PhD, DVM Jourdain Elsa
email: elsa.jourdain@clermont.inra.fr

PhD Olivier Duron

Barry Se ´verine

PhD, DVM Daniel Gonza ´lez-Acun ˜a

PhD, DVM Karim Sidi-Boumedine

Mare Lo

Molecular methods routinely used to detect Coxiella burnetii in ticks cross-react with Coxiella-like bacteria

Keywords: Q fever, tick-borne diseases, tick endosymbiont, false positive, surveillance, PCR primers

Background: Q fever is a widespread zoonotic disease caused by Coxiella burnetii. Ticks may act as vectors, and many epidemiological studies aim to assess C. burnetii prevalence in ticks. Because ticks may also be infected with Coxiella-like bacteria, screening tools that differentiate between C. burnetii and Coxiella-like bacteria are essential. Methods: In this study, we screened tick specimens from 10 species (Ornithodoros rostratus, O. peruvianus, O. capensis, Ixodes ricinus, Rhipicephalus annulatus, R. decoloratus, R. geigy, O. sonrai, O. occidentalis, and Amblyomma cajennense) known to harbor specific Coxiella-like bacteria, by using quantitative PCR primers usually considered to be specific for C. burnetii and targeting, respectively, the IS1111, icd, scvA, p1, and GroEL/htpB genes. Results: We found that some Coxiella-like bacteria, belonging to clades A and C, yield positive PCR results when screened with primers initially believed to be C. burnetii-specific. Conclusions: These results suggest that PCR-based surveys that aim to detect C. burnetii in ticks by using currently available methods must be interpreted with caution if the amplified products cannot be sequenced. Future molecular methods that aim at detecting C. burnetii need to take into account the possibility that cross-reactions may exist with Coxiella-like bacteria.

Q fever is a worldwide zoonosis caused by Coxiella burnetii, a ubiquitous intracellular bacterium that infects humans and a variety of animals. Livestock, especially small ruminants, are the main sources of human infections (1Á3). In domestic ruminants, Q fever's major clinical manifestations are abortions and stillbirths, whose occurrence may translate into significant economic losses (1Á3). In humans, C. burnetii infections range from asymptomatic to severe. Acute forms of the disease may result in high fevers and severe pneumonia or hepatitis, and chronic forms are strongly debilitating and may be fatal when endocarditis develops in patients with underlying heart disease [START_REF]Risk assessment on Q fever. Panel with representatives from the Netherlands[END_REF][START_REF] Anderson | Diagnosis and management of Q Fever Á United States, 2013: recommendations from CDC and the Q Fever Working Group[END_REF]. Both animals and humans essentially become infected through the inhalation of airborne particles contaminated with C. burnetii [START_REF] Efsa | Scientific Opinion on Q fever[END_REF][START_REF] Tissot-Dupont | Wind in November, Q fever in December[END_REF]. Ticks are historically known to be potential vectors for Q fever. Indeed, the first strain of C. burnetii was isolated from a Dermacentor andersoni tick in the 1930s (6Á8). First assigned to the genus Rickettsia (in which infection by arthropods is the rule), it was later recognized as the Q fever etiologic agent and is now considered as C. burnetii reference strain [START_REF] Hechemy | History and prospects of Coxiella burnetii research[END_REF]. Because C. burnetii is frequently detected in field-sampled ticks (10Á13) and because laboratory experiments have revealed that at least some tick species are competent vectors [START_REF] Davis | A filter-passing infectious agent isolated from ticks. I. Isolation from Dermacentor andersoni, reactions in animals, and filtration experiments[END_REF][START_REF] Siroky | Tortoise tick Hyalomma aegyptium as long term carrier of Q fever agent Coxiella burnetii Á evidence from experimental infection[END_REF][START_REF] Daiter | Transovarial and transspermal transmission of Coxiella burnetii by the tick Hyalomma asiaticum and its role in Q-rickettsiosis ecology[END_REF], it is currently considered that ticks may act as vectors and help transmit the bacterium among wildlife and, on occasion, domestic ruminants [START_REF] Efsa | Scientific Opinion on Q fever[END_REF][START_REF] Duron | The importance of ticks in Q fever transmission: what has (and has not) been demonstrated?[END_REF].

Interestingly, ticks also frequently carry Coxiella-like bacteria that are likely involved in mutualistic symbioses with their arthropod hosts (16Á19). To date, there has been no indication that these tick-carried Coxiella-like bacteria are transmitted to vertebrates, although Coxiella-like bacteria have sporadically been detected in pet birds [START_REF] Zhong | Coxiella-like endosymbionts[END_REF][START_REF] Shivaprasad | Coxiella-like infection in psittacines and a toucan[END_REF]. Recent investigations based on multilocus phylogenetic analyses and whole genome sequencing data revealed that all known C. burnetii strains originate within the vast group of Coxiella-like endosymbionts and are the descendants of a Coxiella-like progenitor hosted by ticks [START_REF] Duron | The recent evolution of a maternally-inherited endosymbiont of ticks led to the emergence of the Q fever pathogen, Coxiella burnetii[END_REF].

Because epidemiologic studies that aim at assessing C. burnetii prevalence in ticks frequently rely on DNA detection by polymerase chain reaction (PCR), it is important to make sure that these screening methods are specific for C. burnetii. The objective of this study was to determine whether five molecular methods frequently used to detect or characterize C. burnetii cross-react with Coxiella-like bacteria present in ticks.

Materials and methods

Selection of a panel of 20 ticks infected with specific Coxiella-like bacteria Ten tick species, previously shown to harbor specific Coxiella-like bacteria (17), were investigated.

They were selected with the aim to represent the clades (AÁD) currently described for the Coxiella genus (17) (Fig. 1 cajennense). This panel included three tick species from which C. burnetii had previously been reported, namely O. sonrai (12), I. ricinus (21Á23), and R. annulatus [START_REF] Reye | Pathogen prevalence in ticks collected from the vegetation and livestock in Nigeria[END_REF].

Two tick specimens were examined for each species. They were either obtained from breeding colonies or sampled from their host species or habitats and they were processed as previously described [START_REF] Duron | The recent evolution of a maternally-inherited endosymbiont of ticks led to the emergence of the Q fever pathogen, Coxiella burnetii[END_REF]. Briefly, the ticks were first washed with sterile water to avoid external bacterial contamination. Then, DNA was individually extracted using the DNeasy Blood & Tissue Kit (Qiagen) following manufacturer's instructions. DNA template quality was verified via PCR amplification of 18S ribosomal RNA or cytochrome oxidase 1 arthropod primers. Nested PCR assays were conducted using primers designed to amplify bacteria from the Coxiellacae family (i.e. Coxiella and its sister genus Rickettsiella) and to target the rpoB (DNAdirected RNA polymerase beta) gene and the GroEL/htpB (60 kDa chaperone heat shock protein B) gene as described elsewhere [START_REF] Duron | The recent evolution of a maternally-inherited endosymbiont of ticks led to the emergence of the Q fever pathogen, Coxiella burnetii[END_REF][START_REF] Duron | Diversity and global distribution of the Coxiella intracellular bacterium in seabird ticks[END_REF]. Sequencing of the PCR products obtained showed that each tick species was infected by a specific Coxiella-like bacterium that was genetically related to, but distinct from, C. burnetii. None of these tick DNA templates was found infected with C. burnetii on the basis of multilocus DNA sequencing [START_REF] Duron | The recent evolution of a maternally-inherited endosymbiont of ticks led to the emergence of the Q fever pathogen, Coxiella burnetii[END_REF].

Selection of qPCR primers thought to be specific for C. burnetii

The 20 tick specimens were tested using quantitative PCR (qPCR) methods using primers that are usually considered to be specific for C. burnetii (Table 1). We used TaqMan Universal PCR Master Mix (UMM 2 )) following the amplification protocol: 1 cycle at 508C for 2 min and 1 cycle at 958C for 10 min, followed by 40 PCR cycles of 958C for 15 s and 608C for 1 min. Two of the targeted markers Á the multicopy IS1111 insertion sequence [START_REF] De Bruin | Detection of Coxiella burnetii in complex matrices by using multiplex quantitative PCR during a major Q fever outbreak in the Netherlands[END_REF][START_REF] Joulie | Circulation of Coxiella burnetii in a naturally infected flock of dairy sheep: shedding dynamics, environmental contamination, and genotype diversity[END_REF] and the icd (isocitrate dehydrogenase) housekeeping gene (26) Á are frequently used in surveys that aim to estimate the prevalence of C. burnetii infection in ticks [START_REF] Duron | The importance of ticks in Q fever transmission: what has (and has not) been demonstrated?[END_REF]. The following genes were also targeted: scvA (small-cellvariant protein A), which is likely involved in chromatin condensation when the bacterium is 'sporulating', and porine p1, which encodes an outer membrane protein [START_REF] Coleman | Temporal analysis of Coxiella burnetii morphological differentiation[END_REF]. Finally, we focused on a specific region of the GroEL/htpB, distinct from the region targeted to amplify the genome of Coxiella-like bacteria ( 17) and considered to be specific to C. burnetii [START_REF] Fernandes | Evaluation of the recombinant heat shock protein B (HspB) of Coxiella burnetii as a potential antigen for immunodiagnostic of Q fever in goats[END_REF]. Nine Mile phase II genomic DNA (RSA 493 isolate) was used as a reference. In silico comparisons of the primers and probes with currently published sequences of R. turanicus (GenBank accession number: CP011126) and A. americanum (GenBank accession number: CP007541) suggested that mismatches with these symbionts were unlikely (Table 1).

Results

We found that some Coxiella-like bacteria, belonging to clades A and C, yield positive PCR results when screened with primers initially believed to be C. burnetii-specific (Table 2). Overall, DNA was amplified for at least one marker in 6 of the 10 tick species studied. The most frequently amplified marker was IS1111, which was detected in five different species, whereas GroEL/htpB and scvA were amplified from three species. Porine p1 was solely amplified from a R. geigyi specimen, which was also positive for htpB, scvA, and IS1111, and displayed a particularly low C t value (C t 033) for IS1111. Conversely, icd was not detected in any of our samples. Interestingly, we observed intraspecific variation: one of the Coxiella-like endosymbiont from R. decoloratus was positive for IS1111, whereas the other was positive for scvA. Unfortunately, because all PCR products were poorly concentrated, sequencing was unsuccessful.

Discussion

The marker we most frequently detected in ticks infected with Coxiella-like endosymbionts was the IS1111 transposable element, which is routinely targeted during epidemiological surveys examining C. burnetii prevalence in ticks [START_REF] Duron | The importance of ticks in Q fever transmission: what has (and has not) been demonstrated?[END_REF]. We thus showed that C. burnetii detection assays based only on IS1111 may lead to misidentification with Coxiella-like endosymbionts. The recent work of Duron ( 30) corroborates this finding: several genetically divergent IS1111 copies were found widespread in many Coxiella-like endosymbionts, therefore showing that IS1111 can no longer be considered specific to C. burnetii. These findings may explain why surveys based on IS1111 screening occasionally report prevalence levels !10% (23, 31Á33).

Our results also showed that the use of a combination of primers targeting different markers, as performed in some studies (11, 21, 34Á36), is not sufficient to guarantee the specificity of C. burnetii detection. Indeed, up to four of our markers were detected in a same Coxiella-like endosymbiont. Interestingly, icd, which is frequently used as a PCR target in epidemiological studies [START_REF] Duron | The importance of ticks in Q fever transmission: what has (and has not) been demonstrated?[END_REF][START_REF] Michelet | High-throughput screening of tick-borne pathogens in Europe[END_REF], was not amplified from our panel of Coxiella-like infected ticks. However, Reeves et al. [START_REF] Reeves | Borrelia, Coxiella, and Rickettsia in Carios capensis (Acari: Argasidae) from a brown pelican (Pelecanus occidentalis) rookery in South Carolina, USA[END_REF] were able to amplify a 612-bp icd fragment, displaying 93% homology with C. burnetii, from a Coxiella-like bacterium that infects ticks from the O. capensis complex in South Carolina, USA. This result contrasts with our observation that icd was not amplified from the endosymbiont of O. capensis ticks sampled from Cape Verde and highlights the fact that the amplification of a specific genetic marker strongly depends on the PCR method (PCR, nested PCR, or qPCR) and the primer sequences used.

Á/Á Á /Á Á /Á Á /Á O. occidentalis Á/Á Á /Á Á /Á Á /Á Á /Á D A. cajennense Á/Á Á /Á Á /Á Á /Á Á /Á
The sign '/' is used to separate the results obtained for the first and the second tick specimen; 'Á' indicates that no amplification was observed.

More generally, negative results may be due to low detection sensitivity, which is supported by high detection thresholds for most of the genes. In particular, intraspecific variation may be due to the individual ticks having a low bacterial burden, sex-or stage-specific differences, and the presence of PCR inhibitors. In our study, it is possible that the IS1111-based PCR method was the most sensitive of the tests used, because several copies of this gene are likely present in the genome of Coxiella-like bacteria, as is the case for C. burnetii. This hypothesis is supported by the observation that GroEL/htpB, porine p1, and scvA were detected in the endosymbiont of a R. geigyi specimen that displayed a low C t value for IS1111.

Standardizing methodology across laboratories is essential to allow comparisons among studies. Although remarkable progress has recently been made in designing new PCR-based techniques to detect C. burnetii, these advances have overlooked that an important genetic diversity actually exists within the Coxiella genus [START_REF] Duron | The importance of ticks in Q fever transmission: what has (and has not) been demonstrated?[END_REF]. In this context, it may not be surprising that the PCR primers routinely used to target C. burnetii actually cross-react with Coxiella-like bacteria. Therefore, in the future, molecular methods aiming at detecting C. burnetii should make sure that no cross-reaction exists not only with other abortive agents but also with Coxiella-like organisms. Recent fullgenome sequencing data indeed not only highlighted obvious genetic similarities of C. burnetii with Coxiellalike bacteria but also revealed some mutations specific to Coxiella-like bacteria [START_REF] Smith | A Coxiella-like endosymbiont is a potential vitamin source for the lone star Tick[END_REF][START_REF] Gottlieb | Distinctive genome reduction rates revealed by genomic analyses of two Coxiella-Like endosymbionts in ticks[END_REF]. This pattern likely explains why PCR cross-reactions with Coxiella-like bacteria are partial and variable between markers. Interestingly, identical IS1111 copies were found in C. burnetii and some Coxiella-like bacteria [START_REF] Duron | The IS1111 insertion sequence used for detection of Coxiella burnetii is widespread in Coxiella-like endosymbionts of ticks[END_REF], suggesting that the risk of detecting Coxiella-like bacteria with IS1111 primers designed to detect C. burnetii is very high and must not be underestimated.

PCR-based surveys that aim to detect C. burnetii in ticks must be interpreted with caution if the amplified DNA products are not sequenced. Unfortunately, the ratio of bacterial DNA to tick DNA is frequently low, which makes it challenging to obtain PCR products concentrated enough for direct sequencing via conventional PCR. Additionally, currently available qPCR methods, such as those used in this study, often yield very short DNA fragments that are difficult to concentrate for sequencing purposes and that correspond to rather uninformative sequences. Therefore, there is an urgent need to develop a multiplex qPCR or microchip method that would make it possible to directly differentiate Coxiella-like bacteria from C. burnetii in tick samples and to detect co-infections. Pending development of such a test, useful alternative methods include the sequencing of the 16S rRNA, rpoB, and GroEL genes of Coxiella bacteria, after amplification by nested PCR, as previously described [START_REF] Duron | The recent evolution of a maternally-inherited endosymbiont of ticks led to the emergence of the Q fever pathogen, Coxiella burnetii[END_REF][START_REF] Duron | Diversity and global distribution of the Coxiella intracellular bacterium in seabird ticks[END_REF].

  infection ecology & epidemiology T h e O n e H e a l t h J o u r n a l ae Infection Ecology and Epidemiology 2015. # 2015 Jourdain Elsa et al. This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), permitting all non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

  ): clade A (Ornithodoros rostratus, O. peruvianus, O. capensis), clade B (Ixodes ricinus), clade C (Rhipicephalus annulatus, R. decoloratus, R. geigyi, O. sonrai, O. occidentalis), and clade D (Amblyomma

Fig. 1 .

 1 Fig. 1. Genetic relatedness of the 10 tick species used in this study using as reference the phylogenetic network published by Duron et al. (17) with concatenated 16S rRNA, 23S rRNA, GroEL/htpB, rpoB, and dnaK sequences for 71 tick-borne Coxiella strains, 15 C. burnetii reference strains, and several bacterial outgroups.

  used for the amplification of IS1111 will be soon published by Sidi-Boumedine et al. (in preparation) and remains meanwhile confidential; b GenBank accession number: CP011126; c GenBank accession number: CP007541; d sequence positions are distant from each other on the endosymbiont complete genome.Cross-reactions between C. burnetii and Coxiella-like bacteria

Table 1 .

 1 Details about the qPCR methods used in the study

							% covering with the	% covering with the
				Primers and probe	Fragment		endosymbiont of	endosymbiont of
	Gene	Function	Primer designation	sequences (5?Á3?)	length (bp)	Reference	R. turanicus b	A. americanum c
	IS1111	Insertion sequence	Forward primer	Confidential a
			Reverse primer
			Probe

Table 2 .

 2 C t values obtained using qPCR for both specimens of the 10 tick species tested

	Coxiella-like clade	Tick species	IS1111	icd	GroEL/htpB	p1	scvA
	A	O. rostratus	Á/Á	Á /Á	Á /Á	Á /Á	Á /Á
		O. peruvianus	39/37	Á/Á	30/31	Á/Á	Á /Á
		O. capensis	Á/Á	Á /Á	35/35	Á/Á	Á /38
	B	I. ricinus	Á/Á	Á /Á	Á /Á	Á /Á	Á /Á
	C	R. annulatus	37/38	Á/Á	Á /Á	Á /Á	Á /Á
		R. decoloratus	Á/36	Á/Á	Á /Á	Á /Á	39/Á
		R. geigyi	37/33	Á/Á	Á /38	Á/35	Á/38
		O. sonrai	39/36

(page number not for citation purpose)

(page number not for citation purpose) Citation: Infection Ecology and Epidemiology 2015, 5: 29230http://dx.doi.org/10.3402/iee.v5.29230

Citation: Infection Ecology and Epidemiology 2015, 5: 29230http://dx.doi.org/10.3402/iee.v5.29230

Acknowledgements

We thank Elodie Rousset for reading and providing comments on the manuscript; Aure ´lien Joulie, Se ´bastien Masseglia, and Elise Yang for their involvement in the molecular analyses; and Karen McCoy, Christine Chevillon, Abel Biguezoton, Marcelo Labruna, Patrick Durand, and Franc ¸ois Renaud for collecting the ticks.

Conflict of interest and funding


Thuy-Quynh Duong

Assil Bouzid

Carlo Massobrio

Guido Ori

Mauro Boero

Evelyne Martin
email: evelyne.martin@unistra.fr

First-principles thermal transport in amorphous Ge 2 Sb 2 Te 5 at the nanoscale

Keywords: Thermal conductivity, first-principles molecular dynamics, amorphous, phase-change materials

Achieving a precise understanding of nanoscale thermal transport in phase change materials (PCMs), such as Ge 2 Sb 2 Te 5 (GST), is the key of thermal management in nanoelectronics, photonic and neuromorphic applications using non-volatile memories. By resorting to a first-principles approach to calculate the thermal conductivity of amorphous GST, we found that size effects and heat transport via propagative modes persist well beyond extended range order distances typical of disordered network-forming materials. Values obtained are in quantitative agreement with the experimental data, by revealing a strong size dependence of the thermal conductivity down to the 1.7-10 nm range, fully covering the scale of current PCMs-based devices. In particular, a reduction of thermal conductivity as large as 75% occurs for dimensions lying below 2 nm. These results provide a quantitative description of the thermal properties of amorphous GST at the nanoscale and are expected to underpin the development of PCMs-based device applications.

Computing with non-volatile memories (in-memory computing) is an efficient approach to reduce data transfer and optimize energy consumption within artificial intelligence schemes. [START_REF] Ielmini | In-Memory Computing with Resistive Switching Devices[END_REF] To this purpose, the technology based on phase-change materials (PCMs) proved worth pursuing. [START_REF] Joshi | Accurate Deep Neural Network Inference Using Computational Phase-Change Memory[END_REF] PCMs are crucial for the development of emerging photonic and neuromorphic applications, ranging from non-volatile universal memory to optoelectronic systems suitable for nanophotonic devices and neuro-inspired computing. [START_REF] Wuttig | Phase-Change Materials for Non-Volatile Photonic Applications[END_REF][START_REF] Zhang | Designing Crystallization in Phase-Change Materials for Universal Memory and Neuro-Inspired Computing[END_REF] Thermal management of PCMs enables the optimization of the supplied energy needed to switch between crystalline and amorphous states. At the memory cell level, low power operation calls for minimization of the current required to promote phase change (SET/RESET) via a comprehensive thermal design involving both PCM structural organizations. However, despite the considerable gain in knowledge of thermal transport in crystals, transport modes and size effects in disordered materials have escaped a quantitative assessment. To date, amorphous silicon is the only disordered material for which a reduction of thermal conductivity at short scale has been reported experimentally. [START_REF] Wingert | Thermal Transport in Amorphous Materials: A Review[END_REF] On the theoretical side, it appears that a depletion of thermal conductivity down to reduced dimensions could also occur in disordered chalcogenides. [START_REF] Duong | Thermal Conductivity and Transport Modes in Glassy GeTe 4 by First-Principles Molecular Dynamics[END_REF][START_REF] Duong | Heat Transport in Disordered Network Forming Materials: Size Effects and Existence of Propagative Modes[END_REF] Yet, it has to be established whether or not this behavior is general and holds for materials characterized by reversible structural changes between ordered and disordered phases.

Interest in the ternary compound Ge 2 Sb 2 Te 5 (GST), a chalcogenide featuring prototypical properties for phase-change memories, stems from its high recrystallization speed as well as melting and glass transition points compatible with high data retention. [START_REF] Wuttig | Phase-Change Materials for Rewriteable Data Storage[END_REF][START_REF] Burr | Phase Change Memory Technology[END_REF][START_REF] Noé | Phase-Change Materials for Non-Volatile Memory Devices: From Technological Challenges to Materials Science Issues[END_REF] Thermal optimization of phase-change memories relies on the impact of nanoscale dimensions on the thermal conductivity κ. At the nanometer scale, a reduction of κ affects the operating of devices by slowing down heating and phase switching, with a direct consequence on the temporal response and energy consumption. This specific physical behavior requires reliable theoretical tools allowing for a quantitative description of thermal transport.

In the present work, we study the thermal conductivity of amorphous Ge 2 Sb 2 Te 5 (GST), investigate its dependence on size and quantify the short scale effects. We demonstrate that a sizeable reduction of thermal conductivity can arise in PCMs at small sizes. To this end, we have resorted to first-principles molecular dynamics (FPMD) to generate the disordered structure and to the approach-to-equilibrium molecular dynamics (AEMD) strategy [START_REF] Lampin | Thermal Conductivity from Approach-to-Equilibrium Molecular Dynamics[END_REF] to determine the thermal conductivity. We adopted the Car-Parrinello 12 framework as implemented in the CPMD code. 13 For the exchange-correlation part of the Kohn-Sham energy expression, we selected the exchange functional of Becke [START_REF] Becke | Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior[END_REF] and the correlation part of Lee, Yang and Parr 15 (BLYP). We described the valence-core interaction by norm-conserving pseudopotential as prescribed by Troullier-Martins. [START_REF] Troullier | Efficient Pseudopotentials for Plane-Wave Calculations[END_REF] Valence electrons are represented by a plane-wave basis set with a cutoff of 30 Ry, and expanded at the Γ point only. The fictitious electron mass was set to 500 a.u. and the time step to 5 a.u. to achieve optimal conservation of the constants of motion. The ionic temperature was controlled with a Nosé-Hoover [START_REF] Nosé | A Molecular Dynamics Method for Simulations in the Canonical Ensemble[END_REF][START_REF] Nosé | A Unified Formulation of the Constant Temperature Molecular Dynamics Methods[END_REF][START_REF] Hoover | Canonical Dynamics: Equilibrium Phase-Space Distributions[END_REF] thermostat chain. [START_REF] Martyna | Nosé-Hoover Chains: The Canonical Ensemble via Continuous Dynamics[END_REF] In Ref. [START_REF] Bouzid | Atomic-Scale Structure of the Glassy Ge 2 Sb 2 Te 5 Phase Change Material: A Quantitative Assessment via First-Principles Molecular Dynamics[END_REF] and 300 K (15 ps). Then, model D was duplicated to obtain model D2, annealed for 5 ps at T =600 K and 5 ps at 300 K. In a further step, model D2 (N =504 atoms) was further duplicated to obtain model D4 (N =1008 atoms), this latter being annealed for 10 ps at T =300 K. Periodic boundary conditions are applied to D, D2 and D4. Cell dimensions of the four models are given in Table 1. We stress that our models have the dimensions of the most advanced nanometric phase-change memories. [START_REF] Kersting | Exploiting Nanoscale Effects in Phase Change Memories[END_REF] Our strategy featuring four distinct annealing and relaxation runs is intended to meet the requirement of models statistically uncorrelated while having in common, in the case of D, D2 and D4, the same original simulation box. The four models considered yield of Ref. [START_REF] Bouzid | Atomic-Scale Structure of the Glassy Ge 2 Sb 2 Te 5 Phase Change Material: A Quantitative Assessment via First-Principles Molecular Dynamics[END_REF] The intensities of all the peaks are well reproduced. Interestingly, S T (k) features a prominent bump at k ≈ 1 Å -1 , indicative of intermediate range order extending up to distances in the range 6-8 Å. Partial pair correlation functions are also very similar (see Fig. 2) as well as the coordination numbers n Ge , n Sb , n Te for each species (Table 2). Small differences found among the four realizations have to be ascribed to statistical errors that are typically encountered when producing structures configurationally arrested over the time scales of molecular dynamics. The above pieces of evidence demonstrates unambiguously that the four samples of amorphous GST created by FPMD share the same essential topological features of the network, i.e. D, D2 and D4 do not introduce any relevant changes with respect to the description of Ref. [START_REF] Bouzid | Atomic-Scale Structure of the Glassy Ge 2 Sb 2 Te 5 Phase Change Material: A Quantitative Assessment via First-Principles Molecular Dynamics[END_REF] based on model B. Therefore, we can safely rule out the presence of size effects in the bulk properties of calculated amorphous GST. Stringent evidence on the predictive power of our FPMD approach for chalcogenides with models ranging in between N ≈100 and N ≈500 is summarized in Ref. [START_REF] Duong | Thermal Conductivity and Transport Modes in Glassy GeTe 4 by First-Principles Molecular Dynamics[END_REF] The transient regime is obtained following two phases. During the first (phase 1), the system is divided in two blocks (see inset of Fig. 3). The hot block is kept at T = 400 K and the cold block at T = 200 K via two distinct thermostats maintained during 10 ps. At the end of phase 1, the temperature difference between the blocks is released, leading to a transient regime (phase 2) characterized by the decrease (increase) in temperature of the hot (cold) block. Fig. 3 shows the time evolution of the process for the largest model, D4.

Fig. 4 shows the temperature profiles in the four models averaged during the whole duration of phase 2. The profiles are sinusoidal with a period equal to the extension of the simulation cell along the transport direction (L). This proves that heat propagation occurs in the diffusive regime since the sine form is the solution of the heat equation in a one dimensional periodic system.

The decay time τ of the thermal transient observed during phase 2 of AEMD gives access to the thermal conductivity κ defined as:

25 κ = L 2 4π 2 C.ρ τ . ( 1
)
where C is the heat capacity calculated from the variation of the total energy versus temperature and ρ is the system density. Since the temperature difference ∆T (t) during phase 2 evolves to a very good extent according to an exponential decay, a decay time τ can be extracted for each model. Thermal conductivities presented in Fig. 5 feature a dependence on the dimension of the simulation cell along the transport direction (L). This can be rationalized in terms of behavior of heat carriers. Heat carriers with mean free paths (MFP) smaller than L are those experiencing scattering events, while transport is ballistic for heat carriers with a higher MFP. When increasing L, the contribution of heat carriers of larger MFP increases until the bulk thermal conductivity is reached for L larger than the maximum MFP. For sizes larger than the maximum MFP, the thermal conductivity becomes independent on the system length. [START_REF] Zaoui | Fourier-like Conduction and Finite One-Dimensional Thermal Conductivity in Long Silicon Nanowires by Approach-to-Equilibrium Molecular Dynamics[END_REF][START_REF] Zaoui | Thermal Conductivity of Deca-Nanometric Patterned Si Membranes by Multiscale Simulations[END_REF] The evolution from a mixed ballistic-diffusive to a purely diffusive regime has been de-

κ AJ (L) = κ bulk L 2 2π 2 l 2   1 + 4 πl L 2 -1   , (2)
where κ bulk is the bulk thermal conductivity and l is a parameter with the dimension of a length. Our results are consistent with Eq. 2, as shown in Fig. 5. The resulting bulk thermal conductivity κ bulk equal to 0.26±0.04 W K -1 m -1 agrees with the experimental data reported in Table 3.

The existence of a length dependence in the heat transport direction means that propagative modes with a distribution of MFPs are responsible for heat transport in a way analogous to phonons in crystals. In our FPMD-AEMD results the persistence of such length dependence up to 8 nm (size of model D4) cannot be related to enhanced structural order in the glass. In fact, such extended form of structural organization does exist in prototypical disordered AX 2 materials 36 but it does not extend to distances larger than 6 nm. At the largest sizes, a plateau occurs in the κ(L) behavior for L > 35 nm (Fig. 5). Below this value, a sizeable reduction of thermal conductivity is detectable. It is instructive to consider the thermal conductivities of amorphous GeTe 4 as reported in Fig. 5, for which size effects persist up to even larger dimensions (≈ 50 nm). [START_REF] Duong | Thermal Conductivity and Transport Modes in Glassy GeTe 4 by First-Principles Molecular Dynamics[END_REF] Taken together, these findings prove that propagative modes and size effects are a general feature in chalcogenide glasses and have profound consequences in those prone to nanotechnology applications. This is illustrated in Table 4 where we report the corresponding reductions of thermal conductivities at 10, 5 and 2 nm. The design of phase-change devices should therefore account for such a reduction of thermal conductivity at smaller technological nodes, that could lead to an increase of the switching time that would eclipse the benefits of downscaling. In conclusion, the thermal conductivity of amorphous Ge 2 Sb 2 Te 5 has been obtained within a first-principles methodology allowing for an affordable treatment of system sizes of about 1000 atoms and adequate simulation times. We obtained a quantitative agreement with experimental data, substantiated by a robust analytical extrapolation to macroscopic sizes. We found a length dependence of the thermal conductivity up to 35 nm, a clear indication that propagative carriers contribute to heat transport in spite of structural disorder.

The reduction of the thermal conductivity manifests itself as a general feature in disordered chalcogenides, being quite significant (75% ) in amorphous Ge 2 Sb 2 Te 5 for sizes below 2 nm, bearing an unavoidable impact on the thermal management of phase-change memories.

  this scheme was employed for N =144 atoms (32 Ge, 32 Sb and 80 Te) in a cubic periodic simulation cell of side length 16.86 Å (model B hereafter). To assess the dependence of the thermal conductivity on the dimensions along and across the direction of thermal transport, we have created a new model D made of 252 atoms (56 Ge, 56 Sb and 140 Te) in a cubic simulation cell of 20.32 Å. Stable configurations were obtained from a canonical NVT (constant volume and temperature) trajectory with the following thermal cycle: T = 200 K (5 ps), 300 K (4 ps), 600 K (4 ps), 900 K (12 ps), 600 K (11 ps)

Figure 1 :

 1 Figure 1: Experimental and calculated neutrons structure factor S T (k) of amorphous GST.

24

 24

Figure 2 :

 2 Figure 2: Partial pair correlation functions of the four models of amorphous GST

Figure 3 :

 3 Figure 3: Temperatures in the hot (red line) and cold (blue line) blocks during the two phases of AEMD. Model D4 (N =1008 atoms) is presented in inset with the hot and cold blocks identified.

Figure 4 :

 4 Figure 4: Temperature profiles in the four amorphous GST models during phase 2 of AEMD (dots). The data for the smallest models (B, D and D2) are replicated according to the peridodic boundary conditions. The lines are sine functions fitted to the AEMD data.

Figure 5 :

 5 Figure 5: Thermal conductivities of amorphous GST calculated by AEMD (red dots). The results obtained in Ref. 6 for amorphous GeTe 4 using AEMD are also reported (black dots). The lines are fits following Alvarez and Jou's analytical model of size dependence (Eq. 2). The arrows indicate the maximum MFPs.

Table 1 :

 1 Our four models of amorphous GST. L is the supercell length in the heat transport direction and S is its cross section.

	Name	N	S(Å 2 )	L (Å)
	B	144 16.86×16.86 16.86
	D	252 20.32×20.32 20.32
	D2	504 20.32×20.32 40.65
	D4	1008 20.32×20.32 81.31
	very close structural descriptions of amorphous GST in terms of comparison with available
	experimental quantities and characteristic motifs of the network. For instance, the total
	neutron structure factors S T (k) of models B, D, D2 and D4 are reported in Fig. 1 and
	compared with experiments.

[START_REF] Jóvári | Local Order in Amorphous Ge 2 Sb 2 Te 5 and GeSb 2 Te 4[END_REF]

They exhibit very similar patterns by substantiating the data

Table 2 :

 2 Coordination numbers for Ge (n Ge ), Sb (n Sb ) and Te (n Te ) in the four models.

	Model n Ge n Sb n Te
	B	4.03 3.99 2.58
	D	4.13 3.81 2.66
	D2	4.07 3.98 2.63
	D4	3.98 4.03 2.63
	transient and, in particular, its decay time τ , this methodology being well established as both
	effective and affordable.

Table 3 :

 3 Experimental values of the thermal conductivity of amorphous GST (from top to bottom in chronological order).

	Ref. κ (W K -1 m -1 )	Method	Dimensions (nm)
	29	0.17	Laser-induced temperature distribution	20-85
	30	0.24	3ω	98-200
	31	0.24	3ω	300
	32	0.19	Time-domain thermoreflectance	270
	33	0.19	Photothermal radiometry	100-840
	34	0.25±0.05	Time-domain thermoreflectance	30-150
	35	0.30	Scanning thermal microscopy	100-200

Table 4 :

 4 Reduction of thermal conductivity at short sizes.

		10 nm 5 nm 2 nm
	GST	23%	46% 73%
	gGeTe 4 38%	61% 82%

Acknowledgement

Sébastien Le Roux is acknowledged for constructive comments. Financial support of the French ANR via the project n. ANR-17-CE09-0039-02 "SIRENA" is gratefully acknowledged.

Calculations were performed by using resources from GENCI (Grand Equipement National de Calcul Intensif) (Grants No. 0910296 and 095071).