Julien Pirrello

Cynthia Deluche

Nathalie Frangne

Frederic Gevaudant

Elie Maza

Anis Djari

Mickael Bourge

Jean-Pierre Renaudin

Spencer Brown

Chris Bowler

Pirrello Julien

Deluche Cynthia

Frangne Nathalie

Gévaudant Frédéric

Maza Elie

Djari Anis

Bourge Mickaël

Renaudin Jean-Pierre

Brown Spencer

Zouine Mohamed

Chevalier Christian
email: christian.chevalier@inra.fr

Nathalie Gonzalez

Transcriptome profiling of sorted endoreduplicated nuclei from tomato fruits: how the global shift in expression ascribed to DNA ploidy influences RNA-Seq data normalization and interpretation

Keywords: endoreduplication, fruit development, RNA-Seq profiling, data interpretation, sorted nuclei, tomato, Solanum lycopersicum

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

INTRODUCTION

Most multicellular organisms display variations in cell ploidy levels resulting from somatic endopolyploidy as part of their normal development [START_REF] Brodsky | Cell polyploidy: its relation to tissue growth and function[END_REF][START_REF] Edgar | Endoreplication cell cycles: more for less[END_REF][START_REF] Frawley | Polyploidy[END_REF]. In higher plants, endoreduplication is the major source of endopolyploidy [START_REF] D'amato | Role of Polyploidy in Reproductive Organs and Tissues[END_REF] and is widespread in angiosperms where it takes place in various vegetative and reproductive tissues [START_REF] D'amato | Role of Polyploidy in Reproductive Organs and Tissues[END_REF]Joubès and Chevalier, 2000;Nagl, 1976). During endoreduplication, nuclear DNA duplication occurs in the absence of any obvious condensation and decondensation steps. Chromosomes with multivalent (n=2, 4, 8, 16...) chromatids are thus produced without any change in the karyotype. This typical structure in polytene chromosomes is observed in various plant species, especially in the endosperm, the embryo suspensor and the anther tapetum (Cavalheira, 2000), and also in the fleshy pericarp tissue of developing tomato fruits [START_REF] Bourdon | In planta quantification of endoreduplication using fluorescent in situ hybridization (FISH)[END_REF].

The functional significance of endoreduplication and its adaptive value during plant development are not fully understood and are still actively debated. Endoreduplication is thought to provide a means to sustain plant growth under adverse abiotic and biotic environmental conditions [START_REF] Adachi | Programmed induction of endoreduplication by DNA double-strand breaks in Arabidopsis[END_REF][START_REF] Ceccarelli | Chromosome endoreduplication as a factor of salt adaptation in Sorghum bicolor[END_REF][START_REF] Cookson | Cell and leaf size plasticity in Arabidopsis: what is the role of endoreduplication?[END_REF][START_REF] Hase | A mutation in the uvi4 gene promotes progression of endo-reduplication and confers increased tolerance towards ultraviolet B light[END_REF][START_REF] Scholes | Plasticity in ploidy: a generalized response to stress[END_REF].

Endoreduplication is also clearly associated with cell differentiation and morphogenesis [START_REF] Bramsiepe | Endoreplication controls cell fate maintenance[END_REF][START_REF] Hülskamp | Pattern formation and cell differentiation: trichomes in Arabidopsis as a genetic model system[END_REF][START_REF] Roeder | Variability in the control of cell division underlies sepal epidermal patterning in Arabidopsis thaliana[END_REF]. For example, in Arabidopsis, the developmental program of trichomes (epidermal hair cells) requires four rounds of endoreduplication to produce mature large-branched single cells [START_REF] Hülskamp | Pattern formation and cell differentiation: trichomes in Arabidopsis as a genetic model system[END_REF]. Positive correlations between ploidy level and cell size have also been observed in different plant species, organs and cell types, ascribing to endoreduplication a role in cell growth [START_REF] Chevalier | Elucidating the functional role of endoreduplication in tomato fruit development[END_REF]. During tomato fruit Comment citer ce document : Pirrello, J., Deluche, C., Frangne, N., Gevaudant, F., Maza, E., Djari, A., Bourge, M., Renaudin, J.-P., Brown, Bowler, C., Zouine, M., [START_REF] Pirrello | Transcriptome profiling of sorted endoreduplicated nuclei from tomato fruits: how global shift in expression ascribed to DNA ploidy influences RNA-Seq data normalization and interpretation[END_REF]. Transcriptome profiling of sorted endoreduplicated nuclei from tomato fruits: how global shift in expression ascribed to DNA ploidy influences RNA-Seq data normalization and interpretation. Plant Journal, 93

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development, endoreduplication contributes to establish a highly structured and integrated cellular system that acts as a morphogenetic factor supporting cell growth [START_REF] Bourdon | Evidence for karyoplasmic homeostasis during endoreduplication and a ploidy-dependent increase in gene transcription during tomato fruit growth[END_REF].

Endoreduplication has also been suggested to enhance metabolic activity in both the animal and plant kingdoms, for example during embryogenesis in drosophila or in the endosperm of cereal seeds [START_REF] Inzé | PLAZA 3.0: an access point for plant comparative genomics[END_REF]Lee et al., 2009). This proposed increase in metabolic activity could originate from a global increase of transcription (Lee et al., 2009). This long-standing hypothesis has only been recently supported since we have shown that increased transcription of rRNA and mRNA on a per-nucleus basis is associated with higher ploidy levels in the pericarp tissue of tomato fruit [START_REF] Bourdon | Evidence for karyoplasmic homeostasis during endoreduplication and a ploidy-dependent increase in gene transcription during tomato fruit growth[END_REF]. Various transcriptomic studies have been performed in tomato to profile gene expression in the developing whole ovary and fruit, or in various dissected fruit tissues (Lemaire-Chamley et al., 2005;[START_REF] Vriezen | Changes in tomato ovary transcriptome demonstrate complex hormonal regulation of fruit set[END_REF][START_REF] Wang | Regulatory Features Underlying Pollination-Dependent and -Independent Tomato Fruit Set Revealed by Transcript and Primary Metabolite Profiling[END_REF][START_REF] Ye | Transcriptome profiling of tomato fruit development reveals transcription factors associated with ascorbic acid, carotenoid and flavonoid biosynthesis[END_REF][START_REF] Zhong | Single-base resolution methylomes of tomato fruit development reveal epigenome modifications associated with ripening[END_REF].

Laser-capture microdissection coupled to genome-wide transcriptomics has also been performed for expression analyses of individual cell and tissue types in tomato fruit (Matas et al., 2011;Pattison et al., 2015). Although these studies provide high resolution transcriptomic information, they do not allow the study of the potential influence that endoreduplication may confer on gene expression. Yet [START_REF] Galitski | Ploidy regulation of gene expression[END_REF] showed the ploidy-dependent expression of 17 genes in isogenic yeast strains ranging from ploidy levels of n to 4n. This report prompted us to search for a ploidy-dependent gene expression during fruit development.

To study and compare genome-wide transcript expression, RNA-Seq has become a widely used procedure. After sequencing, an important step in RNA-Seq data analysis is the normalization step in which raw data are adjusted to correct for experimental or biological biases and technical variation that prevent direct comparison of expression measurements across samples. Classical normalization methods, such as the largely used LRE and TMM methods [START_REF] Anders | Differential expression analysis for sequence count data[END_REF][START_REF] Robinson | A scaling normalization method for differential expression analysis of RNA-seq data[END_REF], commonly assume comparable total expression between samples or a specific amount of significantly up-and down-regulated genes (Maza et al., 2013). However, as highlighted by [START_REF] Aanes | Normalization of RNA-sequencing data from samples with varying mRNA levels[END_REF], [START_REF] Chen | The overlooked fact: fundamental need for spike-in control forvirtually all genome-wide analyses[END_REF] and [START_REF] Evans | Selecting between-sample RNA-Seq normalization methods from the perspective of their assumptions[END_REF], the performance of normalization methods can be affected because these assumptions may not always be valid. For example, in zebrafish embryos, due to delayed polyadenylation of maternal transcripts, a large difference in polyA+ mRNA amounts is found between two early developmental stages [START_REF] Aanes | Zebrafish mRNA sequencing deciphers novelties in transcriptome dynamics during maternal to zygotic transition[END_REF]. Such a case of global shift in expression could be observed in samples presenting different levels of ploidy [START_REF] Bourdon | Evidence for karyoplasmic homeostasis during endoreduplication and a ploidy-dependent increase in gene transcription during tomato fruit growth[END_REF]Lemaire-Chamley et al., 2005), therefore indicating that care has to be taken for the analysis of ploidy-dependent transcriptomes.

To investigate the effects of DNA ploidy levels on gene expression in tomato fruit and to further decipher the functional role of endoreduplication, we here report the feasibility of a RNA-Seq approach using total nuclear RNA extracted from purified populations of FACS-sorted nuclei based on their DNA content. We then provide recommendations to analyze transcriptomic data under the influence of ploidy levels, and show ploidy-specific expression profiles suggesting a ploidy-dependent cell differentiation within the fruit pericarp tissue.

Comment citer ce document : Pirrello, J., Deluche, C., Frangne, N., Gevaudant, F., Maza, E., Djari, A., Bourge, M., Renaudin, J.-P., Brown, Bowler, C., Zouine, M., [START_REF] Pirrello | Transcriptome profiling of sorted endoreduplicated nuclei from tomato fruits: how global shift in expression ascribed to DNA ploidy influences RNA-Seq data normalization and interpretation[END_REF]. Transcriptome profiling of sorted endoreduplicated nuclei from tomato fruits: how global shift in expression ascribed to DNA ploidy influences RNA-Seq data normalization and interpretation. Plant Journal, 93

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RESULTS

Genome-wide RNA sequencing using endoreduplicated nuclei from fruit pericarp: experimental setup and data preprocessing

To analyze the influence of endoreduplication on gene expression, RNA-Seq was performed using RNA extracted from purified nuclei sorted based on their DNA content by FACS. Nuclei were prepared from pericarp cells of 30 day-post-anthesis (dpa) fruits because at this developmental stage the immature green tomato fruits have completed their growth and display a wide range of ploidy levels (from 2C to 512C) (Figure 1) (Joubès et al., 1999;[START_REF] Cheniclet | Cell expansion and endoreduplication show a large genetic variability in pericarp and contribute strongly to tomato fruit growth[END_REF]. Four populations of endoreduplicated nuclei, namely of 4C, 8C, 16C, and 32C DNA content, were sorted on a per-fixed number (ca. 100,000 nuclei) and total nuclear RNA was extracted for the construction of cDNA libraries.

Unlike typical RNA-Seq libraries that are prepared from enriched mRNA resulting from poly-A purification of total RNA, the libraries for sequencing in this study were constructed from nuclear nonpolyadenylated RNA. In such samples, due to the high abundance of ribosomal RNA (rRNA), the correct detection of mRNA can be difficult. To estimate and maximize the access to coding information, two sets of libraries were prepared following cDNA synthesis, adapter ligation and PCR amplification steps: with or without a duplex-specific nuclease (DSN) treatment [START_REF] Zhao | Comparison of RNA-Seq by poly (A) capture, ribosomal RNA depletion, and DNA microarray for expression profiling[END_REF] applied to remove highly abundant sequences that reanneal quickly such as highly repetitive sequences and rRNA. In total, the samples analyzed corresponded to 24 RNA-Seq libraries resulting from four DNA ploidy levels in triplicate, with (DSN) or without (no-DSN) DSN treatment.

After sequencing, quality check and pre-processing (see Experimental Procedures and Supplemental Figure S1), the reads were mapped against the Sly2.40 tomato reference genome (Figure 2a). Without DSN treatment, the overall mapping rate ranged between 90 and 98% from 4C to 32C samples, respectively. The multi-mapping rate was relatively high, about 38% for all ploidy levels to be considered, and consisted mainly of rRNA sequences [START_REF] Zhao | Comparison of RNA-Seq by poly (A) capture, ribosomal RNA depletion, and DNA microarray for expression profiling[END_REF]O'Neill et al., 2013).

Uniquely mapped reads corresponding to reads aligned at only one locus represented more than 50% of total reads and reached 60% for 32C samples. For DSN-treated samples, the overall mapping rate fell to 40% in 4C nuclei and increased with ploidy level, reaching 85% for 32C samples. The multimapping rate fell around 11-12% for all the DSN-treated samples. This significant decrease was probably due to the removal of rRNAs by the treatment. The rate of sequences that were uniquely mapped was also reduced compared to non-treated samples, suggesting that the DSN treatment did not only target rRNA sequences. Unlike the multi-mapping rate, uniquely mapped rates seemed to increase with ploidy level since it increased from 31.6% to 69% at 4C and 32C, respectively. The proportion of uniquely mapped reads falling in intergenic, intronic, exonic and ribosomal regions were respectively 33%, 23%,19% and 25% in 4C samples;37%,23%,15% and 25% in 8C samples;39,26,19 and 16% in 16C samples;34%,23%,18% and 25%,in 32C samples (Figure 2b). Overall, these rates were found to be in accordance with those obtained in previous experiments applying DSN treatment [START_REF] Zhao | Comparison of RNA-Seq by poly (A) capture, ribosomal RNA depletion, and DNA microarray for expression profiling[END_REF].

Comment citer ce document : Pirrello, J., Deluche, C., Frangne, N., Gevaudant, F., Maza, E., Djari, A., Bourge, M., Renaudin, J.-P., Brown, Bowler, C., Zouine, M., Chevalier, C., Gonzalez, N. ( 2018). Transcriptome profiling of sorted endoreduplicated nuclei from tomato fruits: how global shift in expression ascribed to DNA ploidy influences RNA-Seq data normalization and interpretation. Plant Journal, 93

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Data normalization is a crucial step for an RNA-Seq analysis of samples displaying different ploidy levels

We have previously shown that the transcription of 5.8S rRNA in endoreduplicated nuclei was enhanced and that RNA polymerase II protein levels were increased proportionally with ploidy, suggesting that gene expression globally doubles between ploidy levels k and k+1 [START_REF] Bourdon | Evidence for karyoplasmic homeostasis during endoreduplication and a ploidy-dependent increase in gene transcription during tomato fruit growth[END_REF]. The classical normalization methods [START_REF] Anders | Differential expression analysis for sequence count data[END_REF][START_REF] Robinson | A scaling normalization method for differential expression analysis of RNA-seq data[END_REF], generally based on the assumption that less than half of the genes are down-or up-regulated in a sample (Maza et al., 2013;Maza, 2016), might not be adequate for the comparison of samples with different ploidy levels, such as in our experimental setup.

To properly identify ploidy-dependent differentially expressed genes, we therefore first evaluated the adequacy of the use of a classical RNA-Seq normalization approach when a global shift in expression between two conditions exists, i.e., when all genes are proportionally expressed in the two given conditions.

Case of a global shift in expression.

We hereafter demonstrated mathematically the inadequacy of classical normalization methods for a case study in which gene expression is globally proportional between two conditions. For the sake of simplicity, we considered an RNA-Seq experiment with only two conditions and one biological sample per condition, but a similar proof could a priori be done with more than two conditions and replicates. Let G be the total number of expressed genes in at least one of the two given conditions. Let X gk be the raw count of gene g in condition k. Up to a centered random error, we can model the expression value X gk by:

gk g gk k k L XN S   with 1 G k gk g g S L    
where µ gk is the unknown number of transcripts of gene g in condition k, L g is the known length of gene g, N k is the known library size, and S k is the size of the transcriptome in condition k which is obviously unknown (Maza et al., 2013). Let us then assume that a global shift in expression exists, which means that, for all genes g, the following proportionality assumption holds: µ g2 = µ g1 with  a given positive coefficient. First, by straightforward calculations, we have that S 2 = S 1 . Then, given both the expression model and the proportionality assumption above, the following calculations show that the raw fold change of gene g expressions between the two conditions, denoted by RFC g , does not depend on the proportionality coefficient:

2 2 2 1 11 1 1 1 2 1 1 RFC 1 g g g g g g g XN SS X N S S          .
Hence, with a classical RNA-Seq normalization approach, such as those defined above, we are not able to estimate the proportionality coefficient  of the global shift assumption. In other words, when the global shift in expression assumption holds, genes with a fold change equal to  will be declared as not differentially expressed (not DE).

Comment citer ce document : Pirrello, J., Deluche, C., Frangne, N., Gevaudant, F., Maza, E., Djari, A., Bourge, M., Renaudin, J.-P., Brown, Bowler, C., Zouine, M., Chevalier, C., Gonzalez, N. ( 2018). Transcriptome profiling of sorted endoreduplicated nuclei from tomato fruits: how global shift in expression ascribed to DNA ploidy influences RNA-Seq data normalization and interpretation. Plant Journal, 93

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Case of a few genes outside of the assumption of a global shift in expression.

We now develop theoretically the case of a few genes that do not hold the global shift assumption. We then wanted to know what happens if a few genes do not hold the proportionality assumption but rather the following one: µ g2 = µ g1 +  g2 with  g2  0. In that case, we have that 2

1 2 1 G gg g S S L      
and then, a priori, contrary to what has been seen above, we have this S 2  S 1 . Then, it follows that, for all genes g, the raw fold change of gene expressions in both conditions can be written as follows:

2 2 2 1 2 11 1 1 1 2 1 2 RFC g g g g g g g g XN SS X N S S        .
Then, an RNA-Seq normalization procedure (such as TMM, RLE or MRN that were compared as in [START_REF] Scholes | Plasticity in ploidy: a generalized response to stress[END_REF]) leads to the following normalized fold change, denoted by NFC g :

    22 12 1 2 1 1 1, , RFC 1 NFC median RFC g g g g gg g gG SS SS         
.

Finally, we obtain the estimation of the true fold change for a given gene g by the following simple formula:

2 1 NFC g g g     . Equation (1)
In conclusion, the formula obtained above implies that if we know a priori the value of the global shift in expression , we can still perform a classical differential expression (DE) analysis (with one of the classical normalization methods defined above) to estimate the fold change of each gene by multiplying the corresponding fold change by . This means also that, by using the classical DE analysis method, a gene declared as not being DE will in fact have a fold change equal to .

Testing the assumption of a global shift in expression for samples with different ploidy levels

In the case study presented here, in which ploidy level doubles from 4C to 8C, then from 8C to 16C, and from 16C to 32C, we have assumed a global shift in expression  = 2 following [START_REF] Bourdon | Evidence for karyoplasmic homeostasis during endoreduplication and a ploidy-dependent increase in gene transcription during tomato fruit growth[END_REF]. This shift was then validated following two approaches.

We first tested the assumption of a global shift in expression in the samples by comparing the concentration of total nuclear RNA obtained per 100,000 nuclei of different ploidy levels (Table 1A).

With a null hypothesis stating that a ploidy level k+1 is twice more concentrated than a ploidy level k, none of the six tests performed was found to be significant, suggesting a global increase of whole transcription in relation to the ploidy level (Table 1B).

Second, we performed RT-qPCR analyses using a subset of genes to validate the assumption of the global shift in expression. In a first step, to identify non-DE and DE genes from the RNA-Seq dataset, based on our assumption of a global shift, we used the classical normalization method from DESeq2 R package (see Experimental Procedures). According to our assumption, non-DE genes

Comment citer ce document : Pirrello, J., Deluche, C., Frangne, N., Gevaudant, F., Maza, E., Djari, A., Bourge, M., Renaudin, J.-P., Brown, Bowler, C., Zouine, M., Chevalier, C., Gonzalez, N. ( 2018). Transcriptome profiling of sorted endoreduplicated nuclei from tomato fruits: how global shift in expression ascribed to DNA ploidy influences RNA-Seq data normalization and interpretation. Plant Journal, 93

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would correspond to genes having transcript levels proportional to the level of ploidy, while DE genes would not follow this proportionality. This analysis identified 1211 genes as being DE, between at least two samples, with a FDR of 0.01 (see details below). In a second step, we compared the fold changes obtained experimentally by the RT-qPCR method for a selected set of 10 genes declared as non-DE to the theoretical fold change obtained with Equation (1) :  k = 2 k with k  1,2,3 (Figure 3 and Supplemental Table S1). For this RT-qPCR analysis, a fifth DNA ploidy level, namely 64C, was included in the test. For proper estimation of transcript levels and to ensure unbiased RT-qPCR analysis, spike-in RNAs were added to each sample prior to RNA extraction [START_REF] Risso | Normalization of RNA-seq data using factor analysis of control genes or samples[END_REF]see Experimental Procedures). We found that: (i) all genes tested displayed increasing fold change dynamics (grey lines) following the theoretical values (red lines); (ii) the means of these dynamics (black lines) were very close to the theoretical ones (red lines).

We then carried out statistical one-sample mean tests to compare these fold changes. Of all tests carried out for all ploidy level comparisons, only the test corresponding to the 64C vs 32C ploidy levels (Figure 3d) was statistically significant (with a p-value around 0.01). We therefore have nine tests out of ten that do not reject the null hypothesis stating that the mean of the fold changes agrees with the theoretical fold changes  k = 2 k with k  1,2,3 (Figures 3a, 3b and3c). This analysis thus showed that the global shift in gene expression goes even beyond the DNA ploidy level of 32C.

We also compared the fold changes obtained by RT-qPCR of 25 genes declared as DE (12 upregulated and 13 down-regulated genes) to their fold changes estimated according to Equation (1) (Figure 4 and Supplemental Table S1). Almost all comparisons were aligned near the first bisector (diagonal dashed line) which represents the fold changes for which both fold changes are identical. Among all 150 statistical two sample mean tests carried out to compare these fold changes, only 23 tests were significant (10 for down-regulated genes and 13 for up-regulated ones). We therefore have about 85% of the tests (87% for down-regulated and 82% for up-regulated genes) that did not reject the null hypothesis stating that the fold changes estimated by qPCR and by Equation (1) are equal.

In conclusion, these analyses indicated that there is probably a global proportional shift in expression depending on the ploidy level suggesting a positive effect of ploidy level on whole transcription, corresponding to a doubling in transcripts. Therefore, we further analyzed the RNA-Seq data, assuming a global shift in expression with a factor = 2, implying that non-DE genes will correspond to genes having an expression proportional to ploidy level.

Differentially expressed genes: distinct functional categories expressed as a function of ploidy

By analyzing the RNA-Seq data with the assumption of a global shift in expression between the samples, we found 24919 genes to be expressed in at least one sample across the samples with different ploidy levels. By pairwise comparison of the expression values, we found that 1211 genes were DE in at least one comparison with a FDR of 0.01 (Supplemental Table S2). The number of genes up-or down-regulated increased by comparing more divergent ploidy levels (Figure 5). After removing genes not expressed in all samples and genes for which variability was too high, 4694 genes were declared as being non-DE, i.e., displaying an expression that was proportional to the ploidy level.

Comment citer ce document : Pirrello, J., Deluche, C., Frangne, N., Gevaudant, F., Maza, E., Djari, A., Bourge, M., Renaudin, J.-P., Brown, Bowler, C., Zouine, M., Chevalier, C., Gonzalez, N. ( 2018). Transcriptome profiling of sorted endoreduplicated nuclei from tomato fruits: how global shift in expression ascribed to DNA ploidy influences RNA-Seq data normalization and interpretation. Plant Journal, 93

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To detect potential specific expression patterns within the DE genes and therefore identify the major transcriptional dynamics associated with changes in ploidy levels, a k-means clustering approach was used on the 1211 DE genes. Genes with similar expression profiles were grouped into six clusters (Figure 6 and Supplemental Table S3). Clusters 1 to 4 contained genes showing higher expression in the nuclei of low ploidy levels (4C and 8C). In Cluster 1, the expression was high in cells with 4C ploidy levels and decreased progressively when ploidy levels increased. In Cluster 2, the expression of genes was high only in cells with 4C ploidy and in Cluster 4 only in cells with 8C ploidy.

In Cluster 3, genes showed high expression levels in both 4C and 8C nuclei. In contrast, in Clusters 5 and 6 the expression of genes increased with ploidy: in Cluster 5, genes had low expression in 4C nuclei and then higher and similar expression in 8, 16 and 32C nuclei, while in Cluster 6 genes had high expression in 16 and 32C nuclei.

For each cluster, we tested the overrepresentation of functional categories by using the GO enrichment tool from PLAZA (Proost et al., 2015) (Figure 6 and Supplemental Table S4). To simplify the functional annotation, we also classified the DE genes into one of the 31 functional categories of tomato genes provided by Pattison et al. (2015) (Supplemental Table S3). In Cluster 1, we found genes mainly involved in photosynthesis, lipid and organic acid metabolic processes and cell wall related processes. In Cluster 2, genes involved in photosynthesis were also found together with genes involved in ATP metabolic processes and transport. In Clusters 3, 4 and 5, due to the small numbers of genes, fewer categories were significantly overrepresented. Finally, the genes in Cluster 6 mainly belonged to categories related to metabolic processes such as genes encoding UDPglycosyltransferases involved in the glycosylation process, a prevalent modification of plant secondary metabolites, or genes involved in flavone metabolism. In conclusion, we found that DE genes display different expression profiles depending on the ploidy level and that for each pattern of expression, genes belong to distinct functional categories.

DISCUSSION

RNA-Seq from endoreduplicated nuclei

The tomato fruit provides an excellent model system to study the role of endoreduplication in the regulation of transcription and in the determination of organ size because the tissues in this fleshy fruit, such as the pericarp and the locular jelly-like tissue, display an extraordinary extent of endoreduplication (Joubès et al., 1999;[START_REF] Cheniclet | Cell expansion and endoreduplication show a large genetic variability in pericarp and contribute strongly to tomato fruit growth[END_REF]. This increase in nuclear ploidy levels leading to DNA content as high as 512C induces an important increase in the nuclear volume and has been correlated to very large cells that can reach spectacular sizes such as thousands of times their initial volume [START_REF] Cheniclet | Cell expansion and endoreduplication show a large genetic variability in pericarp and contribute strongly to tomato fruit growth[END_REF]. Because cells displaying high ploidy levels can reach such huge sizes, their isolation by fluorescence-activated cell sorting using flow cytometry is impossible. To circumvent this bottleneck, we decided to prepare RNA from sorted nuclei in order to generate transcript profiles for ranges of ploidy levels. The use of nuclear RNA for genome-wide transcriptomic analyses has been largely used for animal samples (Grinberg et al., 2013;Krishnaswami et al., 2016;[START_REF] Trask | Microarray analysis of cytoplasmic versus whole cell RNA reveals a considerable number of missed and false positive mRNAs[END_REF], but to a lesser extent in plants [START_REF] Zhang | Global characerization of cell-specific gene expression through fluorescence-activated sorting of nuclei[END_REF][START_REF] Deal | A simple method for gene expression and chromatin profiling of individual cell types within a tissue[END_REF]. In Comment citer ce document : Pirrello, J., Deluche, C., Frangne, N., Gevaudant, F., Maza, E., Djari, A., Bourge, M., Renaudin, J.-P., Brown, Bowler, C., Zouine, M., Chevalier, C., Gonzalez, N. ( 2018). Transcriptome profiling of sorted endoreduplicated nuclei from tomato fruits: how global shift in expression ascribed to DNA ploidy influences RNA-Seq data normalization and interpretation. Plant Journal, 93

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these studies, the comparison of the expression data between nuclei RNA and total cell RNA showed that although some differences exist between these two pools of RNA, the majority of the transcripts is equally represented. These findings indicate that the use of nuclar RNAs does not introduce major bias for gene expression studies. Therefore, using sorted nuclei based on their ploidy level provides probably a good representation of the transcriptional activity within the cells.

Performing RNA-Seq on samples displaying a global shift in expression

The purpose of our present work was to describe genome-wide gene expression profiles from tomato fruit cells with different ploidy levels, based on an RNA-Seq experiment. We first showed that, when a global shift in expression between two conditions exists, i.e. when all genes are proportionally expressed in the two given conditions, a classical RNA-Seq normalization approach, such as the widely used RLE and TMM normalization methods [START_REF] Anders | Differential expression analysis for sequence count data[END_REF][START_REF] Robinson | A scaling normalization method for differential expression analysis of RNA-seq data[END_REF]Maza et al., 2013), is inadequate. Indeed, the normalization methods cited above are generally based on the assumption that less than half of the genes are down-regulated and less than half of the genes are up-regulated (Maza et al., 2013;Maza, 2016) which is a priori not the case with ploidydependent conditions [START_REF] Bourdon | Evidence for karyoplasmic homeostasis during endoreduplication and a ploidy-dependent increase in gene transcription during tomato fruit growth[END_REF]. Such an issue, encountered whatever the organisms, tissues or conditions studied, has been tackled by [START_REF] Aanes | Normalization of RNA-sequencing data from samples with varying mRNA levels[END_REF] and [START_REF] Chen | The overlooked fact: fundamental need for spike-in control forvirtually all genome-wide analyses[END_REF], as well as by [START_REF] Evans | Selecting between-sample RNA-Seq normalization methods from the perspective of their assumptions[END_REF] in a more general framework. Nevertheless, these publications underline the issue of using RNA-Seq experiments for the analysis of transcriptomes that are, one from another, globally over-or under-expressed. A first solution to solve this issue is the use of external control genes named spike-ins [START_REF] Chen | The overlooked fact: fundamental need for spike-in control forvirtually all genome-wide analyses[END_REF][START_REF] Risso | Normalization of RNA-seq data using factor analysis of control genes or samples[END_REF] or sequins [START_REF] Hardwick | Spliced synthetic genes as internal controls in RNA sequencing experiments[END_REF]. This method consists in adding a known amount of artificial sequences to the RNA samples to provide a scaling factor for between-samples normalization after quantification. Another solution for the analysis of a global shift in expression is introduced in the present work and consists in the use of Equation (1). Indeed, on the one hand, if we know a priori the value of the global shift in expression , as is the case during endoreduplication, we can perform a classical DE analysis and then estimate the fold change of each gene by multiplying the corresponding fold change by  as in Equation (1). On the other hand, if the global shift in expression  is unknown, we can estimate it by RT-qPCR analysis of a subset of genes that have been declared non-DE using a classical approach. Obviously, the more genes tested, the more accurate the estimation of .

Ploidy-dependent transcriptome may reflect different cellular functions within the pericarp

To approach the issue of ploidy-dependent gene expression inside the pericarp of immature green tomato fruits that have completed their growth, and as a basis to dissect the genetic regulation of endoreduplication in this tissue, we analyzed the expression profiles obtained from nuclei sorted based on their ploidy. At 30 dpa, the ploidy map representing the distribution of ploidy levels within the pericarp tissue of immature green fruits showed that cells with lower ploidy levels (2C-16C) are located mainly in the exocarp, while cells with high ploidy levels (32C-256C) locate mainly within the mesocarp, at the centre of the pericarp [START_REF] Bourdon | In planta quantification of endoreduplication using fluorescent in situ hybridization (FISH)[END_REF]. The 32C ploidy level is the most prominent one, present in all cell layers within the mesocarp and endocarp [START_REF] Bourdon | In planta quantification of endoreduplication using fluorescent in situ hybridization (FISH)[END_REF].

Comment citer ce document : Pirrello, J., Deluche, C., Frangne, N., Gevaudant, F., Maza, E., Djari, A., Bourge, M., Renaudin, J.-P., Brown, Bowler, C., Zouine, M., [START_REF] Pirrello | Transcriptome profiling of sorted endoreduplicated nuclei from tomato fruits: how global shift in expression ascribed to DNA ploidy influences RNA-Seq data normalization and interpretation[END_REF]. Transcriptome profiling of sorted endoreduplicated nuclei from tomato fruits: how global shift in expression ascribed to DNA ploidy influences RNA-Seq data normalization and interpretation. Plant Journal, 93

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The four levels of ploidy studied here (4C, 8C, 16C, 32C) may thus represent cells with various locations, and thus with various gene expression profiles. Interestingly, cells with the lowest levels of ploidy (4C and 8C) express genes related to photosynthesis and lipid synthesis, while cells with higher ploidy levels (16C and 32C) express genes related to carbohydrate metabolism (Figure 5).

At 30 dpa the fruit has stopped its growth, but has not yet started to ripen. Interestingly, our data suggest that the transcriptome of the largest cells (of high ploidy levels) at this developmental stage has already changed when compared to smaller cells (of low ploidy levels). From this ploidy distribution and the ploidy-specific expression profiles it is suggested that the activity of the cells is related to their ploidy level and tissue location. Therefore not only endoreduplication acts as a morphogenetic factor supporting cell growth during tomato fruit development according to the "karyoplasmic ratio" theory [START_REF] Bourdon | Evidence for karyoplasmic homeostasis during endoreduplication and a ploidy-dependent increase in gene transcription during tomato fruit growth[END_REF][START_REF] Chevalier | Endoreduplication and fruit growth in tomato: evidence in favour of the karyoplasmic ratio theory[END_REF], but it is also likely to be an important determinant of cell identity, as demonstrated to be crucial for cell fate acquisition and maintenance [START_REF] Bramsiepe | Endoreplication controls cell fate maintenance[END_REF][START_REF] Roeder | Variability in the control of cell division underlies sepal epidermal patterning in Arabidopsis thaliana[END_REF], thus contributing to the formation of specialized cell type patterns. The present transcriptomic analysis thus provides new information about the functional role of endoreduplication in orienting cell metabolic activities during specialization in the course of tomato fruit growth. Determining the ploidy distribution in the pericarp of growing fruits and overlapping it with ploidy-specific transcriptional information will be essential for understanding the transcriptional dynamics of fruit growth, for understanding the spatial and temporal specialization of cells.

Conclusion

We here showed that cell-based approaches to study expression profiles by RNA-Seq need to take into account the possible global shift in expression between samples for correct analysis of the data and for valid interpretation of the observed expression measurements. We indeed demonstrated that endoreduplication leads to a global (doubling) shift in gene expression. However, more than a thousand genes were found to be differentially expressed during the endoreduplication process, suggesting a ploidy-and/or cell size-specific gene expression programme. Since endoreduplication is a major source of polyploidization in Eukaryotes [START_REF] Edgar | Endoreplication cell cycles: more for less[END_REF], our data thus provide recommendations and new information that may be useful for analysing transcriptomic data under the influence of ploidy levels not only in plants but in all types of Eukaryotic cells, tissues or organs harbouring developmentally programmed endoreduplication. As far as tomato fruit development is concerned, our ongoing project now intends to apply this methodology for a broader approach, analysing the transcriptome of nuclei-sorted samples based on a whole set of ploidy levels and prepared from pericarp tissue harvested at different developmental stages, to perform a full kinematic study of endoreduplication-influenced gene expression. This methodology now also opens the way to analyse such transcriptomic data from tomato fruit dissected tissues or selected parts of tissues.

Comment citer ce document : Pirrello, J., Deluche, C., Frangne, N., Gevaudant, F., Maza, E., Djari, A., Bourge, M., Renaudin, J.-P., Brown, Bowler, C., Zouine, M., Chevalier, C., Gonzalez, N. ( 2018). Transcriptome profiling of sorted endoreduplicated nuclei from tomato fruits: how global shift in expression ascribed to DNA ploidy influences RNA-Seq data normalization and interpretation. Plant Journal, 93

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This article is protected by copyright. All rights reserved. The major overrepresented functional categories, identified by using the GO enrichment tool from PLAZA [START_REF] Zhao | Comparison of RNA-Seq by poly (A) capture, ribosomal RNA depletion, and DNA microarray for expression profiling[END_REF], are indicated on the right side of each cluster.

Figure 1 .

 1 FIGURES LEGENDS

Figure 2 .

 2 Figure 2. RNASeq general statistic for non-DSN and DSN-treated samples and mapping distribution.

  (a) Distribution of uniquely mapped, multi-mapped and unmapped reads for non-DSN and DSNtreated samples and for each ploidy level. (b) Distribution of reads, using ITAG2.30 annotation, into intergenic, intronic, exonic and ribosomal regions for each ploidy level of DSN-treated samples.

Figure 3 .

 3 Figure 3. Expression obtained by RT-qPCR of selected genes declared as being not Differentially Expressed (non-DE). Grey dots represent the (log 2 ) fold changes of the qPCR expressions of 10 genes that have been declared non DE with DESeq2 (y-axis) depending on the ploidy level (x-axis). Panels (a), (b), (c), and (d) represent respectively the comparisons of levels 8C, 16C, 32C and 64C vs 4C (panel (a)), 16C, 32C and 64C vs 8C (panel (b)), 32C and 64C vs 16C (panel (c)), and 64C vs 32C (panel (d)). Black plus and red multiplication symbols represent respectively the observed (log 2 ) mean and the theoretical ploidy level (1, 2, 3 or 4). A blue star is added between plus and multiplication symbols that are statistically different (by a t-test with a type I error of 5%).

Figure 4 .

 4 Figure 4. Expression obtained by RT-qPCR of selected genes declared as being up-or downregulated as a function of ploidy. Each triangle represents a gene declared as Differentially Expressed (DE) with DESeq2. The x-axis and y-axis represent, respectively, the (log 2 ) fold changes of gene expressions measured by qPCR and by DESeq2 multiplied by  k = 2 k with k  1,2,3 the ploidy level in keeping with Equation (1).Down-pointing and up-pointing triangles represent, respectively, genes that are declared downregulated and up-regulated by DESeq2. Black, green and blue colors represent DE fold changes associated respectively with the three ploidy levels k  1,2,3. The diagonal dashed line is the first bisector representing the genes for which both fold changes are identical.

Figure 5 .

 5 Figure 5. Number of genes up-(yellow) and down-(blue) regulated in pairwise comparisons of the expression values (FDR < 0.01).

Figure 6 .

 6 Figure 6. Clustered expression profiles of DEGs and functional categories. Six clustered expression profiles of DEGs obtained with a k-means clustering approach.

  document : Pirrello, J., Deluche, C., Frangne, N., Gevaudant, F., Maza, E., Djari, A., Bourge, M., Renaudin, J.-P., Brown, Bowler, C., Zouine, M., Chevalier, C., Gonzalez, N. (2018). Transcriptome profiling of sorted endoreduplicated nuclei from tomato fruits: how global shift in expression ascribed to DNA ploidy influences RNA-Seq data normalization and interpretation. Plant Journal, 93

Table 1 . Statistical one-sample t-tests on total nuclear RNA concentrations

 1 . (A) Total nuclear RNA concentrations from four sample replicates (in ng.µL -1 ) using a constant number of nuclei (ca. 100,000). (B) T-tests on concentration ratios with a null hypothesis that a ploidy level k+1 is twice more than a ploidy level k.

	Ploidy level	Replicate 1	Replicate 2	Replicate 3	Replicate 4
	4C	0.91		0.62	0.50		0.44
	8C	1.31		1.10	2.28		2.12
	16C	3.29		2.08	1.64		2.84
	32C	7.27		4.98	3.89		4.60
	B.
	Ploidy level	Ratio 1	Ratio 2	Ratio 3	Ratio 4	Null	p-value
	comparison				Hypothesis
	8C / 4C	1.43	1.77	4.56	4.82	2.00	0.29
	16C / 8C	2.51	1.89	0.72	1.34	2.00	0.39
	32C / 16C	2.51	2.39	2.37	1.62	2.00	0.47
	16 / 4C	3.60	3.35	3.28	6.45	4.00	0.84
	32C / 8C	5.55	4.53	1.71	2.17	4.00	0.62
	32C / 4C	7.96	8.03	7.78	10.45	8.00	0.45

A.

Comment citer ce document : Pirrello, J., Deluche, C., Frangne, N., Gevaudant, F., Maza, E., Djari, A., Bourge, M., Renaudin, J.-P., Brown, Bowler, C., Zouine, M., Chevalier, C., Gonzalez, N. (

2018

). Transcriptome profiling of sorted endoreduplicated nuclei from tomato fruits: how global shift in expression ascribed to DNA ploidy influences RNA-Seq data normalization and interpretation. Plant Journal, 93

ACKNOWLEDGEMENTS

This work was carried out with the financial support of the French Agence Nationale de la Recherche (grant no. ANR-09-GENM-105). The authors declare no conflict of interest.

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This article is protected by copyright. All rights reserved. Version postprint Comment citer ce document : Pirrello, J., Deluche, C., Frangne, N., Gevaudant, F., Maza, E., Djari, A., Bourge, M., Renaudin, J.-P., Brown, Bowler, C., Zouine, M., Chevalier, C., Gonzalez, N. (2018). Transcriptome profiling of sorted endoreduplicated nuclei from tomato fruits: how global shift in expression ascribed to DNA ploidy influences RNA-Seq data normalization and interpretation. Plant Journal, 93 Accepted Article This article is protected by copyright. All rights reserved. Version postprint Comment citer ce document : Pirrello, J., Deluche, C., Frangne, N., Gevaudant, F., Maza, E., Djari, A., Bourge, M., Renaudin, J.-P., Brown, Bowler, C., Zouine, M., Chevalier, C., Gonzalez, N. (2018). Transcriptome profiling of sorted endoreduplicated nuclei from tomato fruits: how global shift in expression ascribed to DNA ploidy influences RNA-Seq data normalization and interpretation. Plant Journal, 93 Accepted Article This article is protected by copyright. All rights reserved. Version postprint Comment citer ce document : Pirrello, J., Deluche, C., Frangne, N., Gevaudant, F., Maza, E., Djari, A., Bourge, M., Renaudin, J.-P., Brown, Bowler, C., Zouine, M., Chevalier, C., Gonzalez, N. (2018). Transcriptome profiling of sorted endoreduplicated nuclei from tomato fruits: how global shift in expression ascribed to DNA ploidy influences RNA-Seq data normalization and interpretation. Plant Journal, 93

Data access

The Illumina short reads generated in this study have been submitted to the European Nucleotide Archive (ENA) with study accession number PRJEB21753, and are available at http://www.ebi.ac.uk/ena.

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EXPERIMENTAL PROCEDURES

Plant material and growing conditions

Cherry tomato (Solanum lycopersicum Mill. cv Wva106) plants were grown in a greenhouse under a thermoperiod of 25°C/20°C and a photoperiod of 14/10 hours (day/night). Fruits were harvested at immature green stage (30 days post anthesis, dpa), and 6 to 12 fruits served for nuclei sorting.

Nuclei sorting and RNA extraction

Tomato pericarp nuclei were prepared as described in [START_REF] Bourdon | In planta quantification of endoreduplication using fluorescent in situ hybridization (FISH)[END_REF], and sorted by flow cytometry using with a MoFlo Astrios cytometer (Beckman Coulter, Roissy, France; www.beckmancoulter.com) using standard isotonic sheath at 25 psi (pound per square inch), 3 drop sorting and coincidence abort.

The flow cytometer-sorted nuclei were collected in 2 mL tubes containing TRIzol® reagent (Ambion, Life Technology) for subsequent RNA extraction with a ratio of 1:4 (vol. of nuclei suspension/vol. of TRIzol®). Since the MoFlo Astrios cytometer allowed obtain 320 nuclei per µL, we sorted 100,000 nuclei in a total volume of 312 µL, which were collected in tubes containing 937 µL of TRIzol® reagent. Tubes containing the nuclei suspension were mixed and frozen in liquid nitrogen and stored at -80°C.

Prior to RNA extraction, the nuclei suspension in TRIzol® was allowed to melt at room temperature. For the extraction of RNA used for qRT-PCR, a mix of four artificial poly(A + ) RNAs (ArrayControl™ Spots and Spikes, Ambion, Life Technologies) at 1.10 9 copy number was added in each nuclei suspension. Two hundred µL of chloroform were added; tubes were gently shaken and left at room temperature for 3 min. After a centrifugation at 12 000 g and 4°C for 15 min, the aqueous phase was transferred to 0.5 volume of EtOH 100%. After precipitation, the RNA was re-suspended and transferred to a RNeasy Mini Spin column Mini Kit (Qiagen) and purified following the manufacturer's protocol. The purified RNAs were then treated with 0.06 units.µL -1 of DNA-free TURBO DNase (Ambion, Life Technology) to remove genomic DNA. The quantification of purified nuclear RNA was accessed using a Qubit 3.0 Fluorometer and its integrity was analyzed using an Agilent 6000 Pico Kit on an Agilent 2100 Bioanalyser.

Library construction and Illumina RNA-Seq runs

To perform Illumina RNA-seq experiments as to investigate the effects of endoreduplication on gene expression, we extracted total nuclear RNA from a fixed number of nuclei (ca. 100,000 nuclei).

According to ploidy levels, total nuclear RNA concentrations ranged from 0.44 to 7.27 ng.µL -1 (Table 1A). A volume of 22 µL for each sample was sent out to Fasteris Life Sciences SA (Plan-les-Ouates, Switzerland) for construction of mRNA-seq libraries following the TruSeq RNA Sample Prep Kit.

After cDNA synthesis, PCR amplification for 15 cycles (4C and 8C) or 18 cycles (16C and 32C) was performed prior to library construction. A total of 24 cDNA libraries were then constructed corresponding to 4 ploidy levels (4C, 8C, 16C and 32C) in 3 replicates, with duplex-specific nuclease (DSN) or without (no-DSN) treatment. The multiplex sequencing reaction was performed on the Illumina HiSeq 2000 machine.

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RT-qPCR

Complementary DNAs of total nuclear RNAs were synthetized using SuperScript IV Reverse Transcriptase (Invitrogen Life Technologies) in the presence of random nonamers. The cDNA obtained were diluted (1/100) in distilled water. For real time PCR, a master mix for each PCR run was prepared with GoTaq® qPCR Master Mix (Promega, France). In a total volume of 20 µL, 0.2 µM of each PCR primer and 10 µL SYBR Green PCR Buffer were added to 5 µL of diluted cDNA. The following amplification program was used: 95°C 3 min, 40 cycles at 95 °C for 10 s followed by 60°C for 15 s. Three biological replicates corresponding to three different nuclei preparations for each level of ploidy were used; all samples were amplified in duplicate from the same RNA preparation and the mean value was considered. PCR amplifications were carried out using the CFX96 System (Bio-Rad).

The real-time PCR efficiency was determined for each gene with the slope of a linear regression model using the spikein as reference genes and the Bio-Rad CFX Manager™ Software version 3.1.

The list of primers used to amplify the genes for RNA-Seq confirmation and the spikein is provided in Supplemental Table S5.

Mapping and normalization of RNAseq data

Sequence quality check and pre-processing. Twenty-four samples were sequenced, 6 per ploidy level. Half of them were treated with duplex specific nuclease (DSN), in order to remove overrepresented RNA. A total of 259 045 386 100bp raw reads were processed through the quantification pipeline (Supplemental Figure S1). Briefly, sequence quality was verified using FASTQC [START_REF] Andrews | FastQC: a quality control tool for high throughput sequence data[END_REF] and sequences were cleaned with TrimGalore (Krueger, 2012) that aims at removing remaining sequencing adaptors and trimming bad quality base pairs. This step removed about 2% of the sequences for a useful total of 258 972 491 reads.

Mapping. The cleaned reads were then mapped against Sly2.40 tomato reference genome with STAR [START_REF] Dobin | STAR: ultrafast universal RNA-seq aligner[END_REF], a splice aware aligner, fixing read length to 100 bp (corresponding to our reads) and leaving other parameters to default. The alignments were finally sorted by genome coordinates and merged by ploidy level with Samtools (Li et al., 2009).

Mapping distribution.

A more in depth analysis of uniquely mapped sequences has been performed with RNA-SeQC (DeLuca et al., 2012). This quality control tool for RNA-seq data provides us with the read mapping distribution between genomic regions. This tool can also produce a BWA mapping against rRNA sequences to estimate the rRNA rate inside the intergenic regions (Supplemental figure 3).

Raw quantification.

Merged alignments obtained from DSN treated sample were then processed with featureCounts (Liao et al., 2014), an efficient read summarization program that counts mapped reads for genomic features such as genes or exons. This program requires an alignment file and an annotation file and we used ITAG2.30 annotation file.

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DE analyses.

Differential Expression (DE) analyses have been performed with the DESeq2 package (Love et al., 2014) in the R environment (Team R Core, 2014) using data obtained from DSN treated samples.

The DESeq function from DESeq2 has been carried out with default parameters. It has been shown in Maza et al. (2013) and Maza (2016) that the LRE normalization method (used as default in DESeq2) is very similar to the TMM method used in the edgeR package (Robinson and Osklack, 2010;Robinson et al., 2010).

Clustering of the differentially expressed genes and GO enrichment analysis

The differentially expressed genes were clustered according to the k-means clustering method using the R base stats package (Team R Core, 2014). All cluster plots were generated with the ggplot2 Rpackage [START_REF] Wickham | ggplot2: Elegant graphics for data analysis[END_REF].

The GO enrichment analysis to determine the over-representation of certain GO terms in the DE gene set was done using the PLAZA tool with a cutoff of 0.05 (Proost et al., 2015). This tool compares the occurrence of a certain GO label in a gene set with the occurrence in the genome. The significance of over-representation is determined using the hypergeometric distribution and the Bonferroni method is applied to correct for multiple testing.

SHORT SUPPORTING INFORMATION LEGENDS

The following materials are available in the online version of this article. S1. RNA-Seq data processing pipeline for expression quantification. S1. Set of genes non-DE and Differentially Expressed (DE) genes selected for RT-qPCR. S2. List of differentially expressed genes in at least one comparison. S3. Classification into six expression clusters and functional category of the Differentially Expressed (DE) genes. S4. Overrepresentation of functional categories for each cluster of DE genes. S5. List of primers used for the RT-qPCR.

Supplemental Figure

Supplemental Table

Supplemental Table

Supplemental Table

Supplemental Table

Supplemental Table

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A Seris

M Feve

F Mechin

J P Pascault

Thermally and Anionically Initiated Cure of Bismaleimide Monomers

A kinetic and thermodynamic study of the thermally or anionically induced cure of aromatic bismaleimide monomers (namely 2,4-bismaleimidotoluene, 4,4'-bismaleimidodiphenylmethane and their eutectic mixture) is presented. Calorimetric investigations allowed the determination of heats of polymerization and activation energies for both types of initiations, and the values found are compared with data in the literature. Isothermal cures were also carried out with and without anionic initiator (typically imidazole). SEC measurements were used to monitor the conversion of the monomers as a function of time. The thermally induced polymerization seems to proceed in a rather heterogeneous way, owing to an initiation that is too slow: gelation appears at first only as the formation of microgels, with no immediate increase in the viscosity; macrogelation occurs some time after. On the contrary, the anionically induced polymerization is more homogeneous. A complete study of a particular reacting system revealed no interference between radical and anionic polymerization over a wide range of temperatures, and in this case gelation results in an immediate increase in viscosity. However, the conversion at the gel point is unexpectedly high, which can be interpreted as the result of a very fast initiation as well as of transfer reactions. Glass transition temperatures were also measured as a function of time and curing temperature in order to study the influence of vitrification on the kinetics and to check for the existence of a unique relation between Tg and conversion. This actually proved to be correct as long as diffusion does not slow down the reaction; in this case Gillham's treatment of Tg versus Int was successfully applied and led to the correct value of the activation energy. All the measurements allowed us to establish the time-temperature-transformation cure diagram for a specific reacting system.

INTRODUCTION

Thermosetting polyimides are of low-molecular weight, especially difunctional monomers, or prepolymers or mixtures thereof, which carry imide groups in their backbone structure and are terminated by reactive groups such as maleimide. Bismaleimide monomers are generally cured by a thermally induced addition reaction to give highly crosslinked systems. The final networks are good heat-resistant polymers and suitable for use in a wide range of materials. In particular they have been utilized in multilayer printed wiring boards for large-scale computers and in carbon fiber composites for the aerospace industry.

However, when bismaleimides are thermally cured, the high temperature needed for the beginning of the reaction and to fully cure the material limits their use in conventional composite processing. The use of initiators can effectively reduce the cure temperature. The initiators can be peroxides, [START_REF] Stenzenberger | Structural Adhesives[END_REF][START_REF] Varma | [END_REF][3][4] resulting in a radical initiation, or they can be tertiary amines or imidazoles, 5 resulting in an anionic initiation.

The purpose of this work is to evaluate the influence of different amounts of imidazole initiator on the reaction rate and on the phase transition process of a mixture of two bismaleimide monomers. During the curing of thermosets there are two kinds of phase transitions: gelation and vitrification. Gelation corresponds to the time when a giant tridimensional macromolecule is formed and the weight average molecular mass, , tends to infinity, because of crosslinking reactions. Vitrification occurs when the length of the macromolecules or the crosslink density increases such that the glass transition temperature, Tg, is the same as the curing temperature, Ti. Once Tg has reached Ti, the system gets very viscous and the reactions become diffusion controlled. Reaction kinetics and physical transformation of a network are thus strongly interdependent. This kind of study is an important step for process optimization and for a better understanding of structure-property relations in the final network.

EXPERIMENTAL

All the experiments were carried out using pure monomers or an eutectic mixture of 4,4'bismaleimidodiphenylmethane (BDM, 70% by weight) and 2,4-bismaleimidotoluene (BT, 30% by weight). The melting point of this eutectic mixture is 143°C. N-phenylmaleimide (N-PMI ) was used as a monofunctional model compound. The monomers were kindly provided to us by Rhône-Poulenc, and their purities were determined by proton nuclear magnetic resonance (NMR) by comparing the integration of the maleimide proton peak to those relative to the central moiety. The only impurity was found to be an acetoxy-derivative resulting from the addition of two acetic acid molecules on the BMI double bonds. Imidazole and benzimidazole (Aldrich) were used as catalysts without further purification.

Preliminary investigations of the reactions were performed using differential scanning calorimetry (DSC) on a Mettler TA 3000 calorimeter. Thermograms were obtained for 5-10 mg samples using heating rates of 10 K/min for reaction enthalpy measurements and 7.5 K/min for glass transition temperature (Tg) determinations (by convention, always taken as the onset value).

The isothermal kinetics of these reactions were then followed by size exclusion chromatography (SEC) performed with a Waters apparatus equipped with a differential refractometer and a UV absorption detector. The eluent was either tetrahydrofurane (THF) at room temperature or dimethylformamide (DMF) at 80°C for poorly soluble samples. Calibrations curves were obtained from polystyrene standards.

The viscosity during isothermal cures was monitored with a coaxial cylinder viscometer using shear rates equal to 100 s -1 or 0.65 s -1 on a Contraves Rheomat 115.

Viscoelastic analysis as a function of time was performed with a RDA2 Rheometrics viscoelasticimeter, by stressing the reacting mixtures, situated between two parallel circular plates, at a frequency equal to 100 rad/s.

In order to monitor the double-bond conversion during cure, a chemical determination of the remaining maleimide groups was sometimes used. For this purpose, the sample was dissolved or suspended in N-methylpyrrolidone plus a small amount of aqueous acetic acid. The double bonds were then reacted with a known excess of morpholine in acetone to yield quantitatively the aspartimide adduct. The residual amine was finally titrated with hydrochloric acid.

RESULTS AND DISCUSSION

Kinetics Investigations from DSC Scans

Maleimides are generally crystalline monomers. However, the two bismaleimides (BMI) used in this study can be obtained in the amorphous state with a glass transition temperature, Tg0, around 46-47°C. But it is difficult to keep the samples amorphous because the crystallization rate is very high, even at room temperature. So during a DSC scan of a monomer sample to 380°C at 10 K/min, we usually observe first an endothermic peak corresponding to the melting temperature Tm, followed by an exothermic peak which represents the reaction of the double bonds, characterized by the peak area, ∆H J/g, and the temperature at the maximum, Tp. Typical DSC scans are shown in Figure 1. DSC has also been used with some assumptions by different workers [6][7][8] to study the kinetics of thermoset curing reactions without attempting to determine the reaction order. The relation between the heating rate, q, and the peak exotherm temperature, Tp, is of the form: (1) where q is the heating rate (K/min) , Tp is the absolute peak exotherm temperature, B is a constant related to an Arrhenius frequency factor, and R is the gas constant. The activation energy Ea can be obtained from the slope of the plot of Ln q versus 1/Tp. Dynamic scans were run at q = 2.5, 5, 7.5, and 10 K/min. The chain polymerization of bismaleimide monomers may result from a chemical initiation if some initiator has been added (bases like alkoxides or imidazoles for anionic polymerizations, or peroxides for radical polymerizations) but it can also be thermally initiated simply by heating the mixture. In order to try and separate the different mechanisms which could be involved in the curing of bismaleimides, DSC scans were run at different heating rates on the monomers with and without anionic initiator. b Exotherm maximum (Tp) and heat of polymerization (∆Hp) are determined from DSC measurements using the heating rate q = 10 K.min -1 , and activation energy are determined using the heating rates q = 2.5, 5, 7.5 and 10 K min -1 . c Relative to one double bond in the case of bismaleimide.

Table I. Thermally induced polymerization of maleimide and bismaleimides

Monomers

The thermally induced polymerization of the monomaleimide (Ar-MI) and two bismaleimides (MI-Ar-MI) was first examined. The results are reported in Table I. Polymerization occurs just after the melting temperature in the case of the two BMI's and at higher temperature in the case of N-PMI (Fig. 1). Several main features appear:

1. Similar results for Tp and Ea have been reported in the literature. [START_REF] Stenzenberger | Structural Adhesives[END_REF][START_REF] Varma | [END_REF]4,9 2. In the case of the BMI, BDM, the presence of impurities even in small quantities enhances tremendously the activation energy (cf. Table I) and shifts the polymerization exotherm to lower temperatures (it also lowers the gelation time and promotes the overall kinetics-results not presented here). This behavior is in agreement with Brown's ESR studies on the radical polymerization of BDM which demonstrated the possible interference of impurities in the mechanism. 10 3. Joshi and Zwolinski [START_REF] Joshi | Vinyl Polymerization. Heats of Polymerization and their Structural and Mechanistic Implications[END_REF] have reported an enthalpy of polymerization, ∆Hp = 87 kJ/mol for the monofunctional monomer N-PMI. We obtained a similar value ∆Hp = 85 kJ/mol. This value for N-PMI is the same as the one reported in the literature for the thermal polymerization of ethylene. 4. But in the case of difunctional monomers the obtained enthalpy of polymerization is lower as compared to single double bond monomers. We obtained 43-44 kJ/mol which is in the same range as those found by H. Stenzenberger, 1,9 42 kJ/mol, and Fry and Lind, [START_REF] Fry | [END_REF] 45 ± 3 kJ/mol. To be sure that the reaction was complete, after running the first scan to 380°C, we cooled the sample to room temperature and repeated the DSC measurement. No residual exotherm was observed during this second scan. Fry and Lind [START_REF] Fry | [END_REF] have performed a similar experiment, but they have also measured the double bond conversion after the first scan with the help of [START_REF] Seris | Sympol 90 Proceedings[END_REF] C-CP Mas-nuclear magnetic resonance (NMR). They found the value x = 0.84 indicating that residual double bonds are buried in the BMI network and cannot polymerize during the first and second DSC scans. Fourier transform infrared (FTIR) analysis of our cured samples (BDM as well as BT) also led to a value in this range.

Taking into account x = 0.84, the reaction enthalpy for BMI can be estimated to be in the range of ∆Hp ~ 52 kJ/mol (mole of double bonds). This is still much lower than that for the monofunctional monomer. This low value can be explained as a result of some steric hindrance.

To verify this assumption, mixtures of mono and difunctional monomers (N-PMI and BMI) have been studied. The reaction enthalpy is constant, 85 ± 3 kJ/mol, from 0 to 25% by weight of BMI; then it decreases rapidly to 62 ± 3 kJ/mol for 30% b.w.; and then to 45 ± 3 kJ/mol for pure difunctional monomers. In Figure 2 this behavior is compared to the increase in Tg with the amount of BMI of the final networks, and to the decrease in ∆Cp at Tg (both difunctional monomers lead to almost exactly the same curves). The Tg of pure N-PMI is 140°C with ∆Cp ~ 0.3 J.g/K, but ∆Cp decreases drastically when the amount of difunctional monomer increases, and is less than 0.05 J.g/K for 30% BMI b.w.. For higher amounts of BMI it is not possible to detect the Tg of the network. ∆Cp is related to the chain mobility, and it is clear that the low values for the heat of polymerization of BMI, ∆Hp, correspond to a very low mobility of the polymeric chains. II.

Table II. Maximum temperatures, heats of polymerization and activation energies as

The addition of imidazole or benzimidazole had two effects: first the temperature of the exotherm peak maximum and the activation energy were lowered, as one might expect from an initiator. This effect was all the more pronounced as the amount of initiator used was increased. But curiously, the use of imidazole in increasing amounts also led to decreasing values for the heat of polymerization, ∆Hp. We did not observe such a behavior for the monofunctional compound N-phenylmaleimide; [START_REF] Seris | Sympol 90 Proceedings[END_REF] in this case, the addition of imidazole lowered Tp as well as the activation energy but did not modify ∆Hp (85 kJ/mol for N-phenylmaleimide) . This stated, it is difficult to account for this dependence of ∆Hp on the amount of imidazole, since if we refer, for example, to a possible transfer to the initiator, a similar mechanism should occur in the polymerization of the monofunctional compound. Residual double bonds were not measured after the first DSC scan for the BMI polymerization.

Table II also shows that benzimidazole was less efficient as an initiator than imidazole.

Isothermal Reactions: Kinetics and Gelation

The kinetics of several isothermal polymerizations was investigated by size exclusion chromatography (SEC), and by viscosity and viscoelastic measurements. Gelation is defined as the critical point at which the curing system yields indefinitely large polymer structures or macrostructures which extend throughout the volume of the system. At the gel point the curing system suddenly transforms from a viscous liquid to an elastic gel. The gelation time may be determined as:

1. The time tins, when the sample starts to be partially insoluble in a strong solvent. For the BMI samples we have chosen the solvent dimethylformamide (DMF) instead of the classical tetrahydrofuran (THF).

2. The time tη when the viscosity tends to infinity. However, it is not practical to have an "infinite" viscosity and by convention we take the time when the viscosity equals 5.10 4 Pa.s.

3. The time tG'=G" at which the elastic and viscous moduli G' and G" are equal. [START_REF] Tung | [END_REF]15 Measurements have been taken at a high frequency, 100 rad/s. If the reaction is not too fast, it is easy to determine this point. An example is given in Figure 3. But in fact this point is frequency dependent, and recent results have shown that it is more correct to take the point at which tan δ is independent of the frequency. In the case of epoxy systems this point is generally obtained for tan δ higher than 1. For example the point independent of the frequency is obtained for tan δ = 1.3 for an epoxy system with a cycloaliphatic diamine curing agent. 16 But on the time scale the difference between tan δ = 1 and tan δ = 1.3 is small. Isothermal polymerizations were carried out using different percentages of imidazole at various temperatures. The monomer conversion, X, may be monitored as a function of time by following the decrease in the monomer peak height, t, in SEC chromatograms, in THF (on the soluble fraction of the samples) :

X = 1 -ht/h0 (2)
Both monomers BDM and BT are consumed at the same rate. Typical curves, which were obtained from the polymerization of BDM/BT mixtures at 200°C, are depicted in Figure 4. According to the DSC scans results, a small quantity of imidazole, 0.5 mol % (or 0.1% b.w.), increases drastically the polymerization rate.

For the thermal polymerization (0% I) the beginning of the reaction is reported on a larger scale. Arrows indicate the gelation times tins and tη found by SEC and viscosity measurements for these systems. Gel times are also reported in Table III. One remarkable fact is that an insoluble fraction appeared well before the increase in viscosity, tins << tη, during thermal polymerizations. At 200°C, monomer conversions are estimated from Figure 4 to be X ~ 0.07 at tins, and X ~ 0.45 at tη.

Statistical parameters of the pre-and post-gel stages may be obtained using different approaches [17][18][19][20] derived from the pioneering work of Flory 21 and Stockmayer. 22 The main assumptions of the Flory-Stockmayer (FS) treatment are: (1) equal reactivities of the functionalities of each species; (2) absence of substitution effects (i.e., the reaction of a particular site does not alter the reactivity of the remaining unreacted sites); (3) absence of cyclic molecules in finite species. These conditions define an ideal polymerization, and in the case of an ideal chain-growth polymerization, the conversion at the gel point is very low, x ≤ 0.01.

For a free-radical crosslinking copolymerization of monovinyl-divinyl systems, cyclization or intramolecular reactions have been found to be an intrinsic property. The consequence was that many experimental gelation results [START_REF] Dusek | Developments in Polymerization[END_REF][START_REF] Ito | [END_REF][25] seemed to greatly deviate from the theoretical prediction by classical FS theory. Dusek et al 26 proposed that, in the early stage of reaction the occurrence of cyclization forms internally crosslinked insoluble and rigid structures in the primary polymer chains referred to as "microgels". Many pendent vinyl groups are buried inside the microgels and show a reduced, or completely suppressed, reactivity. Then when the polymerization goes on, the microgel concentration continuously increases, and when the intermicrogel crosslinking dominate the reaction, the viscosity rises up very rapidly until the gel point, called in this case macrogelation. If we assume this gelation mechanism for the thermal polymerization of BMI, tins corresponds to the microgel formation and tη to macrogelation. This may be the result of numerous cyclization reactions as well as of a decrease in the reactivity of the double bonds, both by a substitution effect and because some of them get trapped inside the microgels. In Figure 4, one can notice that the appearance of insoluble microgels had no immediate influence on the reaction kinetics. A decrease in the rate of conversion was observed but somewhat after, at t ≈ 20 min. This decrease became more pronounced after the system became very viscous, which would agree with a now partly diffusion-controlled reaction or with a lower radical concentration. However, the conversion increased at an even higher rate again after a short while. The overall behavior is difficult to explain. It is easy to explain the decrease in the polymerization rate when the viscosity increases, using a diffusion effect argument. However, it is more difficult to understand why the polymerization rate increases again 10 min after macrogelation. It is possible to refer to the Trommsdorff effect: the increase in viscosity lowers the rates of the reactions involving two polymeric molecules (termination and transfer to the polymer) much more than the rates of the reactions involving at least one small molecule (initiation and propagation) and thus the overall polymerization rate increases tremendously.

Anionic Isothermal Reactions: Influence of Temperature and Initiator Concentration

Imidazole drastically increases the polymerization rate (Table II and Fig. 4). The micro-and macrogelation times at a high isothermal curing temperature, Ti = 200°C, are compared in Table III. There is a large difference between the values in the case of thermal polymerization, but the results are in the range of experimental errors in the case of polymerizations initiated by imidazole. For this reason, experiments have been performed at a lower temperature, 150°C. SEC experiments give the monomer conversion, X. If we assume that all the double bonds are equally reactive (i.e., if there is no substitution effect), the conversion of the vinyl functions, x, may be deduced from X by the expression:

1 -X = (1x) [START_REF] Varma | [END_REF] (3) since 1-X describes the probability of finding a nonreacted BMI molecule and thus of finding simultaneously two nonreacted vinyl functions. Using this assumption we find:

xSEC = 1 -(ht/h0) 1/2 (4)
The evolution of the double-bond conversion, x, is displayed in Figure 5. x was determined from SEC measurements (xSEC) but also chemically by reacting the remaining double bonds with morpholine.

Microgelation occurs at tins = 50 min, which is before macrogelation, tG'=G" = 60 min or tη = 70 min. Both curves of x versus t are parallel up to macrogelation; if eq. ( 4) is correct, all the double bonds are equally reactive before gelation. After gelation the two curves are different: gelation appears on the x conversion curve as a decrease in the polymerization rate. On the xSEC curve, as shown in Figure 4, the polymerization rate starts decreasing, then reaccelerates 10 min after gelation, and finally returns to its former value (both curves are parallel in the end). Note that here the mechanism is anionic and thus the Trommsdorff effect cannot be encountered.

The different behaviors observed on the two conversion curves indicate that after macrogelation there is a strong substitution effect: once the first double bond of a monomer molecule has reacted, the reactivity of the second one becomes very low. A consequence of this substitution effect is that the monomer conversion increases rapidly after macrogelation, and thus explains the form of the curves X versus t in Figure 4 and xSEC versus t in Figure 5. The results obtained for the gelation times at various isothermal curing temperatures, Ti, are displayed in Table IV. In the case of anionic polymerization the different criteria lead to quite close gelation times.

Boots 27 has shown using a simulation, that the degree of heterogeneity of a network during polymerization depends on the ratio of the initiating rate, Ri, to the propagating rate, Rp. When the ratio is equal to 1 (case of a step-growth polymerization) the process of the network formation is homogeneous. When this ratio is high, corresponding to a very low Ri compared to Rp, the process of the network formation is heterogeneous. Thus we can say that the anionic polymerization of BMI is much more "homogeneous" than when it is thermally initiated, which is possibly a result of a faster initiation step.

If this is so, the ratio (5) (where Ri, Rp, Rt, and Rtr are the rates of initiation, propagation, termination, and transfer, respectively) should be less than unity. This is in good agreement with the higher value found for xins in the case of anionic polymerization (x ~ 0.2) as compared to the thermal polymerization for a tetrafunctional monomer, since xgel depends on the parameter, [21][22][START_REF] Dusek | Developments in Polymerization[END_REF] (6) x is determined from SEC measurements (xSEC) except for Ti = 150°C (see Fig. 5). The values given in Table IV indicate that the gelation times become shorter and shorter as the reaction temperature increases. More precisely, in the case of anionic polymerization, the plot of lntins or lntη versus 1/T leads to a straight line as shown in Figure 6. The same mechanism should thus be involved at every temperature, and consequently xgel should be independent of the temperatures. This is roughly the case if we refer to Table IV: all the gel conversions are equal to 22 ± 6%.

This is true up to a cure temperature of 190°C. However, one must keep in mind that the maximum of the exotherm corresponding to the thermally induced polymerization of BDM/BT (70/30) was observed at 240°C. A radical mechanism is thus likely to interfere with the anionic mechanism at temperatures higher than 190°C.

If we assume that the mechanism is the same at all temperatures and that xgel is constant, then an activation energy may be deduced from the Arrhenius plot displayed in Figure 6: here we find Ea = 94 kJ/mol, instead of 115 kJ/mol for the thermally initiated system. The same activation energy determined from DSC measurements (Kissinger's treatment) for the polymerization of BDM/BT (70/30) initiated by 0.5 mol % imidazole was equal to 88 kJ/mol. Both methods thus give consistent results. The same kind of kinetic measurements as reported previously were run for the curing of BDM /BT (70/30) using 1.0 mol % imidazole instead of 0.5 mol %. The results obtained are listed in Table V. The increase in the amount of initiator had two effects: at first, it lowered the gelation time, whatever curing temperature was used; this is quite logical. The activation energy calculated from DSC measurements is equal to 72 kJ/mol, i.e., less than the value of 88 kJ/mol found for 0.5 mol % initiator.

But using double the amount of initiator also led to much higher conversions at the gel point. Here the mean value of xgel is equal to 35%, instead of 22% for 0.5 mol % imidazole. This is compatible with a shorter gelation time if we assume that the initiation rate is greatly enhanced: the ratio decreases and thus the value of increases accordingly.

Vitrification phenomena

In the curing of thermosets, the variations in the glass transition temperature Tg are important to follow since the occurrence of vitrification can have a great influence on the overall kinetics. Epoxy systems often become diffusion-controlled after tvit, the time for which the increasing Tg reaches the value of the curing temperature Ti. 28,29 Moreover, Tg is a parameter characteristic of the structure of the curing network at a particular stage, and, if the chemical phenomena are always the same, Tg should be linked to x by a unique relation depending only on the mechanism but not on Ti. 30 Here the Tg was monitored as a function of time for the curing of BDM/BT (70/30 b.w.; 0.5 mol % imidazole) at various temperatures. For a very high curing temperature such as 200°C, values of Tg could not be obtained from DSC measurements because the heat capacity changes were too small, due to a higher crosslinking density (see Fig. 2). In this case, the Tg was deduced from viscoelastic measurements: in the first step, the sample was cured isothermally for a given time in the viscoelasticimeter. The specimen was then quenched at a temperature below the Tg and G', G" and tan δ were then monitored as a function of temperature using a heating rate of 10 K/min. If we plot G' vs. T (as represented in Fig. 7), we observe at first a decrease in G' (corresponding to the glass transition). Then the elastic modulus increases again, since the network is being postcured: the remaining double bonds start reacting and the network becomes more densely crosslinked. In these experiments, Tg was taken at the first inflection on the G' versus T curves rather than at the maximum of the peak in G" which is more characteristic of the post-cure reaction. . This should result in a shift in the transition temperatures but not in such a different slope after vitrification. It may be a consequence of the thermal initiation of the polymerization (or dimerization) starting to interfere with the anionic mechanism. Even if the mobility of the chains becomes very low after tvit, new radicals can be generated inside the network and give rise to more crosslinks, hence the increase in Tg. In any case, the variations in Tg with x cannot be the same as that observed for lower curing temperatures since there are now two mechanisms instead of one and thus it is not surprising that the general shape of the curve is not the same. For the lower curing temperatures, the thermal initiation (and thus the radical mechanism of polymerization or dimerization ) is unlikely to occur. Since we are considering a very highly crosslinked network, at a lower Ti (150, 160°C) the motions of the reactants can be hindered very early in the reaction, i.e. at low conversions and for values of Tg lower than Ti. Now if we assume that in this case Tg is linked to x by a unique relation, we can consider the part of the curves when the reaction is only kinetically controlled and one can neglect diffusion. In this case, Wisanrakkit and Gillham 29 propose writing the kinetic equation as:

!"# • %! # (7)
where k depends only on the temperature, and f on the conversion x, thus on Tg. The former equation leads to the following expression:

&'" ( ) !"# ) * (8)
For two given curing temperatures T1 and T2, let us denote t1 and t2 as the times corresponding to the same glass transition temperature, Tg.

) !" # ) * ) !" # ) * or ) * ) * ) !" # ) !" # (9)
and thus Int2 -Int1 is a constant (independent of time) which depends only on the curing temperatures. This means in fact that all the Tg versus Int curves may be deduced from one another simply by shifting them along the In t axis (as long as diffusion does not slow down the reaction).

If we plot Tg versus Int in our case, we obtain the curves displayed in Figure 9. One sees that the lower parts of all the curves seem to be superposable (Tg < 130°C); i.e., a master curve which gives the general shape for the variation in Tg with Int actually exists in this temperature range. (This would confirm the assumption made when noticing that the variation of Intgel versus 1/T gave a straight line: the mechanism of the reaction, up to the gel point, seems to be roughly the same at all the curing temperatures, Ti). In these conditions, Wisanrakkit and Gillham 29 also define a shift factor, AT, by choosing a reference curing temperature, T0. Then for any curing temperature, T:

+ ) * ) * , ) ) , ! - # (10)
where Ea represents the single apparent activation energy of the reaction. If we try to apply this equation to our results, we can plot AT = Int -Int0 versus (1/T) choosing for example T0 = 150°C (423 K). The resulting diagram is shown in Figure 10. We obtain a straight line, whose slope yields a value of Ea = 97 kJ/mol. This is consistent with the values deduced from DSC scans using Kissinger's treatment (Ea = 88 kJ/mol) and from the Arrhenius plot of In tgel versus 1/T (Ea = 94 kJ/mol). One should keep in mind that this interpretation is valid only when diffusion has no influence on the reaction kinetics, i.e. on a modest part of some of our curves.

Time-Temperature-Transformation Diagram

After completing the study of the curing of BDM/BT initiated by 0.5 mol % imidazole, it was possible to establish the time-temperature-transformation cure diagram which describes the system. 31 This diagram is shown in Figure 11. Tg∞ (corresponding to a conversion x = 100%) was extrapolated to about 400°C from DSC measurements using decreasing amounts of the monofunctional compound N-PMI (see Fig. 2). Tg0 corresponds to the uncured system (Tg0 = 43°C).

The parameter gelTg is a characteristic of the system. It indicates the curing time and temperature for which gelation and vitrification occur simultaneously.

If we assume that a single mechanism is involved in the cure of this system, xgel must be a constant, independent of the temperature; this is roughly what we found. If Tg is linked to x by a unique relation, then the value of Tg at the gel point must also be a constant independent of the curing temperature.

In particular, this constant value of Tg(gel) should be equal to gelTg. Values of Tg at the gel point were thus measured for the various curing temperatures and are reported in Table VI. There is little dispersion of the values, and they are centered on a mean value of 72°C, which was estimated to be the actual gelTg. When applied to the cure of BDM/BT with 1.0 mol % imidazole, the same method led to a slightly higher value of gelTg = 76°C.

CONCLUSION

Bismaleimide prepolymers are easily cured to produce highly thermostable networks. In this work, we tried to acquire a more precise idea of how the reaction proceeds, whether it is anionically or simply thermally induced, and how both mechanisms may interfere with each other. We are now able to provide a general scheme for this polymerization, although finer experiments would be necessary to make a perfect description of the system.

It appears that the thermally initiated polymerization proceeds in a rather heterogeneous manner: gelation is reached very rapidly but results at first only in the formation of microgels. The macrogelation of the system is sometimes observed much later, as the reaction proceeds. The heats of polymerization have been found to be quite close to the data available in the literature, although the extent of non-reacted functions is sometimes difficult to estimate.

The use of imidazole or benzimidazole as anionic initiators allows the curing of bismaleimides at lower temperatures. The complete study of the system BDM/BT (70/30 b.w.)/0.5 mol % imidazole gave us some insight into the polymerization mechanism which seems much more "homogeneous" than the thermally initiated mechanism; this is probably due to a faster initiation (as compared with the propagation). In the case of this particular system, several experimental observations agree confirming that there is only one mechanism, at least up to 190°C, no matter what curing temperature is used; but diffusion may start to limit the kinetics at low conversions, i.e. well before vitrification. However, the conversion at the gel point is roughly constant and higher than that observed for the radical polymerization. By combining all the measurements, we were able to trace the general shape of the time-temperature-transformation cure diagram which totally depicts the behavior of BDM/BT/0.5 mol % imidazole. Some information about the cure initiated by 1 mol % initiator was also obtained.

An important feature of this polymerization is that the reactivity of the second double bond of a monomer molecule is greatly reduced after gelation.

It is apparently difficult to reach very high conversions, and the nature of the last stages of the reaction (particularly termination) needs to be characterized more precisely. This will be very important to understand the relations between structure and properties of the final networks.

We wish to thank Rhône-Poulenc Co. for their financial and experimental support.

Figure 1 .

 1 Figure 1. DSC thermograms of monofunctional (N-PMI) and difunctional monomers (BDM). Heating rate q = 10 K/min.

  determined from DSC analysis for the polymerization of BDM/BT (70/30 by weight) using various amounts of imidazole 10 K/min. b Relative to a single double bond.

Figure 2 .

 2 Figure 2. Comparison between the enthalpy of polymerization, ∆Hp, per mole of double bonds with the glass transition temperature and the mobility (∆Cp at Tg) of the final networks based on blends of N-PMI and BDM (or BT).

Figure 3 .

 3 Figure 3. Example of viscoelastic measurements (100 rad/s) for the BDM/BT system at Ti = 150°C, with 0.5% mol of initiator.

Figure 4 .

 4 Figure 4. Monomer conversion, X, as a function of time for the polymerization of BDM/BT at 200°C and with different mol % of initiator I (x) 0 % ( ) 0.5% () 1% .

Figure 5 .

 5 Figure 5. Double bond conversion, x, as a function of time for the polymerization of BDM/BT at 150°C (0.5 mol % imidazole) ( ) SEC measurements, xSEC ( ) chemical determination, x.

Figure 6 .

 6 Figure 6. Arrhenius plot for tins (x) and t η ( ) for BDM/ BT (70/30) polymerization initiated by 0.5 mol % imidazole.

Figure 7 .

 7 Figure 7. Elastic modulus G' versus temperature (heating rate: 10 K/min) for partially cured networks of BDM/BT (70/30) and 0.5 mol % imidazole (tcure = 1 h, 2 h, 3.5 h and 5 h; Ti = 200°C).

Figure 8 .

 8 Figure 8. Glass transition temperature Tg during the curing of BDM/BT (70/30) with 0.5 mol % imidazole: Ti = 150°C (); 160°C ( ); 170°C ( ); 180°C ( ); 200°C ( ).

Figure 9 .

 9 Figure 9. Evolution of the glass transition temperature Tg with Int for the curing of BDM/BT (70/30) with 0.5 mol % imidazole at various temperatures: Ti = 150°C (); 160°C ( ); 170°C ( ); 180°C ( ); 200°C ( ).

Figure 10 .Figure 11 .

 1011 Figure 10. Arrhenius plot of the shift factors AT = Int-Int150°C, deduced from Figure 9, vs. 1/T.

Table III . Influence of the initiator concentration on the gelation time, as measured with different techniques for the BDM/BT polymerization at 200°C

 III

			Time (min)
	% mol I	tins (DMF)	tG'=G"	tη
	0	5	-	36
	0.5	3	5	4
	1.0	2	-	(not measurable)

Table IV . Gelation times associated with the polymerization of BDM/BT (0.5 mol % imidazole) at various temperatures Ti

 IV

	Ti (°C)	tins (min)	tG'=G" (min)	tη (min)	x % at tins
	140	180	-	-	28
	150	50	60	70	20
	155	40	-	-	24
	160	30	30	31	27
	170	20	-	19	26
	180	10	-	9	22
	190	5	-	7	16
	200	3	5	4	16

Table V . Comparison of the values of tins and xgel found for the curing of BDM/BT (70/30) at various temperatures, using either 0.5 mol % or 1 mol % of imidazole as the initiator; x is determined from SEC measurements

 V

		tins (min)		xgel (%)
	Ti (°C)	0.5 mol% imidazole	1.0 mol% imidazole	0.5 mol% imidazole	1.0 mol% imidazole
	150	50	40	20	33
	160	30	20	27	30
	170	20	10	26	43
	180	10	6	22	31
	190	5	3	16	42
	200	3	2	16	29