Vinh Le-Van

Gérard Meunier

Olivier Chadebec

Jean-Michel Guichon

Keywords: facet elements, nonlinear magnetostatics, volume integral method

This paper presents a novel and useful 3D nonlinear magnetostatic integral formulation for volume integral method. Like every other integral formulation, its main advantage is that it does not require air region mesh, only ferromagnetic regions being discretized. The formulation is based on magnetic flux density interpolation on facet elements. Special care is taken in order to accurately compute the singularity of Green's kernel. The application of an equivalent circuit approach allows preserving the solenoidality of magnetic induction. It is shown that the formulation is very accurate even if it is associated with coarse meshes. Thus, computation time can be very competitive. Computed results for the TEAM Workshop problem 13 and for a multiply-connected regions case-test are reported.

I. INTRODUCTION

olume Integral Method (VIM) is known to be a powerful approach to model magnetostatic problems like actuator devices. Several academic codes like GFUN [START_REF] Newman | GFUN: an interactive program as an aid to magnet design[END_REF], GFUNET/CORAL [START_REF] Kettunen | A volume integral formulation for nonlinear magnetostatics and eddy currents using edge elements[END_REF], RADIA [START_REF] Chubar | A three-dimensional magnetostatic computer code for insertion devices[END_REF] or CALMAG3D [START_REF] Souza | Nonlinear calculation of 3D static magnetic fields[END_REF] developed since the 1970s have already shown the reliability of the approach. The main advantage of VIM is that neither free space mesh nor boundary conditions are required. Using VIM, only active regions have to be discretized into elementary elements. This allows in general resolving accurately magnetostatic problems with very coarse meshes. VIM has a renewed interest in the last decade by the development of matrix compression algorithms such as the FMM (Fast Multipole Method) [START_REF] Greengard | A fast algorithm for particle simulations[END_REF], the HCA (Hybrid Cross Approximation) [START_REF] Borm | Hybrid cross approximation of integral operators[END_REF], which improve efficiently both storage memory and resolution time of fully populated matrix systems. Moreover, a Nyström discretization technique [START_REF] Young | A Locally Corrected Nyström Formulation for the Magnetostatic Volume Integral Equation[END_REF] [START_REF] Young | Quasi-Mixed-Order Prism Basis Functions for Nyström-Based Volume Integral Equations[END_REF] allows incorporating both higher-order meshes and higherorder basis functions in order to more accurately solve the magnetostatic integral equation. As a result, VIM is an interesting alternative to classical finite element method (FEM) methods in some situations today.

The main idea of the magnetostatic VIM approach is that the magnetic field is created by the inductor sources and all ferromagnetic elements defined in the problem. With a point matching technique or a Galerkin's projection, which ensures the validity of the materials constitutive laws, a matrix system is obtained. It remains to solve this matrix system to get quantity values on the mesh of the ferromagnetic part and then to compute the magnetic field everywhere. Force or flux can also be easily computed.

Different kinds of magnetostatic volume integral formulations based on different quantities interpolations have already been presented in the literature. The oldest and also most popular one is based on uniform magnetization on each element. This formulation is usually known as Magnetic Moment Method (MMM) [START_REF] Harrington | Field computation by moment methods[END_REF] [10] [START_REF] Takahashi | Large-Scale and Fast Nonlinear Magnetostatic Field Analysis by the Magnetic Moment Method With the Adaptive Cross Approximation[END_REF] and is certainly the simplest to implement. The MMM is capable of yielding accurate results for simple geometric devices [START_REF] Chadebec | A review of magnetostatic moment method[END_REF] but can suffer from the "looping pattern" as mentioned in [START_REF] Forsman | Properties of b-and h-type integral equation formulations[END_REF]. If the susceptibility of the material is high, the associated matrix system becomes singular and the solution contains some spurious modes, decreasing its accuracy. This is why better formations associated with more reliable field interpolation basis are preferred. Many authors have proposed volume integral formulations used nodal and edge elements interpolations. The formulation based on nodal elements and magnetic scalar potential φ [START_REF] Han | Integral equation method using total scalar potential for the simulation of linear or nonlinear 3D magnetostatic field with open boundary[END_REF] [14] [START_REF] Kalimov | Three-Dimensional Magnetostatic Field Calculation Using Integro-Differential Equation for Scalar Potential[END_REF] significantly improves the accuracy of VIM in comparing with MMM. The φ-nodal formulation allows for minimizing the number of unknowns. However, it requires a particular cutting technique to resolve multiple-connected regions problems. Moreover, an additional pre-resolution is needed in order to compute the scalar potential φ 0 in the presence of coils. The H-edge formulation that is based on the interpolation of magnetic fields with edge elements also yields accurate results [START_REF] Kettunen | A volume integral formulation for nonlinear magnetostatics and eddy currents using edge elements[END_REF] [START_REF] Canova | Integral solution of nonlinear magnetostatic field problems[END_REF]. It does not require a source pre-resolution and avoids the cutting technique for multiple-connected regions problems by using an edge-tree technique.

Regarding to the nonlinear resolution, all three formulations MMM, φ-nodal, and H-edge have poor convergence rates due to the use B(H) or M(H) curve. If the Newton-Raphson (NR) method is used, relaxation has to be very often required in order to achieve convergence. Yet, the determining of optimal constant relaxation factor involves additional studies, such as by using an energy minimum principle [START_REF] Hafla | Magnetic field computation with integral equation method and energy-controlled relaxation[END_REF]. Different from mentioned formulations above, we propose in this paper a novel magnetostatic VIM formulation based on facet elements of first order associated with magnetic flux density, called Bfacet formulation. The degrees of freedom are associated with the normal component of magnetic flux density on facets of the mesh. The divergence-free magnetic-field condition is achieved by using an equivalent circuit approach. We will demonstrate that the formulation leads to the use of a H(B)

A Volume Integral Formulation Based on Facet Elements for Nonlinear Magnetostatic Problems V curve during the nonlinear resolution, and as a result, good NR convergence rates can be easy obtained without any relaxation.

Some papers have also proposed the use of facet elements interpolation for magnetostatics [START_REF] Vishnevsky | Modeling magnetization using Whitney facet elements[END_REF] [START_REF] Balasubramanian | Fast-integralequation scheme for computing magnetostatic fields in nonlinear media[END_REF]. However, in [START_REF] Vishnevsky | Modeling magnetization using Whitney facet elements[END_REF] Vishnevsky et al. (2002) suggested the interpolation of magnetization on facet elements. This approach can be suitable for linear cases but should not be applied generically for nonlinear problems, because the normal component of the magnetization across facets could not be considered continuous, unlike one of the magnetic flux. In [START_REF] Balasubramanian | Fast-integralequation scheme for computing magnetostatic fields in nonlinear media[END_REF], although [START_REF] Balasubramanian | Fast-integralequation scheme for computing magnetostatic fields in nonlinear media[END_REF] used the B-facet interpolation, the solenoidality of magnetic induction is not strictly satisfied. And this should lead to an inaccuracy of the solution in some situations. In our formulation, the B-facet interpolation is used as well but the solenoidality of magnetic induction is strongly imposed thanks to the use of an equivalent circuit approach. Moreover, the singularity the Green's function is computed accurately by using an analytical formula. A Nyström discretization technique [START_REF] Young | A Locally Corrected Nyström Formulation for the Magnetostatic Volume Integral Equation[END_REF] [8] could be envisaged in order to incorporate both higher-order meshes and higher-order basis functions.

This paper is organized in the following sections. Section II is dedicated to magnetostatic integral equation, Section III presents properties of facet element shape-function. Section IV describes the new volume integral formulation. Numerical examples are shown in the Section V and Section VI is the conclusion.

II. BASIS EQUATIONS

The governing equations for magnetostatic problem are

0 = B div , (1)
J H rot = , (2)
where B, H, J are the magnetic flux density, the magnetic field intensity, the current density respectively. Without any permanent magnetization, the constitutive equation is:

( )B B H ν = , (3)
( )B B B M ν ν - = 0 , (4)
where ν 0 and ν(B) denotes the reluctivity of vacuum and material respectively, M is the magnetization. The magnetic field H can be decomposed into the sum of two terms: H 0 , the source field created by source currents and H r , the reduced field created by ferromagnetic materials. Based on the Maxwell-Ampere's equation ( 2), it can be shown that H r derives from a reduced magnetic scalar potential φ r . Hence, we have

r ϕ grad H H - = 0 . ( 5
)
The scalar potential φ r is determined by

∫ Ω Ω       ⋅ = d 1 4 1 r r grad M π ϕ , ( 6
)
where r is the distance between the observation and integration points and Ω is magnetic region. From (3) and ( 5 The first-order shape-function can be written as

( ) b a c a c b c b a i λ λ λ λ λ λ λ λ λ ∇ × ∇ + ∇ × ∇ + ∇ × ∇ = 2 w , ( 8
)
where λ is the classical node shape function.

The flux of w i across facet i is equal to one and vanishes across other faces. If facet i has an inner orientation, we have

i S 1 = ⋅ i i n w , (9.a) E V 1 = i divw , (9.b)
where n i is the ingoing normal vector, S i the surface of i and V E the volume of E. These properties remain identical, but with opposite sign if the facet i has an outer orientation. Equations (9.a), (9.b) are still valid for hexahedral elements and therefore the all formula developed hereafter in this paper are also valid for hexahedral elements mesh. Details about facet elements properties can be found in [START_REF] Bossavit | Whitney forms: a class of finite elements for threedimensional computations in electromagnetism[END_REF].

IV. FORMULATIONS

A. Facet Elements Discretization

The ferromagnetic body Ω is subdivided into N elementary volume elements. Let Γ be the boundary of Ω; N f be the number of facet elements on Ω; N b the number of facet elements on the boundary Γ.

Vector B can be approximated by facet elements interpolation of first order as

∑ = Φ = f N j j j 1 w B , ( 10
)
where Φ j denotes the magnetic flux across the facet j. Projecting [START_REF] Young | A Locally Corrected Nyström Formulation for the Magnetostatic Volume Integral Equation[END_REF] on Ω by the Galerkin method with facet shape-function w i , we get ( )

Ω ⋅ = Ω ⋅ + ∫ ∫ ∫ Ω Ω Ω d d 0 H w grad w B B i r i ϕ ν . ( 11
)
Then according to [START_REF] Chadebec | A review of magnetostatic moment method[END_REF], we have:

( ) Ω ⋅ = Ω ⋅ + Φ           Ω ⋅ ∫ ∫ ∑ ∫ Ω Ω = Ω d d d 0 1 H w grad w w B w i r i j N j j i f ϕ ν (12)
In matrix-vector form, ( 12) is rewritten as

F r i d = Ω ⋅ + Φ ∫ Ω ϕ grad w R , ( 13
)
where R denotes a finite-element matrix, Φ is the vector of flux through facets, and F is a vector corresponding to the source-field term. Expressions of R and F are ( )

d d 0 , Ω ⋅ = Ω ⋅ = ∫ ∫ Ω Ω H w w B w R i i j i j i F ν . ( 14
)
Applying the divergence theorem, we can write the integral term in [START_REF] Han | Integral equation method using total scalar potential for the simulation of linear or nonlinear 3D magnetostatic field with open boundary[END_REF] as where φ E , φ i are the average reduced scalar potentials of element E and facet i, respectively; ∆ denotes the difference of average potentials between two adjacent elements; ∆ denotes one between the element and its border facet.

Ω - Γ ⋅ = Ω ⋅ = ∫ ∫ ∫ Ω Γ Ω d d d i r i i r r i div w n w grad w I ϕ ϕ ϕ . (15)
In short, ( 13) is represented as

F IN =         ∆ ∆ + Φ Γ ϕ ϕ R , (16)
In the next subsection an equivalent circuit approach is briefly introduced in order to develop explicitly two terms ∆ and ∆ in order to complete the equation system.

B. Equivalent Circuit Approach

The equivalent circuit approach has been widely used for a long time to find numerical solutions of electromagnetic field problems. The key point of the approach is to establish a network model thanks to the analogy between magnetic circuit and electric circuit. In [START_REF] Demenko | Geometric formulation of edge end nodal finite element equations in electromagnetics[END_REF] [22] and [START_REF] Carpenter | Finite-element network models and their application to eddy-current problems[END_REF], network models are established by means of the FEM. In [START_REF] Gimignani | Integral formulation for nonlinear magnetostatic and eddy currents analysis[END_REF] and [START_REF] Nguyen | An Integral Formulation for the Computation of 3-D Eddy Current Using Facet Elements[END_REF], authors introduce the use of networks model into the VIM.

In our approach, the equivalent-circuit-model has nodes which are associated with volume-element centers and an outer domain node ∞, called the infinity node. The circuit branches are either the branches through inner facet which connect centers of both adjacent elements, or the branches through boundary facet and link the center of boundary volume elements with infinity node. The Fig. 2 illustrates an example of equivalent circuit model for a 2D mesh of 6 triangle elements. Based on this approach, equation ( 16) can be interpreted as follows: the matrix R is equivalent to reluctance network, ∆ , ∆ correspond to magnetic flux leakages and F is the magneto-motive force. The aim of the next subsection is to establish the linear system to be solved.

C. Integral Volume Formulation

A common convention is to set the magnetic scalar potential at infinity (φ ∞ ) to zero. Thus, the difference of scalar potential between the infinity node and a border facet i is

i i dΓ - = - = ∆ ∫ Γ Γ ∞ ∞ Γ i r i i S ϕ ϕ ϕ ϕ (17)
According to (4) and ( 6), φ r is expressed as

( ) ( ) ∑ ∫ Ω ∈ Ω Ω Ω       ⋅ - = e e e r r d 1 4 1 E 0 grad B B ν ν π ϕ , (18)
Hence, ( 17) is developed as

i 1 d d 1 1 4 1 Γ         Φ         Γ - = ∆ ∫ ∑ ∫ Γ = Γ ∞ Γ i f N j j j j j j i i r S S δν π ϕ . ( 19
)
where δν j denotes difference of reluctivity either between two adjacent elements or between border element and air. In the matrix-vector form we write [START_REF] Balasubramanian | Fast-integralequation scheme for computing magnetostatic fields in nonlinear media[END_REF] as

0 = Φ + ∆ ∞ Γ L ϕ , ( 20
)
where L is the integral matrix corresponding to border facets and representing the magnetic flux leakage.

ij j i j i j ij i j r S S 0 j d d 1 1 1 4 L L δν π δν = Γ Γ = ∫ ∫ Γ Γ , ( 21
)
with i = 1,2,..N b , j = 1,2,..N f . The singularity of Green's function with self-interaction in ( 21) can be avoided by using a shifting of Gauss's points or the well-known analytical integration. This analytical correction can be found in [START_REF] Rubeck | Analytical Calculation of Magnet Systems : Magnetic Field Created by Charged Triangles and Polyhedra[END_REF]. It must be pointed out that this numerical technique is the key point of the method in order to compute the integral of the Green's kernel associated with this formulation. From ( 16) and ( 20), we have ( )

        ∆ + ∆ ∆ = ∆ = ∆ + Φ + ∞ Γ Γ ϕ ϕ ϕ ϕ ϕ in IN with F L R , ( 22
)
where R is a sparse finite-element-matrix and L is a dense integral matrix. The structures of R and L are illustrated in Fig. 3. In general, we have N b << N f .

The mesh current method is then used to solve the equivalent circuit. Let P be an incidence matrix which links the incidence of the independent loops to the branches. Because of the fact that the vector ∆ in [START_REF] Giuffrida | Finite formulation of nonlinear magnetostatics with integral boundary conditions[END_REF] represents the difference of scalar potential between nodes of circuit including the infinity node, the Kirchhoff's voltage law imposes that 0

= ∆ϕ P . ( 23
)
Combining ( 22) and ( 23), we get

( ) [ ] F P L R P = Φ + , ( 24
)
By means of the mesh current method, ( 24) is written as ( )

F P P L R P = Φ + M T , (25)
where P T is transpose of matrix P and Φ M the vector of mesh fluxes, Φ M is determined by Φ M = P Φ.

An independent-loop-search algorithm proposed in [START_REF] Nguyen | An independent loops search algorithm for solving inductive PEEC large problems[END_REF] can be used for the determining of the incidence matrix P.

D. Matrix Assembly

For the linear case, the size of integral matrix is reduced because the permeability is constant by region. Integral interactions are then limited between elements of Γ and all the borders/ intersections of regions.

From ( 21), it can be remarked that each element of integral matrix L is composed by two terms, one is dependent to material ∆ and the other L 0ij is independent. Consequently, if the NR method is used for solving the nonlinear problem, only the sparse matrix R and the vector ∆ have to be recomputed iteratively. The matrix L 0 is computed one single time before the resolution. This saves both the memory needed and the computation time and is another key point of our approach.

V. NUMERICAL EXAMPLES

The proposed formulation was applied in order to solve a multiply of connected problems with nonlinear material in the first part. In the second part, it was applied to solve the TEAM Workshop Problem 13.

A. Closed Magnetic Circuit Modeling

) ( )         - + = s 0 s 0 2J 1 J 2 H H H B µ µ π π µ r arctg , ( 26
)
where J s the saturation magnetization is 1.0 T, and µ r the initial relative permeability is 500. The problem was solved by the proposed formulation. A coarse mesh -96 elements and a denser one -890 element were considered. And then, the module |B| were computed on the 25 points on the segment PQ in air, with P (-25, 0, -5) and Q (25, 0, -5). These results were compared with the reference values that had performed by the FEM by means of commercial FEM software Flux3D® with 200,000 tetrahedral elements in second order including 120,000 elements in ferromagnetic region. The coarse mesh of 96 elements gives comparable results and the results obtained with mesh are nearly coincided with the reference values.

B. TEAM Workshop Problem 13

Benchmark problem 13 defined in the TEAM Workshop is a nonlinear magnetostatic problem [START_REF] Nakata | Summary of results for TEAM workshop problem 13 (3-D nonlinear magnetostatic model)[END_REF]. An excited coil is set between two steel channels and a steel plate is inserted between the channels. The applied magnetomotive force is 1000 A.T. The iterative solver FGMRES (Flexible Generalized Minimal Residual method) [START_REF] Saad | A flexible inner-outer preconditioned GMRES algorithm[END_REF] is used for the solving linear system and the classic NR method is used to deal with nonlinear system. Three regular tetrahedral meshes (1235, 4,855 and 20,737 elements) were reported. In figure 7, the mesh of 1,235 elements is presented. For this mesh, we needed 6.7 seconds for the NR resolution by using a computer of CPU 3.04 GHz and 1.1 GB of RAM. The convergence of the solution was obtained in five steps without any relaxation. The absolute stopping criterion of NR was set 1E-6. For the mesh of 4,855 elements, the number of iterations was always five and the time of resolution 30,48 seconds.

The curves with 4,855 elements and 20,737 elements are superposed and very close to the measured values. Therefore, it can be concluded that the convergence was reached for a mesh of 4,855 elements. Compared to meshes used in [START_REF] Nakata | Summary of results for TEAM workshop problem 13 (3-D nonlinear magnetostatic model)[END_REF], this mesh is still very coarse. The result of TEAM problem 13 validates the efficiency and accuracy of the method to analyze nonlinear models. For large problems, a fast algorithm such as the FMM, ACA (Adaptive Cross Approximation) [START_REF] Bebendorf | Appfroximation of boundary element matrices[END_REF] or HCA can be applied in order to save the memory and computation time. Information about the implementation of FMM and ACA for the magnetostatic VIM can be found in [START_REF] Balasubramanian | Fast-integralequation scheme for computing magnetostatic fields in nonlinear media[END_REF] [START_REF] Nguyen | Ships magnetic anomaly computation with integral equation and fast multipole method[END_REF] and [START_REF] Takahashi | Large-Scale and Fast Nonlinear Magnetostatic Field Analysis by the Magnetic Moment Method With the Adaptive Cross Approximation[END_REF] [32], respectively.

VI. CONCLUSION

A volume integral formulation based on facet element interpolation and magnetic flux has been developed for nonlinear magnetostatic problems. The key features of the formulation were that the imposition of solenoidality of magnetic induction by using an equivalent circuit approach and the accuracy of Green's function computation. The multiply-connected-regions problem was solved without any cutting surface. The classic NR method was used to solve nonlinear magnetostatic problems. The numerical results of a multiply-connected regions case-test and of the TEAM Workshop Problem 13 demonstrated the strength, the accuracy and the efficiency of this new approach. These encouraging results inspire the use of VIM in order to deal with complex electromagnetic devices. For the further works, a development of the formulation for the resolution of magnetic thin shell as well as a coupling with eddy current formulation using facet elements for the solving of electromagnetic problems should be envisaged.

  SHAPE FUNCTION PROPERTIESShape functions of facet elements can be generated from nodal shape functions. Let facet i belong to a tetrahedral element E. If facet i is defined by a set of three nodes {a,b,c}.

Fig. 1 .-

 1 Fig.1. Facet identification. a) Inner facet. b) Border facet.-For inner facet i (Fig.1.a), the surface integral term in[START_REF] Han | Integral equation method using total scalar potential for the simulation of linear or nonlinear 3D magnetostatic field with open boundary[END_REF] vanishes. So thanks to (9.b) we have

Fig. 2 .

 2 Fig.2. Equivalent circuit model for 2D mesh.

Fig. 3 .

 3 Fig. 3. Structures of R and L matrices

Fig. 4 .

 4 Fig. 4. Geometry of magnetic circuit and coil. a) Front view. b) Horizontal view A closed magnetic circuit is excited by a DC current coil of 100 A.T. The geometry is shown on the Fig. 4 in millimeter scale. The nonlinear ferromagnetic material is specified by an arctangent law as the following equation

(

Fig. 5 .

 5 Fig. 5. Magnetic flux density distribution

Fig. 6 .

 6 Fig. 6. Magnetic field module on the segment PQ

Fig. 7 .

 7 Fig. 7. Mesh of problem 13 with 1235 volume elements

Fig. 8 .

 8 Fig. 8. Distribution of magnetic flux density vector The distribution of magnetic flux density on the steel plates with this mesh is shown in Fig. 8. The average flux densities in the steel plate and in the air at various positions are plotted in Fig.9 and Fig. 10, respectively. Both figures indicate that the computed results are very close to the measured one. The results of spatial distributions of flux in steel plate are very close measured values, but ones in air are slightly different in some points. As shown on the Fig. 9 and Fig. 10, a coarse mesh composed of 1,235 elements can lead to accurate results.For this mesh, we needed 6.7 seconds for the NR resolution by using a computer of CPU 3.04 GHz and 1.1 GB of RAM. The convergence of the solution was obtained in five steps without any relaxation. The absolute stopping criterion of NR was set 1E-6. For the mesh of 4,855 elements, the number of iterations was always five and the time of resolution 30,48 seconds.

Fig. 9 .Fig. 10 .

 910 Fig. 9. Spatial distributions of average flux density in steel plate


Mathieu Picardeau

Dieter M Bulach

Christiane Bouchier

Richard L Zuerner

Nora Zidane

Peter J Wilson

Sophie Creno

Elizabeth S Kuczek

Simona Bommezzadri

John C Davis

Annette Mcgrath

Matthew J Johnson

Caroline Boursaux-Eude

Torsten Seemann

Zoe ´rouy

Ross L Coppel

Julian I Rood

Aure ´lie Lajus

John K Davies

Claudine Me ´digue

Ben Adler
email: ben.adler@med.monash.edu.au

Genome Sequence of the Saprophyte Leptospira biflexa Provides Insights into the Evolution of Leptospira and the Pathogenesis of Leptospirosis

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

Genome Sequence of the Saprophyte Leptospira biflexa Provides Insights into the Evolution of Leptospira and the Pathogenesis of Leptospirosis

Introduction

The genus Leptospira contains pathogenic and saprophytic species that differ in their capacity for survival in a vast array of environments that range from soil and water [START_REF] Trueba | Cell aggregation: a mechanism of pathogenic Leptospira to survive in fresh water[END_REF] to the tissues of mammalian hosts during acute and chronic infection [START_REF] Faine | Leptospira and Leptospirosis[END_REF]. Typically, long term colonization by pathogenic Leptospira of the proximal renal tubules of mammalian maintenance host species provides a persistent source of infection; thus, pathogenic Leptospira is shed in the urine of chronically infected animals, facilitating transmission to naı ¨ve hosts [START_REF] Faine | Leptospira and Leptospirosis[END_REF]. Leptospirosis is of considerable importance to international public health, with more than half a million cases reported annually due largely to environmental exposure to pathogenic Leptospira species, with mortality rates of up to 25% in some outbreaks. In addition, leptospirosis in production animals results in a significant economic burden worldwide [START_REF] Faine | Leptospira and Leptospirosis[END_REF].

Recent applications of molecular taxonomy techniques to this genus reveal extensive genetic diversity within Leptospira, with more than 16 pathogenic and saprophytic species recognized [START_REF] Brenner | Further determination of DNA relatedness between serogroups and serovars in the family Leptospiraceae with a proposal for Leptospira alexanderi sp. nov. and four new Leptospira genomospecies[END_REF][START_REF] Levett | Leptospirosis[END_REF]. A significant challenge in the future will be to more precisely correlate these genetic differences with biological differences. The relationship between leptospiral genome content, pathogenesis and the ability to survive in diverse environmental niches is a particularly important area of investigation, highlighted by our recent findings. A process of genome erosion and loss of gene function in L. borgpetersenii serovar Hardjo [START_REF] Bulach | Genome reduction in Leptospira borgpetersenii reflects limited transmission potential[END_REF] limits its viability outside a mammalian host and likely impairs disease transmission through water, a route commonly used by L. interrogans to infect new hosts.

To gain insight into the genetic potential of Leptospira and to help identify genes that contribute to long-term survival in surface water, we determined the genome sequences of two L. biflexa strains, the first saprophytic Leptospira species to be characterized by genome analysis. Comparison of these data to genomes of the pathogenic species L. borgpetersenii [START_REF] Bulach | Genome reduction in Leptospira borgpetersenii reflects limited transmission potential[END_REF], and L. interrogans [START_REF] Nascimento | Comparative genomics of two Leptospira interrogans serovars reveals novel insights into Physiology and Pathogenesis[END_REF][START_REF] Ren | Unique physiological and pathogenic features of Leptospira interrogans revealed by whole-genome sequencing[END_REF] provides an opportunity to identify features that are unique to pathogenic and saprophytic species, thereby providing new experimental directions and novel perspectives on leptospiral evolution, environmental persistence and the causation of disease.

Results and Discussion

Leptospira genomes vary in replicon content and genetic organization

The genome of Leptospira biflexa serovar Patoc strain Patoc1 (Ames strain) consists of three replicons with a total of 3,956,086 base pairs (bp) (Figure 1). The two larger replicons share extensive similarity to the two chromosomes that comprise the genomes of L. borgpetersenii and L. interrogans and are therefore referred to as chromosome I (CI; 3,603,977 bp; GC% 38.89) and chromosome II (CII; 277,995 bp; GC% 39.27). L. biflexa possesses a third circular replicon (74,114 bp; GC% 37.47), that we designate p74, not found in the previously sequenced pathogenic Leptospira species. (The complete genomic sequences of L. biflexa serovar Patoc strain Patoc1, strains Paris and Ames, have been deposited in GenBank under the Accession Numbers: CP000777, CP000778, CP000779, CP000786, CP000787 and CP000788).

A total of 3,590 protein-coding genes (CDSs) was identified in L. biflexa (Table 1). Most of these genes are located on CI, including two rrf genes, two rrl genes and two rrs genes, coding for 5S, 23S and 16S rRNA molecules respectively. These rRNA genes are not linked to each other, a feature unusual among most bacteria but common among Leptospira. Similar to the slower-growing pathogenic species L. interrogans and L. borgpetersenii, each of which has a relatively low number (37) of transfer RNA (tRNA) genes, the faster-growing L. biflexa surprisingly has only 35 tRNA genes. This finding indicates that the growth rate of Leptospira is not restricted by the low number of tRNA and rRNA genes as previously suggested [START_REF] Ren | Unique physiological and pathogenic features of Leptospira interrogans revealed by whole-genome sequencing[END_REF], but rather may be due to other differing metabolic capacities amongst Leptospira spp. As reported for other Leptospira spp. [START_REF] Zuerner | Comparison of genetic maps for two Leptospira interrogans serovars provides evidence for two chromosomes and intraspecies heterogeneity[END_REF], essential genes such as gltB (glutamate synthase) and asd (aspartate semialdehyde dehydrogenase) are carried on CII in L. biflexa.

It is unclear if replicon III (p74) functions as a chromosome, i.e. carries genes essential for survival, or is an extrachromosomal element or plasmid. Thirteen genes on p74 have orthologs located on CI in pathogenic Leptospira (Table 2). For example, recBCD are located on CI in L. interrogans and L. borgpetersenii, but are located on p74 in L. biflexa. Mutation of these housekeeping genes in other bacterial species can affect transformation competence and viability [START_REF] Kickstein | Deletions of recBCD or recD influence genetic transformation differently and are lethal together with a recJ deletion in Acinetobacter baylyi[END_REF], suggesting that p74 is essential for the survival of L. biflexa.

GC skew analysis (Figure 1) suggests that CI, CII and p74 are theta-type replicons that replicate bi-directionally from a unique origin. Each L. biflexa replicon encodes its own partition proteins from origin-proximal genes that may recognize and interact with a replication-specific binding site. The replication origin of CI resembles typical circular chromosomes from other bacteria, i.e. it is adjacent to dnaA, which encodes the initiator protein, and other genes such as dnaN, recF and gyrAB. In contrast, the replication origins of CII, replicon p74 and the previously reported leptophage LE1 [START_REF] Bourhy | Complete nucleotide sequence of the LE1 prophage from the spirochete Leptospira biflexa and characterization of Its replication and partition functions[END_REF] resemble phage and plasmid replicons; they contain both a partition operon and a downstream putative rep gene. For p74, the predicted replication origin based on GC skew analysis includes a partition operon (pLEPBI0001/LBF_5000 and pLEPBI0002/LBF_5001) and an adjacent gene, pLEPBI0003/ LBF_5003, the product of which shares 63% similarity with the leptophage LE1 Rep protein. Regardless of the similarity between the LE1 Rep protein and the product of pLEPBI003, p74 and the LE1 prophage can co-exist (data not shown). Furthermore, we demonstrated that this region of p74 directs autonomous (1) the coordinates in bp beginning at 0 = oriC; (2) dark pink: genes unique to L. biflexa, not found in L. interrogans serovar Copenhageni and L. borgpetersenii serovar Hardjobovis (identity .40% over 80% of the length of the smallest protein). (3) dark purple: genes found in L. biflexa, L. interrogans and L. borgpetersenii (identity .40% over 80% of the length of the smallest protein). (4) red: genes found in L. biflexa and L. borgpetersenii, but not in L. interrogans (identity .40% over 80% of the length of the smallest protein). ( 5) brown : genes found in L. biflexa and L. interrogans, but not in L. borgpetersenii (identity .40% over 80% of the length of the smallest protein). ( 6) blue: genes found in L. biflexa and other sequenced spirochetes (Borrelia afzelii PKo, Borrelia burgdorferi, Borrelia garinii, Treponema denticola and Treponema pallidum) (identity .40% over 80% of the length of the smallest protein ). [START_REF] Ren | Unique physiological and pathogenic features of Leptospira interrogans revealed by whole-genome sequencing[END_REF] The innermost ring shows GC skew; positive skew is shown in grey, and negative skew is shown in black. doi:10.1371/journal.pone.0001607.g001 replication in L. biflexa (Figure S1). This will facilitate the construction of new shuttle vectors for the genetics of Leptospira and their use in co-transformation experiments with the L. biflexa-E. coli shuttle vector derived from LE1 [START_REF] Girons | The LE1 bacteriophage replicates as a plasmid within Leptospira biflexa: construction of an L. biflexa-Escherichia coli shuttle vector[END_REF].

We suggest that the CII and p74 replicons evolved from a stabilized circular intermediate of a progenitor phage related to LE1 [START_REF] Bourhy | Complete nucleotide sequence of the LE1 prophage from the spirochete Leptospira biflexa and characterization of Its replication and partition functions[END_REF]. Intermediates in this process may be related to the LaiGI-1 Genomic Island [START_REF] Bourhy | A Genomic island of the pathogen Leptospira interrogans serovar Lai can excise from its chromosome[END_REF], which exists both as an element integrated into CI of L. interrogans serovar Lai or as an autonomously replicating plasmid. Stabilization of these intermediates could have occurred through illegitimate recombination resulting in incorporation of essential genes from CI into the smaller replicons. Evidence for this model is provided by the presence of genes located on the CI replicon in pathogenic Leptospira on either CII or p74 in L. biflexa, as noted above.

The genus Leptospira is renowned for the stability of its agglutinating antigens during in vitro culture, with examples of strains maintaining serovar identity during more than 80 years of propagation [START_REF] Faine | Leptospira and Leptospirosis[END_REF], implying considerable genomic stability in the absence of selective pressure for antigenic change. Furthermore, more than 2% of the L. interrogans serovar Copenhageni genome is dedicated to LPS biosynthesis. In L. biflexa about 1.4% of the genome encodes LPS biosynthesis functions with essentially all relevant CDS encoded on the same strand, and these genes are identical in the Ames and Paris strains. In contrast, non-LPS encoding regions in the two L. biflexa strains maintained separately for 17 years show some evidence of minor accumulation of changes. Comparison of the Paris and Ames strains of L. biflexa reveals four indels, three of which are insertions of ISLbi1 elements into the coding regions of genes in the Ames strain (LBF_0259, LBF_2295 and LBF_2512). The first two genes encode proteins of unknown function, and the third encodes a protein with a predicted role in lipid metabolism; the significance of these insertions is not known. In the Paris strain, the insertion element is restricted to one copy each on CII and p74; these copies are maintained in the Ames strain. The fourth difference occurs in CII in which an additional 250 bp are found in an intergenic region in the Ames strain. Aside from these differences, the genomes of the Paris and Ames strains are virtually identical; in this article the term L. biflexa will refer to the Ames strain unless stated otherwise. Approximately two thirds of the genes in L. biflexa have orthologous genes in the pathogens L. interrogans and L. borgpetersenii (Figure 2), consistent with a common origin for leptospiral saprophytes and pathogens. The genes conserved across the three species are distributed in the two chromosomes of all Leptospira species and strains (Table 3). The high sequence identity of the small chromosome parA gene product (.87%) between all Leptospira spp. suggests a shared ancestry for this replicon. Moreover, there is no difference in inter-chromosomal DNA parameters such as GC%, codon preferences and gene density within the three L. biflexa replicons, despite the relatively wide range of these parameters in pathogenic Leptospira. By contrast, codon preferences of genes of the leptospiral bacteriophage LE1 and its host, L. biflexa [START_REF] Bourhy | Complete nucleotide sequence of the LE1 prophage from the spirochete Leptospira biflexa and characterization of Its replication and partition functions[END_REF] are different (data not shown). These data suggest a long-standing relationship between the three L. biflexa replicons and perhaps a more recent acquisition of LE1.

The evolution of the Leptospira species Phylogenetic analysis based on comparison of 16S rRNA sequences indicates that members of the family Leptospiraceae form the deepest branch in spirochete evolution, with divergence of saprophytic and pathogenic Leptospira likely being the result of a single event [START_REF] Paster | Phylogenetic analysis of the spirochetes[END_REF]. Further diversification of species within each of these two evolutionary branches of Leptospira is supported by multilocus sequence analysis and DNA renaturation kinetics [START_REF] Brenner | Further determination of DNA relatedness between serogroups and serovars in the family Leptospiraceae with a proposal for Leptospira alexanderi sp. nov. and four new Leptospira genomospecies[END_REF][START_REF] Haake | Molecular evolution and mosaicism of leptospiral outer membrane proteins involves horizontal DNA transfer[END_REF][START_REF] Ramadass | Genetic characterization of pathogenic Leptospira species by DNA hybridization[END_REF].

We used comparative genome analysis to help identify key features showing patterns of variation consistent with the action of selective evolutionary pressure within Leptospira. The L. biflexa and L. borgpetersenii genomes are similar in size (Table 1), but the gene density in L. biflexa is much higher, probably as a result of ISmediated genome erosion in L. borgpetersenii. In contrast, the L. interrogans genome is larger, probably reflecting the added genetic information required for survival both within mammalian hosts and aquatic environments, whereas L. biflexa and L. borgpetersenii are restricted to aquatic and mammalian host environments, respectively. The dearth of IS-elements in the L. biflexa genome (five ISelements) is in stark contrast to their abundance in the L. interrogans (36 and 69 IS-elements in the Fiocruz LI-130 and Lai 56601 strains, respectively) and L. borgpetersenii (167 IS elements) genomes. The presence of large numbers of IS elements is an indicator of genome plasticity in Leptospira species. Taken together, our results suggest that the L. biflexa gene order is more likely to have a closer relationship to the progenitor genome for the genus Leptospira. There is low synteny between the sequenced pathogenic Leptospira (Figure 3) [START_REF] Bulach | Genome reduction in Leptospira borgpetersenii reflects limited transmission potential[END_REF], despite the short evolutionary distance separating them.

Gene and functional redundancy is also more common in the pathogens in comparison to the saprophytes (Table 4). The pathogens have more paralogs (excluding transposases), with 203 (5.01%) and 438 (10.52%) paralogs for L. interrogans serovar Copenhageni Fiocruz L1-130 and L. borgpetersenii serovar Hardjo L550, respectively, compared to 62 paralogs (1.65%) in the saprophyte L. biflexa. We identified 43, 67, and 53 loci with gene duplication in the genomes of L. biflexa, L. interrogans, and L. borgpetersenii, respectively. The genome of L. biflexa therefore appears to be more stable than those of L. interrogans and L. borgpetersenii. Moreover, the L. biflexa genome (92%) has a greater biflexa. Orthologous CDS were identified in a pair-wise fashion using Whole-Genome Reciprocal Best-Hit BLAST Analysis [START_REF] Fuchsman | Whole-genome reciprocal BLAST analysis reveals that Planctomycetes do not share an unusually large number of genes with Eukarya and Archaea[END_REF]. Manual curation ensured a one to one relationship for orthologous CDS, particularly in situations where sets of paralogous CDS existed and in addition evaluated the nature of the relationship between CDS with reciprocal best-hits but low expect values. This analysis was performed using the L. interrogans serovar Copenhageni strain Fiocruz, L. borgpetersenii serovar Hardjo strain L550 and L. biflexa serovar Patoc strain Ames genome sequences. doi:10.1371/journal.pone.0001607.g002 gene density than the L. borgpetersenii (80%) and L. interrogans genomes (75%) (Table 1). Greater gene density can contribute to a relatively stable gene order. For example, the spirochete Borrelia has a gene density of more than 92% and the B. garinii and B. burgdorferi genomes are essentially collinear [START_REF] Glockner | Comparative analysis of the Borrelia garinii genome[END_REF].

Genetic determinants involved in survival in the environment

The spectrum of ecological niches occupied by diverse Leptospira species raises questions as to how the capacity to survive in these diverse environments has evolved within different species in the genus Leptospira. We propose that their common progenitor had a genome more like L. biflexa. Subsequently, acquisition of genes that enabled Leptospira to infect mammals would have expanded the range of environments that it could successfully occupy. Loss of environmental survival genes then would lead to dependence on a mammalian host and eventually return the genome to a smaller size (i.e. L. borgpetersenii), consistent with our model for IS-mediated genome degradation [START_REF] Bulach | Genome reduction in Leptospira borgpetersenii reflects limited transmission potential[END_REF].

The extensive repertoire of genes (Table 5) encoding proteins involved in signal transduction in L. biflexa (287 CDS) compared with L. interrogans (214 CDS) and L. borgpetersenii (167 CDS) is consistent with an enhanced metabolic capability in L. biflexa reflected by its environmental habitat and likely contributes to its enhanced growth rate relative to the pathogens. An analogous situation is seen in Mycobacterium, where M. marinum which occupies both animal and aquatic environments has many more genes encoding environmental sensing and metabolic proteins than the closely related, obligate human pathogen M. tuberculosis [START_REF] Stamm | Mycobacterium marinum: the generalization and specialization of a pathogenic mycobacterium[END_REF][START_REF] Stinear | Reductive evolution and niche adaptation inferred from the genome of Mycobacterium ulcerans, the causative agent of Buruli ulcer[END_REF].

The genomes of Leptospira spp. contain a number of genes involved in the production of exopolysaccharides. These genes, such as those encoding glycosyltransferases, alginate biosynthesis, and lipopolysaccharide transport systems, may contribute to colonization of both biotic and abiotic surfaces. When investigating the formation of biofilms on solid surfaces, we have observed the production of a strong biofilm by L. biflexa and L. interrogans (Unpublished results). The formation of such a biofilm is consistent with the life of saprophytic species in water; it may facilitate L. biflexa occupying particular environmental niches. The presence of biofilms may also play an important role in chronic carriage of the pathogen L. interrogans in animal reservoirs by facilitating colonization of the renal tubules. Interestingly, genes involved in alginate biosynthesis are present in both L. biflexa (11 genes) and L. interrogans (8 genes), but are absent in L. borgpetersenii, a finding consistent with the reduced environmental survival of L. borgpetersenii [START_REF] Bulach | Genome reduction in Leptospira borgpetersenii reflects limited transmission potential[END_REF].

Comparative genomics of pathogenic and saprophytic Leptospira

The molecular mechanisms of pathogenesis in leptospirosis remain almost entirely unknown. The set of leptospiral, pathogenspecific genes, defined as those with no orthologous gene in L. biflexa, is likely to be enriched for genes that play a role in pathogenesis. Significantly, the majority (893) of these 1,431 genes has no known function (Table S1abc), suggesting the presence of pathogenic mechanisms unique to Leptospira. Among the remaining 538 genes, there are several genes encoding response regulators and environment sensing proteins; these genes are likely to represent adaptations that enable survival in environments not encountered by the saprophytic strain. There is an expansion of genes encoding leucine-rich repeat (LLR) proteins from one gene in L. biflexa to eight and 18 genes in L. borgpetersenii and L. interrogans, respectively. Although these LLR proteins have no obvious function, in Treponema denticola the LRR protein LrrA appears to have roles in attachment and to, and penetration of, host tissues [START_REF] Ikegami | Multiple functions of the leucine-rich repeat protein LrrA of Treponema denticola[END_REF]; the diversity of LRR proteins in pathogenic Leptospira may be important for succesful infection of a wide variety of mammalian host species.

The regulation of transcription differs significantly between the saprophytic and pathogenic strains as indicated by the presence of more than 50 saprophyte-specific, and more than 20-pathogen specific, transcription regulators, whereas there are only 27 transcription regulators that are common to all of the sequenced Leptospira species.

Because the bacterial surface is an interface between the pathogen and the host, any differences in cell-surface proteins might reflect variation in pathogenesis mechanisms among Leptospira spp., which contain a relatively low repertoire of transmembrane proteins in their outer membranes [START_REF] Cullen | Outer membrane proteins of pathogenic spirochetes[END_REF]. However, the outer membranes contain a predominance of lipoproteins, that may be either surface-exposed or located in the periplasm. Predicted lipoproteins are prominent in both saprophytic (164 predicted lipoproteins) and pathogenic Leptospira (184 and 130 predicted lipoproteins in L. interrogans and L. borgpetersenii respectively). Despite these similarities, there are significant differences, most notably the absence in L. biflexa of an ortholog of the major outer membrane lipoprotein, LipL32 [START_REF] Cullen | Outer membrane proteins of pathogenic spirochetes[END_REF]. Moreover, 89 L. biflexa lipoprotein genes have no orthologs in other Leptospira species, and more than 90 lipoproteins from the pathogenic species have no orthologs in the L. biflexa genome. In addition to LipL32, other characterized lipoproteins that have no orthologs in L. biflexa include LipL41, LipL36 and several LipL45 related proteins [START_REF] Cullen | Outer membrane proteins of pathogenic spirochetes[END_REF]. However, LipL21, which was reported as a pathogen-specific lipoprotein [START_REF] Cullen | LipL21 Is a novel surface-exposed lipoprotein of pathogenic Leptospira species[END_REF] based on antibody reactivity, has an ortholog in L. biflexa with 50% similarity. This level of similarity is consistent with a different function for the LipL21 orthologs in the two Leptospira species.

Several putative virulence factors previously identified in pathogenic Leptospira spp. are not present in L. biflexa, including the Lig surface proteins containing immunoglobulin-like repeats predicted to play a role in the adhesion to host tissues [START_REF] Choy | Physiological osmotic induction of Leptospira interrogans adhesion: LigA and LigB bind extracellular matrix proteins and fibrinogen[END_REF]. Similarly, LfhA, a putative factor H binding protein [START_REF] Verma | LfhA, a novel Factor H-binding protein of Leptospira interrogans[END_REF] that has also been shown to bind the extracellular matrix protein laminin [START_REF] Barbosa | A newly identified leptospiral adhesin mediates attachment to laminin[END_REF], is shared among pathogenic Leptospira, but is lacking in L. biflexa. Although the genome of L. biflexa contains putative hemolysins [START_REF] Louvel | Comparative and functional genomic analyses of iron transport and regulation in Leptospira spp[END_REF], its genome is devoid of genes encoding enzymes capable of degrading tissues, such as the range of sphingomyelinases found in pathogenic species [START_REF] Segers | Presence of putative sphingomyelinase genes among members of the family Leptospiraceae[END_REF][START_REF] Segers | Molecular analysis of a sphingomyelinase C gene from Leptospira interrogans serovar hardjo[END_REF][START_REF] Del Real | Cloning of a hemolysin gene from Leptospira interrogans serovar hardjo[END_REF]. The role of sphingomyelinases in the pathogenesis of leptospirosis has been controversial; are they key virulence factors or do they merely play a role in nutrient acquisition? Their absence in L. biflexa strongly supports their involvement in survival within mammalian hosts. Interestingly, the membrane protein, Loa22, the only protein to date that has been shown genetically to be required for virulence in L. interrogans [START_REF] Ristow | The OmpA-like protein Loa22 Is essential for leptospiral virulence[END_REF], has a L. biflexa ortholog with 73% similarity.

Its role in either pathogenic or saprophytic species is unknown, but its presence in the saprophytic species suggests that it is involved in survival rather than being a direct virulence factor and is consistent with the common progenitor hypothesis.

L. interrogans is the most frequently reported agent of human leptospirosis. The disease is also generally more severe with L. interrogans than with L. borgpetersenii [START_REF] Faine | Leptospira and Leptospirosis[END_REF]. On this basis we propose that the subset of L. interrogans genes that have no orthologs in either L. biflexa or L. borgpetersenii may contain virulence factors that are responsible for the more severe form of leptospirosis. Other subsets that may be enriched for genes involved in particular biological functions include those genes that have orthologs in L. biflexa and L. interrogans and not L. borgpetersenii which may contain genes involved in survival outside the animal host. While the loss of many genes from the L. borgpetersenii genome has occurred through genome reduction [START_REF] Bulach | Genome reduction in Leptospira borgpetersenii reflects limited transmission potential[END_REF], the presence of 265 unique genes in L. borgpetersenii (Figure 2; Table S1abc) indicates that these genomes have also gained some additional genes during the course of their evolution. The lateral acquisition of genetic material is often associated with IS-elements. While there is an association between IS-elements and genes that are isolate-or species-specific, in particular in L. interrogans, no mechanism has been determined. Other possible mechanisms for horizontal gene acquisition may include the involvement of bacteriophage, as integrated prophages or bacteriophage remnants are present.

The Core Leptospiral Genes

Saprophytic and pathogenic Leptospira species belong to two distinct phylogenetic groups, leading us to conclude that the 2,052 genes shared by both groups constitute the core genome of this genus (Figure 2). As expected, many of the functional categories that are involved in essential housekeeping functions, such as DNA and RNA metabolism, protein processing and secretion, cell structure, cellular processes, and energetic and intermediary metabolism, are represented in the core gene set.

The presence of orthologous genes in all the sequenced leptospiral species is an indicator that these genes were acquired prior to the radiation of the genus, and as such, is a strong indicator that these genes have not been laterally acquired. The substantial proportion of the total leptospiral genes that are in this category is perhaps an indicator that lateral transfer of genes into the genus Leptospira is a minor contributor to the overall genetic composition of the genus and an indicator that the genus has undergone an extended period of 'genetic isolation'. This notion is supported by the fact that approximately 20% of the core leptospiral genes are unique to the genus. However, this does not preclude horizontal acquisition of some genes or gene clusters.

Implications for genetic studies

Despite the development of basic tools such as transposon mutagenesis for the pathogenic species of Leptospira, targeted gene inactivation is not yet possible. Therefore, there is likely to be continued interest in the use of L. biflexa as a model bacterium for genetic analysis [START_REF] Louvel | Genetic manipulation of Leptospira biflexa[END_REF]. Knowledge of the distribution of orthologous genes in L. biflexa will be an important resource for the elucidation of function for genes common to pathogenic and saprophytic species.

Materials and Methods

Sequencing and annotation of the genome of L. biflexa

The strain, L. biflexa serovar Patoc strain Patoc1, was initially isolated from stream water [START_REF] Babudieri | Studio serologico del gruppo Semaranga-Patoc di Leptospira biflexa[END_REF], maintained in the collection of the National Reference Center of Leptospira (Institut Pasteur, Paris, France) and designated the Paris strain. A second strain was derived from the same source but kept in the culture collection at the National Animal Disease Center (NADC), Ames, IA since 1990 and is designated the Ames strain. Each strain was colony purified before growth for genomic DNA isolation. For each isolate, genomic DNA was randomly sheared by nebulization (HydroShear, GeneMachines) and the ends repaired enzymatically. Small fragments (,1.5-4 kb) were ligated either to a derivative of plasmid pGEM7Zf+ (Promega) (Paris strain) or pSMART-HC and pSMART-LC (Lucigen Corp.) (Ames strain). Large (35-45 kb) DNA fragments were ligated to fosmid pCC1FOS (Epicentre, Madison, WI) (Paris strain). Intermediate sized DNA fragments (7-12 kb) were prepared from partially BamHI-digested Ames strain DNA and ligated into pZERO-1 (Invitrogen). Plasmid DNA preparation was performed with the TempliPhi DNA sequencing template amplification kit (GE Healthcare -Bio-Sciences) or SprintPrep plasmid preparation kits (Agencourt Bioscience). Fosmid DNA purification was performed with the Montage BAC Miniprep96 Kit (Millipore) [START_REF] Louvel | Comparative and functional genomic analyses of iron transport and regulation in Leptospira spp[END_REF]. Sequencing reactions were performed from both ends of DNA templates using ABI PRISM BigDye Terminator cycle sequencing ready reactions kits and run on a 3700 or a 3730 xl Genetic Analyzer (Applied Biosystems) at the Genomics platform (Pasteur Genopole I ˆle-de-France), the Australian Genome Research Facility, Brisbane, Australia or at the Genomics Facility at the NADC. Basecalls from sequence data were made using Phred [START_REF] Ewing | Base-calling of automated sequencer traces using phred. I. Accuracy assessment[END_REF]. Sequences not meeting our production quality criteria (at least 100 bases called with a quality over 20) were discarded. The traces were assembled using Phrap and Consed [START_REF] Gordon | Consed: a graphical tool for sequence finishing[END_REF].

Whole genome shotgun sequencing was performed until approximately 66 genome coverage was achieved. Autofinish [START_REF] Gordon | Automated finishing with Autofinish[END_REF] was used to design primers for improving regions of low quality sequence and for primer walking along templates that spanned the gaps between contigs. Several strategies were used to orientate contigs to enable directed PCR-based approaches to span gaps between contigs. These strategies included Blast-based approaches that identified contig ends with hits to the same gene or to genes within the same locus, provided that there was conservation of gene order in both the L. interrogans and the L. borgpertersenii genomes. Repeated sequences longer than 600 bases, such as IS-elements and the rrl and rrn genes, were identified and curated manually to ensure that at least two templates spanned these regions, thus confirming the assembly of these regions. At this stage, single, circularised contigs representing CII and and p74 were identified. Combinational PCR was used to close the gaps between the final contigs making up CI. Outward-directed primers were designed for each of the contig ends; the primer sequences were subsequently checked and confirmed to be unique on the genome. The combinational PCR process required approximately 600 PCR reactions pairing each of the primers. In each instance where a gap was spanned, the size of the PCR product was less than 2 kb. The sequence of these PCR products was determined and added to the assembly to enable the closing of CI. PCR with independent primers was used to confirm the joins determined by the combinational PCR. In addition, for the Paris strain five fosmid clones were completely sequenced by transposon-assisted sequencing (Finnzymes, TGS II kit). Seven fosmid clones were also selected by Southern hybridization and sequenced in order to verify the 23S RNA and 16S RNA regions and 4 repeat regions. Validation of the final assembly was achieved by comparison of in silico digestion patterns with macrorestriction patterns obtained by PFGE with NotI and AscI. For each genome, the error rate was less than 1 error per 10,000 bp.

The complete genome sequence was obtained from 58,663 and 40,260 sequences for the Paris and Ames strains respectively (giving .86 and 76 coverage). For the Paris strain, coding sequences (CDSs) likely to encode proteins were predicted with the AMIGene software [START_REF] Bocs | AMIGene: Annotation of MIcrobial Genes[END_REF]. Annotation was performed as described previously [START_REF] Louvel | Comparative and functional genomic analyses of iron transport and regulation in Leptospira spp[END_REF] using the MaGe annotation platform [START_REF] Vallenet | MaGe -a microbial genome annotation system supported by synteny result[END_REF]. All the data were stored in SpiroScope, a relational database which is publicly available (http://www.genoscope.cns.fr/agc/mage). The Ames strain was annotated as described previously for the L. borgpetersenii serovar Hardjo genome using the Wasabi interactive platform [START_REF] Bulach | Genome reduction in Leptospira borgpetersenii reflects limited transmission potential[END_REF].

Supporting Information

Figure 1 .

 1 Figure 1. Circular maps of the three L. biflexa replicons. (1) the coordinates in bp beginning at 0 = oriC; (2) dark pink: genes unique to L. biflexa, not found in L. interrogans serovar Copenhageni and L. borgpetersenii serovar Hardjobovis (identity .40% over 80% of the length of the smallest protein). (3) dark purple: genes found in L. biflexa, L. interrogans and L. borgpetersenii (identity .40% over 80% of the length of the smallest protein). (4) red: genes found in L. biflexa and L. borgpetersenii, but not in L. interrogans (identity .40% over 80% of the length of the smallest protein). (5) brown : genes found in L. biflexa and L. interrogans, but not in L. borgpetersenii (identity .40% over 80% of the length of the smallest protein). (6) blue: genes found in L. biflexa and other sequenced spirochetes (Borrelia afzelii PKo, Borrelia burgdorferi, Borrelia garinii, Treponema denticola and Treponema pallidum) (identity .40% over 80% of the length of the smallest protein ).[START_REF] Ren | Unique physiological and pathogenic features of Leptospira interrogans revealed by whole-genome sequencing[END_REF] The innermost ring shows GC skew; positive skew is shown in grey, and negative skew is shown in black. doi:10.1371/journal.pone.0001607.g001

Figure 2 .

 2 Figure 2. Venn diagram showing numbers of unique and shared genes amongst L. interrogans, L. borgpetersenii and L.biflexa. Orthologous CDS were identified in a pair-wise fashion using Whole-Genome Reciprocal Best-Hit BLAST Analysis[START_REF] Fuchsman | Whole-genome reciprocal BLAST analysis reveals that Planctomycetes do not share an unusually large number of genes with Eukarya and Archaea[END_REF]. Manual curation ensured a one to one relationship for orthologous CDS, particularly in situations where sets of paralogous CDS existed and in addition evaluated the nature of the relationship between CDS with reciprocal best-hits but low expect values. This analysis was performed using the L. interrogans serovar Copenhageni strain Fiocruz, L. borgpetersenii serovar Hardjo strain L550 and L. biflexa serovar Patoc strain Ames genome sequences. doi:10.1371/journal.pone.0001607.g002

( 1 )Figure 3 .

 13 Figure 3. Synteny plot between the five Leptospira genomes. The line plots were obtained using synteny results between the large CI(A) or small CII(B) chromosomes of L. biflexa serovar Patoc strain Patoc1, L. interrogans serovar Lai strain 56601, L. interrogans serovar Copenhageni strain Fiocruz L1-130, L. borgpetersenii serovar Hardjo strain L550, and L. borgpetersenii serovar Hardjo strain JB197. A line plot (C) compares synteny between L. borgpetersenii serovar Hardjo strain JB197 and L. interrogans serovar Copenhageni strain Fiocruz L1-130. Comparative analysis was performed using the MaGe interface[START_REF] Bocs | AMIGene: Annotation of MIcrobial Genes[END_REF] in the SpiroScope database (https://www.genoscope.cns.fr/agc/mage). The minimum size of the synteny groups is set to five genes. In green: synteny groups are organized on the same strand; in red: synteny groups are organized on opposite strands. doi:10.1371/journal.pone.0001607.g003

  Found at: doi:10.1371/journal.pone.0001607.s001 (0.05 MB DOC)

Table 1 .

 1 Summary of genome features of pathogenic and saprophytic Leptospira

	Features	¥ L. borgpetersenii	¥ L. interrogans		¥ L. biflexa
		CI	CII	CI	CII	CI	CII	P74	LE-1 prophage b
	Size (bp)	3,614,456	317,335	4,277,185	350,181	3,603,977	277,995	74,116	73,623
	G+C content (%)	41.0	41.2	35.1	35.0	38.9	39.3	37.5	38.5
	Protein-coding percentage	80	80	74.9	75.5	92.3	93.3	90.9	93.4
	Protein coding sequences
	CDS a	2,607	237	3,105	274	3,268	266	56	82
	With assigned function	1,644	135	1,817	159	2,042	141	31	19
	Conserved hypothetical	373	32	484	34	464	43	5	2
	Unique hypothetical	590	70	804	81	762	82	20	61
	Transposases	215	26	26	0	8	1	1	0
	Pseudogenes	340	28	38	3	32	1	0	0
	Transfer RNA genes	3 7	0	3 7	0	3 5	0	0	0
	Ribosomal RNA genes
	2 3 S	2	0	2	0	2	0	0	0
	1 6 S	2	0	2	0	2	0	0	0
	5 S	1	0	1	0	2	0	0	0

¥ L. borgpetersenii serovar Hardjo strain L550, L. interrogans serovar Copenhageni strain Fiocruz, L. biflexa serovar Patoc strain Ames a excluding transposases and pseudogenes b [11,38] doi:10.1371/journal.pone.0001607.t001 Table 2. CDS from Replicon III (p74) that have an ortholog in Chromosome I in other Leptospira GGDEF domain receiver component of a two-component response regulator * Ortholog found on Chromosome II or Chromosome I in other Leptospira. doi:10.1371/journal.pone.0001607.t002

Table 3 .

 3 Distribution of the orthologs over the two chromosomes of Leptospira spp.

	L. biflexa strain	L. interrogans strain	L. interrogans strain	L. borgpetersenii	L. borgpetersenii
	Patoc1	Fiocuz L1-139	Lai 56601	strain L550	strain JB197

No od CDS shared between C1 replicons (1) 1411 (41.58%) 1429 (39.13%) 1429 (37.41%) 1482 (38.73%) 1448(38.20%) No of CDS shared between CII replicons (2 80 (28.46%) 83 (27.66%) 83 (26.17%) 82 (24.47%) 82 (25.07%)

Table 4 .

 4 Comparative genomics of Leptospira spp. Putative orthologous relations between two genomes are defined as gene couples satisfying the bi-directional best hit (BBH) criterion or a blastP alignment threshold, a minimum of 40% sequence identity on 80% of the length of the smallest protein. Putative paralogous relations between two genomes are defined as gene couples satisfying the bi-directional best hit (BBH) criterion or a blastP alignment threshold, a minimum of 60% sequence identity on 80% of the length of the smallest protein.

		L biflexa strain	L. interrogans strain	L. borgpetersenii strain	L. borgpetersenii strain	L. interrogans strain
	Paralogs/orthologs	Patoc 1	Fiocruiz L1-130	L550	JB197	Lai 56601
	L biflexa strain Patoc 1	62 (1.5%)	1650 (44.04%)	1635 (43.64%)	1631 (43.53%)	1652 (44.10%
	L. interrogans strain Fiocruiz L1-130 1633 (40.35%)	203 (5.01%)	2913 (71.97%)	2907 (71.83%)	3745 (92.53%)
	L. borgpetersenii strain L550	1674 (40.23%)	3084 (74.11%)	438 (10.52%)	3936 (94.59%)	3077 (73.94%)
	L. borgpetersenii strain JB197	1636 (39.73%)	3052 (74.13%)	3922 (95.26%)	354 (8.59%)	3044 (73.93%)
	L. interrogans strain Lai 56601	1638 (39.60%)	3778 (91.34%)	2942 (71.13%)	2934 (70.93%)	204 (4.93%)
	doi:10.1371/journal.pone.0001607.t004

Table 5 .

 5 Distribution of general protein functions between leptospiral species based on the COG function classification scheme. § Each COG assignment has been manually curated to ensure consistent classification across orthologous proteins. A feature of the COG scheme is that some COGs have multiple functional classifications. serovar Hardjo strain L550, L. interrogans serovar Copenhageni strain Fiocruz, L. biflexa serovar Patoc strain Ames doi:10.1371/journal.pone.0001607.t005

	COG Function Classification	¥ L. biflexa	¥ L. borgpetersenii	¥ L. interrogans
	INFORMATION STORAGE AND PROCESSING
	J	Translation, ribosomal structure and biogenesis	154	174	153
	K	Transcription	166	104	109
	L	Replication, recombination and repair	94	91	102
	B	Chromatin structure and dynamics	2	2	2
	CELLULAR PROCESSES AND SIGNALING
	D	Cell cycle control, cell division, chromosome partitioning	21	22	22
	V	Defense mechanisms	39	32	37
	T	Signal transduction mechanisms	287	167	214
	M	Cell wall/membrane/envelope biogenesis	230	199	218
	N	Cell motility	93	84	89
	U	Intracellular trafficking, secretion, and vesicular transport	71	73	71
	O	Posttranslational modification, protein turnover, chaperones	105	96	100
	METABOLISM
	C	Energy production and conversion	132	115	119
	G	Carbohydrate transport and metabolism	91	76	91
	E	Amino acid transport and metabolism	163	136	150
	F	Nucleotide transport and metabolism	46	52	52
	H	Coenzyme transport and metabolism	119	112	120
	I	Lipid transport and metabolism	101	83	99
	P	Inorganic ion transport and metabolism	120	72	88
	Q	Secondary metabolites biosynthesis, transport and catabolism	35	23	27
	POORLY CHARACTERIZED
	R	General function prediction only	311	237	294
	S	Function unknown	174	157	192
		CDS Not Classified (not related to any COG)	1,266	931	1,245
		Total CDS (count excludes transposases and pseudogenes)	3,590	2,843	3,378
	§

¥

L. borgpetersenii

Table S1

 S1 Supplementary Table 1 a, b and c Found at: doi:10.1371/journal.pone.0001607.s002 (0.46 MB XLS)

PLoS ONE | www.plosone.org

February 2008 | Volume 3 | Issue 2 | e1607

Acknowledgments

We thank David Alt, Richard Hornsby, A. Magnier and A. Blanchard for technical support.

This work was supported by the following: National Health and Medical Research Council, Australia; Australian Research Council; U.S. Department of Agriculture; Institut Pasteur, Paris, France; French Ministry of Research ANR Jeunes Chercheurs (no. 05-JCJC-0105-01); Consortium National de Recherche en Ge ´nomique (no. RNG-20040057); ACI IMPBio 2004 (MicroScope project). Funders had no role in the planning, performance or analysis of the work.

Author Contributions