Alyssa Imbert
email: alyssa.imbert@inra.fr

Armand Valsesia

Caroline Le Gall

Claudia Armenise

Gregory Lefebvre

Pierre-Antoine Gourraud

Nathalie Viguerie

Nathalie Vialaneix

Nathalie Villa-Vialaneix

Multiple hot-deck imputation for network inference from RNA sequencing data

Introduction

In the last decades, biology and medicine have been profoundly renovated by the access to a large amount of molecular information, at various 'omics levels. Among high-throughput sequencing techniques, RNAseq measures the expression of several thousands of genes for a given tissue. The large amount of generated data has created a need for multiple bioinformatics and statistical post-processing of the raw experimental data. In particular, a great deal of attention has been granted to the search of various types of relations between the genes (co-expression or regulation) [START_REF] Zhang | Inferring gene networks from discrete expression data[END_REF]; [START_REF] Montastier | System model network for adipose tissue signatures related to weight changes in response to calorie restriction and subsequent weight maintenance[END_REF], among others): better understanding those relations gives an insight on the global functioning of the cell in given environments and is a key point to reveal signaling pathways and to identify target genes for a given biological problem. Moreover, network visualization facilitates global analysis of the datasets.

RNA-seq expression data are count data and are thus discrete so standard GGM models usually used for network inferrence and that are based on Gaussianity assumption are not suited to such data. Recent works have considered using a generalized linear model (GLM) based on the i i "imbert_etal_B2018" -2018/5/17 -14:12 -page 2 -#2 i i i i i i

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A.Imbert et al.

Poisson distribution (log-linear graphical model [START_REF] Allen | A log-linear graphical model for inferring genetic networks from high-throughput sequencing data[END_REF] or hierarchical Poisson log-normal model [START_REF] Gallopin | A hierarchical Poisson log-normal model for network inference from RNA sequencing data[END_REF]). In such methods, edge selection is handled by a L 1 penalty as in the continuous case. However, network inference is still a difficult issue as explained in [START_REF] Verzelen | Minimax risks for sparse regressions: ultra-highdimensional phenomenons[END_REF], since the number of available samples (n) is generally much lower than the number of parameters to estimate (that scales as p 2 , where p is the number of genes). Second, network inference can be very sensitive to missing individuals in key genes [START_REF] Picheny | Reconstruction quality of a biological network when its constituting elements are partially observed[END_REF] or to the presence of "influential" individuals. Having a large number of observations is thus a key point for ensuring reliable results in statistical analyses of RNA-seq data [START_REF] Liu | RNA-seq differential expression studies: more sequence or more replication[END_REF].

In this paper, we propose a method to increase the reliability of the inference when RNA-seq expression data have been measured together with other biological data closely related to the phenomenon under study. One typical case for such studies is the one in which RNA-seq measures have been performed on the same individuals simultaneously to another expression experiment using another (less costly) technique (e.g., RT-qPCR). Another case is the one in which two RNA-seq experiments have been performed on two different tissues on the same individuals. It is relevant to try to use the external information brought by the auxiliary dataset in order to improve the quality of inference: when the acquisition cost is lower or when the ability to collect samples is easier, the number of samples acquired on the auxiliary dataset can be much larger. It thus provides additional information on relations between individuals and on biological variability.

We have designed an approach based on imputation in which individuals which are not observed in RNA-seq dataset but are observed on the secondary dataset are considered as missing data. It is called hd-MI and is presented in Section 2). A wide variety of methods falls under the general heading of imputation [START_REF] Enders | Applied Missing Data Analysis[END_REF][START_REF] Little | Statistical Analysis with Missing Data[END_REF] but most of them impute missing values from different variables independently, based on the (non missing) values of the other variables for the same individual. Here, two additional issues are to be faced: first, entire individuals are considered as missing (unit non-responses case) means that entire rows are missing in X and second, for network inference, the correlation structure between variables must be preserved during the imputation and the standard methods described above do not fulfill this need.

hd-MI is based on hot-deck and addresses both of these issues. In addition, the part of the uncertainty in the final result that comes from the imputation process is assessed using the general framework of multiple imputation [START_REF] Rubin | Multlipe Imputation for Nonresponse in Surveys[END_REF][START_REF] Schafer | Multiple imputation: a primer[END_REF][START_REF] Rubin | Multiple imputation after 18+ years[END_REF]. This method has the additional benefit of providing more stable results and only assumes that the secondary dataset provides useful information about the resemblance between individuals and not about the network inference itself. The approach is assessed on two real RNA-seq datasets: one coming from a study on human tissue gene expression and the other coming from a longitudinal study on adipose tissue: the datasets and the methodology used to evaluate the method are presented in Section 3. Results are given and discussed in Section 4.

Methods

Background and notations

In the sequel, X will denote the RNA-seq expression dataset with n 1 rows (individuals) and p columns (genes). x ij is the count of gene j, j ∈ {1, ..., p}, for individual i. Additionally, an auxiliary dataset is available, which will be denoted by Y. Y is supposed to have q columns and n > n 1 rows, including rows corresponding to the same n 1 individuals already observed in X. Without loss of generality, the common individuals between X and Y are supposed to correspond to the first n 1 rows of Y. y ij will denote the observation of variable j, j ∈ {1, ..., q}, for individual i. As already stated in the introduction, the above problem can be viewed as a missing value problem in the matrix [ X, Y] with dimensions n × (p + q) for which row number

i is xi = x i if i ≤ n 1 missing otherwise
. Such a framework is called "unit non-responses", because missing values correspond to the absence of a complete individual. (see Supplementary Figure 1). In this paper, missing individuals i ∈ {n 1 + 1, ..., n} in the RNAseq dataset are supposed to be Missing Completely At Random. This is a standard assumption if individuals have not been chosen according to a specific feature within {1, . . . , n} but because of a random choice or of technical constrains such as failed experiments or lack of tissue or to cost constrains if individual data are expensive or difficult to acquire.

hd-MI

"hot-deck" imputation is often used to impute non-response in surveys [START_REF] Andridge | A review of hot deck imputation for survey non-response[END_REF]. It is based on the concept of "donors": if a respondent, i, called "recipient", has a missing value, xij , a set of similar individuals (donors) are pulled from {i : i = i st xi j is not missing}. This set of donors usually depends on the respondent itself. It is called donor pool and is denoted by D(i). One of the donors is finally randomly selected within D(i) to provide its value xi j for imputing xij . Hot-deck imputation generally preserves the univariate distributions of the data and does not attenuate the variability of the filled-in data to the same extent as other imputation methods [START_REF] Enders | Applied Missing Data Analysis[END_REF].

However, in basic hot-deck imputation, the correlation structure between variables is still modified during the imputation because the imputation of the different variables for an individual i are performed independently. To address this issue in the case of unit non-response problems, [START_REF] Voillet | Handling missing rows in multi-omics data integration: multiple imputation in multiple factor analysis framework[END_REF] proposed to impute simultaneously all variables (x ij ) j=1,...,p by the values coming from a single donor i ∈ D(i) for a 'omic data integration problem.

Our approach, hd-MI (see Figure 1) is closely related to the method described in [START_REF] Voillet | Handling missing rows in multi-omics data integration: multiple imputation in multiple factor analysis framework[END_REF]. It is adapted to the case of network inference with an auxiliary dataset. A multiple hot-deck imputation is performed, in which the imputation step is performed as described below:

1. firstly, for all missing individuals in X, i = n 1 + 1, . . . , n, the pool of donors D(i) is created and contains all individuals i ≤ n 1 which are "similar" to i. To estimate the similarity between individuals, the auxiliary dataset Y is used and different similarities can be calculated between individuals based on this dataset. Among them, we propose to use an affinity score, as in [START_REF] Cranmer | We have to be discrete about this: a nonparametric imputation technique for missing categorical data[END_REF]. This affinity score is computed for all individuals j by s(i, i ) = 1 q q j=1 I {|y ij -y i j |<σ} , in which σ is a fixed threshold. The pool of donors is then obtained as

D(i) = {i : s(i, i ) = max l=1, ..., n 1 s(i, i )}.
This score is the average number of observed variables for which the individuals i and i are "close"; 2. in a second step, an individual, i is picked at random in D(i) and the entire row i of X is imputed with row i of X. This step is repeated for all i = n 1 + 1, . . . , n to produce a complete case dataset X * .

In the framework of multiple imputation, the whole procedure is repeated M times independently to obtain M complete case datasets X * ,m . The second step of the analysis consists in inferring the network for all these complete case datasets, using the model proposed in Allen and Liu (2012) (LLGM). The M networks are finally combined by studying the number of times an edge is predicted among the M networks: r(e) = number of times the edge e is predicted

M

. A reliability threshold, r 0 is finally chosen and the final network is composed of the edges e such The original dataset ( X, left) is duplicated M times (second column). For every duplicate, each missing row is imputed by hot-deck (third column, X * ,m ). A network is inferred from each imputed dataset (fourth column), with LLGM (StARS is used to choose the regularization parameter, λ, in the method). Finally the networks are combined into a single network using a threshold r 0 for edge frequency among the M networks (fifth column).

that r(e) ≥ r 0 . This approach is similar to the stability criterion described in [START_REF] Meinshausen | High dimensional graphs and variable selection with the Lasso[END_REF].

The uncertainty of the imputation is thus handled in a way that is similar to standard approaches for improving the quality of network inference [START_REF] Allouche | A panel of learning methods for the reconstruction of gene regulatory networks in a systems genetics context[END_REF][START_REF] Ballouz | Guidance for RNA-seq co-expression network construction and analysis: safety in numbers[END_REF], which use averaged weights or averaged ranks between multiple networks coming from different bootstrap resampling or from independent experiments.

Finally hd-MI does not require to tune many hyperparameters: only a parameter for the definition of the pool of donors (σ) and the number M of repeats are required. The combination step of multiple imputation also requires to fix the reliability threshold r 0 and network inference requires to tune a regularization parameter. Sound choices for these parameters are discussed in Supplementary Section 1.

Implementation and evaluation

Data description

To evaluate the performance of hd-MI, two real datasets were used coming from 2 distinct projects:

• GTEx [START_REF] Lonsdale | The genotype-tissue expression (GTEx) project[END_REF], in which RNA-seq expression were acquired on several human tissues. We confined our analysis to two tissues: lung and thyroid. Lung expression dataset was used as primary dataset, X 0 , and thyroid expression dataset was used as the auxiliary dataset, Y; • DiOGenes [START_REF] Larsen | The diet, obesity and genes (diogenes) dietary study in eight European countries -A comprehensive design for longterm intervention[END_REF], in which RNA-seq expression were acquired simultaneously to the measure of gene expression with another technique (RT-qPCR), on the same human tissue (adipose tissue) at two different time steps (CID1 and CID2) of a dietary intervention (before and after a 8 week low calorie diet). For n = 189 individuals, RNA-seq expression data were acquired at both CID1 and CID2 but for other individuals, either CID1 or CID2 data only were acquired (see Supplementary Figure 2 for a Venn Diagramm of data acquisition).

Further details on datasets are provided in Supplementary Section 2. The relevance of the method was assessed in two different types of analyses:

1. firstly, common samples between the primary and auxiliary datasets were kept to form the complete case dataset. The selected datasets do not contain missing individual. Artificially removing individuals from the primary dataset, these datasets are used as a reference to evaluate hd-MI and to compare it with other methods (Section 3.2); 2. secondly, all individuals from the DiOGenes project (CID1 and CID2, both common samples and CID specific samples) were used to infer one network for each CID (Section 3.3). These networks were further investigated and evaluated by comparison to previously inferred networks, obtained from different datasets.

The difference between evaluation and application on DiOGenes dataset is illustrated in Supplementary Figure 3.

Evaluation and comparison with existing methods

For each case, only common samples between two RNA-seq datasets (n = 221, for GTEx) or between two expression datasets (RNA-seq and RT-qPCR) and two time steps (n = 189 for DiOGenes) were kept to form the complete case dataset, used as a reference. p = 100 and q = 50 genes were selected for being the most variable in GTEx and p = 317 genes were selected for biological reasons for DiOGenes. The selected datasets do not contain missing individual and will be denoted by X 0 in the sequel. Datasets with missing individuals were then generated by randomly removing some samples in X 0 . More precisely, starting from a complete dataset X 0 , a given percentage f of rows were randomly removed (with f ∈ {10%, 20%, 30%, 40%}) to produce a dataset X with missing values. The corresponding complete case dataset is again denoted by X. Imputation was then performed using hd-MI and two alternative methods: 1/ a simple imputation method, i.e., imputation by the mean and 2/ a state-of-the-art imputation method, Multiple Imputation by PCA (MIPCA) [START_REF] Josse | Multiple imputation in principal component analysis[END_REF]. This led us to infer networks from:

• the full dataset X 0 : the obtained network is referred as reference in the result section. It is used as a gold standard for our comparison; • datasets with varying rates of missing individuals with no imputation (hence the networks were inferred from the complete case dataset X). These networks are referred as missing (possibly followed by a missing rate) in the result section. They are used as the worse case scenario;

• datasets with values imputed by the mean. These networks are referred as mean (possibly followed by a missing rate) in the result section; • M datasets with values imputed by MIPCA, in which the dataset [ X, Y] is used as an input. For DiOGenes, Y (RT-qPCR expression) were scaled before affinity computation. Negative imputations (if any) were replaced by 0. These networks are referred as MIPCA (possibly followed by a missing rate) in the result section; • M datasets with values imputed by our approach (using either the affinity score or the approach to define the donor sets). These networks are referred as hd-MI, possibly followed by a missing rate and, for the second case, by a number indicating the value of k.

For all the datasets described above, networks were inferred as follow:

• for the cases in which a single inference is performed (all datasets except the ones in which multiple imputation is used), the model described in Section 2.2 is performed with a full regularization path for the regularization parameter of the sparse penalty, λ. For each dataset we thus obtained a network for every value of λ in the regularization path. We also computed the StARS criterion to obtain the value of λ related to the most stable network along the path; • for the cases of multiple imputation, a single network was inferred from every imputed dataset X * ,m , using the regularization parameter λ selected by the StARS criterion. This led us to obtain M networks which were combined with varying reliability rates r 0 : a final network was obtained for every value of r 0 .

The detailed evaluation process is illustrated in Supplementary Figure 4. The results obtained with these different methods were assessed through global comparison of the network structures and through more local comparisons that were generally computed using reference as a gold-standard. In addition, for the DiOGenes datasets, 20 replicates of the whole evaluation procedure were obtained, so as to assess the stability of our findings.

Illustration of the interest on complete DiOGenes data

Finally, two networks (one for CID1 and one for CID2) were inferred using all individuals from RNA-seq datasets for the inference and RT-qPCR datasets as the auxiliary dataset. Supplementary Figure 3 provides the flow chart of the DiOGenes dataset processing, distinguishing the evaluation (Section 3.2) from the application for network inference (current section).

All experiments have been performed using R, version 3.2.2 (R Core Team, 2016). Details about which packages have been used are given in Supplementary Section 3. The R package RNAseqNet provides functions to perform hd-MI and network inference using the model of [START_REF] Allen | A log-linear graphical model for inferring genetic networks from high-throughput sequencing data[END_REF]. Facilities for choosing hyperparameters are also provided.

Results and discussion

Evaluation and comparison with existing methods

The distribution of the appearance of an edge in the M (M = 100) inferred networks from datasets imputed by hd-MI is provided in Supplementary Figures 5 and6, respectively for GTEx and DiOGenes datasets. A large proportion of edges are present in less than 10% of networks: these edges are not stable and show the sensitivity of network inference to some individuals. However, a small proportion of edges are very stable and inferred in more than 90% of the M imputed datasets. When evaluating the goodness of networks, the value r 0 = 0.9 was then chosen. In addition, Supplementary Tables 1 and2 provide the global characteristics of the inferred networks and show that hd-MI network is in line with reference with respect to these measures, even if the number of inferred edges is slightly less than for networks reference, missing and mean.

Precision / Recall (PR) curves, as compared to network reference, are displayed in Figure 2. PR curves for mean and missing are obtained for varying values of λ and PR curves for MIPCA and hd-MI are obtained for varying values of r 0 . Top figures show the results obtained for DiOGenes CID1 (left) and GTEx (right) for 20% of missing individuals and bottom figures show the effect of varying the rate of missing individuals for DiOGenes CID1. missing and mean have similar curves, which shows that naive imputation method as mean does not perform better, in this framework, than simply using complete case datasets. On the contrary, hd-MI has the best recall for the highest precision rates. Since real biological networks are known to be sparse, the first few edges are the most important to recover: highest precisions have to be favored over recall for these applications. In the best case (DiOGenes), the precision is much larger than for the naive approaches. In the worst case (GTEx), naive methods do only slightly worse than hd-MI but with no indication on the reliability associated to each edge and on its sensitivity to missing values, contrary to hd-MI.

MIPCA shows poor performance: for all precision rates, MIPCA has the worse precision/recall curve for both GTEx and DiOGenes. hd-MI is much better adapted to the case of network inference than other stateof-the-art approach, such as MIPCA. The reason is twofold: firstly, as already stated before, by imputed missing values in different variables independently from each other, MIPCA does not preserve the correlation structure between variables. Secondly, as shown on this real data problem, MIPCA does not constrain the range of imputed values to be the same than the range of observed values. Sometimes, irrelevant values (e.g., here negative values) are imputed and can strongly affect the results. Naive approaches do not have these drawbacks. Their performances can thus be more similar to those of our method.

For the other rates of missing individuals, the results remain very similar even though the global performances of all methods are deteriorated by an increasing rate of missing individuals (as expected) and if the differences between methods tend to slightly decrease when the rate of missing individuals increases.

To assess the stability of our results, the whole simulation procedure was repeated 20 times for the DiOGenes dataset, at CID1 with 20% of missing individuals. Results show that only hd-MI is consistently able to reach a good recall for the highest precision rates: missing and mean manage to reach the precision rate of 85% for 18 curves over 20 and never manage to reach a 90% of precision rates. MIPCA always reaches the targeted precision rate but with very poor recalls. Statistics (i.e., minimum, maximum and mean) of the recall for these two target precision rates are given in Table 1. They confirm this conclusion by exhibiting a much lower variability of the results obtained for hd-MI and a better recall (in average), as compared to the other methods.

Supplementary Section 5 provides additional results that are similar to the ones presented in the present section. Choices of σ for hd-MI are illustrated in Supplementary 5.1.1 and 5.2.1., respectively for GTEx and for DiOGenes, CID1 (20% of missing individuals). Supplementary material also contains results obtained for CID2 of DiOGenes (Supplementary Section 5.2.2), results obtained with different rates of missing individuals (for both datasets in Supplementary Sections 5.1.2 and 5.2.3). Table 1. Recall statistics for precision rates of 85% (left) and 90% (right).

For 85% precision rate, the recalls of the two cases where missing and mean did not reach the targeted precision rate were replaced by the recall for the highest precision.

method min mean max missing 0.352 0.649 0.746 mean 0.487 0.641 0.733 MIPCA 0.324 0.355 0.397 hd-MI 0.580 0.658 0.729 method min mean max MIPCA 0.227 0.277 0.310 hd-MI 0.545 0.593 0.655

In addition, the impact of different methods to create a pool of donors have been tested. More precisely, we have compared our affinity based approach with an affinity performed on scaled data and with different types of k-NN imputations, respectively performed with Euclidean distance, Mahalanobis distance (so as to avoid the effect of different scales and strong correlations between variables) and a method similar to the one described in [START_REF] Crookston | yaImpute: an R package for kNN imputation[END_REF] based on ridge regularized CCA [START_REF] Vinod | Canonical ridge and econometrics of joint production[END_REF]. The results prove that all these imputation methods perform very similarly with no visible changes in the inferred network (see Supplementary Section 5.2.4).

As explained in [START_REF] De Smet | Advantages and limitations of current network inference methods[END_REF][START_REF] Villa-Vialaneix | The structure of a gene co-expression network reveals biological functions underlying eQTLs[END_REF], gene networks are more relevant to identify groups of related genes (gene modules) than to study pairwise relationships between genes. To evaluate the preservation of gene modules, node clustering was performed by maximizing the modularity quality criterion [START_REF] Newman | Finding and evaluating community structure in networks[END_REF] in reference and in all inferred networks. To avoid an irrelevant number of clusters, clustering was performed only on the largest connected component of the graph. The resemblance between the module structure in reference and in the other inferred networks was assessed using the normalized mutual information (NMI, [START_REF] Danon | Comparing community structure identification[END_REF]). NMI is a quality criterion ranging from 0 to 1, with a maximum equal to 1 when the two sets of clusters (modules) are identical. NMI was computed restricted to the genes in the intersection of the two largest connected components of the two networks (the reference network and the inferred network under study).

The number of gene modules and NMI values for network clustering are given in Supplementary Tables 3 and4 for GTEx and DiOGenes CID1, respectively. Usually, gene modules are better recovered by hd-MI for GTEx dataset than for all the other methods for all missingness rates but this is not the case for DiOGenes. For the latter case, this is explained by the fact that hd-MI has closer performances to missing and mean than in GTEx and the resemblance with the modules of reference is artificially favored by the network selection. Indeed, final network selection is performed by StARS in missing, mean and reference and by r 0 thresholding in hd-MI: this corresponds to two different precision levels in PR curves. However, even in this case, modules in hd-MI network are rather similar to reference, illustrating the good preservation of network structure.

Analysis of networks inferred for complete DiOGenes data

We applied hd-MI to adipose tissue gene expression data obtained using RNA-seq during a dietary intervention. Gene modules were extracted using modularity optimization, as described above. Eight and 7 gene modules were found at CID1 and CID2, respectively (Supplementary Section 6). Because calorie restriction is known to promote body fat loss and alleviate insulin resistance, correlations between gene expression within each module with fat mass or the insulin resistance index, HOMA-IR, were computed and GO term enrichment analysis was performed for each module (Supplementary Section 7). Some features were common to CID1 and CID2. For example, MLX1PL and TWIST1 showed persistent link between module 1 at CID1 and at CID2 (Figure 3).

As a hallmark of the effects of calorie restriction, CID1 and CID2 shown differential signatures. The human TWIST1 gene encodes a transcription factor abundantly expressed in adipocytes from lean individuals that is positively correlated to insulin sensitivity and is potential regulator of adipose tissue remodeling [START_REF] Pettersson | Twist1 in human white adipose tissue and obesity[END_REF]. At CID1, TWIST1 was connected to MLX1PL and PNPLA2. At CID2, it was connected to MLX1PL and to SLC19A2, which was linked to SIRT1. The SLC19A2 gene encodes hTHTR-1, a transporter of thiamine, that plays an essential role in glycolysis. SLC19A2 is one of the 41 strongest candidate gene regions associated to positive natural selection that are involved in nutrient metabolism [START_REF] Sabeti | Genome-wide detection and characterization of positive selection in human populations[END_REF]. The SIRT1 gene encodes a deacetylase that regulates various metabolic pathways [START_REF] Cao | SIRT1 and insulin resistance[END_REF]. Calorie restriction is known to promote histone deacetylase expression. MLX1PL encodes the transcription factor ChREBP, whose activity is induced by glucose [START_REF] Filhoulaud | Novel insights into ChREBP regulation and function[END_REF]. Together with TWIST1 and SIRT1 after calorie restriction it may function as glucose sensor and insulin sensitizer.

Inferred networks were found coherent with previous findings on these genes, which indicates that hd-MI data imputation does not induce a distortion in the relationship between gene expression (as described in Supplementary Section 6). The DiOGenes adipose tissue RNA samples have been previously analyzed using RT-qPCR [START_REF] Viguerie | Determinants of human adipose tissue gene expression: impact of diet, sex, metabolic status and cis genetic regulation[END_REF][START_REF] Montastier | System model network for adipose tissue signatures related to weight changes in response to calorie restriction and subsequent weight maintenance[END_REF] and recently using RNA-seq [START_REF] Armenise | Transcriptome profiling from adipose tissue during a low-calorie diet reveals predictors of weight and glycemic outcomes in obese, nondiabetic subjects[END_REF]. Network analyses were performed using RT-qPCR data on men and women [START_REF] Viguerie | Determinants of human adipose tissue gene expression: impact of diet, sex, metabolic status and cis genetic regulation[END_REF] or a subset of women [START_REF] Montastier | System model network for adipose tissue signatures related to weight changes in response to calorie restriction and subsequent weight maintenance[END_REF]. Several features were common to both studies and were also present in our networks. In particular, a module containing the same group of correlated genes which encode enzymes involved in lipogenesis including FADS1, FADS2 and AACS was found in all CID1 networks (either inferred on women and on men). More interestingly, the links between FADS1 and AACS and between FADS2 and AACS persisted at CID2 only for our inferred network (Supplementary Figure 17). This persistence might be a positive effect of our imputation method, that provides a more comparable basis for CID1 and CID2 because it imputes missing individuals in one of the two CID.

By contrast to our previous network analyses that used a priori selected genes, the present study, by using RNA-seq data, revealed novel features. Especially, a persistent link was found between two transcription factors involved in insulin sensitivity, TWIST1 and MLX1PL (this latter gene was not available in the previous analyses) and connections to novel genes, such as SIRT1 and SLC19A2, appeared after calorie restriction.

Conclusion

We have designed a method to improve network inference from RNA-seq data from additional information about gene expression similarity between individuals. The method hd-MI is based on multiple hot-deck imputation and preserves the correlation structure between variables in a unit nonresponse framework (using the hot-deck approach) while estimating the uncertainty linked to the imputation (with a multiple imputation approach).

hd-MI shows a better precision for edge detection than complete case or naive imputation methods, with the additional advantage to provide information about the reliability of the edge and its sensitivity to missing i i "imbert_etal_B2018" -2018/5/17 -14:12 -page 7 -#7 i i i i i i Multiple hot-deck imputation for network inference from RNA sequencing data 7

individuals. hd-MI has been used in a real world application related to the impact of a low calorie diet on adipose tissue expression. It succeeded in providing relevant networks that were similar to previously inferred networks, based on different dataset and different subsets of individuals. It also predicted the persistence of the links between AACS, FADS1 and FADS2 at CID2 and enlightened adipose tissue SLC19A2 as novel partner in glucose homeostasis, besides TWIST1 and MLX1PL. Its precise role as transporter or undiscovered function is still to be investigated.

  Fig.1: Overview of hd-MI. The original dataset ( X, left) is duplicated M times (second column). For every duplicate, each missing row is imputed by hot-deck (third column, X * ,m ). A network is inferred from each imputed dataset (fourth column), with LLGM (StARS is used to choose the regularization parameter, λ, in the method). Finally the networks are combined into a single network using a threshold r 0 for edge frequency among the M networks (fifth column).

Fig. 2 :

 2 Fig. 2: PR curves, for every method and both datasets. Top figures show the results obtained for DiOGenes CID1 (left) and GTEx (right) for 20% of missing individuals and bottom figures show the effect of varying the rate of missing individuals for DiOGenes CID1. hd-MI provides an improved recall at highest precision rates, especially for DiOGenes and the smallest rates of missing individuals.

Fig. 3 :

 3 Fig. 3: Module 1 for (resp.) CID1 (a) and CID2 (b) as obtained after clustering nodes in the two networks obtained with hd-MI. These modules show direct links between TWIST1 and MLX1PL (a and b) and a novel link of TWIST1 to SIRT1 via SLC19A2 at CID2 (b).

Acknowledgements

The authors thank Mélina Gallopin for sharing personal R scripts. We also thank the three anonymous reviewers for valuable comments and suggestions which helped to improve the quality of the paper.

Funding

AI is a PhD fellow supported by the région Occitanie and Methodomics http://www.methodomics.com. PAG is founder of Methodomics. CLG is employed by Methodomics. CA is employed by Quartz Bio SA. GL, AV are employed by Nestlé Institute of Health Sciences. This work was supported by Inserm, Paul Sabatier University, Agence Nationale de la Recherche (ANR-12-BSV1-0025Obelip), Région Midi-Pyrénées (OBELIP and ILIP projects), Commission of the European Communities (FP6-513946 DiOGenes) and Innovative Medicines Initiative Joint Undertaking (grant agreement n°31 115372). The funders had no role in the study design, analyses, results interpretation and decision to publish.


Martine Armand
email: martine.armand@univ-amu.fr

Jonathan Y Bernard

Anne Forhan

Barbara Heude

Marie-Aline Charles

Isabella Annesi-Maesano

Jérémie Botton

Patricia Dargent-Molina

Blandine De Lauzon-Guillain

Pierre Ducimetière

Maria De Agostini

Bernard Foliguet

Xavier Fritel

Alice Germa

Valérie Goua

Régis Hankard

Monique Kaminski

Béatrice Larroque

Nathalie Lelong

Johanna Lepeule

Guillaume Magnin

Laetitia Marchand

Cathy Nabet

Fabrice Pierre

Rémy Slama

Marie-Josèphe Saurel-Cubizolles

Michel Schweitzer

Olivier Thiebaugeorges

Maternal nutritional determinants of colostrum fatty acids in the EDEN mother-child cohort

Keywords: maternal determinants, colostrum PUFA, pregnant women diet, BMI class, cohort study Monique Malinbaum) for data collection

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

Introduction

Environmental exposures during the first 1,000 days of life (from conception until 2 years of age), a critical window recently targeted by the World Health Organization (WHO), influences children growth, development, and later health. Early nutrition, and especially through mothers dietary intakes, is one of the essential exposure factors in the "Developmental Origin of Health and Diseases" (DOHaD) framework, first via nurturing the preimplantation embryo, then via the placental transfer of nutrients to the fetus, and lastly via human milk to breastfed infants [START_REF] Barker | The fetal origins of adult disease[END_REF][START_REF] Singhal | Early origins of cardiovascular disease: is there a unifying hypothesis?[END_REF][START_REF] Neville | Lactation and neonatal nutrition: defining and refining the critical questions[END_REF].

Human milk is considered the most appropriate food for optimal development of the infant partly because of its n-6 and n-3 polyunsaturated fatty acid (PUFA) content and specifically, linoleic (LA) and arachidonic (AA) acids, and α-linolenic (ALA) and docosahexaenoic (DHA) acids [START_REF] Hamosh | Long-chain polyunsaturated fatty acids (LC-PUFA) during early development: contribution of milk LC-PUFA to accretion rates varies among organs[END_REF]. Indeed, PUFA are constituents of tissue cells membrane and display many regulatory functions as in the inflammatory process through metabolites or for the set-up of gene expression levels [START_REF] Hamosh | Long-chain polyunsaturated fatty acids (LC-PUFA) during early development: contribution of milk LC-PUFA to accretion rates varies among organs[END_REF][START_REF] Arnardottir | Human milk proresolving mediators stimulate resolution of acute inflammation[END_REF][START_REF] Bordoni | Polyunsaturated fatty acids: From diet to binding to ppars and other nuclear receptors[END_REF]. Therefore they are essential for general growth and the development of several key organs in the newborn, such as brain, cardiovascular system and intestine [START_REF] Hamosh | Long-chain polyunsaturated fatty acids (LC-PUFA) during early development: contribution of milk LC-PUFA to accretion rates varies among organs[END_REF][START_REF] Carlson | Early determinants of development: a lipid perspective[END_REF][START_REF] Innis | Impact of maternal diet on human milk composition and neurological development of infants[END_REF][START_REF] Van Rossem | Blood pressure in 12-year-old children is associated with fatty acid composition of human milk: the prevention and incidence os asthma and mite allergy birth cohort[END_REF][START_REF] Garcia | Bioactive compounds in human milk and maturity of the intestine in premature newborns: an overview[END_REF]. PUFA content in human milk is quite variable. It originates from several maternal sources (storage in white adipose tissue, long chain (LC) PUFA biosynthesis from the food precursors LA and ALA in liver), and is sensitive to mother's diet [START_REF] Garcia | French mothers' milk deficient in DHA contains phospholipid species of potential interest for infant development[END_REF][START_REF] Bravi | Impact of maternal nutrition on breast-milk composition: a systematic review[END_REF], lactation period [START_REF] Moltó-Puigmartí | Differences in fat content and fatty acid proportions among colostrum, transitional, and mature milk from women delivering very preterm, preterm, and term infants[END_REF] and maternal overweight [START_REF] Lindholm | Different fatty acid pattern in breast milk of obese compared to normal-weight mothers[END_REF][START_REF] Marín | Long-chain polyunsaturated fatty acids in breast milk in La Plata, Argentina: relationship with maternal nutritional status[END_REF]. Although knowledge about the individual importance of these factors would be helpful to optimize PUFA human milk content, few studies have considered them, and none concomitantly, in a large number of mothers (available studies comprise from 5 to 180 women).

The "early milk", i.e. colostrum, may be of considerable biological importance since it provides the initial supply of PUFA to the breastfed newborns. In the EDEN cohort, we previously reported a lower cognitive development in 2-3 year-old children when formerly breastfed by mothers whose colostrum had the higher LA levels (9.7-15.9% of total fatty acids) as compared to the lower LA levels (5.4-9.7%) [START_REF] Bernard | The association between linoleic acid levels in colostrum and child cognition at 2 and 3 y in the EDEN cohort[END_REF]. In addition, the intelligence quotient at 5-6 years was lower for children previously fed colostrum with highest LA levels combined with lowest DHA (< 0.64%) and AA (< 0.86%) levels [START_REF] Bernard | Breastfeeding, polyunsaturated fatty acid levels in colostrum and child intelligence quotient at 5-6 years: the EDEN cohort[END_REF]. In this context, we aimed at better understanding the sources of variability of colostrum PUFA levels, especially the modifiable maternal and pregnancy factors, using data from the EDEN mother-child cohort [START_REF] Heude | and the EDEN mother-child cohort study group. Cohort Profile: The EDEN mother-child cohort on the prenatal and early postnatal determinants of child health and development[END_REF].

Methods

Study population

The participants are part of the EDEN mother-child cohort study, a French prospective cohort designed to investigate the role of pre-and postnatal environmental factors involved in child development and health. Recruitment started in 2003 in the university hospitals of Poitiers (mid-West part of France) and Nancy (North-East of France) and ended up in 2006 with the inclusion of 2,002 mothers. A detailed protocol of the EDEN cohort study has been previously published [START_REF] Heude | and the EDEN mother-child cohort study group. Cohort Profile: The EDEN mother-child cohort on the prenatal and early postnatal determinants of child health and development[END_REF]. Briefly, the cohort consisted of pregnant women enrolled before 24 wk of gestation and of their newborn (95% full-term) whom development has been followed through numerous parameters until the age of 10 y. For the present study, we focused on 934 women (flowchart on Fig. 1) with available data on fatty acids in colostrum. The local ethics research committee (CCPP for biomedical research, Bicêtre Hospital) and the Data Protection Authority (CNIL) approved the study. Informed written consents were obtained from the mother for herself at inclusion.

Colostrum sampling and analysis of the fatty acid composition

Colostrum samples of about 5 mL were collected at the hospitals between 2 and 5 days after delivery (Mean ± SD: 3.9 ± 1.1 d) during one feed by manual expression and were stored at -80°C until analysis. A direct methylation procedure was performed on 100 µL of colostrum at 100°C for 1 h with methanol/hexane (4:1, v/v) and acetyl chloride by adapting a published method [START_REF] Masood | A simplified and efficient method for the analysis of fatty acid methyl esters suitable for large clinical studies[END_REF]. This quicker procedure was compared to a more time consuming method routinely used in the laboratory (milk lipid extraction using chloroform/methanol 2:1 followed by methylation using boron trifluoride [START_REF] Garcia | Bioactive compounds in human milk and maturity of the intestine in premature newborns: an overview[END_REF]) and showed comparable results (data not shown). Fatty acid methyl-esters (FAME) were analyzed by gas chromatography (Perkin Elmer Clarus 600, flame ionization detector, Totalchrom software, hydrogen as gas carrier) using a fused silica capillary fast column (BPX 70, 10 m x 0.1 mm i.d., 0.2 µm film thickness, Sigma-Supelco). The initial oven temperature was set at 60°C, raised to 200°C at 20°C/min, then to 225°C at 7°C/min with one min hold, and to 250°C at 160°C/min with one min hold. The control of the proportionality between FAME peaks area (in µV*sec), and their identification based on their retention time, were performed using an external calibrator FAME standard (GLC 674, Nu-Chek Prep, Waterville, NM, USA). Each Fatty acid level was expressed as the proportion of total fatty acids present in the chromatogram (weight percent). Intra-assay reproducibility of the direct method was obtained by repeated analysis of three different human milk samples (5 or 10 aliquots each). Coefficients of variability for fatty acids contributing for more than 1% or for 0.1-1% of total fatty acids were comprised from 0.12 to 1.48 or from 0.84 to 2.28, respectively. Internal standard (tridecanoic acid, Sigma-Fluka) was added to quantify total lipid content. We further calculated the sum or ratios of specific fatty acids as surrogate indexes of de novo lipogenesis (DNL) in the liver (sum of 16:0 + 16:1n-7 + 18:1 n-9 + 20:1 n-9), of DNL in the breast (sum of 10:0 + 12:0 + 14:0 + 14:1), of Steaoryl-CoA-Desaturase 1 (SCD1) i.e. Δ9-desaturase activity (SCD1-16 product/substrate ratio: 16:1 n-7/16:0; SCD1-18: 18:1 n-9/18:0), of Δ5-desaturase activity (20:4 n-6/20:3 n-6 i.e. AA/DGLA) and of Δ6desaturase activity (20:3 n-6/18:2 n-6 i.e. DGLA/LA), as previously published for milk [START_REF] Kuipers | Differences in preterm and term milk fatty acid compositions may be caused by the different hormonal milieu of early parturition[END_REF][START_REF] Morales | Genetic variants of the FADS gene cluster and ELOVL gene family, colostrums LC-PUFA levels, breastfeeding, and child cognition[END_REF]. The DHA Sufficiency Index was also calculated (22:6 n-3/22:5 n-6 i.e. DHA/n-6 DPA) [START_REF] Al | Relation between birth order and the maternal and neonatal docosahexaenoic acid status[END_REF].

Dietary assessment

A food-frequency questionnaire (FFQ), adapted from a validated one [START_REF] Deschamps | Reproducibility and relative validity of a food-frequency questionnaire among French adults and adolescents[END_REF], based on 137 different foods or food groups combined with pictures from 12 food types for portion size evaluation, was completed by the women to assess their usual diet during the third trimester of pregnancy, as previously described [START_REF] Drouillet | Maternal fatty acid intake and fetal growth: evidence for an association in overweight women. The 'EDEN mother-child' cohort (study of pre-and early postnatal determinants of the child's development and health)[END_REF]. Total energy, protein, carbohydrate, lipid and alcohol intakes were calculated by using the SU.VI.MAX nutrient database, whereby the majority of the nutrient information comes from French nutrient composition database [START_REF] Drouillet | Maternal fatty acid intake and fetal growth: evidence for an association in overweight women. The 'EDEN mother-child' cohort (study of pre-and early postnatal determinants of the child's development and health)[END_REF]. The 137 items were therefore clustered into 33 food groups according to their nature (e.g. Meat, Eggs, Poultry, Fish & Seafood, Cheese, Fruits, Vegetables, etc).

Except for some cooked dishes (ready meals or dishes with well-known recipes), the nutrient composition of food items was assessed without potential added fat. A specific food group named "Added-Fat after cooking" inquired about the frequency of added fat (butter, margarine, cream), and another one called "Sauces" about added sauces (dressing, ketchup, mayonnaise), in the plate. Intake of different fatty acids including LA, ALA, AA, DHA, eicosapentaneoic acid (EPA) and n-3 docosapentaenoic acid (n-3 DPA) was calculated from the nutrient composition table and by summation within a same food group. We therefore calculated the respective contribution (percentage) of each food group to the total maternal intake of saturated fatty acids (SFA), monounsaturated fatty acids (MUFA), total PUFA, total n-6 PUFA, total n-3 PUFA, LA, ALA, AA, EPA, n-3 DPA and DHA.

In addition, mothers were asked about their habits in fat use for cooking, frying or seasoning (butter, margarine, coconut butter, and different types of vegetable oil). Oils were combined into three groups according to their richness in n-3 PUFA (colza, mixtures), in n-6 PUFA (sunflower, corn) or in MUFA (peanut, olive). Women were therefore categorized into users vs. non-users for each type of added fat and each group of vegetable oil.

Other collected data

Women declared their weight just before pregnancy, and midwives measured mothers height (wall Seca 206 stadiometer, Hamburg Germany) during the first visit scheduled between 24 and 28 weeks of amenorrhea. Pre-pregnancy BMI was calculated (weight kg/height m 2 ), and categorized according to the WHO four classes: underweight (BMI < 18.5), normal weight (18.5-24.9), overweight (25-29.9) and obesity (BMI ≥ 30). Gestational age at delivery was determined from the date of the last menstrual period and early standard ultrasound fetal measurement. Maternal age at delivery, parity and newborn sex were extracted from clinical records. Smoking habits during pregnancy were collected from self-administered questionnaire during pregnancy and after delivery, and women were qualified as smokers or not smokers during pregnancy. Maternal education level was estimated based on the highest diploma obtained and expressed in years of attended school.

Statistical analyses

Data are means ± SD unless otherwise indications. The impact of the number of days between birth and colostrum sampling (referred as "sampling day" throughout the paper) on fatty acid colostrum level was investigated by Spearman's correlation coefficients. For each fatty acid, the colostrum level was compared between BMI categories using multivariable linear regression analysis adjusted for center and sampling day.

Correlations between fatty acids intake during pregnancy (expressed as % of total lipid intake) and fatty acids in colostrum (expressed as % of total fatty acids) were investigated using partial Spearman's correlation coefficients after adjustment for center and sampling day. Because of the existence of strong correlations between the different fatty acids, we did not perform any correction for multiple testing.

We then focused on the levels of LA, ALA, DHA and AA in colostrum to explore their main independent determinants in multivariable linear regression models. Their values were standardized in order to compare the effect size of the different contributors between models. All models initially included center, sampling day, mother's age at delivery, gestational age at delivery, pre-pregnancy BMI categories, primiparous status, smoking, maternal education level, main food groups contributors, potential competitors intake (n-3 PUFA intake for LA and AA, n-6 PUFA intake for ALA and DHA), and Added-Fat intake (for cooking and after cooking). The main food contributors were those accounting for about 33% of the total intake for ALA and LA and for about 55% of total intake for DHA and AA ("Cheese", "Added-fats", and "Fresh/dried fruits" for ALA, "Fish and seafood" for DHA, "Sauces" and "Bread" for LA, "Eggs and meats" regrouping intake from "Eggs", "Poultry" and "Meats" groups for AA). Factors with P-values over 15% were excluded from the models using backward selections.

All analyses were performed with SAS version 9.3 (SAS Institute, Inc., Cary, NC, USA) and significance was assumed at P < 0.05.

Results

Descriptive results

Main characteristics of the population are reported in Table 1. Table 2 displays the colostrum fatty acid levels in the whole study population, and shows that sampling day was positively correlated with LA and ALA levels, and negatively with most of their derivates LC-PUFA, and with LC-MUFA levels including nervonic acid (24:1 n-9). Table 3 shows the women's dietary intake during the last trimester of pregnancy and information on fatty acid food sources. The item "Sauces" was the main food group contributing to LA intake, and "Eggs, Meats & Poultry" were the main sources of AA intake. The two main sources of ALA were "Cheese" and "Added-Fat after cooking", and the main dietary contributors to DHA maternal intake were in decreasing order "Fish and seafood", "Fast foods" (i.e. hamburger, pizza, sandwich, savory pie, toasties and cheese sandwich, puff pastry roll), and "Eggs".

Relationship between colostrum fatty acid levels and maternal pre-pregnancy BMI

Total SFA in colostrum, and especially the pentadecanoic acid (15:0), palmitic acid and stearic acid (18:0), displayed the strongest negative associations with pre-pregnancy BMI (Table 4). On the opposite, total MUFA (mainly palmitoleic acid i.e. 16:1 n-7, 16:1 n-9, and oleic acid) and total n-6 PUFA (mainly LA, dihomo γ-linolenic (DGLA), AA and docosatetraenoic acid (DTA)) levels were positively associated with BMI categories. Among n-3 PUFA, only the DPA showed a positive association with BMI, whereas total n-3 PUFA, ALA and DHA displayed inverse U-shaped associations, the highest values being observed in women with normal BMI. LA/ALA ratio was positively associated with increasing BMI categories. AA/DHA and total n-6/total n-3 PUFA ratios followed an U-shaped association with BMI, i.e. women with normal pre-pregnancy BMI had the lowest ratios and obese mothers the highest. The colostrum DHA Sufficiency Index followed an inverse U-shaped association with BMI. The colostrum indexes for DNL-liver, and for SCD1-16, SCD1-18 and Δ6-desaturase enzymatic activities were all positively associated with BMI, while indexes for DNL-breast and for Δ5-desaturase (P-trend 0.053) enzymatic activity were negatively associated with it.

Correlations between fatty acids dietary intake during the last trimester of pregnancy and colostrum fatty acid levels

Table 5 shows that, after adjusting for center and sampling day, the correlations between maternal intake in a given fatty acid and the corresponding fatty acid in colostrum were in general positive, the strongest correlations being for DHA and EPA. Noticeable exception was observed for AA with no correlation. Regarding ratios, the correlation was strong for AA/DHA, and moderate for total n-6/n-3 PUFA. Correlations between different fatty acid families were noticeable: maternal dietary SFA were negatively associated with colostrum PUFA (especially LA and ALA), and similarly total dietary PUFA (total n-6 and n-3 PUFA) were negatively associated with milk SFA; dietary MUFA were positively associated with colostrum n-6 PUFA, and especially LA, and negatively with colostrum DHA, leading to positive correlations with AA/DHA and total n-6/n-3 PUFA ratios. ALA intake by mothers correlated moderately with EPA and DHA in milk. Dietary AA/DHA and total n-6/n-3 PUFA were negatively correlated with the content in EPA, DPA n-3 and DHA in colostrum lipids.

Respective contribution of maternal factors to ALA, DHA, LA and AA levels in colostrum

Results of the multivariable linear regression models explaining ALA and DHA, and LA and AA colostrum levels variability are shown in Tables 6 and7, respectively. The strongest contributors of ALA levels in colostrum, showing a positive association, were sampling day and n-6 PUFA intake, then use of MUFA-rich oils (i.e. olive and peanut oils) and mother's age at delivery. Main ALA contributors with a negative association were the use of coconut butter (rich in SFA) and pre-pregnancy overweight status. The strongest predictor of DHA was fish and seafood intake with an increase of 0.039 SD of the DHA level for one additional serving per month. The relationship between dietary intake of DHA and DHA level in colostrum was, however, not strictly proportional (Fig. 2). Maternal age at delivery and primiparous status also significantly contributed to the level of DHA in colostrum through a positive association, while sampling day was negatively associated. Abnormal pre-pregnancy BMI and smoking tended to be predictors of lower DHA level in colostrum. All together, theses factors explained 16.3% of colostrum DHA content variability. The consumption of n-6 PUFA-rich vegetable oils (i.e., sunflower and corn oils) was the main contributor of LA levels in colostrum, followed by pre-pregnancy obesity and primiparous status, all showing a positive association. Predictors with a negative association were an underweight status before pregnancy and energy intake. The most important contributors to AA colostrum level were sampling day (negative association) and maternal pre-pregnancy BMI (negative association with underweight status and positive association with overweight/obese status, when normal BMI class was taken as a reference). Colostrum AA level was also positively associated with maternal age and primiparous status, and was lower in mothers who declared using MUFA-rich oil. The variables included in this model explained 13.5% of the colostrum AA content variability. Alcohol consumption was not significantly associated with the colostrum PUFA levels (data not shown). Nevertheless, taken all together the factors we explored explained only a part of the PUFA variability (i.e. 5 to 16% of variance explained).

Discussion

In the EDEN mother-child cohort, we found several maternal (BMI, age, diet, smoking status) or perinatal (parity, lactation period) factors independently associated with LA, ALA, AA and DHA levels in early milk. Albeit the factors we explored showed a modest overall contribution to the PUFA variation in colostrum, the knowledge of their respective impact is valuable due to recent associations reported between early/mature milk PUFA levels and offspring outcomes later in life. Indeed, high LA level and high LA/ALA and total n-6/n-3 PUFA ratios in milk were found correlated to lower psychomotor scores at 14-18 months of age [START_REF] Guxens | Breastfeeding, long-chain polyunsaturated fatty acids in colostrum, and infant mental development[END_REF][START_REF] Sabel | Motor, mental and behavioral developments in infancy are associated with fatty acid pattern in breast milk and plasma of premature infants[END_REF] or at 2-3 or 5-6 years old [START_REF] Bernard | The association between linoleic acid levels in colostrum and child cognition at 2 and 3 y in the EDEN cohort[END_REF][START_REF] Bernard | Breastfeeding, polyunsaturated fatty acid levels in colostrum and child intelligence quotient at 5-6 years: the EDEN cohort[END_REF], a negative correlation was reported between milk DHA level (from 0.34 to 0.59% of total fatty acids) and fat mass in girls of 6-9 years old [START_REF] Pedersen | Polyunsaturated fatty acid content of mother's milk is associated with childhood body composition[END_REF], and diastolic and systolic pressure was lower in 12 years old infants previously breastfed with a milk containing at least 0.51% of n-3 PUFA [START_REF] Van Rossem | Blood pressure in 12-year-old children is associated with fatty acid composition of human milk: the prevention and incidence os asthma and mite allergy birth cohort[END_REF].

The rapid changes in colostrum PUFA profile over time after birth are consistent with other observations reported between day 3 and day 5 [START_REF] Gibson | Effect of sampling on fatty acid composition of human colostrum[END_REF]. This factor turned out to be the strongest predictor of the variability of the colostrum AA level while it explained only about 10% of the total variance for DHA level. This is probably linked to the mobilization of fatty acids stored in the maternal white adipose tissue, which was reported to be richer in AA than DHA [START_REF] Martin | Dependence of human milk essential fatty acids on adipose stores during lactation[END_REF].

Pre-pregnancy BMI represented another important predictor of PUFA levels in early milk. Colostrum of obese mothers had the highest level of n-6 PUFA and lower levels of ALA and DHA, indicating a worse balanced PUFA profile (higher LA/ALA, AA/DHA and total n-6/n-3 PUFA ratios) than women with lower pre-pregnancy BMI. This observation is consistent with what was reported in the colostrum of Swedish obese mothers [START_REF] Lindholm | Different fatty acid pattern in breast milk of obese compared to normal-weight mothers[END_REF], although the n-3 PUFA difference between obese and normal women was lower in our study. A higher level in LA was also reported in mature milk from Argentine obese mothers [START_REF] Marín | Long-chain polyunsaturated fatty acids in breast milk in La Plata, Argentina: relationship with maternal nutritional status[END_REF]. All these PUFA variations due to high pre-pregnancy BMI may worsen during lactation by being more pronounced in mature milk [START_REF] Lindholm | Different fatty acid pattern in breast milk of obese compared to normal-weight mothers[END_REF][START_REF] Marín | Long-chain polyunsaturated fatty acids in breast milk in La Plata, Argentina: relationship with maternal nutritional status[END_REF]. A novelty raised herein is that being underweight before pregnancy was associated with lower DHA level to the same extent than obesity, leading to higher total n-6/n-3 PUFA and AA/DHA ratios. Interestingly the average intake in DHA during the last trimester of pregnancy in each BMI class subgroup was similar (0.17-0.18 g/d) and so did not seem to intervene in these differences. In contrast, colostrum fatty acids indexes orientated towards specific maternal metabolic anomalies. Indeed, increase in DNL liver index together with a decrease in DNL breast index, an increase in SCD1-16, SCD1-18 and Δ6-desaturase indexes, and a decrease in Δ5-desaturase index, were evocative of the known decrease in insulin sensitivity associated with increasing BMI [START_REF] Kuipers | Differences in preterm and term milk fatty acid compositions may be caused by the different hormonal milieu of early parturition[END_REF][START_REF] Corpeleijn | Improvements in glucose tolerance and insulin sensitivity after lifestyle intervention are related to changes in serum fatty acid profile and desaturase activities: the SLIM study[END_REF]. Furthermore, a recent meta-analysis highlighted a high plasma lipids DGLA level in overweight/obese subjects as a very relevant biomarker in the pathogenesis of obesity, that reflects disturbances in Δ6 (elevated through DGLA/LA ratio) and Δ5 (decreased through AA/DGLA ratio) desaturases activities [START_REF] Fekete | Long-chain polyunsaturated fatty acid status in obesity : a systematic review and meta-analysis[END_REF]. We found that this altered LC-PUFA status also characterized the fatty acid profile of early milk from overweight/obese mothers. Since foods DGLA content is very low, the increased level of DGLA in the colostrum of obese women may reflect an increased conversion rate of LA and a decreased conversion rate of DGLA in AA, as reported by others in plasma lipids [START_REF] Fekete | Long-chain polyunsaturated fatty acid status in obesity : a systematic review and meta-analysis[END_REF]. The lower Δ5-desaturase activity consecutive to adiposity [START_REF] Zhou | Decreased activity of desaturase 5 in association with obesity and insulin resistance aggravates declining long-chain n-3 fatty acid status in Cree undergoing dietary transition[END_REF] can explain the lower DHA level in their colostrum, while the higher AA level (as well as the higher LA level) could be due to a higher supply from the elevated amount of white adipose tissue, since a higher storage of AA was reported to correlate with obesity and metabolic dysregulations [START_REF] Fekete | Long-chain polyunsaturated fatty acid status in obesity : a systematic review and meta-analysis[END_REF]. This explains the consistent linear relationship between colostrum AA levels and pre-pregnancy BMI. The lower colostrum DHA level in underweight women could be linked to a lower DHA status of these women as suggested by their lower milk DHA sufficiency index.

Maternal diet is known to influence milk fatty acids composition, however, the share attributable to diet is less documented [START_REF] Garcia | French mothers' milk deficient in DHA contains phospholipid species of potential interest for infant development[END_REF][START_REF] Bravi | Impact of maternal nutrition on breast-milk composition: a systematic review[END_REF][START_REF] Kim | Breast milk fatty acid composition and fatty acid intake of lactating mothers in South Korea[END_REF]. The inverse relationship we report between mother dietary SFA and PUFA in milk is consistent with others [START_REF] Bravi | Impact of maternal nutrition on breast-milk composition: a systematic review[END_REF][START_REF] Kim | Breast milk fatty acid composition and fatty acid intake of lactating mothers in South Korea[END_REF]. In addition, a specific source of SFA (coconut butter) led to low ALA level in our colostrums samples. We confirm a positive association between dietary MUFA and colostrum PUFA level [START_REF] Bravi | Impact of maternal nutrition on breast-milk composition: a systematic review[END_REF], especially with LA, and to a lesser extent with ALA. MUFA oil was one contributor influencing n-6 and n-3 PUFA in colostrum probably because of the existing competition between the n-9 (via oleic acid), n-6 (via LA as precursor) and n-3 (via ALA as precursor) pathways for the same desaturase and elongase enzymes in the body. The colostrum of mothers declaring using MUFA oil was thus higher in ALA and lower in AA possibly because of a lower conversion rate of ALA into DHA and of LA into AA. Due to competition, dietary n-6 fatty acids were predictive of a higher ALA and a lower DHA levels in colostrum, while dietary n-3 fatty acids would be associated with higher LA and lower AA levels. Moreover, while the daily dietary intake of LA was high (mainly from sauces and the use of n-6 PUFA oils), it correlated moderately to LA level in colostrum. The daily dietary supply in AA (mainly from meat, chicken and eggs) was close to the DHA supply (mainly from fish and seafood), but the AA level in early milk was not related to the dietary intake [START_REF] Kim | Breast milk fatty acid composition and fatty acid intake of lactating mothers in South Korea[END_REF], whereas the DHA intake showed the highest association with colostrum level [START_REF] Kim | Breast milk fatty acid composition and fatty acid intake of lactating mothers in South Korea[END_REF]. The moderate relationship we found between the dietary LA and its level in colostrum is consistent with a study estimating that about 30% of dietary LA is transferred into milk lipids [START_REF] Demmelmair | Metabolism of U13C-labeled linoleic acid in lactating women[END_REF]. In addition, the AA converted from dietary LA represents about 1% of total milk AA secreted [START_REF] Demmelmair | Metabolism of U13C-labeled linoleic acid in lactating women[END_REF]. It means that a major proportion of LA and AA of milk lipids derives from storage in the adipose tissues [START_REF] Martin | Dependence of human milk essential fatty acids on adipose stores during lactation[END_REF]. A strong positive association between fish and other seafood consumption and DHA in milk has been known for long [START_REF] Lauritzen | Fluctuations in human milk long-chain PUFA levels in relation to dietary fish intake[END_REF], but herein the association was moderately high (Rho = 0.29, P < 0.0001) and not proportional to the amount of DHA intake (from 19 to 735 mg/d) in accordance with the literature [START_REF] Garcia | French mothers' milk deficient in DHA contains phospholipid species of potential interest for infant development[END_REF][START_REF] Bravi | Impact of maternal nutrition on breast-milk composition: a systematic review[END_REF]. This can be explained by the fact that DHA in early milk is likely to originate from many sources i.e. diet, mobilization from adipose tissue storage and biosynthesis from dietary ALA (Rho = 0.13, P < 0.0001, herein). In addition, maternal variants of genes involved in LC-PUFA biosynthesis such as the FADS1/FADS2 cluster [START_REF] Xie | Genetic variants of the FADS1 FADS2 gene cluster are associated with altered (n-6) and (n-3) essential fatty acids in plasma and erythrocyte phospholipids in women during pregnancy and in breast milk during lactation[END_REF][START_REF] Moltó-Puigmartí | FADS1 FADS2 gene variants modify the association between fish intake and the docosahexaenoic acid proportions in human milk[END_REF][START_REF] Lattka | Genetic variants in the FADS gene cluster are associated with arachidonic acid concentrations of human breast milk at 1.5 and 6 mo postpartum and influence the course of milk dodecanoic, tetracosenoic, and trans-9-octadecenoic acid concentrations over the duration of lactation[END_REF], also capable of modifying the association between fish intake and DHA level in milk [START_REF] Moltó-Puigmartí | FADS1 FADS2 gene variants modify the association between fish intake and the docosahexaenoic acid proportions in human milk[END_REF], and the ELOVLs [START_REF] Morales | Genetic variants of the FADS gene cluster and ELOVL gene family, colostrums LC-PUFA levels, breastfeeding, and child cognition[END_REF], are powerful factors controlling the levels of AA and DHA in milk.

Other maternal factors were found independently associated with ALA, DHA, LA or AA levels in colostrum. Primiparous status was one of them possibly because optimal essential fatty acids and LC-PUFA maternal status is not attained after several pregnancies [START_REF] Al | Relation between birth order and the maternal and neonatal docosahexaenoic acid status[END_REF]. Maternal age could explain AA and DHA levels through an increased in Δ5-desaturase activity with age [START_REF] Zhou | Decreased activity of desaturase 5 in association with obesity and insulin resistance aggravates declining long-chain n-3 fatty acid status in Cree undergoing dietary transition[END_REF]. The negative association of smoking with colostrum DHA, but not AA level, could be due to a decreased conversion rate of ALA via a specific inhibition of the Δ5 desaturation by toxic xenobiotics [START_REF] Marangoni | Cigarette smoke negatively and dose-dependently affects the biosynthetic pathway of the n-3 polyunsaturated fatty acid series in human mammary epithelial cells[END_REF]. Some limitations and strengths of our study can be pointed out. A first limitation is the collection of a fraction of colostrum (5 mL) taken during breast-feeding instead of a sample from a total production (i.e. from 15-60 mL). However, the colostrum fatty acids profile is quite homogeneous throughout a single production, at the contrary of mature milk (fore versus hind milk), and the analysis of sample collected any time during suckling is representative of the entire produced colostrum [START_REF] Gibson | Effect of sampling on fatty acid composition of human colostrum[END_REF]. Another limitation is the collection of colostrum at the maternity unit where mothers received a standard hospital diet instead of following their usual diet. However, it is more likely that the high inter-individual variability obtained resulted from the impregnation of the personal diet and maternal status rather than of the homogeneous food received during the few days of hospitalization [START_REF] Bravi | Impact of maternal nutrition on breast-milk composition: a systematic review[END_REF]. The main strength of this study is to rely on a large sample of women through the use of the Eden cohort's database, which renders these results very robust.

In conclusion, our study brings new insights in the understanding of the main maternal factors involved in PUFA levels variability in early milk. These data are important to consider for dietary counseling for women prior to and during pregnancy. For instance, a normal prepregnancy BMI and a better choice in dietary fat sources for improving PUFA's storage quality and biosynthesis, represent two main targets to achieve for improving the PUFA status in early milk.

Funding sources

EDEN (French study of pre-and early postnatal determinants of the child's development and Mutuelle Générale de l'Education Nationale (MGEN), French National Agency for Food Security, and the French-speaking association for the study of diabetes and metabolism (ALFEDIAM). The present project received specific funding from the PremUp foundation (foundation for scientific cooperation in connection with pregnancy and prematurity) and the Groupe Lipides Nutrition (GLN) for the biological analyses of colostrum samples.

Study sponsors were not involved in the design of the study, data collection and analysis, interpretation of data, decision to publish, or preparation of the manuscript.

Statement of authorship

MA: colostrum samples analysis, data folders; JYB, BH, and AF: dietary records analysis, statistical analyses; MAC and BH: principal investigators of the EDEN mother-child cohort Colostrum DHA level (mean ± SEM; expressed as % of total fatty acids) according to quartiles of DHA maternal intake during pregnancy in the EDEN cohort (n = 802). The y-axis represents leastsquare means after adjustment for BMI (4 classes), center of recruitment, sampling day, primiparous status, mothers' age at delivery, gestational age at delivery, smoking during pregnancy, total n-6 PUFA intake, fish and seafood intake. P-trend was < 0.001. -0.05 Abbreviations: AA, arachidonic acid; ALA, α-linolenic acid; DGLA, dihomo γ-linolenic acid; DHA, docosahexaenoic acid; DPA, docosapentaenoic acid; DTA, docosatetraenoic acid; EPA, eicosapentaenoic acid; GLA, γ-linolenic acid; LA, linoleic acid; MUFA, monounsaturated fatty acids; PUFA, polyunsaturated fatty acids; SFA, saturated fatty acids. a Data are means ± SD and range (minimal and maximal values), and fatty acid levels are expressed as % total fatty acids. b Spearman's correlation coefficients between fatty acid and sampling day; * <0.05, ** <0.01, *** <0.001. Abbreviations: AA, arachidonic acid; ALA, α-linolenic acid; DHA, docosahexaenoic acid; n-3 DPA, n-3 Docosapentaenoic acid; E, energy; EPA, eicosapentaenoic acid; LA, linoleic acid; MUFA, monounsaturated fatty acids; PUFA, polyunsaturated fatty acids; SFA, saturated fatty acids.

TABLES

a Data are means ± SD [min-max] or percentages. b Alcohol consumption represents 0.53% ± 1.6% of total energy intake. c "Added-Fat" corresponds to any fat added after cooking by the mother in the plate (butter, margarine, cream).

d "Sauces" corresponds to any fat added by the mother in the plate (dressing, ketchup, mayonnaise). Abbreviations: ALA, α-linolenic acid; DHA, docosahexaenoic acid; MUFA, monounsaturated fatty acids; SE, standard error. a adjusted for center. b As ALA and DHA values expressed in % of colostrum total fatty acids were standardized (value-means/ standard deviation), the beta coefficients (β) represent the difference of their respective standard deviation related to one unit variation in the explanatory variable. c Total variance explained by the full model. Abbreviations: AA, arachidonic acid; LA, linoleic acid; MUFA, monounsaturated fatty acids; PUFA, polyunsaturated fatty acids; SE, standard error. a adjusted for center and gestational age at delivery. b As LA and AA values expressed in % of colostrum total fatty acids were standardized (value-means/standard deviation), the beta coefficient (β) represents the difference of their respective standard deviation related to one unit variation in the explanatory variable. c Total variance explained by the full model.

  health) was supported by Foundation for Medical Research (FRM), National Agency for Research (ANR), National Institute for Research in Public Health (IRESP: TGIR cohorte santé 2008 program), French Ministry of Health (DGS), French Ministry of Research, INSERM Bone and Joint Diseases National Research (PRO-A) and Human Nutrition National Research Programs, Paris-Sud University, Nestlé, French National Institute for Population Health Surveillance (InVS), French National Institute for Health Education (INPES), the European Union FP7 programmes (FP7/2007-2013, HELIX, ESCAPE, ENRIECO, Medall projects), Diabetes National Research Program (through a collaboration with the French Association of Diabetic Patients (AFD)), French Agency for Environmental Health Safety (now ANSES),

Fig. 1 .

 1 Fig. 1. Flowchart of selected women for whom colostrum fatty acid content was analyzed and who answered the Food Frequency Questionnaires within the EDEN mother-child cohort study.

Fig. 2 .

 2 Fig.2. Colostrum DHA level (mean ± SEM; expressed as % of total fatty acids) according to quartiles of DHA maternal intake during pregnancy in the EDEN cohort (n = 802). The y-axis represents leastsquare means after adjustment for BMI (4 classes), center of recruitment, sampling day, primiparous status, mothers' age at delivery, gestational age at delivery, smoking during pregnancy, total n-6 PUFA intake, fish and seafood intake. P-trend was < 0.001.

Table 1 :

 1 Characteristics of the population from the EDEN mother-child cohort study (n = 934).

	Variables	% (n)	or	Mean ± SD
	Center (Poitiers)	33.6 (314)
	Mother's age at delivery, y			29.6 ± 4.7
	Gestational age at delivery, wks			39.3 ± 1.6
	Primiparous (yes)	45.6 (426)
	BMI, kg/m²			22.8 ± 4.3
	Underweight	10.0 (93)
	Normal	68.5 (640)
	Overweight	14.5 (135)
	Obese	7.1 (66)
	Smoker	23.1 (216)
	Maternal education, y			14.1 ± 2.6
	Sampling day, d			3.9 ± 1.1
	Type of fat used for cooking/seasoning 1
	Butter (yes)	19.1 (154)
	Margarine (yes)	25.9 (208)
	Coconut butter (yes)	27.2 (218)
	n-3 PUFA oil (yes)	27.9 (224)
	n-6 PUFA oil (yes)	40.6 (326)
	MUFA oil (yes)	58.3 (468)
	Sauces and bread intake 1 , time per mo			85.7 ± 37.4
	Cheeses, added-fat, fresh/dried fruits 1 , time per mo			114.0 ± 71.3
	Fish & seafood intake a , time per mo			8.6 ± 6.9
	Meat/Poultry/Eggs intake a , time per mo			13.5 ± 11.5

Abbreviations: MUFA, monounsaturated fatty acids; PUFA, polyunsaturated fatty acids. a n = 803 for dietary intakes variables.

Table 2 :

 2 Colostrum total lipid content and fatty acid levels, and correlation with sampling day in the EDEN cohort a .

	Lipids	All samples (n = 934)	Range	Correlation with sampling day b
	Total lipid g/L	23.31 ± 12.15	3.1 -91.6	0.09 **
	SFA	44.85 ± 3.59	34.8 -57.6	-0.03
	10:0	1.87 ± 1.63	0 -19.2	0.01
	12:0	3.07 ± 1.21	0.7 -8.3	0.40 ***
	14:0	6.38 ± 1.45	2.8 -16	0.03
	15:0	0.42 ± 0.07	0 -0.7	-0.01
	16:0	26.12 ± 1.82	20.4 -33.5	-0.19 ***
	17:0	0.28 ± 0.05	0.1 -0.4	0.12 ***
	18:0	6.72 ± 1.06	3.6 -10.6	-0.19 ***
	MUFA	40.90 ± 2.89	28.6 -51.3	0.05
	14:1 n-5	0.28 ± 0.07	0.1 -0.5	0.16 ***
	15:1	0.05 ± 0.03	0 -0.2	-0.18 ***
	16:1 n-9	0.59 ± 0.13	0 -0.9	-0.11 **
	16:1 n-7	2.39 ± 0.66	0.8 -5.1	0.20 ***
	18:1 n-9	36.32 ± 2.63	24.4 -47.5	0.04
	20:1 n-9	0.96 ± 0.42	0 -12.3	-0.34 ***
	24:1 n-9	0.31 ± 0.09	0 -0.8	-0.41 ***
	n-6 PUFA	12.20 ± 1.92	7.8 -19.0	-0.02
	18:2 n-6 (LA)	9.85 ± 1.85	5.4 -16.8	0.07 *
	18:3 n-6 (GLA)	0.12 ± 0.05	0 -0.4	0.11 **
	20:3 n-6 (DGLA)	0.61 ± 0.16	0.3 -1.2	-0.14 ***
	20:4 n-6 (AA)	0.86 ± 0.16	0.4 -1.5	-0.24 ***
	22:4 n-6 (DTA)	0.55 ± 0.18	0 -1.3	-0.46 ***
	22:5 n-6 (DPA)	0.11 ± 0.04	0 -0.3	-0.27 ***
	n-3 PUFA	2.05 ± 0.41	0.8 -3.5	-0.07 *
	18:3 n-3 (ALA)	0.65 ± 0.22	0.3 -1.6	0.17 ***
	18:4 n-3	0.28 ± 0.07	0 -0.5	-0.15 ***
	20:4 n-3	0.24 ± 0.07	0.1 -0.6	-0.24 ***
	20:5 n-3 (EPA)	0.06 ± 0.03	0 -0.2	0.11 **
	22:5 n-3 (DPA)	0.28 ± 0.10	0.1 -0.6	-0.26 ***
	22:6 n-3 (DHA)	0.64 ± 0.19	0.2 -1.5	-0.12 ***
	Ratio
	LA/ALA	16.58 ± 5.47	6.4 -36.7	0.04
	AA/DHA	1.43 ± 0.38	0.6 -3.4	-0.13 ***
	Total n-6/n-3 PUFA	6.18 ± 1.52	3.3 -13.1

Table 3 :

 3 Maternal macronutrient and fatty acid intakes during the last trimester of pregnancy and description of lipid main food group sources in the EDEN cohort (n = 803) a .

		Daily intakes (m ± SD [min-max]) or
	Nutritional factors	food group contribution (%)
	Total energy intake, kcal/d b	2231 ± 726 [1003 -4929]
	Total energy intake, kJ/d	9327 ± 3035 [4192 -20604]
	Proteins, E%	16.6 ± 3.1 [7.4 -31.2]
	Carbohydrates, E%	43.6 ± 7.5 [19.9 -70.3]
	Lipids, E%	39.3 ± 6.6 [21.8 -62.4]
	SFA, E%	18.0 ± 3.7 [7.9 -33.1]
	SFA, g/d	45.2 ± 19.7 [13.6 -150.4]
	Cheese, SFA%	21.0
	Added-Fat c , SFA%	16.6
	Fermented milk, SFA%	8.1
	Fast Foods, SFA%	6.2
	Cakes, SFA%	6.2
	MUFA, E%	14.2 ± 2.6 [7.3 -24.9]
	MUFA, g/d	35.4 ± 14.4 [11.0 -124.6]
	Cheese, MUFA%	13.4
	Added-Fat, MUFA %	12.1
	Sauces d , MUFA %	10.1
	Meats, MUFA %	8.5
	PUFA, E%	4.7 ± 1.2 [2.1 -10.6]
	PUFA, g/d	11.6 ± 5.0 [3.1 -38.9]
	Sauces, PUFA%	21.8
	Bread, PUFA%	8.0
	Snacks, PUFA%	6.2
	Added-Fat, PUFA%	5.9
	Cakes, PUFA%	5.7
	Fast Foods, PUFA%	5.6
	PUFA n-6, E%	4.0 ± 1.2 [1.6 -9.6]
	PUFA n-6, g/d	9.9 ± 4.5 [2.3 -34.4]
	LA, E%	3.9 ± 1.2 [1.6 -9.5]
	LA, g/d	9.7 ± 4.5 [2.3 -33.8]
	Sauces, LA%	25.1
	Bread, LA%	8.4
	Snacks, LA%	6.9
	Cakes, LA%	5.8
	Added-Fat, LA%	5.6
	Fast Foods, LA%	5.4
	AA, E%	0.06 ± 0.03 [0.02 -0.21]
	AA, g/d	0.15 ± 0.08 [0.02 -0.66]
	Eggs, AA%	19.3
	Meats, AA%	16.8
	Poultry, AA%	14.6

Table 4 :

 4 Total lipid content, fatty acid levels and fatty acid indexes for enzymatic activities of colostrum according to maternal pre-pregnancy BMI categories in the EDEN cohort (n = 934) a,b . Data are means ± SEM, and fatty acid levels are expressed as % total fatty acids. b Means are adjusted for center and sampling day. c Sum of 16:0 + 16:1n-7 + 18:1n-9 + 20:1n-9, for DNL index in the liver. d Sum of 10:0 + 12:0 + 14:0 + 14:1, for DNL index in the breast. e Product/substrate ratio for SCD 1 (or Δ9 desaturase) activity index: 16:1n-7/16:0. f Product/substrate ratio for SCD 1 (or Δ9 desaturase) activity index: 18:1n-9/18:0. g Product/substrate ratio for Δ5 desaturase activity index: 20:4 n-6/20:3 n-6 (AA/DGLA). h Product/substrate ratio for Δ6 desaturase activity index: 20:3 n-6/18:2 n-6 (DGLA/LA). i DHA Sufficiency Index: 22:6 n-3/22:5 n-6 (DHA/n-6 DPA).

	Lipids	Underweight (n = 93)	Normal (n = 640)	Overweight (n = 135)	Obese (n = 66)	P
	Total lipid g/L	22.81 ± 1.26	23.35 ± 0.48	23.07 ± 1.05	24.10 ± 1.51	0.9
	SFA	46.27 ± 0.37	45.01 ± 0.14	43.97 ± 0.3	43.09 ± 0.44 <.0001
	10:0	2.09 ± 0.16	1.88 ± 0.06	1.75 ± 0.14	1.69 ± 0.20	0.32
	12:0	3.32 ± 0.11	3.06 ± 0.04	2.94 ± 0.09	3.06 ± 0.13	0.07
	14:0	6.77 ± 0.15	6.37 ± 0.06	6.14 ± 0.12	6.31 ± 0.18	0.01
	15:0	0.43 ± 0.01	0.43 ± 0.00	0.40 ± 0.01	0.38 ± 0.01	<.0001
	16:0	26.40 ± 0.18	26.21 ± 0.07	25.95 ± 0.15	25.30 ± 0.22	0.0003
	17:0	0.27 ± 0.01	0.28 ± 0.00	0.28 ± 0.00	0.27 ± 0.01	0.7
	18:0	6.99 ± 0.11	6.80 ± 0.04	6.51 ± 0.09	6.07 ± 0.13	<.0001
	MUFA	39.94 ± 0.29	40.76 ± 0.11	41.74 ± 0.24	41.94 ± 0.35 <.0001
	14:1 n-5	0.29 ± 0.01	0.28 ± 0.00	0.27 ± 0.01	0.26 ± 0.01	0.02
	15:1	0.05 ± 0.00	0.05 ± 0.00	0.05 ± 0.00	0.05 ± 0.00	0.8
	16:1 n-9	0.56 ± 0.01	0.58 ± 0.00	0.61 ± 0.01	0.62 ± 0.01	0.001
	16:1 n-7	2.25 ± 0.07	2.37 ± 0.03	2.55 ± 0.05	2.55 ± 0.08	0.001
	18:1 n-9	35.53 ± 0.27	36.20 ± 0.10	37.00 ± 0.22	37.20 ± 0.32 <.0001
	20:1 n-9	0.95 ± 0.04	0.97 ± 0.02	0.95 ± 0.04	0.94 ± 0.05	0.9
	24:1 n-9	0.31 ± 0.01	0.31 ± 0.00	0.31 ± 0.01	0.32 ± 0.01	0.8
	n-6 PUFA	11.81 ± 0.20	12.15 ± 0.08	12.29 ± 0.16	12.98 ± 0.24	0.001
	18:2 n-6 (LA)	9.56 ± 0.19	9.83 ± 0.07	9.84 ± 0.16	10.39 ± 0.23	0.05
	18:3 n-6 (GLA)	0.13 ± 0.01	0.12 ± 0.00	0.13 ± 0.00	0.13 ± 0.01	0.5
	20:3 n-6 (DGLA)	0.57 ± 0.02	0.60 ± 0.01	0.64 ± 0.01	0.69 ± 0.02	<.0001
	20:4 n-6 (AA)	0.82 ± 0.02	0.85 ± 0.01	0.90 ± 0.01	0.93 ± 0.02	<.0001
	22:4 n-6 (DTA)	0.51 ± 0.02	0.54 ± 0.01	0.58 ± 0.01	0.63 ± 0.02	<.0001
	22:5 n-6 (DPA)	0.11 ± 0.00	0.11 ± 0.00	0.11 ± 0.00	0.11 ± 0.00	0.6
	n-3 PUFA	1.98 ± 0.04	2.08 ± 0.02	2.00 ± 0.04	1.99 ± 0.05	0.03
	18:3 n-3 (ALA)	0.65 ± 0.02	0.66 ± 0.01	0.60 ± 0.02	0.63 ± 0.03	0.02
	18:4 n-3	0.28 ± 0.01	0.28 ± 0.00	0.27 ± 0.01	0.25 ± 0.01	0.001
	20:4 n-3	0.24 ± 0.01	0.24 ± 0.00	0.24 ± 0.01	0.25 ± 0.01	0.7
	20:5 n-3 (EPA)	0.06 ± 0.00	0.06 ± 0.00	0.06 ± 0.00	0.05 ± 0.00	0.3
	22:5 n-3 (DPA)	0.26 ± 0.01	0.28 ± 0.00	0.30 ± 0.01	0.31 ± 0.01	0.001
	22:6 n-3 (DHA)	0.59 ± 0.02	0.65 ± 0.01	0.63 ± 0.02	0.61 ± 0.02	0.03
	Ratio
	LA/ALA	15.83 ± 0.53	16.27 ± 0.20	17.84 ± 0.44	18.09 ± 0.63	0.0004
	AA/DHA	1.50 ± 0.04	1.39 ± 0.01	1.50 ± 0.03	1.60 ± 0.04	<.0001
	Total n-6/n-3 PUFA	6.25 ± 0.16	6.07 ± 0.06	6.39 ± 0.13	6.65 ± 0.19	0.006
	Fatty acid indexes
	DNL liver c	65.13 ± 0.29	65.74 ± 0.11	66.44 ± 0.24	65.98 ± 0.35	0.0057
	DNL breast d	12.47 ± 0.29	11.59 ± 0.11	11.10 ± 0.24	11.33 ± 0.35	0.0036

a

Table 5 :

 5 Correlations between fatty acid intake during pregnancy and colostrum fatty acid levels in the EDEN cohort (n = 803) a,b . EPA, eicosapentaenoic acid; LA, linoleic acid; MUFA, monounsaturated fatty acids; PUFA, polyunsaturated fatty acids; SFA, saturated fatty acids. Bold: low, moderate and highest significant correlations.

	Fatty acids
	in diet						Fatty acids in colostrum (% total fatty acids)
	(% lipids)
		SFA MUFA PUFA	PUFA n-6	LA	AA	PUFA n-3	ALA EPA	DPA	DHA LA/ALA AA/DHA n-6/n-3
	SFA	0.10	-0.02	-0.13 -0.14 -0.15 0.00	-0.04	-0.10 -0.01	0.02	0.01	0.00	-0.01	-0.06
	MUFA	-0.02 -0.04	0.09	0.11	0.11 -0.01	-0.04	0.06 -0.05	-0.08	-0.09	0.01	0.10	0.11
	PUFA	-0.12	0.04	0.15	0.14	0.16 -0.01	0.11	0.12 0.06	0.02	0.05	-0.02	-0.06	0.01
	n-6 PUFA -0.11	0.03	0.14	0.14	0.16 -0.01	0.09	0.12 0.04	0.00	0.02	-0.02	-0.04	0.02
	LA	-0.11	0.03	0.14	0.14	0.16 -0.01	0.09	0.12 0.04	0.00	0.02	-0.02	-0.04	0.02
	AA	0.00	-0.02	0.03	0.02	0.01 -0.01	0.04	0.05 0.02	0.02	0.02	-0.04	-0.03	-0.02
	n-3 PUFA -0.07	0.03	0.09	0.04	0.05 -0.02	0.23	0.07 0.24	0.20	0.27	-0.03	-0.34	-0.17
	ALA	-0.07	0.03	0.08	0.05	0.07 -0.01	0.17	0.10 0.13	0.10	0.13	-0.06	-0.17	-0.11
	EPA	-0.04	0.02	0.05	0.00	0.00	0.01	0.20	0.02 0.25	0.21	0.30	-0.01	-0.35	-0.17
	DPA	-0.02 -0.02	0.06	0.03	0.02	0.01	0.11	0.06 0.14	0.11	0.15	-0.03	-0.17	-0.08
	DHA	-0.02	0.00	0.04	-0.01 -0.01 -0.01	0.20	0.03 0.24	0.21	0.29	-0.02	-0.35	-0.18
	LA/ALA	-0.06	0.00	0.10	0.11	0.12 -0.01	0.02	0.08 -0.03	-0.03	-0.03	-0.01	0.04	0.07
	AA/DHA	0.05	-0.04	-0.04	0.01	0.01 -0.01	-0.22	-0.01 -0.28	-0.24	-0.33	0.00	0.38	0.20
	n-6/n-3	-0.05	0.01	0.07	0.10	0.11 -0.02	-0.07	0.07 -0.14	-0.13	-0.16	-0.01	0.18	0.13
	Abbreviations: AA, arachidonic acid; ALA, α-linolenic acid; DHA, docosahexaenoic acid; DPA, n-3
	Docosapentaenoic acid;

a Partial Spearman's correlation coefficients adjusted for center and sampling day. b Absolute correlation coefficients under 0.07 did not significantly differ from 0 (P-value > 0.05). Absolute correlation coefficients over 0.13 had corresponding P-values < 0.0001.

Table 6 :

 6 Multivariable models a for predictors of ALA or DHA colostrum levels in the EDEN cohort (n = 803).

		Model for standardized b ALA colostrum	Model for standardized b DHA colostrum level as
		level as the outcome		the outcome
		β (SE)	P	% explained variance	β (SE)	P	% explained variance
	Fish & seafood intake (times/mo)				0.039 (0.005)	<.0001	6.28
	Cheese, Added-Fat, Fresh/dried fruits, (times/mo)	-0.001 (0.001)	0.044	0.45
	MUFA Oil (Yes)	0.113 (0.068)	0.097	0.30
	Coconut butter (Yes)	-0.181 (0.075)	0.016	0.63
	n-6 fatty acids intake (g/d)	0.022 (0.008)	0.006	0.82	-0.002 (0.001)	0.11	0.27
	Sampling day (d)	0.091 (0.032)	0.005	0.87	-0.122 (0.032)	0.0001	1.54
	Mother's age at delivery (y)	0.015 (0.008)	0.058	0.40	0.028 (0.008)	0.0003	1.41
	Body Mass Index		0.123	0.63		0.08	0.73
	Underweight	0.07 (0.115)			-0.261 (0.113)
	Normal	Taken as reference			Taken as reference
	Overweight	-0.216 (0.098)			-0.019 (0.096)
	Obese	-0.069 (0.135)			-0.191 (0.132)
	Primiparous (Yes)	0.104 (0.074)	0.16	0.22	0.206 (0.073)	0.005	0.85
	Smoker (Yes)				-0.145 (0.078)	0.06	0.37
	Total c (for explained variance)			13.5			16.3

Table 7 :

 7 Multivariable models a for predictors of LA or AA colostrum levels in the EDEN cohort (n = 803).

		Model for standardized b LA colostrum level	Model for standardized b AA colostrum level as
		as the outcome		the outcome
		β (SE)	P	% explained	β (SE)	P	% explained
				variance			variance
	Eggs & meats (times/mo)				-0.005 (0.003)	0.12	0.26
	Sauces & bread (times/mo)	0.001 (0.001)	0.44	0.07
	n-6 PUFA Oil (Yes)	0.253 (0.073)	0.0005	1.46
	MUFA Oil (Yes)				-0.197 (0.067)	0.004	0.94
	Energy intake (Kcal/100/d)	-0.024 (0.09)	0.011	0.79
	n-3 fatty acids intake (g/d)	0.184 (0.141)	0.19	0.21	-0.035 (0.075)	0.64	0.02
	Sampling day (d)	0.023 (0.033)	0.49	0.06	-0.283 (0.032)	<.0001	8.50
	Mother's age at delivery (y)				0.024 (0.008)	0.002	1.05
	Body Mass Index		0.15	0.63		<.0001	2.75
	Underweight	-0.092 (0.119)			-0.196 (0.114)
	Normal	Taken as reference			Taken as reference
	Overweight	0.069 (0.102)			0.275 (0.097)
	Obese	0.286 (0.142)			0.501 (0.134)
	Primiparous (Yes)	0.141 (0.072)	0.050	0.46	0.241 (0.074)	0.0011	1.17
	Total c			5.4			13.5

Acknowledgments

The authors thank the participating families, the midwife research assistants (Lorraine Douhaud, Sophie Bedel, Brigitte Lortholary, Sophie Gabriel, Muriel Rogeon, and

Conflict of interest

None of the authors declared a conflict of interest.