Hakanpää et al. show that reticular adhesions are assembled at flat clathrin lattices, a process inhibited by fibronectin and its receptor, integrin α5β1. This novel adhesion assembly mechanism is coupled to cell migration and reveals a unique crosstalk between cell-matrix adhesions. Reticular adhesions (RAs) consist of integrin αvβ5 and harbor flat clathrin lattices (FCLs), long-lasting structures with similar molecular composition as clathrin-mediated endocytosis (CME) carriers. Why FCLs and RAs colocalize is not known. Here, we show that RAs are assembled at FCLs in a process controlled by fibronectin (FN) and its receptor, integrin α5β1. We observed that cells on FN-rich matrices displayed fewer FCLs and RAs. CME machinery inhibition abolished RAs and live-cell imaging showed that RA establishment requires FCL coassembly. The inhibitory activity of FN was mediated by the activation of integrin α5β1 at Tensin1-positive fibrillar adhesions. Conventionally, endocytosis disassembles cellular adhesions by internalizing their components. Our results present a novel paradigm in the relationship between these two processes by showing that endocytic proteins can actively function in the assembly of cell adhesions. Furthermore, we show this novel adhesion assembly mechanism is coupled to cell migration via unique crosstalk between cell-matrix adhesions.  Integrins are nonenzymatic dimeric transmembrane receptors that recognize ECM components. These mechanosensory proteins govern cell adhesion to the ECM maintaining correct tissue development and function, with elaborate connections to cellular homeostasis and disease . Ligand Cells can form a variety of integrin-based adhesions. Small integrin clusters engaged to the ECM, called nascent adhesions, form on the cell periphery and establish their connection to the actin cytoskeleton via adaptor proteins such as Talin. A balancing act of traction forces and signaling molecules determines whether nascent adhesions mature into larger and molecularly more complex focal adhesions FAs; . In migrRecently, a novel type of integrin-based cell adhesion was discovered . Called Intriguingly, RAs colocalize with large, persistent forms of clathrin structures at the cell membrane called flat clathrin lattices . These experiments were performed using U2Os cells with an endogenously GFP-tagged α adaptin 2 Sigma-Aldrich subunit . AP2 is a widely used CME marker that faithfully mirrors clathrin dynamics . We usedU2Os cells on non-coated dishes presented typical and abundant FCLs , we found that cells plated on non-coated dishes displaying fewer FCLs were predominantly lying on top of an FN-rich region of the culture .Next, we asked if the reduction in FCL proportions observed in FN-coated samples is a cell-wide effect or specific to cellular regions in direct contact with the extracellular substrate. For that, we used patterned dishes containing FN-coated regions interspersed with uncoated regions, where single U2Os-AP2-GFP cells could adhere simultaneously to both an FN- and a non-coated region. In line with a contact-dependent effect, low FCL proportions were observed in cellular regions in contact with FN whereas FCL proportion was high in cellular regions contacting non-coated surfaces .The abundance of an alternative splice variant of the clathrin heavy chain containing exon 31 was recently shown to increase the frequency of clathrin plaques in myotubes . We thusAs discussed in the introduction, FCLs localize to RAs. To check how ECM composition affects these structures, U2Os AP2-GFP cells plated on FN, VTN, Col IV, Col I, or LN111 and stained with the RA component integrin αvβ5 and—to be able to distinguish integrin αvβ5 on RAs or FAs—were also stained with an FA marker . Cells plated overnight without coating formed abundant RAs . On FN-cNext, we used our substrate patterning strategy to check if the local FN effects on FCLs were also similar for RAs. Strikingly, cells plated on patterned FN revealed that RAs, akin to FCLs, were completely inhibited on cellular regions in contact with FN. Cellular regions in contact with non-coated surfaces displayed many FCLs colocalizing with RAs while regions in contact with FN presented no RAs or FCLs . InteresNext, we checked if the effects we see in U2Os cells are also true for other cell lines. To avoid problems of overexpression, we endogenously tagged AP2 with either Halo tag or GFP in various human cell lines: HeLa , MCF7 , HDF , Caco2 , and hMEC . These cell lines presented a large variation in the amount of FCLs and the morphology of RAs. Importantly, these cells could be divided into two groups in terms of endogenous FN secretion, and this division clearly correlated with the amount of FCLs and RAs . U2Os, HWe next evaluated the response of these cell lines to FN precoating. In low-FN-producing cell lines , RA coverage dropped significantly . Among tTo evaluate if changes in the amount of RAs are reflected in the amount of FAs, we measure FA coverage  from U2Os, Hela, and MCF7. We did not observe any clear difference in the coverage of FAs for these three cell lines plated on uncoated or FN-coated dishes . These rFor all experiments so far, we used media supplemented with serum, which is known to contain ECM components, including FN. Given that our cells are left to attach overnight in this media, it would be reasonable to expect that the FN present in serum would coat the dishes and completely mask our results. To test why this does not seem to happen , we compTaken together, the presence of FN controls the formation of RAs and FCLs in a very similar manner and in different cell lines , suggestNext, we set out to dissect the relationship between the formation of FCLs and RAs. It has been shown that integrin αvβ5 is required for the establishment of FCLs . We confWhile all FCLs colocalize to RAs, FCL-free areas of larger RAs are rather common e.g., , which mTo confirm these results, we expressed the AP180 C-terminal fragment (AP180ct), which acts as a strong dominant negative of CME . AP180ctNext, we set out to visualize the dynamics of AP2 during RA formation. For that, we generated a double U2Os knock-in cell line AP2-GFP and integrin β5 (ITGB5)-mScarlet. RAs are remarkably stable structures  and theiTaken together, our results show that the relationship between FCLs and RAs is beyond a simple colocalization. In fact, our data reveal strict codependency, where FCLs are required for the stabilization and growth of integrin αvβ5 clusters, thereby establishing RAs, and vice versa, with integrin αvβ5 being required for the formation of FCLs .To understand the mechanism controlling the coassembly of FCLs and RAs, we turned our attention back to FN. While integrin αvβ5 binds to VTN at FAs and RAs, the major FN receptor is integrin α5β1 . First, In line with these results, integrin β1 silencing in U2Os-AP2-GFP cells plated on FN resulted in a high FCL proportion and large, prominent RAs . DespiteA significant increase in RAs was also seen in cells silenced for integrin α5, the α subunit which pairs with integrin β1 for FN binding . Taken tWhen bound to FN, integrin α5β1 translocates centripetally from FAs to form elongated structures called FBs along actin stress fibers. This movement generates long FN fibrils in a process called FN fibrillogenesis and is mediated by the cytoskeleton scaffolding protein Tensin1 . To deteNext, to determine which active integrin β1 pool is more important for the inhibition of FCLs and RAs, we silenced FAs and FB components on U2Os-AP2-GFP cells and plated them on FN. In accordance with the higher accumulation of active integrin β1 in FBs, silencing of Tensin1 led to a marked increase of RAs and FCLs accompanied by a reduction in the presence of active integrin β1 on the membrane , cells are laterally confined. U2Os-AP2-GFP cells were plated on slides with arrow- and H-shaped micropatterns either precoated with FN or not and stained for integrin αvβ5 and p-Pax and imaged to measure RA coverage. In addition, to measure integrin β1 activation, U2Os-AP2-GFP-ITGB5-mScarlet cells were plated similarly and stained for active integrin β1. Supporting our hypothesis, we could detect clear FCL and RAs in FN-coated micropatterns , FCLs and RAs were abundant and equally distributed at the edge and away from the wound . Within The extracellular environment is a key regulator of cellular physiology with integrins playing a key role translating the chemical composition of the extracellular milieu into intracellular signals. Among various mechanisms controlling integrin function, integrin trafficking via endocytosis and exocytosis plays a major role . Thus faOur results support the idea that FCLs and RAs are two sides of the same structure . PreviouWe observed that RA formation events are rare, which led us to use non-physiological conditions—a Cilengitide washout experiment—to detect them. Therefore, the physiological trigger leading to the formation of FCLs and establishment of RAs remains to be understood. VTN, the ligand for integrin αvβ5, could be considered a good candidate. However, as we show in Recent evidence showed that EGFR activation led to the enlargement of FCLs in an integrin β5 phosphorylation-dependent manner , pointinAnother key unknown aspect of RA formation by FCL and αvβ5 coassembly concerns how these structures can be molecularly differentiated from canonical endocytic events. The connection between integrin αvβ5 located in RAs and FCLs occurs primarily via the endocytic adaptors ARH and NUMB . ImportaRecently, a correlation was found between the presence of clathrin plaques and an alternatively spliced isoform of clathrin containing exon 31 in myotubes . We did E. coli infection, the CME machinery is co-opted to form a clathrin-based actin-rich adhesive structure for the bacteria called pedestal  correlated with integrin αvβ5 localizing to FAs over RAs . MoreoveGiven the fact that RAs are long-lasting cellular adhesion structures, it is tempting to hypothesize that these structures act as a “parking brake” for a cell. As the cell is triggered to migrate, this brake needs to be released for efficient cell movement. This process would be analogous to the loss of cell–cell contacts, which happens during epithelial to mesenchymal transition , but insWe showed that FN regulates CCAC assembly in all the cell lines we tested. However, how these in vitro findings will operate in vivo is still unknown. Even though the ECM composition in tissues is complex, the FN effect on CCAC formation is local and strictly contact dependent, which opens the possibility that, in vivo, tissues may use focal changes in ECM composition to control these structures.U2Os, U2Os-AP2-GFP, U2Os-AP2-halo, U2Os-AP2-GFP-ITGB5-mScarlet, HeLa-AP2-GFP, and HeLa-AP2-halo were cultured in MEM supplemented with 10% FBS (Gibco) and penicillin–streptomycin . HDF-AP2-halo and Caco2-AP2-halo were cultured in DMEM supplemented with 10% FBS (Gibco) and penicillin–streptomycin . MCF7-AP2-halo was cultured in DMEM supplemented with 10% FBS (Gibco) and penicillin–streptomycin , 2 mM glutamine, 5 µg/ml human insulin, and 1 µM sodium pyruvate. hMEC-AP2-GFP was cultured in MEGM complete medium (Lonza).The following primary antibodies were used: anti-human integrin β1 clones 12G10 , mAb13 , total integrin β1 , anti-human integrin αvβ5 clone 15F11 , anti-human integrin α5 clone SNAKA51 , anti-human Tensin1 , anti-human p-paxillin Y118 , anti-human-Talin1 , anti-α-tubulin , and anti-GAPDH . Corresponding secondary antibodies raised against rabbit or mouse IgG were purchased from Jackson Immunoresearch.To compare the effects of major ECM proteins on AP2 lifetimes, the glass coverslip areas (14 mm diameter) of imaging dishes (Mattek) were precoated with 10 or 20 µg/ml (300 μl in PBS) of the following ECM proteins: recombinant human FN , recombinant human VTN , Col IV , Col I , and LN111 . Coatings were incubated overnight at +37°C, except Col I, which was incubated at RT overnight, and LN111 was incubated at +4°C overnight. Alternatively, as non-ECM protein controls, 1% BSA  or 0.3% PLL  were used to coat the dishes overnight at +37°C. Throughout this study, the standard FN coating was always performed similarly, 10 µg/ml (300 μl in PBS), overnight at +37°C.To study local vs. global effects of FN, FN was mixed with 50 ng/ml of Alexa647-labeled BSA and used to precoat the imaging dishes overnight at +37°C. The coated surface was subsequently scratched with a needle to allow partial reappearance of non-coated surface. After scratching, the dishes were heavily rinsed with PBS. 20,000 U2Os-AP2-GFP cells were seeded on patterned imaging dishes to ensure sufficient single-cell attachment to border areas.The clathrin inhibitor AP180 C-terminal fragment  cDNA, from rat origin, was described previously . This coTransient transfections were carried out with PEI MAX transfection reagent  using 70% confluent U2Os cells.https://wge.stemcell.sanger.ac.uk//). gRNAs were cloned into pSpCas9(BB)-2A-Puro (PX459) V2.0  using BbsI sites and confirmed by Sanger sequencing.Three gRNA sequences (Integrated DNA Technologies) were designed using the Welcome Sanger Institute Genome online editing tool (gRNAs were transfected with the donor template for homologous recombination and the most effective gRNA (5′-TGCTACAGTCCCTGGAGTGA-3′), judged by the percentage of fluorescent cells by FACS, was used for single-clone selection, genotyping, and confirmation by microscopy.TGAGGGCAGGCGAGCCCCACCCCGGCCCCGGCCCCTCCTGGACTCGCCTGCTCGCTTCCCCTTCCCAGGCCCGTGGCCAACCCAGCAGTCCTTCCCTCAGCTGCCTAGGAGGAAGGGACCCAGCTGGGTCTGGGCCACAAGGGAGGAGACTGC-3′, where C-terminal tagging with GFP is in green (codon-optimized) and short linker in purple. 150-bp homology arms (orange) were incorporated via PCR amplification from a synthesized (IDT), codon-optimized monomeric EGFP.The donor template sequence was: 5′-GGCCAGCATCCTGGGGGGCCTCGTCTCACCCCAGGGTCTCCCCTCACACAGGTTTACACGGTCGTGGACGAGATGTTCCTGGCTGGCGAAATCCGAGAGACCAGCCAGACGAAGGTGCTGAAACAGCTGCTGATGCTACAGTCCCTGGAGGGAAGTGCATCTGGGAGCTCAGGCGCTAGTGGTTCAGCGAGCGGGGTGAGCAAGGGCGAGGAGCTGTTCACCGGGGTGGTGCCCATCCTGGTCGAGCTGGACGGCGACGTAAACGGCCACAAGTTCAGCGTGTCCGGCGAGGGCGAGGGCGATGCCACCTACGGCAAGCTGACCCTGAAGTTCATCTGCACCACCGGCAAGCTGCCCGTGCCCTGGCCCACCCTCGTGACCACCCTGACCTACGGCGTGCAGTGCTTCAGCCGCTACCCCGACCACATGAAGCAGCACGACTTCTTCAAGTCCGCCATGCCCGAAGGCTACGTCCAGGAGCGCACCATCTTCTTCAAGGACGACGGCAACTACAAGACCCGCGCCGAGGTGAAGTTCGAGGGCGACACCCTGGTGAACCGCATCGAGCTGAAGGGCATCGACTTCAAGGAGGACGGCAACATCCTGGGGCACAAGCTGGAGTACAACTACAACAGCCACAACGTCTATATCATGGCCGACAAGCAGAAGAACGGCATCAAGGTGAACTTCAAGATCCGCCACAACATCGAGGACGGCAGCGTGCAGCTCGCCGACCACTACCAGCAGAACACCCCCATCGGCGACGGCCCCGTGCTGCTGCCCGACAACCACTACCTGAGCACCCAGTCCAAGCTGAGCAAAGACCCCAACGAGAAGCGCGATCACATGGTCCTGCTGGAGTTCGTGACCGCCGCCGGGATCACTCTCGGCATGGACGAGCTGTACAAGPCR product was purified and 150 ng was used directly for transfection together with gRNAs. 70–80% confluent 24-well plates of U2Os cells were transfected with 2 µg PEI (1 µg/ml), 150 ng of plasmid, and 150 ng of the PCR product. In addition, hMEC-AP2-GFP were treated with 1 μM DNA-PKc inhibitor NU7441 for 48 h after transfection. 2 d after transfection, cells were treated with puromycin (1 µg/ml) to enrich for successfully transfected cells. After expansion, GFP-positive cells were sorted by FACS and single clones were expanded and genotyped.U2Os-AP2-halo and HeLa-AP2-halo cell lines were generated with the same protocol as the U2Os-AP2-GFP cell line.GGCCAGCATCCTGGGGGGCCTCGTCTCACCCCAGGGTCTCCCCTCACACAGGTTTACACGGTCGTGGACGAGATGTTCCTGGCTGGCGAAATCCGAGAGACCAGCCAGACGAAGGTGCTGAAACAGCTGCTGATGCTACAGTCCCTGGAGGGAAGTGCATCTGGGAGCTCAGGCGCTAGTGGTTCAGCGAGCGGGGCAGAAATCGGTACTGGCTTTCCATTCGACCCCCATTATGTGGAAGTCCTGGGCGAGCGCATGCACTACGTCGATGTTGGTCCGCGCGATGGCACCCCTGTGCTGTTCCTGCACGGTAACCCGACCTCCTCCTACGTGTGGCGCAACATCATCCCGCATGTTGCACCGACCCATCGCTGCATTGCTCCAGACCTGATCGGTATGGGCAAATCCGACAAACCAGACCTGGGTTATTTCTTCGACGACCACGTCCGCTTCATGGATGCCTTCATCGAAGCCCTGGGTCTGGAAGAGGTCGTCCTGGTCATTCACGACTGGGGCTCCGCTCTGGGTTTCCACTGGGCCAAGCGCAATCCAGAGCGCGTCAAAGGTATTGCATTTATGGAGTTCATCCGCCCTATCCCGACCTGGGACGAATGGCCAGAATTTGCCCGCGAGACCTTCCAGGCCTTCCGCACCACCGACGTCGGCCGCAAGCTGATCATCGATCAGAACGTTTTTATCGAGGGTACGCTGCCGATGGGTGTCGTCCGCCCGCTGACTGAAGTCGAGATGGACCATTACCGCGAGCCGTTCCTGAATCCTGTTGACCGCGAGCCACTGTGGCGCTTCCCAAACGAGCTGCCAATCGCCGGTGAGCCAGCGAACATCGTCGCGCTGGTCGAAGAATACATGGACTGGCTGCACCAGTCCCCTGTCCCGAAGCTGCTGTTCTGGGGCACCCCAGGCGTTCTGATCCCACCGGCCGAAGCCGCTCGCCTGGCCAAAAGCCTGCCTAACTGCAAGGCTGTGGACATCGGCCCGGGTCTGAATCTGCTGCAAGAAGACAACCCGGACCTGATCGGCAGCGAGATCGCGCGCTGGCTGTCGACGCTCGAGATTTCCGGCTGAGGGCAGGCGAGCCCCACCCCGGCCCCGGCCCCTCCTGGACTCGCCTGCTCGCTTCCCCTTCCCAGGCCCGTGGCCAACCCAGCAGTCCTTCCCTCAGCTGCCTAGGAGGAAGGGACCCAGCTGGGTCTGGGCCACAAGGGAGGAGACTGC-3′, where C-terminal tagging with halo is underlined (codon-optimized) and flexible linker region (GSASGSSGASGSASG) is bold. 150-bp homology arms  were incorporated via PCR amplification from a synthesized (IDT), codon-optimized monomeric halo tag.The donor template sequence was: 5′-The most effective gRNA (5′-TGCTACAGTCCCTGGAGTGA-3′) was ordered as single guide RNA (sgRNA) from Synthego, and Cas9 protein (purified in the lab) was used instead of plasmid. The donor templates for these cell lines to insert either EGFP or Halo tag were the same as above, respectively.5 cells were combined with 4 µg Cas9 protein, 45 pmol sgRNA, and 300 ng purified PCR product into a nucleofection cuvette. The nucleofection protocols were the following: MCF7-AP2-halo: EN130, buffer SF (Lonza #V4XC-2031); HDF-AP2-halo: EO114, buffer SF (Lonza #V4XC-2031); Caco2-AP2-halo: DG113, buffer SF (Lonza #V4XC-2031); HeLa-AP2-GFP: CN114, buffer SF (Lonza #V4XC-2031).2 × 10Cell lines were then treated with 1 µM DNA-PKc inhibitor NU7441 for 48 h after nucleofection.This cell line was produced by the same protocol as the U2Os-AP2-GFP cells with the following changes:ATATAACGGCACTGTTGACGGAAGTGCATCTGGGAGCTCAGGCGCTAGTGGTTCAGCGAGCGGGGTGAGCAAGGGCGAGGCAGTGATCAAGGAGTTCATGCGGTTCAAGGTGCACATGGAGGGCTCCATGAACGGCCACGAGTTCGAGATCGAGGGCGAGGGCGAGGGCCGCCCCTACGAGGGCACCCAGACCGCCAAGCTGAAGGTGACCAAGGGTGGCCCCCTGCCCTTCTCCTGGGACATCCTGTCCCCTCAGTTCATGTACGGCTCCAGGGCCTTCATCAAGCACCCCGCCGACATCCCCGACTACTATAAGCAGTCCTTCCCCGAGGGCTTCAAGTGGGAGCGCGTGATGAACTTCGAGGACGGCGGCGCCGTGACCGTGACCCAGGACACCTCCCTGGAGGACGGCACCCTGATCTACAAGGTGAAGCTCCGCGGCACCAACTTCCCTCCTGACGGCCCCGTAATGCAGAAGAAGACAATGGGCTGGGAAGCATCCACCGAGCGGTTGTACCCCGAGGACGGCGTGCTGAAGGGCGACATTAAGATGGCCCTGCGCCTGAAGGACGGCGGCCGCTACCTGGCGGACTTCAAGACCACCTACAAGGCCAAGAAGCCCGTGCAGATGCCCGGCGCCTACAACGTCGACCGCAAGTTGGACATCACCTCCCACAACGAGGACTACACCGTGGTGGAACAGTACGAACGCTCCGAGGGCCGCCACTCCACCGGCGGCATGGACGAGCTGTACAAGTAATGTTTCCTTCTCCGAGGGGCTGGAGCGGGGATCTGATGAAAAGGTCAGACTGAAACGCCTTGCACGGCTGCTCGGCTTGATCACAGCTCCCTAGGTAGGCACCACAGAGAAGACCTTCTAGTGAGCCTGGGCCAGGAGCCCACAGTGCCT-3′, where A = silent mutations in 5′ homology arm, flexible linker region (GSASGSSGASGSASG) is bold, and mScarlet is italic.The gRNA sequence was 5′-CAAATCCTACAATGGCACTG-3′ and the donor template was: 5′-GGTTTGAGTGTGTGAGCTAACATGTGTCCTCATCCTCTTCCCCGCCGTGTTCTGTAGGCTTCAAATCCATTATACAGAAAGCCTATCTCCACGCACACTGTGGACTTCACCTTCAACAAGTTCAACAAATCLentiviruses for shRNA production were produced using packaging plasmids pCMVR and pMD2.g and specific shRNAs in pLKO.1 vector as follows: 80% confluent HEK293T cells in DMEM supplemented with 10% FBS and 100 U penicillin–streptomycin were transfected using PEI MAX transfection reagent. 5 h later, the medium was changed to DMEM supplemented with 4% FBS and 25 mM Hepes. Media containing lentiviral particles were harvested after 48 and 72 h, filtered (0.45 µm), aliquoted, and stored at −80°C.U2Os-AP2-GFP cells were transduced with lentiviral media expressing respective shRNAs in the presence of Polybren 8 µg/ml  for 5 h and replaced with culture medium. 48 h later, puromycin (1 µg/ml) was added for 24 h to allow selection of transduced cells. Experiments targeting AP2 subunits were performed otherwise similarly but without puromycin selection. All shRNA-silenced cell lines were replated on non-coated glass-bottomed imaging dishes 1 d prior to imaging.ITGB5 shRNAs: TRCN0000057744 (5′-GCATCCAACCAGATGGACTAT-3′) and TRCN0000057745 (5′-GCTGTGCTATGTTTCTACAAA-3′).ITGB1 shRNAs: TRCN0000029644 (5′-CCTGTTTACAAGGAGCTGAAA-3′) and TRCN0000029645 (5′-GCCTTGCATTACTGCTGATAT-3′).AP2S1 shRNAs: TRCN0000060263 (5′-GACGCCAAACACACCAACTTT-3′), TRCN0000060266 (5′-GTGGAGGTCTTAAACGAATAT-3′), and TRCN0000060267 (5′-CACAACTTCGTGGAGGTCTTA-3′).AP2A1 targeting shRNAs: TRCN0000065108 (5′-GCTGAATAAGTTTGTGTGTAA-3′) and TRCN0000065109 (5′-GCACATTGACACCGTCATCAA-3′)Integrin α5 (ITGA5) targeting shRNAS: TRCN0000029651 (5′-CCACTGTGGATCATCATCCTA-3′) and TRCN0000029652 (5′-CCTCAGGAACGAGTCAGAATT-3′).Tensin1 targeting (TNS1) shRNAs: TRCN0000002953 (5′-GAGGATAAGATTGTGCCCATT-3′) and TRCN0000002954 (5′-CCCAAAGAAGGTACGTGCATT-3′).Talin1 targeting (TLN1) shRNA: TRCN0000123106 (5′-GCCTCAGATAATCTGGTGAAA-3′)The following sequences were targeted:Cell culture dishes were coated with 10 µg/ml of FN in a cell culture incubator or left uncoated. The next day, U2Os cells were plated to reach confluency in 24 h. RNA extraction, cDNA synthesis, and PCR followed those described by U2Os were silenced for respective proteins, as mentioned above, and lysed into 150 mM NaCl, 50 mM Tris, pH 8, and 1% NP-40 (Sigma-Aldrich). Protein concentrations were measured with the Pierce BCA kit (Thermo Fisher Scientific) and boiled in Laemmli loading buffer with 10% β-mercaptoethanol. Equal amounts of protein lysates were loaded onto SurePAGE Bis-Tris 4–20% gels (Genscript) and transferred either to 0.2 µm polyvinylidene difluoride (PVDF) or 0.45 µm nitrocellulose  membranes. Membranes were blocked in 5% BSA or skimmed milk for 1 h, incubated with primary antibodies at +4°C overnight, and HRP-conjugated secondary antibodies  for 1 h in RT. HRP was activated with Supersignal West Femto or Pico reagents (Thermo Fisher Scientific) and bands were detected with ChemiDoc XRS+ (BioRad).All live videos and images from fixed samples were acquired with the ONI nanoimager microscope equipped with 405, 488, 561, and 647 lasers, an Olympus 1.49NA 100× super achromatic objective, and a Hamamatsu sCMOS Orca flash 4 V3 camera. Image acquisition software used was NimOS. Fixed samples were imaged in RT and live imaging was carried out at +37°C. Used fluorochromes were GFP, mScarlet, JF-646, Alexa-488, Alexa-594, and Alexa-647.35,000 U2Os-AP2-GFP cells were plated on precoated/non-coated areas of the dish resulting in ∼70–80% confluence 16–20 h later, at the onset of imaging. Alternatively, shRNA-silenced cell lines were plated. After overnight culture, 25 µM Hepes was added and samples were subjected to live TIRF imaging in a preheated +37°C chamber.The ONI Nanoimager microscope set to TIRF angle was used to acquire AP2 lifetimes at the cell membrane from 300 frames (1 frame/s) with an exposure time of 330 ms. Each video represents endocytic events from two to three cells .Acute modulation of ligand binding activity for integrin β1 was achieved using the function-blocking antibody mab13 (0.3 µg/ml). U2Os-AP2-GFP cells were plated on FN, as explained above, and 16–20 h later subjected to live TIRF imaging. 0-min sample has no mab13 added to control baseline FCL proportions. Immediately after mab13 addition, 5-min time lapses were continuously collected until 35 min; control videos (time point 0) had no mab13 added.To acutely induce the inhibition of integrin αvβ5, we used the small molecular inhibitor Cilengitide . U2Os-AP2-GFP cells plated on non-coated imaging dishes were treated with Cilengitide for 15 or 45 min, fixed, stained, and imaged with the ONI Nanoimager microscope at TIRF angle and analyzed for the resulting reduction of RA coverage.U2Os-AP2-GFP-ITGB5-mScarlet cells were plated on non-coated imaging dishes and 1 d later confluent monolayers were treated with 1 µM Cilengitide for 15–25 min, during which most FCLs and RAs were dissociated from the cell membrane. Samples were then washed twice and immediately subjected to live TIRF imaging to detect the de novo formation of FCLs and RAs. 1-h time-lapses were acquired with the ONI Nanoimager microscope at TIRF angle, at 30 s intervals, with an exposure time of 100 ms for AP2 and 300 ms for integrin β5.For immunofluorescence experiments, cells were fixed with 4% paraformaldehyde–PBS for 15 min in a +37°C incubator, washed with PBS, and blocked with 1% BSA-PBS. Primary antibodies diluted in 1% BSA–PBS were incubated for 1 h, samples were washed with PBS, and secondary antibodies diluted in 1% BSA–PBS were let to bind for 30 min. Samples were imaged with the ONI Nanoimager microscope using a TIRF angle and exposure times of 500 or 1,000 ms.Clathrin assembly at the cell membrane was reduced by silencing two subdomains of AP2 or by overexpressing AP180 ct, which acts as a dominant negative for AP2. U2Os AP2-GFP cells silenced for AP2A1 shRNA #1 and #2 or AP2S1 shRNA #1, #2, and #3, and control shRNA, and plated on non-coated imaging dishes were fixed and stained for integrin αvβ5 and FA marker p-Pax. Alternatively, AP180 ct was overexpressed in U2Os AP2-GFP cells, and cells were plated on non-coated imaging dishes, fixed the next day, and stained for integrin αvβ5 and p-Pax. RA formation (integrin αvβ5 adhesions without FA marker) and FAs  were imaged using TIRF microscopy.We performed time-series experiments to block integrin β1 active conformation with the mab13 antibody or to inhibit integrin αvβ5 with Cilengitide. Experiments utilizing mab13 were performed with U2Os-AP2-GFP cells plated on FN-coated dishes to disfavor the preformation of FCLs and RAs. Mab13 (0.3 µg/ml) was added to replicate samples and fixed 15, 30, or 45 min later. Similarly, U2Os-AP2-GFP cells plated on non-coated dishes to favor the preformation of FCLs and RAs were treated with Cilengitide. Samples were stained for integrin αvβ5 and FA marker p-Pax and imaged using TIRF microscopy.Cilengitide washout experiments were developed to study acute reappearance of FCLs and RAs in cell cultures. Cells were treated for 15–25 min with 1 µM Cilengitide (or DMSO as control) and washed two times. Unwashed controls were collected. Washed samples were let to recover for indicated time points, fixed, stained for p-Pax, subjected to TIRF imaging, and analyzed for the reappearance of FCLs and RAs (RA coverage).U2Os-AP2-GFP cells silenced for integrin β1, integrin β5, integrin α5, or Tensin1 and controls were plated either on FN-coated dishes  or on non-coated dishes (control shRNA and ITGB5 shRNAs) and fixed the next day, 16–20 h later. Samples were stained for integrin αvβ5 and FA marker p-Pax and imaged using TIRF microscopy.U2Os-AP2-GFP or U2Os-AP2-GFP-ITGB5-mScarlet cells were seeded onto micropatterned glass coverslips (CYTOO) either precoated with FN 10 µg/ml or left uncoated. Excess amount  of cells were plated and monitored for attachment to the patterns. The cells plated on FN had attached in 1 h and the cells plated on non-coated micropatterns had attached in 4 h. After attachment, excess cells were carefully rinsed and the samples were fixed 16–20 h later, stained, and subjected to immunofluorescence analysis with TIRF microscopy.U2Os-AP2-GFP-ITGB5-mScarlet cells were plated confluent onto non-coated imaging dishes for 2 d. Fully confluent monolayers were wounded with a micropipette tip, washed twice with fresh complete medium, and let to migrate. 0-min samples were collected directly after wounding. After fixing, samples were stained and subjected to TIRF imaging. Tile images (5 × 1), starting at the edge of the wound, were acquired with a 25% overlap and stitched using the pairwise stitching plug-in Image J.n” refers to a movie, which contained two to four cells. To determine the proportion of FCLs, we used the output from u-track to count the number of pits (events lasting longer than 20 s and shorter than 120 s) and the number of FCLs  and p-Pax channels were transformed into binary masks using the Robust Automatic Threshold Selection function. The Robust Automatic Threshold Selection parameters used for segmentation  were defined by visual inspection for each experiment. The mask of the p-Pax channel was then subtracted from the mask of the ITGB5 (or αvβ5) channel using the “image calculation” function. This calculation results in a mask containing only the RAs . RA coverage was then calculated by dividing the area covered by RAs in the RA mask (integrated density/255) by the area of each marked cell (or cells) in the image. An illustration of this method is shown in Focal adhesion coverage  was calcFor the wound healing experiment, a line on the migration front of each image was manually drawn. This line was then used as a reference to automatically draw a box 100 pixels in width (11.7 µm). RA coverage (as above) was calculated for this box, which was then moved inward in the culture in 50-pixel steps, where the RA coverage analysis was repeated. Values are normalized to the average RA coverage on the three innermost areas in the culture.Events showing the appearance of both AP2 and ITGB5 were identified by visual inspection of videos. For the generation of graphs, we selected only events where we could unambiguously ensure that significant FCLs and ITGB5 signals were not present in the region for at least 3 min. For the events where an RA was established , left, tAP2, ITGB5, and p-Pax channels were segmented using the Robust Automatic Threshold Selection function (similarly to what was done in the RA coverage experiments). Individual AP2 spots were identified as regions of interest (ROIs) using the “analyze particles” function. The fluorescence intensity for each AP2 spot  was then measured from the original image. Using the same AP2 ROIs in the ITGB5 and p-Pax binary masks, we then classified each AP2 spot for their colocalization with either marker. In this case, an AP2 ROI with a non-zero signal in either mask was considered colocalizing. We used full images for these analyses.Individual cells were marked and AP2, ITGB5, and p-Pax channels were segmented using the Robust Automatic Threshold Selection function. RAs were defined as ITGB5 signals not colocalizing with p-Pax. In the conditions used for these experiments (FN + mab13), RAs were primarily individual spots. The colocalization of RAs to AP2 was classified by measuring the intensity of each RA region at the segmented AP2 channel.AP2, ITGB5, and P-Pax channels were segmented using the Robust Automatic Threshold Selection function. Each segmented AP2 spot had the fluorescence intensity measured from the original image. A 3 µm × 3 µm region was drawn around each AP2 spot and used to measure the intensity of FN from the original image. Data are presented as the fluorescence for each AP2 spot.n-values and individual repeats used in analyses. For multiple comparisons, one-way ANOVA was performed followed by Tukey’s multiple comparison. Pairwise comparisons were performed using two-tailed Student’s t test with two-tailed distributions. Data distributions were assumed to be normal, but this was not formally tested. All graphs and statistical calculations were performed with GraphPad Prism 9.Figure legends state the exact Review HistoryClick here for additional data file.SourceData FS1is the source file for Fig. S1.Click here for additional data file.SourceData FS4is the source file for Fig. S4.Click here for additional data file.SourceData FS5is the source file for Fig. S5.Click here for additional data file.


Scientific Reports 10.1038/s41598-023-31831-1, published online 20 March 2023Correction to: The original version of this Article contained errors in the Results and discussion, under the subheading ‘Mechanisms for Fe-DOMP formation and isolation’,FeCl3 + 6NaOH + 6DOM − COOH = 2Fe3 + 6DOM − COO− + 2NaCl3 + 6H2O.”“2now reads:FeCl3 + 6NaOH + 6DOM − COOH = 2Fe3 + 6DOM − COO− + 6NaCl + 6H2O.”“2The original Article has been corrected.


Correction to: Neuropsychology Review10.1007/s11065-022-09536-5g = 0.21” and “g = 0.21” were incorrect and should be corrected to “Hedges’ g = 0.20” and “g = 0.20”, respectively.In the original published paper, it was belatedly discovered that there was a data entry error in pages 1 and 15. The value of “Hedges’ The original article has been corrected.


We prove that there exists a global weak solution of this initial‐boundary value problem and provide a representation for the solution in terms of the solution of a Riemann–Hilbert problem. Using this representation, we obtain asymptotic formulas for the long‐time behavior of the solution. In particular, by restricting our asymptotic result to solutions whose initial data are close to the initial profile of the stationary one‐soliton, we obtain results on the asymptotic stability of the stationary one‐soliton under any small perturbation in H1,1(R+). In the focusing case, such a result was already established by Deift and Park using different methods, and our work provides an alternative approach to obtain such results. We treat both the focusing and the defocusing versions of the equation.We consider the nonlinear Schrödinger equation on the half‐line  It arises in a variety of situations such as the modeling of slowly varying wave packets in nonlinear media 1 and [A]2 denote the first and second columns of a 2×2 matrix A.–A is n×m matrix, we define |A|⩾0 by |A|2=Σi,j|Aij|2. Then |A+B|⩽|A|+|B| and |AB|⩽|A||B|.If –γ⊂C and 1⩽p⩽∞, we write A∈Lp(γ) if |A| belongs to Lp(γ). We write ∥A∥Lp(γ)≔∥|A|∥Lp(γ).For a (piecewise smooth) contour –C+={k∈C|Imk>0} and C−={k∈C|Imk<0} denote the open upper and lower halves of the complex plane.–R+=, that is, eσ^3A=eσ3Ae−σ3. Define the functions a(k) and b(k) byr(k) and Δ(k) byq is the constant appearing in the Robin boundary condition  lies in H1,1(R) and depends continuously on u0 whenever Δ has no real zeros.Proposition 2.1 Given u0∈H1,1(R+) and q∈R, define a(k), r(k), and Δ(k) by ((i)Δ(k) is continuous for Imk⩾0 and analytic for Imk>0.(ii)Δ(k) obeys the symmetry(iii)Δ(0)=−iq.(iv)k→∞, Δ(k) satisfiesAs (v)Δ(k)≠0 for all k∈R, then r∈H1,1(R). Moreover, the map u0↦r:H1,1(R+)∩{u0|Δ(k)≠0forallk∈R}→H1,1(R) is continuous.If  Δ(k) by –2.4). T. T, the following also hold:(a)|r(k)|<1 for all k∈R.(b)q<0, then Δ has no zeros in C¯+={k∈C|Imk⩾0}.If (c)q>0, then Δ has no zeros on R and exactly one simple zero in C+. Moreover, this zero is pure imaginary.If (d)q=0, then Δ(k)≠0 for all k∈C¯+∖{0}, but Δ(0)=0.If (e)a(k)≠0 for all k∈C¯+.In the defocusing case The statements of our main theorems involve four spectral functions ondition . The folλ=−1. Recall that we introduced the notion of a global weak solution in H1,1(R+) in Definition Proposition 2.2 Suppose λ=1 or λ=−1. Let q∈R and u0∈H1,1(R+). Then there exists a unique global weak solution in H1,1(R+) of the Robin IBVP for NLS with parameter q and initial data u0. Moreover, for each T>0, the data‐to‐solution mapping u0↦u is continuous from H1,1(R+) to C).Before stating our main results we also need the following well‐posedness result for the Robin IBVP. The proof, which is given in Appendix Remark 2.3q in  well‐posedness, we give an independent proof of Proposition q is constant is much easier to handle than the case considered in ⊂2 of μ. The second column of the Volterra Equation =∑l=0∞ψl converges absolutely and uniformly for x⩾0 and Imk⩾0 to a continuous function ψ. Using the uniform convergence of the series  satisfies ∈C1(R+) for each k∈C¯+ and the second column of =1 follows from =∑uation =ψuation =ψolumn of  follows uation =ψmmetries  then folmmetries . The uniows from  and the |U0(x′)|⩾0, we findx to ∞ gives∥u0∥L1(R+)⩽∥u0∥H1,1(R+), we obtainC>0 depends on u0 but is independent of x and k. Sincex⩾0 and Imk⩾0,□Let us prove . Equatio.Hence|ψ^olumn of  follows  obtain|ψ−olumn of  then fololumn of .□a(k)=μ22 and b(k)=μ12, we immediately obtain the following properties of a(k) and b(k).Corollary 3.2u0∈H1,1(R+), then a(k) and b(k) defined in ∩{u0|Δ(k)≠0forallk∈R} into H1,1(R).Lemma 3.3g↦f(x)≔∫x∞g(x′)dx′ is continuous H0,1(R+)→L2(R+).The linear map The next few lemmas are needed to show that g∈H0,1(R+). Then, by definition, g,xg∈L2(R+). The estimatef(x) is well defined and absolutely continuous. Also, f is bounded since limx→∞f(x)=0. Consider the Sobolev space H1(R)={h∈L2(R)|h′∈L2(R)}. A function h belongs to H1(R) if and only if k↦⟨k⟩h^(k) lies in L2(R), where h^(k)=∫Rh(x)e−ikxdx denotes the Fourier transform of h. Let us extend g(x) and f(x) to the negative real axis by setting g(x)=0 and f(x)=0 for x<0. Then, since ⟨x⟩g∈L2(R), the Fourier transform g^(k) of g(x) belongs to H1(R). Moreover, the Fourier transform f′^=ikf^ is well defined as a tempered distribution and, for a test function ϕ, we haveikf^(k)=g^(0)−g^(k) in the sense of distributions. Since g^∈H1(R), g^ is absolutely continuous and soAssume that H1(R)→L2(R). Since the Fourier transform is bounded H0,1(R)→H1(R) and the inverse Fourier transform is bounded L2(R)→L2(R), it would follow that the composition g↦g^↦f^↦f is a bounded linear map H0,1(R)→L2(R). Thus it only remains to show that the linear map (H1(R)→L2(R). To prove this, note thatMφ of φ is defined byφ↦Mφ is a bounded linear map L2(R)→L2(R). HenceH1(R)→L2(R).□Suppose that we can show that the mapg^↦−1ik∫g^↦−1ik∫E and ψ0 be as in −1=1+K+⋯ is the Neumann series. Properties of ψ can be obtained by analyzing the operator K. In the following, Lxp) denotes the space of Lkq(R)‐valued Lxp(R+)‐functions with the normLemma 3.4(Compare with 2 of μ∼ satisfies the Volterra equationK′ is the operator defined in , we have h1∈Lx∞) by Lemma h2∈Lx∞) by Lemma u0 has compact support, then b′(k)a′(k)=ϕ∈L2(R) so that a(k)−1 and b(k) lie in H1(R). To extend this result to the case of general u0∈H1,1, we consider the continuity of the u0‐dependence.Let us now again consider the case of a general potential u0,uˇ0∈H1,1(R+) and let ψ,ψˇ,ϕ,ϕˇ be the associated solutions of the Equations ) and ∥Δϕ∥Lx∞) in terms of ∥Δu0∥H1,1. Note that Δψ satisfies the Volterra equationu0,uˇ0 in bounded subsets of H1,1(R+). Moreover, using parts (d) and (f) of Lemma u0,uˇ0 in bounded subsets of H1,1(R+). Similarly, Δϕ satisfies the Volterra equationu0,uˇ0 in bounded subsets of H1,1(R+). The inequalities ∥L2 and ∥Δϕ∥L2 tend to zero whenever ∥Δu0∥H1,1 tends to zero, provided that u0,uˇ0 remain in a bounded subset of H1,1(R+). Since , a continuity argument implies that μ∈H1(R) for any u0∈H1,1(R+) and that the relation . We conclude that a−1,b∈H1(R) and that the maps in  lies in the weighted Sobolev space H1,1(R), but the spectral functions a(k)−1 and b(k) are not in H1,1(R). To proceed, we therefore need to subtract suitable constants.Lemma 3.7u0∈H1,1(R+) and define b1∈C bykb(k)−b1∈L2(R).Let We want to show that the reflection coefficient ψ=ψ1ψ2T, we haveb(k)=ψ1, we deduce from (kb(k)−b1∈L2(R). Here we have used that by the Fubini–Tonelli theorem, if f∈Lk2) or f∈Lx2), then ∥∥f∥Lx2∥Lk2=∥f∥Lk2∥Lx2.□If we expand Equation  in compouce from  and  and let ψ,ψˇ be the associated solutions of  hold also for the spectral function a(k). Namely, if for u0∈H1,1(R+) we define a1:=−λ2i∫0∞|u0(x)|2dx, then the mappingsk(a(k)−1)−a1∈L2(R); given this fact, the continuity follows by arguments similar to those used in the proof of Lemma k(a(k)−1)−a1∈L2(R), note that Equation (1⟨x⟩ is in Lx∞(R+)∩Lx2(R+), we can estimate the three terms on the right‐hand side of  as follows:∥k(a(k)−1)−a1∥Lk2<∞.Conclusions similar to those established in Lemma Equation  impliesEquation , we haveuation −uation  and to establish the continuity of the map u0↦r.Lemma 3.11u0∈H1,1(R+) and q∈R, define the reflection coefficient r(k) by the formula (Δ(k)≠0 for all k∈R, then r∈H1,1(R). Moreover, the map u0↦r:H1,1(R+)∩{u0|Δ(k)≠0forallk∈R}→H1,1(R) is continuous.Given  formula . If Δ(k)We are now ready to prove that We have↦fg:H1×H1→H1 is continuous. Since 2k+iq2k−iq∈1+H1(R), we see thata−1∈H1(R) by Lemma kb(k)−b1∈L2(R) by Lemma fa∈H1(R) and fb∈L2(R) such thata and b, we can writeb1∈C, fa∈H1(R), fb∈L2(R), a∈1+H1(R), b∈H1(R) depend continuously on u0∈H1,1(R+). Thus, using Lemma □By Lemma o Lemma u0↦F:H1,ow thatu0↦(2k−i3.3Δ(k) is continuous for Imk⩾0 and analytic for Imk>0. The symmetry (k=0 and using the unit determinant relation (Δ(0)=−iq. The asymptotic formula =Δ(k)/(2k−iq) be the function defined in |<1 for all k∈R if λ=1. This proves (a). To prove (b)–(d), we employ (b(−k¯)¯ from the right‐hand side of (Let fined in . A straifined in  shows thned in (1−λ|r(k)e employ  to elimi side of  and use  side of  to see tλ=1. Then Equation (a(k)≠0 for all k∈R, and thus (Δa(k)≠0 for all k∈R. Let ZΔa and PΔa denote the number of zeros and poles of Δa in C+ counted with multiplicity, and let Za denote the number of zeros of a(k) in C+ counted with multiplicity. Recalling the asymptotic formulas 2πi|k=−∞+∞ denotes the winding number of f(k) around the origin as k traverses the real axis from −∞ to +∞. On the other hand, by ≠0 for all k∈R, the assertions (b)–(d) about the zeros of Δ follow.Suppose now that Equation  implies and thus  shows thformulas  and a of the Robin IBVP, then the RH problem of Theorem m, and u can be recovered from m via (Proposition 4.1λ=1 or λ=−1. Let u0∈S(R+) be such that q≔−u0x(0)/u0(0)∈R. If λ=−1, suppose that Assumption u of the Robin IBVP for NLS with initial data u0. Then the RH problem of Theorem m and, for each ∈ be a smooth cut‐off function such that η is even, η≡1 in a neighborhood of 0, η(x)=0 for |x|⩾1, and ∫Rη(x)dx=1. Let u0e∈H1,1(R) be an extension of u0 to R such that u0e(x)=u0(x) for x⩾0 and u0e(x)=0 for x⩽−1. Standard mollifier arguments show that vε(x)≔∫Ru0e(y)ηε(x−y)dy, where ηε(x)≔η(x/ε)/ε, are smooth compactly supported functions such that vε(x)→u0e in H1,1(R) as ε↓0. If u0(0)≠0, then vε(0)≠0 for all sufficiently small ε, and we can obtain the desired sequence by settingε=1/(N+n) and N is large enough. If u0(0)=0, then by modifying u0e so that u0e(−x)=−u0(x) for all sufficiently small x>0, we may assume that vε(0)=0 for all small enough ε, and then straightforward estimates show thatε=1/(N+n) provides a sequence with the desired properties.□Let Lemma 6.2u0↦a and u0↦b are continuous H1,1(R+)→L∞(C¯+).The maps Δψ=KΔu0ψˇ+Ku0Δψ, where, by . Setting x=0 in this estimate, the lemma follows.□Using the same notation as in the proof of Lemma here, by , 3.9), , Δψ=KΔu0here, by ,| and suppose that the associated spectral functions Δˇ,aˇ satisfy Assumption u0 sufficiently close to uˇ0 in H1,1(R+). Moreover, if {ξi}1M are the simple zeros in C+ of Δ(k), then the maps u0↦M∈Z and u0↦∈CM are continuous at uˇ0∈H1,1(R+).Let q<0. The function Δa(k)∈1+H1(R) defined in  by Lemma Δa, and hence also Δ, is nonzero on R for any u0 sufficiently close to uˇ0. Moreover, Δa has the same number of zeros and poles in C+ as Δ, and Δa→1 as k→∞. Since Δ has no poles in C+, the argument principle applied to a large semicircle enclosing the upper half‐plane yieldsZΔ is the number of zeros of Δ in C+ counted with multiplicity. Using again that Δa(k)∈H1(R) depends continuously on u0∈H1,1(R+), we infer that the map u0↦ZΔ∈Z is continuous at uˇ0∈H1,1(R+).Suppose first that fined in  depends q<0, the function Δa has the same zeros as Δ in the upper half‐plane, and Cauchy's integral formula shows that if ξj∈C+ is a simple zero of Δa, thenγj is a small circle in C+ around ξj which contains no other zeros of Δa. By Lemma u0↦Δa is continuous H1,1(R+)→L∞(C¯+). Since Δa is analytic in C+, it follows that u0↦Δ˙a is continuous H1,1(R+)→L∞(K) where K is any compact subset of C+. Since the zeros {ξˇj}1M of Δˇ(k) are simple by assumption, we conclude that the zeros {ξj}1M of Δ(k) are simple and depend continuously on u0 for u0 in a H1,1(R+)‐neighborhood of uˇ0.Since Δa(k) show that the above conclusions hold also if q>0 (note that the identity (Δa replaced by Δb).□Analogous arguments applied to the functionidentity  holds alΔ is nonempty, we replace the poles in the RH problem of Theorem Dj⊂C+, j=1,⋯,M, be small disjoint open disks centered at the zeros ξj, j=1,⋯,M, of Δ. Let Dj∗ be the image of Dj under complex conjugation. Define the contour Γ by∂Dj is oriented clockwise and ∂Dj∗ is oriented counterclockwise. Let{cj}1M are the residue constants defined in (m satisfies the RH problem of Theorem m∼ satisfies the following RH problem.RH problem 6.4m∼) with the following properties.(a)m∼:C∖Γ→C2×2 is analytic.(b)m as k approaches Γ from the left (+) and right (−) exist are continuous on Γ, and satisfyv∼ is defined byThe boundary values of (c)m∼→I as k→∞.If the set of zeros of fined in . Then m Definition 6.5U⊂H1,1(R+) denote the set of all potentials u0∈H1,1(R+) such that the corresponding spectral functions satisfy the assumptions of Theorem λ=−1, then U consists of all u0∈H1,1(R+) for which the associated spectral functions satisfy Assumption if λ=1 and q<0, then U=H1,1(R+);if λ=1 and q>0, then U consists of all u0∈H1,1(R+) for which the RH problem of Theorem m for each ∈[0,∞)×[0,∞).if We let We next consider the set of all initial data for which the assumptions of Theorem h∈L2(Γ), we define the Cauchy transform Ch byC+h and C−h for the left and right boundary values of Cf on Γ. Then C+ and C− are bounded operators on L2(Γ) and given w∈L2(Γ)∩L∞(Γ), we define Cw:L2(Γ)+L∞(Γ)→L2(Γ) by Cw(f)=C−(fw).Lemma 6.6u0∈U and q∈R∖{0}. Then RH problem m∼ for each ∈[0,∞)×[0,∞) and this solution admits the representationw∼=v∼−I andLet For r∈H1,1(R). By Morrey's inequality, every function in H1,1(R+)⊂H1(R+) is Hölder continuous with exponent 1/2. Hence, if λ=−1, the unique existence of m∼ follows by the same vanishing lemma arguments already used to prove Proposition λ=1 and q<0, because in this case M=0. If λ=1 and q>0, then m, and hence also m∼, exists by assumption. Standard theory for RH problems then yields the representation formula . Moreover, the mapμ∼ is defined by  is continuous. Recalling the definition ↦v−I:[0,∞)2×U→(L2∩L∞)(R) is continuous. On the other hand, since Δa∈L∞(C+) depends continuously on u0∈H1,1(R+) by Lemma ξj depends continuously on u0∈U by Lemma Δ˙(ξj)∈C depends continuously on u0∈U. The continuous dependence of a(ξj),b(−ξ¯j)∈C on u0∈H1,1(R+) follows from Lemma u0↦cje2iθ is continuous [0,∞)2×U→C for each j. We conclude that ↦w∼=v∼−I:[0,∞)2×U→(L2∩L∞)(Γ) is continuous.By Proposition finition  of v, stB(L2(Γ)) denote the space of bounded linear operators on L2(Γ). The set of invertible operators is open in B(L2(Γ)) and the linear map w∼↦Cw∼I lies in B(L2(Γ)). Also, since ∥Cw∼∥B(L2(Γ))⩽C∥w∼∥L∞(Γ), the map w∼↦I−Cw∼ is continuous L∞(Γ)→B(L2(Γ)). Since ↦μ∼−I with μ∼ given by (I−Cw∼↦(I−Cw∼)−1, this proves that the map in  is trivially open. Suppose therefore that λ=1 and q>0. Then Δ≠0 on R, and Δ has exactly one zero ξ1 in C+ by Proposition a(ξ1) is nonzero by Proposition H1,1(R+), implying thatu0‐dependence explicitly for clarity. Fix uˇ0∈U. By assumption, the RH problem for m∼ corresponding to uˇ0 has a solution for each ∈[0,∞)×[0,∞). By standard theory for RH problem, this is equivalent to the map I−Cw∼:L2(Γ)→L2(Γ) being invertible for each ∈[0,∞)×[0,∞). On the other hand, since w∼→I−Cw∼:L∞(R)→B(L2(Γ)) is continuous, the continuity of the map (F defined byV denote the open set of invertible operators in B(L2(Γ)). Then F−1(V) is open. Given any compact set K⊂[0,∞)2, K×{uˇ0} is a compact subset of F−1(V), and hence there is a neighborhood U1⊂H1,1(R+) of uˇ0 such that ⊂F−1(V) for all ∈K, that is, such that the solution m∼ exists whenever u0∈U1 and ∈K. On the other hand, by a Deift–Zhou steepest descent analysis of the RH problem for m∼, one obtains that there is a neighborhood U2⊂H1,1(R+) of uˇ0 such that m∼ exists for all u0∈U2 whenever x2+t2 is large enough. Indeed, for large x2+t2, the solution is well approximated by the global parametrix, which in this case is the solution of the RH problem corresponding to the pure stationary one‐soliton and always exists  is an open neighborhood of uˇ0 such that m∼ exists for all u0∈U1∩U2 and all ∈[0,∞)2, that is, U1∩U2⊂U. This shows that U is open.□If ng thatexample, ). By choProof of Theorem 1q∈R∖{0} and u0∈U. Let {u0(n)}n=1∞⊂S(R+) be a sequence such that u0(n)→u0 in H1,1(R+) as n→∞ and such that (u0(n))′(0)+qu0(n)(0)=0 for each n⩾1. Such a sequence exists by Lemma U is open in H1,1(R+). Hence, passing to a subsequence if necessary, we may assume that {u0(n)}n=1∞⊂U, which means that the assumptions of Proposition u0(n). Applying Proposition u(n) of the Robin IBVP for NLS with parameter q and initial data u0(n) for each n.Let m∼ and μ∼ corresponding to u0, as well as the functions m∼(n) and μ∼(n) corresponding to u0(n), are all well defined and satisfy (u(n) satisfies, for each n⩾1,By Lemma  satisfy  and  in H1,1(R+) of the Robin IBVP for NLS with parameter q and initial data u0. The Schwartz class solution u(n) is clearly also a solution in H1,1(R+) and by the continuity of the data‐to‐solution mapping established in Proposition u(n)→u as n→∞ for each . Hence, letting n→∞ in the (12)‐entry of R, and∈[0,∞)×[0,∞). By Lemma μ∼(n)→μ∼ in I+L2(Γ) as n→∞. By Lemma w∼(n)→w∼ in H1,1(R+) as n→∞. Hence, Xn→0 and Yn→0 as n→∞, so letting n→∞ in the (12)‐entry of (6.11)2,t)and2ilimk→∞his into , we obtahis into  for u. T77.1λ=1 and q>0. Let u0∈H1,1(R+) and suppose that the RH problem of Theorem m for each ∈[0,∞)×[0,∞). By Proposition Δ(k) has one simple zero ξ1∈iR>0, which means that m has simple poles at ξ1 and ξ¯1. We will use a Darboux transformation to remove these poles and consider a solution mreg of an associated regular RH problem without poles. Definer,rreg∈H1,1(R) and |r(k)|=|rreg(k)|<1 for k∈R. Let mreg be the unique solution of the RH problem of Theorem r(k) replaced by rreg(k) and with no poles in C∖R. Such a solution exists by a standard vanishing lemma argument as described in the proof of Lemma detmreg=1. Define B1 bym and mreg imply that B1 is an entire function of k which is O(1) as k→∞; hence, B1≡B1 is independent of k. Evaluating  is given in terms of m by 12.Lemma 7.1(a)t→∞, the function ureg defined in , where urad(1) is given by (As fined in  obeys thfined in  with r rgiven by .(b)ξ1∈C+, thent→∞ uniformly for x∈[0,∞), whereIf Let e B1 byB1=−kI+mnditions  satisfiee B1 byB1=−kI+m of m by . Accordi of m by  and (7.5mreg has the same form as the RH problem associated to the defocusing NLS equation on the line with reflection coefficient given by rreg(k). The lemma therefore follows from well‐known results (see [□The RH problem for lts (see ) in the t→∞, we havex∈[0,∞), where usol and urad(2) are given by  of the defocusing NLS equation whenever the initial data u0 lie in the subset U of H1,1(R+) defined in Definition us0 clearly lie in U. Moreover, by Lemma U is open in H1,1(R+). Hence there exists a neighborhood U of us0 such that U⊂U. It follows that if u0∈U, then the global weak solution u with parameter q and initial data u0 satisfies  associated to u0 has exactly one simple zero in C+. By Lemma ξ1 and ξs1 be the zeros of u0 and us0, respectively, then |ξ1−ξs1|→0 as |u0−us0|H1,1(R+)→0. This completes the proof of the Theorem Suppose atisfies  as t→∞. 7.3λ=−1 and let q=ωtanhϕ∈R∖{0} be the value of q associated with the stationary one‐soliton.Suppose q>0. In this case, the spectral functions Δs and as corresponding to the stationary one‐soliton initial data us0 fulfill Assumption Δs has only one simple zero in C¯+ at ξs1:=iω/2, and as has no zeros in C¯+  defined in Definition U is open, and hence the desired conclusions follow immediately from Proposition Suppose first that C¯+  also has a simple zero at ξs2, Assumption Suppose now that u0(x) be a small perturbation of us0 in H1,1(R+). Let a(k) and Δ(k) be the spectral functions corresponding to u0. By Lemma Δ(k) has two simple zeros ξ1 and ξ2 and these zeros are such that ξ1→ξs1 and ξ2→ξs2 as u0→us0. In particular, ξ1≠ξ2 and ξ1≠ξs2 for u0 sufficiently close to us0. The symmetry →L∞(C¯+), so the same arguments used to prove Lemma u0 is close to us0, a(k) has exactly one simple zero k1 in C+ and this zero satisfies k1→ξs2 as u0→us0. We distinguish two cases depending on whether ξ2 coincides with ξs2 or not.Let symmetry  implies ξ2=ξs2). Suppose that ξ2 coincides with ξs2. Equation (k=ξs2=−iq/2 readsΔ(k) vanishes at ξs2, we deduce that a(k) also vanishes at ξs2. This means that both Δ and a have simple zeros at ξs2. In particular, Assumption ξ2 of Δ is excluded from the list of poles of m. Indeed, consider the derivation of the residue conditions (ξ1 is in the present situation a simple zero of Δ(k) and a(ξ1)≠0. This means that m satisfies the residue conditions }, where c^1 is defined in  defined by  defined by Equation (σ^d and the reflection coefficient r(k) given by =−fined in . We concfined in  holds asfined by  and uradEquation  with thegiven by . This coξ2≠ξs2). Suppose that ξ2 does not coincide with ξs2. In this case, we have a(ξ2)≠0. Indeed, evaluating  corresponding to us0, we see that bs is nonzero everywhere in the upper half‐plane. Furthermore, by Lemma u0↦b is continuous H1,1(R+)→L∞(C¯+). Hence, b(ξ2)≠0 for all u0 close to us0. Since ξ2≠−iq/2 by assumption, we have 2ξ2±iq≠0, and hence (a(ξ2)≠0. We conclude that whenever u0 is sufficiently close to us0, Assumption m of Theorem ξ1,ξ2 in C+. This means that the RH problem involves the modified discrete scattering data σ^d={,}, and that we have the long‐time asymptotics formula  defined by  defined by (Case 2 (aluating  at ξ2, wpression  for the  obtain0=(2ξ2−ibtain7.60=(2ξ2− formula  as t→∞ wfined by  and uradfined by . This coProceedings of the London Mathematical Society is wholly owned and managed by the London Mathematical Society, a not‐for‐profit Charity registered with the UK Charity Commission. All surplus income from its publishing programme is used to support mathematicians and mathematics research in the form of research grants, conference grants, prizes, initiatives for early career researchers and the promotion of mathematics.The


Germline-produced Hedgehog signals require PTR-6 and PTR-16 receptors for mating-induced shrinking and death. Our results reveal an unconventional role of the piRNA pathway in transcriptional regulation of Hedgehog signaling and a new role of Hedgehog signaling in the regulation of longevity and somatic maintenance: Hedgehog signaling is controlled by the tunable piRNA pathway to encode the previously unknown germline-to-soma pro-aging signal. Mating-induced piRNA downregulation in the germline and subsequent Hedgehog signaling to the soma enable the animal to tune somatic resource allocation to germline needs, optimizing reproductive timing and survival.The reproductive system regulates somatic aging through competing anti- and pro-aging signals. Germline removal extends somatic lifespan through conserved pathways including insulin and mammalian target-of-rapamycin signaling, while germline hyperactivity shortens lifespan through unknown mechanisms. Here we show that mating-induced germline hyperactivity downregulates piRNAs, in turn desilencing their targets, including the Hedgehog-like ligand-encoding genes  Caenorhabditiselegans. The authors find that germline piRNAs influence longevity and somatic maintenance by transcriptionally regulating germline-to-soma Hedgehog signaling.This study identifies a new germline-to-soma aging signal tuned by mating in  Conversely, the status of worm, fly, mouse, and human germlines influence their somatic tissues: germline removal and ovary transplantation extend lifespan11, while germline hyperactivity decreases lifespan and leads to dramatic changes in somatic physiology in animals across great evolutionary distances14. While these studies in animals ranging from invertebrates to humans support the existence of a pro-aging signal from the germlines, the nature and identity of that signal remains elusive.Longevity is plastic and is influenced by external factors, for example, diet, and internal factors such as reproductive demands. Communication between the germline and soma allows a coordinated response to physiological and environmental challenges. Animals couple nutrient availability to reproduction18. However, concomitant removal of the somatic gonad eliminates lifespan extension and other somatic benefits, suggesting the existence of two opposing signals: a germline pro-aging signal and a somatic gonad prolongevity signal19. The somatic gonad prolongevity signal pathway has been characterized using germlineless worms28. Dafachronic acids, insulin, mTOR, and steroid signaling are required in the soma for germline loss-mediated lifespan regulation, suggesting that they mediate the somatic gonad prolongevity effect30. By contrast, the identity of the initial pro-aging signal originating from the germline remains elusive. Identifying this pro-aging signal is critical for understanding how animals tune their aging rates in response to germline activity and reproductive needs.Removal of the germline extends lifespan, increases fat accumulation, and enhances resistance to various stresses19, less is known about the role of the hyperactive germline. Mating accelerates germline proliferation and ultimately leads to somatic collapse, shrinking and early death13, suggesting that the germline pro-aging signal is substantially amplified by mating. Therefore, mated worms are an ideal system in which to identify the mysterious germline pro-aging signal.While most studies of the influence of germline on lifespan have compared germlineless animals with intact, unmated animalsWe set out to identify the underlying mechanism of hyperactive germline-induced shrinking and early death. Our transcriptional analyses of isolated germlines revealed that a specific subset of piRNAs is downregulated in response to mating, de-repressing Hedgehog-related genes. Hedgehog signaling communicates the status of the germline to somatic cells, resulting in mating-induced shrinking and early death. Thus, somatic responses to germline hyperactivity are tuned by piRNA regulation of an important developmental signaling pathway.12. Day 1 adult self-spermless hermaphrodites (fog-2) mated for 24 h with Day 1 adult males live 40% shorter than their unmated counterparts, and shrink by up to 30%12  In addition to shrinking, mated animals also display an acceleration in age-related autofluorescence31 and intestinal barrier dysfunction , we used an equal amount of RNA, rather than an equal number of worms or germline, from each germline sample to make our sequencing libraries, and sequencing reads were normalized in our analysis. In unmated hermaphrodites, over 8,000 mRNAs were previously reported to have reduced expression in the distal germline compared with whole animals35  and small RNA sequencing (RNA-seq) Fig. . Hermaphs35 Fig. , left. Ts35 Fig. , right. sri-40   Fig. , indicat36. Endogenous siRNAs are required for maintenance of proteostasis and lifespan extension in germlineless worms37, and play critical roles in shaping the germline transcriptome35. PIWI-associated RNAs (piRNAs) are expressed predominantly in the germline and are required to maintain germline integrity and fertility38. Differential expression analysis of small RNAs from dissected mated and unmated germlines revealed 440 significantly upregulated and 296 downregulated small RNAs in the mated germline  or when shrinking is obvious (Day 7)  to preserve genome integritynes Fig. , suggest 42 Fig. . P granu 7) Fig. , suggest 7) Fig. , these s 7) Fig. . Togethe12. We mated mutant hermaphrodites with young males for 2 days starting on Day 1 of adulthood and measured their body size on Day 6/7 of adulthood , matura-1 refs. –52, seco-3 refs. , 53), anl-2 ref. ), as weling Fig. , none ofing Fig. , indicatCaenorhabditis elegans germ granules)56, and disruption of P granules compromises piRNA-mediated silencing43. P granule distribution and assembly/disassembly dynamics depend on maternal-effect germline (MEG) proteins57. We found that meg double mutants in which P granule functionality is severely impaired57 were also resistant to mating-induced shrinking  revealed that the lack of a functional piRNA pathway in prde-1 worms eliminated most germline transcriptional differences induced by mating  of 148 significantly downregulated piRNAs identified in the mated germline (Supplementary Data 64) to the 34 genes and found that 13 are predicted to encode secreted proteins. We then ranked the final 13 genes according to their expression fold change in the germline and in the whole worm, and their consistency in expression patterns across the samples  genes, A.7 Fig. . KnockinA.7 Fig. , but notA.7 Fig.  or the iA.7 Fig. , was sufwrt-1 provided over 50% protection against mating-induced early death ; Fig. wrt-10 yielded a much milder effect . Therefore, while inhibiting germline piRNA-mediated Hedgehog signaling is beneficial to the mothers, as it prevents mated worms from shrinking and largely rescues mating-induced death, such benefits do not come without a cost to progeny. Signaling from the mated germline, while deleterious to the mother’s soma and ultimately leading to her death, may be an unavoidable cost of activation of the germline upon mating that is necessary for sufficient nutrient provisioning to progeny.Finally, we wondered whether there is any generational penalty for eliminating mating-induced shrinking and death, as these processes are deleterious to the mother. While ype Fig. , knockdo14; however, the underlying mechanisms are poorly understood. Here we found that mating-induced piRNA downregulation in the germline releases suppression of the Hedgehog signaling pathway, which in turn leads to body size and lifespan decrease in mated worms . Our results suggest that there is likely a trade-off between somatic integrity and progeny production in mated animals, as demonstrated by the reduced mated brood size of animals with reduced Hedgehog signaling ine Fig. . These r78 and the reduction in energy devoted to somatic integrity maintenance, reflecting the direct cost of germline hyperactivity and substantially increased progeny production. Signaling from the mated germline, while deleterious to the mother’s soma and ultimately leading to her death, may be an unavoidable cost of activation of the germline upon mating that is necessary for sufficient nutrient provisioning to progeny. Our study reveals a mechanism that can efficiently convey germline status to the soma in adulthood, allowing the animals to better organize the balance between reproduction and somatic maintenance, optimizing reproductive fitness.Mating-induced germline-to-soma piRNA-mediated Hedgehog signaling elegantly coordinates germline function and somatic aging. In an unmated female with low or no germline proliferation, the priority of the germline is to maintain its integrity until mating occurs, while avoiding unnecessary proliferation or differentiation of the germ cells. piRNAs contribute to this process by suppressing errant TE expression and developmental programs, including those regulated by Hedgehog signaling. By contrast, upon mating, the germline switches to progeny production mode, and the previous suppression of Hedgehog signaling by piRNAs is released to allow rapid germline stem cell proliferation and further differentiation Fig. . As Hedg13. Seminal fluid kills the mother by turning off her IIS/FOXO protective pathway13, which is unnecessary for successful reproduction. By contrast, germline activation upon mating is the most likely to be both necessary and shared with other animals, as germline activity correlates with shorter lifespan in worms, flies, mice, and possibly humans14. Because germline proliferation may be induced by mating in other organisms, and piRNAs are ubiquitous in animal germlines, it will be interesting to see whether mating-induced piRNA regulation of signaling from germline to somatic tissues is conserved.Of the three mating-related killing mechanisms—male pheromone, seminal fluid, and sperm activation of germline proliferation—the last has the highest chance of being evolutionarily conserved. Male pheromone-induced killing kills hermaphrodites only at nonphysiologically high concentrations, and kills males specifically but only in androdioecious speciesC.elegans strains used in the study were as follows:79. Worms were transferred to iced M9 buffer for dissection. Heads or tails were removed with 26G needles, allowing the distal portion of the germline to pop out of the worm. Glass capillaries pulled with an opening just large enough to fit the end of the germline were used to detach them rapidly at the ventral-to-distal bend. Dissected distal germlines were transferred immediately into 1.5 ml Eppendorf tubes filled with 500 μl Trizol. About 200 germlines were collected for each biological replicate.Germline dissection was modified from a previous publicationTubes containing dissected germlines (immersed in Trizol) were put in an Eppendorf MixMate Vortex Mixer at 800 r.p.m. and 65 °C for 1 h before the isolation process. Total RNA was extracted from Trizol using the mirVana miRNA isolation kit (ThermoFisher). mRNA libraries for directional RNA-seq were prepared using the SMARTer Apollo System and were sequenced (150-nt single-end) on the Illumina NovaSeq platform. RNA samples for small RNA-seq were treated with 5′ polyphosphatase (Lucigen) and prepared using the SMARTer Apollo system with modifications for small RNA library preparation. Small RNA-containing libraries were Blue Pippin size selected (15–30 nt insert size) before 75-nt single-end sequencing.C. elegans genome  using Bowtie. Count matrices were generated using featureCounts. Data were normalized with a variance-stabilizing transformation (DESeq2). DESeq2 was used for differential expression analysis. Genes at Padj < 0.05 were considered significantly differentially expressed. PCA was carried out using the R method (prcomp). Heatmaps were generated in R using normalized read counts (variance-stabilizing transformation). Tissue enrichment and gene ontology (GO) term enrichment analysis were performed using wormbase enrichment analysis (https://wormbase.org/tools/enrichment/tea/tea.cgi) for significantly differentially-expressed genes. Predicted targets of piRNAs were retrieved from piRTarBase (http://cosbi6.ee.ncku.edu.tw/piRTarBase/) using the default ‘relaxed’ piRNA targeting setting, see Supplementary Data PRJNA892981.FASTQC was used to assess read quality scores. Universal adapter sequences were trimmed from small RNA library sequences using Cutadapt. Reads were mapped to the glp-1(e2141) was retrieved from a previous publication34. Microarray data of mated and unmated fog-2(q71) was retrieved from a previous publication61. Hermaphrodites were mated on Day 1 of adulthood for 24 h in a 2:1 male:hermaphrodite ratio. About 200 hermaphrodites were collected on Day 2/3 of adulthood for each biological replicate. RNA was extracted by the heat vortexing method. Two-color Agilent microarrays were used for expression analysis. Significantly differentially-expressed gene sets were identified using significance analysis of microarrays (SAM)80. One-class SAM was performed to identify genes that are significantly differentially expressed after mating. The lists were then compared with significantly upregulated genes in dissected germline (RNA-seq).Microarray data of mated and unmated ekl-1 and drh-3 homozygous mutants, we confirmed successful mating empirically by observing the decrease in darkness of mated sterile worms under normal light, which indicates mating-induced fat loss. About 25 synchronized Day 1 hermaphrodites were transferred onto each plate. The hermaphrodites were transferred daily onto new seeded plates in the first week of the lifespan assay. Afterward, they were transferred once every 2 days. When RNAi was used in lifespan assay, RNAi treatment always started from eggs for all the experiments in this study. Kaplan–Meier analysis with log-rank (Mantel–Cox) method was performed to compare the lifespans of different groups. ‘Bagged’ worms were censored on the day of the event.NGM plates (60 mm) plates were used to set up group mating. Each 60 mm NGM plate was seeded with OP50 to make a bacterial lawn of around 3 cm in diameter 2 days before mating. All lifespan assays were performed at room temperature (20–21 °C). About 50 hermaphrodites and 100 young (Day 1−2 of adulthood) males were transferred onto the plate. Then, 24–48 h later, the hermaphrodites were transferred onto newly seeded 60 mm NGM plates in the absence of males for lifespan assays. No 5-fluro-2′-deoxyuridinevwas added to the plates. We confirmed successful mating for all worms by checking their progeny. With successful mating, about half of the progeny are male. For the only two sterile strains used in this study, ekl-1 and drh-3 homozygous mutants, we confirmed the successful mating empirically by observing the decrease in darkness of mated sterile worms under normal light, which indicates mating-induced fat loss. Images of live hermaphrodites on 60 mm plates were taken on Day 6/7 of adulthood with a Nikon SMZ1500 microscope. When RNAi was used, RNAi treatment always started from eggs for all the experiments. ImageJ was used to analyze the body size of the worms. The middle line of each worm was delineated using the segmented line tool and the total length was documented as the body length of the worm. A t-test was performed to compare the body size differences between groups of worms in the same day.Mating set up was the same as described in Individual hermaphrodites after mating were transferred onto 3 cm NGM plates seeded with 25 ml OP50 and moved to fresh plates daily until reproduction ceased. The old plates were left at 20 °C for 2 days to allow the offspring to grow into adults, which were counted manually for daily production and total brood size. Between 10 and 25 plates of individual worms of each genotype per treatment were counted to account for individual variation.t-test was performed to compare the P granule density differences between mated and unmated germlines.mCherry-tagged fluorescent PGL-1 was visualized in living nematodes (YY968) by mounting young adult animals on 2% agarose pads with M9 buffer with 20 mM levamisole. Fluorescent images were captured using a Nikon Ti microscope with a ×100 objective. Images were processed and quantified in ImageJ. The quantification of germline granule fluorescence was performed using ImageJ. For every image, a region of interest (ROI) with a clear focus of P granules was selected manually. The area of the whole ROI was kept the same for all images. The number of puncta within the ROI was measured blindly for each germline and image. The densities of germline P granules were calculated as: the number of puncta within the ROI per the area of the whole ROI. Densities of germline granules were determined for 50–60 ROIs, and the mean and s.d. were calculated using GraphPad Prism. A 65 to overexpress endogenous piRNAs. The scaffold information was obtained from the website https://www.wormbuilder.org/piRNAi/. Cluster was generated using simple search option with the default setting (targeted gene: wrt-1 or wrt-10). Synthetic piRNAs were replaced by endogenous piRNAs as indicated by the text and figure legends. The sequences (about 1.5 kb) were synthesized by Twist Bioscience. The injection mix consisted of 20 ng μl–1 synthetic dsDNA piRNA overexpression cluster with adapters that were not further purified (Twist Bioscience), 2 ng μl–1 coinjection marker (Pmyo2::mCherry::unc-54 3′ UTR), and 1 kb DNA ladder to a final total DNA concentration of 100 ng μl–1. F1 progeny with red pharynx were selected from injected animals. Synchronized F2 progeny from positive transgenic F1 worms were used in mating and body size measurement assays.We modified recently developed piRNAiThe sequences of piRNA overexpression clusters used in this study are as follows:wrt-1 (uppercase: piRNAs)piRNA overexpression cluster targeting cgcgcttgacgcgctagtcaactaacataaaaaaggtgaaacattgcgaggatacatagaaaaaacaatacttcgaattcatttttcaattacaaatcctgaaatgtttcactgtgttcctataagaaaacattgaaacaaaatattaagtTAGAACTTCATCTTTAGAACActaattttgattttgattttgaaatcgaatttgcaaatccaattaaaaatcattttctgataattagacagttccttatcgttaattttattatatctatcgagttagaaattgcaacgaagataatgtcttccaaatactgaaaatttgaaaatatgtttttatggcaggtgctgacggattgccagaactcaaaatatgaaatttttatagttttgttgaaacagtaagaaaatcttgtaattactgtaaactgtttgctttttttaaagtcaacctacttcaaatctacttcaaaaattataatgtttcaaattacataactgtgtgaagttgggcgcccagttgtactgtagagcttcaatgttgataagatttattaacacagtgaaacaggtaatagttgtttgttgcaaaatcggaaatctctacatttcatatggtttttaattacaggtttgttttataaaataattgtgtgatggatattattttcagacctcatactaatctgcaaaccttcaaacaatatgtgaagtctactctgtttcactcaaccattcatttcaatttggaaaaaaatcaaagaaatgttgaaaaattttcctgtttcaacattatgacaaaaatgttatgattttaataaaaacaatTGTCATAAACGTAGAATCATCttctgtttttcttagaagtgttttccggaaacgcgtaattggttttatcacaaatcgaaaacaaacaaaaatttttttaattatttctttgctagttttgtagttgaaaattcactataatcatgaataagtgagctgcccaagtaaacaaagaaaatttggcagcggccgacaactaccgggttgcccgatttatcagtggaggatctacaaggctaactgcgttatctaatgtgatgtacacggttttcatttaaaaacaaattgaaacagaaatgactacattttcaaattgtctatttttgctgtgtttattttgccaccaacaatgagataatgtgttagccttgtcaatctagtaaactcacttaatgcaattcctccagccacatatgtaaacgttgtatacatgcagaaaacggttttttggttttaatgggaacttttgacaaattgttcgaaaatcttaagctgtcccatttcagttgggtgatcgatttwrt-10 (uppercase: piRNAs)piRNA overexpression cluster targeting cgcgcttgacgcgctagtcaactaacataaaaaaggtgaaacattgcgaggatacatagaaaaaacaatacttcgaattcatttttcaattacaaatcctgaaatgtttcactgtgttcctataagaaaacattgaaacaaaatattaagtTAAATGAAAAGCTGGCTATGGctaattttgattttgattttgaaatcgaatttgcaaatccaattaaaaatcattttctgataattagacagttccttatcgttaattttattatatctatcgagttagaaattgcaacgaagataatgtcttccaaatactgaaaatttgaaaatatgtttttatggcaggtgctgacggattgccagaactcaaaatatgaaatttttatagttttgttgaaacagtaagaaaatcttgtaattactgtaaactgtttgctttttttaaagtcaacctacttcaaatctacttcaaaaattataatgtttcaaattacataactgtgtgaagttgggcgcccagttgtactgtagagcttcaatgttgataagatttattaacacagtgaaacaggtaatagttgtttgttgcaaaatcggaaatctctacatttcatatggtttttaattacaggtttgttttataaaataattgtgtgatggatattattttcagacctcatactaatctgcaaaccttcaaacaatatgtgaagtctactctgtttcactcaaccattcatttcaatttggaaaaaaatcaaagaaatgttgaaaaattttcctgtttcaacattatgacaaaaatgttatgattttaataaaaacaatTGGAATAGCGTAAACAAAAGAttctgtttttcttagaagtgttttccggaaacgcgtaattggttttatcacaaatcgaaaacaaacaaaaatttttttaattatttctttgctagttttgtagttgaaaattcactataatcatgaataagtgagctgcccaagtaaacaaagaaaatttggcagcggccgacaactaccgggttgcccgatttatcagtggaggatctacaaggctaactgcgttatctaatgtgatgtacacggttttcatttaaaaacaaattgaaacagaaatgactacattttcaaattgtctatttttgctgtgtttattttgccaccaacaatgagataatgtgttagccttgtcaatctagtaaactcacttaatgcaattcctccagccacatatgtaaacgttgtatacatgcagaaaacggttttttggttttaatgggaacttttgacaaattgttcgaaaatcttaagctgtcccatttcagttgggtgatcgatttpiRNA overexpression cluster control (uppercase: piRNAs)cgcgcttgacgcgctagtcaactaacataaaaaaggtgaaacattgcgaggatacatagaaaaaacaatacttcgaattcatttttcaattacaaatcctgaaatgtttcactgtgttcctataagaaaacattgaaacaaaatattaagtTAGAAACTGATCTCTGAAAGTctaattttgattttgattttgaaatcgaatttgcaaatccaattaaaaatcattttctgataattagacagttccttatcgttaattttattatatctatcgagttagaaattgcaacgaagataatgtcttccaaatactgaaaatttgaaaatatgttACTTTCCATAACGTCGACAAAattgccagaactcaaaatatgaaatttttatagttttgttgaaacagtaagaaaatcttgtaattactgtaaactgtttgctttttttaaagtcaacctacttcaaatctacttcaaaaattataatgtttcaaattacataactgtgtAATTCGGGAGTCCTAATTCTAactgtagagcttcaatgttgataagatttattaacacagtgaaacaggtaatagttgtttgttgcaaaatcggaaatctctacatttcatatggtttttaattacaggtttgttttataaaataattgtgtgatggatattattttcagacctcatactaatctgcaaaccttcaaacaatatgtgaagtctactctgtttcactcaaccattcatttcaatttggaaaaaaatcaaagaaatgttgaaaaattttcctgtttcaacattatgacaaaaatgttatgattttaataaaaacaatGAAAATTTTGCTGAACACCTTttctgtttttcttagaagtgttttccggaaacgcgtaattggttttatcacaaatcgaaaacaaacaaaaatttttttaattatttctttgctagttttgtagttgaaaattcactataatcatgaataagtgagctgcccaagtaaacaaagaaaatttggcagcggccgacaactaccgggttgcccgatttatcagtggaggaGATCGAGGCTTAATGAACGGAatctaatgtgatgtacacggttttcatttaaaaacaaattgaaacagaaatgactacattttcaaattgtctatttttgctgtgtttattttgccaccaacaatTAAAAGTGGCTCCGAGCTAGGtcaatctagtaaactcacttaatgcaattcctccagccacatatgtaaacgttgtatacatgcagaaaacggttttttggttttaatgggaacttttgacaaattgttcgaaaatcttaagctgtcccatttcagttgggtgatcgatttTwist Primer Set 2 Fw: 5′-CAATCCGCCCTCACTACAACCG-3′Twist Primer Set 2 Rev: 5′-TCCCTCATCGACGCCAGAGTAG-3′–1. Single colonies of each type were inoculated and allowed to grow overnight at 30 °C to reach stationary phase (OD > 1.5). From the culture, 20 μl of undiluted, 5×, 25×, 125× and 625× dilutions were spotted on the assay plates. Plates were imaged after incubating for 4 days at 30 °C. Quantification of yeast growth was performed according to the published protocol81.Yeast two-hybrid assay was performed using Takara Matchmaker Gold Yeast Two-Hybrid System . WRT-1 and WRT-10 cDNA were cloned in frame into the bait construct pGBKT7, whereas PTR-6 and PTR-16 cDNA were cloned in frame into the prey construct pGADT7. pGBKT7-53, which encodes the Gal4 DNA-BD fused with murine p53, and pGADT7-7, which encodes the Gal4 AD fused with SV40 large T-antigen, were used as positive interaction controls in the assay. The bait constructs and the prey constructs were cotransformed into Y2HGold yeast strain in various combinations to test potential interaction. A dominant mutant version of the AUR1 gene that encodes the enzyme inositol phosphoryl ceramide synthase is expressed in Y2HGold Yeast strain in response to positive interaction between the bait and prey, conferring strong resistance to the otherwise highly toxic drug Aureobasidin A (AbA). The final concentration of AbA used in the assay was 200 ng mlC. elegans program, v.1.0 (http://worm-tissue.princeton.edu/search/multi). The tissue-specific enrichment scores were used to generate the heatmap in Fig. https://worm.princeton.edu/). The prediction scores of principal tissues were used to generate the heatmap in Fig. Tissue enrichment prediction analyses for ptr genes were performed using two methods: (1) the Tissue Expression Predictions for 82 with a few modifications. Briefly, synchronized Day 1 worms were set up for mating. About 50 worms were removed from the mating plate or the control plate 48 h later, and suspended overnight in liquid cultures of OP50 bacteria mixed with blue dye . Animals were then washed three times with M9 buffer before imaging using Nikon Ti with RGB illumination under ×10 or ×20 magnification.The intestinal barrier function assay (Smurf assay) was performed according to the published protocol–1). mRNA libraries for directional RNA-seq were prepared using the SMARTer Apollo System and were sequenced (150-nt single-end) on the Illumina NovaSeq platform. Reads from germline mRNA-seq were mapped to the C. elegans RepBase database (https://www.girinst.org/server/RepBase/protected/repeatmaskerlibraries/RepBaseRepeatMaskerEdition-20181026.tar.gz) using Bowtie. Raw counts were then normalized on the total number of mapping reads and multiplied by 1,000,000, obtaining expression values indicated as reads per million mapped reads (RPM). Transposon type was determined according to RepBase’s annotation.In addition to grouped germline samples collected for mRNA-seq and small RNA-seq, we collected single distal germline (four for each condition) into 10 μl 0.2% Triton X100 with RNase inhibitor  to over 100. When quantifying the P granule intensities of mated and unmated worms, images were scored blindly. No randomization was necessary for this study because mated and unmated worms of specific genotype/treatment were always compared with each other.t-test was used for all comparisons to determine statistical significance in this study. Detailed information of each assay can be found in the corresponding figure legends.Lifespan data were plotted as Kaplan–Meier survival curves and statistical analyses were performed using the log-rank (Mantel–Cox) test and two-way ANOVA. For body size measurements and fluorescence intensity quantification, two-tailed Source Data for sequencing data and statistics displayed in the main figures are provided as Supplementary Files.Further information on research design is available in the Reporting SummarySupplementary Table 1.fog-2 whole worms with intact germlines.List of germline-specific upregulated genes that are also upregulated in mated Supplementary Table 2.List of predicted targets of 148 downregulated piRNAs in the mated germline.Supplementary Table 3.List of piRNA-targeted germline-specific mating-induced genes (genes in Supplementary Data 1 that belong to the predicted targets of piRNAs in Supplementary Data 2).