained unsuccessful. 169Real-time PCR approach directed toward HBoV DNA gave no positive signal 170 in any of the samples tested. 171

  time approaches were used[START_REF] Touinssi | Detection of human bocavirus in respiratory, fecal, and blood samples by 284 real-time PCR[END_REF]. It is obvious that 222 detection strategies correlate directly with the progressive estimation of the real 223 genetic diversity of the virus. The fact that new, divergent, human and animal 224 variants were identified recently highlights the need to optimize detection methods 225 consistently. 226

  234

Fig. 1 .

 1 Fig. 1. Alignment of PARV4 partial sequences showing location of point mutations in 292

  Real-time PARV4 and HBoV amplification products (from negative or positive 129 samples, n=15 when available) were chosen at random in both cohorts tested, and 130 analysed by agarose gel electrophoresis. Positive PCR products were excised and 131 purified from agarose (Qiaquick Gel extraction kit, Qiagen, Courtaboeuf, France), 132 cloned into the pGEM-T Easy Vector System (Promega, Charbonnieres les Bains, 133France) and further sequenced on both strands with M13 universal primers (BigDye 134

	126	.
	127
	128	Sequence analysis
	135	Terminator v1.1 Sequencing Kit, Applied Biosystems) on an ABI PRISM 3130XL
	136	genetic analyzer (Applied Biosystem, Courtaboeuf, France).
	137	Sequences were compared with those deposited in the GenBank database
	138	using NCBI's online BLAST2 program (http://blast.ncbi.nlm.nih.gov/Blast.cgi).
	139
	140
	141	RESULTS
	142

Hokovirus in German wild boar populations. Virol J 7:171.

Allander T, Tammi MT, Eriksson M, Bjerkner A, Tiveljung-Lindell A, Andersson B.

Tozer SJ, Lambert SB, Whiley DM, Bialasiewicz S, Lyon MJ, Nissen MD, Sloots TP.

haemodialysis and lung transplant patients, respectively (GenBank accession nos