A De Lataillade

S Blanco

Y Clergent

J L Dufresne

M El Haÿ

R Fournier

Monte Carlo method and sensitivity estimations

Keywords:

It is shown that, starting from any existing Monte Carlo algorithm for estimation of a physical quantity A, it is possible to implement a simple additional procedure that simultaneously estimates the sensitivity of A to any problem parameter. The corresponding supplementary cost is very low as no additional random sampling is required. The principle is presented on a formal basis and simple radiative transfer examples are used for illustration.

Introduction

Monte Carlo methods are commonly used for the simulation of various transport phenomena [START_REF] Hammersley | Monte Carlo methods[END_REF][START_REF] Howell | Application of Monte Carlo to heat transfer problems[END_REF][START_REF] Mackeown | Stochastic simulation in physics[END_REF]. The term Monte Carlo is, however, used to cover such a wide range of distinct statistical approaches that it is always a source of ambiguity to address any Monte Carlo methodology on a general basis. In the present paper, we restrict the analysis to methods that may be shown to rely on the generic Monte Carlo algorithm for the estimation of multiple integrals.

We address the question of estimating parametric sensitivities with Monte Carlo algorithms. Parametric sensitivity estimates are required in numerous physical contexts [START_REF] Tomovic | Sensitivity analysis of dynamic systems[END_REF][START_REF] Beck | Parameter estimation in engineering and science[END_REF], in particular that of inverse radiative transfer problems as a basis for numerous retrieval algorithms [START_REF] Rodgers | Inverse methods for atmospheric sounding[END_REF][START_REF] Spurr | A linearized discrete ordinate radiative transfer model for atmospheric remote sensing retrieval[END_REF]. For our purposes, sensitivities are mainly considered as a way of deriving ÿrst-order radiative transfer models for unstationary coupling with other complex phenomena such as natural convection [START_REF] Clergent | uence du Rayonnement Thermique sur les Ecoulements de Convection Naturelle en Espace Conÿnà e[END_REF] or chemical reactions in combustion systems [START_REF] De Guilhem De Lataillade | Modà elisation dà etaillà ee des transferts radiatifs et couplage avec la cinà etique chimique dans des syst emes en combustion[END_REF]. In such contexts, the Monte Carlo method is of particular interest because of its ability to deal with complex geometries and=or complex spectral properties [START_REF] Cherkaoui | Monte Carlo simulation of radiation in gases with a narrow-band model and a net-exchange formulation[END_REF][START_REF] Cherkaoui | Radiative net exchange formulation within one dimensional gas enclosures with re ective surfaces[END_REF]. To our knowledge, the question of computing corresponding parametric sensitivities has not yet been addressed.

We ÿrst show that low-cost sensitivity computations can be easily associated with Monte Carlo methods, provided that the underlying integral formulation is explicit. This is seldom the case, however, for good reason, as we illustrate with a simple radiative transfer problem. The central aim of the paper is then to show how this problem may be e ectively bypassed, making possible the computation of non-trivial sensitivity examples.

Principle (1)

Let us brie y recall the Monte Carlo algorithm in order to deÿne the vocabulary and notation. If A is the integral (to be computed) of a function f over a multiple dimension domain D, the ÿrst step is to introduce arbitrarily a non-zero probability density function p over D and to formulate A as the expectation of W = f(X )=p(X ) where X is a random variable distributed according to p:

A = D f(x) dx = D f(x) p(x) p(x) dx = E f(X ) p(X ) = E(W ): (1)
The second step is to sample numerically a large number, N , of realizations x 1 ; x 2 ; : : : ; x N of the random variable X , that is to say according to the arbitrarily chosen probability density function p.

Then, for each realization x i , the so-called Monte Carlo weight w i = f(x i )=p(x i ) is computed and the corresponding average value is retained for numerical estimation of A (see Appendix):

A ≈ 1 N N i=1 w i : (2)
Once presented this way, the question of implementing sensitivity estimations inside Monte Carlo algorithms is of no particular subtlety. If the function f to be integrated now depends on any parameter , the sensitivity of A to , noted @ A hereafter, may be expressed as

@ A = D @ f(x; ) dx = D @ f(x; ) p(x) p(x) dx = E @ f(X ; ) p(X ) = E(@ W ) (3)
and then estimated as

@ A ≈ 1 N N i=1 @ w i : (4)
This means that for any Monte Carlo algorithm inside the above-described family, where Monte Carlo weights are computed analytically on the basis of randomly generated variables, sensitivity estimations may be performed by computing the weight sensitivities and taking the average. This operation generally represents a very low additional cost because no further sampling is required (the same set of random generations is used for sensitivity estimations as for integral estimation). Fig. 1 proposes a schematic representation of this simple way of associating sensitivity estimations to most standard Monte Carlo algorithms. The ÿrst conceptual di culty is that for most Monte Carlo algorithms the underlying integral formulation is not explicit. The reason is to be found in what is commonly considered as the main quality of Monte Carlo algorithms: they preserve strong analogies with the involved physics. This means that a Monte Carlo algorithm may be successfully designed and implemented by reproducing physical statistical events one after another, without requiring any complete mathematical translation. We consider below a simple radiative transfer example for illustration.

Example (1)

Consider the surface radiative power emitted by a blackbody and absorbed by an adjacent plane parallel to uniform slab of gray absorbing material of thickness z (see Fig. 2). The blackbody temperature is denoted by T and the slab absorption coe cient by k. The addressed problem is hereafter to compute the sensitivity to k of this absorbed power.

Classically, the design of a corresponding Monte Carlo algorithm would strictly follow available statistical models of photon emission and photon transport. For instance, the surface ux emitted by the blackbody, T 4 , is split into N bundles of power T 4 =N and for each bundle an emission direction ũ is randomly generated according to the well-known distribution of blackbody-emission directions (Lambert law): p ; e (ũ)=ũñ= where the vector ñ is normal to the slab. Then the bundle is followed along a straight line through the absorbing layer, with an exponential extinction to represent absorption, and when leaving the layer the remaining bundle-power is ( T 4 =N ) exp(-kz=cos(Â)) where  is the angle between the emission direction and the normal. (

T 4 =N )[1 -exp(-kz=cos(Â))]
is therefore the bundle-power that was absorbed by the slab.

From these random angular generations, the absorbed ux is simply estimated as the sum of all the absorbed fractions:

A ≈ N i=1 T 4 N 1 -exp - kz cos(Â i ) : (5)
No formal integral expression is required to produce this algorithm. It is, however, very easy to identify the Monte Carlo weight as w(Â) = T 4 [1 -exp(-kz=cos(Â)] and the sensitivity of A to the parameter k may therefore be estimated as

@ k A ≈ 1 N N i=1 @ k w i with @ k w i = z T 4 cos(Â i ) exp - kz cos(Â i ) : (6)

Principle (2)

From this example, it could be concluded that sensitivity estimations within existing Monte Carlo algorithms are trivial to implement even if the formal integration is not explicit: (1) identifying the Monte Carlo weight expression, and (2) deriving it as a function of the considered parameter and taking the average. This is true only if the probability density function used for random generations is independent of the parameter (note that in Eq. ( 3) the probability density function p(x) has no parametric dependence on ). In our ÿrst example, this was the case as the directional probability density function was independent of the absorption coe cient.

In the general case, the probability density function p chosen for random sampling of x 1 ; x 2 ; : : : ; x N may depend on the considered parameter (see Fig. 1). Let us therefore consider that a given Monte Carlo algorithm is available, without the corresponding integral (which can be cumbersome for multiple dimension problems as will be illustrated below), and that sensitivity estimations are required. All we know is that the addressed quantity A is estimated as the average of a Monte Carlo weight W that is a function of a random variable X . The probability density function has a parametric dependence on . We may formally write A = D w(x; )p(x; ) dx [START_REF] Spurr | A linearized discrete ordinate radiative transfer model for atmospheric remote sensing retrieval[END_REF] and the sensitivity of A to is

@ A = D [@ w(x; )p(x; ) + w(x; )@ p(x; )] d x = D @ w(x; ) + w(x; ) @ p(x; ) p(x; ) p(x; ) dx = E @ W + W @ p(X ; ) p(X ; ) : (8)
It appears that a correction term is required in comparison with the simple case of an insensitive probability density function

@ A ≈ 1 N N i=1 @ w i + w i @ p(x i ; ) p(x i ; ) : (9)
Implementing a sensitivity estimation inside any existing Monte Carlo algorithm is therefore a source of no practical di culty, as all the information required for Eq. ( 9) is accessible by simple analysis of the considered original algorithm.

Example (2)

To illustrate such a practical implementation, let us reconsider the preceding example, the layer being now both absorbing (absorption coe cient k a ) and scattering (scattering coe cient k s ). An example of the application of standard Monte Carlo algorithms consists of emitting bundles at the source and following them until they exit the layer by a random walk corresponding to the pure di usion assumption [START_REF] Hammersley | Monte Carlo methods[END_REF]. The traveled length before exit is then used to compute the extinction of the bundle-power according to the pure-absorption exponential extinction. As before, the algorithm starts with the random sampling of an emission direction ũ 1 for each of the N bundles of initial power T 4 =N . Then a scattering path length 1 is sampled according to an exponential distribution on ]0; +∞[ : p ( 1 ; k s ) = k s exp(-k s 1 ). This path length is used, starting at the emission point in the direction ũ 1 , to deÿne a ÿrst scattering location P 1 (see Fig. 3). If P 1 is outside the layer, the length l to the layer exit is used to compute the fraction of the bundle-power that is absorbed within the slab as ( T 4 =N )[1 -exp(-k a l)]. If P 1 is inside the layer, a scattering direction ũ 2 is sampled according to the scattering phase function: p ; s (ũ 2 ;ũ 1 ). A new scattering path length 2 is then sampled and from P 1 in the direction ũ 2 the next scattering location P 2 can be deÿned, etc. As before, when the bundle ÿnally leaves the layer (either transmitted or re ected), the fraction of its initial power that was absorbed within the slab is computed as ( T 4 =N )[1 -exp(-k a l)] where l is now the total length of the multi-di usion path.

This algorithm is quite simple in the sense that it is physically intuitable, but the underlying integral formulation is cumbersome as there is no limit to the number of possible scattering events before exit. This means that the vector x of all sampling events required for Monte Carlo weight computation is formally of inÿnite dimension:

x = (ũ 1 ; 1 ;ũ 2 ; 2 ;ũ 3 ; 3 ; : : :):

Practically speaking, however, Eq. ( 9) may be used directly without entering this formalization exercise. First, the Monte Carlo weight is without ambiguity

w(x; k a ) = T 4 [1 -exp(-k a l)] (11)
and the probability density function of any bundle path with n scattering events before the layer exit is the product of successive emission and scattering probability density functions: p(x; k s ) = p ; e (ũ 1 )p ( 1 ; k s )p ; s (ũ 2 ;ũ 1 )p ( 2 ; k s ) p ; s (ũ 3 ;ũ 2 ) : : : p ; s (ũ n ;ũ n-1 )p ( n ; k s ); [START_REF] Goody | Atmospheric radiation[END_REF] where p ; e (ũ 1 ) is the angular probability density function of the emission direction ũ 1 ; p ( j ; k s ) is the probability density function of the scattering mean free path at the jth scattering event, and p ; s (ũ j ;ũ j-1 ) is the angular probability density function of the jth scattering direction ũ j knowing that the incident direction was ũ j-1 .

For estimation of the sensitivities to the absorption coe cient, we follow the same conditions as in the preceding example: the sampling probability density functions are independent of k a and Eq. ( 9) can be used with

@ k a w(x; k a ) = l T 4 exp(-k a l) (13)
and @ k a p(x; k s ) p(x; k s ) = 0: (14)

For estimation of the sensitivities to the scattering coe cient, they are the contrary to the sensitivities of the absorption coe cient: the Monte Carlo weight is insensitive to k s and therefore only the Fig. 4. Fraction of the surfacic ux (A) emitted by a blackbody that is absorbed by an adjacent, uniform, isotropically scattering slab of thickness z, absorption coe cient k a and scattering coe cient k s . The absorption optical thickness k a z is ÿxed to unity and the scattering optical thickness k s z is varied from 0 (which corresponds to Section 3) to 100. Absorbed fractions (+) correspond to the right axis, whereas the sensitivities to k a ( * ) and k s (x) correspond to the left axis.

correction term remains:

@ k s w(x; k a ) = 0 (15)
and thanks to logarithmic derivations, using the fact that p ; e and p ; s are independent of k s , @ k s p(x; k s ) p(x; k s ) = @ k s p ; e (ũ 1 ) p ; e (ũ 1 ) + @ k s p ( 1 ; k s ) p ( 1 ; k s ) + @ k s p ; s (ũ 2 ;ũ 1 ) p ; s (ũ 2 ;ũ 1 )

+ • • • = n j=1 1 k s -j = n k s - n j=1 j : (16)
Fig. 4 1 displays results obtained for both sensitivities with a strict application of Eq. ( 9) for a case of isotropic scattering using 10 6 bundle generations.

The same methodology may be used, in the case of anisotropic scattering, to compute sensitivities to the parameters of the scattering phase function. Sensitivities to the asymmetry factor g are displayed in Fig. 5 2 using a Henyey-Greenstein phase function [START_REF] Goody | Atmospheric radiation[END_REF]. According to this phase function model, cosine of the angle between the incident and scattering directions is distributed according 1 For a ÿxed value of the absorption coe cient, the absorbed ux decreases with increasing scattering coe cient. The reason is that when k s increases, more photons are re ected after very short distances. @ k s A is therefore negative. The fact that the sensitivity of the absorbed ux to k a is positive is trivial. Its decrease with increasing k s may be explained by considering again the fact that when k s increases more photons are re ected after very short distances, reducing the possibility of absorption.

2 A simple physical interpretation of these results may be obtained by considering the medium reduced scattering coe cient k ′ s = (1 -g)k s that allows the establishment of an approximate equivalence between an anisotropically scattering medium and an isotropically scattering medium with a lower scattering coe cient: increasing g at constant k s can be seen as equivalent to decreasing k ′ s in an isotropically scattering medium. The physical interpretations proposed for Fig. 4 can therefore be directly translated for interpretating the increase of A with increasing g in the present ÿgure. A / T 4 g Fig. 5. Fraction of the surfacic ux emitted by a blackbody that is absorbed by an adjacent, uniform, anisotropically scattering slab of thickness z, absorption coe cient k a and scattering coe cient k s . Absorption optical thickness k a z and scattering optical thickness k s z are ÿxed to unity. Anisotropic phase functions are represented with Henyey-Greenstein model and the asymmetry factor g is varied from 0 (isotropic scattering) to 1 (forward scattering). Absorbed fractions (+) correspond to the right axis, whereas the sensitivities to g( * ) correspond to the left axis. Error bars correspond to the estimated standard deviation of the Monte Carlo estimate.

to the probability density function (at the jth scattering event) p M ( j ; g)= 1 2 (1-g 2 )=(1+g 2 -2g j ) 3=2 where j =cos( j )=ũ j+1 •ũ j . The limit g=1 corresponds to the pure forward-scattering case, g=-1 to the pure backward-scattering case, and g = 0 to isotropic scattering. The sampling probability density function p(x; k s ; g) now exhibits both sensitivities to k s and g with @ g p(x; k s ; g) p(x; k s ; g)

= n-1 j=1 g 3 -5g + g 2 j -3 j (1 -g 2 )(g 2 + 1 -2g j ) : (17)
The Monte Carlo weight is insensitive to g and therefore @ g w(x; k a ) = 0 (18)

and the last two expressions can be used in conjunction with Eq. ( 9) to produce sensitivities to the phase function parameter g as illustrated in Fig. 5. Note 1. On these last simulation results, one may note that the ux and its sensitivity to g are associated with very distinct statistical relative uncertainties. As a matter of fact, for g close to 1, Monte Carlo computation of sensitivities to g is unpractical. Generally speaking, the reason is that the Monte Carlo weights corresponding to A and @ A may have very distinct statistical distributions (see appendix). In such extreme cases, it may be impossible to optimize the sampling probability density functions for simultaneous e cient computation of the addressed quantity, on the one hand, and its sensitivities, on the other hand.

Note 2. Another parametric study concerning this physical problem could be to analyze sensitivities to the slab thickness z. On the basis of Eqs. [START_REF] Cherkaoui | Radiative net exchange formulation within one dimensional gas enclosures with re ective surfaces[END_REF] and [START_REF] Goody | Atmospheric radiation[END_REF], one could be led to estimate that both the Monte Carlo weight and the sampling probability density function are insensitive to z. The conclusion would be that slab absorption is insensitive to slab thickness, which is an obvious nonsense. The reason is that the space of all possible optical paths changes with slab thickness. Generally speaking, if the integration domain D depends on the considered parameter , Eqs. ( 3) and ( 8) are incorrect because the partial derivation may not be reported inside the integral. In such cases, reformulation exercises may be required and the main interest of the simple above-presented methodology (low-cost implementation of sensitivity procedures) is lost.

Conclusion

Our purpose was to show that sensitivity estimations are easy to implement in most Monte Carlo algorithms, provided that they are based on an underlying multiple integral formulation, even if this formulation is not explicit. We used radiative transfer examples for illustration but this approach can be extended to a wider range of applications. If the sampling pdfs are independent of the considered parameter, it is su cient simply to compute the sensitivity of the Monte Carlo weight and take the average. If the sampling pdfs do depend on the considered parameter, a correction term must be added that is simply the product of the Monte Carlo weight with the logarithmic derivative of the sampling pdf (or the sum of the logarithmic derivative of the pdfs of the successive sampling events).

Appendix. Statistical uncertainties

The numerical behavior of a Monte Carlo algorithm is commonly appreciated referring to the standard deviation of the estimator. With the notations of Section 4, A= D f(x; ) dx= D w(x; )p(x; ) dx is estimated with any realization of the random variable S deÿned as the average of N independent realizations of W

A ≃ s = 1 N N i=1 w i :
The standard deviation of S is related to the standard deviation of W according to

S = 1 √ N W :
Similarly for the sensitivity @ A, the estimation is made with any realization of the random variable R deÿned as the average of N independent realizations of

V @ A ≃ r = 1 N N i=1 v i
with v i = @ w(x i ; ) + w(x i ; ) @ p(x i ; ) p(x i ; ) :

The standard deviation of R is related to the standard deviation of V according to

R = 1 √ N V :
Both S as R tend to zero when increasing N to inÿnity, which ensures the convergence of the Monte Carlo algorithm, but the convergence speed is entirely driven by the values of W and V , respectively. The choice of the sampling probability density function p is therefore essential to ensure fast convergence (small number of required sampling events) as it ÿxes the distributions of the Monte Carlo weights W and V . One of the advantages of the presented methodology is that the same sampling events may be used both for estimation of A and @ A. The same sampling probability density function p must therefore be used for W and V . Consequently, the question arises of the possibility that p be adjusted in such a way that both W and V are satisfactory.

There is no systematic answer to this question. Generally speaking, detailed understanding of the physical processes at work allows successful optimization of the integral evaluation [START_REF] De Lataillade | A net exchange Monte Carlo approach to radiation in optically thick systems[END_REF]. This does not necessarily ensure that the sensitivity estimation is optimized. For problems in which the sensitivity estimation is essential, similar physical reasoning may be concentrated on the sensitivity itself. But as illustrated in the following example, there is no mathematical constraint relating the statistics of W and V .

Consider the case where the function to be integrated is

f(x; ) = + g(x);
where is a constant and g is any function of x independent of the parameter . In the particular case = 0; f becomes independent of x. If p is taken as uniform on D; w(x; 0) = f(x; 0)=p is independent of x and therefore W = 0. This corresponds to an ideal optimization of A estimate. Correspondingly, v(x; 0) = g(x)=p and the standard deviation V can take any value depending on g.

Fig. 1 .

 1 Fig. 1. Schematic representation of a Monte Carlo algorithm for estimation of an integral A together with its sensitivity to a parameter .

Fig. 2 .

 2 Fig. 2. One-dimensional slab geometry for Example (1): pure absorption (no scattering).

Fig. 3 .

 3 Fig. 3. One-dimensional slab geometry for Example (2): absorption and scattering.


S Romano-Bertrand
email: sara.romano-bertrand@univ-montp1.fr

M Beretta

H Jean-Pierre

J.-M Frapier

B Calvet

S Parer

E Jumas-Bilak

: H Jean-Pierre

Propionibacterium acnes populations involved in deep pathological samples and their dynamics along the cardiac surgical pathway

Propionibacterium acnes belongs to the normal skin microbiota, but it is also responsible for acne vulgaris and causes serious infections such as endocarditis and surgical site infections (SSI). The P. acnes population is structured into phylogenetic groups, with phylotype I being associated with acne. Herein, we explore the link between phylotypes and clinical origins in a collection of P. acnes isolated from different body sites, involved in deep infections or healthcareassociated infections (HAI), with particular emphasis on strains from cardiac SSI. Cardiac SSI have been further studied in terms of P. acnes population dynamics during the care pathway. The recA and tly genes phylotypes were compared to hemolytic behavior, susceptibility to antimicrobial agents, and clinical origins. An original approach of recA polymerase chain reaction temporal temperature gel electrophoresis (PCR-TTGE) was developed and applied for the direct identification of P. acnes phylotypes in surgical samples, in order to assess their temporal dynamics during the surgical course. Our results underlined the preferential involvement of IA-2/IB and II phylogroups in HAI and SSI. Unlike IA and II, type IA-2/IB presented a gradual increase with the depth of sampling in the peroperative phase of cardiac surgery. Phylotypes IA and IA-2/IB were both predominant in scar tissues and on postoperative skin, suggesting a specific predisposition to recolonize skin. Particular association of the phylotype IA-2/ IB with SSI and its propensity to colonize wounds in cardiac surgery was observed. We assumed that the follow-up of P. acnes phylotypes during pathological processes could give new clues for P. acnes pathogenicity.

Introduction

Propionibacterium acnes is an anaerobic Gram-positive bacillus member of the human microbiota mainly on skin [START_REF] Delgado | Identification, typing and characterisation of Propionibacterium strains from healthy mucosa of the human stomach[END_REF], but also in the oral cavity, and digestive and genital tracts [START_REF] Whitman | Bergey's manual of systematic bacteriology: volume 5: the actinobacteria[END_REF]. In clinical samples, P. acnes is often overlooked as a contaminant and is underestimated due to its growth requirements [START_REF] Kunishima | Presence of Propionibacterium acnes in blood components[END_REF][START_REF] Brüggemann | Insights in the pathogenic potential of Propionibacterium acnes from its complete genome[END_REF][START_REF] Qin | Propionibacterium acnes induces IL-1β secretion via the NLRP3 inflammasome in human monocytes[END_REF]. However, P. acnes can produce putative virulence factors involved in inflammation processes [START_REF] Brüggemann | Insights in the pathogenic potential of Propionibacterium acnes from its complete genome[END_REF], as observed in acne vulgaris [START_REF] Qin | Propionibacterium acnes induces IL-1β secretion via the NLRP3 inflammasome in human monocytes[END_REF] and other inflammatory pathologies, such as sarcoidosis [START_REF] Eishi | Etiologic link between sarcoidosis and Propionibacterium acnes[END_REF], or potentially in prostatic pathologies [START_REF] Hrbacek | Thirty years of research on infection and prostate cancer: no conclusive evidence for a link. A systematic review[END_REF]. P. acnes can also cause severe deep infections like endocarditis [START_REF] Noel | Pacemaker endocarditis caused by Propionibacterium acnes: a case report[END_REF][START_REF] Pan | Endocarditis caused by Propionibacterium acnes: an easily ignored pathogen[END_REF][START_REF] Zedtwitz-Liebenstein | Pacemaker endocarditis due to Propionibacterium acnes[END_REF] and surgical site infections (SSI) in orthopedic [START_REF] Sampedro | Species of Propionibacterium and Propionibacterium acnes phylotypes associated with orthopedic implants[END_REF][START_REF] Berthelot | Outbreak of postoperative shoulder arthritis due to Propionibacterium acnes infection in nondebilitated patients[END_REF], cardiac [START_REF] Unemo | Genetic homogeneity/heterogeneity of Propionibacterium acnes isolated from patients during cardiothoracic reoperation[END_REF][START_REF] Jakab | Severe infections caused by Propionibacterium acnes: an underestimated pathogen in late postoperative infections[END_REF], or neurological surgeries [START_REF] Sampedro | A biofilm approach to detect bacteria on removed spinal implants[END_REF].

Metagenomics [START_REF] Fitz-Gibbon | Propionibacterium acnes strain populations in the human skin microbiome associated with acne[END_REF] and comparative genomics [START_REF] Tomida | Pan-genome and comparative genome analyses of Propionibacterium acnes reveal its genomic diversity in the healthy and diseased human skin microbiome[END_REF] showed strain variations supporting the existence of specific P. acnes subpopulations. The strain HL096PA1 causing severe acne displayed a plasmid encoding adhesion factors and a high amount of pseudogenes, suggesting its adaptation to pathogenic behavior in a narrow niche [START_REF] Kasimatis | Analysis of complete genomes of Propionibacterium acnes reveals a novel plasmid and increased pseudogenes in an acne associated strain[END_REF]. Moreover, population genetics indicated the roles of distinct lineages of P. acnes in different diseases. In this context, several multilocus sequence typing (MLST) schemes, including from 3 to 9 loci according to studies, were proposed. They identified three main distinct phylotypes, named I, II, and III [START_REF] Davidsson | Multilocus sequence typing and repetitivesequence-based PCR (DiversiLab) for molecular epidemiological characterization of Propionibacterium acnes isolates of heterogeneous origin[END_REF][START_REF] Kilian | Multilocus sequence typing and phylogenetic analysis of Propionibacterium acnes[END_REF][START_REF] Mcdowell | A novel multilocus sequence typing scheme for the opportunistic pathogen Propionibacterium acnes and characterization of type I cell surface-associated antigens[END_REF][START_REF] Lomholt | Population genetic analysis of Propionibacterium acnes identifies a subpopulation and epidemic clones associated with acne[END_REF][START_REF] Mcdowell | A new phylogenetic group of Propionibacterium acnes[END_REF]. Phylotype I is subdivided into groups IA (subdivided into IA-1 and IA-2), IB, and IC [START_REF] Mcdowell | A new phylogenetic group of Propionibacterium acnes[END_REF][START_REF] Niazi | Propionibacterium acnes and Staphylococcus epidermidis isolated from refractory endodontic lesions are opportunistic pathogens[END_REF], but recombination events occur between IA-2 and IB groups, leading to misidentification of these subtypes [START_REF] Mcdowell | An expanded multilocus sequence typing scheme for Propionibacterium acnes: investigation of 'pathogenic', 'commensal' and antibiotic resistant strains[END_REF]. The genes recA (recombinase A) and tly (putative hemolysin) were widely used in MLST schemes because they presented satisfactory discriminative power among the three phylotypes I, II, and III [START_REF] Mcdowell | A new phylogenetic group of Propionibacterium acnes[END_REF][START_REF] Mcdowell | Propionibacterium acnes types I and II represent phylogenetically distinct groups[END_REF]. The association of recA and tly allowed the identification of IA-1 but not the separation of IA-2 from IB [START_REF] Mcdowell | An expanded multilocus sequence typing scheme for Propionibacterium acnes: investigation of 'pathogenic', 'commensal' and antibiotic resistant strains[END_REF]. Moreover, recA structuration is correlated to antigens, cell wall sugar, and matrix-assisted laser desorption/ionization time-of-flight (MALDI-TOF) types [START_REF] Nagy | MALDI-TOF MS fingerprinting facilitates rapid discrimination of phylotypes I, II and III of Propionibacterium acnes[END_REF].

Phylotype I appeared to be the most prevalent in the whole population of P. acnes and gathered mainly isolates from acne and healthy skin [START_REF] Mcdowell | A new phylogenetic group of Propionibacterium acnes[END_REF][START_REF] Niazi | Propionibacterium acnes and Staphylococcus epidermidis isolated from refractory endodontic lesions are opportunistic pathogens[END_REF]. Division IA comprised the majority of isolates from inflammatory acne lesions [START_REF] Kwon | Analysis of distribution patterns of Propionibacterium acnes phylotypes and Peptostreptococcus species from acne lesions[END_REF]. It included the epidemic clone ST18 (=eST1) and its descendants in the IA-1 group [START_REF] Lomholt | Population genetic analysis of Propionibacterium acnes identifies a subpopulation and epidemic clones associated with acne[END_REF][START_REF] Mcdowell | An expanded multilocus sequence typing scheme for Propionibacterium acnes: investigation of 'pathogenic', 'commensal' and antibiotic resistant strains[END_REF], which were never detected in healthy skin [START_REF] Kilian | Multilocus sequence typing and phylogenetic analysis of Propionibacterium acnes[END_REF].

Besides phylotype IA and acne, links between genetic group and pathogenic behavior were not fully meaningful. Isolates of phylotypes II and III were described as originating mainly from healthcare-associated infections (HAI) [START_REF] Davidsson | Multilocus sequence typing and repetitivesequence-based PCR (DiversiLab) for molecular epidemiological characterization of Propionibacterium acnes isolates of heterogeneous origin[END_REF], but this association was not exclusive because type I strains were also involved in HAI [START_REF] Kilian | Multilocus sequence typing and phylogenetic analysis of Propionibacterium acnes[END_REF]. Types IB and II were often encountered in prostatectomy specimens from cancer [START_REF] Mak | Multilocus sequence typing (MLST) analysis of Propionibacterium acnes isolates from radical prostatectomy specimens[END_REF], without prediction of infection or disease [START_REF] Shannon | Polymerase chain reaction-based identification of Propionibacterium acnes types isolated from the male urinary tract: evaluation of adolescents, normal adults and men with prostatic pathology[END_REF]. Similarly, phylotypes IB and II were often detected during revising prosthetic surgeries, but their presence did not differentiate infection from colonization [START_REF] Sampedro | Species of Propionibacterium and Propionibacterium acnes phylotypes associated with orthopedic implants[END_REF]. Despite an unclear association between a particular genetic group and a specific pathogenic behavior in some cases, the published data lend support to the view that pathogenic versus truly commensal lineages of P. acnes may exist [START_REF] Mcdowell | An expanded multilocus sequence typing scheme for Propionibacterium acnes: investigation of 'pathogenic', 'commensal' and antibiotic resistant strains[END_REF]. The determination of relationships between lineages and infections is likely to have important therapeutic and diagnostic implications [START_REF] Mcdowell | An expanded multilocus sequence typing scheme for Propionibacterium acnes: investigation of 'pathogenic', 'commensal' and antibiotic resistant strains[END_REF].

In cardiac surgery, P. acnes is the third most prevalent bacterium in deep SSI [START_REF] Unemo | Genetic homogeneity/heterogeneity of Propionibacterium acnes isolated from patients during cardiothoracic reoperation[END_REF][START_REF] Romano-Bertrand | Temporal temperature gel electrophoresis to survey pathogenic bacterial communities: the case of surgical site infections[END_REF][START_REF] Tammelin | Mediastinitis after cardiac surgery: improvement of bacteriological diagnosis by use of multiple tissue samples and strain typing[END_REF], making it important to consider. A previous study based on universal 16S polymerase chain reaction temporal temperature gel electrophoresis (PCR-TTGE) describing the dynamic of bacterial communities in c a r d i a c s u rg e r y w o u n d s s h o w e d h i g h r a t e s o f Propionibacterium spp. at different stages of patients' hospitalization [START_REF] Romano-Bertrand | Temporal temperature gel electrophoresis to survey pathogenic bacterial communities: the case of surgical site infections[END_REF]. However, no study has yet described the phylotypes involved in cardiac SSI, preventing rare isolates from SSI being included in the currently available MLST studies [START_REF] Davidsson | Multilocus sequence typing and repetitivesequence-based PCR (DiversiLab) for molecular epidemiological characterization of Propionibacterium acnes isolates of heterogeneous origin[END_REF][START_REF] Mcdowell | An expanded multilocus sequence typing scheme for Propionibacterium acnes: investigation of 'pathogenic', 'commensal' and antibiotic resistant strains[END_REF].

The purpose of this study was to explore the links between the main phylotypes based on recA and tly sequencing and clinical origins, hemolytic behavior, and resistance in a collection of P. acnes involved in deep infections or HAI, with particular emphasis on strains from cardiac SSI. Based on the recA phylogeny, an original culture-independent method was applied for the direct identification of P. acnes phylotypes involved in cardiac surgical samples in order to assess their dynamics during the surgical pathway of the patients.

Materials and methods

Propionibacterium acnes isolates, culture conditions, antibiotic susceptibilities, and hemolysis test Ninety-nine P. acnes clinical isolates collected from different infectious sites between May 2011 and March 2013 at the Hospital of Montpellier (France) were analyzed (Table 1). The isolates were included considering at least one of the following criteria: (i) isolation in normally sterile sites, (ii) isolation in deep infectious processes, (iii) antimicrobial assay on the isolate for therapeutic purposes, (iv) prescription of antimicrobials targeted against P. acnes. Among the 99 strains, 27 were isolated from cardiothoracic samples (including 19 from cardiac SSI). Hemolysis tests were performed by culture on nutritive medium supplemented with 5 % sheep blood (COS Agar, bioMérieux, France) at 37 °C in an anaerobic atmosphere. The degree of hemolysis was assessed after 72 h of culture and noted negative if absent, weak if present but light or moderate, and strong if important or total. Antibiotic susceptibilities were tested for cefamandole, vancomycin, and clindamycin by an agar diffusion assay (members of the Société Française de Microbiologie committee, 2003).

Surgical samples and ethic statements

Surgical site samples were obtained from 14 patients undergoing cardiac surgery at the Cardio-thoracic Surgery Unit of Montpellier University Hospital (France). They were collected superficially and deeply at the different steps of hospitalization (before hospitalization, during the surgical procedure, during postoperative hospitalization, and 3 months after discharge). Primary human materials used in this study were collected on sterile cotton swabs as performed for the routine clinical diagnostic process without change in the surgical procedures or nursing care. Each patient included gave oral informed consent. The study proposal was approved by the ethical committee of our institution: Comité de Protection des Personnes Sud Méditerranée IV, N°ID -RCB: 2011-A00078-33.

DNA extraction and PCR amplification

DNA was extracted from colonies or from surgical samples on cotton swabs by an enzymatic method (MasterPure Gram Positive DNA Purification Kit, Epicentre, France) and diluted at a final concentration of 50 ng/μL. The 16S rRNA gene was amplified using the primers HDA1f-HDA2r [START_REF] Romano-Bertrand | Temporal temperature gel electrophoresis to survey pathogenic bacterial communities: the case of surgical site infections[END_REF][START_REF] Saleh | A descriptive study of bacterial load of full-thickness surgical wounds in dermatologic surgery[END_REF]. The recA and tly genes were amplified by the primers PAR-1 (5′-AGCTCGGTGGGGTTCTCTCATC-3′) and PAR-2 (5′-GCTTCCTCATACCACTGGTCATC-3′) and PAT-1 (5′-CAGGACGTGATGGCAATGCGA-3′) and PAT-2 (5′-TCGTTCACAAGACCACAGTAGC-3′), respectively [START_REF] Niazi | Propionibacterium acnes and Staphylococcus epidermidis isolated from refractory endodontic lesions are opportunistic pathogens[END_REF].

A nested PCR approach was needed because of the low bacterial load in surgical samples (<10 3 UFC/tube, assessed by 16S rRNA gene-based PCR as previously described [START_REF] Romano-Bertrand | Temporal temperature gel electrophoresis to survey pathogenic bacterial communities: the case of surgical site infections[END_REF]). The recA nested PCR approach consisted of a preamplification (with primers PAR-1 and PAR-2), followed by a second amplification of a 333-pb fragment overlapping the terminal region of the recA gene, using the primers PR264-GC (corresponding to the primer PR264 5′-GCAGGCAGAGTT TGACATCC-3′ [START_REF] Shannon | Polymerase chain reaction-based identification of Propionibacterium acnes types isolated from the male urinary tract: evaluation of adolescents, normal adults and men with prostatic pathology[END_REF] with a "GC clamp" rich in GC added at the 5-extremity) and PAR-2. The PCR mixture of 50 μL consisted of 1 μL of DNA extract, 200nM of each primer, 200 mM of each dNTP (Fermentas), and 2.5U FastStart Taq DNA Polymerase (Roche, France) in the appropriate reaction buffer containing 1.8 mM MgCl 2 . PCR conditions were an initial denaturation at 94 °C for 3 min, followed by 35 cycles of 95 °C for 1 min, 64 °C for 30 s, and 72 °C for 1 min 30 s, and a final elongation at 72 °C for 10 min.

Sequencing and phylogenetic analyses on recA and tly genes Amplification products were sequenced using both primers PAR-1 and PAR-2 for recA and forward primer PAT-1 for tly on an ABI 3730xl sequencer (Cogenics, France). Sequences were deposited in the GenBank database (accession numbers KJ572580 to KJ572777). Gene sequences were aligned using ClustalW [START_REF] Qin | Propionibacterium acnes induces IL-1β secretion via the NLRP3 inflammasome in human monocytes[END_REF] in order to determine the polymorphic positions. A number was attached to each sequence according to the recA and tly alleles available in the http://pacnes.mlst.net/ and http://pubmlst.org/pacnes/ databases. Phylogenetic trees were constructed based on maximum likelihood (ML) analysis using PhyML software (http://www.phylogeny.fr). The general time-reversible (GTR) model plus gamma distribution and invariant sites was used as the substitution model and bootstrap supports were computed after 100 reiterations. Reference recA sequences for the types IA (AY642073), IB (AY642092), II (AY642090), and III (DQ672252) were included in the phylogenetic analysis [START_REF] Mcdowell | A novel multilocus sequence typing scheme for the opportunistic pathogen Propionibacterium acnes and characterization of type I cell surface-associated antigens[END_REF][START_REF] Mcdowell | Propionibacterium acnes types I and II represent phylogenetically distinct groups[END_REF]. An isolate that belonged to a clade containing a reference sequence was affiliated to the corresponding phylotype. Some tly and recA alleles in the subphylotype IA-2 are shared with phylotype IB [START_REF] Mcdowell | An expanded multilocus sequence typing scheme for Propionibacterium acnes: investigation of 'pathogenic', 'commensal' and antibiotic resistant strains[END_REF]. Therefore, the phylotype IB will be named IA-2/IB in this study to avoid confusion.

recA-based phylotyping by temporal temperature gel electrophoresis TTGE migration was performed in the DCode Universal Mutation Detection System (Bio-Rad Laboratories). Gels contained 7 % (w/V) bisacrylamide (37.5:1), 7 M urea, 40 ml N,N,N9,N9-tetramethylethylenediamine, and 0.1 % (w/v) ammonium persulfate, and were run in 16 Tris acetate EDTA (TAE) buffer at pH 8.3. The electrophoresis migration conditions were a pre-migration at 20 V for 15 min and a migration of 17.5 h at 53 V from an initial temperature of 67 °C to a final temperature of 70.5 °C (increase of 0.2 °C per hour). Bands were visualized on UV illuminator after gel incubation in an ethidium bromide bath. For band sequencing, gel slices excised with a sterile scalpel were washed twice in DNA-free water and DNA was eluted by an overnight incubation in 10 mM Tris buffer (pH 8.5) at 37 °C. Amplification of the 5′-terminal recA region was performed using 1 μL of band eluate and the primers PR264 without GC clamp and PAR-2 as previously described. PCR products were sequenced on an ABI 3730xl sequencer (Beckman Coulter Genomics) and compared to reference recA sequences for phylotype affiliation.

Results

Phylogenetic structure of the P. acnes clinical collection based on recA and tly genes The recA and tly consensus sequences of 1,119 bp and 848 bp, respectively, were obtained for the 99 clinical isolates. Partial sequences were compared and numbered according to the MLST databases (Table 1). The alignment of the 1,119-bp recA sequences showed 22 polymorphic sites (1.97 % against 1.86 % for the 753-pb recA sequence used in the MLST databases), whereas the 848-bp tly sequences were more variable, with 39 polymorphic positions (4.6 % against 4.12 % for the 777-pb tly sequence used in the MLST databases). Phylogeny affiliated recA clades to phylotypes according to the reference sequences included in the analysis (Fig. 1). Tree topologies appeared robust and were globally congruent between recA and tly markers (Fig. 1), except for strains PA27, PA49, and PA90 (corresponding, respectively, to phylotypes IA-2/IB, IA and II in the recA tree, and to phylotypes IA, III, and IA-2/IB in the tly tree). These incongruences suggested recombination among phylotypes. It was noteworthy that the group PA6/PA101/PA102 was in phylotype IA in the recA tree and in a yet undescribed phylotype with a new allele related to allele 2 in the tly tree. The phylogenetic structure and isolates distribution did not significantly change when the concatenated sequence were analyzed. However, the tly undescribed clade (PA6, PA101, and PA102) was supported by a high bootstrap value in the concatenated tree, suggesting the emergence of a robust subpopulation (data not shown).

The clades IA and IA-2/IB gathered the majority of isolates (77/99) in both the recA and tly trees. However, some atypical isolates in each clade differed from the reference sequences and from the majority of isolates. Among them, PA25 and PA69 displayed undescribed new recA alleles. PA99, PA109, and PA73 had allelic affiliation in MLST, but their incongruent phylogenetic positions were due to mutations out of the region used for MLST, suggesting the emergence of new lineages in phylotype I by gene mutation rather than by gene exchange.

Phylotype II was less robust and displayed higher diversity in the recA tree. However, the majority of isolates (n=12) were grouped with the reference sequences and corresponded to the recA allele 6 in the MLST scheme in http://pacnes.mlst. net/ (Fig. 1, left side). The other isolates (n = 7) were distributed in six branches supported by low bootstrap values, making their relative phylogenetic positions uncertain. They corresponded to alleles 6 and 8, but were also related to new alleles in http://pacnes.mlst.net/. In the tly tree, phylotype II displayed low diversity and formed a robust clade (Fig. 1, right side) that fully matched tly allele 10 in MLST. Finally, phylotype III was the least represented in our collection (n=3 in the recA tree and n=4 in the tly tree), which displayed low variability and high robustness. Links between phylotypes and clinical origin Phylotype I was largely the most prevalent in our collection focused on strains involved in deep or severe infections (from 67 to 100 %, depending on the clinical origin). Type II represented 19.2 % of the collection and type III was represented by only three strains (Fig. 2). The distribution of clinical isolates by phylotypes appeared to be globally independent of their origin (Fig. 2). However, some particularities deserved to be underlined. Strains from the abdominal area and from orthopedic or neurological infections belonged to the four phylotypes IA, IA-2/IB, II, and III, and phylotype III was not detected from the other origins. On the contrary, the eight isolates from neonates, mostly from gastric liquid, belonged to type I. Phylotype IA was mainly found in head and neck infections, with 68 %, 63 %, and 45 % from ophthalmologic, neurological, and oropharyngeal origins, respectively. For all the other clinical origins, the genetic diversity of isolates was dominated by phylotype IA-2/IB. This is noteworthy for strains implicated in orthopedic surgery and bacteremia. Among the oropharyngeal strains included herein, type II was particularly prevalent (36.4 %). The distribution in phylotypes of the 27 isolates from cardiothoracic infections, also considering the strains from cardiac SSI separately, was roughly similar to that of the whole population (Fig. 2).

Hemolytic phenotypes in clinical strains

The repartition in phylotypes of the hemolytic behavior for the 99 isolates is presented in Fig. 3a. Non-hemolytic strains were distributed in the recA-tly phylotypes IA, IA-2/IB, II, and III.

No strains in phylotype III and only 2 isolates among 18 in phylotype II were hemolytic. In contrast, phylotype I was weakly (33.7 %) or strongly hemolytic (36.3 %). Phylotypes IA and IA-2/IB displayed 61 % and 78 % hemolytic strains, respectively. Of note, strain PA49 corresponding to recA type IA and tly type III was non-hemolytic, as for other typical type III strains. The hemolytic capacities appeared to be rather related to the phylotype but varied slightly according to the origin of infections (Fig. 3b,c,d). The distribution of cardiothoracic isolates was roughly similar to that of the whole population, except for a few strains, mainly of type IA-2/IB, which were more often non-hemolytic in cardiothoracic isolates (Fig. 3b). Of note, the six isolates from cardiac valves were nonhemolytic IA-2/IB or II types, whereas strains from sternal wounds were mostly hemolytic (10/11) (Table 1). Nonhemolytic IA strains were all isolated from pacemaker lodge or devices. Cardiothoracic and neurological IA strains were either non-hemolytic or strongly hemolytic (Fig. 3b,d). No obvious hemolytic phenotype was related to neurological infections. In orthopedics, phylotype IA-2/IB dominated and was always hemolytic but often weakly (Fig. 3c). The three strains from blood culture were strongly hemolytic.

Identification of the main phylotypes by recA PCR-TTGE

The denaturing gel PCR assay was based on the genetic diversity of the 3′ part of the recA gene, containing 13 polymorphic sites in a 333-bp fragment (Table 2). This method was applicable to complex microbiota without subculturing and allowed the direct detection of the main recA phylotypes in a single experiment, by comparison to a ladder (Fig. 4). 2. Thirty-five of the 36 isolates belonging to phylotype IA shared an identical sequence type (IA-3′recA1). The strain PA55, remote from the other IA strains in the recA tree, displayed a T/C mutation in position 275 (IA-3′recA2), which conferred to the corresponding 333bp fragment a particular migration behavior in TTGE (Fig. 4). Almost all (41/42) of the type IA-2/IB strains shared the same allele (IA-2/IB-3′recA1). PA69 isolated from a neonatal gastric fluid was the sole strain with IA-2/IB-3′recA2 because of an SNP (C/A) in position 125. Despite a single SNP (G/A) in position 167 between IA-3′recA1 and IA-2/IB-3′recA1, they were clearly separated in TTGE (Fig. 4). The three clinical isolates PA47, 48, and 87 belonging to type III in the recA tree shared the same sequence type III-3′recA1 that migrated differentially from other ST. The type III-3′recA1 TTGE band displayed a fuzzy aspect compared to bands corresponding to the other phylotypes (Fig. 4).

As expected from the recA tree topology, phylotype II was more variable, with four different ST that roughly corresponded to the four branches in the tree (Fig. 1). Allele II-3′recA1 was shared by 13 of the 19 type II strains (Fig. 4), mostly grouped in the main cluster that contains the reference sequence of phylotype II in the recA tree (Fig. 1). Four clinical isolates presented the same II-3′recA2, differing from II-3′ recA1 by one SNP (C/T in 98). The three other type II clinical strains PA36, 37, and 57 in the external position in the recA tree (Fig. 1) displayed two different sequences (Fig. 4).

Finally, phylotype II displayed four migration profiles, each differing from the other phylotypes. The ten bands corresponding to ten 3′-recA types were included in a ladder to represent the recA PCR-TTGE diversity of our collection (Fig. 4).

P. acnes phylotypes involved in cardiac surgery

We obtained 154 superficial and deep samples from 14 patients during the different stages of hospitalization in cardiac surgery. Seventy samples were positive when they were screened for significant bacterial load using universal 16S rRNA gene PCR. Therefore, these samples constituted the set for the direct detection of the P. acnes phylotypes by recA PCR-TTGE. Among them, 54 were collected during the surgical procedure, 34 superficially (19/34 and 15/34 cutaneous and subcutaneous samples, respectively) and 20 deeply (11/20 and 9/20 sternal edges and mediastinum samples, respectively). Seven samples concerned the skin before hospitalization, seven samples the skin and scar tissues after the surgical intervention, and only two samples involved the skin 3 months after the surgery. The TTGE fingerprints of ten representative samples are shown in Fig. 4. The phylotypes present in the 70 perioperative samples were identified by comparison to the diversity ladder. Four bands that did not match the ladder were separately analyzed and did not correspond to any known sequence type (data not shown).

The P. acnes phylotyping for all perioperative and peroperative samples from each patient is presented in Table 3. As previously described for clinical isolates, phylotype I predominated in surgical samples, with 32 (46 %) and 55 (78 %) samples sharing types IA and IA-2/IB, respectively, whereas phylotype III was found in only three samples (Table 3). Surprisingly, phylotype II was widely represented in surgical samples (n=30, 43 %), principally in superficial and lowdepth samples (i.e., cutaneous and subcutaneous tissues). We observed major variations among patients, some of them presenting a wide diversity of P. acnes with three or four phylotypes during the hospitalization pathway (patients AQ and AR, for example) and others with only one phylotype at only some stages of the surgery (patients AB and AL) (Table 3).

The phylotype diversity curves according to the stage of surgery and hospitalization were constructed for the whole population of patients (Fig. 5). These curves represented the relative distribution of each P. acnes phylotype according to the surgical stage and depth of sampling in the surgical site. Despite high variability depending on the patient, the diversity curves showed common themes in the patient population and Table 3 Origins and characteristics of the samples collected during the hospitalization course of 14 patients in cardiac surgery. The empty cells correspond to negative samples in 16S rRNA gene polymerase chain reaction (PCR). The shaded cells show the detection of P. acnes phylotypes on samples with positive 16S rRNA gene PCR Fig. 4 recA polymerase chain reaction temporal temperature gel electrophoresis (PCR-TTGE) experiment showing the migration of strains representative of phylotypes IA, IB, II, and III and the migration of ten representative samples from patients in cardiac surgery. The four bands representative of the major 3′ recA types are included in the ladder an interesting dynamics of the different phylotypes according to the depth of the wound and the step of surgical intervention (Fig. 5). Types IA and II displayed similar evolutions: they were present in superficial and low-deep tissues both at the beginning and at the end of the surgery, but they decreased in deep samples. Type IA greatly increased in postoperative samples such as scar tissues and in samples taken 3 months after surgery at a greater level than before surgery, while type II returned to its preoperative level. Type IA was also more present in sternal edges samples at the end than at the beginning of the intervention, suggesting peroperative colonization.

Type IA-2/IB presented an outstanding evolution, with a gradual increase with the depth of sampling, but also with the time of sampling in subcutaneous and cutaneous samples. This result suggested a particular resistance of phylotype IA-2/IB to the antimicrobial agents used in perioperative prophylaxis. However, both P. acnes IA and IA-2/IB cardiothoracic isolates were susceptible to antibiotics used in perioperative prophylaxis: cefamandole, vancomycin, and clindamycin.

Despite its low prevalence, type III displayed an increase in deep mediastinal tissues and subcutaneous tissues at the core phase of the surgery, but disappeared in superficial samples. Phylotypes IA and IA-2/IB were both predominant in scar tissues and on postoperative skin a long time after intervention, suggesting a specific predisposition to recolonize skin.

Discussion

P. acnes is an usual member of healthy skin microbiota, often considered a good bacterium devoid of pathogenicity [START_REF] Mcdowell | An expanded multilocus sequence typing scheme for Propionibacterium acnes: investigation of 'pathogenic', 'commensal' and antibiotic resistant strains[END_REF]. However, its role in inflammatory processes in acnes vulgaris and in several infections has been established [START_REF] Sampedro | Species of Propionibacterium and Propionibacterium acnes phylotypes associated with orthopedic implants[END_REF][START_REF] Saleh | A descriptive study of bacterial load of full-thickness surgical wounds in dermatologic surgery[END_REF][START_REF] Dessinioti | The role of Propionibacterium acnes in acne pathogenesis: facts and controversies[END_REF][START_REF] Farrar | Acne: inflammation[END_REF]. In opposition to allopatric true pathogens, mutualistic bacteria are generally organized in species complex [START_REF] Georgiades | Defining pathogenic bacterial species in the genomic era[END_REF] and the comprehension of their opportunistic pathogenic behavior occurs through deciphering of the population structure inside the species complex. Most population genetic studies were focused on healthy skin and acne isolates, despite a wider the pathogenic spectrum of P. acnes. Deep or severe infections such as HAI were rarely studied, except for large collections of strains from failed hip replacements [START_REF] Mcdowell | Propionibacterium acnes types I and II represent phylogenetically distinct groups[END_REF] and orthopedic implants [START_REF] Sampedro | Species of Propionibacterium and Propionibacterium acnes phylotypes associated with orthopedic implants[END_REF]. Here, we aimed to determine if genetic subpopulations were specifically linked to specific sites or severe infections, as for the IA phylotype to acne. This hypothesis is supported by linkage disequilibrium analysis suggesting that the different phylogroups of P. acnes may occupy distinct ecological niches [START_REF] Mcdowell | An expanded multilocus sequence typing scheme for Propionibacterium acnes: investigation of 'pathogenic', 'commensal' and antibiotic resistant strains[END_REF] and, therefore, may display different behaviors in different body sites. To meet our objective, we constituted a collection of natural isolates of P. acnes identified during severe infectious processes or from different origins in the routine exercise of hospital microbiology. The collection consisted mainly of strains from orthopedic and cardiothoracic surgeries, as well as head and neck infections. Our collection is also original owing to strains from origins rarely represented or unrepresented in previous studies: peritoneal dialysis, gastric fluid in neonates, and otolaryngologic samples.

Several studies have already analyzed the P. acnes population structure by different methods, based first on serotyping and biotyping [START_REF] Kishishita | New medium for isolating propionibacteria and its application to assay of normal flora of human facial skin[END_REF] and later by multilocus genetics and genomics [START_REF] Tomida | Pan-genome and comparative genome analyses of Propionibacterium acnes reveal its genomic diversity in the healthy and diseased human skin microbiome[END_REF][START_REF] Davidsson | Multilocus sequence typing and repetitivesequence-based PCR (DiversiLab) for molecular epidemiological characterization of Propionibacterium acnes isolates of heterogeneous origin[END_REF][START_REF] Lomholt | Population genetic analysis of Propionibacterium acnes identifies a subpopulation and epidemic clones associated with acne[END_REF][START_REF] Mcdowell | A new phylogenetic group of Propionibacterium acnes[END_REF][START_REF] Mcdowell | An expanded multilocus sequence typing scheme for Propionibacterium acnes: investigation of 'pathogenic', 'commensal' and antibiotic resistant strains[END_REF][START_REF] Mcdowell | Propionibacterium acnes types I and II represent phylogenetically distinct groups[END_REF]. Comparative genomics based on 123,223 SNP nucleotides in the core regions highlighted that the recA classification of the strains was consistent with the major genomic clades [START_REF] Mcdowell | An expanded multilocus sequence typing scheme for Propionibacterium acnes: investigation of 'pathogenic', 'commensal' and antibiotic resistant strains[END_REF]. The gene tly also has a recognized typing power [START_REF] Mcdowell | A new phylogenetic group of Propionibacterium acnes[END_REF][START_REF] Mcdowell | An expanded multilocus sequence typing scheme for Propionibacterium acnes: investigation of 'pathogenic', 'commensal' and antibiotic resistant strains[END_REF][START_REF] Mcdowell | Propionibacterium acnes types I and II represent phylogenetically distinct groups[END_REF]. In previous studies on large populations, the recA and tly genes showed good phylogenetic discriminative power and high genetic diversity index (0.67 each), making them good genetic markers [START_REF] Kilian | Multilocus sequence typing and phylogenetic analysis of Propionibacterium acnes[END_REF][START_REF] Mcdowell | An expanded multilocus sequence typing scheme for Propionibacterium acnes: investigation of 'pathogenic', 'commensal' and antibiotic resistant strains[END_REF]. Moreover, despite the use of only two genes, we gained in allele variability because we analyzed larger sequences than that in major MLST schemes (available in http://pacnes.mlst.net/ and http://pubmlst.org/pacnes/). Consequently, we found a greater genetic polymorphism than in other studies, with some polymorphic sites being present at the extremities of recA and tly sequences not included in previously published studies. The high polymorphism in the 3′ part of the recA gene met our second objective, which was to develop a rapid and efficient tool (recA PCR-TTGE) to identify the major P. acnes phylotypes in complex communities without a first step of isolation by culture. The primary stratification of the P. acnes populations performed herein would be used as a basis for downstream MLST analysis on selected strains or selected phylotypes potentially associated with a particular type of deep infection.

However, deep MLST analyses [START_REF] Mcdowell | An expanded multilocus sequence typing scheme for Propionibacterium acnes: investigation of 'pathogenic', 'commensal' and antibiotic resistant strains[END_REF] underscored the lack of specificity of recA due to the sharing of some type IB alleles with members of clonal complex 4 in phylotype IA-1 and with all type IA-2 members. Moreover, some tly alleles such as allele 8 were also shared between IA-2 and IB types [START_REF] Mcdowell | An expanded multilocus sequence typing scheme for Propionibacterium acnes: investigation of 'pathogenic', 'commensal' and antibiotic resistant strains[END_REF]. Indeed, allele 8 is detected in 100 % of IB isolates and 97 % of IA-2 isolates [START_REF] Mcdowell | An expanded multilocus sequence typing scheme for Propionibacterium acnes: investigation of 'pathogenic', 'commensal' and antibiotic resistant strains[END_REF]. In our phylogenetic tree, all the strains affiliated to the clade IA presented the tly allele 1. Therefore, considering the global congruence between the tly and recA trees, they certainly do not belong to IA-2 and probably corresponded to IA-1 isolates. For the alleles described herein, types IB and IA-2 could not be differentiated with certainty but type IA-2/IB differed clearly from type IA-1. The MLST schemes showed that IA-2 and IB underwent numerous recombination events involving most of the genes studies. Despite general linkage disequilibrium among phylotypes I, II, and III, the clonality of subtypes within phylotype I is less obvious. Particularly, IA-2 and IB phylotypes merged in split trees [START_REF] Mcdowell | An expanded multilocus sequence typing scheme for Propionibacterium acnes: investigation of 'pathogenic', 'commensal' and antibiotic resistant strains[END_REF][START_REF] Mcdowell | Propionibacterium acnes in human health and disease[END_REF] as the single clade named IA-2/IB with many parallelogram structures, indicating recombination events. The consequence is that lineages in phylotype I are not clearly separated; particularly, IA-2 and IB should be considered as an undifferentiated group IA-2/IB whatever the typing scheme considered because of the high level of allele recombinations.

In the collection tested, we did not show a strict correlation between origins of infection and phylotypes. While previous studies showed that phylotypes II and III were rarely present in skin samples [START_REF] Davidsson | Multilocus sequence typing and repetitivesequence-based PCR (DiversiLab) for molecular epidemiological characterization of Propionibacterium acnes isolates of heterogeneous origin[END_REF][START_REF] Lomholt | Population genetic analysis of Propionibacterium acnes identifies a subpopulation and epidemic clones associated with acne[END_REF][START_REF] Niazi | Propionibacterium acnes and Staphylococcus epidermidis isolated from refractory endodontic lesions are opportunistic pathogens[END_REF], we highlight their higher prevalence in deep infection sites. To our knowledge, we describe for the first time among strains from oropharyngeal sphere that about 35 % of them belong to type II. Not enough strains from blood cultures were included in this study but we observed a high prevalence of IA-2/IB and II. McDowell et al. [START_REF] Mcdowell | An expanded multilocus sequence typing scheme for Propionibacterium acnes: investigation of 'pathogenic', 'commensal' and antibiotic resistant strains[END_REF] underlined the association of types IA-2/IB and II with medical devices, which are frequently the source of bacteremia in HAI. Both types IA and IA-2/IB are found in gastric fluids in neonatology. Therefore, we can hypothesize that the transmission from mother microbiota to newborn during delivery involves principally P. acnes type I.

As described previously [START_REF] Sampedro | Species of Propionibacterium and Propionibacterium acnes phylotypes associated with orthopedic implants[END_REF], we found that phylotype I was the most often involved in orthopedic surgery, and type IA-2/IB (with 8 of the 12 isolates in the recA tree) more frequently than IA. Considering the lack of discrimination of recA underlined by McDowell et al. in 2012 [START_REF] Mcdowell | An expanded multilocus sequence typing scheme for Propionibacterium acnes: investigation of 'pathogenic', 'commensal' and antibiotic resistant strains[END_REF], one can say that orthopedic surgery isolates more often belong to type IA-2/IB than to IA1. This was also the case for strains involved in cardiac SSI, unlike the data previously published by Davidsson et al. in 2012 [19], with a majority of type IA (only ten strains typed). These results suggest a particular tropism of type IA-2/IB for surgical wounds in orthopedic and cardiac surgeries, but not in neurosurgical infections, where phylotype IA was more often isolated.

Besides its genetic typing value, we studied the tly gene because it encodes a putative virulence factor that could be related to a particular pathogenic behavior. Except for three strains that probably encountered recombination events, tly and recA markers give congruent population structures, suggesting that tly coevolve with housekeeping genes. In spite of the general role of hemolysins in bacterial pathogenesis, comparative genomics prove that tly belongs to the core genome of P. acnes [START_REF] Mcdowell | An expanded multilocus sequence typing scheme for Propionibacterium acnes: investigation of 'pathogenic', 'commensal' and antibiotic resistant strains[END_REF], but not to island-like genomic regions, encoding a variety of traits that differ between phylotypes [START_REF] Brzuszkiewicz | Comparative genomics and transcriptomics of Propionibacterium acnes[END_REF]. Mc-Dowell et al. [START_REF] Mcdowell | An expanded multilocus sequence typing scheme for Propionibacterium acnes: investigation of 'pathogenic', 'commensal' and antibiotic resistant strains[END_REF] hypothesized the importance of tly for both mutualistic and pathogenic lifestyles. Brzuszkiewicz et al. [START_REF] Brzuszkiewicz | Comparative genomics and transcriptomics of Propionibacterium acnes[END_REF] concluded that the virulence of different P. acnes strains is not only determined by the phylotype-specific genome content but also by variable gene expression. For instance, despite the presence of tly in the P. acnes core genome, all strains do not express a hemolytic phenotype [START_REF] Mcdowell | Propionibacterium acnes types I and II represent phylogenetically distinct groups[END_REF]. Moreover, tly hemolysin is not the only putative virulence factor able to induce hemolysis; several others like the group of CAMP factors and other cytotoxins, known to have this ability, have been identified in the P. acnes genome [START_REF] Brüggemann | Insights in the pathogenic potential of Propionibacterium acnes from its complete genome[END_REF][START_REF] Valanne | CAMP factor homologues in Propionibacterium acnes: a new protein family differentially expressed by types I and II[END_REF].

Our results showed an interesting expression of hemolytic activity: the absence or very low hemolytic activity within phylotypes II and III, whereas about half of the IA strains and almost all IA-2/IB strains expressed hemolysis. Studies describing the hemolysis activities according to the genetic type in the P. acnes population are rare [START_REF] Kasprowicz | A comparison of biochemical and genetic classification of Propionibacterium acnes strains isolated from skin lesions of patients with acne[END_REF]. We found 70 % of phylotype I strains to be hemolytic, suggesting a potential role of hemolysin activity in infectious processes occurring in deep tissues. Concerning phylotype II, acne strains and deeper infection strains display similar hemolytic behavior, with about 10 % of hemolytic isolates in this study versus 12 % in the population of acne strains described by Kasprowicz et al. [START_REF] Kasprowicz | A comparison of biochemical and genetic classification of Propionibacterium acnes strains isolated from skin lesions of patients with acne[END_REF]. Besides hemolysis, biofilm formation is a virulence mechanism with potential importance in HAI [START_REF] Ziebuhr | Nosocomial infections by Staphylococcus epidermidis: how a commensal bacterium turns into a pathogen[END_REF]. P. acnes biofilm allows a latent growth [START_REF] Holmberg | Biofilm formation by Propionibacterium acnes is a characteristic of invasive isolates[END_REF][START_REF] Coenye | Biofilm formation by Propionibacterium acnes is associated with increased resistance to antimicrobial agents and increased production of putative virulence factors[END_REF] that could lead to lateonset deep infections like SSI on foreign materials in orthopedic surgery or in endocarditis and prosthetic valves in cardiac surgery [START_REF] Noel | Pacemaker endocarditis caused by Propionibacterium acnes: a case report[END_REF][START_REF] Pan | Endocarditis caused by Propionibacterium acnes: an easily ignored pathogen[END_REF][START_REF] Sampedro | Species of Propionibacterium and Propionibacterium acnes phylotypes associated with orthopedic implants[END_REF][START_REF] Farrar | Acne: inflammation[END_REF][START_REF] Holmberg | Biofilm formation by Propionibacterium acnes is a characteristic of invasive isolates[END_REF]. No correlation has been yet found between phylotypes and biofilm production, as all phylotypes contain isolates with different levels of biofilm production [START_REF] Holmberg | Biofilm formation by Propionibacterium acnes is a characteristic of invasive isolates[END_REF]. However, in sebaceous follicles, P. acnes biofilms are predominantly composed of types IA and II strains [START_REF] Jahns | An increased incidence of Propionibacterium acnes biofilms in acne vulgaris: a case-control study[END_REF].

Finally, as for most opportunistic pathogens originating in the host microbiota, the virulence of P. acnes is difficult to decipher. Members of complex microbiota, such as humanassociated microbiota, encounter complex relationships with host and other microbes. Therefore, the pathophysiology of the infection should take the microbiota dynamics into account as a major factor involved in infectious process. For this purpose, we propose a follow-up of the P. acnes diversity during the hospitalization courses of patients in cardiac surgery. Taking the opportunity for the high variability of the 3′terminal region of the recA gene (13 variable positions in 333 bp), we developed an original culture-independent approach, the recA PCR-TTGE. This approach appears suitable to survey P. acnes populations during cardiac surgery procedures, allowing rapid screening of the main phylotypes involved in several samples. Our results showed that different phylotypes coexist in the same sample. This finding, which presented a certain novelty, is difficult to achieve when the P. acnes detection is based on culture because culture-based methods request the isolation of one pure bacterial colony. Phylotype IA-2/IB seems to be particularly adapted to colonize deep sternal and thoracic tissues (both sternal edges and mediastinum), as well as scar tissues after surgery. Type II was also very present at the different steps of hospitalization except in deep tissues, and did not increase during surgical intervention. These behaviors seemed to be not linked to particular resistance to antimicrobial agents used in cardiac surgical prophylaxis.

This study highlights a particular adaptation of phylotype IA-2/IB to cardiac surgery, in both the wound surgical colonizing community and SSI. However, the strains isolated from cardiac SSI were obtained by cultural methods and did not reflect the whole P. acnes population initially involved in the sample. To confirm and complete the distribution scheme of P. acnes phylotypes in severe human infections, it would be necessary to increase the number of isolates from the different clinical sites and explore the dynamics of P. acnes phylotypes in diverse complex communities and their pathological variations. For this purpose, the specific culture-independent approach proposed herein would provide an efficient tool. Moreover, it also seems relevant to specify the phylotype(s) and/or the clonal complex (CC) present in surgical samples, thereafter to explore potential virulence characteristics involved in the pathophysiology of SSI.

Fig. 1

 1 Fig.1Multilocus (ML) phylogenetic trees reconstructed from recA and tly sequences of Propionibacterium acnes isolates, left and right sides, respectively. The recA sequences of reference strains (underlined) are included for phylotype affiliation. For each branch, the corresponding allele is numbered according to the MLST scheme deposited in http://

Fig. 2

 2 Fig. 2 Relative prevalence of the different phylotypes of P. acnes according to clinical origin

Fig. 3

 3 Fig. 3 Hemolytic phenotype according to the phylotype for: (a) the whole P. acnes population, (b) isolates from cardiothoracic infections, (c) isolates from orthopedic infections, and (d) isolates from neurological infections

Fig. 5

 5 Fig. 5 Dynamics of the P. acnes phylotypes in samples chronologically collected during hospitalization and cardiac surgical procedures of 14 patients. The curves display the percentage of samples positive for each P. acnes phylotype according to the surgical stage and depth of sampling in the surgical site. C preop preoperative cutaneous sample, C cutaneous samples, SC subcutaneous samples, SE sternal edges samples, M mediastinal samples, beginning at the beginning of the surgical intervention,

Table 1

 1 Origins, genotype, and hemolytic capacity of the Propionibacterium acnes isolates. a According to the nomenclature of the http://pacnes.mlst.net/ database. b According to the nomenclature of the http://pubmlst.org/pacnes/ database. Allele numbers marked with an asterisk correspond to new alleles displaying >99 % identity in the sequence with the original allele. SSI surgical site infections, STM skintissue-muscle. IB corresponded to IA-2/IB, the two types being undistinguishable by recA/tly typing

	Strains and origins

Table 1

 1 (continued)

	Strains and origins

Table 2

 2 Phylotypes of the 3′-end of the recA gene sequence types (ST) of P. acnes isolates with the corresponding polymorphic sites. *The nomenclature indicates the phylotype followed by the sequence type of the 3′ part of the recA gene

		13	(299/333)
		12	(281/333)
		11	(275/333)
		10	(254/333)
		9	(202/333)
		8	(176/333)
		7	(167/333)
		6	(164/333)
		5	(125/333)
		4	(122/333)
	Nucleotidic polymorphic sites	1 2 3	(62/333) (98/333) (116/333)
		Clinical isolates	PA5, 6, 12, 17, 25, 28, 29, 31,	38, 41, 42, 45, 46, 49, 50, 52,	60, 74, 75, 77, 78, 79, 81, 86,	92, 93, 101, 102, 103, 105,	106, 107, 110, 111, 114
		Phylotypes*	IA-3′recA1

Acknowledgments We thank Brigitte Lamy, Hélène Marchandin, and Anne-Laure Michon from the Bacteriology Laboratory of Montpellier Hospital for providing the clinical strains, and all the members of the cardiothoracic surgery team of Montpellier Hospital for the surgical samples collections. We also thank Valérie Macioce from Département d'Information Médicale of Montpellier Hospital for her help in reviewing the English language. This work was supported by a public grant from the French research ministry and by the association ADEREMPHA, Sauzet, France.

Conflict of interest

The authors declare that they have no conflict of interest.