Unc-51-like kinase 4 (Ulk4), a pseudokinase and a member of the Ulk kinase family, acts in conjunction with another Ulk family member Stk36 to promote Gli2 phosphorylation and Hh pathway activation. Ulk4 interacts with Stk36 through its N-terminal region containing the pseudokinase domain and with Gli2 via its regulatory domain to bridge the kinase and substrate. Although dispensable for Hh-induced Stk36 kinase activation, Ulk4 is essential for Stk36 ciliary tip localization, Gli2 phosphorylation, and activation. In response to Hh, both Ulk4 and Stk36 colocalize with Gli2 at ciliary tip, and Ulk4 and Stk36 depend on each other for their ciliary tip accumulation. We further show that ciliary localization of Ulk4 depends on Stk36 kinase activity and phosphorylation of Ulk4 on Thr1023, and that ciliary tip accumulation of Ulk4 is essential for its function in the Hh pathway. Taken together, our results suggest that Ulk4 regulates Hh signaling by promoting Stk36-mediated Gli2 phosphorylation and activation at ciliary tip.The Hedgehog (Hh) family of secreted proteins governs embryonic development and adult tissue homeostasis through the Gli family of transcription factors. Gli is thought to be activated at the tip of primary cilium, but the underlying mechanism has remained poorly understood. Here, we show that  Unc-51-like kinase 4 (Ulk4), which is a member of Ulk kinase family found in most eukaryotes (Drosophila Fused (Fu), a Ser/Thr kinase implicated in Hedgehog (Hh) signaling (Gli-luc reporter gene expression and Smoothened (Smo) ciliary localization  undergoes ubiquitin/proteasome-mediated proteolytic processing to generate a truncated transcriptional repressor form (GliR) (R and converts GliF to an active form (GliA) that enters the nucleus to turn on the expression of Hh target genes  . Hh inhim (GliR) . Activatet genes .F into GliA at ciliary tip  cells  in NIH3T3 cells, a well-established system for studying Hh signaling. We found that Ulk4 depletion significantly decreased Shh-induced expression of 4 hUlk4; . The reqF) cells .Our previous study revealed that Stk36 and Ulk3, which are Ulk family kinases, act in parallel to promote Gli2 phosphorylation and Hh pathway activation . To deteOur previous study demonstrated that Ulk3 and Stk36 phosphorylate Gli2 at multiple sites including S230/232 to promote Gli2 activation . We founA previous study using proximity-dependent biotin identification (BioID) identified Stk36 as a proximity interactor . To veriUlk4 contains an N-terminal pseudokinase domain and the C-terminal regulatory domain with armadillo (Arm) repeats . We genein vitro kinase assay using GST-Gli2N, which contains the Ulk3/Stk36 phosphorylation site S230, as substrate and either Fg-Stk36 or Fg-Stk36/hUlk4-HA complex immunopurified from HEK293T cells as kinase. GST-Gli2N containing S230A substitution was used as a negative control. As shown in Pseudokinases could regulate the enzymatic activity of interacting kinases, as has been shown for LKB1 kinase activation by its binding to the pseudokinases STRADα and STARADβ . To deteDrosophila, Hh activates Fu by promoting its kinase domain dimerization and trans-autophosphorylation on multiple S/T residues in its activation loop (AL), including T151, T154, T158, and S159 (WT) or its kinase dead form (CFP-Stk36KR) into NIH3T3 cells with endogenous Stk36 and Ulk3 deleted (KO Stk36KOUlk3) by CRISPR  increased, whereas phospho-deficient mutation (Stk36AA) abolished Stk36 kinase activity as determined by both Stk36 T158/S159 phosphorylation and Gli2 S230/S232 phosphorylation  to mimic phosphorylation or to A (AA) to block phosphorylation on these sites . We founrylation , which irylation , suggestTo determine whether Ulk4 is required for Shh-induced Stk36 kinase activation, we employed RNAi to deplete Ulk4 from NIH3T3 cells that express CFP-Stk36. As shown in Another possible mechanism for Ulk4 to influence Gli2 phosphorylation by Stk36 is to function as a scaffold that brings Stk36 and Gli2 into the same protein complex. Indeed, we found that Ulk4 depletion diminished the association between exogenously expressed Stk36 and Gli2 in HEK293T cells as determined by Co-IP experiments . By domaWe next determined whether Ulk4 mediated Stk36/Gli2 interaction in NIH3T3 cells and whether this was regulated by Shh. NIH3T3 cells were infected with lentiviruses expressing low levels of a Flag-tagged Stk36 (Fg-Stk36) and Myc-Gli2 and treated with or without Shh. Co-IP experiments showed that Fg-Stk36 and Myc-Gli2 formed a complex regardless of Shh treatment .A at the ciliary tip  but not its kinase inactive form (Stk36AA) restored Shh-induced Ulk4-HA ciliary tip accumulation in DKO cells (WT) nor its kinase dead form (Ulk3KR) could rescue ciliary tip accumulation of Ulk4-HA in DKO cells  by the CRISPR-Cas9 system . As showKO cells . By contKO cells . These r1-450; 451-1275) also abolished its ciliary tip localization in response to Shh, suggesting that binding to Stk36 is essential for Ulk4 ciliary localization. We generated two small deletions from the C-terminus of hUlk4 S/(P)T[X1-3] S/T  or T1088A/T1090A (hUlk4T1088A/T1090A) substitutions. These hUlk4 variants were expressed in NIH3T3 cells with endogenous Ulk4 depleted by shRNA. We found that hUlk4T1088A/T1090A but not hUlk4T1021A/1023A accumulated at ciliary tip in response to Shh stimulation  as substrate. As shown in WT) but not its kinase inactive variant (Fg-Stk36AA) phosphorylated GST-hUlk4C. Mutating both T1021 and T1023 to A (T1021A /T1023A) abolished the phosphorylation; however, mutating T1021A reduced but not eliminated the phosphorylation, suggesting that in the absence of T1021 phosphorylation, T1023 could also be phosphorylated by Stk36. Interestingly, T1023 but not T1021 is conserved in mouse Ulk4 (mUlk4) and mUlk4 contains an Ala at T1021 (T1021A) did not affect its ciliary tip accumulation in response to Shh  and hUlk4WT in NIH3T3 cells with endogenous Ulk4 depleted by shRNA. We found that both hUlk4T1021A and hUlk4WT rescued Shh-induced ciliary tip localization of coexpressed Myc-Stk36  the enzymatic activity of Stk36; (2) Shh-induced Stk36 kinase activation; (3) the association of Stk36 and its substrate; and (4) ciliary localization Stk36. In an as Stk36 . TherefoDrosophila, the kinesin-like protein Costal2 (Cos2) mediates the activation of Fu kinase by Hh. Therefore, it would be interesting to determine whether mammalian homologs Cos2, Kif7, and/or Kif27 participate in Stk36 kinase activation in response to Shh stimulation.Although Stk36/Ulk4/Gli2 complex formation appears to be constitutive regardless of the presence or absence of Shh, Stk36 kinase activation depends on Shh stimulation. Like Fu, Stk36 is phosphorylated on multiple sites in the activation loop of its kinase domain in response to Shh likely through trans-autophosphorylation, and activation loop phosphorylation is essential for its kinase activation. Using a phospho-specific antibody that recognized pT158/pS159 in the kinase activation loop of Fu/Stk36, we found that Ulk4 depletion did not affect Shh-induced phosphorylation of Stk36 on T158/S159, a readout for Stk36 kinase activation, suggesting that Ulk4 is dispensable for Shh signaling to activate Stk36. In A) in this ciliary compartment. Consistent with this notion, we found that Shh induced ciliary accumulation of both Ulk4 and Stk36 that colocalized with Gli2 at the ciliary tip. Furthermore, we found that Ulk4 is required for ciliary tip accumulation of Stk36. On the other hand, ciliary tip accumulation of Ulk4 depends on Stk36 kinase activity and phosphorylation of its C-terminal region on T1023. Preventing Ulk4 phosphorylation on T1023 abolished its ciliary tip accumulation and its ability to promote Stk36 ciliary tip accumulation, Gli2 phosphorylation, and Hh pathway activation. These results suggest that ciliary tip accumulation of Ulk4 is critical for its function in Hh signal transduction, likely by increasing the local concentration of Stk36 and Gli2 to promote effective phosphorylation of Gli2. It would also be important to examine the localization of endogenous Ulk4 and Stk36 in the future as exogenously expressed epitope-tagged protein might cause artifacts. In addition, the precise mechanism and dynamics of Ulk4 ciliary targeting remain to be determined in the future. For example, it would be important to determine how phosphorylation of T1023 promotes ciliary accumulation of Ulk4. A recent study identified several motor proteins of the kinesin family  as the interaction partners of Ulk4  proteins were subcloned into the pGEX 4T-1 vector using EcoRI and XhoI sites. N-terminally CFP-tagged mouse Ulk3WT, Ulk3KR, N-terminally 6XMyc-tagged human Stk36, N-terminally 3XFg-tagged human Stk36WT, Stk36AA and the C-terminally 3XHA-tagged human Ulk4WT, Ulk41-451, Ulk4452-1275, Ulk41-1000, Ulk41-1200, Ulk4T1021/1023A, Ulk4T1088/1090A, Ulk4T1021A were subcloned into the FUGW vector with the EcoRI and BamHI sites. N-terminally 3XFg-tagged human Stk36WT, Stk36EE, Stk36AA, Stk361-260, Stk36261-1315, and C-terminally 3XHA-tagged human Ulk4WT, Ulk41-451, Ulk4452-1275 were subcloned in the PLVX vectors using the EcoRI and MluI sites. The Ulk4T1021/1023A, Ulk4T1088/1090A, Ulk4T1021A, Stk36EE, Stk36AA were generated by PCR-mediated site-directed mutagenesis.Myc-Gli2 and GST-Gli2 were described previously . All GSTin vitro DNA transfection kit according to the manufacturer’s instruction (SignaGen). HEK293T cells  were cultured in DMEM (Sigma) supplemented with 10% fetal bovine serum (Gibco) and 1% penicillin/streptomycin (Sigma). PolyJet in vitro DNA transfection kit (SignaGen) was used to do the transfection according to the manufacturer’s instruction. MEF cells  were cultured in DMEM (Sigma) containing 10% FBS (Gibco) and 1% streptomycin/penicillin (Sigma) according to the standard protocol. For Shh-N treatment, cells were cultured at 50%-confluent densities in plate or chamber slides for 1 d and starved in serum-free medium (0.5% BCS for NIH3T3 cells or 0.5% FBS for MEF cells) for 12 hr to allow ciliation. The recombinant human Shh N-terminal fragment  was then added to the same serum-free medium for 12 hr or overnight.NIH3T3 cells  were cultured in Dulbecco’s modified Eagle’s medium  containing 10% bovine calf serum (Gibco) and 1% penicillin/streptomycin (Sigma). The transfection was carried out by using the GenJet Plus 3VO4, 1% CA630, 10% glycerol, and 0.5 M EDTA (pH 8.0). Cell lysates were incubated with protein A-Sepharose beads (Thermo Scientific) for 1 hr at 4°C to eliminate nonspecific binding proteins. After removal of the protein-A beads by centrifugation, the cleared lysates were incubated with Myc (HA or Flag) antibody for 4 hr or overnight. Protein complexes were collected by incubation with protein A-Sepharose beads for 1 hr at 4°C, followed by centrifugation. Immunoprecipitates were washed three times for 5 min each with lysis buffer and were separated on SDS-PAGE. Western blot was carried out using standard protocol. Western blot quantification was carried out by employing fluorogenic secondary antibody (IRDye 680LT goat anti-mouse: 926-68020 or goat anti-rabbit: 926-68021), and the blot was scanned and quantified with an Odyssey CLx imaging system (LI-COR). The antibodies used in this study were as follows: mouse anti-Myc , mouse anti-Flag , mouse anti-HA , mouse anti-acetylated Tubulin , rabbit anti-Myc , rabbit anti-HA , and goat anti-Gli2 .The protocol for Ulk4-HA/Myc-Stk36 immunostaining was carried out as previously described . ImmunofIn vitro kinase assay was performed by incubating 25 μl of reaction mixtures containing 150 mM Tris-HCl (pH 7.5), 0.2 mM Mg2+/ATP, 1 μg of purified GST-Ulk4/Gli2 fusion proteins, together with appropriate amount of kinase for 30 min at 30°C. The reaction was terminated by adding 2× SDS loading buffer. The resultant samples were loaded on SDS-PAGE and subjected to pIMAGO phospho-protein detection kit with fluor-680 (Sigma) detection kit and LI-COR Odyssey platform for western blot analyses of phosphorylated proteins (MilliporeSigma). Fg-Stk36WT and Fg-Stk36AA were immunopurified from HEK293 cells transfected with the Fg-Stk36WT or Fg-Stk36AA construct.pLKO.1 vectors expressing shRNA or FUGW vectors expressing transgenes were co-transfected with package vectors (PSPAX2 and PMDG2) into HEK293T cells using PolyJet (SignaGen). The supernatants were collected after 48 hr and 72 hr transfection, filtered through a 0.45 mM filter, and centrifuged at 20,000 × g for 2 hr. The sediment containing the viruses was resuspended, aliquoted in small volume of culture medium, and stored at –80°C for future use. For cell infection, lentiviruses were added to 70% confluent wild type NIH3T3 or MEF cells together with Polybrene  overnight to make the stable NIH3T3 or MEF cell lines expressing transgene or shRNA. The mouse Ulk4 shRNA lentiviral vector was purchased from Sigma . The non-target shRNA plasmid DNA  was used as control.For lentivirus generation, GUGUACAAGGCCUACGCCA-3′ (Cat# SASI_ Mm02 _ 00444409) and 5′-CUGAGAAGGUGGCCCGUGU-3′ (Cat# SASI_Mm02_00444410). The sequences for Stk36 silencing were 5′- GGUAUACUGGCUUCAGAAA-3′ (Cat# SASI_ Mm02 _00345637) and 5′-GCCUUAUGUGCUUUGCUGU-3′ (Cat# SASI_Mm01_00167751). The target sequence of mouse Ulk4 shRNA is CTGCGAAGATTATCGAGAATG. The target sequence of human Ulk4 shRNA is CCACTAGGTCACTCTTTCAGA. The sequences for negative control were 5′-UUCUCCGAACGUGUCACG U-3′. The RNAi MAX reagent  was used for the transfection of siRNA. The knockdown efficiency was validated via real-time PCR.For RNAi experiments in NIH3T3 or MEF cells, the siRNAs were purchased from Sigma. The sequences for Ulk3 silencing were 5′-6 cells using the RNeasy Plus Mini Kit (QIAGEN), and cDNA was synthesized with High-Capacity cDNA Reverse Transcription Kit  and qPCR was performed using Fast SYBR Green Master Mix  and a Bio-Rad CFX96 real-time PCR system . The RT-qPCR was performed in triplicate for each of three independent biological replicates. Quantification of mRNA levels was calculated using the comparative CT method. Primers: Gli1, 5′-GTGCACGTTTGAAGGCTGTC-3′ and 5′-GAGTGGGTCCGATTCTGGTG-3′; Ptch1, 5′-GAAGCCACAGAAAACCCTGTC-3′ and 5′-GCCGCAAGCCTTCTCTACG-3′; Ulk3, 5′- ACGAAACATCTCTCACTTG-3′ and 5′-TGCTGGGCAAAGCCAAAGTC-3′; Ulk4, 5′- ATGCAGAGTGTGATTGCGTTG-3′ and 5′-GAGTGGCAGTTTCTGTGAACA-3′; Stk36, 5′- CGCATCCTACACCGAGATATGA-3′ and 5′-AAATCCAAAGTCACAGAGCTTGA-3′; GAPDH, 5′-GTGGTGAAGCAGGCATCTGA-3′ and 5′-GCCATGTAGGCCATGAGGTC-3′.Total RNA was extracted from 1 × 10 fundamental study substantially advances our understanding of how the pseudokinase ULK4 interacts with an active member of the same kinase subfamily (STK36) to promote GLI phosphorylation and Hedgehog pathway activation. The evidence supporting the proposed mechanism is compelling, with rigorous biochemical assays and state-of-the-art cell-based imaging techniques. The work will be of broad interest to cell biologists and biochemists.This  In their study, Zhou et al. unveil the pivotal role of ULK4 in conjunction with STK36, shedding light on their collective impact on GLI2 phosphorylation and the subsequent activation of the SHH pathway. The research delves deep into the intricate interactions between ULK4 and various components of the SHH pathway within the primary cilium.The main strength of the study lies in the careful and systematic sequence of logical methods. The authors apply the expression of a range of different deletion and mutation constructs and carry out a comprehensive biochemical study of the consequences of depletion and reintroduction of various components in the context of STK36 and ULK4.Their findings reveal that ULK4 forms dynamic interactions with a complex composed of STK36 and GLI2. It is proposed that ULK4 acts as a scaffold, facilitating the essential interaction between STK36 and GLI2, thereby driving GLI2 phosphorylation by STK36. Notably, the research reveals that the N-terminal pseudokinase domain of ULK4 binds to Stk36, while the C-terminal regulatory domain of ULK4 interacts with Gli2. Moreover, the study presents compelling evidence for co-localization of ULK4 and STK36 with GLI2 at the ciliary tip within NIH 3T3 cells. Importantly, ULK4 and STK36 mutually rely on each other for their accumulation at this ciliary tip.This intricate mechanism, orchestrated by ULK4, brings to light the nuanced modulation of the SHH pathway. The research is substantiated by rigorous Co-IP experiments, kinase assays, and confocal imaging localization studies. To unravel the fine details of GLI2 phosphorylation at the primary cilium tip, the authors meticulously employ a diverse array of mutated and wild-type constructs of STK36 and ULK4.In summary, the studiy provide compelling insights into the intricate regulation of signaling pathways. Zhou et al.'s work on ULK4 and STK36 in the SHH pathway deepen our understanding of these complex processes, offering potential avenues for drug development, particularly in the context of cancer therapeutics. The authors provide solid molecular and cellular evidence that ULK4 and STK36 not only interact, but that STK36 is targeted (transported?) to the cilium by ULK4. Their data helps generate a model for ULK4 acting as a scaffold for both STK36 and its substrate, Gli2, which appear to co-localise through mutual binding to ULK4. This makes sense, given the proposed role of most pseuodkinases as non-catalytic signaling hubs. There is also an important mechanistic analysis performed, in which ULK4 phosphorylation in an acidic consensus by STK36 is demonstrated using IP'd STK36 or an inactive 'AA' mutant, which suggests this phosphorylation is direct.The major strength of the study is the well-executed combination of logical approaches taken, including expression of various deletion and mutation constructs and the careful  effects of depleting and adding back various components in the context of both STK36 and ULK3, which broadens the potential impact of the work. The biochemical analysis of ULK4 phosphorylation appears to be solid, and the mutational study at a particular pair of phosphorylation sites upstream of an acidic residue (notably T2023) is further strong evidence of a functional interaction between ULK4/STK36. The possibility that ULK4 requires ATP binding for these mechanisms is not approached, though would provide significant insight: for example it would be useful to ask if Lys39 in ULK4 is involved in any of these processes, because this residue is likely important for shaping the ULK4 substrate-binding site as a consequence of ATP binding; this was originally shown in PMID 24107129 and discussed more recently in PMID: 33147475 in the context of the large amount of ULK4 proteomics data released.The discussion is excellent, and raises numerous important future work in terms of potential transportation mechanisms of this complex. It also explains why the ULK4 pseudokinase domain is linked to an extended C-terminal region. Does AF2 predict any structural motifs in this region that might support binding to Gli2?A weakness in the study, which is most evident in Figure 1, where Ulk4 siRNA is performed in the NIH3T3 model (and effects on Shh targets and Gli2 phosphorylation assessed), is that we do not know if ULK4 protein is originally present in these cells in order to actually be depleted. Also, we are not informed if the ULK4 siRNA has an effect on the 'rescue' by HA-ULK4; perhaps the HA-ULK4 plasmid is RNAi resistant, or if not, this explains why phosphorylation of Gli2 never reaches zero? Given the important findings of this study, it would be useful for the authors to comment on this, and perhaps discuss if they have tried to evaluate endogenous levels of ULK4 (and Stk36) in these cells using antibody-based approaches, ideally in the presence and absence of Shh. The authors note early on the large number of binding partners identified for ULK4, and siRNA may unwittingly deplete some other proteins that could also be involved in ULK4 transport/stability in their cellular model.The sequence of ULK4 siRNAs is not included in the materials and methods as far as I can see, though this is corrected in the next version of the manuscript. In this manuscript, Zhou et al. demonstrate that the pseudokinase ULK4 has an important role in Hedgehog signaling by scaffolding the active kinase Stk36 and the transcription factor Gli2, enabling Gli2 to be phosphorylated and activated.Through nice biochemistry experiments, they show convincingly that the N-terminal pseudokinase domain of ULK4 binds Stk36 and the C-terminal Heat repeats bind Gli2.Lastly, they show that upon Sonic Hedgehog signaling, ULK4 localizes to the cilia and is needed to localize Stk36 and Gli2 for proper activation.This manuscript is very solid and methodically shows the role of ULK4 and STK36 throughout the whole paper, with well controlled experiments. The phosphomimetic and incapable mutations are very convincing as well.I think this manuscript is strong and stands as is, and there is no need for additional experiments.Overall, the strengths are the rigor of the methods, and the convincing case they bring for the formation of the ULK4-Gli2-Stk36 complex. There are no weaknesses noted. I think a little additional context for what is being observed in the immunofluorescence might benefit readers who are not familiar with these cell types and structures.The revised manuscript has improved some of the unclear areas. The following is the authors’ response to the original reviews.Reviewer #1 (Public Review):The Hedgehog (HH) protein family is important for embryonic development and adult tissue maintenance. Deregulation or even temporal imbalances in the activity of one of the main players in the HH field, sonic hedgehog (SHH), can lead to a variety of human diseases, ranging from congenital brain disorders to diverse forms of cancers. SHH activates the GLI family of transcription factors, yet the mechanisms underlying GLI activation remain poorly understood. Modification and activation of one of the main SHH signalling mediators, GLI2, depends on its localization to the tip of the primary cilium. In a previous study the lab had provided evidence that SHH activates GLI2 by stimulating its phosphorylation on conserved sites through Unc-51-like kinase 3 (ULK3) and another ULK family member, STK36 . Recently, another ULK family member, ULK4, was identified as a modulator of the SHH pathway . However, the underlying mechanisms by which ULK4 enhances SHH signalling remained unknown. To address this question, the authors employed complex biochemistry-based approaches and localization studies in cell culture to examine the mode of ULK4 activity in the primary cilium in response to SHH. The study by Zhou et al. demonstrates that ULK4, in conjunction with STK36, promotes GLI2 phosphorylation and thereby SHH pathway activation. Further experiments were conducted to investigate how ULK4 interacts with SHH pathway components in the primary cilium. The authors show that ULK4 interacts with a complex formed between STK36 and GLI2 and hypothesize that ULK4 functions as a scaffold to facilitate STK36 and GLI2 interaction and thereby GLI2 phosphorylation by STK36. Furthermore, the authors provide evidence that ULK4 and STK36 co-localize with GLI2 at the ciliary tip of NIH 3T3 cells, and that ULK4 and STK36 depend on each other for their ciliary tip accumulation. Overall, the described ULK4-mediated mechanism of SHH pathway modulation is based on detailed and rigorous Co-IP experiments and kinase assays as well as confocal imaging localization studies. The authors used various mutated and wild-type constructs of STK36 and ULK4 to decipher the mechanisms underlying GLI2 phosphorylation at the tip of the primary cilium. These novel results on SHH pathway activation add valuable insight into the complexity of SHH pathway regulation. The data also provide possible new strategies for interfering with SHH signalling which has implications in drug development .in vivo. Is there evidence that genetic ablation of ULK4 in animal models leads to less efficient SHH pathway induction? It also remains to be resolved how ULK3 and ULK4 act in distinct or common manners to promote SHH signalling. Another remaining question is, whether cell type- and tissue-specific features exist, that play a role in ULK3- versus ULK4-dependent SHH pathway modulation. In particular for the studies on ciliary tip localization of factors, relevant for SHH pathway transduction, a higher temporal resolution will be needed in the future as well as a deeper insight into tissue/ cell type-specific mechanisms. These caveats, mentioned here, don't have to be addressed in new experiments for the revision of this manuscript but could be discussed.However, it will be necessary to explore additional model systems, besides NIH3T3, HEK293 and MEF cell cultures, to conclude on the universality of the mechanisms described in this study. Ultimately, it needs to be addressed whether ULK4 modulates SHH pathway activity in vivo function Ulk4 in Shh signaling, the relationship between Ulk3 and Ulk4/Stk36, and possible cell type/tissue specificity of these two kinase systems. This will need the generation of single and double knockout mice and examine Hh related phenotypes in different tissues and developmental stages. The precise mechanism by which Ulk4 and Stk36 are translocated to the ciliary tip is also an important and unsolved issue. We include several paragraphs in the “discussion” section to address these outstanding questions for future study.We agree with the reviewer that it would be important to investigate in the future the Reviewer #2 (Public Review):The authors provide solid molecular and cellular evidence that ULK4 and STK36 not only interact, but that STK36 is targeted (transported?) to the cilium by ULK4. Their data helps generate a model for ULK4 acting as a scaffold for both STK36 and its substrate, Gli2, which appear to co-localise through mutual binding to ULK4. This makes sense, given the proposed role of most pseuodkinases as non-catalytic signaling hubs. There is also an important mechanistic analysis performed, in which ULK4 phosphorylation in an acidic consensus by STK36 is demonstrated using IP'd STK36 or an inactive 'AA' mutant, which suggests this phosphorylation is direct.The major strength of the study is the well-executed combination of logical approaches taken, including expression of various deletion and mutation constructs and the careful  effects of depleting and adding back various components in the context of both STK36 and ULK3, which broadens the potential impact of the work. The biochemical analysis of ULK4 phosphorylation appears to be solid, and the mutational study at a particular pair of phosphorylation sites upstream of an acidic residue (notably T2023) is further strong evidence of a functional interaction between ULK4/STK36. The possibility that ULK4 requires ATP binding for these mechanisms is not approached, though would provide significant insight: for example it would be useful to ask if Lys39 in ULK4 is involved in any of these processes, because this residue is likely important for shaping the ULK4 substrate-binding site as a consequence of ATP binding; this was originally shown in PMID 24107129 and discussed more recently in PMID: 33147475 in the context of the large amount of ULK4 proteomics data released.The reviewer raised an interesting question of whether ATP binding to the pseudokinase domain of Ulk4 might be required for its function, i.e., by regulating the interaction with its binding partner. In a recent study , the critical Lys39 for ATP binding was converted to Arg (KR mutation); however, unlike in most kinases the KR mutation affect ATP binding, the K39R mutation in the Ulk4 pseudokinase did not affect ATP binding although it slightly increased ADP binding (PMID: 33147475). Another mutation made by Preuss et al(PMID: 33147475), N239L, affected protein stability, making it impossible to determine whether this mutation affect ATP binding. Therefore, in the absence of clear approach to perturb ATP binding without affecting the overall structure of Ulk4, it would be challenging to address whether ATP binding regulates the ability of Ulk4 to bind its substrates.Nevertheless, we discuss the possibility that ATP binding might regulate Ulk4/Stk36 interaction and Shh signaling.The discussion is excellent, and raises numerous important future work in terms of potential transportation mechanisms of this complex. It also explains why the ULK4 pseudokinase domain is linked to an extended C-terminal region. Does AF2 predict any structural motifs in this region that might support binding to Gli2?The extended C-terminal domain of Ulk4 contains Arm/HEAT repeats (protein-protein interacting domain), which are predicted by AF2 to form alpha helixes.A weakness in the study, which is most evident in Figure 1, where Ulk4 siRNA is performed in the NIH3T3 model (and effects on Shh targets and Gli2 phosphorylation assessed), is that we do not know if ULK4 protein is originally present in these cells in order to actually be depleted. Also, we are not informed if the ULK4 siRNA has an effect on the 'rescue' by HA-ULK4; perhaps the HA-ULK4 plasmid is RNAi resistant, or if not, this explains why phosphorylation of Gli2 never reaches zero? Given the important findings of this study, it would be useful for the authors to comment on this, and perhaps discuss if they have tried to evaluate endogenous levels of ULK4 (and Stk36) in these cells using antibody-based approaches, ideally in the presence and absence of Shh. The authors note early on the large number of binding partners identified for ULK4, and siRNA may unwittingly deplete some other proteins that could also be involved in ULK4 transport/stability in their cellular model.Due to the lack of reliable Ulk4 and Stk36 antibodies, we were unable to confirm knockdown efficiency by western blot analysis. Therefore, we relied on the measure Ulk4 and STk36 mRNA expression by RT-qPCR to estimate the knockdown efficiency . We used mouse Ulk4 shRNA to carry out the knockdown experiments in NIH3T3 and MEF cells while the human version of Ulk4 (hUlk4) was used for the rescue experiments . We have confirmed that the mUlk4 shRNA targeting sequence is not conserved in hUlk4; therefore, the hULK4 construct is RNAi resistant. The rescue experiments strongly argue that the effect of Ulk4 RNAi on Shh signaling is due to loss of endogenous Ulk4. This argument is further strengthened by the observations that mutations that affected Ulk4 and Stk36 ciliary tip localization also affected Shh signaling such as Gli2 phosphorylation and Ptch1/Gli expression .The sequence of ULK4 siRNAs is not included in the materials and methods as far as I can see.We have added the mouse Ulk4 RNAi target sequence in the revised version.Reviewer #3 (Public Review):In this manuscript, Zhou et al. demonstrate that the pseudokinase ULK4 has an important role in Hedgehog signaling by scaffolding the active kinase Stk36 and the transcription factor Gli2, enabling Gli2 to be phosphorylated and activated.Through nice biochemistry experiments, they show convincingly that the N-terminal pseudokinase domain of ULK4 binds Stk36 and the C-terminal Heat repeats bind Gli2.Lastly, they show that upon Sonic Hedgehog signaling, ULK4 localizes to the cilia and is needed to localize Stk36 and Gli2 for proper activation.This manuscript is very solid and methodically shows the role of ULK4 and STK36 throughout the whole paper, with well controlled experiments. The phosphomimetic and incapable mutations are very convincing as well. I think this manuscript is strong and stands as is, and there is no need for additional experiments.Overall, the strengths are the rigor of the methods, and the convincing case they bring for the formation of the ULK4-Gli2-Stk36 complex. There are no weaknesses noted. I think a little additional context for what is being observed in the immunofluorescence might benefit readers who are not familiar with these cell types and structures.We thank this reviewer for the positive comments.Recommendations For the AuthorsReviewer #1 (Recommendations For The Authors):This elegant study has been thoroughly and thoughtfully designed and the dataset is solid. The biochemistry results are overall very convincing. Some data lack quantification and there needs to be more information on data analyses and statistics. The following suggestions and comments aim at strengthening the manuscript.1. Please provide quantification normalized to input for IP experiments . More information on data analyses and statistics should be provided and included as information in the figure legends.Thanks for the suggestions, we have done the quantification and statistics analyses for Figures 1E-G and Figure8 C as requested.1. Did the authors investigate whether overexpressing hULK4 in the control NIH3T3 cells leads to an increase in pS230/232 ? This would nicely support the notion of a promoting effect of ULK4 on GLI2 phosphorylation.We did not. We speculated that overexpressing hULK4 may not significantly promote GLI2 phosphorylation because Ulk4 is a pseudokinase and endogenous Stk36 (the kinase partner of Ulk4) is limited.1. The CO-IP experiments to show GLI2 activation were performed in NIH3T3 cells, whereas HEK293 cells were used for the experiments shown in Figure 2. Is there a specific reason for switching between cell lines also for experiments shown in Figures 3 C- I? Did the authors repeat some of the key experiments in both cell lines?In mammalian cells, Shh-induced activation of GLI2 depends on primary cilia . NIH3T3 cells form the primary cilia but HEK293T cells do not. Therefore, we used NIH3T3 cells to examine the processes that are regulated by the Shh treatment assay . The HEK293 cells were used to map binding domain between ULK4 and STK36/GLI2/SUFU due to the high transfection efficiency.1. In Figure 2 D-E the authors nicely showed that hUlk4N-HA interacted with CFP-Stk36 but not with Myc-Gli2/Fg-Sufu whereas hUlk4C-HA formed a complex with Myc-Gli2/Fg-Sufu but not with CFP-Stk36. In Figure 4E the authors showed in their Co-IP experiments that Fg-Stk36 and Myc-Gli2 form a complex independent of SHH treatment. Did the authors see some pull down of Stk36, still in complex with Gli2, using hUlk4C IP and pull down of Gli2, still in complex with Stk36, using hUlk4N IP?We did not test that. As we have shown in Figures 4A and 4E, knockdown of endogenous ULK4 nearly abolished the interaction between Myc-GLi2 and Fg-Stk36, suggesting that Ulk4 is the major scaffold to bring Skt36 and Gli2 together, and that there is little if any direct interaction between GLi2 and Stk36.1. Another method to verify hULK4-Stk36-Gli2 complex formation  would be helpful. For example, proximity ligation assays, tripartite split GFP assays, or colocalization based on expansion STED immunofluorescence microscopy could be performed to temporally and spatially resolve localization of Ulk4, Stk36 and Gli2 upon SHH stimulation in the primary ciliumThanks for the suggestions. We think that our current study using biochemical and cell biology approaches have provide sufficient evidence that Ulk4, Stk36 and Gli2 form complexes. We will keep in mind of those more sophisticated methods in our future endeavors.1. Please provide more representative images of Ulk4, Stk36 and Gli2 localization in NIH3T3 cells or lower magnification overview images showing more than one cell .We have provided more representative images in Figure 5- figure supplement 1A-F of the revised manuscript.1. Confirmation of the results shown in Figure 5 in a second cell line would strengthen the data.We have confirmed the results in MEFs 1. Did the authors add immunofluorescence for tubulin as a ciliary base marker to ensure correct assignment of ciliary tip versus ciliary base localization for quantification experiments ?It has been well documented that GLi2 is accumulated at the ciliary tip in respond to Shh treatment; therefore, we used Gli2 as a marker for ciliary tip where both Ulk4 and Stk36 were also accumulated. γ tubulin staining could be another marker to assign the ciliary tip vs base; however, the antibody combination we have did not allow us to simultaneously stain γ tubulin and acetylated tubulin (Ac-Tub).1. SMO localization as a further readout of SHH pathway activation might be considered to be added for some of the key results . Is SMO trafficking affected after depletion or overexpression of ULK4?Due to the lack of a workable antibody to detect endogenous Smo in our hands, we did not determine whether the trafficking of SMO is affected after depletion or overexpression of ULK4. However, we noticed that a recent study reported that the SHH-induced ciliary SMO accumulation was impaired in Ulk4 siRNA treated cells . We include this information and its implication in the discussion section1. Do the authors see ULK4 only at the ciliary tip after SHH stimulation or is there also a dynamic time-dependent localization along the ciliary shaft? The image in Figure 6E (dKO + Stk36 WT) seems to show ULK4 also in the shaft.Unlike Smo that is evenly distributed alone the axoneme of primary cilia, ULK4 is mainly accumulated at ciliary tips upon Shh stimulation. Ulk4 is also located at low levels outside the cilia and sometimes in the ciliary shaft during its transit to the ciliary tip .1. Is the immunofluorescence signal for Ulk4 significantly reduced after shRNA treatment to deplete Ulk4 ?We constructed a cell line that stably expressed ULK4 shRNA. The knockdown efficiency was determined by measuring Ulk4 mRNA expression . Because we were unable to obtain a reliable ULK4 antibody for immunostaining, we did not examine by whether ULK4 signal was depleted by Ulk4 shRNA.1. The labelled ciliary tip resembles in some cases images seen for ciliary abscission. The authors could use membrane/ciliary membrane markers to ensure "intraciliary" localization of the investigated factors.Thanks for the suggestion. We will try that in our future experiments.1. How many replicates were used in the three independent quantitative RT-PCR experiments ?We used 3 replicates in each independent quantitative RT-PCR assay.1. Please provide p values or statement on no significance for the comparison between Ulk3 single and Ulk3/Ulk4 double knockdown  and between Stk36 single and Stk36/Ulk4 double knockdown .Thanks for the suggestion, we have added the p value or “ns” as asked.1. Figure legends in general are a bit short could have some more detailed information.Thank you for the suggestion, we have revised the Figure legends as asked.1. What do the asterisks present in Figure 4 C-D?Thanks for the suggestion. The asterisks in Figure 4C-D indicated the full length STK36 and truncated form STK36N and STK36C fragments. We that included this information in the figure legend.1. The authors state that a previous study described ULK4 as a genetic modifier for holoprosencephaly and that this raised the possibility that ULK4 may participate in HH signal transduction. Primary ciliary localization of ULK4 in mouse neuronal tissue and SHH pathway modulation by ULK4 in cell culture have been shown by Mecklenburg et al. 2021 before. Maybe the authors could rephrase their introduction and discussion accordingly.Thanks for the suggestion, we have changed the introduction and discussion accordingly.1. Overexpression studies in heterologous systems using tagged proteins can potentially have an influence on their subcellular localization and function. Please discuss this caveat.We have mentioned this caveat in the “discussion” section of the revised manuscript. However, we have tried to express the transgene at low levels using the lentiviral vector containing a weak promoter to ensure that the exogenously expressed proteins are still regulated by Hh signaling. We have also confirmed that the tagged Ulk4 and Stk36 can rescue the loss of endogenous genes.1. More details in the Methods section should be provided on the SHH induction in NIH3T3 cells, HEK293 cells and MEFs.We have revised the methods section on Shh induction.1. ULK4 is known to have at least three isoforms that exhibit varying abundance across developmental stages in mice and humans  (DOI:10.1242/jcs.137604). Can the authors speculate on potential common and distinct functions of the different ULK4 isoforms on SHH pathway modulation based on their present results?It is interesting that Ulk4 has multiple isoforms in both mouse and human. Several short isoforms in both mouse and human lack the pseudokinase domain while one short isoform in mouse lacks the C-terminal region essential for Ulk4 ciliary tip localization. We speculate that the C-terminally deleted isoform may not have a function in the Shh pathway based on our results shown in Fig. 7 and 8 but might still have functions in other cellular processes.Reviewer #2 (Recommendations For The Authors):The paper is well written, and clear throughout, with excellent (up-to-date) citations to the field.We thank reviewer #2 for the positive comments.Reviewer #3 (Recommendations For The Authors):My only quibble is that the immunofluorescence images are a little confusing, especially to people outside of the field. Please include an image of the whole field and improve the captions. Is that a single cell for each cilia? Why are there so few cilia? The DAPI makes it seem like What are we looking at? Are those multiple nuclei in Figure 6? They seem a little small if that's the 5 uM scale barWe provide uncropped images of Figure 5E to show the entire cells (below). We have added some context to improve the captions. Most of the mammalian cells such as MEF and NIH3T3 cells contain a single primary cilium; however, mutilated cells do exist. The DAPI staining indicated the nuclei. The cells shown in Figure 6 have single nucleus . Due to the unevenness of DAPI signals in the nuclei, only the strong signals (puncta) were shown for individual nuclei.One small typo: GLL2 instead of GLI2 on line 363Thanks, we have corrected this spelling mistake.


S-N equations of concrete with a failure probability p of 0.1~0.5 were derived through statistical analysis of the test results. The fatigue life of the tested specimens exhibited a two-parameter Weibull distribution. In addition to the maximum stress level Smax, the stress ratio R is also a key factor affecting the flexural fatigue life of concrete N. The semi-logarithmic and logarithmic equations were almost identical at the tested stress levels, the latter predicting longer fatigue life for Smax < 0.70. The restraining effect from steel reinforcement slightly lengthened the concrete’s fatigue cracking initiation life. The insight into concrete flexural fatigue properties from this study not only contributes to a better understanding of structural concrete, but also provides a basis for the practical evaluation of concrete or composite bridge decks.Many bridge structural components are subjected to repetitive vehicle load and temperature gradient action. The resulting cyclic tensile stresses within the structures could cause premature fatigue failure of concrete, dramatically impairing structural components’ durability and sustainability. Although substantial knowledge of fatigue properties on low-strength pavement concrete and high-strength structural concrete has been obtained, research on the most widely used normal-grade ordinary concrete in bridge engineering is still ongoing. Therefore, a four-point bending fatigue test of 97 C50 concrete specimens under a constant amplitude sinusoidal wave was conducted in the laboratory, the flexural fatigue behavior of plain and reinforced concrete specimens was studied, and the cyclic deformation evolution of concrete under fatigue loading was obtained. The empirical fatigue  With the increasing vehicle axle loads, concrete bridge decks and other bridge components are prone to fatigue cracking under repeated wheel loading . Once thS-N equations under a fixed stress ratio were proposed in the literature [S-N equations considering the influence of the stress ratio and failure probability were proposed in [The flexural tensile fatigue properties of concrete are primarily obtained through constant amplitude fatigue tests of small-scale beam specimens loaded in four-point or three-point bending. Scholars have conducted numerous experimental studies on the flexural tensile fatigue of concrete since the 1970s , and theterature , and proposed in . In the posed in ,12, mineposed in , lightweposed in ,15, and posed in ,17,18. EWhile fatigue life is still the primary focus in concrete fatigue research, more and more researchers are paying attention to the accumulation and evolution of fatigue damage during the entire process of fatigue loading . DiffereAlthough reinforced concrete members are often used in actual engineering structures, plain concrete specimens are usually employed in bending fatigue tests. The effect of steel reinforcement on concrete fatigue cracking has yet to be fully explored . TherefoThe ordinary concrete selected for this study was commercial C50 concrete, thanks to its wide application in bridge engineering. The mix ratio was cement/sand/stone/water = 1:1.93:3.02:0.46. Among these, the cement was ordinary 425 Portland cement produced by a local plant, the sand was medium natural sand with a fineness modulus of 2.4, and the coarse aggregate was rubble and cobble gravel with a maximum particle size of 25 mm. The target slump was 180 ± 20 mm. A high-performance water-reducing agent STD-PCS of 1.99% was added for improved workability. The water-reducing agent STD-PCS was a polycarboxylic acid-type superplasticizer manufactured by a local company . The workability of fresh mixtures was evaluated with the standard slump cone with dimensions of a 100 mm diameter on the top, a 200 mm diameter on the bottom, and 300 mm high. More information about the concrete mix is given in The steel reinforcement under consideration was the commonly used grade HRB400. The standard values of the steel’s yield strength, tensile strength, elastic modulus, and elongation percentage are 400 MPa, 540 MPa, 200 GPa, and 16%, respectively.Standard flexural strength specimens with dimensions of 150 mm × 150 mm × 550 mm, as shown in The reinforced concrete specimens were identical to their plain concrete counterparts except for reinforcement. A reinforcement ratio of 1%, which is typical in concrete bridge decks, was provided in the reinforced concrete specimens. Two full-length grade HRB400 Φ12 mm reinforcing bars were placed in the bottom part of each specimen, with a concrete cover of 30 mm. A schematic diagram of the reinforced concrete specimens is shown in All specimens were produced with a wooden formwork. After concrete pouring, the specimens were covered with a polyethylene sheet and cured for 28 days under standard curing conditions (at a temperature of 22 °C and a relative humidity of 95%). After 28 days of standard curing, the specimens were stored in the Mechanics Laboratory near the testing machine. No special treatment was provided. Roughly, they were exposed to a room temperature of 17~27 °C and relative humidity of 30~80%. At the time of testing, the age of the specimens was 35~60 days. All beam specimens were tested under four-point bending conditions, as shown schematically in The fatigue test was conducted with a QBS-50A electro-hydraulic servo-controlled universal testing machine in the Engineering Mechanics Laboratory at the Beijing University of Technology. The testing machine, manufactured by Changchun Qianbang Testing Equipment Co., Ltd. , has a maximum load capacity of 50 kN and a loading frequency of 0.1~10 Hz, as shown in R is the ratio between the minimum stress level Smin and the maximum stress level Smax. Smax in the range of 0.65~0.90, and Smin of 0.10, 0.25, and 0.4 were considered in the test program. The fatigue test matrix for the PC series (plain concrete specimens) and RC series (reinforced concrete specimens) is shown in A fatigue loading matrix with combinations of the maximum and minimum stress levels was designed. Stress levels are defined as the fatigue stresses divided by the static strength. The stress ratio Fatigue failure is defined when a plain concrete specimen breaks or a macroscopic concrete crack appears at the side surfaces of a reinforced concrete specimen. The fatigue test was terminated at the time of failure or after a predetermined number of cycles. A specimen undergoing no signs of failure after 1 million loading cycles was terminated in the fatigue test for plain concrete specimens and was termed run-out. For the reinforced concrete specimens, fatigue loading usually continued after the first sign of concrete cracking until far surpassing the observed fatigue life of the plain concrete counterparts tested under similar stress levels. The predetermined number of cycles for the fatigue test termination of the RC series was between 10,000 and 80,000, depending on the tested stress levels.The fatigue testing machine automatically recorded load, displacement, and the number of cycles of the actuator, and a real-time stress-versus-time curve was displayed to facilitate test monitoring. For continuous measuring of the strain during the fatigue test, an extensometer was used to determine the average strain at the bottom surface of the specimen over the pure bending region, i.e., the middle third of the span. A YYJ-(–2)-5/6 extensometer, manufactured by NCS Testing Technology Co., Ltd. , has a default gauge length of 6 mm, a measurement range between –2 mm and 5 mm, and a measuring sensitivity of 0.001 mm. Rigid Z-shaped angles were glued to the bottom surfaces of test specimens to ensure cracks occurred within the gauge length. The gauge length was thus extended to 90 mm for plain concrete specimens and 146 mm for reinforced concrete specimens, respectively. p of a particular specimen could be estimated by the average rank as in the following expression [i denotes the failure order, and k is the total number of specimens tested at a particular stress level.The observed fatigue life of concrete specimens is a random variable with great discreteness. When the fatigue life data were arranged in ascending order, the failure probability pression :(1)p=ik+p satisfies Equation (2). Equation (3) can be derived to test whether a group of experimental results follows the two-parameter Weibull distribution. Suppose the regression analysis of the experimental data can show a good statistical linear relationship between lnln(1/(1 − p)) and lnN; that is, the coefficient of determination R2 is relatively high. In that case, this assumption is valid, and vice versa.m is the shape parameter, and the scale parameter can be expressed as Concrete fatigue life is generally assumed to conform to the two-parameter Weibull distribution ,9. AccorSmax is of primary concern, it is desirable to consider the effect of the stress ratio R on the probabilistic distribution of fatigue life. According to the literature [Smax can be combined for statistical analysis. The equations for the Weibull distribution test can be rewritten as follows:Recall that the experiment program includes specimens tested with combinations of the maximum and minimum stress levels, as described in terature , using eS-N equations have been proposed. The maximum stress level Smax has traditionally been written as S for conciseness. While the dependent variable fatigue life N is always expressed in logarithm, the independent variable can either be S or the logarithm of S. Some S-N curves apply to fatigue tests conducted at a fixed minimum stress level, usually close to 0, and others can consider the effect of the stress ratio R.Various fatigue a or A is the basic strength corresponding to N = 1, and slope b or B is called the fatigue strength exponent.The semi-logarithmic and logarithmic fatigue equations for specimens fatigue-tested with a fixed minimum stress level are expressed as follows:R, can be expressed as follows:a, b, A, and B have the same physical meaning as those in Equations (6) and (7), except equivalent fatigue life The semi-logarithmic and logarithmic fatigue equations, when considering the stress ratio Smin of 0.10, and Equations (8) and (9) when considering the stress ratio. If the fatigue life or equivalent fatigue life correlates with two-parameter Weibull distribution, the fatigue life N, or equivalent fatigue life p, can be calculated by Equation (10) by rewriting Equations (2) and (4).A direct quantitative relationship between fatigue life and failure probability could be established for reliability analysis applications. Probabilistic fatigue equations are obtained by substituting the fatigue life of various failure probabilities into Equations (6)–(9), Equations (6) and (7) for constant Fatigue test results were obtained from 55 plain concrete specimens (PC series) and 42 reinforced concrete specimens (RC series). The maximum and minimum fatigue stresses were determined from the preset stress levels  and the The compressive strength was obtained from standard tests on six cubic specimens for each series. The test results, along with the statistical values, are shown in Concrete flexural strength was obtained from standard four-point bending tests on 9 PC series beam specimens and 24 RC series specimens. The six beams in Sets 7 and 8 of the RC series were specimens with reinforcement. While all plain concrete specimens fractured in the middle third region, the reinforced concrete specimens did not fail due to the strength of reinforcement. Therefore, the flexural strength of the concrete in the reinforced concrete specimens was determined when macroscopic cracks appeared on the side surfaces of the beams.The measured static flexural strengths of the two batches of concrete, along with the statistical values, are shown in Towards the end of the fatigue test, a vertical crack was observed to develop in the middle region in most plain concrete specimens, followed by a sudden fracture. The location of the fracture surface was random. However, all beams failed in the middle third pure bending region, and the fracture surface was generally planar. Most of the coarse aggregates were fractured, and a few pullouts of coarse aggregates along the interface between the coarse aggregates and cement mortar made the fracture surface zigzag. A typical fatigue failure of the plain concrete specimen is presented in For reinforced concrete specimens under fatigue loading, small cracks also occurred initially on the bottom surface within the pure bending region. After these cracks became macroscopic, they appeared on the side surfaces of the concrete specimen and slowly extended upward with the application of cyclic loading. At the same time, concrete cracks continued to develop at other locations of the pure bending region and gradually merged. Since there was tensile reinforcement, the specimen stiffness did not change apparently after concrete cracking, and it did not break abruptly. As the fatigue cracking life of concrete was the primary interest in this work, the fatigue test was stopped after visible cracks appeared on the side surfaces of specimens. A typical concrete fatigue failure of the reinforced concrete specimen is shown in Fatigue life is the number of cycles a specimen can sustain before failure. The fatigue life of plain concrete specimens is summarized in Even in carefully controlled tests, it is observed in Similarly, the reinforced concrete specimen is designated with an additional “J”, as J-S-a-b-x, where all other parameters have the same meaning as in the PC series. With an extensometer installed on the bottom fiber of the specimen, the longitudinal deformation and strain of the concrete were continuously recorded during the fatigue test. Under fatigue loading, the concrete strain increased non-uniformly with the elapse of loading cycles. This phenomenon was observed in all specimens under different stress levels.The strain-versus-time curve of a typical plain concrete specimen in The strain amplitude is the difference between the corresponding strains under the maximum and the minimum loads. While the strain amplitude stays stable for most specimens during the fatigue loading cycles, the increase in the strain amplitude is prominent for specimens tested under higher stress levels and whose fatigue life is less than 1000 cycles, as shown in Some peculiarities in strain measurement were observed during the fatigue testing. For example, in For the test specimens whose fracture occurred within the measurement range of the extensometer, the measured minimum and maximum strains during the last cycle of fatigue loading are summarized in As seen in The number of cycles when a macroscopic crack was observed on the side surfaces of a reinforced concrete specimen is shown in the figure as a dotted line, and the right end shows when the fatigue test was terminated.For the typical reinforced concrete specimens shown in The strain-versus-time curve in To analyze the fatigue strain development in the reinforced concrete specimens, the measured minimum strain, measured maximum strain, and extrapolated residual strain (the remaining strain if the specimen is unloaded to 0) just before fatigue concrete cracking of the specimens are summarized in As observed in A continuous cyclic stress-versus-strain curve can be obtained, with stress as the ordinate and strain as the abscissa. The measured cyclic stress–strain curves of typical plain concrete specimens are shown in Since the fatigue test was under load control, both the maximum and minimum stresses remained constant during fatigue loading. As shown in n/N are also depicted in n is the number of fatigue loading cycles and N is the total fatigue life. During the earlier stages of fatigue loading, the stress–strain response became more linear elastic. With the increase in the cycle ratio, plastic damage in the concrete accumulated gradually. As the fatigue loading continued, the loading and unloading branch in a cycle tended to form a hysteresis loop. The area of the hysteresis loop, to some extent, represents the strain energy consumed by the concrete and the fatigue damage accrued during each fatigue loading cycle.The stress–strain curves at the specified cycle ratio The measured cyclic stress–strain curves of typical reinforced concrete specimens are shown in n/N increased from 0.5 to 1.Similarly, the cyclic stress–strain curves of the reinforced concrete specimens show a decrease in the deformation modulus as the fatigue loading continued. Because of restraint from the reinforcement, the decreasing trend in the concrete deformation modulus and specimen stiffness in the reinforced concrete specimens with the number of loading cycles was less noticeable compared to the plain concrete specimens. While a significant decrease in the deformation modulus within the last 10% of fatigue life for the PC series is evident in Smax of 0.65 did not fail after 1 million cycles and were termed run-outs. Four outliers in m and lnt0 in Equations (3) and (5), respectively.In p)) and lnN  and (7) were then obtained from simple transformation.When the minimum stress level was fixed as 0.10, the fitting of the plain concrete (PC series) and reinforced concrete (RC series) fatigue test results to the fatigue R2 close to 0.90. However, the R2 of the PC series was about 0.60, which indicates that only 60% of the variation in N can be explained by the regression relationship. Large discreteness can be observed between the PC specimens with the same stress level, particularly at a lower stress level of 0.75. The reinforced concrete specimens show a slightly longer fatigue life than the plain concrete counterparts, indicating that although reinforcement mainly controlled the fatigue crack propagation in the reinforced components, the existence of reinforcement did affect the flexural fatigue cracking of concrete beneficially.It can be seen in S and substituting S with the semi-logarithmic fatigue equation, a relationship between lgS and lgN can be obtained, that is, S to a lower value of less than 0.70, the logarithmic fatigue equation predicts a fatigue life longer than the semi-logarithmic fatigue equation. This observation is consistent with previous research [By taking the logarithm of S was also taken as an independent variable when considering the influence of the stress ratio R. Similar to R and fatigue life N as a, b, A, and B in Equations (8) and (9) were obtained through simple transformation.The maximum stress level ss level . This N¯R, the fatigue equations of the plain and reinforced concrete specimens are comparable, with the RC series showing a slightly longer fatigue life. However, the coefficients of determination of the fitted equations are not high (0.61~0.66). This low linearity correlation reflects the complexity of the concrete fatigue phenomenon, especially in the sense of significant variation.It can be seen in S and substituting S with the semi-logarithmic fatigue equation, a relationship between lgS and lgN can be obtained, that is, Similarly, by taking the logarithm of S-N curves from this study are summarized in The mean fatigue m and t0 from The regression analysis in a, b, A, and B under different failure probability p were obtained. The values are shown in R2 value of the regression analysis was obtained as 0.83 under a failure probability of 0.1, indicating a linear relationship between S (or lgS for logarithmic equation) and lgN. Comparing The data in S-N curves have similar slopes, but the intercept increases with higher failure probability [The fatigue equations of the plain concrete specimens under different failure probabilities are also shown in bability .In this section, we compare the fatigue equations obtained from the experimental investigation with those proposed by other scholars based on their fatigue test results. Since probabilistic fatigue equations are not available explicitly in the literature, only the mean fatigue equations were analyzed. Similarly, the comparison focuses on the fatigue analysis results of the plain concrete specimens.When the minimum stress level was fixed at 0.10, the fatigue equations of the plain concrete specimens obtained in the current study were compared with those proposed in References ,8,13. A f and slightly lower fatigue strength. The large discreteness of the test results observed in the test program might have caused some discrepancies. The difference in the S-N curves’ slope in As can be seen in R is considered, the fatigue equations of the plain concrete specimens obtained in the current study were compared with those proposed in References [When the effect of the stress ratio ferences ,10. A suf of three batches of concrete was relatively close. In short, the difference between the fatigue equations obtained from similar test conditions when considering the effect of the stress ratio is slight. Regarding the influencing factors for the fatigue characteristics of concrete, both the maximum stress level and stress ratio are essential parameters, followed by the influence of the concrete strength grade, with slightly less significance. This observation confirms the conclusions from earlier research [It can be seen in research .Large discreteness in the fatigue life and longitudinal strain of concrete was observed for specimens tested under the same stress conditions, even in carefully controlled fatigue tests. This large discreteness was partly caused by imperfections in the fatigue testing machine and measuring techniques. It also reflects that concrete fatigue is a complicated problem, and deep understanding of the important affecting parameters and the failure mechanism still needs to be improved. With upgraded test facilities, more fatigue tests with lower stress levels (0.65~0.75) and possibly extending the fatigue loading up to 2 million cycles are desirable in future investigations.The longitudinal strain in nearly 100 concrete specimens was continuously recorded during the fatigue test. The maximum strain just before fatigue failure was analyzed. Much work is required to utilize the collected strain data fully. For example, the evolution of the maximum, minimum, residual strains, and strain amplitude during the entire process of fatigue loading is still ongoing, from which a strain-based damage variable could be constructed, and its evolution studied. Following this, the evolution of the elasticity modulus of concrete (both tangent and secant modulus) should be analyzed. Eventually, a cyclic constitutive model will be proposed, considering flexural tensile fatigue damage. With the aid of standard finite element software, the fatigue behavior of structural components such as concrete bridge decks, could be practically predicted with relative ease.S-N curves. Comparative studies, like the one in the literature [At last, it should be pointed out that only the Chinese standard was used in this study. One might justify that concrete is an engineering product highly dependent on local raw materials, and concrete must be produced, tested, and evaluated strictly according to national standards. Differences in the technical rules exist between various national and international codes and standards. For example, while Φ150 mm × 300 mm cylinders are adopted to obtain the axial compressive strength in CEB-FIP, 150 mm × 150 mm × 300 mm prisms are specified in the governing Chinese code ,29. It wp varying from 0.1 to 0.5 for specimens with a fixed minimum stress level of 0.10, and when considering a stress ratio R varying from about 0.11 to 0.44, were obtained respectively through regression analysis. These fatigue equations were then compared to those available in the literature. The following conclusions are drawn:(1)Smax. The semi-logarithmic and logarithmic equations were nearly identical at the tested stress levels, with the latter predicting longer fatigue life for Smax < 0.70.Two-parameter Weibull distribution could describe the fatigue life of specimens tested under the same maximum stress level (2)R is an essential factor affecting the fatigue life of concrete, the effect of which shall not be ignored and can be conveniently considered through the equivalent fatigue life The stress ratio (3)Although the PC specimens failed in brittle fracture and the RC series exhibited ductile behavior after macroscopic concrete cracking appeared, the fatigue cracking life of these series are relatively close, with the latter slightly longer. The restraining effect from steel reinforcement influences the fatigue crack initiation of concrete.(4)Fatigue equations of normal-grade C50 ordinary concrete lie slightly below those of high-strength concrete. Although not as important as the maximum stress level and the stress ratio, the material strength grade affects ordinary concrete’s flexural fatigue properties.(5)During the stress-controlled bending fatigue tests, the measured concrete strain developed in a three-stage manner with a continuously increasing value. The maximum longitudinal strain in the concrete just before fatigue failure was in reverse proportion to the maximum stress level applied.Four-point bending fatigue tests of 55 plain concrete (PC series) and 42 reinforced concrete (RC series) beams were conducted for the flexural fatigue properties of normal-grade C50 ordinary concrete, and the fatigue life data of test specimens were analyzed and fitted to semi-logarithmic and logarithmic equations. Probabilistic fatigue equations with a failure probability In the future, the evolution of cyclic strain, the stiffness degradation, and the fatigue damage constitutive relationship shall be established to lay a foundation for the fatigue assessment of reinforced concrete structures.