Noelya Planchard

Pierre Bertin

Martine Quadrado

Céline Dargel-Graffin

Isabelle Hatin

Olivier Namy
email: olivier.namy@i2bc.paris-saclay.fr

Hakim Mireau
email: hakim.mireau@inra.fr

The translational landscape of Arabidopsis mitochondria

Messenger RNA translation is a complex process that is still poorly understood in eukaryotic organelles like mitochondria. Growing evidence indicates though that mitochondrial translation differs from its bacterial counterpart in many key aspects. In this analysis, we have used ribosome profiling technology to generate a genome-wide snapshot view of mitochondrial translation in Arabidopsis. We show that, unlike in humans, most Arabidopsis mitochondrial ribosome footprints measure 27 and 28 bases. We also reveal that respiratory subunits encoding mRNAs show much higher ribosome association than other mitochondrial mRNAs, implying that they are translated at higher levels. Homogenous ribosome densities were generally detected within each respiratory complex except for complex V, where higher ribosome coverage corroborated with higher requirements for specific subunits. In complex I respiratory mutants, a reorganization of mitochondrial mRNAs ribosome association was detected involving increased ribosome densities for certain ribosomal protein encoding transcripts and a reduction in translation of a few complex V mRNAs. Taken together, our observations reveal that plant mitochondrial translation is a dynamic process and that translational control is important for gene expression in plant mitochondria. This study paves the way for future advances in the understanding translation in higher plant mitochondria.

INTRODUCTION

The functioning of eukaryotic cells relies on the integrated activity of several highly specialized subcellular or-ganelles. Among them, mitochondria represent essential energy conversion powerhouses that produce most of the energy of cells through aerobic respiration. Mitochondria have an exogenous origin and the prevailing view is that they arose from the endosymbiotic acquisition of an ancient ␣-proteobacteria [START_REF] Gray | Mitochondrial evolution[END_REF][START_REF] Gray | Mitochondrial evolution[END_REF]. Throughout evolution, the adoption of mitochondria has been associated with a substantial reduction in their genetic content. Modern mitochondrial genomes encode only a handful of mRNAs (33 in Arabidopsis thaliana) that are translated within the organelle. This requires the existence of a complete gene expression machinery whose most factors are encoded by nuclear genes. Gene expression in mitochondria therefore involves the cooperation between highly degenerated bacterial-like features inherited from the original endosymbiont and eukaryotic-derived nuclear-encoded trans-factors that appeared throughout evolution. This dual origin has resulted in complex mRNA expression processes involving a high number of post-transcriptional modifications [START_REF] Lightowlers | Mitochondrial protein synthesis: figuring the fundamentals, complexities and complications, of mammalian mitochondrial translation[END_REF][START_REF] Hammani | RNA metabolism in plant mitochondria[END_REF]. In recent years, significant progress has been made concerning certain aspects of gene expression in plant mitochondria [START_REF] Hammani | RNA metabolism in plant mitochondria[END_REF]. However, mitochondrial translation, the last level of mRNA expression that is also the least prone to easy molecular analyses, has remained largely unexplored in plants. Nevertheless, we know that the mitochondrial translation machinery differs profoundly from its bacterial counterpart in many essential aspects, and that the major translation-associated components are substantially different from those found in bacteria [START_REF] Lightowlers | Mitochondrial protein synthesis: figuring the fundamentals, complexities and complications, of mammalian mitochondrial translation[END_REF][START_REF] Janska | Mitoribosomal regulation of OXPHOS biogenesis in plants[END_REF][START_REF] Ott | Organization and regulation of mitochondrial protein synthesis[END_REF]. In particular, the rRNA and protein composition of mitoribosomes differ extensively from those of Escherichia coli ribosomes [START_REF] Bonen | Translational Machinery in Plant Organelles[END_REF][START_REF] Greber | Structure and function of the mitochondrial ribosome[END_REF]. Additionally, the constraints associated with the translation of mRNAs encoding mostly hydrophobic respiratory subunits have led to highly specialized translation mechanisms guided by membrane-associated mitochondrial ribosomes (mitoribosomes) to facilitate cotranslational insertion of mitochondria-encoded proteins into the inner mitochondrial membrane [START_REF] Pfeffer | Organization of the mitochondrial translation machinery studied in situ by cryoelectron tomography[END_REF]. The divergence with bacteria is also particularly obvious for the translation initiation step since plant mitochondrial mRNAs lack the typical ribosome anchoring motifs in their 5 leaders that are used in prokaryotes to help position the start codon at the P-site of the ribosome [START_REF] Bonen | Translational Machinery in Plant Organelles[END_REF]. Thus, we currently do not know how mitochondrial ribosomes are recruited to 5 untranslated regions (UTR), nor how the correct translation initiation codon is recognized by the small ribosomal subunit. The high degree of sequence divergence among 5 leaders of plant mitochondrial mRNAs has suggested a ribosome recruitment mechanism involving gene-specific cis-sequences and transfactors [START_REF] Hazle | Comparative analysis of sequences preceding protein-coding mitochondrial genes in flowering plants[END_REF][START_REF] Choi | Mapping of wheat mitochondrial mRNA termini and comparison with breakpoints in DNA homology among plants[END_REF]. Up until now only two proteins belonging to the large family of pentatricopeptide repeat (PPR) proteins have been shown to promote mitochondrial translation initiation in higher plants [START_REF] Manavski | An essential pentatricopeptide repeat protein facilitates 5 maturation and translation initiation of rps3 mRNA in maize mitochondria[END_REF][START_REF] Haïli | The MTL1 pentatricopeptide repeat protein is required for both translation and splicing of the mitochondrial NADH DEHYDROGENASE SUBUNIT7 mRNA in Arabidopsis[END_REF]. The mechanisms by which these PPR proteins help to recruit the mitoribosome toward the AUG codon of their target mitochondrial mRNA have, however, not yet been determined. Moreover, the sequence of mitochondrial transcripts in plants is extensively modified through a process called RNA editing in which more than 400 precisely-selected cytidine residues are converted into uridines. In general, C-to-U RNA editing restores conserved codons of coding sequences and is thus essential for the proper function of mitochondrial proteins and subsequently the activity of the organelle. However, a large number of these sites are not edited to 100%, rendering plant mitochondrial mRNA sequences heterogeneous [START_REF] Bentolila | Comprehensive high-resolution analysis of the role of an arabidopsis gene family in RNA editing[END_REF][START_REF] Takenaka | RNA Editing in plants and its evolution[END_REF]. How mitochondrial translation and RNA editing machineries functionally coordinate remains an open question. Contradictory results have been obtained with regard to a few mitochondrial transcripts [START_REF] Lu | Fully edited and partially edited nad9 transcripts differ in size and both are associated with polysomes in potato mitochondria[END_REF][START_REF] Lu | Protein polymorphism generated by differential RNA editing of a plant mitochondrial rps12 gene[END_REF][START_REF] Lu | A single homogeneous form of ATP6 protein accumulates in petunia mitochondria despite the presence of differentially edited atp6 transcripts[END_REF][START_REF] Phreaner | Incomplete editing of rps12 transcripts results in the synthesis of polymorphic polypeptides in plant mitochondria[END_REF][START_REF] Williams | Editing and translation of ribosomal protein S13 transcripts: unedited translation products are not detectable in maize mitochondria[END_REF], but a genomewide view of the functional relationship between RNA editing and translation is currently lacking.

The recent development of ribosome profiling technology has greatly facilitated the detailed measurement of translation at the single-nucleotide level and on a genome-wide scale [START_REF] Ingolia | Genome-wide analysis in vivo of translation with nucleotide resolution using ribosome profiling[END_REF]. Its general principal consists in the purification and subsequent sequencing of short mRNA segments covered by the translating ribosomes. These mRNA segments are called ribosome footprints and measure about 30-nt long in most species [START_REF] Brar | Ribosome profiling reveals the what, when, where and how of protein synthesis[END_REF]. The statistical analysis of their distribution reveals the identity and boundaries of translated RNA regions and provides measurements of their relative translational levels. This technology has recently revealed interesting functional aspects about ribosome behavior in plastid and human mitochondria, but had been never used to study plant mitochondrial translation [START_REF] Zoschke | A rapid ribosome profiling method elucidates chloroplast ribosome behavior in vivo[END_REF][START_REF] Rooijers | Ribosome profiling reveals features of normal and disease-associated mitochondrial translation[END_REF][START_REF] Chotewutmontri | Dynamics of chloroplast translation during chloroplast differentiation in maize[END_REF]. In order to gain a comprehensive view of the Arabidopsis mitochondrial translatome and the functioning of the plant mitochondrial machinery, we have prepared and sequenced total ribosome footprints from Arabidopsis inflorescences and mapped them to the Arabidopsis mitochondrial genome. Notably, this approach has allowed us to estimate and compare the translational activity among mitochondrial mR-NAs, to see how mitochondrial translation is reorganized in respiratory mutants and whether edited mRNAs preferentially associate with mitochondrial polysomes.

MATERIALS AND METHODS

Plant material

Arabidopsis (A. thaliana) Col-0 plants were obtained from the Arabidopsis Stock Centre of Institut National de la Recherche Agronomique in Versailles (http:// dbsgap.versailles.inra.fr/portail/). Arabidopsis mtsf1 and mtl1 mutants were previously described [START_REF] Haïli | The MTL1 pentatricopeptide repeat protein is required for both translation and splicing of the mitochondrial NADH DEHYDROGENASE SUBUNIT7 mRNA in Arabidopsis[END_REF][START_REF] Haïli | The pentatricopeptide repeat MTSF1 protein stabilizes the nad4 mRNA in Arabidopsis mitochondria[END_REF]. Plants were grown in a greenhouse in long day conditions for 10-12 weeks before use. Flowers were harvested simultaneously for all genotypes, snap-frozen in liquid nitrogen and stored at -80 • C until use.

Ribosome footprints preparation

Total ribosome footprints were prepared from a mix of flower buds and open flowers following a procedure adapted from [START_REF] Zoschke | A rapid ribosome profiling method elucidates chloroplast ribosome behavior in vivo[END_REF][START_REF] Baudin-Baillieu | Translation analysis at the genome scale by ribosome profiling[END_REF]. About 2.5 g of flowers were ground in liquid nitrogen and resuspended in 15 ml of ribosome extraction buffer (0.2 M sucrose, 0.2 M KCl, 40 mM Tris-acetate, pH 8, 10 mM MgCl 2 , 10 mM ␤-mercaptoethanol, 2% polyoxyethylene 10 tridecyl ether, 1% Triton X-100, 100 g/ml chloramphenicol and 100 g/ml cycloheximide). The obtained solution was centrifuged twice for 10 min at 15 000 g at 4 • C to remove the cell debris and the supernatant was transferred to a new tube. To estimate the RNA concentration contained in the supernatant, total RNA was extracted from a 0.5 ml aliquot using the TRI Reagent ® (Sigma-Aldrich) following the manufacturer's instructions. The supernatant was then digested with 10 U/OD260nm/ml of RNAse I (Ambion), and incubated 1 h at 25 • C to degrade unprotected RNA. The solution was then layered on an equal volume of a sucrose cushion (1 M Sucrose, 0.1 M KCl, 40 mM Tris-acetate, pH 8, 15 mM MgCl 2 , 5 mM ␤-mercaptoethanol, 100 g/ml chloramphenicol and 100 g/ml cycloheximide) and centrifuged for 3 h at 55 000 g at 4 • C in a TFT 65-13 rotor (Kontron). The obtained pellet was resuspended in 0.6 ml of RNA extraction buffer I (0.1 M EGTA pH 8, 0.1 M NaCl, 1% sodium dodecyl sulphate (SDS), 10 mM Tris-HCl pH 8 and 1 mM ethylenediaminetetraacetic acid (EDTA)), and RNAs were extracted with the TRI Reagent ® (Sigma-Aldrich) following the manufacturer's recommendations. Ribosomal footprints were further purified on 17% (v/v) acrylamidebisacrylamide (19:1) gel made with 7 M urea and 1 × Trisacetate-EDTA (TAE) buffer. For this, 600 g of RNAs were electrophoresed in two separated 15 cm-wide wells. The gel was pre-run for 1 h at 50 • C and then run for 15-16 h at 90 V at the same temperature. A mix comprising 100 ng of 27mer and 33-mer RNA oligonucleotides was loaded on both gel extremities and used as size marker. After staining for 30 min in 1× SYBR Gold (Life Technologies) diluted in 1× TAE, RNA contained in the 27 and 33 nt regions were separately excised from the gel. The gels slices were stored at least 2 h at -20 • C and then physically disrupted by centrifugation through a needle hole made in a 0.5 ml microcentrifuge tube nested in an outer 1.5 ml collection microtube. The tube assembly was centrifuged at maximum speed for 5 min. RNAs were eluted overnight from gel fragments by passive diffusion in 5 ml of RNA extraction buffer II (10 mM Tris-HCl pH 8, 1 mM EDTA, 0.1 M NaCl, and 0.2% C on a rotating wheel. The recovered RNAs were then isolated with the TRI Reagent ® (Sigma-Aldrich) following the manufacturer's instructions, resuspended in 30 l of RNAse-free water and stored at -80 • C until use.

Ribosome footprints were depleted from ribosomal RNA with the Ribo-Zero Plant kit (Illumina) following manufacturer's recommendations. Sequencing libraries were prepared with the TruSeq Small RNA library preparation kit (Illumina). Next generation sequencing was performed by Beckman (single end, 50 nt).

Total RNA quantification

The abundance of mitochondrial mRNAs contained in each genotype used was determined by quantitative RT-PCR as described in [START_REF] Haïli | The MTL1 pentatricopeptide repeat protein is required for both translation and splicing of the mitochondrial NADH DEHYDROGENASE SUBUNIT7 mRNA in Arabidopsis[END_REF]. Primers were designed to quantify the abundance of each exon of mitochondrial mRNAs of known function, except for the nad5 exon 3 that is too small to be quantified by quantitative RT-PCR (see Supplementary Table S1).

RNA-seq analysis

A total of 5 g of RNA (derived from the initial step of ribosome footprint purifications) were depleted from ribosomal RNA with the Ribo-Zero Plant kit (Illumina) following manufacturer's recommendations. Sequencing libraries and next generation sequencing was performed by Beckman (single end, 50 nt).

Bioinformatic analysis

From raw data to alignment files. Raw data were first trimmed to remove the 3 adapter sequence with CutAdapt 1.9.1 (28) configured with -e 0.12, -m 24, -M 35 anda options to select a read size in a range from 24 to 35 nt allowing 12% of error. The trimmed reads were then mapped against the rRNA sequences of A. thaliana (www. arabidopsis.org) with Bowtie 1.1.2 (29) set up with -all andun options. The -un option was used to select all unmapped reads. These filtered reads were finally mapped against the complete Col-0 mitochondrial genome (JF729201.1) or only the coding sequences with Bowtie 1.1.2. The latter alignments were configured with two mismatches allowed (-n 2) and only uniquely mapped reads were selected (-m 1). The sam formatted files generated by the aligner were converted to sorted and indexed bam formatted files using the Samtools program [START_REF] Li | Genome Project Data Processing Subgroup (2009) The Sequence Alignment/Map format and SAMtools[END_REF]. All the pipeline was automatized through the use of Snakemake workflow engine version 3.5.2 [START_REF] Rahmann | Snakemake-a scalable bioinformatics workflow engine[END_REF].

Differential expression.

The number of reads for each gene was calculated with featureCounts 1.5.0-p2 program [START_REF] Liao | featureCounts: an efficient general purpose program for assigning sequence reads to genomic features[END_REF] and normalized with DESeq2 method (33) through SAR-Tools R Package [START_REF] Varet | SARTools: a DESeq2-and edgeR-Based R pipeline for comprehensive differential analysis of RNA-Seq data[END_REF]. Snakemake workflow engine was also used to automatize the steps of this analysis.

For the analysis of editing, we generated new alignment files by mapping the filtered reads on the non-edited Col-0 mitochondrion genome and the edited one. These alignments were done with zero mismatch allowed and selecting only uniquely mapped reads. Then, with a homemade Python3 script, we parsed the alignment files and extracted the percentage of C and U for each mitochondrial editing position listed in [START_REF] Bentolila | Comprehensive high-resolution analysis of the role of an arabidopsis gene family in RNA editing[END_REF]. Using this approach, editing efficiencies were calculated from both Ribo-seq and RNAseq sequencing data that were generated in the course of the present analysis.

The data discussed in this publication have been deposited in NCBI's Gene Expression Omnibus and are accessible through GEO Series accession number GSE104028.

Mapping of RNA-seq reads to mitochondrial mRNA extremities. Reads alignments were performed with Bowtie 1.1.2 [START_REF] Langmead | Ultrafast and memory-efficient alignment of short DNA sequences to the human genome[END_REF].

RESULTS

Most mitochondrial ribosome footprints in Arabidopsis measure 27 and 28 nt

To get a comprehensive view of all ribosome-associated mRNA regions in Arabidopsis mitochondria, we generated total ribosome footprints and mapped the obtained reads to the Arabidopsis mitochondrial genome. To optimize the recovery of mitochondrial ribosome footprints from total extracts, polysomes were prepared from Arabidopsis flowers which are known to contain high amounts of active mitochondria [START_REF] Huang | Flower-enhanced expression of a nuclear-encoded mitochondrial respiratory protein is associated with changes in mitochondrion number[END_REF]. The presence of 1% Triton in the extraction buffer allowed us to extract both soluble and membranebound mitochondrial polysomes and thereby obtain good ribosome protected fragment (RPF) coverage along all mitochondrial transcripts. Since the size of selected RNA fragments from preparative gels can strongly influence the recovery of the desired ribosome footprints, we built upon a recent publication indicating that ribosome footprints in human mitochondria showed a bimodal distribution peaking at 27 and 33 nt [START_REF] Rooijers | Ribosome profiling reveals features of normal and disease-associated mitochondrial translation[END_REF]. To determine whether Arabidopsis mitoribosome footprints measured either or both of these sizes, RNA bands at 27 and 33 bases were extracted from preparative polyacrylamide gels and sequenced. Sequence analysis of the reads mapping to the mitochondrial genome indicated that the 27-nt RNA population mostly contained fragments of 27, 28 and 29 bases, whereas the 33-nt band was essentially composed of 32, 33 and 34-base RNA fragments (Supplementary Figure S1). The strongest evidence that these fragments corresponded to ribosomal footprints was their biased repartition relative to the start codon of mitochondrial coding sequences. Indeed, ribosomes move triplet by triplet, and we were expecting to observe the same regularity for their footprints. In fact, the two RNA categories show very different behavior regarding their bias to the start codon (Figure 1). The longest fragments (32/34-mers) displayed a perfect random distribution in the three possible reading frames whereas the smallest fragments (27/29-mers) showed a clear repartition bias. We could effectively observe a bias toward the phase 2 for all the k-mers when analyzing their 3 extremities, whereas the phase bias differed for each k-mer at their 5 end. Mapping to mitochondrial genes further revealed that the 27 and 28nt reads mapped primarily to coding sequences and to a much lesser extent to UTRs and introns (Supplementary Figure S2A). In contrast, the 32/34-mers mapped mostly to the 5 UTRs of genes and much less frequently to mitochondrial coding sequences (Supplementary Figure S2B). Overall, this preliminary analysis showed us that the majority of Arabidopsis mitochondrial ribosomes footprints are 27-29 nt long, and that those with 32-34 nt contribute very poorly to the mitoribosome footprint population. Consequently, all our subsequent analyses were done after recovery of the 27-29 nt RNA band from preparative gels.

Analysis of ribosome footprint distributions along mitochondrial genes sequences

A first global analysis of the distribution of Arabidopsis mitochondrial RPF was done from a total of 900 million high quality reads obtained from wild-type plants. Less than 2% (1.9%) of these reads could be aligned to the mitochondrial genome of the Col-0 accession (JF729201.1) and 38% to the nuclear and plastid genomes, indicating that mitochondrial ribosome footprints represent a mere fraction of total ribosome footprints generated from flowers. The vast majority of reads aligned with exons corresponding to known mitochondrial genes, further supporting that they were indeed mitochondrial ribosome footprints. Despite its relative small size, the Arabidopsis mitochondrial genome contains a large number of duplicated regions, preventing the correct mapping of RPF along the entire sequence. This was particularly obvious for atp6-1 and atp6-2 genes that share identical 3 regions. The partial overlap be-tween the rps3 and rpl16 genes was also problematic in this respect. Despite these classical limitations, the alignments obtained allowed us firstly to examine the translation initiation and termination sites of genes of known function. For most genes, the ribosome footprint distributions were coherent with the proposed positions of start and stop codons (http://www.arabidopsis.org/). We focused on the few mitochondrial transcripts for which the translational initiation and termination codons were shown to be removed by post-transcriptional mRNA processing. This concerns the rps4 mRNA that has been shown to be processed two bases downstream of its AUG and the nad6, mttB and ccmC mR-NAs that are matured 17, 10 and 46 nt upstream of their annotated stop codon, respectively [START_REF] Raczynska | Plant mitochondrial genes can be expressed from mRNAs lacking stop codons[END_REF][START_REF] Forner | Mapping of mitochondrial mRNA termini in Arabidopsis thaliana: t-elements contribute to 5 and 3 end formation[END_REF]. We first used the RNA-seq data we obtained from Col-0 plants to check these transcript extremities. This allowed us to unambiguously confirm that the vast majority rps4 transcripts are effectively devoid of any AUG (Figure 2A) and that nad6 and ccmC mRNAs do not carry any translational stop codon (Figure 2B). The situation is more mitigated for mttB, however most mttB mRNAs lack any translational termination codon. In agreement with these truncated mRNA ends, we observed that the ribosome footprints on rps4 initiate 14 bases downstream of the annotated AUG (Figure 2A). Similarly, the RPF distributions along nad6 and ccmC terminate a few bases upstream of their mapped 3 extremity and do not extend until the predicted stop codon (Figure 2B). No ribosome footprints was found to cover the annotated stop codon of mttB and the presence of a high RPF peak just upstream suggest a ribosome pausing site resulting from the post-transcriptional removal of the terminal UGA. Altogether, these observations suggest that the translation initiation and termination in plants show surprising flexibility and that the plant translational machinery evolved ways to efficiently decode mRNAs devoid of conventional AUG or STOP codons.

To potentially identify new coding regions within the mitochondrial genome, we also searched for RPF signals located outside of annotated regions. We looked for regions of at least 100 bases long, comprising a minimum of 10 ribosome footprints overall and in which 70% of the nucleotides are covered by at least 1 RPF. The 5 and 3 extremities of these regions were defined when a minimum of 40 nt with no RPF was encountered. Using these criteria, no signal outside of known genes could be identified, therefore, our approach did not reveal any new translated protein-coding ORFs in Arabidopsis mitochondria.

Arabidopsis mitochondrial mRNAs show highly different ribosome association levels and ribosome entry mechanisms

To estimate and compare the translational efficiencies of Arabidopsis mitochondrial mRNAs, we determined the relative density of ribosome footprints per gene. To allow comparison between genes, the calculated densities were normalized to both transcript length and abundance. This approach revealed clear differences in ribosome density between mRNAs (Figure 3). Globally, mRNAs encoding respiratory chain subunits showed much higher ribosome loading levels compared to other mitochondrial transcripts, implying a greater translational activity for these genes. Within each respiratory complex, small differences in translational efficiencies were observed except for the ATP synthase complex (V). The atp1, atp4, atp8 and mostly atp9 showed significantly higher ribosome densities compared to atp6-1 and atp6-2. Interestingly, the two copies of the atp6 gene also appear to be translated at different levels, and the atp6-1 gene showed much higher ribosome density compared to atp6-2 (Figure 3 and Supplementary Figure S3). All other mitochondrial genes, notably the ones coding for c-type cytochrome maturation and ribosomal proteins, had particularly low ribosome loading densities along their transcripts suggesting that they are translated at low levels. Low levels of ribosome footprints were also detected for the matR and mttb coding sequences, supporting the proposed functionality of these two genes [START_REF] Sultan | The reverse transcriptase/RNA maturase protein MatR is required for the splicing of various group II introns in brassicaceae mitochondria[END_REF][START_REF] Carrie | Plant mitochondria contain the protein translocase subunits TatB and TatC[END_REF].

The relative distributions of ribosome footprints along the five di-cistronic mitochondrial transcripts [START_REF] Forner | Mapping of mitochondrial mRNA termini in Arabidopsis thaliana: t-elements contribute to 5 and 3 end formation[END_REF] showed different patterns, implying different mechanisms to guide the ribosomes toward the downstream cistrons. Regarding the nad4L-atp4 (3300 reads per kilobase million (RPKM)) for nad4L versus 4500 for atp4) and rpl5-cob (1150 versus 4600 RPKM) transcripts, the ribosome density in the downstream cistron appeared to be higher compared to the upstream open reading frame (Supplementary Figure S4). An internal entry of mitoribosomes just upstream of the translation start codon of the downstream cistron in these two cases may explain this increase. The translation of rps3-rpl16 also implies independent entry of mitoribosomes, as the two orfs overlap and are encoded on different reading frames. Conversely, the ribosome density along the downstream open reading frame was much lower in the case of the nad3-rps12 mRNA (4900 versus 450 RPKM), suggesting a less efficient translation of rps12 (Supplementary Figure S4). This could be explained either by an inefficient internal entry of ribosomes upstream of rps12 or by a weak re-initiation downstream of nad3.

The translation of mitochondrial mRNAs is not dependent on their editing status

The C-to-U RNA editing process corrects more than 400 positions in plant mitochondrial transcripts [START_REF] Bentolila | Comprehensive high-resolution analysis of the role of an arabidopsis gene family in RNA editing[END_REF][START_REF] Takenaka | RNA Editing in plants and its evolution[END_REF]. Most editing events reestablish a correct identity to codons so that edited mRNAs encode functionally optimal mitochondrial proteins [START_REF] Takenaka | RNA Editing in plants and its evolution[END_REF]. Nevertheless, many mitochondrial sites are not edited to 100% and a large proportion of plant mitochondrial mRNAs can encode potentially sub-optimal, if not inactive, proteins. To see whether the plant mitochondrial translation machinery preferentially associates with fully edited transcripts or not, we evaluated the editing status of transcripts associated with Arabidopsis mitochondrial ribosomes. We calculated the editing levels of all known mitochondrial RNA editing sites from both total and ribosome-associated RNAs (Supplementary Table S2). Of the 434 previously identified editing sites [START_REF] Bentolila | Comprehensive high-resolution analysis of the role of an arabidopsis gene family in RNA editing[END_REF], 81 appeared to be covered by less than 10 ribosome footprints and were therefore excluded from further analysis because of insufficient coverage. Among the 353 remaining sites, most partially edited sites remained partially edited in polysome-associated mRNAs, revealing at the level of the entire mitochondrial transcriptome that complete editing of mitochondrial mRNAs is not an absolute prerequisite for their translation. A slight increase in C-to-U transition efficiencies could, however, be detected at many positions in polysomal mRNAs. In effect, we observed that 70% of sites (58 out of 80) whose editing levels range between 10 and 90% showed increased editing levels when contained in mitoribosome-associated mRNAs compared to total mR-NAs (Figure 4A). The editing increase for these more-edited To identify potential variations in editing efficiencies, only sites that are partially edited and whose editing efficiencies is comprised between 10 and 90% in total RNAs were considered in the analysis. (B) Average editing levels of mitochondrial mRNAs were determined from both ribosome footprint and total RNA populations. The differences of editing levels calculated from both RNA samples (polysomal RNA--total RNA) are shown.

sites is around 16% overall and most of them are distributed in different mitochondrial transcripts (Figure 4B). Nevertheless, quite a few are contained in ccmB, ccmF c , nad3 and rps12 RNAs, whose global editing levels are much higher in ribosome-protected RNAs compared to total RNAs (Fig- ure 4B). Most of the sites whose editing levels reach almost 100% when associated with ribosomes are contained in these four mitochondrial transcripts.

Mitochondrial translation is reorchestrated in respiratory complex I mutants

To better understand the plasticity of mitochondrial translation and the extent to which it participates in regulating gene expression in the organelle, we determined mitochondrial translational changes in two complex I respiratory mutants. For this approach, we chose the mtl1 and mtsf1 mutants, which are two ppr mutants affected in the translation of nad7 mRNA and in the stability of nad4 transcript respectively [START_REF] Haïli | The MTL1 pentatricopeptide repeat protein is required for both translation and splicing of the mitochondrial NADH DEHYDROGENASE SUBUNIT7 mRNA in Arabidopsis[END_REF][START_REF] Haïli | The pentatricopeptide repeat MTSF1 protein stabilizes the nad4 mRNA in Arabidopsis mitochondria[END_REF]. These two mutants show different growth retardation phenotypes, with mtsf1 plants being much more impaired in their development than the mtl1 plants. In both mutants, the ribosome densities and the steady state levels of mitochondrial mRNAs were quantified. In response to the lack of respiratory complex I, we observed a global overaccumulation of most mitochondrial transcripts in both mutants (Supplementary Figure S5). The increase in transcript abundance varied among genes and was comprised between 1.5-and 4.5-folds. Interestingly, this change did not correlate with an equivalent increase in ribosome density for most transcripts. Effectively, many mRNA species showing higher abundance contained either similar or even lower ribosome loading compared to the wild-type, suggesting that mitochondrial translation is a tightly regulated process that does not simply follow the changes in transcript abundance (Figures 5 and6; Supplementary Figures S6 and7). Other-wise, the major transcript expression defects that are known to occur in mtl1 and mtsf1 mutants were confirmed by our analysis. Regarding mtl1, our ribosome profiling data confirmed the strong and specific reduction of nad7 mRNA translation despite a 1.7-time over-accumulation of its transcript (Figure 5 and Supplementary Figures S6). A strong reduction in the association of ribosomes with nad4 mRNA was detected in mtsf1 (Figure 6 and Supplementary Fig- ures S7), which correlated with the strong destabilization of the nad4 transcript, excluding a role of MTSF1 in nad4 translation. For other transcripts, the comparison of mtsf1 and mtl1 translation profiles identified differences, but interesting overlaps were also observed. Among mRNAs whose translation varied most significantly in both mutants (Pvalue < 0.05 and RP log 2 (FC) ≥ or ≤ 1) several corresponded to ribosomal protein genes. Of the seven genes showing increased ribosome occupancy in mtsf1 compared to the wild-type, five corresponded to ribosomal protein mRNAs, namely rps3, rps12, rpl2, rpl5 and rpl16 (Figure 6). In the mtl1 mutant, rps12 and rpl5 transcripts also showed significant increases in ribosome loading in comparison to the wild-type (Figure 5). The translation of the nad9 transcript also appeared to vary in a similar manner in both mutants. An ∼2-fold decrease in nad9 translation was measured in both mutants, whereas the abundance of nad9 transcripts remained the same in mtl1 and was slightly increased in mtsf1 compared to the wild-type (Figures 5 and6; Supplementary Figure S5). Interestingly, moderate but significant reductions in ribosome loading on several F 1 F O -ATP synthase transcripts were also detected in both mutants. This concerned the atp8, atp9, atp6-1 and atp6-2 transcripts in mtsf1 plants and the atp6-1 transcript in mtl1 plants (Figures 5 and6).

DISCUSSION

Unlike in human and yeast mitochondria, Arabidopsis mitoribosome footprints measure 27-29 nt long

Messenger RNA translation is a complex multi-step process that is still poorly understood at the molecular level in genome-containing organelles like mitochondria. Growing evidence indicates that although these organelle are of prokaryotic origin, mitochondrial translation has significantly diverged from its bacterial counterpart. Additionally, mitochondrial translation displays considerable species-specific specialization that evolved to adapt translation requirements to mitochondrial genome organization [START_REF] Burger | Mitochondrial genomes: anything goes[END_REF]. These adaptations are exemplified by the variable composition and structure of mitoribosomes that differ not only between species, but also from modern bacterial ribosomes [START_REF] Amunts | The structure of the human mitochondrial ribosome[END_REF][START_REF] Greber | The complete structure of the 55S mammalian mitochondrial ribosome[END_REF][START_REF] Desai | The structure of the yeast mitochondrial ribosome[END_REF]. In this analysis, we have used ribosome profiling technology to generate a genome-wide snapshot of mitochondrial translation in Arabidopsis, and obtained the first global analysis of a plant mitochondrial translatome. This approach revealed that Arabidopsis mitochondrial ribosome footprints measure mainly 27 and 28 nt in length and thereby do not seem to follow a bimodal distribution peaking at 27 and 33 nt as previously found for human mitochondria [START_REF] Rooijers | Ribosome profiling reveals features of normal and disease-associated mitochondrial translation[END_REF]. In effect, the 27 and 28 nt RPFs presented a frame-specific distribution whereas those of 33 bases did not show any periodicity with respect to the start codons of mitochondrial genes (Figure 1). Additionally, the 27 and 28 nt RPFs aligned to translationally active mitochondrial coding sequences (Supplementary Figure S2A), as shown by the lack of coverage of nad7 mRNA in the mtl1 mutant that is specifically deficient in the translation of this transcript (Supplementary Figure S8; [START_REF] Haïli | The MTL1 pentatricopeptide repeat protein is required for both translation and splicing of the mitochondrial NADH DEHYDROGENASE SUBUNIT7 mRNA in Arabidopsis[END_REF]). In contrast, the 33nt RNA population aligned poorly with Arabidopsis mitochondrial coding sequences (Supplementary Figure S2B) and was accordingly found to represent a very minor fraction of mitoribosome-protected fragments in maize [START_REF] Chotewutmontri | Dynamics of chloroplast translation during chloroplast differentiation in maize[END_REF]. Thus, these fragments make only a modest contribution to the mitoribosome footprint population in Arabidopsis. Interestingly, a recent study indicated that mitoribosome footprints in yeast measure around 38 nt [START_REF] Couvillion | Synchronized mitochondrial andcytosolic translation programs[END_REF]. Fragments of this size are almost inexistent in the maize mitoribosome RPF population [START_REF] Chotewutmontri | Dynamics of chloroplast translation during chloroplast differentiation in maize[END_REF] and do not appear, therefore, to be major representatives of mitoribosome footprints in plants. The discrepancy between human, yeast and Arabidopsis regarding the size distribution of mitochondrial RPFs is currently unclear, but may result from differences in sample preparation or in mitoribosome structures between plants, yeast and animals [START_REF] Rooijers | Ribosome profiling reveals features of normal and disease-associated mitochondrial translation[END_REF].

A global alignment to the mitochondrial genome showed that mitochondrial RPFs are distributed over all the open reading frames of most genes of known function. For mR-NAs like rps4, ccmC, nad6 or mttB for which the start or the stop codons are removed post-transcriptionally the RPF distributions coincide with their mapped 5 or the 3 extremities (Figure 2), confirming that despite the truncations in their coding sequence these transcripts are still competent for translation. Indeed, our RNA-seq data revealed that ccmC, nad6 and mttB mRNAs bear highly heterogeneous 3 extremities and that most transcripts contain more or less extensive deletions at the end of the coding sequence (Figure 2B). The RPF distributions suggest that production of full-length CcmC and Nad6 proteins relies on the translation of the longest transcript forms that, nonetheless, lack any stop codon [START_REF] Forner | Mapping of mitochondrial mRNA termini in Arabidopsis thaliana: t-elements contribute to 5 and 3 end formation[END_REF]. Together, these observations raise questions about the mechanisms guiding mitoribosomes toward translation initiation sites in plants and also how they are released from 3 -truncated transcripts lacking stop codons such as ccmC or nad6. As suggested in mammalian mitochondria, specialized translational release factors or peptidyl hydrolases could intervene to release plant mitoribosomes stalled at the 3 extremity of mRNAs lacking stop codons [START_REF] Mai | The process of mammalian mitochondrial protein synthesis[END_REF]. Several lines of evidence also support that translation initiation in plant mitochondria is a relaxed process with mitoribosomes accommodating different kinds of non-AUG start codons or initiating translation internally in di-cistronic mRNAs as suggested for nad4L-atp4, rpl5-cob and rps3-rpl16 (Supplementary Figure S4). Accordingly, we find that mitochondrial orfs like ccmF N2 , mttB and matR that do not start with a classical AUG codon (37) are actively translated by mitoribosomes (Figure 3). Almost nothing is known about translation initiation and termination in plant mitochondria and major genetic and biochemical analyses will be required to shed light on the behavior of plant mitoribosomes.

Arabidopsis mitochondrial mRNAs are translated to highly different levels

The number of RPFs per gene, normalized by both transcript size and steady-state abundance, was used as a proxy to estimate the translational level of each mitochondriaencoded Arabidopsis mRNA. Assuming that the average of translation elongation rates are similar for all mitochondrial genes, this approach revealed large differences in ribosome coverage between mitochondrial protein-coding transcripts. We effectively observed that respiratory subunit mRNAs show much higher ribosome association than other types of mRNAs, notably those coding for ribosomal and c-type cytochrome maturation proteins, which appear to be translated at very low levels from our analysis (Figure 3). These results are coherent with recent quantification of plant mitochondrial proteomes which indicated that steady-state levels of respiratory chain proteins are abundant and well represented in mitochondrial proteome lists, whereas proteins of the genetic apparatus are much less abundant [START_REF] Salvato | The potato tuber mitochondrial proteome[END_REF][START_REF] Rao | The proteome of higher plant mitochondria[END_REF]. The c-type cytochrome maturation proteins, the MttB transporter or the MatR maturase are present at such low levels in mitochondria that they are generally not detected at all in plant mitochondrial proteomes. The high sensitivity of the ribosome profiling technology allowed us to detect the translational activity of these very poorly translated mitochondrial mR-NAs, strongly supporting their functionality. Among respiratory complexes subunits, we observed very similar ribosome densities for genes encoding proteins belonging to the same complex, except for the F 1 F O -ATP synthase. Large differences were detected between complex V mRNAs, particularly for the atp1, atp4, atp8 and atp9 transcripts, which showed higher RPF coverage than other atp mRNAs (Figure 3). The atp1 and atp9 mRNAs encode the c and ␣ subunits of the F 1 F O -ATP synthase, respectively, and are present at 10 and 3 copies in complex V. The higher ribosome densities of these two transcripts, therefore, correlates with their relative stoichiometry in complex V, corroborating the proportional translation of the different ATP synthase subunits previously described in E. coli [START_REF] Li | Quantifying absolute protein synthesis rates reveals principles underlying allocation of cellular resources[END_REF]. Conversely, the higher translational activity of atp8 compared to other single-copy complex V subunits (atp4 and atp6) cannot be explained by its higher stoichiometry in the F 1 F O -ATP synthase, but suggest higher requirements for this specific subunit for reasons that need to be clarified. Interestingly, we also observed a large difference in mitoribosome coverage between the two copies of atp6 encoded in the Arabidopsis mitochondrial genomes, with atp6-1 being translated significantly more than atp6-2 (Supplementary Figure S3). The two genes show small sequence variations in their 5 UTRs, which likely account for their differential association with mitoribosomes. Together, the large differences in ribosome densities between the various mitochondrial mR-NAs reveal that translational control is an important component of gene expression in plant mitochondria. How this control operates at the molecular level is currently unclear, as we still do not know how ribosomes are recruited to mitochondrial mRNAs in the absence of Shine and Dalgarno (SD) sequences in their 5 UTR [START_REF] Bonen | Translational Machinery in Plant Organelles[END_REF]. This control can operate at the level of translation initiation, which is often pro- posed as being the most rate-limiting step of translation in most systems [START_REF] Sonenberg | Regulation of translation initiation in eukaryotes: mechanismsand biological targets[END_REF][START_REF] Shah | Rate-limiting steps in yeast protein translation[END_REF]. The combinatory action of cis-acting elements within the 5 UTRs and gene-specific trans-factors may be responsible for the differential recruitment of ribosomes on mitochondrial mRNAs. Nonetheless, to date very few translational activators have been found to operate in plant mitochondria [START_REF] Manavski | An essential pentatricopeptide repeat protein facilitates 5 maturation and translation initiation of rps3 mRNA in maize mitochondria[END_REF][START_REF] Haïli | The MTL1 pentatricopeptide repeat protein is required for both translation and splicing of the mitochondrial NADH DEHYDROGENASE SUBUNIT7 mRNA in Arabidopsis[END_REF][START_REF] Kazama | Suppression mechanism of mitochondrial ORF79 accumulation by Rf1 protein in BT-type cytoplasmic male sterile rice[END_REF][START_REF] Uyttewaal | Characterization of raphanus sativus pentatricopeptide repeat proteins encoded by the fertility restorer locus for ogura cytoplasmic male sterility[END_REF][START_REF] Uyttewaal | PPR336 is associated with polysomes in plant mitochondria[END_REF] and the way by which they control translation of their cognate mRNA target remains to be determined. In bacteria, SD-like sequences within coding sequences were shown to impact translation elongation and to have a major effect on mRNA translation rates [START_REF] Li | The anti-Shine-Dalgarno sequence drives translational pausing and codon choice in bacteria[END_REF][START_REF] O'connor | rRNA:mRNA pairing alters the length and the symmetry of mRNA-protected fragments in ribosome profiling experiments[END_REF]. The lack of anti-SD sequence at the 3 end of the mitochondrial SSU rRNA strongly suggests that this mechanism cannot account for the differential translation of Arabidopsis mitochondrial mRNAs. Much remains to be discovered, therefore, before we understand how mitochondrial translation is regulated in plant mitochondria.

Mitoribosome-associated mRNAs are more edited than in total RNAs

Mitochondrial mRNAs from land plants undergo hundreds of specific C-to-U changes by RNA editing [START_REF] Takenaka | RNA Editing in plants and its evolution[END_REF]. In the present analysis, of the 353 Arabidopsis editing sites for which we obtained more than 10 reads per sites in both RNAseq and Riboseq data, 80 showed partial editing with C-to-U changes comprised between 10 and 90%. The accessibility of non-edited or partially edited mitochondrial mRNAs by the mitochondrial translation machinery has long remained an intriguing question. The translation of non-edited mitochondrial mRNA was previously suggested in a few specific cases [START_REF] Lu | Fully edited and partially edited nad9 transcripts differ in size and both are associated with polysomes in potato mitochondria[END_REF][START_REF] Lu | Protein polymorphism generated by differential RNA editing of a plant mitochondrial rps12 gene[END_REF][START_REF] Lu | A single homogeneous form of ATP6 protein accumulates in petunia mitochondria despite the presence of differentially edited atp6 transcripts[END_REF][START_REF] Phreaner | Incomplete editing of rps12 transcripts results in the synthesis of polymorphic polypeptides in plant mitochondria[END_REF][START_REF] Williams | Editing and translation of ribosomal protein S13 transcripts: unedited translation products are not detectable in maize mitochondria[END_REF], but no genome-wide view was available to date. By comparing C-to-U transition efficiencies in total and ribosome-associated mRNAs we observed that most partially edited sites remained incompletely edited in polysomal mRNAs confirming at a genome-wide level that complete editing of mitochondrial mRNAs is not an absolute pre-requisite for their translation (Figure 4A). Nonetheless, around 70% of these sites showed, on average, a 16% increase in their editing levels when loaded on mitoribosomes (Figure 4A andB). The origin of this increase is currently unclear, as no obvious inter-functionality between the mitochondrial translational and editing machineries has yet been revealed. As indicated, large differences in C-to-U transition efficiencies are consistently observed between editing sites in plant mitochondria ( 14). These differences likely result from variable functional constraints between sites, making some of them less efficiently recognized and/or processed by the editing machinery than others. Maybe, the accessibility of RNA editing sites to the editosome complex is increased when mR-NAs are being translated, generating the rather global raise in editing efficiency that we observed in our riboseq data. In particular, the strong RNA helicase activity of translating ribosomes may be responsible for rendering editing sites more accessible to the editing machinery. Even with this increase, our results indicate that partially edited mRNAs are decoded by mitoribosomes, confirming at the level of the entire mitochondrial transcriptome that transcript recruitment by mitochondrial polysomes does not a priori discriminate between unedited and edited RNAs. A proportion of mitochondrial polypeptides derives thus from the translation of unedited mRNAs, making 'unedited' proteins a non-negligible part of plant mitochondrial proteomes. Posttranslational processes must therefore be at play to limit any potential negative effects of these likely sub-optimal 'unedited' polypeptides.

Mitochondrial translation is reorganized in Arabidopsis complex I mutants

The regulation of mitochondrial gene expression is fundamental not only to ensure proportional synthesis of both mitochondria and nuclear-encoded subunits belonging to the same complexes but also to adapt mitochondrial activity to the changing requirements of plants throughout their life cycle or in response to environmental stimuli. The basis of this regulation is not well understood, however several lines of evidence support that most of the control is exerted at the post-transcriptional and/or at the post-translational levels [START_REF] Janska | Mitoribosomal regulation of OXPHOS biogenesis in plants[END_REF][START_REF] Giegé | RNA degradation buffers asymmetries of transcription in Arabidopsis mitochondria[END_REF][START_REF] Giegé | Coordination of nuclear and mitochondrial genome expression during mitochondrial biogenesis in Arabidopsis[END_REF][START_REF] Holec | Relaxed transcription in Arabidopsis mitochondria is counterbalanced by RNA stability control mediated by polyadenylation and polynucleotide phosphorylase[END_REF]. To better understand to what extent mitochondrial translation participates in these regulatory circuits and gain hints about its plasticity, we measured mitochondrial translational and transcriptional changes in two contrasted complex I Arabidopsis mutants that accumulate either no complex I (mtl1) or a truncated version of it (mtsf1). Although both mutants have strong delays in their development compared to wild-type, the growth defects exhibited by the mtsf1 mutant were more severe than those of mtl1 [START_REF] Haïli | The MTL1 pentatricopeptide repeat protein is required for both translation and splicing of the mitochondrial NADH DEHYDROGENASE SUBUNIT7 mRNA in Arabidopsis[END_REF][START_REF] Haïli | The pentatricopeptide repeat MTSF1 protein stabilizes the nad4 mRNA in Arabidopsis mitochondria[END_REF]. First, in response to complex I deficiency, we observed a 2-to 5-fold over-accumulation of most mitochondrial transcripts in mutants compared to wild-type (Supplementary Figure S5). Nonetheless, this increase in transcript abundance was not associated with an equivalent rise in ribosome coverage along mitochondrial mRNAs (Figures 5 and 6). Our analysis thus revealed that mitochondrial translation is a precisely regulated process that does not simply follow the changes in transcript abundance and that a transcript-specific translational control clearly operates in plant mitochondria. Significant changes in ribosome loading for several transcripts were, however, detected in the mutants. The most important translational change concerned the strong decrease in nad7 ribosome occupancy in mtl1, confirming previously published data for this mutant [START_REF] Haïli | The MTL1 pentatricopeptide repeat protein is required for both translation and splicing of the mitochondrial NADH DEHYDROGENASE SUBUNIT7 mRNA in Arabidopsis[END_REF]. The impact on other mitochondrial genes was less pronounced, although some interesting tendencies were uncovered. The first one concerned the 2-fold decrease in nad9 translation in both mutants, suggesting that the lack of functional complex I may induce a negative feedback control on the translation of this specific mRNA. As we did not detect any significant decrease in the ribosome loading of other complex I mRNAs, this means that complex I deficiency does not induce a global down-regulation of all nad gene translation. Interestingly, and despite a significant rise in transcript abundance, the translation of several mRNAs encoding ATP synthase subunits was lower in both complex I mutants. This negative translational control impacted a few more atp genes in mtsf1 than in mtl1 (Figures 5 and6) and may, therefore, be correlated with the gravity of developmental alterations associated with complex I deficiency. It has recently been demonstrated that complex I-lacking Arabidopsis mutants compensate for the deficit in Downloaded from https://academic.oup.com/nar/advance-article-abstract/doi/10.1093/nar/gky489/5033161 by guest on 05 June 2018 ATP production derived from the respiratory chain by inducing higher metabolic fluxes through glycolysis and the tricarboxylic acid cycle [START_REF] K Ühn | Complete mitochondrial complex I deficiency induces an Up-Regulation of respiratory fluxes that is abolished by traces of functional complex I[END_REF]. Our analysis thus reveals that these increased metabolic fluxes correlate with a slight reduction in the translation of mitochondria-encoded ATP synthase subunits. Whether or not this reduction results from a negative feedback loop induced by the reduced activity of the respiratory chain in complex I mutants remains to be clarified. Interestingly, we also observed higher ribosome association with several ribosomal protein encoding mR-NAs in both mtsf1 and mtl1 mutants. The ribosome densities of four ribosomal protein mRNA transcripts in mtsf1 (rps12, rpl2, rpl5, rpl16) and two in mtl1 (rps12, rpl5) appeared to be increased compared to the wild-type. These observations corroborate nicely recent analyses showing that reducing the production of a mitochondria-targeted ribosomal protein resulted in an altered translation pattern in Arabidopsis mitochondria [START_REF] Kwasniak | Silencing of the nuclear RPS10 gene encoding mitochondrial ribosomal protein alters translation in arabidopsis mitochondria[END_REF]. In this mutant context, ribosomal proteins were translated more efficiently at the expense of respiratory chain encoding mRNAs. Our results suggest that an analogous reorganization of mitochondrial translational occurs in respiratory mutants, further demonstrating that plant mitoribosomes do not translate mRNAs non-selectively, but that a certain level of translational control likely operates in plant mitochondria.

Concluding remarks

Using ribosome profiling technology, we have generated a genome-wide snapshot of mitochondrial translation in Arabidopsis and monitored certain aspects of its dynamics. We show that mitochondria-encoded mRNAs are differentially translated and that proportional translation levels correlate with the stoichiometry of respiratory chain subunits, in particular for complex V. Moreover, a slight reorganization of mitochondrial translation could be detected in complex I respiratory mutants involving a reduction in ribosome densities for F 1 F O -ATP synthase mRNAs and an increase in the translation of several ribosomal protein encoding transcripts. We thus reveal that mitochondrial translation is controlled at the level of individual mRNAs and that it participates in regulating the activity of plant mitochondria. Our analysis also reveals that translation of mitochondriaencoded transcripts can be satisfactorily measured from total ribosome footprint extracts and does not necessarily require the purification of mitochondria.

F ATCTTTTTGCGGTGTGCTCT CcmFC exon 1 R ATTTCGTCGTTGCTCATTCC cox2 exon Cox2 exon1 F GATTCTTCGGACCATCTTTCC Cox2 exon1 R TCCGATACCATTGATGTCCA cox2 exon2 Cox2 exon2 F TCGTCGTAGAAGCTGTTCCT Cox2 exon2 R TTGGGGGATTAATTGATTGG nad1 exon Nad1a exon 1 F TGATGTAGTGGGATCGTTCG Nad1a exon 1 R AGCCACTGGAGCCATTCTAA nad1 exon Nad1b exon2 F ATGCCTTTCTAGGAGCATTACG Nad1b exon2 R ACTTCATAAGAGACCATTTGAGCTG nad1 exon Nad1b exon3 F TGGTTTGGTATTCCCCTGTT Nad1b exon3 R TAATTCAGCTTCCGCTTCTG nad1 exon Nad1c exon4 F TCTTCAATGGGGTCTGCTCT Nad1c exon4 R CATTAAGATCATATTGGCATACTCTCC nad1 exon Nad1c exon5 F TTAATGGGACTTGGCTGGAA Nad1c exon5 R AGGAAGCCATTGAAAGGTGA nad2 exon Nad2a exon1 F TTTAGCGGTTTTCCCAGAGA Nad2a exon1 R TAATCCAAGCCAACCCACAT nad2 exon Nad2a exon2 F GGCTGGTACCATTTCGATGT Nad2a exon2 R TGAGCCGAGATCATAAAGAGC nad2 exon Nad2b exon3 F CTGGAGCTACCCACTTCGAT Nad2b exon3 R CGAAAAGGAACTGCAGTGAT nad2 exon Nad2b exon4 F GGATGCATTCGCCATAGTTT Nad2b exon4 R GGGGTATTCCTGCGTATGAG nad2 exon Nad2b exon5 F TTTTTGATACACCTAGGACATGGAT Nad2b exon5 R ATGAACTGAGTGCCATTTGATG nad4 exon1 Nad4 exon1 F TTGCATTTTAGTGGGTTGGTC Nad4 exon1 R TAGGGATTAGCACGCTTTCG nad4 exon2 Nad4 exon2 F GGAGTATGGGGTTCGAGACA Nad4 exon2 R AAATCGGTGGTTCCTGTTTG nad4 exon3 Nad4 exon3 F CCATGCCGAATTTTTCTACC Nad4 exon3 R GCGCTGCTAATGTGGCTACT nad4 exon Nad4 exon4 F GATGGGTGTTTACCCCAAAG Nad4 exon4 R TGAAATTTGCCATGTTGCAC nad5 exon Nad5a exon1 F GCTCGGTAGTTCCGTAGCAG Nad5a exon1 R AGCGCGACTTCATAAAAAGC nad5 exon Nad5a exon2 F ATTGGTGCTGTTGGGAAATC Nad5a exon2 R AAAGGGGAGCACCTTGCTAT nad5 exon Nad5c exon4 F GCCTTTGCAATGTTACTTGG Nad5c exon4 R TCAAAATGAAAGACGATCGATTA nad7 exon1 Nad7 exon1 F GACCTCAACATCCTGCTGCT Nad7 exon1 R CCACCACTTCTCCGTTCATT nad7 exon2 Nad7 exon2 F GAGGGACTGAGAAATTAATAGAGTACA Nad7 exon2 R GATCAAAATAAGGTAAAGCTTGAAGA nad7 exon3 Nad7 exon3 F GCTATGGATGTGGGAGCATT Nad7 exon3 R AGGCAGATCTTGTGCCACTC nad7 exon4 Nad7 exon4 F GTATGCTGGGATTTGCGAAG Nad7 exon4 R CATTGCACAATGATCCGAAG nad7 exon5 Nad7 exon5 F ATACCGCAGTTGAAGCACCT Nad7 exon5 R TCCTTGTAAATGGGCAAAGC rpl2 exon1 Rpl2 exon1 F TGATGGCCGCTTATGTAGTG Rpl2 exon1 R TTTGGAGAGGAGAAGGCAGA rpl2 exon2 Rpl2 exon2 F GAAGCAGGCAAAATGGTGAT Rpl2 exon2 R ACACAGTGAATAAGGGCTTAGGA rps3 exon1 Rps3 exon1 F CCGATTTCGGTAAGACTTGG Rps3 exon1 R CACTGAACCGACTTGAATCTGA rps3 exon2 Rps3 exon2 F AGGTTGACCCACTTCATTCG Rps3 exon2 R GTTCCCGAGCATCAAGGTTA nad9 QM0070F GGATGACCCTCGAAACCATA QM0070R CACGCATTCGTGTACAAACC rpl16 QM0080F GAGCATTTGCCAAACTCACA

Figure 1 .

 1 Figure 1. The 27-nt RPF population shows a better periodicity relative to mitochondrial gene start codons compared to the 33-nt RNA population. (A) 5 phasing of the 27-mer and 33-mer populations. (B) 3 phasing of the 27-mer and 33-mer populations.

Figure 2 .

 2 Figure 2. Ribosome footprint densities near the extremities of Arabidopsis mitochondrial mRNAs for which the start or the stop codons are removed by post-transcriptional processing. Ribosome footprint distributions are shown as red curves and RNA-seq read densities are depicted in gray. (A) Close-up view showing the first 300 nt of the rps4 mRNA. (B) Close-up view showing the last 300 nt of the nad6, mttB and ccmC mRNAs. Black arrows materialize the positions of the theoretical translation start or stop codons and their coordinate on the mitochondrial genome of Col-0 is specified. Red arrows and the associated numbers indicate the start (rps4) or the end (nad6, mttB and ccmC) of observed Ribo-seq signals, respectively to either the translational start or stop codon of each transcript. Gray arrows and the associated numbers indicate the position of the 5 (rps4) or 3 (nad6, mttB and ccmC) mRNA extremities mapped by circular RT-PCR in (36,37).

Figure 3 .

 3 Figure 3. Protein-coding mitochondrial mRNAs show large differences in ribosome footprint densities in Arabidopsis. RPF densities normalized to both mRNA length and abundance are shown. Mitochondrial mRNAs are indicated and color-coded according to the respiratory complex or the functional category to which they belong. Means ± SE (n = 2).

Figure 4 .

 4 Figure 4. Mitochondria-encoded mRNAs are more edited when they associate with mitoribosomes. (A) C-to-U editing levels calculated from total (RNA-seq) and ribosome-associated (Ribo-seq) RNA populations are presented.To identify potential variations in editing efficiencies, only sites that are partially edited and whose editing efficiencies is comprised between 10 and 90% in total RNAs were considered in the analysis. (B) Average editing levels of mitochondrial mRNAs were determined from both ribosome footprint and total RNA populations. The differences of editing levels calculated from both RNA samples (polysomal RNA--total RNA) are shown.

Figure 5 .

 5 Figure 5. Differential transcriptional and translational profiles of mitochondria-encoded mRNAs in mtl1 and wild-type plants. For each mitochondrial mRNA, relative RPF densities (Y-axis) and transcript abundance (X-axis) are reported. Genes whose names are indicated show significant changes in ribosome occupancies compared to the wild-type (P-value < 0.05). Colored triangles show genes whose changes in ribosome loads are larger than 2-fold compared to wild-type plants.

Figure 6 .

 6 Figure 6. Differential transcriptional and translational profiles of mitochondria-encoded mRNAs in mtsf1 and wild-type plants. For each mitochondrial mRNA, relative RPF densities (Y-axis) and transcript abundance (X-axis) are reported. Genes whose names are indicated show significant changes in ribosome occupancies compared to the wild-type (P-value < 0.05). Colored triangles show genes whose changes in ribosome loads are larger than 2-fold compared to wild-type plants.

Figure S1 :

 S1 Figure S1: K--mer distribu-ons in the 27 and 33--mers short RNA popula-ons. A. Quan-fica-on of sequencing results indicates that the 27--mers popula-on is predominantly composed of 27, 28 and 29--base fragments. B. As shown, the 33--mer RNAs are predominantly composed of 32, 33 and 34-nucleo-de fragments.

Figure S2 :

 S2 Figure S2: Most reads derived from the 27--mer popula5on map to the mitochondrial coding sequences.A. Reads derived from the 27--mer popula5on were aligned against the Arabidopsis mitochondrial genes (from the Col--0 accession). As shown, 12 % of them aligned to 5'UTRs, 79 % to CDS, 7 % to 3'UTR and 2 % to introns. B. In contrast, only 33% of the 32/34--mers align with mitochondrial CDS, as most of them (62%) of them align to genes' 5' UTRs.

Figure S4 :

 S4 Figure S4: RPF coverage along the di--cistronic mRNAs encoded in Arabidopsis mitochondria. RPF densi:es, normalized by both mRNA length and abundance, are shown. Coding sequences and UTRs are delimited with yellow and blues lines respec:vely.

Figure S5 :

 S5 Figure S5: Quan&ta&ve RT--PCR analysis measuring the steady state levels of mitochondrial mRNAs exon by exon in the indicated genotypes (Col--0, mtl1, mtsf1). Numbers represent rela&ve abundances to nuclear 18s rRNA. Values of each exon obtained in the wild type were arbitrarily set to 100; values obtained in the mutants are indicated accordingly. Means ± SE (n = 3).

Figure S6 :

 S6 Figure S6: RPF coverage of mitochondrial mRNAs in the Arabidopsis mtl1 mutant. RPF densi;es normalized by both mRNA length and abundance are shown. Mitochondrial mRNAs are indicated and color--coded according to the respiratory complex or the func;onal category to which they belong. Means ± SE (n = 2).

Figure S7 :

 S7 Figure S7: RPF coverage of mitochondrial mRNAs in the Arabidopsis mtsf1 mutant. RPF densi;es normalized by both mRNA length and abundance are shown. Mitochondrial mRNAs are indicated and color--coded according to the respiratory complex or the func;onal category to which they belong. Means ± SE (n = 2).

Figure S8 :

 S8 Figure S8: RPF coverage along the nad7 mRNA in Col--0 (grey) and mtl1 (black) plants. Ribosome footprint coverage in Col--0 is shown in light grey, coverage in mtl1 is in black.

Table S1 -

 S1 -Primers used for q--RT--PCR analysis

	Gene / Exon	Name	Séquence	Name	Sequence
	ccmFc exon	CcmFC exon 2 F AATCACTTCATGCCGACCTC	CcmFC exon 2 R GCGATTCTTCATCCACCAAT
	ccmFc exon1	CcmFC exon 1

Table S2 : C--to--U transition efficiencies of mitochondrial editing sites calculated from total (RNASEQ) and ribosome--associated (RIBOSEQ) RNA samples.

 S2 Each site are identified by the transcript to which they belong and its position relatively to the first base of the translational start codon (TrPos). Numbers of reads identified per sites (Coverage) are also indicated. NA: Not applicable

	QM0080R QM0110R QM0210R QM0220R QM0270R QM0290R QM0410R QM0480R QM0520R QM0570R QM0640R QM0650R QM0730R QM0830R QM0900R QM0960R QM0980R QM0990R QM1080R QM1170R QM1190R QM1270R QM1360R QMR26SR nuc18S_R Observed_RNASEQ Observed_RIBOSEQ Coverage_RNASEQ Coverage_RIBOSEQ CGGACACTTTCATCGTGCTA QM0110F TCTTGGAATCACATCCAGCA CGAGACCGAAATTGGAAAAA QM0210F AAGGGGTTCGACAGGAAAGT CGTATTTCGACCGGAAAATC QM0220F TGCCGGAATGGTATTTCCTA GCCAAAAGCAACCAAAACAT QM0270F TCGTCGGAATACATCCTGTCT GTGAGTGGGTCAGTCGTCCT QM0290F ACCCATCACAGAGATGCACA TCACACAAACCCTTCGATGA QM0410F TCTTTTGCGAGTCAATGCAC TCTCGCGTATCTCACATTGC QM0480F CCGTCGACTTATTGGGAAAA TTCCTTGGCCATGTACAACA QM0520F AATTTTTGCGAGAGCTGGAA TTGAACCCCGTCCTGTAGAC QM0570F GGGGTCTTTCTTTGGAAACC TCTCCCTCATTCCACTCGTC QM0640F GGATCAGCTTGCGAATTTGT GCAAATTGCTTCCCCACTAA QM0650F GGGGAATCCTCCTTAATAGACG AACGAAAATGGCTAACCCAATA QM0730F CCGTAACTTGGGCTCATCAT AAACCATGAAAGCCTGTTGC QM0830F AGCTCTTGGCATTGCTTTGT AGTGCCACAATCCCATTCAT QM0900F AGCTACGCGCAAATTCTCAT GCCGTGGCGATATAAACAAT QM0960F CGTGTCGTTCGTAATGGAAA TGATAAGCCCACCAACTTCC QM0980F AGCCAAAGTACGGTTGAGCA TTTGGGTTTTTCTGCACCAT QM0990F CGAATGTGGTTTCGATCCTT GCACCCCTTTTCCATTCATA QM1080F GGAGCTGCTATCGGTATTGG TAGAGCAAAGCCCAAAATGG QM1170F GCTTGGCAATCCTTGGTAGA GACCAAGATGCAAGGGAAAA QM1190F TCACTTCGACACGTCTTTGC GGAATGGCCTTGAATCTTGA QM1270F CTCGAACTGAACGCGATGTA AAGCTGCTTCAAGGATCCAA QM1360F GTAGCTGCGGTGAAGTAGGC CTGCCTGGATTCGGTATCAT QMR26SF GACGAGACTTTCGCCTTTTG CTTGGAGCGAATTGGATGAT nuc18S_F AAACGGCTACCACATCCAAG ACTCGAAAGAGCCCGGTATT Forward Primer Reverse Primer 0,14 0,09 8625 2268 0,99 1 6755 4321 0,99 1 5143 3467 0,99 1 2544 680 0,99 1 4428 2658 0,05 0,1 768 105 0,16 0,24 1324 41 0,82 0,83 2388 1636 0,93 0,99 714 100 0,98 1 849 427 0,99 1 1119 59 0,99 1 1934 49 0,99 1 1136 31 1 1 2166 1263 1 1 2397 1687 0,99 1 28353 3302 0,99 1 15368 520 0,99 1 17847 1770 1 1 26108 370 0 NA 95 3 0,02 NA 95 3 0,03 0 197 46 0,06 0,17 109 12 0,08 NA 79 7 0,22 0,3 251 23 0,27 0,96 120 28 0,33 1 125 28 0,55 1 77 13 0,61 NA 141 2 0,62 NA 134 2 0,71 NA 268 5 0,75 0,94 301 16 0,77 1 338 55 0,82 NA 240 9 0,89 1 262 18 0,93 NA 304 6 0,95 NA 130 2 0,99 1 254 53 0,99 NA 305 5 0,99 NA 162 5 1 1 132 11 1 1 234 53 1 NA 163 7 1 NA 126 5 1 NA 123 5 0,05 0 227 14 0,07 0,09 255 35 0,17 0,25 155 16 0,93 NA 122 0 0,94 0,99 244 199 0,94 NA 18 4 0,95 1 18 0,95 NA 4 0,96 1 206 0,96 1 18 0,96 NA 4 0,97 1 28 0,97 NA 3 0,98 1 19 0,99 0,96 82 0,99 1 36 0,99 1 15 0,99 NA 1 0,99 NA 7 1 1 45 1 1 40 1 1 14 1 NA 18 3 NA NA 6 5 0,01 0 31 0,02 0 14 0,1 0,26 62 0,14 0,33 68 0,25 0,48 21 0,38 0,22 41 0,53 1 20 0,54 0,74 23 0,64 0,78 18 0,64 0,98 41 0,66 0,88 40 0,71 1 17 0,74 0,76 38 0,76 1 23 0,77 NA 0 0,89 1 22 0,9 NA 2 0,91 0,96 27 0,95 NA 0 0,99 NA 0 1 NA 0 0 NA 3 0,01 0,07 118 0,15 0,06 53 18 0,78 1 37 26 0,79 NA 1 0,93 0,93 56 0,93 NA 85 6 0,96 0,97 72 0,96 NA 1 0,97 1 23 0,97 NA 3 0,98 1 14 0,98 NA 4 0,99 1 21 0,99 1 28 0,99 NA 6 0,15 0,11 mttb ccmB rpl5 cob nad6 rps4 atp6--1 atp8 matR mttb atp4 nad4L cox3 ccmFN1 ccmC ccmFN2 rps12 nad3 atp9 atp6--2 atp1 rps7 cox1 rRNA 26S (mt) rRNA 18S (nuc) GeneName TrPos atp1 1470 atp1 1538 atp1 1652 atp1 1775 atp1 1844 atp4 atp4 atp4 atp4 atp4 atp4 atp4 atp4 atp4 atp4 atp9 atp9 atp9 atp9 ccmB ccmB ccmB ccmB ccmB ccmB ccmB ccmB ccmB ccmB ccmB ccmB ccmB ccmB ccmB ccmB ccmB ccmB ccmB ccmB ccmB ccmB ccmB ccmB ccmB ccmB ccmC 1059 ccmC ccmC ccmC ccmC ccmC 1139 ccmC 883 ccmC 586 ccmC 662 ccmC 980 ccmC 616 ccmC 1004 ccmC 1031 ccmC 878 ccmC 950 ccmC 929 ccmC 941 ccmC 1051 ccmC 1091 ccmC 904 ccmC 919 ccmC 1058 ccmC 1133 ccmC 1156 ccmFC 1048 ccmFC 1273 ccmFC 684 ccmFC 501 ccmFC 1338 ccmFC 456 ccmFC 173 ccmFC 298 ccmFC 529 ccmFC 457 ccmFC 538 ccmFC 226 ccmFC 1403 ccmFC 1369 ccmFC 246 ccmFC 1450 ccmFC 283 ccmFC 1295 ccmFC 245 ccmFC 278 ccmFC 269 ccmFN1 348 ccmFN1 632 ccmFN1 519 ccmFN1 526 ccmFN1 857 ccmFN1 437 ccmFN1 305 ccmFN1 1103 ccmFN1 858 ccmFN1 291 ccmFN1 939 ccmFN1 417 ccmFN1 252 ccmFN1 410 ccmFN1 927 ccmFN1 954 ccmFN2 821 531 0,37 NA 7 mttb 288 0,46 0,36 36 mttb 618 0,52 NA 9 mttb 810 0,53 0,59 37 mttb 725 0,72 0,73 26 mttb 849 0,82 0,74 35 mttb 890 0,82 0,75 16 mttb 241 0,87 0,97 34 mttb 584 0,88 0,94 18 mttb 203 0,9 1 15 mttb 649 0,94 0,97 38 mttb 837 0,96 0,98 51 mttb 289 0,96 1 39 mttb 505 0,96 NA 2 mttb 508 0,96 NA 2 mttb 787 0,96 NA 8 mttb 793 0,96 NA 4 mttb 674 0,97 1 18 mttb 682 0,99 1 49 mttb 809 0,99 1 37 mttb 844 0,99 1 46 mttb 731 1 NA 9 nad1 1467 0,91 0,96 1259 52 nad1 1399 0,92 1 2457 443 nad1 951 0,94 1 604 nad1 952 0,94 1 622 nad1 1180 0,95 0,99 372 nad1 1542 0,96 0,99 1628 377 nad1 909 0,96 1 857 nad1 1215 0,96 1 34 nad1 1387 0,96 1 2507 706 nad1 1224 0,98 0,99 2055 nad1 1279 0,98 0,99 1018 378 nad1 1318 0,98 0,99 1055 177 nad1 811 0,98 1 48 nad1 1136 0,99 0,99 215 nad1 1020 0,99 1 557 nad1 1369 0,99 1 1367 172 nad1 1137 1 0,99 255 nad1 1134 1 1 168 nad2 406 0,04 0,01 182 nad2 763 0,09 0,05 1154 777 nad2 1357 0,15 0,08 1066 336 nad2 679 0,28 0,25 296 nad2 149 0,66 0,67 42 nad2 211 0,87 NA 7 nad2 1560 0,91 NA 10 nad2 1403 0,94 0,95 181 nad2 465 0,95 0,98 1177 60 nad2 462 0,95 1 1142 51 nad2 1557 0,95 NA 8 nad2 180 0,97 1 25 nad2 548 0,97 1 113 nad2 582 0,97 1 28 nad2 945 0,97 1 20 nad2 1404 0,98 0,98 173 nad2 510 0,98 1 146 nad2 816 0,98 1 909 1160 nad2 966 0,98 1 604 32 nad2 1215 0,98 1 858 29 nad2 210 0,98 NA 574 8 nad2 1284 0,98 NA 637 10 nad2 1077 0,99 0,99 934 nad2 515 0,99 1 1004 nad2 521 0,99 1 1013 nad2 651 0,99 1 750 nad2 1085 0,99 1 940 nad2 1115 0,99 1 871 nad2 1119 0,99 1 942 nad2 1433 1 0,99 737 84 nad2 1614 NA 1 10 88 nad3 377 0,84 0,99 403 nad3 580 0,84 0,99 415 nad3 292 0,85 0,99 195 nad3 236 0,87 1 582 nad3 575 0,88 1 404 nad3 254 0,89 1 638 nad3 482 0,89 1 344 2441 nad3 311 0,9 0,99 213 nad3 478 0,91 1 329 2615 nad3 439 0,94 1 273 nad3 440 0,94 1 274 nad4 645 0,02 0 1133 nad4 974 0,05 0,07 691 nad4 1628 0,11 0,21 1372 nad4 1358 0,13 0 1786 23 nad4 1433 0,19 0,1 1772 nad4 311 0,27 0,27 1390 nad4 1328 0,83 0,75 1739 nad4 1063 0,96 0,97 1562 nad4 391 0,97 0,96 971 nad4 256 0,98 0,99 1245 80 nad4 1644 0,98 0,99 1454 1175 nad4 886 0,98 1 1701 nad4 1660 0,98 1 848 2708 nad4 630 0,99 0,99 1134 nad4 351 0,99 1 1394 nad4 393 0,99 1 962 nad4 544 0,99 1 1076 nad4 589 0,99 1 1046 11 nad4 603 0,99 1 1170 nad4 835 0,99 1 974 nad4 1011 0,99 1 860 16 nad4 1123 0,99 1 1293 nad4 1204 0,99 1 1868 nad4 1237 0,99 1 2665 nad4 1375 0,99 1 1664 11 nad4 1399 0,99 1 1364 nad4 1582 0,99 1 2142 40 nad4 1600 0,99 1 1567 nad4 1632 0,99 1 1528 nad4 301 0,99 NA 1377 4 nad4 334 1 1 1116 1811 nad4 385 1 1 1166 nad4 1 1 612 252 nad4 1 1 1079 258 nad4 1 1 1067 258 nad4 1 1 975 91 nad4 1260 1 1 2811 169 nad4 1356 1 1 1786 23 nad4L 0,97 0,99 811 150 nad4L 0,97 1 2641 370 nad4L 0,98 0,97 1810 37 nad4L 0,98 0,97 2630 718 nad4L 0,98 0,99 2475 159 nad4L 0,99 0,98 754 178 nad4L 0,99 1 1765 299 nad4L 0,99 1 2839 648 nad4L 1 1 1576 11 nad4L 1 1 1691 18 nad5 2000 0,04 0 609 5513 nad5 1802 0,06 0,05 4455 1270 nad5 1736 0,09 0,05 2710 504 nad5 0,21 0,21 1642 76 nad5 0,71 0,82 802 124 nad5 0,93 1 730 227 nad5 0,95 1 834 406 nad5 1681 0,95 1 1258 291 nad5 0,96 1 945 1079 nad5 1621 0,96 1 1993 47 nad5 0,97 1 802 124 nad5 0,97 1 1529 570 nad5 0,97 1 1392 129 nad5 2029 0,97 1 312 248 nad5 0,98 0,98 743 776 nad5 0,98 1 672 328 nad5 0,98 1 1100 305 nad5 0,98 1 1059 224 nad5 0,98 1 1736 1607 nad5 0,98 1 2183 1349 nad5 0,98 1 2291 80 nad5 1651 0,98 1 1242 84 nad5 1966 0,98 1 508 87 nad5 1989 0,98 1 576 281 nad5 0,98 NA 1208 6 nad5 0,99 1 1139 22 nad5 0,99 1 1129 440 nad5 0,99 1 1334 92 nad5 0,99 1 1153 390 nad5 1561 0,99 1 1140 221 nad5 1 1 1003 189 nad5 1346 1 1 1468 110 nad5 1987 1 1 586 220 nad6 0,84 NA 3069 6 nad6 0,97 1 1611 96 nad6 0,99 0,97 1167 67 nad6 0,99 0,98 1342 49 nad6 0,99 1 2641 151 nad6 0,99 1 1752 64 nad6 0,99 1 1500 72 nad6 1 1 1 1 1385 151 nad6 1 1 1131 147 nad6 1 NA 443 3 nad7 1163 0,06 0,12 1116 371 nad7 1424 0,13 0,1 2321 494 nad7 0,31 0,51 1112 1845 nad7 1511 0,49 0,3 1337 30 nad7 1169 0,52 0,69 1200 252 nad7 0,88 0,98 716 767 nad7 0,91 1 829 468 nad7 1337 0,93 1 1789 125 nad7 1072 0,96 0,98 1481 52 nad7 1300 0,97 0,97 1287 117 nad7 0,97 1 501 60 nad7 0,97 1 848 19 nad7 0,98 0,99 718 142 nad7 0,98 1 581 159 nad7 0,98 1 950 118 nad7 1431 0,98 1 1909 406 nad7 1462 0,98 1 2424 359 nad7 1498 0,98 1 1397 43 nad7 1053 0,99 0,79 1136 71 nad7 0,99 0,97 453 144 nad7 0,99 1 789 541 nad7 0,99 1 708 240 nad7 0,99 1 547 240 nad7 0,99 1 693 179 nad7 1098 0,99 1 1375 341 nad7 1113 0,99 1 1533 645 nad7 1143 0,99 1 1095 825 nad7 1453 0,99 1 2849 366 nad7 1477 0,99 1 2642 45 nad7 1 1 2200 703 nad7 1108 1 1 1365 718 nad9 0,97 1 2547 290 nad9 0,98 1 2411 223 nad9 0,99 1 1995 690 nad9 0,99 1 1812 202 nad9 0,99 1 1632 169 nad9 0,99 1 2074 297 rpl16 0,94 NA 1115 10 rpl16 0,95 0,86 1713 21 rpl16 0,97 1 1783 17 rpl16 0,97 1 943 19 rpl16 33 NA NA 0 0 rpl16 60 NA NA 0 0 rpl2 0,03 0,05 794 19 rpl2 0,07 0,1 1142 69 rpl2 0,75 0,75 691 12 rpl5 0,01 0,07 446 68 rpl5 0,7 0,78 522 117 rpl5 0,91 1 705 52 rpl5 0,91 1 454 119 rpl5 0,93 0,99 458 165 rpl5 0,93 0,99 468 124 rpl5 0,95 0,99 534 74 rpl5 505 0,96 0,99 135 rpl5 787 0,97 1 33 rps12 329 0,74 0,98 54 rps12 128 0,87 0,98 107 rps12 265 0,9 1 14 rps12 148 0,91 1 62 rps12 328 0,93 1 60 rps12 313 0,94 1 100 rps12 240 0,96 1 20 rps12 190 0,98 NA 9 rps3 677 0,02 0 37 rps3 288 0,02 0,02 1196 198 rps3 349 0,04 0 13 rps3 1742 0,04 NA 72 0 rps3 1422 0,07 NA 4 rps3 1506 0,37 0,52 33 rps3 765 0,55 0,47 15 rps3 1696 0,75 NA 3 rps3 1049 0,77 0,88 32 rps3 1632 0,83 0,91 11 rps3 1733 0,83 NA 0 rps3 1514 0,89 0,97 35 rps3 226 0,93 0,98 41 rps4 255 0,86 NA 6 rps4 1072 0,87 0,97 34 rps4 204 0,87 NA 4 rps4 1071 0,88 0,94 36 rps4 406 0,88 1 66 rps4 117 0,9 0,99 485 rps4 264 0,9 NA 1 rps4 996 0,91 1 11 rps4 361 0,92 0,97 36 rps4 328 0,93 NA 8 rps4 985 0,94 0,95 20 rps4 337 0,94 NA 4 rps4 1021 0,95 0,98 94 rps4 553 0,95 NA 7 rps4 106 0,96 0,98 108 rps7 242 0,01 NA 8 rps7 231 0,11 NA 6 1346 nad6 nad9 0,99 1 3142 2182 rps7 779 0,87 0,96 57

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FUNDING

Institut National de la Recherche Agronomique (INRA) [UMR 1318]; French Ministère de l'Enseignement et de la Recherche and Fondation pour la Recherche Médicale [FDT20160736470 to N.P.]; LabEx Saclay Plant Sciences-SPS [ANR-10-LABX-0040-SPS]; INCa [RiboTEM 2014-092]; ANR [Rescue Ribosome ANR-17-CE12-0024-01 to O.N.]. Funding for open access charge: IJPB; INRA [UMR 1318].

DATA AVAILABILITY

The data have been deposited in NCBI's Gene Expression Omnibus and are accessible through GEO Series accession number GSE104028.


Dominique Fourer
email: dominique.fourer@univ-evry.fr

Franc ¸ois Auger
email: francois.auger@univ-nantes.fr

Second-order Time-Reassigned Synchrosqueezing Transform: Application to Draupner Wave Analysis

This paper addresses the problem of efficiently jointly representing a non-stationary multicomponent signal in time and frequency. We introduce a novel enhancement of the time-reassigned synchrosqueezing method designed to compute sharpened and reversible representations of impulsive or strongly modulated signals. After establishing theoretical relations of the new proposed method with our previous results, we illustrate in numerical experiments the improvement brought by our proposal when applied on both synthetic and real-world signals. Our experiments deal with an analysis of the Draupner wave record for which we provide pioneered time-frequency analysis results.

I. INTRODUCTION

Time-frequency and time-scale analysis [START_REF] Cohen | Time-Frequency Analysis: Theory and Applications[END_REF], [START_REF] Flandrin | Time-Frequency/Time-Scale analysis[END_REF], [START_REF] Hlawatsch | Time-Frequency Analysis: Concepts and Methods[END_REF], [START_REF] Flandrin | Explorations in Time-Frequency Analysis[END_REF] aim at developing efficient and innovative methods to deal with non-stationary multicomponent signals. Among the common approaches, the Short-Time Fourier Transform (STFT) and the Continuous Wavelet Transform (CWT) [START_REF] Grosssmann | Decomposition of Hardy functions into square integrable wavelets of constant shape[END_REF] are the simplest linear transforms which have been intensively applied in various applications such as audio [START_REF]Signal Processing Methods for Music Transcription[END_REF], biomedical [START_REF] Poh | Analysis of neonatal EEG signals using Stockwell transform[END_REF], seismic or radar.

Unfortunately, these tools are limited by the Heisenberg-Gabor uncertainty principle. As a consequence, the resulting representations are blurred with a poor energy concentration and require a trade-off between the accuracy of the time or frequency localization. Another approach, the reassignment method [START_REF] Kodera | Analysis of time-varying signals with small BT values[END_REF], [START_REF] Auger | Improving the readability of time-frequency and time-scale representations by the reassignment method[END_REF] was introduced as a mathematically elegant and efficient solution to improve the readability of a timefrequency representation (TFR). The inconvenience is that reassignment provides non-invertible TFRs which limits its interest to analysis or modeling applications.

More recently, synchrosqueezing [START_REF] Daubechies | Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool[END_REF], [START_REF] Auger | TF reassignment and synchrosqueezing: An overview[END_REF] was introduced as a variant of the reassignment technique due to its capability to provide sharpen and reversible TFRs. This reconstruction capability make this method continuously gaining interest since it paves the way of an infinite number of synchrosqueezingbased applications such as noise removal [START_REF] Pham | A novel thresholding technique for the denoising of multicomponent signals[END_REF], signal components extraction or separation [START_REF] Daubechies | Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool[END_REF], [START_REF] Flandrin | Time-frequency filtering based on spectrogram zeros[END_REF], [START_REF] Fourer | Fast and adaptive blind audio source separation using recursive levenberg-marquardt synchrosqueezing[END_REF], [START_REF] Flandrin | Explorations in Time-Frequency Analysis[END_REF].

Nowadays, efforts are made to efficiently compute the synchrosqueezed version of several linear transforms such as STFT, CWT or S-transform [START_REF] Fourer | Recursive versions of the Levenberg-Marquardt reassigned spectrogram and of the synchrosqueezed STFT[END_REF], [START_REF] Fourer | The ASTRES toolbox for mode extraction of nonstationary multicomponent signals[END_REF] and to improve the localization of strongly modulated signals using enhanced instantaneous frequency estimators [START_REF] Oberlin | Second-order synchrosqueezing transform or invertible reassignment? Towards ideal time-frequency representations[END_REF], [START_REF] Fourer | Chirp rate and instantaneous frequency estimation: application to recursive vertical synchrosqueezing[END_REF], [START_REF] Pham | High-order synchrosqueezing transform for multicomponent signals analysis-with an application to gravitationalwave signal[END_REF]. To deal with impulses and strongly modulated signals, a new variant of the synchrosqueezing was introduced and called time-reassigned synchrosqueezing method [START_REF] He | Time-reassigned synchrosqueezing transform: The algorithm and its applications in mechanical signal processing[END_REF]. However, this method cannot efficiently deal with mixed-content signals containing both impulsive and periodic components.

In the present paper, we propose to introduce a novel transform called the second-order horizontal synchrosqueezing aiming to improve the energy localization and the readability of the time-reassigned synchrosqueezing while remaining reversible. To this end, we use an enhanced group-delay estimator which can be mathematically related to our previous results [START_REF] Fourer | Chirp rate and instantaneous frequency estimation: application to recursive vertical synchrosqueezing[END_REF].

This paper is organized as follows. In Section II, the proper definitions of the considered transforms with their properties are presented. In Section III, we introduce our new secondorder time-reassigned synchrosqueezing transform. Section IV presents numerical experiments involving both synthetic and real-world signals. Finally, future work directions are given in Section V.

II. TIME-REASSIGNED SYNCHROSQUEEZING IN A NUTSHELL

A. Definitions and properties

We define the STFT of a signal x as a function of time t and frequency ω computed using a differentiable analysis window h as:

F h x (t, ω) = R x(τ )h(t -τ ) * e -jωτ dτ (1)
where j 2 = -1 is the imaginary unit and z * is the complex conjugate of z. A TFR also called spectrogram is defined as |F h x (t, ω)| 2 . Thus, the marginalization over time of F h x (t, ω) leads to:

R F h x (t, ω) dt = R 2 h(t -τ ) * x(τ ) e -jωτ dtdτ (2) = R 2 h(u) * x(τ ) e -jωτ dudτ (3) = R h(u) * du R x(τ ) e -jωτ dτ (4) = F h (0) * F x (ω) (5)
with F x (ω) = R x(t) e -jωt dt the Fourier transform of signal x. Now, from Eq. ( 5) one can compute the Fourier Transform of x as:

F x (ω) = 1 F h (0) * R F h x (t, ω) dt (6)
and the following signal reconstruction formula can be deduced after applying the Fourier inversion formula:

x(t) = 1 2πF h (0) * R 2 F h
x (τ, ω) e jωt dτ dω.

B. Reassignment

To improve the readability of a TFR, reassignment moves the signal energy according to: (t, ω) → ( tx (t,ω), ωx (t,ω)), where tx (t, ω) is a group-delay estimator and ωx (t, ω) is an instantaneous frequency estimator [START_REF] Auger | Improving the readability of time-frequency and time-scale representations by the reassignment method[END_REF]. Both time-frequency reassignment operators t and ω can be computed as follows in the STFT case [START_REF] Behera | Theoretical analysis of the second-order synchrosqueezing transform[END_REF], [START_REF] Fourer | The ASTRES toolbox for mode extraction of nonstationary multicomponent signals[END_REF]:

tx (t,ω) = Re tx (t,ω) , with tx (t,ω) =t - F T h x (t,ω) F h x (t,ω) (8)
ωx (t,ω) = Im (ω x (t,ω)) , with ωx (t,ω)=jω + F Dh x (t,ω) F h x (t,ω) (9)
where T h(t) = th(t) and Dh(t) = dh dt (t) are modified versions of the analysis window h.

Finally, a reassigned spectrogram can be computed as

RF h x (t, ω) = R 2 |F h x (τ, Ω)| 2 δ t -tx (τ, Ω) δ (ω -ωx (τ, Ω)) dτ dΩ. (10)
The resulting reassigned spectrogram RF x (t, ω) is a sharpened but non-reversible TFR due to the loss of the phase information.

C. Time-reassigned synchrosqueezed STFT

To overcome the problem of non reversibility, synchrosqueezing proposes to move the signal transform instead of its energy, to preserve the phase information of the original transform.

Hence, time-reassigned synchrosqueezed STFT can be defined as [START_REF] He | Time-reassigned synchrosqueezing transform: The algorithm and its applications in mechanical signal processing[END_REF]:

S h x (t, ω) = R F h x (τ, ω)δ t -tx (τ, ω) dτ (11)
where tx (t, ω) corresponds to the time reassignment operator which is classically computed using Eq. ( 8).

The marginalization over time of the resulting transform leads to:

R S h x (t, ω)dt = R 2 F h x (τ, ω)δ t -tx (τ, ω) dtdτ (12) = R F h x (τ, ω)dτ = F h (0) * F x (ω). (13)
Hence, an exact signal reconstruction from its synchrosqueezed STFT can be deduced from Eq. ( 13) as:

x(t) = 1 2πF h (0) * R 2 S h
x (τ, ω) e jωt dτ dω.

III. SECOND-ORDER HORIZONTAL SYNCHROSQUEEZING A. Enhanced group-delay estimation

Let's consider a linear chirp signal model expressed as [START_REF] Fourer | Chirp rate and instantaneous frequency estimation: application to recursive vertical synchrosqueezing[END_REF]:

x(t) = e λx(t)+jφx(t) (15) with λ x (t) = l x + µ x t + ν x t 2 2 (16)
and

φ x (t) = ϕ x + ω x t + α x t 2 2 ( 17
)
where λ x (t) and φ x (t) respectively stand for the log-amplitude and phase and with q x = ν x +jα x and p x = µ x +jω x . For such a signal, it can be shown [START_REF] Fourer | Chirp rate and instantaneous frequency estimation: application to recursive vertical synchrosqueezing[END_REF] that p x = ωx (t,ω) -q x tx (t,ω), and therefore:

ω x = Im(ω x (t,ω) -q x tx (t,ω)) = ωx (t,ω) -Im(q x tx (t,ω)) (18)
The proposed second-order horizontal synchrosqueezing consists in moving F h x (t,ω) from the point (t,ω) to the point (t (2) x ,ω) located on the instantaneous frequency curve, i.e. such that φ(t

x ) = dφx dt (t

(2) x ) = ω x + α x t (2)
x = ω. This leads to:

t (2) x = ω -ω x α x = tx (t,ω) + ω -ωx (t,ω) α x + ν x α x Im( tx (t,ω)) (19)
which can be estimated by:

t(2) x (t,ω) = ω-ωx(t,ω)+Im(qx(t,ω) tx(t,ω)) αx(t,ω) if αx (t,ω) = 0 tx (t, ω) otherwise (20)
where qx (t,ω) = νx (t,ω) + j αx (t,ω) is an unbiased estimator of q x . This expression can be compared to the second-order group delay estimator introduced by Oberlin et al. [START_REF] Oberlin | Second-order synchrosqueezing transform or invertible reassignment? Towards ideal time-frequency representations[END_REF] t(2b)

x (t,ω) = tx (t, ω) + ω-ωx(t,ω) αx(t,ω) if αx (t,ω) = 0 tx (t, ω) otherwise . (21)
It can be shown using Eq.( 19) that this estimator is biased when ν x = d 2 λx dt 2 (t) = 0. Finally, a new second-order horizontal synchrosqueezing transform can thus be obtained using Eq.( 11) by replacing the group-delay estimator t(t, ω) by our enhanced estimator given by Eq. [START_REF] He | Time-reassigned synchrosqueezing transform: The algorithm and its applications in mechanical signal processing[END_REF].

B. Theoretical considerations and computation issue

In [START_REF] Fourer | Chirp rate and instantaneous frequency estimation: application to recursive vertical synchrosqueezing[END_REF], [START_REF] Fourer | Local AM/FM parameters estimation: application to sinusoidal modeling and blind audio source separation[END_REF] we introduced two families of unbiased estimators called (tn) and (ωn) involving n-order derivatives (n ≥ 2) respect to time (resp. to frequency) which enable to compute Eqs. ( 20) and ( 21):

q(tn) x (t, ω) = F D n h x F h x -F D n-1 h x F Dh x F T h x F D n-1 h x -F T D n-1 h x F h x (22)
q(ωn)

x (t, ω) = (F T n-1 Dh x + (n-1)F T n-2 h x )F h x -F T n-1 h x F Dh x F T n-1 h x F T h x -F T n h x F h x ( 23
)
with D n h(t) = d n h dt n (t) and T n h(t) = t n h(t). Our preliminary investigations [START_REF] Fourer | Local AM/FM parameters estimation: application to sinusoidal modeling and blind audio source separation[END_REF] showed a slight improvement using the (ω2) estimator in terms of accuracy in comparison to higherorder and (tn) estimators. Our implementations use the discrete-time reformulations of our previously described expressions combined with the rectangle approximation method. Thus F h x [k, m] ≈ F h

x ( k Fs , 2π mFs M ), where F s denotes the sampling frequency, k ∈ Z is the time sample index and m ∈ M is the discrete frequency bin. The number of frequency bins M is chosen as an even number such as M = [-M/2 + 1; M/2]. It results that our method has the same computational complexity of the previously introduced second-order vertical synchrosqueezing.

The proposed method is valid for any differentiable analysis window. In our implementation 1 , the STFT uses a Gaussian window and is also called Gabor transform. The window function is expressed as

h(t) = 1 √ 2πT e -t 2
2T 2 where T is the time-spread of the window which can be related to L = T F s .

IV. NUMERICAL RESULTS

A. Analysis of a synthetic signal

In this experiment, we consider a synthetic 500-sample-long multicomponent real-valued signal made of two impulses, one sinusoid, one chirp and one sinusoidally modulated sinusoid. Fig. 1 compares the following TFRs: spectrogram, reassigned spectrogram, classical (frequency-reassigned) synchrosqueezing, second-order vertical synchrosqueezing, time-reassigned 1 matlab code freely available at: http://www.fourer.fr synchrosqueezing and second-order time-reassigned horizontal synchrosqueezing. Our computations use M = 600, L = 8 and a Signal-to-Noise Ratio (SNR) equal to 25 dB obtained by the addition of a Gaussian white noise. The local modulation estimator q(ω2)

x is used for computing both secondorder synchrosqueezing methods. The TFRs provided by the previously proposed methods are computed using the matlab implementions provided by the ASTRES toolbox [START_REF] Fourer | The ASTRES toolbox for mode extraction of nonstationary multicomponent signals[END_REF].

The results clearly illustrate the improvement of the new second-order time-reassigned synchrosqueezing over the timereassigned synchrosqueezing for representing the whole signal. When compared with frequency-reassigned synchrosqueezing methods, our new method has the advantage to perfectly localize the two impulses while providing a sharpened representation of the chirp and of the sinusoidally modulated sinusoid. Unfortunately, as for the time-reassigned synchrosqueezing, our method cannot localize the non-modulated sinusoid (such signal is rare in the real world). To assess the signal reconstruction capability, we compare in Table I the Reconstruction Quality Factor (RQF) of each TFR computed using [START_REF] Fourer | Recursive versions of the Levenberg-Marquardt reassigned spectrogram and of the synchrosqueezed STFT[END_REF]: RQF = 10 log 10

n |x[n]| 2 n |x[n]-x[n]| 2
. Thus, our results show again the advantage of the time-reassigned synchrosqueezing methods which obtain significantly higher RQF (if M is chosen at least equal to the signal length) due to its theoretically exact reconstruction formula.

B. Draupner wave signal analysis

Now we consider a record of a possible freak wave event measured on the Draupner Platform in 1995 [START_REF] Haver | A possible freak wave event measured at the draupner jacket january 1 1995[END_REF]. The signal displayed in Fig. 2(a) corresponds to the sea surface elevation deduced from the measures provided by a wave sensors consisting of a down-looking laser. The sampling frequency of this signal is F s = 2.13 Hz and its duration is 20 minutes.

1) Time-frequency representation: Fig. 2 compares the resulting TFRs provided by the STFT and its different synchrosqueezed versions (i.e. all the combination of the firstand second-order of the frequency-reassigned and timereassigned). For our numerical results, we empirically choose M = 2660 and L = 25 which provide sufficiently readable results. In order to focus to the impulsive part of the signal, we have limited the analysis between 0.2 Hz and 1 Hz. As expected, the second-order time-reassigned synchrosqueezing provides the best representation to localize the 4 impulses visible in the signal. Interestingly, our results reveal the main impulse located at t 1 ≈ 4.39 min (also visible in Fig. 2(a)) but also 3 supplementary impulses respectively located at t 2 ≈ 7.72 min, t 3 ≈ 13.36 min and t 4 ≈ 19.47 min. These impulses were almost invisible in the waveform representation of the signal but have been revealed by our proposed timefrequency analysis methods.

2) Impulses detection and disentangling: Now we propose to use the synchrosqueezing signal reconstruction capability for recovering the 4 impulse signals. To this end, we compute a saliency function defined as the root mean square of the marginal over frequency band Ω = [0.4; 1] Hz of the signal energy contained in its synchrosqueezing transform:

G(t) = Ω |S h x (t, ω)| 2 dω 1 2 . ( 24
)
A binary masked version of the transform S h x (t, ω) can thus be computed using G(t) as:

Ŝ(t, ω) = S h x (t, ω) if G(t) > Γ 0 otherwise . ( 25
)
where Γ is a defined threshold. Finally the components are extracted by applying the reconstruction formula given by Eq.( 14) on Ŝ(t, ω). Our numerical computation presented in Fig. 3 uses Γ = 3.37 which corresponds to 5 times the mean value of G(t). It allows us to recover the impulses locations through a peak picking and to reconstruct the corresponding waveform signal initially merged in the whole signal.

V. CONCLUSION AND FUTURE WORK

A new extension of the time-reassigned synchrosqueezing called second-order horizontal synchrosqueezing was introduced for the STFT. Our experiments show a significant improvement to compute invertible and sharpened timefrequency representations of impulsive signals which cannot be addressed by vertical synchrosqueezing. Moreover, we have shown the efficiency of this technique when applied on both synthetic and real-word signals. In fact, our method helped to discover new signal components in the Draupner wave signal which could probably help to better understand the phenomenon of freak waves. Future work consist in theoretically strengthening this method, and developing new applications.

Fig. 1 .

 1 Fig. 1. Comparisons of the resulting TFRs of a synthetic multicomponent signal. The TFRs obtained using the synchrosqueezing methods (b),(c), (e) and (f) correpond to their squared modulus.

Fig. 2 .

 2 Fig. 2. Waveform (a) and TFRs of the Draupner wave signal. spectrogram (d), synchrosqueezing (b), second-order vertical synchrosqueezing (c), time-reassigned synchrosqueezing (e) and second-order horizontal synchrosqueezing (f).

Fig. 3 .

 3 Fig.3. Saliency function G(t) deduced from second-order horizontal synchrosqueezed STFT (a) and reconstructed signal after applying mask on timereassigned synchrosqueezed STFT.

TABLE I SIGNAL

 I RECONSTRUCTION QUALITY OBTAINED FOR THE REVERSIBLE TFRS PRESENTED IN FIG. 1.

	Method	RQF (dB)
	STFT	269.27
	classical synchrosqueezing	35.89
	second-order vertical synchrosqueezing	23.80
	time-reassigned synchrosqueezing	116.67
	second-order time-reassigned synchrosqueezing	116.67

ACKNOWLEDGMENT

The authors would like to thank Dr. Sverre Haver who kindly agreed to answer our questions and share with us the Draupner wave signal record.