Dominic Johnson

Margaret Crawford

Corentin Tim Cooper

Claeys Bouuaert

Scott Keeney

Bertrand Llorente

Valerie Garcia
email: valerie-corinne.garcia@inserm.fr

Matthew J Neale
email: m.neale@sussex.ac.uk

Corentin Claeys Bouuaert

Concerted cutting by Spo11 illuminates DNA break mechanisms and initiates gap repair during meiosis

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Advances in the sensitivity of Spo11-oligo analysis reveal additional higher molecular weight signals detectable via either radiolabelling of the 3′ OH group [START_REF] Mohibullah | Numerical and spatial patterning of yeast meiotic DNA breaks by Tel1[END_REF] (Fig. 1b,c) or western blotting (Fig. 1d). The discrete banding of these Spo11 oligos is distinct from the heterogenous smear generated when Mre11 exonucleolytic activity is impaired [START_REF] Garcia | Bidirectional resection of DNA doublestrand breaks by Mre11 and Exo1[END_REF] , and is instead reminiscent of molecules observed in mouse Atm -/-mutants [START_REF] Lange | ATM controls meiotic double-strand-break formation[END_REF] and in yeast lacking the Atm orthologue TEL1 [START_REF] Mohibullah | Numerical and spatial patterning of yeast meiotic DNA breaks by Tel1[END_REF] .

We hypothesised that these longer Spo11 oligos could arise independently of Mre11 by Spo11 cleaving DNA at adjacent locations [START_REF] Mohibullah | Numerical and spatial patterning of yeast meiotic DNA breaks by Tel1[END_REF][START_REF] Garcia | Tel1(ATM)-mediated interference suppresses clustered meiotic double-strand-break formation[END_REF] (Fig. 1a, right). Moreover, such Spo11 double-cuts (Spo11-DCs) might be increased in Atm -/-mutants, wherein DSB frequency increases ~10-fold [START_REF] Lange | ATM controls meiotic double-strand-break formation[END_REF] . Consistent with this hypothesis, sae2 mutants retained the ladder of higher molecular weight Spo11 oligos but not, as expected, oligos shorter than ~30 nt (Fig. 1b-d). Sae2 is an essential activator of the Mre11 nuclease [START_REF] Cannavo | Regulatory control of DNA end resection by Sae2 phosphorylation[END_REF] .

High resolution gel analysis demonstrated that the ladder has a ~10 nt periodicity-matching the helical pitch of B-form DNA-from ~33 nt to >100 nt (Fig. 1c,S1a,b). The ladder was also visible when SAE2 is present (Fig. 1b-d), and made up ~14% of total Spo11 oligos in wild type. As with canonical (shorter) Spo11 oligos, the ladder was increased ~2-fold in the absence of TEL1 (Fig. 1e). Temporal analysis in wild type and tel1∆ revealed Spo11-DCs to arise concomitantly with Spo11 oligos, but to have longer apparent lifespan, suggesting greater stability (Fig. 1f,g).

Importantly, the ladder requires Spo11 catalytic activity (Fig. S1c), and is present in mre11 and rad50 separation-of-function mutants (Fig. S1d) that, like sae2∆, cannot nucleolytically remove Spo11 [START_REF] Moreau | The nuclease activity of Mre11 is required for meiosis but not for mating type switching, end joining, or telomere maintenance[END_REF][START_REF] Neale | Endonucleolytic processing of covalent protein-linked DNA double-strand breaks[END_REF][START_REF] Garcia | Bidirectional resection of DNA doublestrand breaks by Mre11 and Exo1[END_REF][START_REF] Cao | A pathway for generation and processing of double-strand breaks during meiotic recombination in S. cerevisiae[END_REF] . From these analyses we conclude that Spo11 often cleaves DNA at adjacent positions within both wild type and resection-deficient cells. If this idea is correct, we reasoned that the average size of Spo11-DCs should be increased in a strain where catalytically inactive (but DNA-binding competent) Spo11 is expressed alongside wild-type Spo11, because this should result in a greater average spacing between adjacent Spo11 complexes that are able to cut the DNA. This prediction was met (Fig. S1e) suggesting that inactive Spo11 complexes can bind DNA stably and act as competitive inhibitors of adjacent catalysis.

Spo11-DCs are detected within whole-genome Spo11-oligo libraries

We reasoned that because Spo11-DC molecules are detected in the presence of SAE2, they may also be detected within the deep-sequencing Spo11-oligo libraries from wild type and tel1∆ strains [START_REF] Mohibullah | Numerical and spatial patterning of yeast meiotic DNA breaks by Tel1[END_REF] . To test this idea, we remapped the raw sequence reads using pairedend alignment, generating a length distribution of Spo11 oligos (Fig. 2a). In close agreement with the physical gel analyses, we detected not just the prominent class of previously characterised Spo11 oligos (20-40 nt), but also peaks at ~43, ~53, ~63, and ~73 nt (Fig. 2a).

Moreover, a shoulder on the main peak was apparent at ~33 nt in wild type and was more prominent in tel1∆. Approximately 25% of the mapped reads are >40 nt in length. Based on our physical analysis, a proportion of these are likely to be Spo11-DCs.

On average, Spo11 displays a characteristic DNA sequence bias spanning ±15 nt around the cleavage site, including preferred cleavage 3′ to a C nucleotide and flanking A/T skews [START_REF] Pan | A Hierarchical Combination of Factors Shapes the Genome-wide Topography of Yeast Meiotic Recombination Initiation[END_REF][START_REF] Gittens | A nucleotide resolution map of Top2-linked DNA breaks in the yeast and human genome[END_REF] (Fig. 2b). We reasoned that if the molecules ascribed to Spo11-DCs indeed arise from two coincident DSBs, the Spo11 oligos should have this sequence bias at both termini and not just the 5′ end.

To test this prediction, we stratified by Spo11-oligo length and assessed the base composition around the 3′ end of each molecule (Fig. 2b-d). As expected, 27-nt molecules within the major peak displayed a 3′ signature unlike Spo11 (Fig. 2b), attributed to sequence biases of Mre11 nuclease [START_REF] Pan | A Hierarchical Combination of Factors Shapes the Genome-wide Topography of Yeast Meiotic Recombination Initiation[END_REF] . By contrast, 43-nt Spo11 oligos revealed a clear echo of the Spo11 sequence bias at their 3′ ends (Fig. 2c). Importantly, a Spo11-like bias was largely absent when assessing one of the troughs in the length distribution profile, 39 nt (Fig. 2d).

Next, we filtered the sequence reads to include only overlapping forward-strand (Franklin) and complementary-strand (Crick) read pairs with 5′ and 3′ ends separated by 2 bp (the overhang created by Spo11 cleavage [START_REF] Liu | The location and structure of double-strand DNA breaks induced during yeast meiosis: evidence for a covalently linked DNA-protein intermediate[END_REF][START_REF] Pan | A Hierarchical Combination of Factors Shapes the Genome-wide Topography of Yeast Meiotic Recombination Initiation[END_REF] )-with the expectation that this will enrich for Spo11-DC molecules (Fig. 2e). Remarkably, this exercise enhanced the ~10 nt periodicity even though the filter did not include an explicit constraint on read length (Fig. 2e-f). The Spo11-like sequence bias was also enhanced at the 3′ ends (Fig. 2g). These results strongly support the conclusion that the periodic Spo11-oligo lengths detected both within sequencing libraries (Fig. 2e-f) and physically (Fig. 1), are indeed mostly Spo11-DCs. Similar sequence biases were observed when selecting other peaks in the filtered distribution-including an otherwise undetectable peak at ~33 bp (Fig. 2e; Fig. S2a-d).

Spo11-DCs (defined as filtered Spo11 oligos >30 nt; Fig. 2e) make up ~4.6% and 7.9% of the total Spo11-oligo pool in wild type and tel1∆ strains, respectively (Fig. 2h). Presumably, these values are lower than our gel-based estimates due to size selection during library preparation and to the stringency of the filtering.

We hypothesized that the absence of Spo11-DCs <30 bp in length (Fig. 1c and Fig. 2e,f) is due to the inability of two DSB-forming complexes to assemble on DNA in such close proximity. This idea is consistent with the size of the region showing biased base composition (likely attributable to preferences in protein-DNA binding interactions) ±15 bp around each DSB end [START_REF] Pan | A Hierarchical Combination of Factors Shapes the Genome-wide Topography of Yeast Meiotic Recombination Initiation[END_REF] (e.g. Fig. 2b).

To directly test this idea, we examined recombinant Spo11-Rec102-Rec1104-Ski8 complexes, which can bind tightly and noncovalently to dsDNA ends in vitro (Claeys Bouuaert & Keeney, in preparation). Spo11 complexes were incubated with dsDNA fragments of varying length and assessed for their ability to bind one versus both ends (Fig. 2i and Fig. S2e). Remarkably, double-end binding was efficient for DNA molecules that were 30-34 bp or 24-25 bp, but not sizes in between (Fig. 2j and Fig. S2e). We interpret this result to mean that adjacent Spo11 complexes clash sterically with one another at distances below ~30 bp if they are oriented in the same direction, but this clash can be alleviated by a relative rotation of 180˚ (half a helical turn) between the two Spo11 complexes (Fig. 2j).

Because molecules shorter than 30 nt are not detected in our physical and filtered Spo11oligo analyses, we propose that adjacent Spo11 complexes capable of making double cuts must have interacted with DNA from the same orientation. Collectively, our data support the view that Spo11 can catalyse adjacent DSBs on the same DNA molecule; that Spo11-DCs arise much more frequently than current thinking had supposed; and that DSB centres in Spo11-DCs are separated by distances that increment in ~10-bp steps from a minimum of ~33 bp (approximately three helical turns of B-form DNA).

Mapping Spo11 double-cuts within DSB hotspots

In S. cerevisiae and mouse, Spo11 preferentially cleaves DNA within regions of low nucleosome occupancy, generating a punctate map of preferred DSB 'hotspots' distributed non-randomly across the genome [START_REF] Pan | A Hierarchical Combination of Factors Shapes the Genome-wide Topography of Yeast Meiotic Recombination Initiation[END_REF][START_REF] Lange | The Landscape of Mouse Meiotic Double-Strand Break Formation[END_REF] . To determine the relationship between Spo11-DSB hotspots and Spo11-DCs, we generated comparative genome-wide maps of both, in which Spo11-DCs are represented as frequency-weighted arcs that link the 5′ ends of overlapping Franklin-and Crick-strand filtered reads (Fig. 3a-c and Fig. S3a).

Spo11-DCs are distributed non-uniformly across hotspots, with evidence of subdomains identifiable as peaks in Spo11-DC maps (Fig. 3a and Fig. S4a). Narrower hotspots display a simple pattern with centrally focussed Spo11-DC formation (Fig. 3b and Fig. S4b), whereas very wide hotspots contain multiple discrete Spo11-DC zones (Fig. 3c and Fig. S4c).

Overall, nearly all (~95%) Spo11-DCs map within hotspots (Fig. S5a), more so than total Spo11 oligos (~86%), suggesting that Spo11-DCs are more prevalent where Spo11 activity is strongest. Although the proportion of Spo11-DCs within each hotspot varied widely from <0.1% to >10% of the Spo11-oligo signal, ~86% of hotspots displayed a Spo11-DC fraction of at least 1%, and ~18% of hotspots displayed Spo11-DC fractions over 5% (Fig. S5b). In tel1∆, these fractions increased to ~94% and ~47%, respectively (Fig. S5b), consistent with the median frequency of Spo11-DCs per hotspot being ~1.7-fold greater (Fig. S5b; P<0.0001, Kruskal-Wallis H-test). Whilst Spo11-DC frequency correlated positively with total Spo11-oligo counts (Fig. S5c), the relationship was nonlinear, such that Spo11-DCs were observed disproportionately more frequently within the strongest hotspots (Fig. S5d).

Finally, although Spo11-DCs were globally more frequent in tel1∆ compared to wild type, this relationship was not uniform across all hotspots (Fig. S4d and Fig. S5e).

Spo11-DCs arise within regions of Spo11-oligo strand disparity

Every DSB is expected to generate two Spo11 oligos, one each mapping to the Franklin and Crick strands of the genome, but many individual DSB sites display strong disparity between strands [START_REF] Pan | A Hierarchical Combination of Factors Shapes the Genome-wide Topography of Yeast Meiotic Recombination Initiation[END_REF] . Because Spo11 oligos <15 nt are not mapped, this disparity was thought to reflect differences in the relative numbers of longer and shorter canonical Spo11 oligos [START_REF] Neale | Endonucleolytic processing of covalent protein-linked DNA double-strand breaks[END_REF][START_REF] Pan | A Hierarchical Combination of Factors Shapes the Genome-wide Topography of Yeast Meiotic Recombination Initiation[END_REF] .

However, the molecular explanation for strand disparity at some but not all cleavage sites has been unclear. Critically, we found an unanticipated alternating pattern of strand-biased Spo11-oligo enrichment across hotspots that was spatially associated with Spo11-DC subdomains (Fig. 3a-c). Specifically, the left flanks of Spo11-DC peaks appeared to be enriched for Franklin-strand hits, whereas the right flanks were enriched for Crick-strand hits (Fig. 3a-c and Fig. S4a-d). This pattern was most pronounced at narrow, low frequency hotspots (Fig. 3b and Fig. S4b) and was retained upon TEL1 deletion (Fig. S4d).

To investigate the generality of these observations, we assessed strand-specific Spo11-oligo signal when averaged around the centres of the strongest Spo11-DC peaks in all ~3900 annotated DSB hotspots (Fig. 3d). Mapped 5′ ends of bulk Spo11 oligos displayed peaks ±20 bp from Spo11-DC centres and were associated with ~2-fold skews towards Franklinstrand hits on the left and Crick-strand hits on the right (Fig. 3e). A similar disparity in local Spo11 oligos was observed at the left (Fig. 3f) and right (Fig. 3g) ends of individual Spo11-DCs regardless of their size, resulting in a ~4-fold differential towards Franklin on the left and Crick on the right (Fig. 3h), also seen upon TEL1 deletion (Fig. S6a-d). Importantly, no net disparity was observed within the bulk Spo11-oligo population (Fig. S6e-f), indicating that these strand-specific patterns are a special feature of genomic sites that generate Spo11-DCs. We conclude that our observations are not unique to specific hotspots, nor to specific mutants, but are, instead, a general feature of the meiotic recombination process.

Spo11-DCs lead to double-strand gap repair

The molecular data presented so far show that closely spaced DSBs can arise on the same DNA molecule. Because Spo11-DCs are recovered in a wild-type background, we infer that resection initiation is inefficient in between such coincident DSBs. Therefore, Spo11-DCs might be repaired as short double-strand gaps, leading to unidirectional transfer of genetic information from the uncut donor DNA to the gapped molecule (Fig. 4a).

To test this idea, we analysed meiotic recombination 'scars' in a hybrid yeast strain containing ~65,000 nucleotide sequence polymorphisms [START_REF] Martini | Genome-wide analysis of heteroduplex DNA in mismatch repair-deficient yeast cells reveals novel properties of meiotic recombination pathways[END_REF][START_REF] Marsolier-Kergoat | Mechanistic View and Genetic Control of DNA Recombination during Meiosis[END_REF] . To reduce analytical ambiguity from correction of mismatches in heteroduplex DNA, we deleted the mismatch repair factor MSH2 [START_REF] Martini | Genome-wide analysis of heteroduplex DNA in mismatch repair-deficient yeast cells reveals novel properties of meiotic recombination pathways[END_REF][START_REF] Marsolier-Kergoat | Mechanistic View and Genetic Control of DNA Recombination during Meiosis[END_REF] . In msh2∆ cells, recombination events initiated by a single DSB are expected to generate heteroduplex DNA, visible as segments of 5:3 marker segregation within a recombination scar [START_REF] Martini | Genome-wide analysis of heteroduplex DNA in mismatch repair-deficient yeast cells reveals novel properties of meiotic recombination pathways[END_REF] . By contrast, 6:2 marker segregation should be enriched within events initiated by gaps (Fig. 4a). As previously noted [START_REF] Martini | Genome-wide analysis of heteroduplex DNA in mismatch repair-deficient yeast cells reveals novel properties of meiotic recombination pathways[END_REF] , a large fraction (~37%) of recombination events in msh2∆ cells contained at least one patch of 6:2 segregation (Fig. 4b). We filtered these events to include only those with 6:2 segments between 30 and 150 bp (~25% of total events), consistent with the sizes of Spo11-DCs determined physically.

Next, because 6:2 patches can also be generated by mechanisms other than adjacent Spo11 DSBs [START_REF] Marsolier-Kergoat | Mechanistic View and Genetic Control of DNA Recombination during Meiosis[END_REF] , we sorted events into three categories (A-C) based on the flanking patterns of heteroduplex DNA (Fig. 4c and Fig. S7a. See Methods for details). Category A events are compatible with gap repair because flanking heteroduplex DNA patterns are in trans orientation, whereas category B events are incompatible because the flanking heteroduplex DNA patterns are in cis orientation. Category C events lack the flanking heteroduplex DNA patterns necessary to assign the event.

Category A (compatible) accounts for ~3% of all events, category B (incompatible) is ~5% and category C (ambiguous) is ~12% (Fig. 4b and Fig. S7a-g). Loss of Tel1 had no impact on the relative proportion of categories A-C (Fig. S7a and Fig. S8a), but increased the frequency of events with 6:2 segments >150 bp (Fig. S8a), consistent with a loss of DSB interference increasing the probability of coincident DSBs at adjacent hotspots [START_REF] Garcia | Tel1(ATM)-mediated interference suppresses clustered meiotic double-strand-break formation[END_REF] .

6:2 segments that do not arise from Spo11-DCs may arise from the DNA nicking action of Mlh1-3 and Exo1 during repair [START_REF] Marsolier-Kergoat | Mechanistic View and Genetic Control of DNA Recombination during Meiosis[END_REF] . Importantly-and consistent with this idea-abrogation of these nicking activities led to a specific reduction in the frequency of category B and C events, whereas category A events were unaffected (Fig. 4d and Fig. S7a; P<0.0001 twotailed Z-test).

We further reasoned that 6:2 segments arising from gap repair should correlate strongly with the location of DSB initiation, whereas nick translation during repair has the potential to arise away from the initiation site. Thus, to further test the validity of these categorisations, we computed both the frequency of 6:2 segments overlapping Spo11 hotspots (Fig. 4f), and the density of Spo11 oligos within the 6:2 segments (Fig. 4g) of all categories. By both metrics, Category A events displayed the greatest association with Spo11 activity (P<0.00001, twotailed Z-test and Kruskal-Wallis H test, respectively). Collectively, these analyses support the view that category A events arise from gap repair.

Spo11-DCs arise during mouse meiosis

DSB formation by Spo11 is evolutionarily conserved [START_REF] Keeney | Spo11 and the Formation of DNA Double-Strand Breaks in Meiosis[END_REF] . Notably, in the absence of ATM, mouse SPO11 oligos are more abundant and display a distinct size distribution, including a ladder of molecules larger than the canonical SPO11-oligo signal [START_REF] Lange | ATM controls meiotic double-strand-break formation[END_REF] similar to those in S. cerevisiae.

To investigate whether SPO11-DC formation occurs in mammals, we explored SPO11-oligo sequences from mouse spermatocytes [START_REF] Lange | The Landscape of Mouse Meiotic Double-Strand Break Formation[END_REF] . Mouse SPO11-oligo size distribution is distinct between wild type and Atm -/-, with prominent populations at ~10-20 nt and ~25-30 nt in the wild type, and larger molecules (25-60 nt) more abundant in Atm -/-(Fig. 5a). Filtering to retain only overlapping SPO11 oligos, whilst less efficient than in S. cerevisiae, disproportionately retained putative mouse SPO11-DCs in the 30-60 nt range in Atm -/- (Fig. 5b-c). Moreover, subtle periodic peaks of enrichment at ~32 nt, 43 nt, and 53 nt emerged, reminiscent of S. cerevisiae Spo11-DC sizes (Fig. 5c).

Filtered SPO11 oligos were approximately 10-fold more enriched within annotated hotspots in Atm -/-than the control (Fig. 5d; P<0.0001, Kruskal-Wallis H test). Interestingly, bulk SPO11-oligo signals >30 nt in length were offset from hotspot centres in a strand-specific manner reminiscent of the left-right Franklin-Crick disparity observed at S. cerevisiae hotspots (Fig. 5e). Arc maps revealed alternating domains of strand disparity associated with locations of filtered SPO11 oligos (Fig. 5f-g and Fig. S9), similar to S. cerevisiae (Fig. 3). These observations suggest that Spo11-DC formation is evolutionarily conserved.

Discussion

Although double-strand gap repair assays were instrumental in establishing the DSB repair model more than 35 years ago [START_REF] Szostak | The double-strand-break repair model for recombination[END_REF] , direct Spo11-dependent gap formation in vivo was not anticipated, nor does it feature within current models. Indeed, despite the DNA interaction surface of Spo11 likely being <30 bp [START_REF] Pan | A Hierarchical Combination of Factors Shapes the Genome-wide Topography of Yeast Meiotic Recombination Initiation[END_REF][START_REF] Diaz | Identification of residues in yeast Spo11p critical for meiotic DNA double-strand break formation[END_REF] , it has been generally assumed that only a single DSB is created within any given hotspot at a time even though most meiotic hotspots are many times wider [START_REF] Pan | A Hierarchical Combination of Factors Shapes the Genome-wide Topography of Yeast Meiotic Recombination Initiation[END_REF][START_REF] Lange | The Landscape of Mouse Meiotic Double-Strand Break Formation[END_REF] (100-1000 bp).

Challenging this idea, we show that adjacent Spo11 dimers can cleave coincidentally at close proximity within hotspots, and we provide evidence that Spo11-DCs yield doublestrand gaps that cause mismatch repair-independent unidirectional transfer of genetic information. Our conclusions agree with and substantially extend interpretations of segregation patterns in mismatch repair-defective strains [START_REF] Martini | Genome-wide analysis of heteroduplex DNA in mismatch repair-deficient yeast cells reveals novel properties of meiotic recombination pathways[END_REF] , and Spo11-oligo sizes in tel1 mutants [START_REF] Mohibullah | Numerical and spatial patterning of yeast meiotic DNA breaks by Tel1[END_REF] .

The ladder of yeast Spo11-DCs represents ~14% of total Spo11 oligos. A Spo11-DC should generate four Spo11-oligo complexes instead of the two oligos generated at a single Spo11 DSB. If we assume that there is at most only one Spo11-DC per recombination initiation event, we estimate that ~16% of events contain a Spo11-DC (Methods). The lower frequency estimated for gap repair in recombination data (~3%) likely reflects uncertainty in ascribing recombination events to gap repair, inability to detect intersister recombination, and effects of limited polymorphism density (1 per ~200 bp), which disproportionately reduces the chance of detecting gaps the shorter they are (Fig. S7h).

The ~10-bp periodicity of Spo11-DC sizes is intriguing. Similar periodicity occurs for DNase I cleavage of DNA when wrapped around histones [START_REF] Noll | Internal structure of the chromatin subunlt[END_REF] . Within nucleosomal DNA, the periodicity arises due to only one face of the helix being solvent exposed, with the alternating majorminor groove pattern then repeating once per helical turn. Importantly, however, DSB hotspots have a largely open chromatin structure, and stable nucleosomes occlude Spo11 access to DNA in vivo [START_REF] Pan | A Hierarchical Combination of Factors Shapes the Genome-wide Topography of Yeast Meiotic Recombination Initiation[END_REF] , similar to other topoisomerase family members [START_REF] Gittens | A nucleotide resolution map of Top2-linked DNA breaks in the yeast and human genome[END_REF] . Therefore, we consider it likely that something other than nucleosomes restricts Spo11-DC endpoints to these periodic positions.

We envision a mechanism wherein multiple Spo11 proteins create a platform that enables coordinated Spo11-DSB formation (Fig. 6a). In this model, periodic spacing arises from adjacent Spo11 molecules being restricted to accessing the same face of the DNA helix, with preferred cleavage opportunities arising only every helical turn (~10.5 bp) because of the relative inflexibility of B-form DNA over these short distances. This model also explains why the minimum Spo11-DC size is ~33 bp despite our DNA binding observations indicating that adjacent Spo11 complexes can come as close as 24 bp in vitro when not constrained to be in the same orientation relative to the DNA helical axis. Moreover, a multimeric DSBforming 'machine' made up of many catalytic centres may explain the previously perplexing observation that SPO11/spo11-Y135F catalytic heterozygosity has little effect on overall DSB formation despite the expectation of negative dominance [START_REF] Diaz | Identification of residues in yeast Spo11p critical for meiotic DNA double-strand break formation[END_REF] .

In our model, the alternating strand disparity in Spo11-oligo libraries arises from the Spo11 platform selectively protecting a subset of DSB ends from the endonuclease and/or 3'→5' exonuclease activities of Mre11 [START_REF] Garcia | Bidirectional resection of DNA doublestrand breaks by Mre11 and Exo1[END_REF] . For DSB ends within the platform, or facing inwards from the platform edges, this protection would yield Spo11-DCs as well as the canonical Spo11 oligos of larger sizes (Fig. 6b-c and Fig. S3d). In contrast, the outermost DSB ends would be less protected, yielding Spo11 oligos vulnerable to more extensive digestion by Mre11, in turn leading to their under-representation in Spo11-oligo maps that omit short oligos (Fig. 6b-c and Fig. S3d). Thus, we propose that the two prominent size classes of Spo11 oligo detected physically [START_REF] Neale | Endonucleolytic processing of covalent protein-linked DNA double-strand breaks[END_REF] arise from asymmetric hotspot-axis interactions that generate differential sensitivity to nucleolytic degradation.

In broad terms, our model for a surface-bound Spo11 platform agrees with how Spo11 and its essential cofactors interact with the chromosomal axis as measured by ChIP [START_REF] Prieler | The control of Spo11's interaction with meiotic recombination hotspots[END_REF][START_REF] Panizza | Spo11-accessory proteins link double-strand break sites to the chromosome axis in early meiotic recombination[END_REF][START_REF] Kugou | Rec8 guides canonical Spo11 distribution along yeast meiotic chromosomes[END_REF] and by immunofluorescent staining of spread chromosomes [START_REF] Li | Saccharomyces cerevisiae Mer2, Mei4 and Rec114 form a complex required for meiotic double-strand break formation[END_REF][START_REF] Kee | Spatial organization and dynamics of the association of Rec102 and Rec104 with meiotic chromosomes[END_REF][START_REF] Kumar | Functional conservation of Mei4 for meiotic DNA double-strand break formation from yeasts to mice[END_REF] , such that Spo11 would be organised alongside other pro-DSB factors in a two-dimensional protein array. Whilst we draw the axis in a planar form, our ideas do not exclude a model where the axis and DNA curve or writhe in concert with one another, and it is upon the exposed surface of such a structure that Spo11 catalysis occurs. However, the fact that we detect no major DNA sequence skews towards more flexible A or T bases in the centre of Spo11-DC fragments (Fig. S2d), disfavours the idea that DNA is subject to significant localised bending forces during Spo11-DC formation.

Tel1/ATM has an evolutionarily conserved function in negatively regulating DSB numbers 15- 18,34-36 . In yeast, at hotspots ~2 kb apart, loss of Tel1-mediated DSB interference increases coincident DSB formation ~10-fold [START_REF] Garcia | Tel1(ATM)-mediated interference suppresses clustered meiotic double-strand-break formation[END_REF] . By contrast, TEL1 deletion increases Spo11-DCs much less (~2-fold; Fig. 1b-e), despite each Spo11-DC also being formed by a pair of adjacent DSBs. We interpret this difference to indicate that-unlike DSBs arising in two separate hotspots-the closely spaced DSBs that generate a Spo11-DC are less subject to Tel1dependent negative regulation between one another. We envisage a mechanism where, in response to a DSB, Tel1 inactivates adjacent patches of assembled Spo11 in which DSB formation has yet to happen. By contrast, we propose that coincident DSBs often arise within a hotspot before the inhibitory effect of Tel1 can act-promoted by the high-density Spo11 array (Fig. 6).

Our exploration of mouse Spo11-oligo libraries supports the view that Spo11-DC formation within meiotic hotspots is evolutionary conserved-an interpretation consistent with recent molecular analysis of recombination in Atm -/-mouse spermatocytes (A. Lukaszewicz, S.

Keeney, and M. Jasin, unpublished). However, the frequency of SPO11-DCs increases much more in mouse Atm -/-than it does in tel1∆ yeast (~10-fold, Fig. 5d vs ~2-fold, Fig. 2h).

We interpret this difference to suggest that SPO11 double cutting in mouse is subject to direct inhibition by ATM. Such an effect may be a consequence of the more central role ATM plays within the generalised DNA damage response in mammals. Alternatively, or in addition, it may point to as-yet-uncharacterised differences between how SPO11-DSB formation is controlled within the two organisms.

Methods

Strains and culture methods

S. cerevisiae strains used in this study are listed in Table S1. Synchronous meiotic cultures were grown using standard methods. Briefly, YPD cultures (1% yeast extract, 2% peptone, 2% glucose) were diluted 100-fold into YPA (1% yeast extract, 2% peptone, 1% K-acetate) and grown vigorously for 14 h at 30˚C. Cells were collected by centrifugation, washed once in water, resuspended in an equal volume of prewarmed 2% K-acetate containing diluted amino acid supplements, and shaken vigorously at 30˚C. For mapping meiotic recombination patterns in hybrid octads SK1 and S288c haploid parents were mated for 8-14 hours on YPD plates as described [START_REF] Crawford | Separable roles of the DNA damage response kinase Mec1(ATR) and its activator Rad24(RAD17) within the regulation of meiotic recombination[END_REF] . Cells were washed and incubated in sporulation media at 30°C with shaking, and tetrads were dissected after 72 hours. To generate octads, dissected spores were allowed to grow for 4-8 hours on YPD plates until they had completed the first post-meiotic division, after which mother and daughter cells were separated by microdissection, and allowed to grow for a further 48 hours. Spore clones were subsequently grown for 16 hours in liquid YPD prior to genomic DNA isolation using standard techniques [START_REF] Garcia | Tel1(ATM)-mediated interference suppresses clustered meiotic double-strand-break formation[END_REF] . Only octads generating eight viable progeny were used for genotyping by deep sequencing.

Spo11-oligo and Spo11-DC physical analysis

Spo11-oligo complexes were isolated by immunoprecipitation using anti-FLAG antibody from 10 ml aliquots of sporulating cells harvested at the indicated timepoint(s), and labeled with alpha-32P cordycepin triphosphate using Terminal deoxynucleotidyl transferase (Fermentas) as described [START_REF] Johnson | Removal of Spo11 from meiotic DNA breaks in vitro but not in vivo by Tyrosyl DNA Phosphodiesterase 2[END_REF] , and separated by 7.5% SDS-PAGE, or treated with Proteinase K (Fisher) for 1 hour at 37˚C prior to overnight precipitation in 90% ethanol at -80˚C, then denatured in 1x formamide loading dye and separated on 19% denaturing urea/PAGE in 1x TBE. Where indicated, deproteinised samples were further treated with 300 nM recombinant mammalian TDP2 for 30 minutes at 30˚C [START_REF] Johnson | Removal of Spo11 from meiotic DNA breaks in vitro but not in vivo by Tyrosyl DNA Phosphodiesterase 2[END_REF] prior to electrophoresis, to remove residual phosphotyrosyl linked peptides, thereby enabling an accurate estimate of Spo11-oligo DNA length.

Radioactive signals were collected on phosphor screens, scanned with a Fuji FLA5100 and quantified using ImageGauge software. For analysis of Spo11-oligo species by Western, SDS-PAGE gels were transferred to PVDF membrane, blocked with 5% non-fat dry milk (NFDM) / 1x TBST, and incubated with anti-FLAG-HRP at 1:1000 in 1% NFDM / 1xTBST.

To estimate the fraction of events containing a Spo11-DC, we apply the simplifying assumption that, at most, only a single Spo11-DC arises per event such that each Spo11-DC makes four Spo11-oligos (two internal, two external) whereas each single Spo11 DSB makes only two oligos (two external). Applying these assumptions, the estimated fraction of events containing a Spo11-DC simplifies to the equation: Spo11 oligos>30 nt / Spo11 oligos<30 nt

Remapping of S. cerevisiae Spo11-oligo libraries

S. cerevisiae Spo11-oligo libraries [START_REF] Mohibullah | Numerical and spatial patterning of yeast meiotic DNA breaks by Tel1[END_REF] were aligned to the Cer3H4L2 reference genome using Bowtie2, with identical GLOBAL and LOCAL mapping parameters: -X1000 --no-discordant -very-sensitive --mp 5,1 ----np 0. Cer3H4L2 is identical to the sacCer3 reference genome (R64-1-1), with the addition of two ectopic insertions: 1173 bp of hisG sequence inserted at the LEU2 locus at position 91965, and 3037 bp of LEU2 sequence including 77 bp of associated unidentified bacterial sequence 39 at position 65684. Before mapping, reads were trimmed to remove adapters and trailing G or C bases introduced during library preparation using Perl (OligoTrim.pl). Specifically, 5′ ends of Read1 were trimmed using Perl to remove the following sequences at the first 9 or 8 bases of each read: NNNNNCCCC (or NNNNNCCC if prior sequence not found). Read1 3′ ends were trimmed to truncate before any GGGGAGAT (or GGGAGAT if prior sequence not found) sequences should they be present. Similarly, Read2 5′ ends were trimmed to remove leading CCCC (or CCC if prior sequence not found) sequences, and 3′ ends truncated before GGGGNNNNNAGAT (or GGGNNNNNAGAT if prior sequence not found) sequences. In each case, the need to trim the NNNNN string arises from the use of custom barcoded adapters during library preparation [START_REF] Mohibullah | Numerical and spatial patterning of yeast meiotic DNA breaks by Tel1[END_REF] . The AGAT string is the reverse complement of the first 4 bp of the universal Illumina adapter. Following trimming and paired end alignment, the Read1 5′ base is expected to have a high probability of being a true Spo11-oligo 5′ end, and the terminal mapped base a true 3′ end. Nevertheless, some ambiguity is impossible to avoid due to inherent uncertainties in the number of terminal rG bases added during library preparation [START_REF] Mohibullah | Numerical and spatial patterning of yeast meiotic DNA breaks by Tel1[END_REF] .

Resulting SAM files were processed via terminalMapper (https://github.com/Neale-Lab) using the 'DOUBLE' setting, generating 1 bp resolution histogram files of 5′ Spo11 oligo ends mapping to either Franklin or Crick strands of the genome. Additional "CoordinateAB" files report frequencies, strand, and position of molecules with unique 5′ and 3′ ends, enabling filtering for overlapping pairs. In these files, the 3′ reported is 2 nt more distal than the actual 3′ end such that it corresponds to any putative 5′ end on the complementary strand. As such, and because the AB coordinates listed include the first and last mapped base, the raw oligo lengths are 1 nt shorter than than obtained by subtracting the B coordinate from A.

Remapping of mouse Spo11-oligo libraries

Mouse Atm -/-SPO11-oligo libraries [START_REF] Lange | The Landscape of Mouse Meiotic Double-Strand Break Formation[END_REF] , were trimmed in a similar way. Specifically, 5′ ends of Read1 were trimmed using Perl to remove the following sequences at the first 9 or 8 bases of each read: NNNNNCCCC (or NNNNNCCC if prior sequence not found). Read1 3′ ends were trimmed to truncate before any GGGG (or GGG if prior sequence not found) sequences should they be present. Similarly, Read2 5′ ends were trimmed to remove leading CCCC (or CCC if prior sequence not found) sequences, and 3′ ends truncated before GGGG (or GGG if prior sequence not found) sequences. Resulting SAM files were processed with terminalMapper as above, but additionally processed to expand the called 5′ and 3′ ends by ±1 bp in a manner that averages the frequency of reads mapped at a specific pair of coordinates equally across the nine resulting combinations. This additional step was introduced due to our lower confidence in the accuracy of 5′ and 3′ mapped coordinates based on our inability to trim many reads based on their expected sequence composition. This process increases the likelihood of isolating reciprocal pairs of SPO11 oligos (which otherwise requires a precise 2 bp offset between 5′ and 3′ ends of the reciprocal pair), at the expense of 9-fold lowered absolute frequency of any given molecular coordinates.

Reciprocal filtering of Spo11-oligo libraries to isolate Spo11-DC compatible molecules

To enrich for putative Spo11-DC molecules in both S. cerevisiae and mouse libraries, Spo11-oligos were discarded unless a reciprocal partner mapped with 2 bp offset was present within the library. Spo11-DCs were then reported as twice the minimum frequency of either the Franklin or Crick oligo (whichever was lower). Additionally, for quantitative analyses and the plotting of arc-diagrams, all oligos <31 nt were discarded, justified by our physical gel-based analysis of Spo11-DCs in sae2∆ cells, and the periodic enrichment of Spo11-DCs for oligos >30 nt.

Calculating DNA sequence composition at 5′ DSB ends

DNA sequence orientated 5′→3′ around 5′ cleavage sites for the relevant library fraction was aggregated using seqBias (Perl, v5.22.1; https://github.com/Neale-Lab) and plotted as fractional base composition at each base for the top strand.

Calculating strand disparities

When Spo11 5′ ends are mapped to a reference genome, the 2 bp overhang at cleavage sites translates to a 1 bp offset for the mapped 5′ base on each strand. Thus to compute the relative strand disparity (ratio of the frequency of mapping, in hits per million, HpM, on each strand at a given cleavage site), the mapped Crick coordinates were first shifted by -1 bp.

Before calculating disparity ratios, 0.01 HpM were added to both denominator and numerator to avoid errors arising when one of the values was zero. Net, left-right, disparity for individual Spo11-DC molecules was defined as: (Franklinleft / Crickleft) / (Franklinright / Crickright).

(ambiguous). Despite these uncertainties, the fact that the fraction of events falling into Category A is unaffected by deletion of EXO1, MLH1 or MLH3 (which when mutated abrogate the generation of 6:2 events arising from spurious nicking [START_REF] Marsolier-Kergoat | Mechanistic View and Genetic Control of DNA Recombination during Meiosis[END_REF] ), whereas Category B and C are reduced ~3-fold and ~7-fold, respectively, by these mutations, provides confidence in the validity of our classifications. Precise categorisation rules are presented below: NCO events: NCO 6:2 segments flanked by hDNA tracts in trans orientation (e.g. CN4; the hDNA pattern matches the known phasing of the strands (e.g. CN3; Fig. S7f). In this latter case, we infer that the missing information on one side of the event may be absent due to lack of variant coverage. One-sided NCO events with incorrect strand phasing are classified as incompatible. One-sided NCO events where the strand orientation could not be phased were classed as ambiguous.

CO events: There are two places a 6:2 segment can appear; in the centre of the CO exchange (e.g. CC1-CC4; Fig. S7b-c) or offset from the CO exchange (e.g. CC5,CC7; Fig. S7d-e), but involves one of the two chromatids already involved in the CO, and falls within the 1.5 kb inter-event threshold. Central CO gaps are considered compatible if there are trans hDNA patterns either side of the 6:2 segment. However, unlike the case with NCOs, the trans patterns can be across two chromatids if the 6:2 segment is at the CO point (e.g. CC1; Fig. S7b). In this latter case then the strand orientation phasing can be taken into account, and for all COs where the phasing of both chromatids was known, the hDNA patterns are confirmed to be in trans (e.g. CC5; Fig. S7d). CO 6:2 segments where strand orientation phasing of either chromatid is not known but display a trans hDNA-like pattern are retained in the compatible category (e.g. CC1-2; Fig. S7b). COs containing offset 6:2 segments are classed as compatible when the gap has full flanking trans hDNA (e.g. CC5; Fig. S7d), or half-hDNA which is in the correct phased orientation (e.g. CC7; Fig. S7e). COs containing offset 6:2 segments with hDNA in the incorrect orientation (where phasing was possible) are classified as incompatible. Note that the analysis included all CO events, including complex ones showing bi-directional conversions that involve at least two initiating DNA lesions on two non-sister chromatids (e.g. CC3, CC5, CC7; Fig. S7c-e) [START_REF] Marsolier-Kergoat | Mechanistic View and Genetic Control of DNA Recombination during Meiosis[END_REF] . Such events were included when the outcomes of the initiating lesions could be reasonably anticipated.

Overlap of 6:2 segments with annotated hotspots

To calculate hotspot overlap, 6:2 segments, up to but not including the non-6:2 flanking markers, were tested for their intersection with the coordinates of a list of previously annotated Spo11-DSB hotspots [START_REF] Mohibullah | Numerical and spatial patterning of yeast meiotic DNA breaks by Tel1[END_REF] , generating a binary, yes/no result for each 6:2 segment within each category (A-C). Proportions were then calculated and reported. For these analyses the Spo11-oligo datasets utilised were obtained from SK1 nonhybrid diploids.

Measuring Spo11 activity within, and surrounding 6:2 segments

To assess the correlation between 6:2 segment locations and local, population average, Spo11-DSB activity, each HR event was partitioned into 6:2 and non-6:2 segments, and the observed amount of Spo11-oligo signal [START_REF] Mohibullah | Numerical and spatial patterning of yeast meiotic DNA breaks by Tel1[END_REF] falling within each partition calculated. For this analysis, 6:2 segments were defined as the region up to but not including the non-6:2 flanking markers. Expected Spo11 signal for the 6:2 segment was calculated based on the fraction of total Spo11-oligo signal expected to fall within this segment were Spo11-DSBs arising uniformly across the entire event region. Finally, observed/expected ratios were calculated for each 6:2 segment within each category (A-C), and plotted as individual points on a log2 scale. Box-and whisker plots indicate median (horizontal bar), upper and lower quartiles of the range (box), and minimum and maximum points within 1.5-fold of interquartile range (whiskers). For these analyses the Spo11-oligo datasets utilised were obtained from SK1 nonhybrid diploids.

Analysis of exo1∆, mlh1∆ and mlh3∆ data in msh2∆ background

To determine the impact of abrogating the putative nicking activity promoted by Exo1, Mlh1 and Mlh3, previously published datasets [START_REF] Marsolier-Kergoat | Mechanistic View and Genetic Control of DNA Recombination during Meiosis[END_REF] were analysed using the methods described above. Due to the limited number of repeats (2 meioses for each genotype), and the expected similarity in phenotype of each null mutation [START_REF] Marsolier-Kergoat | Mechanistic View and Genetic Control of DNA Recombination during Meiosis[END_REF] , these data were pooled and analysed in aggregate ("exo-mlh∆") in order to increase statistical power.

Method for handling incomplete octads

Occasionally we encountered octads where a mother-daughter pair had not been separated correctly, resulting in a 'septad'-identified by a chromatid displaying no visible hDNA information. In these cases, we removed the affected chromatids from our analysis, and thus any HR events arising on these chromatids were subtracted from the total event count.

Electrophoretic mobility shift assays

DNA substrates were generated by annealing complementary oligos (sequences below).

Oligos were mixed in equimolar concentrations (10 mM) in STE (100 mM NaCl, 10 mM Tris-HCl pH 8, 1 mM EDTA), heated and slowly cooled. Substrates were 5′ end-labeled with gamma-32 P-ATP and T4 polynucleotide kinase and purified by native polyacrylamide gel electrophoresis. The core complex containing Spo11, Rec102, Rec104 and Ski8 from S. cerevisiae was purified from baculovirus-infected insect cells (Claeys Bouuaert et al., in preparation).

Binding reactions (20 µl) were carried out in 25 mM Tris-HCl pH 7.5, 7.5% glycerol, 100 mM NaCl, 2 mM DTT, 5 mM MgCl2 and 1 mg/ml BSA with 0.5 nM DNA and the indicated concentration of core complexes. Complexes were assembled for 30 minutes at 30 °C and separated on a 5% Tris-acetate-polyacrylamide/bis (80:1) gel containing 0.5 mM MgCl2 at 200 V for two hours. Gels were dried, exposed to autoradiography plates and revealed by phosphorimaging.

Oligonucleotides for substrate preparation

For

  many years, a mechanistic understanding of the nature of Spo11-DSB formation has remained out of reach. The features of Spo11-oligo and Spo11-DC sizes and locations broaden understanding of the meiotic recombination pathway to include concerted DSB formation and gap repair as a frequent and evolutionarily conserved feature of meiotic recombination, and provide a tantalising glimpse into how the elusive biochemistry of Spo11 works in vivo. patterns in S. cerevisiae octads in msh2∆ and tel1∆ msh2∆ are deposited in the following NCBI SRA archives, PRJNA479661 and PRJNA480956, respectively. Funding Statement D.J., V.G., T.J.C., and M.J.N. were supported by an ERC Consolidator Grant (311336), the BBSRC (BB/M010279/1), the Wellcome Trust (200843/Z/16/Z), and a Career Development Award from the Human Frontier Science Program (CDA00060/2010). B.L. and V.G. were supported by the ANR-13-BSV6-0012-01 and ANR-16-CE12-0028-01 grants from the Agence Nationale de la Recherche and a grant from the Fondation ARC pour la Recherche sur le Cancer (PJA20181207756). Work in the S.K. lab was supported by the Howard Hughes Medical Institute; MSK core facilities are supported by National Institutes of Health grant P30 CA008748.

Fig. S7g )

 S7g Fig. S7g) are considered highly compatible because the hDNA segments are suggestive of repair synthesis tracts. NCO 6:2 segments flanked by hDNA in cis orientation are classed as incompatible. NCO 6:2 segment with hDNA on only one side are classified as compatible if

Figure 1 .

 1 Figures and Legends

Figure 2 .

 2 Figure 2. Identification of Spo11-DC within whole-genome Spo11-oligo libraries. Spo11-oligos 16 isolated from the indicated strains were remapped using paired-end Bowtie2 alignment. a, Size distribution of all Spo11-oligos reveal periodic peaks >40 bp. b-d, Nucleotide composition of Spo11 oligos of the indicated size was computed for each base position, revealing Spo11 signature at both ends (c), or Spo11 signature at 5′ end plus Mre11 signature at 3′ end (b, d). e, Size distribution of the Spo11-oligo library after filtering to retain only those molecules that are part of a complementary pair with the expected 2 bp 5′ overhang created by Spo11 cleavage at both ends (Spo11-DCs). f, Ratio of filtered to total Spo11 oligos as a function of molecule length. g, Nucleotide composition of the 43-nt filtered molecules. h, Percentage of total Spo11-oligo library in the filtered (Spo11-DC) set for indicated size ranges. i, In vitro double-end binding assay. Spo11 associated with partners Rec102, Rec104 and Ski8 ('core complex') was incubated with short double-stranded DNA substrates with 2-nt 5′ overhangs, thereby mimicking the product of Spo11-mediated cleavage. The core complex binds such DNA ends with high affinity (Claeys Bouuaert et al., in preparation). j, The formation of double-end bound complexes was quantified with DNA substrates of different lengths. Double-end binding was efficient when the substrates were 25, 24 bp, and 30 bp or longer (Fig.S2e).

Figure 3 .

 3 Figure 3. Fine scale analysis of Spo11-DCs within DSB hotspots. a-c, Arc diagram of Spo11-DCs mapped within three representative hotspots: strong (a), narrow (b), wide/complex (c). Top panel, unfiltered strand-specific Spo11 oligos (Franklin, red; Crick, blue; HpM, hits per million mapped reads). Arcs link 5′ ends of each Spo11-DC (i.e., filtered Spo11 oligos, Fig. 3a). Lower panel, smoothed unfiltered strandspecific Spo11-oligos, overlaid with frequency histogram of Spo11-DC midpoints (grey). Note the spatial association of Spo11-DC sub-domains with Franklin-Crick strand disparity. d-h, Strand disparity at Spo11-oligo 5′ ends is a genome-wide feature of Spo11-DCs. Average strand-specific Spo11-oligo signal (d), and strand ratio (e), centred upon the strongest Spo11-DC midpoint (asterisks in a-c) within every annotated DSB hotspot (3910 loci). Strand ratio (Franklin/Crick for total Spo11-oligo HpM) was computed at the left and right 5′ end of every unique Spo11-DC molecule (Fig. S3b), stratified by length (f-g). Strand ratio differential (h) indicates the fold difference in the ratios when comparing the left and right 5′ ends of each Spo11-DC molecule (Fig. S3b).

Figure 4 .

 4 Figure 4. Identification of gap repair events during meiosis. a, Gap repair is predicted to generate segments of 6:2 marker segregation flanked by 5:3 segments in mismatch repair-deficient strains. b-d, Quantification of recombination event types in (b) control (msh2∆), and (d) pooled exo1∆ msh2∆, mlh1∆ msh2∆, mlh3∆ msh2∆ ('exo-mlh∆ msh2∆') strains based on representative categorisations presented in (c) based on the patterns of flanking heteroduplex DNA marker segregation (trans, cis, none). Upper panels in (c) are the genotype calls made at each SNP marker (vertical line). Adjacent segments of the same genotype are joined with horizontal bars (red or blue) to aid visualisation of patterns. Each horizontal bar is sequenced haplotype from one meiotic octad. 6:2 segments are indicated in pale blue. Lower panels are smoothed histograms of total Spo11-oligo (blue) and the filtered Spo11-DC signals (purple). e, Frequency of 6:2 segments per event was calculated for each category and genotype. P values indicate Z-test of proportions relative to msh2∆. f, Fraction of 6:2 segments (msh2∆) overlapping annotated hotspots. g, Log2 ratio of observed Spo11-oligo density within each 6:2 segment divided by the mean Spo11-oligo density within the entire event, in msh2∆, for each category. P values indicate Z-test of proportions (f) and Kruskal-Wallis H-test (g).

Figure 5 .

 5 Figure 5. Fine-scale analysis of SPO11-DCs within mouse DSB hotspots. Mouse SPO11-oligo libraries 15 were remapped using paired-end Bowtie2 alignment. a-c, SPO11-oligo length distribution of the entire (a) and reciprocally filtered (b) library enriches peaks in Atm -/-(c) that display a ~10 bp periodicity. As for S. cerevisiae, SPO11-DCs are defined as filtered molecules >30 nt in length. d, Percentage of total SPO11 oligos that are SPO11-DCs, plotted for every hotspot. P value indicates Kruskal-Wallis H-test. e, Total Atm -/- SPO11 oligos were filtered into two size classes then aggregated around ~21,000 hotspot centres revealing a strandspecific disparity for Spo11-oligos >30 nt. f-g, Representative arc diagrams of SPO11-DCs (grey-scale frequencyweighted arcs) in wild-type and Atm -/-relative to total strand-specific SPO11 oligos (upper, raw; lower, smoothed; red, Franklin; blue, Crick). Percentage of total SPO11 oligos that are SPO11-DCs is indicated.

Figure 6 .Supplementary Figure 2 .

 62 Figure 6. Model for Spo11-DC formation. a, Hotspot DNA interacts with multiple Spo11-dimers (pale orange ellipses) bound within a relatively flat surface. Single or coincident DSBs may form depending upon spatially-periodic favoured interactions between Spo11 and the repeating structure of the DNA helix (dark orange Spo11 dimers). b, Coincident DSB formation generates internal Spo11-DCs with lengths that are multiples of the helical pitch (~10.5 bp). Resection initiates efficiently in the flanking regions generating short, external, Spo11-oligos, and inducing gap repair. c, Single DSBs are processed by nucleases on both sides, but resection proceeds less efficiently within the axis-associated DNA, generating a Spo11oligo length asymmetry and consequent mapped strand disparity (see also Fig. S9).

Acknowledgements

We thank Shintaro Yamada for help analysing the mouse Spo11-oligo datasets, Marie-Claude Marsolier-Kergoat for sharing Python scripts, Jesús Carballo and Michael Lichten for sharing S. cerevisiae strains containing relevant constructs (tel1∆::hphNT2 and sae2∆::kanMX6, respectively), and Rachal Allison for critical reading of the manuscript.

Data availability

Raw S. cerevisiae and mouse Spo11-oligo FASTQ data were obtained from published archives GSE84896 and GSE84689 respectively. Nucleotide-resolution maps generated by paired-end Bowtie2 alignment are provided as supplementary files. The S. cerevisiae maps generated here were equally-mixed pools of the following biological samples: wild type, GSM2247761-GSM2247765; tel1∆, GSM2247766-GSM2247769, GSM2354276, and GSM2354277). For mouse, maps used here were generated from the following biological samples: wild type, GSM2247728; Atm -/-, GSM2247731. FASTQ files used for mapping HR

Author contributions

M.J.N. and V.G conceived the project and prepared the manuscript. D.J., V.G, C.C.B., and M.J.N performed physical analysis of Spo11-DCs. M.C. prepared and analysed whole genome recombination maps with B.L. advising upon the mechanistic interpretation. T.C. and M.J.N mapped and analysed Spo11-oligo library data. C.C.B. and S.K. contributed protein biochemistry and provided critical mechanistic interpretations. All authors helped write the manuscript.

Analysis of 6:2 recombination patterns in msh2∆ hybrid octad data

All analysed meioses included the msh2∆, which abrogates mismatch repair, thereby enabling the retention of heteroduplex DNA (hDNA) strand information, which then segregates (becoming homoduplex) in the first post-meiotic cell division (octad stage).

Whole-genome DNA libraries for each haploid member of every octad were independently prepared and barcoded using Illumina NexteraXT according to manufacturer's instructions, and sequenced at ~16-plex on a MiSeq using 2 x 300 bp paired-end reads, obtaining a minimum of at least 20x average genome coverage. Paired-end mapping, genotyping of the ~65,000 SNP and Indels present in each of the eight haplotypes in each octad, and HR event calling across each octad were performed as described [START_REF] Crawford | Separable roles of the DNA damage response kinase Mec1(ATR) and its activator Rad24(RAD17) within the regulation of meiotic recombination[END_REF] using publically available scripts (https://github.com/Neale-Lab/ OctadRecombinationMapping), generating Event Tables listing position, type, and detailed information describing each isolated HR event (Supplementary Tables XXX). An integral stage of event calling is the partition of the octad into genomic segments of identical adjacent marker segregation (e.g. 5:3, 6:2, 4:4, etc). As with prior work [START_REF] Marsolier-Kergoat | Mechanistic View and Genetic Control of DNA Recombination during Meiosis[END_REF] , an inter-event merging threshold of 1.5 kb was used-that is, a minimum of at least 1.5 kb of 4:4 marker segregation was necessary between two adjacent regions of non-4:4 marker segregation for the region to be recorded as two independent HR events. In HR events from msh2∆ mutants, segments of 6:2 marker segregation are not expected from simple models of DSB repair, but may arise due to either secondary nicking by an associated nuclease [START_REF] Marsolier-Kergoat | Mechanistic View and Genetic Control of DNA Recombination during Meiosis[END_REF] , or from initiation by an adjacent pair of Spo11-DSBs [START_REF] Martini | Genome-wide analysis of heteroduplex DNA in mismatch repair-deficient yeast cells reveals novel properties of meiotic recombination pathways[END_REF] -referred to here as a Spo11-DC.

In order to focus on events that may have arisen from putative gap repair-and compatible with the range of Spo11-DC sizes detected physically (Fig. 1)-events were filtered to include only those containing a 6:2 segment, and then further categorised depending upon the estimated length of the 6:2 segment, whether there was more than one 6:2 segment within the event (single vs multi), and the marker segregation patterns flanking the 6:2 segment (categories A, B, C; Fig. 4 and Fig. S7). Because of the perceived length (and visibility) of any segment is affected by local variant density, categorisations are inherently uncertain, but represent our reasonable estimates. Firstly, 6:2 segments were excluded from consideration when the maximum possible length of a 6:2 segment was <30 bp, and when the minimum length of a 6:2 segment was >150 bp. Whilst we don't exclude the possibility that coincident Spo11-DSBs separated by more than 150 bp might arise (e.g. Fig. 1c and Fig. S1a; [START_REF] Garcia | Tel1(ATM)-mediated interference suppresses clustered meiotic double-strand-break formation[END_REF] ), we favour the view that the more separated DSBs are, the more likely they will behave as two independent DSBs-each with two recombinationally-active DNA ends-and thus less likely to generate products compatible with a simple model of gap repair.

Additionally, most events were classified as Category C (ambiguous) due to lack of useful flanking heteroduplex information. Nevertheless, when possible, flanking heteroduplex segregation patterns were used to exclude some events (Category B, incompatible)-for example, when the flanking hDNA was in cis, rather than trans orientation (Fig. 4c). In other instances strand polarity information-inferred from the overall phasing of the haplotypes based on NCO trans hDNA patterns present elsewhere in the octad [START_REF] Marsolier-Kergoat | Mechanistic View and Genetic Control of DNA Recombination during Meiosis[END_REF] -were used to aid classification. NCOs without phasing information were classified as Category C S3b). e-f, Strand ratio (Franklin/Crick total Spo11-oligo HpM) was computed at the 5′ end of all observed (unfiltered) Franklin or Crick strand Spo11 oligos (as in Fig. S3c). Unlike at Spo11-DC sites (Fig. 3f-h), bulk Spo11 oligos, across all sites, display no strand disparity in either wild type (e) or tel1∆ (f) strains. Supplementary Figure 7. Categorisation of events containing short 6:2 segments. (Related to Fig. 4) a, Summary of frequencies of each subclassification event type for the indicated strains. Only events containing 6:2 segments 30 to 150 bp in length are considered. Events were separated into those with a single or multiple such 6:2 segments. Fractions of total for each subtype are not calculated for multi events because they frequently contain more than one sub-type. b-g, Example event sub-classifications. Genotype calls are made at each marker (vertical line). Adjacent segments of the same genotype are joined with horizontal bars (red or blue) to aid visualisation of patterns. Each horizontal bar is sequenced haplotype from one meiotic octad. 6:2 segments are indicated in pale blue. Event limits are indicated by beige (crossover) or pink (noncrossover) bars. Orientation of 5′ and 3′ strands are indicated in instances where it was possible to obtain phasing information from noncrossover trans events within the event, or from events elsewhere in the octad. In (c), a second segment of 6:2 segregation is not considered because the minimum length is >1.2 kb. h, To estimate probable detection rates of theoretical Spo11-DC of varying size, sliding windows of increasing size were moved across the reference genome, and the number of genetic markers within each window was recorded for each position. As examples, on average, Spo11-DCs 30 bp and 150 bp in size will be detected only 15% and 50% of the time, respectively. We note that due to the non-uniform distribution of genetic markers-in particular the slightly greater density within intergenic regions where Spo11 DSBs most often arise-the probability of detection may be slightly greater than that estimated from the genome-wide polymorphism density.

Supplementary Figures and Legends

Supplementary

Strain name

Genotype Origin VG296 MATa/alpha, ho::LYS2/", lys2/", ura3/", arg4/", leu2::hisG/", his4X::LEU2,/" nuc1::LEU2/", SPO11-His6-FLAG3-loxP-KanMX-loxP/"

This study

VG303

MATa/alpha, ho::LYS2/", lys2/", ura3/", arg4/", leu2/", his4X::LEU2,/" nuc1::LEU2/", SPO11-His6-FLAG3-loxP-KanMX-loxP/", sae2∆::KanMX6/"

This study VG300 MATa/alpha, lys2/", ura3/", arg4/", leu2/", his4X::LEU2,/" nuc1::LEU2/", SPO11-His6-FLAG3-loxP-KanMX-loxP/", tel1∆::HphMX4/"

This study VG302 MATa/alpha, lys2/", ura3/", arg4/", leu2/", his4X::LEU2,/" nuc1::LEU2/", SPO11-His6-FLAG3-loxP-KanMX-loxP/", tel1∆::HphMX4/", sae2∆::KanMX6/" Table S1. Strains used in this study.

Unless indicated, all strains are of the SK1 genetic background [START_REF] Kane | Carbohydrate metabolism during ascospore development in yeast[END_REF] . For recombination mapping in octads, haploids were mated directly prior to sporulation as described [START_REF] Marsolier-Kergoat | Mechanistic View and Genetic Control of DNA Recombination during Meiosis[END_REF][START_REF] Crawford | Separable roles of the DNA damage response kinase Mec1(ATR) and its activator Rad24(RAD17) within the regulation of meiotic recombination[END_REF] .


Audric Neveu

Vincent Pelé

Valerie Pralong
email: valerie.pralong@ensicaen.fr

Exploration of Li-P-S-O composition for Solid-State Electrolyte materials discovery

Keywords: solid state electrolyte, thio-LISICON, LPSO, LGPS, Ionic conductivity

A new solid state electrolyte in the system Li-P-S-O is reported with the composition of Li 3.2 PS 3.7 O 0.3 . This material is isostructural with Li 10 GeP 2 S 12 , LGPS-type structure. A higher conductivity and lower activation energy than other LPSO materials is reported due to the lattice volume slightly higher. In a full solid-state battery, our material exhibits higher performance than Li 10 GeP 2 S 12 thank to the formation of an effective SEI. These results indicate that Li-P-S-O system is very promising to find solid electrolyte and should be explored in order to improve the stability of the family of solid state electrolyte at ambient moisture.

Introduction

Li-ion batteries represent a growing market with the development of electric vehicles.

However, the Li-ion technology requires the use of a highly flammable non-aqueous liquid electrolyte that poses safety concerns [1]. Intensive research studies over the past 5 years have focused on the development of all solid state batteries, wherein solid electrolytes are a key components. Solid electrolytes must meet technological requirements such as high ionic conductivity in combination with negligible electronic conductivity, wide voltage window stability (0-5 V), chemical compatibility with cathode and anode materials, relatively simple fabrication at large scale and low cost [2]. Solid lithium conductors can be listed in three groups: inorganic ceramics, organic polymers and composite or hybrid electrolytes being a combination of the first two classes of materials [3]. Within the ceramics electrolytes several oxides with outstanding performances (conductivity in the range of 10 -4 -10 -2 S/cm) have been discovered, such as garnets Li 7 La 3 Zr 2 O 12 [4], perovskites Li 3x La 2/3-x TiO 3 [5], NASICON (Na,Li)M 2 (PO 4 ) 3 (M=Ge, Ti, Zr) [6] and LISICON Li 14 Zn(GeO 4 ) 4 [7]. Argyrodite-type electrolyte Li 6 PS 5 X (X=Cl, Br, I) [8] and thio-LISICON Li 3 PS 4 thioposphates have been extensively studied due to their superior ionic conductivity with respect to oxides (~10 - 3 S/cm). For Li 3 PS 4, the highest conductivity is obtained for the -Li 3 PS 4 form, stable from 195°C. These phases are promising due to the formation of a stable SEI with lithium displaying good cyclability and long-term compatibility [8]. Large efforts have been dedicated to stabilize -Li 3 PS 4 at room temperature by means of cationic substitution. As an example one can cite Li 3.25 [Si 0.25 P 0.75 ]S 4 [9] showing a conductivity of 1. 22 10 -3 S/cm at room temperature. Interestingly, Within the exploration of the system Li-(Si/Ge/Sn)-P-S, trying to generate thio-LISICON type structure, Kanno and co-workers [10] reported new thiophosphates with the general formula Li 4-x Ge 1-x P x S 4 (0 < x < 1) showing a conductivity of 2.2 10 -3 S/cm at room temperature. Amongst the different solid electrolyte compositions explored in this system (Li-(Ge/Si/Ge/Sn)-P-S), an ionic conductivity comparable to that of liquid electrolytes has been achieved for the composition Li 10 GeP 2 S 12 (LGPS) reaching a conductivity of 1.2 10 -2 S/cm at room temperature [11]. LGPS crystallizes in tetragonal space group with a body centered cubic lattice whereas the thio-LISICON family exhibits an orthorhombic structure with hexagonal close pack sulfur sub lattice which is found to be less favorable to the ionic conductivity [12]. The structure of LGPS (Fig. 1, [13]) consists of a 3D network of tetrahedra (Ge/P)S 4 and LiS 6 octahedra, which share a common edge and form a 1D chain along the c axis. These chains are connected by tetrahedra PS 4 and Li4S 4 by the sharing of a common corner. One-dimensional tunnels along the c-axis are occupied by mobile lithium cations in Li1 and Li3 sites. First principle calculations by Mo et al. [14] predicted the LiS 6 octahedrons were also participating to the conduction along the ab plane (0.9mS/cm), in addition to the lithium ion diffusion along the c axis (40mS/cm), leading to a 3D conductor for this structural family as illustrated by the lithium diffusion (Fig. 1b). In spite of the high conductivity displayed by LGPS, the large concentration of germanium makes this material expensive for widespread applications. Researchers have explored the replacement of germanium by other elements of the IVa group like tin [15], with potential to reduce the raw material cost by a factor of 3 [2], or silicon [16,17]. On Fig. 1c, the main phases showing a LGPS-type structure are reported and we clearly observe the large composition range that could be use. However, LGPS phase has a poor coulombic efficiency due the degradation of the cathode/Solid Electrolyte Interface (SEI) during charge, which results in the formation of a Li-depleted LGPS layer ultimately leading to capacity fading and increased impedance due to mechanical failure [18]. In addition, LGPS is also instable towards lithium metal anode: Li-Ge alloys, Li 3 P and Li 2 S were observed by in-situ XPS analysis leading to an increase of the interfacial resistance [19]. In an effort to increase the electrochemical stability window in LGPS, Sun et al. [20] investigated the partial substitution of sulfur by oxygen in Li 10 GeP 2 S 12-x O x (LGPSO) with 0<x<0.9, which result in an increase of the coulombic efficiency. Following this idea of oxygen-sulfur substitution together with the aim to reduce the amount of germanium, Kanno et al. [20,21] have discovered a new family of solid electrolytes based also on Thio-phosphate in the system Li 2 S-P 2 S 5 -P 2 O 5 , showing the

LGPS type structure, Li 3+5x P 1-x S 4-z O z (LPSO) with x = 0.03-0.08, z =0.4-0.8. Despite a lower ionic conductivity, LGPSO and LPSO solid electrolytes are showing a better stability when cycled in half-cells due to the partial substitution of S for O in LPSO. The SEI formed during the cycling of these compounds is more efficient and allows a much better coulombic efficiency [22].

Interestingly, A new stable composition was also discovered by Kanno group [23] in the system Li-P-S with the composition Li 9.6 P 3 S 12 (i.e. Li 3.2 PS 4 ). For such a composition, a mix valence is required and the phosphorous oxidation state is expected to be +4.8. This phase crystallizes also with the LGPS type structure and shows a good conductivity of 1. 19 10 -3 S/cm at room temperature associated with a good stability toward lithium metal with minimum irreversible capacity [25]. Note that this phase seems to be difficult to prepare with a high purity and was previously reported with 35 wt% of -Li 3 PS 4 as a secondary phase.

In this work, we report the synthesis and electrochemical characterizations of Li 3.2 P +4.8 S 3.7 O 0.3 . Indeed, based on the literature report, we believe that a partial substitution of S for O in Li 3.2 PS 4 will also lead to LGPS type structure with enhanced chemical stability properties and make also this phase easier to be prepared.

Experimental techniques

For the synthesis, we use classical mechanochemical synthesis followed by annealing at 200°C in sealed tubes under vacuum [17,25,26]. Li 2 S (Alfa Aesar 99.9%), P 2 S 5 (Aldrich 99%), P 2 O 5 (Alfa Aesar 99.99%), GeS 2 (home made with stoichiometric amount of Ge° and S in sealed tube at 500°C) and red phosphorus (Aldrich 99,99%) were used and all the chemicals were handled under a high purity argon atmosphere (H 2 O<0.1 ppm, O 2 <0.1ppm).

Regarding the source for the oxygen, we have tried different precursor such as Li 3 PO 4 , Li 2 O or P 2 O 5 . Interestingly, the synthesis was successful only starting from P 2 O 5 as precursor. Note therefore that we choose the oxygen concentration of 0.3 which corresponds to 7,5% of oxygen substitution. Such value is in the range of other substitution amount reported in the literature (between 2,5 and 17%). The precursors were weighed in stoichiometric ratios and ground by planetary milling for 35h at 500 RPM (Fritsh, 25 ml ZrO 2 bowls with 4 balls).

Bowls are scraped every 5 hours in order to peel off the powder from the walls. The mixture is then pelletized at 160 MPa, placed in a sealed tube with a carbon coating and then heated at 200°C for 4h for Li 3.2 PS 3.7 O 0.3 compounds and at 500°C for 4 hours to prepare the phase Li 10 GeP 2 S 12 .

Li 3.2 PS 3.7 O 0.3 was measured in capillary (radius = 0.25 mm, thickness = 0.01 mm) with a Philips X'Pert diffractometer with Bragg-Brentano geometry (CuK α1,2 radiation). Rietveld Refinement of the patterns was carried out using the Rietveld method in Fullprof suite software. Temperature X-ray diffraction analysis was carried out between 30 and 300°C using a Philips X'Pert diffractometer with Bragg-Brentano geometry (Co radiation). The specimen was put under vacuum and heated with a rate 1°C/min in chamber temperature. Diffraction data were collected from 10° to 50.0° in 2θ.

The thermal properties of the Li 3.2 PS 3.7 O 0.3 were investigated by combined Differential scanning calorimetry (DSC) and Thermogravimetric analysis (TGA) with a Netzsch STA 449F3. Sample was put under argon in alumina crucible and heated with a rate 1°C/min.

For impedance spectroscopy measurement, samples were pelletized (diameter = 10 mm, thickness ≈ 0.1 cm) under 160 MPa and gold plated. The sample is then placed in the Biologic Controlled Environment Sample Holder (CESH). A signal with an amplitude of 50 mV and frequencies between 1 MHz and to 0.1 Hz was applied using a frequency response analyzer (Solartron, 1260). Temperature was controlled by the Bio-logics Intermediate Temperature System (ITS) between 80°C and -40°C.

For symmetric cell, 50mg of Li 3.2 PS 3.7 O 0.3 was pressed at 255 MPa in the cell presented previously [24]. Li metal was then added on each side of the electrolyte and pressed with the screws of the cells. Note therefore that we only cycle at 0.1mA/cm 2 this type of cell. For cycling voltammetry, 50mg of Li 3.2 PS 3.7 O 0.3 was pressed at 255 MPa. Platine electrode was added on one side of the electrolyte and pressed at 255MPa. Lithium metal was added on the other side of the electrolyte and pressed with screws of the cells. For full cells, two mixtures are prepared. A mixture of 70w% of pure LiNi x Co y Al z O 2 (NCA) without any coating and 30w% of electrolyte, which forms the positive electrode, and a mixture with 66w% of graphite (MGPT16) and 33w% of electrolyte, which forms the negative electrode. For assembling, About 40 mg of an electrolyte was pressed at 255MPa and then negative and positive electrodes (about 15mg for each) were pressed on each side of the electrolyte at 255MPa. The calculated loading was about 38 mg/cm² (surface of the cell is 0.28cm²). The pressure is maintained by the screws of the cell. Half-cell were made with the same protocol: about 40mg of Li 3.2 PS 3.7 O 0.3 was pressed at 255 MPa and a mix of NCA/electrolyte was pressed on one side of the electrolyte at 255MPa. The lithium was finally added on the other side of the electrolyte and pressed with screws of the cells The amount of H 2 S generated from the lithium solid electrolyte exposed at ambient was measured with a H 2 S sensor (Croncow, Gasman). About 30±2 mg of powder was placed in 4000 cm 2 desiccator. In order to insure a constant humidity level, 20mL of H 2 O are placed in the desiccator. The H 2 S (in mg/m 3 ) generated was calculated from the H 2 S concentration measured by the H 2 S sensor in ppm. For the conversion, we use 1mg/m 3 = (22.4/M H2S )=0.67ppm. Note that 7 mg/m 3 is the exposure limit value for the French standards from the National Research and Security Institute.

Results and discussion

The XRD pattern of the phase Li 3.2 PS 3.7 O 0.3 is reported on Figure 2. The material could be indexed with space group (P4 2 /nmc) and lattice parameters similar to those of other LGPStype compounds [11,23,27]. Despite our synthesis optimization, 5.23wt% of Li 2 S is still present as impurity. Our material is air sensitive therefore chemical analysis are difficult to do and in order to properly confirm the exact composition of this phase, a combined neutronsynchrotron analysis needs to be performed. Nevertheless, taking into account the 5% of Li 2 S impurity, one could hypothesis that the composition will be close to 'Li 3 P +4.8 S 3,6 0,1 O 0,3 '. The structural model reported for the phase Li 3.2 PS 4 were used as initial parameters for the Rietveld refinement [23]. Atomic positions and the occupancy of lithium were fixed. Smaller lattice parameters are observed for Li 3.2 PS 3.7 O 0.3 compare to Li 10 GeP 2 S 12 [11] and Li 3.2 PS 4 [23], (Table 1). A similar effect has been observed with other LPSO compound that was explained by the difference of the substituted element [27]. Germanium has an ionic radius of 0.39 Å while phosphorus has an ionic radius of 0.17 Å. Likewise with oxygen, which is smaller than sulfur (1.34 Å for 1.84 Å). As we substituted less sulfur than Li 3.35 P 0.93 S 3.5 O 0.5 , higher lattice parameters are observed for Li We test the thermal stability of our compound under argon by means of coupled DSC-TGA and also thermodiffraction (Fig. 3a). The phase Li 3.2 PS 3.7 O 0.3 is stable in the temperature range of 30-300°C under vacuum. Indeed, no change could be observed on the thermodiffraction. Only 2Wt% of mass change is observed between 25°C and 150°C on TGA, associated with a small variation on the DCS response and could be ascribe to a surface reaction (Fig. 3b). No phase crystallization is observed, suggesting that there was no amorphous phase in the composite. The impedance response consists of a succession of resistance and a constant-phase element (CPE) in parallel, with all being in series with a CPE. The capacity of the CPE can be estimate with the Brug formula [28]:

With Q 0 and  the CPE parameters. The capacity calculated for the first and second cycle is about 10 -12 F and 10 -9 F respectively. Following this values, the first cycle can be attribute to the bulk conductivity and the second to the grain boundary conductivity [29]. The total conductivity is obtain by summing the value of the two resistance. These conductivities are reported in an Arrhenius diagram with others compounds from literature (Fig. 4c). The total conductivity of our compound is 1. 19 10 -4 S/cm at 25°C (Table 1). This value is one order lower than Li 3.2 PS 4 , consistent with the smaller lattice volume [23]. However, this ionic conductivity is higher than other LPSO as the lattice volume is higher [27].

The activation energies were calculated from linear extrapolation of the Arrhenius plot.

The values obtained for Li 3.2 PS 3.7 O 0.3 was 33.9 kJ/mol (0.35 eV). This value is larger than Li 3.2 PS 4 but lower than Li 3.35 P 0.93 S 3.5 O 0.5 meaning that stronger electrostatic attraction between O atoms and Li ions have a function in conduction mechanism. The ionic conductivity and activation of energy of the best-reported thio-LISICON solid electrolytes are compared in Table 1. Even if the pure LGPS shows better conductivity than LPSO type phases with a conductivity one order of magnitude higher, due to the reaction between Ge and lithium reported in literature [30], we expect a better electrochemical stability of our material. Then, a symmetric Li/Li 3.2 PS 3.7 O 0.3 /Li cell was configured to demonstrate the cyclability and long-term compatibility of this composition with metallic lithium. The flat voltage-time profiles of the solid electrolyte symmetric cells are shown in Figure 5 at a current of 0.1 mA/cm 2 . They exhibit a good cycling stability of discharge and charge and good compatibility between solid electrolytes and lithium metal compare to the cell with

LGPS. The overpotential of our material during cycling remains stable around at 25 mV after 25 cycles whereas the overpotential of Li/LGPS/Li reach 50 mV. Note that in addition to the large polarization increase upon cycling for the Li/LGPS/Li cell, one observe for each current step, a potential decrease versus time. Such behavior characterize a poor conductivity at the interfaces, suggesting an insulating SEI formation. The resultant dc Li ionic conductivity ( dc ) can be derived from the polarization voltage divided by the applied current. Thus, we found a  dc of 2.2 10 -4 S/cm. This value is consistent with the one obtained from the Nyquist plot from EIS measurement ( ac = 1.19 10 -4 S/cm). When comparing with the cycling behavior of the symmetric cell with LGPS, it is clear that our material is compatible with metallic lithium electrode.

For the CV measurement (Fig. 5b), we use a potential window -0.2 -5 V vs Li + /Li with a scan rate of 10mV/s in a Li/Li 3.2 PS 3.7 O 0.3 /Pt cell. No significant redox peaks (expecting the one at 0.0V) are observed in the potential window of 0 to 5V vs Li + /Li, showing then the excellent electrochemical stability of this material that could be used in a wide voltage range.

Note that the small current observed between 0.25 and 1.25V could be due to the low ionic conductivity of this material. As our material showed good result with symmetric cell and CV measurement, we tested it as solid electrolyte in half all-solid-state batteries. Half-cell were assembled with LiNi 1/3 Co 1/3 Al 1/3 O 2 (NCA) as active material. The positive electrode is a mixture of NCA and Li 3.2 PS 3.7 O 0.3 at a weight ratio of 7:3 in order to ensure a good ionic conductivity between different solid element [31]. The first 5 cycles of this cell at a rate of C/40 are represented on Figure 6a. The first charge gives a capacity of 166 mAh/g and an irreversible of 56 mAh/g is observed during the the first discharge. This irreversible implying some Li was consumed in the 1 st cycle probably by interfacial reactions [23,31]. The other charge-discharge showed a good reversibility of about 100mAh/g. The small change between each cycle can by explained by our cell that is not designed for lithium metal which is a very soft metal.

Then, we test Li 3.2 PS 3.7 O 0.3 as solid electrolyte in full all-solid-state batteries. Full cells were assembled with the same active material as half-cell (NCA) and graphite as negative material. The same mixture as the half-cell is used for active material and mixture of graphite and Li 3.2 PS 3.7 O 0.3 at a weight ratio of 66:33 is used as negative material. Figure 6b shows 10 charges and discharges curves of the solid-state full-cell battery at a rate of 0.05 C (I=0.038mA/cm 2 ) made with Li 3.2 PS 3.7 O 0.3 material. The first charge achieves a capacity of 180 mAh/g. However, as we observed with half-cell, a large irreversible capacity were observed at the first cycle (50mAh/g), implying some Li was consumed in the 1 st cycle probably by interfacial reactions [23,31]. The performance of Li 3.2 PS 3.7 O 0.3 have been compared with Li 10 GeP 2 S 12 (Fig. 6c,d). Li 10 GeP 2 S 12 showed a coulombic efficiency of 18% in the first cycle. As the literature already shown, the lowest performance of Li 10 GeP 2 S 12 comes to a none-effective SEI formation [19,22,31]. A more effective SEI was formed with Li 3.2 PS 3.7 O 0.3 as a better coulombic efficiency is observed (71%). These interface result in better performance. For Li 3.2 PS 3.7 O 0.3, the first discharge has a capacity of 128 mAh/g and the 10 th keep a capacity of 110 mAh/g where Li 10 GeP 2 S 12 reports at the first discharge a capacity of 29.7 mAh/g and fading to 12.7 mAh/g for the 10 th discharge. Kanno demonstrated the same trend for LGPS in his paper [20]. In order to evaluate the stability in ambient environment, these compounds were exposed to humidity of the ambient atmosphere. Figure 7 shows the H 2 S amount generated from LPSO compound, Li 2 S and Li 10 GeP 2 S 12 . The new synthetized compound shows a weak stability at ambient moisture, which is due to the 5wt% of Li 2 S impurity. The gas released after 30 min for Li 3.2 PS 3.7 O 0.3 is 25 mg/m 3 . This value is more than 2.5 times the amount of gas released for Li 10 GeP 2 S 12 (10 mg/m 3 ) but consistent with the value that is expected with a material containing 5% amount of Li 2 S as impurity.

Figure 1 :

 1 Figure 1: Projection of Li 10 GeP 2 S 12 structure showing the 1D tunnel along the c axis

Figure 3 .

 3 Figure 3. Thermodiffraction of Li 3.2 PS 3.7 O 0.3 under vacuum (a) and DSC-TGA plot under

Figure 4 .

 4 Figure 4. Nyquist impedance plots for Li 3.2 PS 3.7 O 0.3 from -40°C to 80°C (a) and at -40°C

Figure 5 .

 5 Figure 5. Lithium cyclability in the symmetric Li/ Li 3.2 PS 3.7 O 0.3 /Li and Li/LGPS/Li cells under a current density of 0.1mA/cm 2 at room temperature (a) and Cycling voltammetry of a

Figure 6 :

 6 Figure 6: Charge-discharge profiles of half cells NCA:Li 3.2 PS 3.7 O 0.3 /Li 3.2 PS 3.7 O 0.3 /Li° at a

Figure 7 .

 7 Figure 7. H 2 S amount generated from Li 3.2 PS 3.7 O 0.3 , Li 2 S and Li 10 GeP 2 S 12 compound after

Table 1 .

 1 3.2 PS 3.7 O 0.3 . Lattice parameter, volume cell, conductivity and activation energy of Li 3.2 PS 3.7 O 0.3

					Conductivity	Activation
		a (Å)	c (Å)	V (Å3)
					(S/cm)	energy (kJ/mol)
	Li 10 GeP 2 S 12				12 10 -3 (25°C)	24.0 (25 eV)
		8.71771(5) 12,63452(10)	960.20
	LGPS [11]
	Li 3.2 PS 4 [23]	8.7144(4)	12.4677(7)	946.80	1.19 10 -3 (27°C)	28.0 (0.29 eV)
	Li 3.35 P 0.93 S 3.5 O 0.5 [27]	8.3702(3)	12.3023(6)	861.92(6)	8.76 10 -5 (27°C)	36.6 (0.38 eV)
	Li 3.2 PS 3.7 O 0.3 [this				1.19 10 -4 (25°C)	33.9 (0.35 eV)
		8.591(1)	12.315(1)	908.912(1)
	work]

and different compounds from literature. Figure 2. Rietveld refinements of XRD pattern of Li 3.2 PS 3.7 O 0.3 .

Acknowledgement

The authors thank J. Jean, S. Gascoin for technical help and M. Diaz-Lopez for scientific discussions. We gratefully acknowledge the CNRS, the Minister of Education and Research, Normandy region and SAFT through the contract SAFT-CNRS n°2019-42356.

Conclusions

New compound from LPSO family was synthetized by typical ball milling-annealing synthesis. The structure of Li 3.2 PS 3.7 O 0.3 is isostructural with Li 10 GeP 2 S 12 with smaller lattice volume. This compound exhibit a higher conductivity and lower activation energy than other LPSO material, as the lattice volume was slightly higher than other LPSO. In a full solid-state battery, synthetized LPSO exhibits higher performance than Li 10 GeP 2 S 12 thank to the formation of an effective SEI. A combined neutron diffraction and X-ray synchrotron study will be necessary to refine the structure and access to the chemical composition with accuracy. These results indicate that Li-P-S-O system is very promising as solid electrolyte and should be explored in order to improve the stability of the family of solid-state electrolyte at ambient moisture.