Since the discovery of the T cell receptor (TcR), immunologists have assigned somatic hypermutation (SHM) as a mechanism employed solely by B cells to diversify their antigen receptors. Remarkably, we found SHM acting in the thymus on α chain locus of shark TcR. SHM in developing shark T cells likely is catalyzed by activation-induced cytidine deaminase (AID) and results in both point and tandem mutations that accumulate non-conservative amino acid replacements within complementarity-determining regions (CDRs). Mutation frequency at TcRα was as high as that seen at B cell receptor loci (BcR) in sharks and mammals, and the mechanism of SHM shares unique characteristics first detected at shark BcR loci. Additionally, fluorescence in situ hybridization showed the strongest AID expression in thymic corticomedullary junction and medulla. We suggest that TcRα utilizes SHM to broaden diversification of the primary αβ T cell repertoire in sharks, the first reported use in vertebrates. All jawed vertebrates share fundamental components of the adaptive immune system. The cartilaginous fish (including sharks) are the most divergent jawed vertebrate group relative to mammals and use a polymorphic major histocompatibility complex (MHC) , multiplAlthough in general immunologists think TcR loci do not undergo somatic hypermutation, a few reports do exist of AID-mediated SHM in T cells. However, non-productive TcRα rearrangements in hybridomas , TcRβ seCarcharhinus plumbeus) revived the notion of SHM at TcR loci. Sequencing of the entire TcRγ translocon in C. plumbeus showed definitively that SHM is occurring at that locus  and perhaps in the alpha chain of MHC-restricted αβ T cells  in sandbar shark spleen  using peWe then investigated the possibility of mutation occurring at the TcRδ locus. We analyzed mutation in clones from nurse shark thymus, peripheral blood leukocytes, and spiral valve, conservatively grouping 111 clones into 12 V genes from 7 TcRδ families . Only ononly clones containing the same CDR3 encoding rearrangement and N and P nucleotide sequences provided us the assurance that we had distinct αVs descendant from clonal T cells, since it would be extremely unlikely that two T cells created receptors that contained the exact same nucleotide sequence by chance.We identified 17 germline α/δ V gene sequences corresponding to 12 unique V segments. Unfortunately, these segments matched only two groups of sequences in our TcRα dataset (TcRα/δ V4 and V9), likely due to inter-individual polymorphisms. In the absence of a complete germline sequence for this locus, we limited our database for TcRα to thymocyte clones with the same unique CDR3 signature. The CDR3 region results from the somatic recombination and assembly of variable (V) and joining (J) gene segments during lymphocyte development in the thymus . The recWith SHM confirmed in γ and δ TcR chains but apparently not the TcR beta chain of nurse shark, we checked for mutation of the TcRα locus. One might expect mutation in γδ T cells since antigen binding more closely mirrors that of B cells. However, mutations to receptors of MHC-restricted αβ T cells would be surprising given that even minor modifications to these receptors could risk incompatibility with MHC.Joanie, Mary Junior). Of this total, only 447 sequences contained complete CDR3-J junctions , each V α family containing anywhere from one to ten clonal groups (Our preliminary V α dataset contained 539 TcRα clones (encoding 286 unique amino acid sequences representing nine V α families) from three tissues  of two sharks (l groups . The majl groups . We inclaV7.4m_THY09_051410 and aV5J_SPV17_102810) contained one 3-base insertion and one sequence (aV1.4J_SPV07_090110) contained an 18-base insertion; although SHM can result in insertions and deletions . The highest mutation frequency occurred in CDR1 and accumulated significantly more mutations overall than other regions  and 2931 A/T base pairs within WA/WT hotspot motifs , although they were 2.3x as likely to mutate within hotspots than outside hotspots. Further, while A:T mutations occurred more often than expected in both FRs and CDRs (p=0.0015), the frequency of A:T mutations were 1.9x more likely in CDRs than FRs. We found 1327 G/C base pairs within Dhotspots . OverallWe identified 283 mutations within the eleven CDR3 groups. There was a bias toward mutations of G and C nucleotides (p=0.0022) and G:C changes comprised 57% of all mutations . More muSince we cloned TcR αV sequences in both central (thymus) and peripheral  lymphoid tissues, we analyzed mutation frequencies by tissue type. Although data were limited to only six sequences in two CDR3 groups , we found more mutations to FRs of peripheral sequences, though this was not significant  in the thymus. We confirmed the expression of AID in the thymus through real-time RT-qPCR, where thymus tissue expressed AID at more than half (0.7x) the levels found in spleen  and nearly 6x the levels observed in forebrain  that hybridize along the length of the target RNA, the resulting signal is detectable only when tens of probes hybridize to the target. This makes the technology very specific -- only those transcripts bound to numerous probes are visible -- and limits the potential for false-positive or false-negative results (We refined our CISH results with RNA fluorescence in situ hybridization (FISH) using probes against the TcR alpha constant region (αC) and exons 2 and 3 of  results . Our FIS results , regions results . Thus, w−3 mutations per base pair per cell division (GYW/WRCH (and less to WA/TW)  . The seqo WA/TW) . The abio WA/TW) . Despiteo WA/TW) , the asso WA/TW) . Despiteo WA/TW) .Recent studies reported the incidence of SHM in the γ chain of γδ T cells of sandbar shark  and in bCH/DGYW motifs per sequence than do human V segments (p=0.02). Further, motifs in CDRs of shark occurred 2-3x as often as in humans . The bias we found for nonsynonymous and non-conservative mutations in TcRα CDRs in the shark thymus are consistent with more than simple repertoire diversification; it suggests selection for changes in paratope.In the present study, we verified SHM occurring within the γ and δ chains of γδ T cells in both thymic and peripheral immune tissue of nurse shark. Remarkably, we also detected SHM occurring in the α chain of αβ T cells. We observed mutational characteristics within α chain of nurse sharks similar to those found in B cell SHM. We observed an overall mutation frequency of 0.0226 substitutions per nucleotide (S/N) and a bias toward transition mutations. Further, we detected both single and tandem mutations, a pattern unique to sharks that also occurs in shark B cells. Changes to G and C nucleotides comprise 66.1% of all mutations. Mutation was twice as frequent in CDRs as in FRs , and substitutions in CDRs were significantly more likely to result in amino acid changes. Further, mutations were strongly associated with AID hotspots, and substitutions to G and C nucleotides occurred nearly 1.4x as often within CDR hotspots than FR hotspots. Out of curiosity, we compared counts of AID hotspot motifs within CDR and FR regions between our 11 nurse shark TcR αV consensus sequences and 6 human TcR αV segments . We found that shark TcR V segments exhibit far more WRreceptor editing  could be involved in salvaging cells for positive selection or rescuing cells from death by negative selection. If AID-induced SHM occurs in conjunction with receptor editing and positive selection, AID should be upregulated in cells undergoing RAG-mediated alpha rearrangement . However, if SHM occurs pression  suggest pression  and redupression . Howeverpression . We cann+ T cells and immature B cells in mice. T cells that expressed AID also produce a distinctive cytokine profile, are associated with cell activation, and increase in abundance with age, suggesting these cells have distinctive long-term functions in aging cells. In immature B cells, AID expression may help negatively select autoreactive B cells and contribute to primary repertoire diversity. Together these results may indicate that AID expression in mice is a relic of a more extended expression in earlier species  rearrange Ig-TcR chimera using IgM and IgW V exons with TcR D-J-C . The TcRIn the broader scope of lymphocyte evolution, we must consider whether the ancestral vertebrate lymphocyte employed APOBEC-family-mediated diversification before the ‘big bang’ of RAG (reviewed in ). LampreFrom this trend of comparative TcR studies, we conclude with two hypotheses that we will test with further immunogenetic and functional studies in shark and other vertebrate models. First, the division between B and T cell repertoire diversification components and mechanisms was not as clear-cut in ancestral lymphocytes as in modern humans and mice. The second is that different vertebrate groups have not only evolved myriad diversifications for Ig repertoires and function, but TcR biology may be just as varied. This premise is already accumulating ample supporting evidence as IgHV domains , high alGinglymostoma cirratum) delivered by caesarian section off the Florida Keys and matured in the aquatic vivarium of the University of Maryland’s Center of Marine Biotechnology. We used published T cell αV sequences  overdose, and immediately purified RNA with TRIzol reagent . Nurse shark thymi are located dorsomedial to the gills  in the cWe generated a 5’ RACE (Rapid Amplification of cDNA Ends) library using the GeneRacer Kit (Life Technologies) and reverse primers designed to the end of the shark TcRβ, TcRγ, or TcRδ variable (V) region or to the middle of the shark TcRα constant (C) region. We amplified RACE products using Phusion High-Fidelity DNA polymerase  to minimize PCR errors under these specific PCR conditions: primary denaturing at 94°C for 2 min; 30 cycles at 94°C for 30 s and 78°C for 1 min; and a final extension at 72°C for 10 min. Using this RACE library, we then amplified a specific α V region using a gene-specific primer to its leader region and the following PCR conditions: 98°C for 1 min; 25 cycles of 98°C for 5 s, 49–60°C for 30 s, 72°C for 150 s; 72°C for 10 min. Annealing temperatures varied for each amplified αV see . We visuEco RI restriction enzyme , then amplified and purified the sequencing reaction using BigDye xTerminator Sequencing and Purification Kit . We submitted samples for sequencing to the DNA Technologies Core Lab on the Texas A and M University campus . We deposited sequences in GenBank with the following accession numbers: Alpha KY189332-KY189354 and KY366469-KY355487; Beta KY351708-KY366487; Gamma KY351639-KY351707; Delta KY346705-KY346816.We transformed PCR amplicons into One-Shot Top10-competent cells (Thermo Fisher) using a pCR4-TOPO TA blunt end vector and cloning kit (Thermo Fisher) followed by a Zyppy plasmid miniprep kit  for plasmid purification of individual clones . We checJoanie, Mary Junior). Using this dataset, we separated sequences containing identical CDR3 rearrangements and counted mutations within each TcR ‘clone family’ bearing the V-J rearrangement from single founder thymocytes.We used Geneious and BioEdit  software to manage DNA sequence data. We aligned nucleotide and amino acid sequences using the ClustalW Multiple Alignment tool in Geneious with a gap penalty of 15, a gap extension penalty of 6.66, and free end gaps. We manually adjusted the alignments as necessary. We determined sequence relationships phylogenetically using the Geneious tree builder with default settings. We grouped sequences into unique V families based on 70% nucleotide sequence identity and 75% amino acid sequence identity  using thG. cirratum BAC library  of shark ‘Yellow’ and screened with variable segment and constant region probes for TcRα and TcRδ. We cultured several positive clones and isolated BAC DNA according to manufacturer’s protocol with the Qiagen Large Construct Kit . We sent purified BAC DNA to the Duke University Center for Genomic and Computational Biology  for PacBio SMRT  large insert (15–20 kb) library preparation, sequenced on the PacBio RSII platform with P6-C4 chemistry. Read correction and contig assembly were performed with the PBcR software .We probed the filter sets for the software , using tOur search yielded 17 α/δ V germline segments, significantly fewer than expected based on TcR αV segment numbers in other species . Of thesWe compared these 17 germline α/δ V segments to our TcR αV database containing all nine potential V families from two different sharks. All 17 germline α/δ V segments aligned to our αV4 data with >75% nucleotide identity, while 15 segments shared >93% nucleotide identity to at least one sequence in our αV4 dataset. Of the 60 sequences in our αV4 dataset, 37 sequences aligned specifically to eight germline α/δ V segments, with alignments containing one to 17 aV4 sequences per germline segment  based on differences to a consensus sequence. We classified all nucleotide changes as either synonymous (SYN) or non-synonymous (NSYN) mutations based on whether or not the codon was unaltered or altered, respectively. For tandem base changes, we assessed the effect of each nucleotide change independent of its neighboring mutation(s). We then compared mutation frequencies between CDR and FR regions for all clone families that contained mutations using a Student’s 1-tailed t-test unless otherwise noted.GYW/WRCH (G:C mutable target) and WA/TW (A:T mutable target) using the motif search function in Geneious. These motifs serve as common ‘hotspots’ for SHM within Ig variable regions, where AID favors the G/C bases within DGYW/WRCH motifs during the first phase of SHM while low-fidelity polymerases  preferentially target A/T bases within WA/TW motifs during the second phase of SHM (GYW/WRCH or WA/TW hotspots. We then examined each mutation to determine if it occurred inside or outside a hotspot. We counted changes from the consensus sequence to a target nucleotide within its respective motif as a hotspot mutation. We defined the frequency of hotspot mutation as the number of mutations (of target nucleotides) occurring within hotspots divided by the total number of mutations for each region. From these data, we compared the mutability of bases between FR and CDR regions using χ2 Analysis.We searched for the ProSite motifs De of SHM . We coun2 analysis to compare mutability indices between FR and CDR regions.We calculated a mutability index for each nucleotide using methods similar to G. cirratum AID mRNA with primers NSAIDEH2 and NSAIDEH1  available online at www.biosearchtech.com/stellarisdesigner (Version 2). We hybridized TcR αC with the CalFluor Red 610 fluorophore and the AID sequence with the Quasar 670 fluorophore for the Stellaris RNA FISH Probe set . We followed all manufacturer’s instructions for frozen tissue (available online at www.biosearchtech.com/stellarisprotocols), allowing hybridization probes to incubate for 16 hr. We counterstained slides with wash buffer containing 5 ng/mL of DAPI . We obtained 10x, 20x, and 63x images using a Zeiss Stallion Digital Imaging Workstation including a 2x CoolSnap HQ Camera and Zeiss Stallion software. We merged Z-stacked images of each fluorophore together and edited and processed images using ImageJ software, version 1.47  on adult nurse shark (‘Black’) thymus tissue. Slides contained two 8 μm thick sections of flash frozen thymus tissue preserved in OCT. We designed custom Stellaris FISH Probes against the TcR alpha constant region (αC) for T cell identification and exons 1 and 2 of ion 1.47 .We synthesized cDNA from nurse shark spleen, thymus, muscle, and forebrain RNA (see RNA purification and extraction methods above) using SuperScript III First-strand Synthesis System  and a 1:1 mixture of oligo-dT and random hexamer primers. We then amplified cDNA using touchdown PCR on an MJ mini thermal cycler  and GoTaq colorless DNA polymerase (Promega Corp) using the following conditions: primary denaturing at 94°C for 2 min, five cycles at 94°C for 30 s and 56°C for 4 min; five cycles at 94°C for 30 s and 54°C for 4 min; 20 cycles at 94°C for 30 s, and 52°C for 30 s, and 72°C for 4 min; with a final extension at 72°C for 10 min. We visualized PCR products using agarose gel electrophoresis (as described above) to verify presence of AID in each tissue. We then cloned and sequenced the resulting PCR products to confirm the sequence was AID.We looked for relative AID expression in shark spleen , thymus, and forebrain (negative control) at four tissue concentrations  using the SYBR-green RT-PCR reagents kit  on a LightCycler 480 System . We analyzed relative quantification using the LightCycler480 software and quantified relative AID expression using the ΔΔCq method. We normalized results against shark muscle tissue using beta2-microglobulin (β2M) as a reference gene. We present data as expression-fold changes of AID to β2M. In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses. A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included.eLife. Your article has been favorably evaluated by Michel Nussenzweig (Senior Editor) and three reviewers, one of whom, David Schatz (Reviewer #1), served as a Guest Reviewing Editor. The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.Thank you for submitting your article "Somatic hypermutation of T cell receptor α chain contributes to thymic positive selection in nurse sharks thymus" for consideration by Summary:The authors demonstrate and characterize somatic hypermutation (SHM) in TcRα, γ, and δ chains in the nurse shark. TcRα hypermutation is described for the first time in any TcRαβ system, although it was previously observed in sandbar shark TcRγδ chains. No mutation was observed for nurse shark TcRβ. SHM had been predicted to be disallowed in TcRαβ systems as it was never observed in mammals and has the potential to disrupt TcR-MHC I/II interactions. The findings here challenge that view and suggest that at least in shark, SHM of TcRα in the thymus contributes to repertoire diversification and potentially to α-β T cell positive selection. Consistent with the findings from TcR chain sequencing, the authors provide evidence in favor of AID expression in the thymic cortex and corticomedullary junction. The authors are experts in the field of comparative VDJ immunity and have published widely on this topic. The presentation of the findings and the discussion of their implications are clear and interesting. The finding highlights an important and unexpected aspect of TcR biology with implications for TcRαβ function in jawed vertebrates. This study should be of significant general interest to immunologists and evolutionary biologists.Essential revisions:1) The major challenge facing the authors is that they do not have the germline sequence of most nurse shark Vαα gene segments, and hence they have to infer a germline sequence from the cDNA sequences they obtain. To do this, the authors assume that if the same CDR3 sequence arises more than once, it must derive from the same original V-to-J rearrangement, and hence that sequence differences between two such clones must represent somatic mutations. Unfortunately, while this argument is strong for IgH, TcRδ, and TcRβ sequences that include D segments, it is potentially weak for TcRα rearrangements where a single joint is formed and junctional diversity can be low. To have confidence that duplicate CDR3 sequences represent unique rearrangements, one would want to examine the extent of nucleotide deletion and addition; only in joints with significant addition/deletion would one be confident that the junction is likely to be unique. The problem is compounded by the fact that VDJ recombination has a tendency to use microhomologies (if they exist) at the ends of the two gene segments to mediate joining, and this can lead to the same junction repeatedly. Was the same CDR3 sequence ever observed in different sharks? The authors need to justify their underlying assumption and provide an explicit discussion of the specificity of CDR3 sequence for rearrangements in each chain.2) In addition, the data contain a significant puzzle: a very high level of shared CDR3 among a relatively small number of unique sequences. Specifically, 72 unique amino acid sequences, representing 12 V-α families, were obtained, which would correspond to an average of 6 unique sequences per V family, and an average of only 3 unique sequences per V family per shark. Given that the starting 5 microgram aliquots of RNA should derive from hundreds of thousands of cells, each starting RNA sample should contain a large number of independent V-J rearrangements for any given V. Given this and that there appear to be multiple Jα gene segments in the nurse shark, the chance of finding the same CDR3 sequence in a handful of sequences for a given V would be predicted to be very low. The chance of finding 42 sequences out of the 72  that share CDR3 with another sequence seems exceedingly unlikely. The authors need to carefully address this issue. The authors should provide a table that lists the number of unique aa sequences obtained for each V family within the 72 sequences, and of those, the number that have an identical CDR3.The authors did in fact derive the germline sequence of two V family members (V4 and V9). Why not focus the analysis on these two families, where such ambiguities would be less of an issue? Furthermore, one of the reported set of sequences does arise from the V4 family, but it does not appear that the germline sequence information was taken advantage of. Why? And, were other sequences from V4 and V9 obtained in the dataset, and did they show mutations compared to the germline sequences?It is noted that all reviewers agreed that the nature of the sequence differences observed  are consistent with the mutations being real SHM events.3) Expression of Aicda is not particularly clear in the ISH analysis. The data show a generally darker appearance with the antisense compared to the sense probe, but these differences are not completely convincing. Furthermore, it was difficult to distinguish the cortex vs. the medulla and the appearance is so uniform overall that claims for region specificity for Aicda are unconvincing. More annotation highlighting thymic structure and the probes used would be helpful. Scale bars should be included instead of objective magnification. Overall, it was felt that the Aicda ISH data need to be improved. Possibly other images or higher magnification images would help.4) There were some concerns about the Aicda RT-PCR data. The results are expressed in delta Ct, which is a logarithmic measure, and it would be better to calculate a fold-difference in the expression of AID in spleen and thymus. How much of a difference in expression is there between the negative control (forebrain) and thymus? Was the resulting PCR product cloned and sequenced to confirm its identity? Are there B cells in the nurse shark thymus as there are in mouse and perhaps other cartilaginous fish such as the skate? If so, are the authors sure that AID expression is in T cells in the ISH and RT-PCR analyses? The authors should consider discussing this in the manuscript.eLife. Your article has been favorably evaluated by Michel Nussenzweig (Senior Editor) and three reviewers, one of whom served as Guest Reviewing Editor.Thank you for resubmitting your work entitled "Somatic hypermutation of T cell receptor α chain contributes to positive selection in nurse shark thymus" for further consideration at The manuscript has been improved but there are some remaining issues that need to be addressed before acceptance, as outlined below:The authors have added new RNA fluorescence in situ hybridization data that strengthen the claim that AID is expressed in the shark thymus, and have adequately addressed some of the points previously raised. There remain a number of significant issues that need to be addressed satisfactorily before publication can be considered.Major Points:1) Based on the information provided by the authors in their response to the review, it is now clear that the analysis of mutations in TcRβ, γ, and δ (no CDR3 sequence obtained) was less rigorous and less definitive than in TcRαα ). Hence, all claims that mutations were not found in TcRβ must either be removed or carefully qualified. For example, the second sentence of the Abstract contrasts the findings at TcRβ (no mutation) and TcRα (mutation found) with no qualification, leaving the reader with the mistaken impression that the two analyses were equivalent and the two conclusions equally strong. The same problem was found in the last paragraph of the Introduction, subsection “Somatic hypermutation in TcR γV and TcR δV but not TcR βV”, and in the third paragraph of the Discussion.2) "Since it is highly improbable that two thymocytes would generate identical CDR3 sequences during VJ recombination…" As was pointed out in the original review, this claim is not obvious; it should not be stated in this fashion. Indeed, there are a priori reasons to think that the same CDR3 sequence could readily arise from independent V-J rearrangements. The authors should present this claim as a hypothesis that they then carefully validate with data (which they begin to do in the first paragraph of the subsection “Somatic hypermutation in nurse shark TcR αV”). Furthermore, the conclusion of this sentence that "amplicons containing identical CDR3 sequences must have derived from the same progenitor" is overstated. At best, the conclusion could be that they are "likely to have derived from the same progenitor". A statistical analysis of the V-J sequences might allow the authors to make a quantitative claim of just how likely this is, but in the absence of such an analysis, the claims should be stated cautiously. The manuscript needs to be rewritten to accommodate these points. Same issue in the aforementioned paragraph.3) Closely related to this: The authors have clarified that a larger number of sequences were obtained than was apparent in the initial submission, but this information is not provided in the Results section. Since most readers will not look at the Materials and methods section, it is suggested that the authors add information to the second paragraph of the subsection “Somatic hypermutation in nurse shark TcR αV” to inform readers of the total number of underlying sequences from the two relevant sharks. In addition, the Materials and methods states that sequences were obtained from four sharks; it is confusing that data from only two of the sharks was actually used. Why are all 4 sharks mentioned if data from only two of them were used? How many total sequences were obtained from the two relevant sharks? This is highly relevant given that these are (apparently) the only data from which the analyzed TcRα sequences are derived. This is directly relevant to the concern, expressed in the original review, that the identification of so many repeated CDR3 regions from a small sequence dataset is extremely unlikely. This issue has not been satisfactorily resolved in the resubmission. The requested table that shows how many unique aa sequences were obtained for each V family, and of those, the number that have an identical CDR3, was not provided. Nor have the authors provided a detailed description of the proportion of TcRα sequences that have N/P nucleotides (which would provide higher confidence of assigning SHM) versus those that are directly joined (less confidence). The reviewers remain concerned by the possibility that the number of repeat CDR3 sequences is exceedingly unlikely given the number of sequences obtained. The authors should carefully address this concern.4) The new RNA fluorescence FISH analysis is a significant improvement over the ISH analysis, but despite the claimed specificity of the method used, experiments to document specificity are needed. Ideally, a tissue not expressing AID would be analyzed (or do the authors feel that the negative portions of the thymus provide sufficient specificity controls?). Given that the authors now present a detailed model for AID expression/SHM in shark thymus  based on the RNA fluorescence FISH data, it is particularly important to address specificity.5) The claim made in the last paragraph of the subsection “Mutations, in situ hybridization, and AID expression in thymus “that TcRα expression is more diffuse than that of AID is unconvincing. TcRαA and AID expression appear to coincide in all areas visible in Figure 9. The authors should not push their interpretation just because it fits with the proposed role of AID in selection. Similarly, the organization of AID in rings around TcRα+ regions is intriguing and while the authors' interpretation in terms of relative timing of expression is plausible, it is quite speculative and should be clearly stated as such.6) The in situ hybridization in Figure 8B  for AID is still hard to interpret as the signal is weak and diffuse. The apparent expression pattern suggested by these images does not seem to correspond to the localized patterns seen in the fluorescent in situs in Figure 9 and Figure 9—figure supplement 1. Why is this? Is this a matter of scale? It is a concern that one set of data seems to contradict the other. Essential revisions:1) The major challenge facing the authors is that they do not have the germline sequence of most nurse shark Vα gene segments, and hence they have to infer a germline sequence from the cDNA sequences they obtain. To do this, the authors assume that if the same CDR3 sequence arises more than once, it must derive from the same original V-to-J rearrangement, and hence that sequence differences between two such clones must represent somatic mutations. Unfortunately, while this argument is strong for IgH, TcRδ, and TcRβ sequences that include D segments, it is potentially weak for TcRα rearrangements where a single joint is formed and junctional diversity can be low. To have confidence that duplicate CDR3 sequences represent unique rearrangements, one would want to examine the extent of nucleotide deletion and addition; only in joints with significant addition/deletion would one be confident that the junction is likely to be unique. The problem is compounded by the fact that VDJ recombination has a tendency to use microhomologies (if they exist) at the ends of the two gene segments to mediate joining, and this can lead to the same junction repeatedly. Was the same CDR3 sequence ever observed in different sharks? The authors need to justify their underlying assumption and provide an explicit discussion of the specificity of CDR3 sequence for rearrangements in each chain.In our shark sequences, we found substantial diversity within CDR3 regions. We present data to illustrate CDR3 junctional diversity and include a new figure  depicting this diversity. (We observed similar results in other α V segments as well.) We never observed the same CDR3 sequence in more than one shark.We included a paragraph under the “Somatic hypermutation in nurse shark TcR αV” section of the results to discuss these data: “Despite the absence of diversifying segments, α CDR3s exhibited substantial variation within our shark sequences. For example, TcRα V1 sequences using the same V and J segments had CDR3 lengths that differed by as many as 6 amino acids (12 nucleotides), and few CDR3s shared more than one amino acid within this V-J join . Further, we never observed the same CDR3 sequence in more than one shark, suggesting both exonuclease activity and addition of N and P nucleotides help diversify α CDR3s in nurse shark.”2) In addition, the data contain a significant puzzle: a very high level of shared CDR3 among a relatively small number of unique sequences. Specifically, 72 unique amino acid sequences, representing 12 V-α families, were obtained, which would correspond to an average of 6 unique sequences per V family, and an average of only 3 unique sequences per V family per shark. Given that the starting 5 microgram aliquots of RNA should derive from hundreds of thousands of cells, each starting RNA sample should contain a large number of independent V-J rearrangements for any given V. Given this and that there appear to be multiple Jα gene segments in the nurse shark, the chance of finding the same CDR3 sequence in a handful of sequences for a given V would be predicted to be very low. The chance of finding 42 sequences out of the 72  that share CDR3 with another sequence seems exceedingly unlikely. The authors need to carefully address this issue. The authors should provide a table that lists the number of unique aa sequences obtained for each V family within the 72 sequences, and of those, the number that have an identical CDR3.As written, the paper does suggest an incredible coincidence of shared CDR3s among our sequences. However, we actually acquired significantly more sequences than the 72 we describe in the paper. We have revised this section to include a discussion of the total number of sequences (564) from which we found those with shared CDR3s.Within the Materials and methods section titled “Sequence Alignment and Tree Building,” we added: “Our preliminary dataset contained 564 TcRα clones (encoding 286 unique amino acid sequences representing nine Vα families) from three tissues  of four sharks . Using this dataset, we separated sequences containing identical CDR3 rearrangements and counted mutations within each TcR “clone family” bearing the V-J rearrangement from single founder thymocytes.”The authors did in fact derive the germline sequence of two V family members (V4 and V9). Why not focus the analysis on these two families, where such ambiguities would be less of an issue? Furthermore, one of the reported set of sequences does arise from the V4 family, but it does not appear that the germline sequence information was taken advantage of. Why? And, were other sequences from V4 and V9 obtained in the dataset, and did they show mutations compared to the germline sequences?We added two figures and a couple of paragraphs in the Materials and methods section “Identification of TcR Genes in the Nurse Shark Genome” explaining our reasons for not using germline alignments for SHM analysis:“Our search yielded 17 α/δ V germline segments, significantly fewer than expected based on TcR αV segment numbers in other species . […] Thus, we chose not to rely on these data for mutational analysis.”It is noted that all reviewers agreed that the nature of the sequence differences observed  are consistent with the mutations being real SHM events.3) Expression of Aicda is not particularly clear in the ISH analysis. The data show a generally darker appearance with the antisense compared to the sense probe, but these differences are not completely convincing. Furthermore, it was difficult to distinguish the cortex vs. the medulla and the appearance is so uniform overall that claims for region specificity for Aicda are unconvincing. More annotation highlighting thymic structure and the probes used would be helpful. Scale bars should be included instead of objective magnification. Overall, it was felt that the Aicda ISH data need to be improved. Possibly other images or higher magnification images would help.We present new fluorescence in situ hybridization (FISH) data to illustrate more clearly the thymic architecture and regional specificity of AID expression within the shark thymus. The development of this technique delayed our resubmission. In a new figure , we provide a composite of seven Z-stacked images (10x) depicting the localization of AID expression to the cortico-medullary junction and medullary regions of shark thymus. We also present individual fluorophore images of DAPI, TcRα, and AID and the Z-stacked merged images  to illustrate the pattern of AID and TcRα expression within four locations of shark thymus. To ensure our probes were hybridizing independently of one another, we probed AID and TRA individually on adjacent slides and looked for co-localization of the probes .We also included a paragraph in the Results section describing these data: “We confirmed our colorimetric ISH results with RNA fluorescence in situ hybridization (FISH) using probes against the TcR α constant region (αC) and exons 2 and 3 of AID. […] These daughter T cells then express AID, promoting somatic hypermutation within their TcR α sequences during a time when cells also undergo positive and negative selection.”4) There were some concerns about the Aicda RT-PCR data. The results are expressed in delta Ct, which is a logarithmic measure, and it would be better to calculate a fold-difference in the expression of AID in spleen and thymus. How much of a difference in expression is there between the negative control (forebrain) and thymus?We present expression-fold changes in the different tissues . We also included the expression-fold difference between forebrain and thymus: “We confirmed the expression of AID in the thymus through real-time RT-qPCR, where thymus tissue expressed AID at roughly half (0.7x) the levels found in spleen (where B cell SHM is known to occur) and nearly 6x the levels observed in forebrain .”Was the resulting PCR product cloned and sequenced to confirm its identity?Yes. We included a sentence in the qPCR Materials and methods section to inform readers: “We then cloned and sequenced the resulting PCR products to confirm the sequence was AID.”Are there B cells in the nurse shark thymus as there are in mouse and perhaps other cartilaginous fish such as the skate? If so, are the authors sure that AID expression is in T cells in the ISH and RT-PCR analyses? The authors should consider discussing this in the manuscript.We addressed thymic B cells in the Discussion: “Although recent studies report B cells present in the thymus of mice , Miracle et al. (2001) examined B cell expression levels (IgM and IgX) in various tissues (including thymus) at different ages in the clearnose skate. […] Further, preliminary results using FISH probes to IgM constant region also indicate that adult nurse sharks do not express IgM in the thymus."These preliminary data (both RT-qPCR and FISH) give us confidence that the phenomenon we are seeing is not due to the presence of B cells in the thymus. However, these data are part of a larger study with a different aim, and we prefer not to report the data in this paper. However, we provide them here for you to assess their potential importance. The bar graph  illustraUsing FISH , we founMajor Points:1) Based on the information provided by the authors in their response to the review, it is now clear that the analysis of mutations in TcRβ, γ, and δ (no CDR3 sequence obtained) was less rigorous and less definitive than in TcRα ). Hence, all claims that mutations were not found in TcRβ must either be removed or carefully qualified. For example, the second sentence of the Abstract contrasts the findings at TcRβ (no mutation) and TcRα (mutation found) with no qualification, leaving the reader with the mistaken impression that the two analyses were equivalent and the two conclusions equally strong. The same problem was found in the last paragraph of the Introduction, subsection “Somatic hypermutation in TcR γV and TcR δV but not TcR βV”, and in the third paragraph of the Discussion.Agreed. We are in the process of repeating the mutation analysis of the other chains to the same rigor as α. Collecting enough CDR3-sharing sequences is taking some time. However, for this manuscript, we removed language that implies the analyses or conclusions are equivalent. In the above order, these changes are as follows:“Remarkably, we found SHM acting in the thymus on α chain of shark T cell receptors (TcR).”“Our data suggest that SHM of TcRα is involved in primary T cell repertoire diversification and the enhancement of positive selection in the thymic cortex.”“Somatic hypermutation in TcR γV and TcR δV”.“Remarkably we also detected SHM occurring in the α chain of αβ T cells.”2) "Since it is highly improbable that two thymocytes would generate identical CDR3 sequences during VJ recombination…" As was pointed out in the original review, this claim is not obvious; it should not be stated in this fashion. Indeed, there are a priori reasons to think that the same CDR3 sequence could readily arise from independent V-J rearrangements. The authors should present this claim as a hypothesis that they then carefully validate with data (which they begin to do in the first paragraph of the subsection “Somatic hypermutation in nurse shark TcR αV”). Furthermore, the conclusion of this sentence that "amplicons containing identical CDR3 sequences must have derived from the same progenitor" is overstated. At best, the conclusion could be that they are "likely to have derived from the same progenitor". A statistical analysis of the V-J sequences might allow the authors to make a quantitative claim of just how likely this is, but in the absence of such an analysis, the claims should be stated cautiously. The manuscript needs to be rewritten to accommodate these points. Same issue in the aforementioned paragraph.We modified this section to be less speculative. “Since it is highly unlikely that two thymocytes would generate identical CDR3 sequences during VJ recombination, we predict that amplicons containing identical CDR3 sequences derived from the same progenitor and thus must contain the same germline V and J segments. […] Therefore, even in the absence of an assembled locus, we were able to evaluate mutation to germline αV segments by considering changes within only those thymocyte clones containing identical CDR3s.”3) Closely related to this: The authors have clarified that a larger number of sequences were obtained than was apparent in the initial submission, but this information is not provided in the Results section. Since most readers will not look at the Materials and methods section, it is suggested that the authors add information to the second paragraph of the subsection “Somatic hypermutation in nurse shark TcR αV” to inform readers of the total number of underlying sequences from the two relevant sharks. In addition, the Materials and methods states that sequences were obtained from four sharks; it is confusing that data from only two of the sharks was actually used. Why are all 4 sharks mentioned if data from only two of them were used? How many total sequences were obtained from the two relevant sharks? This is highly relevant given that these are (apparently) the only data from which the analyzed TcRα sequences are derived. This is directly relevant to the concern, expressed in the original review, that the identification of so many repeated CDR3 regions from a small sequence dataset is extremely unlikely. This issue has not been satisfactorily resolved in the resubmission. The requested table that shows how many unique aa sequences were obtained for each V family, and of those, the number that have an identical CDR3, was not provided. Nor have the authors provided a detailed description of the proportion of TcRα sequences that have N/P nucleotides (which would provide higher confidence of assigning SHM) versus those that are directly joined (less confidence). The reviewers remain concerned by the possibility that the number of repeat CDR3 sequences is exceedingly unlikely given the number of sequences obtained. The authors should carefully address this concern.We apologize for not including the requested table. We misunderstood the initial request. We include this table now (Table 1) and discuss the table in the Results section titled “Somatic hypermutation in nurse shark TcR αV”:“Our preliminary V α dataset contained 539 TcRα clones (encoding 286 unique amino acid sequences representing nine V α families) from three tissues  of two sharks . […] We include these 45 sequences in our TcR Vα dataset (see Table 1 – source data for sequence data).”During the construction of this new table, we realized we had omitted sequences in our initial mutation analysis. Further, we decided to divide our aV4 group so that we estimated mutation even more conservatively. Thus, we reanalyzed our entire mutation data set. While the overall conclusions of this study did not change, some of the results did change. Most notably, we found that A:T mutations did not prefer WA/TW hotspots. This is consistent with data reported in sandbar sharks for TcR γ . However, our data suggest a different A:T motif may be targeted or that sharks employ a different mechanism than DNA pol eta use during mismatch repair to alter A:T nucleotides.A/TW hotspots (p=0.2248), though they were 2.3x as likely to mutate within hotspots than outside hotspots. […] This result suggests that an alternate A:T motif is targeted or that sharks employ another mechanism altogether to alter A:T nucleotides.”“A:T nucleotides did not appear to prefer WFurther, we no longer found a significant difference in tandemly mutated bases between CDRs and FRs, which is consistent with results observed for TcR-γ in sandbar sharks. “Finally, though we found more tandemly mutated bases in CDRs  than in FRs , this difference was not significant; p=0.721; Table 2).”Ginglymostoma cirratum) delivered by caesarian section off the Florida Keys and matured in the aquatic vivarium of the University of Maryland’s Center of Marine Biotechnology. We used published T cell αV sequences  as a baseline for αV locus numbering (sharks Yellow and 1299), though we did not analyze any of these sequences for mutation.”We also added a section at the beginning of the Materials and methods to clarify the confusion over sharks. We used sequences from only two sharks in our mutation analyses. However, we used published data from two different sharks to aid in loci identification to ensure consistency. This paragraph reads as follows: “Study Animals: TCR sequence data used in this study came from two adult female nurse sharks  The new RNA fluorescence FISH analysis is a significant improvement over the ISH analysis, but despite the claimed specificity of the method used, experiments to document specificity are needed. Ideally, a tissue not expressing AID would be analyzed (or do the authors feel that the negative portions of the thymus provide sufficient specificity controls?). Given that the authors now present a detailed model for AID expression/SHM in shark thymus  based on the RNA fluorescence FISH data, it is particularly important to address specificity.We analyzed a non-immune tissue (shark brain) as a negative FISH control for AID and TcRα fluorescence. We created a new supplementary figure with images of these slides . This figure depicts some background fluorescence regardless of probe application. However, we observed no AID or TcRα expression in brain tissue like the patterns we saw in thymus (immune tissue).5) The claim made in the last paragraph of the subsection “Mutations, in situ hybridization, and AID expression in thymus “that TcRα expression is more diffuse than that of AID is unconvincing. TcRαA and AID expression appear to coincide in all areas visible in Figure 9. The authors should not push their interpretation just because it fits with the proposed role of AID in selection. Similarly, the organization of AID in rings around TcRα+ regions is intriguing and while the authors' interpretation in terms of relative timing of expression is plausible, it is quite speculative and should be clearly stated as such.We modified the text to better reflect what our images depict . “Our FISH results indicated a more specific TcR αC signal within the inner cortex and medulla adjacent to the CMJ , regions where, in mammals, cells actively rearrange their α chain and where mature αβ T cells are found. […] Thus, we observed a consistent pattern of expression where a “ring” of cells expressing both TcR αC and AID surround a central cell expressing only TcR αC.”6) The in situ hybridization in Figure 8B  for AID is still hard to interpret as the signal is weak and diffuse. The apparent expression pattern suggested by these images does not seem to correspond to the localized patterns seen in the fluorescent in situs in Figure 9 and Figure 9—figure supplement 1. Why is this? Is this a matter of scale? It is a concern that one set of data seems to contradict the other.We auto-adjusted the colors on the CISH image in ImageJ to darken the signal expression  These daughter T cells then express AID (and TcR αC), promoting somatic hypermutation within their TcR α sequences during a time when cells also undergo positive and negative selection.”


Further we give the bounds for the identities related to the generalization of the refinement of Jensen’s inequality using inequalities for the Cebyšev functional. Some results relating to the Grüss and Ostrowski-type inequalities are constructed.In this paper, we formulate new Abel-Gontscharoff type identities involving new Green functions for the ‘two-point right focal’ problem. We use Fink’s identity and a new Abel-Gontscharoff-type Green’s function for a ‘two-point right focal’ to generalize the refinement of Jensen’s inequality given in (Horváth and Pečarić in Math. Inequal. Appl. 14: 777-791,  Divided difference is a helpful tool when we are dealing with functions that have different degrees of smoothness. In , p.14, tg be a real valued function defined on rth order divided difference is defined recursively byLet r-convex function is characterized by the rth order divided difference as follows . Th. ThLet\The proofs of these identities requires some simple integration scheme, therefore we just give the proof of  only as Simplifying we get the result .f is concave on I. □We define the following functionals by taking the differences of refinement of Jensen’s inequality given in :17\docuAssume (and letbe a function such that foran integer) is absolutely continuous. Also, letbe positive real numbers such thatAssume thatandare the same as defined in (and (respectively. Then: (i)Forwe have the following identities:(ii)Forwe havefined in , 10)-(1-(1Assumefined in  and 17)Assume  Using Abel-Gontsharoff-type identities , 15), ,  in \docuFrom identity , we getUsing  and 23)23) and a(ii) Substituting Abel-Gontschroff-type inequality  in \docu, we get . □Assume (and letbe a function such that foran integer) is absolutely continuous. Also, letare positive real numbers such thatAssume thatandare the same as defined in Forthe following holds:(ii)Forwe havefined in , 10)-(1-(1Assumefined in  and 17)Assume  Since (ii) Similar to (i). □For two Lebesgue integrable functions In , the folLetbe a Lebesgue integrable function andbe an absolutely continuous function withThen we have the inequalityThe constant nt}12 in  is the bLetbe an absolutely continuous withand letis monotonic non-decreasing onThen we have the inequalityThe constant nt}12 in  is the bNow we consider Theorem Assume Foras defined in  an anFor\d in Foras defined in Assume  Setting where the remainder satisfies the estimation . Using i(ii) Similar to the above part. □The Grüss-type inequalities can be obtained by using Theorem Assume Identity (where the remainder satisfies the estimationIdentity  where th(ii)Identity (where the remainder satisfies the estimationIdentity  where thed as in  and 31)Assume (\(i) Setting ), using , 37) an an\docum), using .(ii) Similar to above part. □Assume Forwe have(ii)Forwe havefined in , 10)-(1-(1Assumefined in  and 17)Assume  can be constructed for the functional defined as the difference between the R.H.S. and the L.H.S. of the generalized inequalities n-exponen


Strikingly, the resulting single crystals exhibit electron mobility comparable to that for bulk crystals grown by the conventional sodium flux method. This approach not only affords control of both crystal and pore size through synthetic modification, but proves generic, thus opening up the possibility of designing macroporous crystals in a wealth of other materials.The functionalities of porous materials could be significantly enhanced if the materials themselves were in single-crystal form, which, owing to structural coherence, would reduce electronic and optical scattering effects. However, growing macroporous single crystals remains a fundamental challenge, let alone manufacturing crystals large enough to be of practical use. Here we demonstrate a straightforward, inexpensive, versatile method for creating macroporous gallium nitride single crystals on a centimetre scale. The synthetic strategy is built upon a disruptive crystal growth mechanism that utilises direct nitridation of a parent LiGaO 2 crystals.Porous single crystals are desirable for optoelectronic applications, but their fabrication remains challenging. Here the authors produce centimetre-sized macroporous GaN single crystals with electron mobility comparable to that of bulk crystals via in situ inward epitaxial growth on parent LiGaO Introducing such porosity has traditionally been achieved through processing and thermal sintering of nanocrystalline powders, eventually resulting in polycrystalline ceramics, with pore sizes generally larger than 500 nm. The development of porous materials has generated much excitement and is expected to play an important role in creating new generations of (opto)-electronic devices, catalysts and supercapacitors. Synthesising porous materials is generally template based to direct the shape and size of the inorganic matrix and pores. Whereas this yields materials with regular pore size distribution and excellent long-range order of the porous structure, the inorganic matrix itself is often amorphous or at best polycrystalline. The field of modern electronics and optoelectronics, however, requires materials with extended long-range order, i.e., bulk single crystallinity to minimise losses through scattering at grain boundaries. Additionally introducing porous architecture into these single crystals would allow the development of next generation highly efficient light-emitting diodes (LED), low loss waveguides and solar cells7. Porosity can also be used to steer refractive indexes in photonic crystals, a highly sought after quality9.Porous solid-state materials find widespread use in a variety of applications such as (electro)-catalysis, separation, photovoltaics and chemical/electrical energy storage, where the porosity affords large surface areas, boosting efficiency, capacity and reaction kinetics10, de-alloying12, the Kirkendall effect13, gels–aerogels transformation14 and collective osmotic shock15, but these often result in significant degrees of polycrystallinity or the presence of amorphous phases. Template assisted bottom-up epitaxial growth, where the template can be removed after crystal growth to leave controlled porosity, has seen much progress recently, but crystal size so far seems to be limited to the micrometre scale20. Similar issues are associated with Zn or Cd leaching during transition metal oxide nitridation24 and top-down etching approaches28. Electrochemical etching is another technique which has received attention, but its effectiveness seems confined to specific materials or architectures and is therefore not universally applicable. All progress points to a fact that synthesising bulk single crystals with porosity remains a major challenge.Attempts to introduce porosity into single crystals have been made through various strategies, including ‘off-bubbling’34. Bulk single crystals on the centimetre scale have never been grown using Czochralski method, which is due to nitrogen loss and sample decomposition in molten GaN phase. Although millimetre size GaN bulk crystal can be prepared using ammonothermal methods or sodium flux method, the limitation in crystal size and the complicated preparation method hinders practical applications. In addition, only thin GaN layers can be grown onto many substrates including commercial-size LiAlO2, Al2O3 and LiGaO2 single crystals using hydride vapour phase epitaxy, due to the close matching of lattice parameters. However, an alternative is the nitridation of LiGaO2 at elevated temperatures, causing Li and O to evaporate with concomitant formation of the GaN phase, which is then expected to prepare large-size GaN single crystal through in situ conversion of bulk LiGaO2 into GaN single crystal for practical application. Moreover, LiGaO2 is a suitable sacrificial substrate material since large crystals can easily be grown using the Czochralski method35. Previous attempts at epitaxially growing GaN by nitridation of LiGaO2 have resulted in polycrystalline and amorphous films, however, and formation of an intermediate phase, ‘LixGa2−xO2xN2(1−x)’36.GaN is a wide band gap semiconductor, whose properties are desirable in many applications, including data storage, displays and photonic devices2 using chemical vapour deposition (CVD). We show that by carefully controlling the process parameters, single crystallinity is preserved with interconnected porosity over unprecedented centimetre scales. We further discuss the crucial interplay between the initial epitaxially grown thin film and subsequent crystallisation into the substrate to form the macroporous GaN single crystals. Remarkably, the obtained single crystals exhibit comparable electron mobility to that of bulk crystals grown by conventional sodium flux method.Here we demonstrate in situ inward epitaxial growth of macroporous GaN bulk single crystals onto LiGaO2 and wurtzite GaN are closely related, with the former having 52% of the Ga density relative to GaN. It follows that ~48% porosity can thus be in situ introduced within the original single crystal upon nitridation and Li/O evaporation in the process of transition of LiGaO2 into GaN single crystal. LiGaO2 parent single crystals (001) with dimensions 40 mm × 20 mm × 0.5 mm underwent nitridation, resulting in the formation of macroporous GaN crystals with more or less the same dimensions. Figure 2 parent single crystal to prepare macroporous single crystals. In this process, the initial nitridation produces a macroporous single-crystal film while a free-standing macroporous crystal can be anticipated after a sufficient nitridation process. And Fig. c-planes for GaN and LiGaO2, with the latter disappearing on extending nitridation times. The observed peaks are in line with the (001) orientation of the parent LiGaO2 single crystal, indicating successful epitaxial growth of GaN, whereas the lack of diffraction peaks belonging to any other lattice planes also indicates preservation of single crystallinity upon nitridation. An XRD phi scan of (10–11) planes on a nitrided sample rotating around its c-axis shows peaks spaced 60° apart, confirming six-fold symmetry of these GaN planes.As shown in Fig. 2 crystal. Figure 2 (001) substrates and suggests excellent three-dimensional connectivity of the pore structure. The macroporous structure of hexagonal nature covers the entire surface of the substrate material homogeneously. The typical morphology of the pores originates from the hexagonal nature of the GaN c-planes. In this instance, the average pore diameter is around 100 nm, but as discussed later, pore size is controllable. The tested porosity is around 48% with an Archimedes method and this is well consistent with the calculated porosity. Although the controllable pore structure is formed with a fixed porosity, the pore/porosity could be larger if the macroporous crystal is treated using wet etching methods.Field emission scanning electron microscopy (FE-SEM) was additionally used to characterise the macroporous GaN crystals. As can be seen in Fig. 2 was obtained by performing transmission electron microscopy (TEM) analysis on cross-sectional samples prepared by focused ion beam (FIB). Figure 2, with good adherence and well-connected porosity. The excellent connectivity of the pore structure is further evident from TEM images of cross sections with [0002] axes, shown in the Supplementary Fig. 2/GaN interface is characterised by good lattice correlation between both phases, as indicated in Fig. 2 [010] zones, reflecting the direct conversion and epitaxial relationship between substrate and newly synthesised GaN single crystal. Another HRTEM image with accompanying SAED pattern can be found in the Supplementary Fig. 37.Further in-depth information about the nature of the pore structure and growth of GaN onto LiGaO41. The PL spectrum in Fig. 19 cm–3, and Hall mobility of 30.4 cm2 V–1 s–1. This mobility observed in our macroporous GaN samples is close to value for dense GaN bulk single crystals grown by Na flux method (30.0 cm2 V–1 s–1)42 and much higher than any reported polycrystalline GaN46. These properties suggest macroporous GaN has serious potential for applications in electronics and optoelectronics.To further assess the quality of the in situ grown macroporous GaN bulk single crystals, we evaluated both the optical and electrical properties by means of cathodoluminescence (CL) and Hall mobility measurements, respectively. The CL spectrum at room temperature, shown in Fig. 2 parent single-crystal substrate, and both macroporous GaN film and bulk single crystals as synthesised by in situ inward epitaxial growth. As detailed in Fig. 2 substrate and GaN could be observed. The latter are those at 142.8 [E2(low)], 533.5 [A1(TO)], 560.7 [E1(TO)], 569.4 [E2(high)] and 736.8 [A1(LO)] cm–1. The appearance of A1(TO) and E1(TO) modes reveals the breakdown of the Raman polarisation selection rules, demonstrating the light disorder scattering as caused by the presence of an inner porous structure39. The signal for the strain-susceptive E2 (high) phonon is shifted by ~2.4 cm–1 towards higher frequency relative to the bulk value, indicating compressive strain of the macroporous film, due to small lattice mismatches, as well as strong chemical bonding at the interface between the macroporous GaN film and the LiGaO2 (001) parent single-crystal substrate. The micro-Raman spectrum of the macroporous GaN bulk single-crystal features signals exclusively for wurtzite GaN, with phonons at 143.4 [E2(low)], 533.1 [A1(TO)], 559.0 [E1(TO)], 567.8 [E2(high)] and 738.7 [A1(LO)] cm–1. The symmetry and strength of E2(high) in both films and bulk crystals confirms the high crystallinity of the macroporous GaN, whereas its position at 567.8 cm–1 in bulk single crystals indicates a near stress-free state. These macroporous GaN in single crystal form reduces electronic and optical scattering effects and would find wide applications in the field of ideal substrate for the epitaxial growth of single crystalline GaN films, high-efficiency light-emitting diodes, hydrogen gas sensing application and excellent photoanode for photoelectrochemical cells49.Micro-Raman was additionally used to evaluate phonon modes within the LiGaOm-plane porous GaN can be grown along the [10] direction on (100) LiGaO2 and the a-plane porous GaN can be grown along the [11–20] direction on (010) LiGaO2, respectively. XRD performed in the 2θ/ɷ configuration of GaN thus grown only show peaks for the GaN m-planes or a-planes, respectively, as shown in Supplementary Fig. Due to the close matching lattices, macroporous GaN single crystals can also be grown in different orientations. The 2 is dependent on careful control of the CVD process parameters. Through systematic variation, we were able to identify the critical parameters as being temperature, system pressure and NH3 flow rate. We have also established that adding hydrogen to the ammonia flow can increase the reaction kinetics, without affecting the resulting crystal quality.Successful growth of GaN single crystals on LiGaO3, but for significant growth over 20 h, reaction temperatures of 950 °C or higher are required. Supplementary Figure At first, GaN growth is evident from temperatures as low as 750 °C, when the reaction is performed at 267 mbar and a flow rate of 200 sccm of NH3 flow rate is an important factor. Supplementary Figure 3 flow rate from 50 to 600 sccm at 950 °C and a pressure of 267 mbar (20 h of reaction time), indicating an improvement of long-range order and thus crystal quality with increasing flow rate. In fact, at 50 sccm, no decent film or crystals could be grown and the sample disintegrated instead, which is indicative of poor matching of LiGaO2 decomposition and GaN growth.Secondly, the NH3 flow rate of 600 sccm, the FWHM  of the rocking curves increase after a reaction time of 20 h. At 933 mbar samples disintegrate. A careful matching of NH3 flow rate and pressure is obviously required to ensure parallel decomposition of host lattice and growth of macroporous single-crystal GaN.Thirdly, the crystal quality is additionally observed to improve with decreasing CVD system pressure, as can be seen in Supplementary Fig. 2 gas to the ammonia flow was found to improve decomposition rates for LiGaO2. Similar observations have been reported previously, and the phenomenon is believed to be due to the formation of more volatile compounds, such as LiH, LiOH, LiNH2 or Li2NH44. Where the conversion from LiGaO2 to GaN normally takes 20 h to complete at 1000 °C and 700 sccm NH3 at 67 mbar, it can be completed in 1 h under identical conditions upon adding 100 sccm of H2, without affecting the quality of the final GaN single crystal. Sufficient flow of NH3 must be provided to ensure the growth of GaN can match the LiGaO2 decomposition.Finally, adding H28. In our case, GaN is grown epitaxially on wurtzite-like LiGaO2 parent single crystal under a reducing atmosphere, through decomposition of NH3 into N2 and H2. Such a reducing atmosphere causes surface decomposition of the parent crystal, accompanied by Li and O evaporation, allowing the remaining Ga to react with N2/NH3 and re-crystallise as GaN. GaN initially re-crystallises epitaxially on pristine LiGaO2, where the excellent lattice matching of substrate and newly formed film guarantees crystallisation with well-defined orientations . The ~52% lower crystal density of the newly formed phase leads to the formation of GaN surface islands, separated by hexagonal voids  in our optimised process at 1000 °C is estimated to be 1:1, apparently providing the ideal conditions for macroporous GaN single-crystal formation.Our characterisation results confirm that 3D interconnected macroporous GaN films and bulk single crystals can be fabricated using our nitridation approach. The growth process and therefore the resulting microstructure are significantly different from previously reported porous materials, which were produced through typical etching methods, leaching or template-based procedures2 and GaN in NH3 (267 mbar) at different temperatures. As shown in Supplementary Fig. 2 single crystal treated in ammonia for 10 h is ~0.35%, 2.5% and 5% at 900, 950 and 1000 °C, respectively. The weight loss is related to the transformation of LiGaO2 single crystal into GaN single crystal through an inward epitaxial growth process. This indicates that the nitridation rate of LiGaO2 single crystal is very slow at 900 °C, while it is significantly enhanced if the temperatures are increased to 950–1000 °C, which is well consistent with the observed growth behaviour at low temperatures. As shown in Supplementary Fig. 2 single crystal for 10 h at different temperatures. The single crystal of GaN has formed at 900 °C while the (0002) diffraction intensity is very weak in contrast to (002) LiGaO2 single crystal, which may be due to the macroporous GaN single crystal is pretty thin on the parent crystal surface. However, the higher nitridation temperature at 950–1000 °C facilitates the nitridation process as confirmed by the XRD diffraction.We conduct experiments on the thermochemical properties of LiGaO2 that may have influence on the growth mechanism. The LiGaO2 crystals used in our work are grown using Czochralski growth method35. No cracks, domains or inclusions are observed in the bulk of our LiGaO2 single crystals. We use chemical etching, an effective approach, to study the distribution, nature and origin of defects such as dislocations and inclusions. The defect density of the polished (001) LiGaO2 substrates is estimated to be 4.6 × 104 cm−2, which is quite small in large-size bulk single crystals. However, the presence of defects would favour the formation of pores in the single-crystalline GaN growth progress, while the inverse epitaxial growth process may be not largely influenced. Moreover, TEM investigation confirms that no inclusions or polycrystalline defects exist in macroporous GaN single crystal upon completion of the nitridation process of LiGaO2 parent single crystal. Furthermore, the process can be halted at any time by removing the reactant atmosphere or by reducing the temperature. This provides flexibility and allows for the manufacture of thin films as well as bulk single crystals.We further consider the imperfections in the LiGaOIn conclusion, we have demonstrated a novel, general yet facile approach for producing large-size macroporous single crystals through in situ inward epitaxial growth on parent single crystals. The obtained single-crystalline macroporous GaN films and bulk crystals containing 3D interconnected pores of tens to hundreds of nanometres are on an unprecedented centimetre scale, i.e., the size of a typical wafer. The pores single crystals possess good crystallinity, high optical quality and appealing electronic transport properties. The mechanically and chemically robust, biocompatible, and electrically and optically active nature of GaN single crystals, together with high surface area properties of the macroporous architecture makes it a promising building block for advanced technological applications in for instance optoelectronics and electronics. Furthermore, the CVD process used in this study is straightforward, economical and compatible with industrial GaN-based technology and would therefore be suitable for further scale-up and device integration. Moreover, our method has the potential to provide large-size macroporous GaN single crystals in large quantities at reduced cost. This novel approach in synthesising these large-scale porous single crystals should be highly adaptable as well and apply to other materials and research fields, paving the way for low-cost and high-throughput fabrication.2 crystals into macroporous GaN materials was performed in a typical CVD system. The polished LiGaO2 (001) single-crystal substrate (45 mm × 20 mm × 0.5 mm) was placed in the centre of the reactor. The horizontal alumina ceramic tube reaction chamber was initially evacuated to a base pressure of 2.0 × 10–3 torr to remove residual oxygen and then a constant flow of NH3 gas  was introduced to maintain the CVD reactor at 50–700 torr. The furnace was then heated to 750–1100 °C from room temperature at a heating rate of 40 °C min–1. The furnace temperature was maintained at 750–1100 °C for 1–72 h and then cooled naturally under the flowing gas.In situ inward epitaxial growth of single-crystalline macroporous GaN crystals: The nitridated conversion of LiGaO1 radiation; operated at 40 kV and 45 mA; λ = 1.54052 Å). Additional microstructural and orientational characterisation of the macroporous GaN was performed using field emission TEM (Tecnai F20 G2) at 200 kV. TEM samples were prepared using the FIB lift-out method. CL spectra were acquired using a Gatan MonoCL3 spectrometer in a JEOL JSM 6330F SEM system; these measurements were performed under an electron beam energy having an acceleration voltage of 10 kV at room temperature. Raman spectra were recorded at room temperature using a Jobin Yvon Horiba HR-800 confocal micro-Raman system coupled with a high-stability microscope. The spectrometer was calibrated using the silicon phonon line at 520.6 cm−1. An objective of ×100 was used to collect the signal in the back scattering geometry from a focal spot (diameter: ca. 2 µm) on the samples. Raman spectra (resolution: 0.2 cm−1) in the wave number range 100–800 cm–1 were recorded under internal He–Ne laser excitation at a wavelength of 632.8 nm and low incident power (ca. 4 mW) to avoid sample damage or laser-induced heating.The morphologies of the single-crystalline macroporous GaN samples were investigated through FE-SEM (JEOL JSM-6330TF) at an accelerating voltage of 10 kV. The orientation and structure were determined through XRD using a Bede D1 high-resolution X-ray diffractometer .Supplementary InformationPeer Review File


Our demonstration opens new possibilities for group IV lasers for photonic-integrated circuits.The integration of efficient, miniaturized group IV lasers into CMOS architecture holds the key to the realization of fully functional photonic-integrated circuits. Despite several years of progress, however, all group IV lasers reported to date exhibit impractically high thresholds owing to their unfavourable bandstructures. Highly strained germanium with its fundamentally altered bandstructure has emerged as a potential low-threshold gain medium, but there has yet to be a successful demonstration of lasing from this seemingly promising material system. Here we demonstrate a low-threshold, compact group IV laser that employs a germanium nanowire under a 1.6% uniaxial tensile strain as the gain medium. The amplified material gain in strained germanium can sufficiently overcome optical losses at 83 K, thus allowing the observation of multimode lasing with an optical pumping threshold density of ~3.0 kW cm Integrating group IV lasing devices into technologically relevant CMOS architectures has proven challenging. Here, the authors demonstrate low-threshold lasing, which is important for potential electronic and photonic circuits, using strained germanium nanowires as the gain material. However, the realization of fully functional PICs is currently limited by the absence of an efficient laser source on silicon (Si)5.Photonic-integrated circuits (PICs) are a key enabler for the miniaturization of various technologies such as light detection and ranging (LIDAR) for autonomous vehicles6. Unlike Si, the energy difference between the direct Г and indirect L conduction valleys of Ge is only ~140 meV, and therefore it is possible to force some electrons to populate the direct Г conduction valley and to create a population inversion in Ge6. By employing heavy n-type doping in ~0.2% biaxially strained Ge to assist with population inversion, optically and electrically pumped Ge-on-Si lasers have been demonstrated9. However, these lasers suffered from an extremely high lasing threshold current density (~280 kA cm−2) that precludes practical integration. It was well known that intrinsic losses from free carriers were a major culprit for this inefficiency10, which other researchers identified more specifically as the inter-valence band absorption (IVBA) process from free holes12.Approximately a decade ago, germanium (Ge) began attracting much attention as a potential gain medium for integrated group IV lasers18. Recently, a Fabry–Perot type GeSn waveguide with 12.6% Sn demonstrated lasing with an optical pumping threshold density of 325 kW cm−2 at 20 K16, and a couple of more successful demonstrations have since followed18. However, the lasing threshold of those GeSn lasers was still too high to be practical, possibly owing to faster than desired non-radiative recombination processes16.During the last few years, researchers have been making relentless efforts to overcome the drawback of indirect bandgap Ge through a variety of techniques. Among those, tin (Sn) alloying into Ge has shown great promise because GeSn alloy with a reasonably high Sn concentration (> 6.5%) can achieve a direct bandgap25; the small energy difference between the Г and L conduction valleys can be reduced even further with tensile strain, resulting in an increased material gain25. This hypothesis has been supported by numerous theoretical simulations that predict a significant reduction in lasing threshold through tensile strain26. With regard to practical realization, several innovative platforms for inducing large mechanical strain have been experimentally demonstrated23, thus suggesting the possibility of low-threshold group IV lasers.On the other hand, the application of large mechanical tensile strain can also address the challenge of the indirect bandgap in Ge by fundamentally altering the bandstructure34, there has been no successful demonstration of optical amplification in such a seemingly promising material system. Most notably, El Kurdi et al.32 investigated photoluminescence from direct bandgap Ge under a 1.75% biaxial tensile strain; however, no lasing action was observed even at cryogenic temperatures, possibly owing to a non-uniform strain distribution in the gain medium and/or a poor thermal conduction arising from suspended structures. The authors also performed theoretical calculations on the actual device temperature under the same pump conditions used in their measurements23, and found that the temperature rises to 210 K which is significant enough to preclude lasing because of the increased material loss. This temperature-dependent optical characteristic is discussed theoretically and experimentally throughout this study.While lasing from highly strained Ge has been pursued intensively in several recent reports−2 that is two orders of magnitude lower than the state-of-the-art Ge-based lasers16, we observe an unambiguous multimode lasing action evidenced by clear threshold behaviours in output power and linewidth as a function of pump power. Theoretical modelling shows that the IVBA, the recently discovered dominant loss factor in Ge12, is markedly reduced at cryogenic temperatures35 and therefore can be compensated by the amplified material gain in strained Ge, leading to the development of a large optical net gain of ~415 cm−1. By presenting unambiguous quantitative evidence of low-threshold lasing action in a fully CMOS-compatible material system, our results pave the way towards a monolithic realization of PICs.Here, we present the observation of low-threshold lasing from Ge nanowires under 1.6% uniaxial tensile strain. With a pulsed optical pumping threshold density of ~3.0 kW cm34 and further optimized in the present study to minimize optical loss. The strain amplification method first introduced in ref. 36 allows for a convenient tuning of the strain level by changing the length of the stressing pads  Fig. . The DBRThe unique design of our Ge laser possesses several advantages such as a highly homogeneous strain distribution and an excellent optical mode overlap with the gain medium. Figure 32, our laser structures hold the strained Ge nanowire in close contact with silicon dioxide (SiO2), which provides superior thermal conduction to the air gap while confining optical fields within the Ge layer .Figure We successfully observe multimode lasing by optically exciting a 1.6%-strained Ge nanowire integrated with DBRs Fig.  at a low−2, the emission shows broad spontaneous emission which consists of two overlapping peaks arising from optical transitions of Γ-VB1 and Γ-VB237. At an increased pump power of 1.4 kW cm−2, visible longitudinal cavity modes owing to the presence of DBRs emerge on the long wavelength side as the optical loss is gradually compensated by the material gain. Although such cavity modes near the band edge from highly strained Ge have been already observed numerous times34, all the previous reports showed the apparent intensity saturation and linewidth broadening of cavity modes with pump powers possibly owing to insufficient gain at low strain33, poor optical cavity29 and/or unsatisfactory thermal management34.At a low pump power of 0.7 kW cm−2. This phenomenon clearly presents the evidence of optical amplification in highly strained Ge gain medium. Interestingly, the spontaneous emission well above the band edge (<1550 nm) also collapses into sharp cavity modes, thus suggesting that the entire emission band is close to the transparency condition. The full-width at half-maximum (FWHM) of the emission band at this pump power is ~150 nm (marked by two blue arrows). The mode spacing is measured to be ~8 nm, which is consistent with FDTD simulation  appear to saturate. At the highest pump power of 14.6 kW cm−2, the cavity modes near 1530 nm obtain >20× higher intensity than the background spontaneous emission, and exhibit a well-defined bell-shaped curve following the net gain spectrum with the FWHM bandwidth of < 50 nm while the bandwidth of the background emission is ~150 nm. The large bandwidths of both spontaneous emission37 and net gain38 have been previously observed in highly strained Ge, and can be attributed to the unusually large amount of strain-induced valence band splitting . The FWHM of a single-cavity mode at 1530 nm is determined to be ~1.3 nm by fitting to an individual Lorentzian function  followed by a linear growth in the lasing regime, which clearly indicates a distinctive lasing action. The corresponding double-logarithmic plot of the output intensity dependence on the pump power  and aluminium oxide (Al2O3).Lasing action can also be quantitatively evidenced by the nonlinear behaviour of the integrated output intensity within the gain bandwidth as a function of pump power Fig. . The outwer Fig. , inset m−2 (black) and 14.6 kW cm−2 (red). The emission spectrum at 0.7 kW cm−2 is broad and does not exhibit clear cavity resonances, similarly to the spectrum from the 1.6%-strained Ge nanowire under low pumping  are also performed  and IVBA, and IVBA is the dominant factor as previously discovered in refs. 12  for computing the bandstructure of highly strained Ge, and numerical analysis is employed to calculate the material gain via Fermi’s golden rule19 cm−3 (blue), 5 × 1019 cm−3 (green) and 8 × 1019 cm−3 (red). At an injection density of 4 × 1019 cm−3, the material gain attains its peak intensity above 1600 nm, which corresponds to the optical transition between the Γ conduction valley and the top valence band, VB1. As the injection density is increased to 5 × 1019 cm−3, a large number of holes start filling up the second valence band, VB2, resulting in the emergence of another gain peak below 1600 nm. The significantly increased gain bandwidth extends down to ~1500 nm, thus explaining the experimental observation of cavity modes within such a large spectral range for the spectrum taken at 3.5 kW cm−2 in Fig. 19 cm−3 and allows the achievement of a large optical net gain of ~415 cm−1 at ~1510 nm. The gain for unstrained Ge at an injection density of 8 × 1019 cm−3 (black solid line) is overwhelmed by the loss for the same injection density (red dashed line), highlighting the significance of tensile strain for obtaining optical net gain in Ge.Figure 19 cm−3. Although there exist two gain bands associated with optical transitions of Γ-VB1 and Γ-VB2, the gain band centred at ~1510 nm only surpasses the experimental threshold gain of 336 cm−1. The measured gain bandwidth is also presented as a blue arrow, which is in reasonable agreement with the theoretical gain bandwidth. The slight discrepancy between the theoretical and experimental gain bandwidths may be ascribed to the uncertainty in bandstructure calculation for such highly strained Ge.Figure −2. In contrast to the spectrum for 83 K showing the dominant lasing modes over the background spontaneous emission, the cavity modes are highly suppressed at 173 K and do not show a superlinear growth in intensity at higher pump powers, which displays a strong temperature dependence of gain characteristics in strained Ge. The gain and loss analysis for 300 K shows that optical net gain is not achievable in 1.6%-strained Ge owing to a substantial IVBA, thus highlighting the significant role of IVBA in realizing Ge lasers  gratings. The realization of a low threshold, electrically pumped Ge laser is also possible by using a lateral p–i–n junction39. In addition, the ability to tune the strain conveniently by a conventional lithography36 should enable the creation of multiple lasers operating at different spectral ranges on a single chip, which is crucial for wavelength division multiplexed optical interconnects. Our demonstration of a low-threshold, highly strained Ge nanowire laser markedly narrows the gap between conventional III–V lasers and their group IV counterparts, thus opening up new avenues for PICs.In summary, we have demonstrated lasing from highly strained Ge nanowires. Our nanowire laser design secures robust mechanical, optical, and thermal properties, which played major roles in enabling low-threshold lasing from highly strained Ge. Excitation-, temperature-, and polarization-dependent optical characterizations showed the achievement of pulsed lasing at 83 K with an optical pumping threshold density of ~3.0 kW cmThe GOI substrate used in the present work is made via hetero-epitaxy, wafer bonding, grinding, chemical-mechanical polishing (CMP), etc. Detailed explanations along with figures showing step-by-step fabrication processes are provided in Supplementary Note −1, the strain value can be derived from the Raman measurement. Raman mapping was conducted to measure the strain distribution over the laser structure. The piezo stage step size was set to 200 nm during the mapping.A micro-Raman spectroscopy system with a 532-nm laser source was used to measure the Raman peak shift of a strained Ge laser structure. By using Lorenz fit of the peak shift with a uniaxial strain-shift coefficient of 152 cmFor photoluminescence spectroscopy, a 1064-nm pulsed laser was focused using a ×50 magnification lens. The pulse duration and repetition period were 20 and 100 ns (duty cycle of 20%), respectively, to minimize heating. All pump power values refer to the peak laser intensity considering 20% duty cycle. The spot size was set to ~15 µm to uniformly illuminate 8 µm long nanowires. The laser emission is scattered in a random direction at the DBR mirrors and a fraction of the scattered emission propagating towards the top surface is collected via the same ×50 magnification lens which is used to focus the pump laser Fig. . The scaThe data that support the findings of this work are available from the corresponding author upon request.Supplementary Information


Parallel arrays of Ni nanotubes with an external diameter of 150 nm, a wall thickness of 15 nm, and a length of 1.2 ± 0.3 µm were successfully fabricated in ion-track etched polycarbonate (PC) templates by electrochemical deposition. The morphology and crystal structure of the nanotubes were characterized by scanning electron microscopy (SEM), transmission electron microscopy (TEM), and X-ray diffraction (XRD). Structural analyses indicate that Ni nanotubes have a polycrystalline structure with no preferred orientation. Angle dependent hysteresis studies at room temperature carried out by using a vibrating sample magnetometer (VSM) demonstrate a transition of magnetization between the two different magnetization reversal modes: curling rotation for small angles and coherent rotation for large angles. Furthermore, temperature dependent magnetic analyses performed with a superconducting quantum interference device (SQUID) magnetometer indicate that magnetization of the nanotubes follows modified Bloch’s law in the range 60–300 K, while the deviation of the experimental curve from this law below 60 K can be attributed to the finite size effects in the nanotubes. Finally, it was found that coercivity measured at different temperatures follows Kneller’s law within the premises of Stoner–Wohlfarth model for ferromagnetic nanostructures. L, and outer and inner radii, R and r. In this way, nanotubes are becoming increasingly interesting functional nanomaterials for a wide range of applications , where α = 1.5 [c = HoH[1 − BT/T]1/2 1/2 ,39, wherer’s law . A similIn this work, Ni nanotube arrays were fabricated using a nanoporous polycarbonate membrane via an electrochemcial deposition technique. The structure and morphology of the prepared Ni nanotubes were characterized by scanning electron microscopy (SEM), transmission electron microscopy (TEM), and X-ray diffraction (XRD), respectively. The angular dependence of coercivity and remanence for Ni nanotube arrays were investigated via a vibrating sample magnetometer (VSM), while magnetic properties at different temperatures ranging from 5 K to 300 K were measured via a superconducting quantum interference device (SQUID). The aim of this research was to present a systematic study of the magnetic characterization of Ni nanotubes including angle- and temperature-dependent magnetic properties and to tune and tailor these properties for possible technological applications of these nanotubes.209Bi ions with an initial kinetic energy of 9.5 MeV/u and a fluence of 5 × 108 ions/cm2. In the second step, the membranes were etched in a 5 M NaOH solution at 50 °C for 5 min to obtain cylindrical nanopores with diameters of about 150 nm. Prior to deposition, a thin Au film (~60 nm) was sputtered onto one side of the membrane and served as a conducting substrate (acted as cathode) for the deposition of nanotubes. This method has been previously reported for nanotubes prepared via potentiostatic deposition in an AAO template   , where (Tα) with Bloch’s exponent as large as 1.68. In Therefore, in the case of Ni nanotubes, the spin wave structure is modified in the form of a power law  is attributed to the finite size effect in the case of Ni nanotubes at the nanoscale.