Idiopathic pulmonary fibrosis (IPF) is a heterogeneous disease that is pathologically characterized by areas of normal-appearing lung parenchyma, active fibrosis (transition zones including fibroblastic foci) and dense fibrosis. Defining transcriptional differences between these pathologically heterogeneous regions of the IPF lung is critical to understanding the distribution and extent of fibrotic lung disease and identifying potential therapeutic targets. Application of a spatial transcriptomics platform would provide more detailed spatial resolution of transcriptional signals compared to previous single cell or bulk RNA-Seq studies.We performed spatial transcriptomics using GeoMx Nanostring Digital Spatial Profiling on formalin-fixed paraffin-embedded (FFPE) tissue from 32 IPF and 12 control subjects and identified 231 regions of interest (ROIs). We compared normal-appearing lung parenchyma and airways between IPF and controls with histologically normal lung tissue, as well as histologically distinct regions within IPF .We identified 254 differentially expressed genes (DEGs) between IPF and controls in histologically normal-appearing regions of lung parenchyma; pathway analysis identified disease processes such as EIF2 signaling (important for cap-dependent mRNA translation), epithelial adherens junction signaling, HIF1α signaling, and integrin signaling. Within IPF, we identified 173 DEGs between transition and normal-appearing lung parenchyma and 198 DEGs between dense fibrosis and normal lung parenchyma; pathways dysregulated in both transition and dense fibrotic areas include EIF2 signaling pathway activation (upstream of endoplasmic reticulum (ER) stress proteins ATF4 and CHOP) and wound healing signaling pathway deactivation. Through cell deconvolution of transcriptome data and immunofluorescence staining, we confirmed loss of alveolar parenchymal signals , gain of secretory cell markers  as well as dysregulation of the upstream regulator ATF4, in histologically normal-appearing tissue in IPF.Our findings demonstrate that histologically normal-appearing regions from the IPF lung are transcriptionally distinct when compared to similar lung tissue from controls with histologically normal lung tissue, and that transition zones and areas of dense fibrosis within the IPF lung demonstrate activation of ER stress and deactivation of wound healing pathways.The online version contains supplementary material available at 10.1186/s12931-023-02572-6. Idiopathic pulmonary fibrosis (IPF) is a progressive and fatal disease of the aging lung , 2 that KRT17-expressing “aberrant basaloid” cells [Previous investigations of transcriptional profiles of IPF lung have largely been performed on whole lung tissue and have identified several thousand genes that are differentially regulated in IPF –17; consd” cells  and “secd” cells  cells. Hd” cells , suggestIn the past several years, spatial transcriptomics technology has emerged as an approach to capture whole transcriptome information from histological or morphological regions of interest. These methods can be applied to frozen or FFPE tissue allowing for application to a broad range of studies involving patient samples. The general approach is to quantify RNA in FFPE tissue using probe-based mount specimens in which slides are stained directly with relevant morphology markers or serial staining with H&E. The slides are then imaged for selection of regions of interest (ROI) via a software platform Fig. . The plaA recent application of spatial transcriptomic technology in IPF focused on alveolar regions, fibroblastic foci, immune infiltrates, and blood vessel regions, however, this study was limited to only 10 cases of IPF . In addiWe used the Nanostring GeoMX Digital Spatial Profiler to obtain spatial transcriptomic data on histologically different regions of interest (ROIs) from FFPE tissue from IPF subjects and controls with histologically normal lung tissue. We compared whole transcriptome expression between IPF subjects and controls with histologically normal lung tissue within histologically normal tissue types . In addition, we compared increasingly diseased tissue regions to their comparative normal tissue in IPF subjects; dense fibrosis and transition zones which included fibroblastic foci were compared to normal appearing lung parenchyma, and honeycomb epithelial metaplasia was compared to normal appearing bronchiolar epithelium. To determine transcriptional differences independent of differences in cell composition, we estimated cell proportions of human lung cell types relevant to IPF by applying the cell deconvolution method, SpatialDecon . We perf2) for areas of classic UIP appearance or normal lung in controls with histologically normal lung tissue. The corresponding areas in the formalin-fixed paraffin-embedded (FFPE) tissue blocks were dissected and a new block consisting of up to 12 subjects was prepared. These macroarray blocks . Patients were consented and tissue was collected through the NHLBI-sponsored Lung Tissue Research Consortium (LTRC) and at the University of Colorado. IPF was diagnosed in the LTRC using American Thoracic Society/European respiratory Society (ATS/ERS) criteria [We used the Nanostring GeoMX Digital Spatial Profiler (DSP) platform to obtain human whole transcriptome data from lung tissue macroarrays . Region We followed the GeoMx RNA-Seq pipeline to convert raw DCC files to normalized expression data –30. We kPrincipal component analysis was performed on the log2 Q3 normalized counts. To perform differential expression, we modeled the log2 Q3 normalized counts using linear mixed effects model with a categorical variable representing disease and region as the main predictor (Eq. 2). Based on initial QC and investigation of PCA plots, all models were adjusted for batch based on day of macrorray processing. We included a random effect for subject to account for the correlation of ROIs within the same subject.ij is the Q3 normalized expression data for a given gene for sample i for subject j. βGroup represents the coefficient for the fixed effect term Groupij. Groupij is the disease region variable which included control normal lung parenchyma, control normal bronchiolar epithelium, IPF normal lung parenchyma, IPF normal bronchiolar epithelium, IPF transition, IPF dense fibrosis and IPF honeycomb epithelium metaplasia. We applied contrast statements to compute differential expression between groups of interest. For the disease-focused research question, we compared IPF to control within normal lung parenchyma and normal bronchiolar epithelium. For the region focused research question within IPF, we compared normal lung parenchyma tissue to transition and dense fibrosis tissue and compared normal bronchiolar epithelium to honeycomb epithelium. To adjust for multiple comparisons, we applied a Benjamini-Hochberg adjustment where genes with an FDR adjusted p-value < 0.05 were considered significant. We did not consider genes significant if the model was determined to be singular. Linear mixed models were computed using the lmerSeq R package [ package .To examine how the selected ROIs differ in the composition of different lung cell types, we applied a cell deconvolution method, SpatialDecon, developed specifically for spatial transcriptomic data . This meTo adjust for differences in cell composition, we applied the linear mixed model outlined above and included the estimated cell proportions as covariates. Our primary differential expression analysis adjusted for cell types estimated from the normal human lung reference and selected based on biological relevance in IPF pathology , alveolar epithelial cells Type 2 (AEC2), fibroblasts and ciliated cells).We applied the Ingenuity Pathways Analysis , 26 to tFor validation of GeoMx data, immunofluorescence microscopy was used to compare normal alveolar regions from control and IPF tissue using the same macroarrays included in the GeoMx assays above. Samples were deparaffinized using xylene and antigens retrieved by boiling in 10mM citrate, pH 6.0. Specimens were blocked for 1 h using 2.5% BSA in PBS, then labelled with specific antibodies overnight in PBS containing 0.25% BSA at 4̊C. Slides were washed 3x with 0.1% Triton-X100 in PBS, then labelled with secondary antibodies for one hour at room temperature. Samples were then washed 3x again in 0.1% Triton-X100 in PBS, washed again to remove detergent, and stained with DAPI, then mounted with Floromount G (Southern Biotech). For a complete list of antibodies and concentrations used in these studies, see Additional file We selected a total of 231 ROIs from 32 IPF subjects (ROI N = 196) and 12 controls with histologically normal lung tissue (ROI N = 35). The distribution of age, sex, smoking status and race were comparable between IPF subjects and controls with histologically normal lung tissue (Table −5) between IPF and controls with histologically normal lung tissue in the normal parenchymal regions  and B cell specific transcripts (IGKC). This was reflected in the canonical pathway analysis  between IPF and controls with histologically normal lung tissue in histologically normal appearing regions of lung parenchyma. The number of DEGs remained the same (N = 254) after adjusting for cell proportions of AEC1, AEC2, fibroblasts, and ciliated cells  or REDD1, a member of the same gene family as CHOP/DDIT3 which is known to be induced via HIF1α-mediated transcription [We observed a smaller number of transcriptional differences in normal bronchiolar regions between IPF and control samples. There were 61 DEGs between IPF and controls with histologically normal lung tissue in normal bronchiolar epithelium Fig. C. The nucription  and is iTo determine how histologically different regions of the IPF lung diverge transcriptionally, we compared transcriptional changes in non-fibrotic IPF lung to transition areas of lung fibrosis and to areas of dense fibrosis. To understand the progression of lung tissue from non-fibrotic lung parenchyma to dense fibrosis, we individually compared non-fibrotic regions of IPF lung parenchyma to either transition regions of lung fibrosis or regions of dense fibrosis, and then explored the overlap between these comparisons. We identified 347 DEGs between transition and non-fibrotic regions; however, the number of DEGs decreased to 173 after adjusting for cell composition of AEC1, AEC2, fibroblasts, and ciliated cells  and confirmed by histology . McDonouThe most highly activated canonical pathway that was identified in both the normal regions IPF lung and the areas of increased lung fibrosis was EIF2 signaling. EIF2α facilitates cap-dependent translation but can be phosphorylated by the unfolded protein response (UPR) activator protein PERK to promote translation of cap-independent ER stress proteins ATF4 and CHOP . We obseAmong the activated upstream regulators are HIF1α and ATF4. Activation of pathologic ER stress pathways, including ATF4 specifically, has been identified by others as a key molecular feature of IPF . In a luAmong upstream regulators that are activated in both transition zones and densely fibrotic areas of IPF lung are MYC and YAP transcriptional programs. Aberrant activation of YAP/TAZ has been associated with increased fibrotic remodeling in IPF in the alveolar epithelium and activated fibroblasts  as well The use of the GeoMX platform to perform spatial transcriptomics on lung specimens allowed for careful selection of normal appearing lung parenchyma, as well as disease relevant regions of interest. Current single cell approaches such as droplet-based technologies capture the transcriptional information for a single cell from dissociated tissue, where the loss of spatial information can be critical to understanding the disease process. This is especially relevant in the context of a heterogenous disease of the lung, as is the case in IPF. Though the GeoMx platform does not provide single cell level information, the ability to capture normal-appearing regions within IPF, as well as transition zones which include fibroblastic foci, makes this approach advantageous to current single cell studies on dissociated lung tissue. In this study, we used two existing single cell datasets to elucidate the cellular changes between histologically distinct regions, however, direct investigation of single cell data to characterize molecular changes could be useful. Future work to utilize emerging platforms that perform spatial transcriptomics with single cell resolution will greatly improve our understanding of the early disease processes in the normal parenchyma and transition zones.We recognize that the findings of this study could be limited to the patient demographic that was captured, predominantly males (69%), ever-smokers (66%) and NHW (94%); however, these demographics are representative of IPF . RegardiPatients with IPF are usually diagnosed only after the fibroproliferative process has caused permanent and extensive lung parenchymal damage. Considering the irreversible nature of this disease, even approved treatments for IPF . Figure S3. Mean cell proportions estimated with SpatialDecon based on normal human lung reference. Figure S4.A Lung-specific protein-protein interactome (PPI) network of IPF vs control normal alveolar DEGs. B Ingenuity upstream regulator analysis of IPF vs control normal alveolar DEGs adjusted for batch and estimated cell proportions of AEC1, AEC2, fibroblasts and ciliated cells. Figure S5. Ingenuity upstream regulator analysis of IPF transition vs normal alveolar (A) and IPF dense fibrosis vs normal alveolar DEGs adjusted for batch and estimated cell proportions of AEC1, AEC2, fibroblasts and ciliated cells. Figure S6. Immunofluorescence changes in YAP, CDKN1A, KRT8, KRT5, SCGB3A2 and SFTPB between IPF and control in normal parenchyma regions.  All pairwise comparisons are Mann-Whitney U test with significance set to (*) p<0.05, (**) p<0.01, (***) p<0.001, (****) p<0.0001. Table S1.  Estimates and corresponding p-values from comparing different cell type proportions from IPF reference between regions.  Proportions were log transformed and modeled by disease region using a linear mixed model adjusting for batch and subject as a random effect.  Estimates represent the difference in log transformed proportions and p-values have been adjusted for multiple comparisons for the number of cell types using a Benjamini-Hochberg adjustment. Table S2.  Antiobodies and concentrations used for this study.  Additional file 2: Datafile S1.  Differential expression results for main comparisons of interest (IPF normal appearing lung parenchyma vs control normal lung parenchyma, IPF normal bronchiolar vs control normal bronchiolar, IPF transition zones of fibrosis vs IPF normal appearing lung parenchyma, IPF dense fibrosis vs IPF normal appearing lung parenchyma and IPF honeycomb epithelium metaplasia vs IPF normal bronchiolar.  All gene lists are adjusted for batch and cell proportions of AECI, AECII, fibroblasts and ciliated.  ***Denotes McDonough core IPF gene.


In the present study, we generalize our recently proposed nomenclature scheme for porous graphene structures to include graphene flakes and (periodic) edges, i.e., nanographenes and graphene nanoribbons. The proposed nomenclature scheme is a complete scheme that similarly treats all these structures. Beyond this generalization, we study the geometric features of graphene flakes and edges based on ideas from the graph theory, as well as the pore–flake duality. Based on this study, we propose an algorithm for the systematic generation, identification, and numbering of graphene pores, flakes, and edges. The algorithm and the nomenclature scheme can also be used for flakes and edges of similar honeycomb systems. Although graphene is a semi-metal, graphene flakes  and graphene nanoribbons, which are the zero- and one-dimensional counterparts of graphene, are semiconductors, due to quantum confinement. This makes them particularly useful for optoelectronic applications  and explDepending on their sizes, shapes, and edge structures, these structures exhibit a variety of different electronic, optical, and chemical properties ,10,22. FThe infinite number of nanographenes and graphene nanoribbons, due to their different edge structures, and the increasing interest in them, give rise to the necessity for a nomenclature scheme, which would have the ability to accurately distinguish them from each other and provide a particular and accurate name for each such different structure.Carbon, regarding the nomenclature of graphene-based two-dimensional materials [So far, attempts for naming nanographenes are restricted to (a) the smaller members of polycrystalline aromatic hydrocarbons and (b) high symmetry flakes. For the former, empirical names have been adopted, for instance, coronene, ovalene, pentacene, pyrene, anthracene, etc. . For theaterials , mainly aterials  suggesteRecently, we proposed a nomenclature scheme for porous graphene structures based on the arrangement of two-fold coordinated atoms (2-FCAs) in the pore boundary . In the It is worth noting that the proposed nomenclature scheme and the generation and numbering algorithm apply to graphene flakes and edges, which are composed of hexagonal rings, including either three-fold coordinated atoms (3-FCAs) or two-fold coordinated atoms (2-FCAs) only. Flakes or edges, including (i) atoms bonded with only one atom, (ii) parts of the flake (or the edge) bonded with the rest of the flake (or the edge) system with only one bond, (iii) helical-like flakes , or (iv)edges (bonds) and vertices (atoms), we showed that each such closed path  can be uniquely defined by the sequence of path lengths In the current section, we show the connection between flakes and edges with pores, which has been studied previously . Considee 2-FCAs .non crossed” means that if we move along that path, each vertex and edge is visited only once. The term “closed path” or “circuit” means that the path begins and ends at the same vertex. In terms of graph theory, these properties describe both an Eulerian and Hamiltonian circuit. The term “path length” is also used from the point of view of graph theory, i.e., it is the number of edges along the path. For convenience, we use the term “2-2 path” for the path along the pore boundary connecting two adjacent 2-FCAs, and the term “2-2 hexagon” for the hexagon of the vacuum space associated with the 2-2 path, which contains the 2-2 path, i.e., the edges of the 2-2 path are edges of the associated 2-2 hexagon. As we showed in our recent work [i is an integer number between 1 and 4  of the pore boundary. The direction of i denotes the 2-2 path and j the edge vector belonging to the i 2-2 path, and considering that I is the In Ref. , for porIn Ref. , we showAs we have shown in Ref. , ei,j ca in Ref. . Therefo5)ϕi,j=k−i+1π/3,a5)ϕi,j=k−i+1π/3,aIn conclusion, cases for The case for i, as shown in i and j are the same as those used in the notation of the edge vectors k is given in Equation 13) are ti and j indices of For Equation  yields Lture see h. In conAs in pores and flakes, a boundary path representing an edge should not be a crossed path. The conditions for a non-crossed path in the edges are the same as those in pores and flakes.It is worth noting that in the case of a path Obviously, a circuit representing a pore boundary can be either considered the boundary of a pore, or the boundary of a flake, depending on the side where the vacancies are. A flake boundary can be considered  the dual of a pore boundary, and vice versa, although, as we have already mentioned in the introduction and will explain below, not all pores have a flake as a dual, and not all flakes have a pore as a dual.The dual of the dual of a pore (flake) is the pore (flake) itself. As a consequence, the dual is unique, i.e., there is a one-to-one correspondence between a pore and its dual flake and between a flake and its dual pore. If this is not true, we consider that the dual of a pore or flake does not exist.The pore (or flake) boundary is the same as that of its dual. The difference is that the edge vectors of the pore (flake) boundary have opposite directions compared to those of its dual flake (pore). This convention for the direction of edge vectors is used so that we have the same determination of the vacuum area and graphene bulk area, regarding their relative position, with respect to the direction of the edge vectors (see above).Excluding the atoms of the boundary, all other atoms are transformed into vacancies and vacancies are transformed into atoms.If the dual exists, then for the transformation of a pore to its dual flake, and the transformation of a flake to its dual pore, we consider the following:L. Moreover, 2-FCAs of a pore (flake) are transformed into 3-FCAs in its dual flake (pore) and vice versa. Thus, The above can be seen in Considering that Equation , for k0=In Ref. , we showsee Ref. ). MoreovLet us now examine cases of flakes that do not have a pore as a dual and pores that do not have a flake as a dual. Pores or flakes that include three adjacent 2-2 paths in their boundaries with length The above cases are not the only cases for which a pore or a flake does not have a dual. In fact, those cases can be considered as special cases of a more general one, where two 3-FCAs of the pore (or flake) boundary, which are not adjacent along the pore (or flake) path, are bonded with each other. The reason is that the transformation from the pore to the flake (or from the flake to the pore) is expected to be accompanied by the conversion of 3-FCAs to 2-FCAs. However, two such 3-FCAs of the pore or flake boundary will remain 3-FCAs in the transformation from the pore to the flake or from the flake to the pore since their bond will not be lost in the transformation. Thus, those atoms will not be converted to 2-FCAs, and the converted structure will have a different boundary compared to the initial one, not allowing the transformed one to be considered as the dual of the initial one. This can be clearly seen in the examples shown schematically in (i)i with The central edge vector (ii)i with The central edge vectors (iii)i and The (iv)i and Two adjacent 2-2 paths (v)i with length A 2-2 path If the dual of a pore (or a flake) exists, the conversion of the pore (or the flake) to its dual implies the replacement of 2-FCA vertices and 2-2 paths of its boundary to other 2-2 paths, according to the following scheme:For example, the dual of the 444 pore is the 112112112 flake. The transformations are shown schematically in L, there are L of the circuit is Considering that in a flake circuit with a total length N of atoms constituting a flake. Using the same strategy as the one used to find the number of vacancies in a pore (see Ref. [An interesting question that needs to be answered has to do with the number see Ref. ), we can in Ref. . This meh of the above notation is used to distinguish the coordinates expressed in the base of N.Let us assume that the Equation  and FiguEquation , the hexEquation , we can A graphene edge can be considered a non-crossed, non-closed, and theoretically infinite path, dividing the honeycomb lattice into two discrete areas. One of them only has vacancies and the other one is the remaining graphene structure. Practically, however, a graphene edge is part of the boundary of a typically large graphene flake and not the boundary of a semi-infinite plane. Therefore, in terms of graph theory, a graphene edge is both an Eulerian and Hamiltonian path, which, contrary to the boundaries of flakes and pores, is a path and not a circuit. Such a path should not form a spiral because a spiral might correspond to a non-crossed and non-closed infinite path, but it does not divide the honeycomb lattice plane into the two discrete areas described above.L is the period of edge lengths at the boundary. This means that after the sequence From the point of view of an infinite path, the graphene edge can be considered periodic. Even if it is not periodic, it can be considered periodic with infinite periodicity. Let us assume that the smallest possible period of a specific edge is represented by the sequence Equation  not to bEquation . As alre(i)(ii)(iii)This means that any combinations of the sets (i) A = {2}, (ii) B = {1, 3} and/or (iii) C = {1, 1, 4} of 2-2 path lengths provide an infinitely periodic path, unless that path crosses itself, and any infinitely periodic path is composed of the combinations of the above sets of 2-2 paths. This does not mean that those sets of 2-2 paths should necessarily follow one another in the periodic A question that rises is whether or not there are specific combinations of path lengths for which It is worth noting that the Equation  . Let us…, Recalling that for flakes Equation  for edgeEquation , one canThe second step of the algorithm checks whether or not the sequence In the third step, the algorithm checks whether or not In the fourth step, the algorithm calculates the Equation , and in Equation , i.e., sEquation , the um If any of the above cases is true, the 2-2 hexagons determined by In the sixth step, which applies to flakes, but not to edges, the algorithm checks if Equation  is satisrelation (19)0≤moThe above procedure is repeated recursively for all possible If our aim is to find and number the N of atoms in a flake, we find the number N. Thus, the eighth step of the algorithm, which will follow each successful i, i,--------The details of these results can be found in Ref. [To find the number  in Ref. . The valConsidering that the hexagonal graphene structure can be constructed by vectors https://github.com/fthenak/Graphene-Pores-Flakes-Edges (accessed on 3 July 2023). The first one with the name “pore_flake_edge_generation.f90” takes as input (i) the system kind  and (ii) the number L of the pore or flake circuit, or periodic edge path. Moreover, for flakes, it provides (iv) the number of hexagons of the flake and (v) the number of atoms constituting the flake, and for pores, (iv) the number of hexagons in the vacuum area and (v) the number of vacancies. The second code with the name “pore_flake_edge_structure.f90” takes as input (i) the system kind , (ii) the number d of atoms around the pore is also an input, considering that pores are periodically arranged in the infinite graphene sheet. If that sequence corresponds to the selected system , it provides as output (i) the structure in the structure.xyz”, (ii) the corresponding minimum image of the sequence, (iii) and the length L of the circuit or path. Moreover, (a) for a flake, it provides (iv) the number of hexagons and (v) the number of atoms in the flake, (b) for a pore, (iv) the number of hexagons in the vacuum area and (v) the number of vacancies, and (c) for an edge, (iv) the number of ribbon atoms and the vector period Using the algorithm described above, we developed two Fortran codes, which can be found at  of Ref. .Using the first code, we find the number of graphene flakes , which appears in some lines of In pore_flake_edge_generation.f90 code, for the generation and numbering of the pore, flake, and edge For completeness, we present in Generalizing our nomenclature scheme for graphene pores, we propose a general, unique, systematic, accurate, and simple nomenclature scheme for naming graphene flakes and edges, which is based on the arrangement of 2-fold coordinated atoms in their boundaries. In the proposed nomenclature scheme, flakes and edges are named after the minimum images of sequences The proposed nomenclature scheme can be easily expanded to name pores, flakes, and edges of other two-dimensional systems , as well as functionalized pores, flakes, and edges, according to the scheme described in our previous work, thus opening up a new window in the nomenclature of such systems.


Due to low vaccination uptake and measles outbreaks across Europe, public health authorities have paid increasing attention to anthroposophic communities. Public media outlets have further described these communities as vaccine refusers or “anti-vaxxers”. The aim of this review was to understand the scope of the problem and explore assumptions about vaccination beliefs in anthroposophic communities. For the purpose of this review, we define anthroposophic communities as people following some/certain views more or less loosely connected to the philosophies of anthroposophy. The systematic review addresses three research questions and (1) collates evidence documenting outbreaks linked to anthroposophic communities, (2) literature on vaccination coverage in anthroposophic communities, and (3) lastly describes literature that summarizes theories and factors influencing vaccine decision-making in anthroposophic communities.This is a systematic review using the following databases: Medline, Web of Science, Psycinfo, and CINAHL. Double-blinded article screening was conducted by two researchers. Data was summarized to address the research questions. For the qualitative research question the data was analysed using thematic analysis with the assistance of Nvivo12.0.There were 12 articles documenting 18 measles outbreaks linked to anthroposophic communities between the years 2000 and 2012. Seven articles describe lower vaccination uptake in anthroposophic communities than in other communities, although one article describes that vaccination coverage in low-income communities with a migrant background was lower than in the anthroposophic community they studied. We found eight articles examining factors and theories influencing vaccine decision making in anthroposophic communities. The qualitative analysis revealed four common themes. Firstly, there was a very broad spectrum of vaccine beliefs among the anthroposophic communities. Secondly, there was a consistent narrative about problems or concerns with vaccines, including toxicity and lack of trust in the system. Thirdly, there was a strong notion of the importance of making individual and well-informed choices as opposed to simply following the masses. Lastly, making vaccine choices different from public health guidelines was highly stigmatized by those outside of the anthroposophic community but also those within the community.Continuing to further knowledge of vaccine beliefs in anthroposophic communities is particularly important in view of increasing measles rates and potential sudden reliance on vaccines for emerging diseases. However, popular assumptions about vaccine beliefs in anthroposophic communities are challenged by the data presented in this systematic review.The online version contains supplementary material available at 10.1186/s12889-023-17081-w. Vaccines save lives . VaccineAnthroposophy is a spiritualist movement that was established by scientist and philosopher Rudolf Steiner born in 1861 in Austria . SteinerAnthroposophic medicine was founded in the early 1920s by Rudolf Steiner and Ita Wegman . DrawingAnthroposophic medicine is practiced in 78 countries worldwide, predominantly in Central Europe. There are circa 24 anthroposophic medical institutions – these include hospitals, departments in hospitals, rehabilitation centres, and other inpatient healthcare centres in six countries  [The 2019 official statement of the international centre of anthroposophic medicine, the Medical Section of the Goetheanum, and the International Federation of Anthroposophic Medical Associations (IVAA) clearly states that they do not support the anti-vaccine movement. Rudolf Steiner did not oppose vaccines, however, vaccination and anthroposophic medicine constitutes a somewhat contentious point . This isTherefore, this review aims to understand the scope of the problem and explore popular assumptions about vaccine beliefs in anthroposophic communities. To achieve this, this systematic review summarizes the existing literature that investigates the relationship between anthroposophy and vaccination beliefs.This is a systematic review, including both quantitative and qualitative studies. The review is based on current best practices utilising the Joanna Briggs Institute systematic review framework , 19.What are the documented outbreaks associated with low vaccination coverage in anthroposophic communities?What is the evidence for vaccination rates in anthroposophic communities?What is the evidence that describes factors and theories for low vaccination uptake in anthroposophic communities?We used the population/concept/context (PCC) framework to guide the development of our research questions . The popNo review protocol exists, and the systematic review has not been registered.A systematic literature search was performed by two researchers in the following databases: Medline, Web of Science, Psycinfo, and CINAHL. The last search was conducted 2022–09-05. The search strategy was developed in Medline (Ovid) in collaboration with librarians at the Karolinska Institutet University Library. For each search concept Medical Subject Headings (MeSH-terms) and free text terms were identified (see appendix). No language restriction was applied. Databases were searched from inception. The strategies were peer reviewed by another librarian prior to execution. De-duplication was done using the method described by Bramer et al. [Independent study selection was completed by two reviewers (SHvW and KA). Inclusion criteria for the first round of screening (title and abstract) were all articles that discussed anthroposophy and vaccination (this was conducted by KA and SHvW). Articles in Swedish and German were only reviewed by SHvW due to language restrictions. Inclusion criteria for the second and more in-depth round of screening – conducted double-blinded by KA and SHvW were all papers relevant to the three research questions, including both quantitative and qualitative studies. Exclusion criteria were, not peer-reviewed papers, opinion pieces, systematic reviews, nor papers that were not relevant to the research question .A quality assessment of the selected papers was conducted double-blinded by two researchers (KA and SHvW). For the qualitative studies, we used the JBI Critical Appraisal Tool for Qualitative Research . This isTo address research questions one and two, the data was summarized in Tables The search revealed 27 papers see Fig. . Twelve Table Table Table The systematic search revealed eight articles examining factors and theories influencing vaccine decision-making in anthroposophic communities  vaccines and meningitis vaccines. Recent studies have highlighted the important effect the HPV vaccine on the reduction of cervical cancer – therefore understanding the views of parents from the anthroposophic community on the HPV vaccine would have important public health implications.In terms of the qualitative findings, the review revealed a broad range of vaccination beliefs and highlighted the importance of individual choice in the vaccine decision process. Although parents consider themselves well-informed, it is unclear from the studies where they obtain their information, although some refer to the use of scientific information. Understanding knowledge and information sources in greater detail would be helpful to understand how certain rumours are maintained. The challenge of reliance on poor information sources to make a vaccine decision was particularly noted during the COVID-19 pandemic and arguably hindered COVID-19 vaccine uptake . Some in“It is not a matter of being in opposition to the school of medicine that is working with the accepted scientific methods of the present time. We fully acknowledge its principles. …we therefore feel compelled to work for an extension of clinical medicine, based on these wider insights into the nature of the world and the human being” [.Although there are currently 27 articles that have investigated the relationship between vaccines and anthroposophy, it remains somewhat nebulous why anthroposophy as a religion or belief system is often considered as an anti-vax movement by popular media. Anthroposophical medicine does not reject vaccines, nor does it reject modern medicine. This was clearly stated at the inception of anthroposophical medicine and it has been a clear statement by Gotheanum. In 1925, Dr Rudolf Steiner and Dr Ita Wegman clearly stated n being” .Sobo’s article described in this review was the only paper that engaged with the anthroposophic movement, particularly the Waldorf school context that arguably cultivated vaccine hesitancy . The notThe anthroposophic community prides itself on being different, communal, and supportive as opposed to following principles of consumerism and individualism. However, none of the studies, except briefly by Sobo, mentioned vaccines as a means for social action and to protect the vulnerable . DistrusLastly, the stigma this group experiences highlights a problem that requires careful attention. This could also be an important finding for other so-called vaccine hesitant groups . One couThere are some limitations to this systematic review. The review only includes peer-reviewed articles; this means that there have probably been other disease outbreaks linked to anthroposophic communities, which were only described in the grey literature. Moreover, some of the studies purely described the outbreaks rather than conducted an analysis; therefore, it is difficult to analyse in depth what actually happened. Regarding the thematic analysis of the qualitative studies, there are limits to conducting such an analysis of results of existing studies, since we could not base our analysis on the full data set.This systematic review showed that there have been several measles outbreaks linked to anthroposophic communities in Europe. Although studies on vaccination coverage in anthroposophic communities are limited, it appears that coverage is lower than in the general population. Monitoring outbreak numbers and vaccination coverage could be important. Popular beliefs about the anthroposophic communities’ vaccination beliefs are challenged in this review. As the evidence shows the communities are not categorically against vaccines. Moreover, there are a myriad of factors that influence vaccine decision-making of parents belonging to an anthroposophic community. The importance of experiencing childhood illnesses and concerns over long-term side effects were mentioned. Moreover, parents want to be able to individually select vaccines for their children. They consider themselves actively engaged in vaccine decision-making and well-informed. Stigma regarding vaccine choices was mentioned repeatedly mostly by people outside of the anthroposophic community but also by people within the community. This review calls for a better understanding of vaccine choices and beliefs for vaccines beyond MMR, in particular HPV vaccines. The review also highlights a potentially important research gap, which constitutes understanding not only a belief system but the role that stigma may play in making decisions about vaccines.Additional file 1.


OpenAI, CA, US), Google Bard , and Bing Chat  [Recent years have witnessed an increasing interest in the application of Artificial Intelligence (AI) and deep learning in Ophthalmology . Large l WA, US) –5. LLMs  WA, US) , 6, 7.We evaluated the performance of LLM-driven AI chatbots on the Fellowship of Royal College of Ophthalmologists (FRCOphth) exams required for autonomous Ophthalmology practice in the UK. We focused on testing the capability of these models in the Part 1 and Part 2 FRCOphth Written exams. These advanced postgraduate exams consist of multiple-choice questions and cover the learning outcomes of the Ophthalmology Specialty Training curriculum in the first two years of training and towards the end of training, respectively.We obtained sample multiple-choice questions from the Royal College of Ophthalmologists website, covering both the Part 1 and Part 2 examinations , 9. We eWe tested each LLM-chatbot three times on the sample questions at different timepoints. Additionally, for Part 2 questions, we evaluated ChatGPT-4.0 using various prompting strategies, such as asking the chatbot to answer the question from the perspective of a pharmacist or statistician. When the LLM-chatbot could not answer the question, it was recorded as incorrect. We did not provide additional instruction or training data.We analysed the association between accuracy and LLM-chatbot using Chi-squared testing and multilevel (mixed effect) logistic regressions. Difficulty and topic were included as fixed effects, and question ID as a random effect. We selected the models with the lowest Akaike information criterion. Part 1 and Part 2 data were analysed separately. All statistical analyses were conducted in R.P < 0.001). Despite a 4% mean difference in accuracy with each iteration, no statistically significant differences in performance were observed for any individual LLM-chatbot.The LLM-chatbots achieved overall accuracies of 65.5% and 67.6% for Part 1 and Part 2 questions, respectively  and Google Bard  in Part 1 questions. No significant associations were found between accuracy and question difficulty or topic. In Part 2 questions, ChatGPT-3.5’s performance was surpassed by both ChatGPT-4.0 and Bing Chat, regardless of whether prompting was used or not  are being developed to aid clinical decision-making through free-text explanations, spoken recommendations, or image annotations.Previous studies have shown that LLMs can achieve accuracies of up to 67.6% in generalist medical examinations using different training data and instruction prompt tuning.This study is the first to demonstrate that LLMs can consistently provide accurate responses to postgraduate Ophthalmology specialty examinations, achieving an impressive accuracy rate of up to 82.9% without prompting or instruction tuning.LLMs outperformed the standards of these specialist examinations, indicating that traditional assessments may not adequately measure clinical competence.Issues related to validation, computational expenses, data procurement, and accessibility must be addressed to ensure the safe and effective integration of AI systems into online learning and clinical practice.Supplementary Materials


We would like to thank the reader for their interest in our paper and for their thoughts on endothelial cell (EC) proliferation and endothelial-to-mesenchymal transition (EndMT) in the Sugen5416/hypoxia (SuHx) model of pulmonary arterial hypertension (PAH).1 which the reader disagreed with. They reasoned this was because the differentially expressed genes between control and PAH were associated with the gene ontology (GO) terms regulation of angiogenesis (GO:0045765), regulation of vasculature development (GO:1901342), and EC proliferation (GO:0001935). We believe that GO term analysis alone is insufficient for making conclusions about cell proliferation. The GO terms highlighted by the reader also contain genes that regulate those processes in either a positive or negative direction, or both. Importantly, angiogenesis involves an intricate coordination and balance of EC proliferation, sprouting, and migration. It is overly simplistic to assume that because angiogenesis is induced, ECs must therefore be proliferating. Various studies have also provided evidence showing that opposing EC proliferative and migratory responses could present together in different pathologies and mechanistic contexts.2–4 The reader also suggested upregulation of Bmpr2, caveolin (Cav) 1/2, and secreted protein acidic and cysteine rich (Sparc) in PAH as markers of EC proliferation. This not only conflicts with our observation of Bmpr2 downregulation in PAH,1 but also with the expression plot in their letter and findings in the wider PAH field of reduced BMPR2 signalling,5 EC hyperproliferation in Cav1 and Cav2 knockout mice,6 and unclear contributions of SPARC in proliferation and angiogenesis.7 Furthermore, we do not believe they are as direct or established a marker of proliferation as cell cycle–related genes . We are thus confident in our finding, which is based on robustly assessing established proliferation/cell cycle markers and the discrete cell cycle phases of each EC.Our study reported no increase in proliferating ECs in SuHx PAH mice,1 though it is unclear from their plot label if it is 24% or 0.24%. Their analysis also showed control and intermittent hypoxia having similar proportions of Acta2+ ECs. This conflicts with their claim and matches our finding, which they had disputed. Although the reader provided immunofluorescent staining of PECAM1 and ACTA2 in lung cryosections from mice in normoxia or SuHx, there was lack of quantification of double-positive cells and statistical evaluation of the difference between groups. Furthermore, they have only evaluated one EndMT marker, ACTA2, where we know that a suite of markers should be used.8In their letter, the reader raised questions about our observation of limited EndMT in control and SuHx-induced PAH, reporting very high levels of Acta2 + control ECs in their analysis of murine whole lungs. We do not expect ECs to express any mesenchymal markers in control. As such, the 24% of Acta2 + control ECs they reported seem unexpectedly high, unlike the 1% Acta2 + control ECs we observed,et al.8 have extensively reviewed the challenges posed by a lack of standard molecular definition. We used a panel of genes that could mark the following EndMT characteristics: reduced endothelial phenotype, increased mesenchymal phenotype, and increased expression of EndMT mediators.8 Our comprehensive assessment did not reveal any EC populations distinctly expressing these markers, suggesting EndMT was not present in our data. We also have no reason to believe that the tamoxifen induction efficiency and the fluorescence-activated cell sorting strategy we used are limitations in this context. EndMT has previously been studied in tamoxifen-induced condition.9 We found 95.5% of highTdTomato cells in our Cdh5-CreERT2-TdTomato mouse line, which were also highCdh5 and highPecam1 and were independently annotated as ECs by SingleR.1 Considering how EndMT could present as a transient phenomenon9 and how scRNA-seq only reveals a static snapshot of the cell state, we acknowledge that it is possible for EndMT to have occurred in earlier stages of our model, but this was not captured in our study. Importantly, we would like to emphasize that EndMT in PAH, and the wider cardiovascular disease field, has thus far been largely observational (i.e. being associated with a disease) and not causal.8EndMT is in itself a highly complex phenomenon and field of study, and Kovacic 10 However, the exact contribution of CD74 to the non-immune components of EC dysfunction in PAH remains unclear. We thus chose to extend our investigation of CD74 beyond inflammation, through targeted assays of EC proliferation and barrier function, with HUVECs as an initial in vitro model system, before extending these findings further into other EC types and ultimately into in vivo models.The final point raised by the reader was that our functional validation of CD74 should have focused on its immune function, rather than its impact on EC proliferation and barrier integrity. They also proposed using pulmonary artery ECs, instead of human umbilical vein ECs (HUVECs). PAH is a complex disease that involves not only an immune component, and the immune contribution of CD74 in ECs has been previously studied.


Graphene has been under intense scientific interest because of its remarkable optical, mechanical and electronic properties. Its honeycomb structure makes it an archetypical two-dimensional material exhibiting a photonic and phononic band gap with topologically protected states. Here, we assemble colloidal graphene, the analogue of atomic graphene using pseudo-trivalent patchy particles, allowing particle-scale insight into crystal growth and defect dynamics. We directly observe the formation and healing of common defects, like grain boundaries and vacancies using confocal microscopy. We identify a pentagonal defect motif that is kinetically favoured in the early stages of growth, and acts as seed for more extended defects in the later stages. We determine the conformational energy of the crystal from the bond saturation and bond angle distortions, and follow its evolution through the energy landscape upon defect rearrangement and healing. These direct observations reveal that the origins of the most common defects lie in the early stages of graphene assembly, where pentagons are kinetically favoured over the equilibrium hexagons of the honeycomb lattice, subsequently stabilized during further growth. Our results open the door to the assembly of complex 2D colloidal materials and investigation of their dynamical, mechanical and optical properties. Colloidal particles bonding via attractive patches mimic the bonding of atoms in atomic compounds and materials. By assembling patchy particles into the graphene lattice, the authors obtain insight into lattice defects in this important 2D material. The most prominent representative, graphene, consists of a monolayer of carbon atoms bonded in a honeycomb lattice. The strong covalent bonds within the honeycomb lattice make the material particularly strong and light, while the honeycomb structure gives rise to a photonic and phononic band gap5. On a larger length scale, micrometre-size particles assembled into colloidal graphene, the analogue of atomic graphene assembled from colloidal particles, would open the door to two-dimensional multifunctional materials with photonic and phononic band gap for applications as 2D photonic and phononic crystals. However, producing large defect-free single-crystalline graphene of both atoms and colloids remains a great challenge, crucially limiting its applications.Two-dimensional materials have attracted intense scientific interest, both from an application and a fundamental point of view, offering applications from light-weight materials to optoelectronic devices. These materials combine extraordinary mechanical, optical and electronic properties compared to bulk materials6. However, while defects are introduced unavoidably during growth or added on purpose to tune mechanical and electronic properties, a comprehensive understanding of their formation is missing: because the trivalent carbon atoms or particles can arrange into a variety of polygons and structures, a coherent lattice exists even with defects, and rearrangements can take many paths. Despite advances in direct visualization of graphene defects using electron microscopy8, defect kinetics and healing remain poorly understood, and defect-free graphene challenging to produce.Structural defects are known to be central to all of graphene’s properties, enabling among others band-gap tuning in graphene-based electronic devices11. One advantage of colloidal systems is that defect formation14 and dynamics16 can be conveniently studied directly in real time with single particle resolution using optical microscopy18, which remains challenging in atomic systems, especially under the harsh high-temperature atomic deposition used for graphene growth19. The recently-gained ability to synthesize anisotropic particles23, in particular colloidal particles with attractive patches providing specific valency and bond angles, has opened a design space for assembling more complex structures such as molecule analogues26 and covalently bonded crystals28.Although colloidal particles are several orders of magnitude larger than atoms, their phase behaviour and dynamics are governed by the same thermodynamics principles. Phase behaviour of both atoms and colloids is largely governed by thermal forces, which means we can use colloidal aggregation and crystallization as a simple model for atomic crystallization29. Experimentally realizing these structures remains challenging, as they require fine control over specifically coordinated interactions, or purposeful geometric design to block kinetically favoured nonequilibrium routes, as recently shown for the realization of colloidal diamond31. In contrast to tetrahedrally coordinated diamond, graphene relies on the trivalent coordination of particles. Patchy particles with patches at 120∘ angles can mimic these covalent bonds; yet, achieving such valency and controlling these directed bonds on the scale of kBT, the thermal energy, remains challenging, but would open up the assembly of structurally complex 2D materials, and investigation of their structural and mechanical properties.Simulations and experiment have shown that these colloidal molecules can grow into larger assemblies, yielding rich structures ranging from the kagome lattice to buckyball-like clustersHere, we assemble colloidal graphene and elucidate the kinetic pathways of crystallization and defect formation of this 2D material. We form the graphene lattice using pseudo-trivalent patchy particles adsorbed at a substrate, and directly follow the crystallization, defect formation and healing with great temporal and spatial resolution using confocal microscopy. Fine control of the patch-patch bond strength allows observation of near-equilibrium assembly in analogy to high-temperature deposition of atomic graphene. From the number of saturated bonds and the bond strain, we determine the configurational energy of the lattice and follow its evolution during lattice rearrangement and healing. Our results reveal that the most prominent defect motif of colloidal and atomic graphene, a pentagon, is kinetically favoured in the early stages of graphene growth, and acts as seed for extended defects during subsequent growth. These results hint at the importance of the early stages of assembly in generating defect-free graphene.23. The synthesis yields tetrahedrally coordinated particles with a PS bulk and fluorescently labelled TPM patches  and 3-(trimethoxysilyl)propyl methacrylate (TPM) spheres by colloidal fusionhes Fig. . The parcL = 0.25 close to the critical volume fraction cL,c = 0.2736, and solvent demixing temperature Tcx = 33.95 °C, and add 1 millimolar of MgSO4 to screen the particles’ electrostatic repulsion and enhance the lutidine adsorption of the hydrophobic patches25. The suspension is injected into a glass capillary with hydrophobically treated walls  in Fig. 43. However, CVD-grown atomic graphene does not normally show vacancy defects, even though experiments show that vacancies are generated during the early stages of the CVD process44. Unlike the substrate-adsorbed colloidal particles, carbon atoms can approach vacancies from outside the plane during CVD growth, filling the vacancies with feedstock carbon44. Hence, unlike vacancies in colloidal graphene, vacancies in atomic graphene anneal in the CVD process, and irradiation or chemical treatment is used to induce them. These generated vacancies typically reconfigure to a (slightly) lower-energy structure that contains fewer dangling bonds. For instance, a divacancy can reconfigure into two 5-membered and one 8-membered ring45. In contrast, the divacancy in Fig. 46, making reconfigurations in colloidal graphene unlikely due to high energy barrier  51, or aligning graphene islands before merging57. While crystallization and defect dynamics in atomic graphene are ultimately governed by quantum mechanics, we expect that in the high-temperature limit studied here, where the quantum-mechanical states become quasi-continuous, our colloidal system provides a good model. Yet, differences arise from the different form of the potential and the different nature of the in-plane  versus interlayer bonding . Despite these differences, the energy scales are similar: at typical high-temperature deposition (~800 K) the covalent bond energy of graphene on a metal substrate is ~1 eV58, corresponding to 14.5kBT - similar to our critical Casimir bond strength of 12–15kBT. During higher temperature annealing procedures of graphene (~2000 K) the corresponding energy (6kBT) is lower, allowing together with the higher atomic attempt frequency for faster dynamics, with rearrangements occurring on the order of seconds59 rather than hours as in our colloidal case. The assembly of colloidal graphene demonstrates the increasing control over bottom-up assembly of complex materials. The honeycomb lattice is of specific interest because it is the simplest metamaterial exhibiting a photonic and phononic bandgap61, and topologically protected states. While achieving the structural complexity of macroscopic mechanical metamaterials remains still a challenge, our results demonstrate that the necessary structural motifs can be assembled using patchy particles, opening the door to microscale mechanical metamaterials4.Trivalent colloidal particles adsorbed at a substrate form the colloidal analogue of graphene, allowing direct observation of its crystallization and defect dynamics. The fine interaction control opens near-equilibrium crystallization and annealing pathways. We find that colloidal graphene defects originate in the early stages of crystallization from pentagonal motifs that are kinetically favoured over the equilibrium hexagonal motifs, further stabilized by adjacent heptagonal motifs, together forming stable grain boundaries. These results are reminiscent of high-resolution electron microscopy observations of atomic graphene, which however are limited to fully grown graphene, and cannot access the initial stages of crystallization. Grain boundaries and extended polyvacancies reconfigure towards lower-energy states by an interplay of dangling-bond saturation and lattice distortions, ultimately increasing the number of hexagons. Strategies for synthesizing large atomic graphene crystals tend to circumvent this issue by either generating as few graphene seeds as possible4 . The particles are washed several times in the water-lutidine mixture. The resulting particle dispersion is injected into a silanized hydrophobic glass capillary  and sealed with teflon grease (Krytox GPL-205). The full silanization procedure is given in Supplementary Method Tetrapatch particles  are dispersed in a binary solvent of 25% 2,6-lutidine  and 75% milliQ water with 1 millimolar MgSOT ≊ 0.6 °C), which causes one of the particle patches to attach to the sample wall. For heating, we use a well-controlled temperature stage in combination with an objective heating element to obtain a relative temperature accuracy of about 0.01 °C with minimal temperature gradients.Particles are left to sediment to the bottom of the sample at room temperature before measurements. We tilt the sample slightly during sedimentation, so a small density gradient is present in the sample. We then heat the sample to approximately 33.35 °C  to determine the centre of each patchy particle. Because one of the patches is attached to the glass, each particle centre is approximately given by this lower patch. The three remaining patches are suitable for bonding, and form a single blob with another bonded patch if bonded. This tells us if two nearby particles are actually bonded or merely randomly meeting. For more tracking details, see Supplementary Note We image the assembled structures using confocal microscope image stacks, sometimes alternating with bright field images. The images are processed using particle tracking software , and the composition of the binary solvent, as detailed in ref. 46. By formulating the critical Casimir potential model presented in ref. 46 for patchy particles and benchmarking it onto our patchy particles as shown in ref. 63, we determine the attractive minimum of the pair potential to be 12–15kBT in the studied temperature range of ΔT = 0.25–0.1K. The full potential is given in Supplementary Note The critical Casimir potential is short ranged, its magnitude and range are set by the temperature offset ΔThe bond-bending potential is harder to estimate theoretically, but can be determined from experimental measurements by following clusters of three particles, and tracking the fluctuations of the internal angle of these particles. The resulting angle probability distribution can then be converted to a potential, as shown in Fig. Supplementary InformationPeer Review FileDescription of Additional Supplementary FilesSupplementary Movie 1Supplementary Movie 2


This exceptional performance underscores the potential of the algae-graphene composite as a highly efficient and durable electrode material for supercapacitor applications.This study focuses on the synthesis and characterization of supercapacitor materials derived from pyrolyzed natural compounds. Four compounds were investigated: methylcellulose with lysine (ML), methylcellulose with lysine-graphene composite (MLG), algae (A), and algae-graphene composite (AG). The pyrolysis process was utilized to convert these natural compounds into carbon-based materials suitable for supercapacitor applications. The properties of the resulting materials were analyzed extensively to evaluate their potential as supercapacitor electrodes. The electrochemical performance, including specific capacitance, cyclic stability, and rate capability was measured using various characterization techniques. The effects of incorporating graphene into the lysine-methylcellulose and algae matrices were also studied to explore the enhancements in supercapacitor performance. In both cases, the addition of graphene resulted in a positive effect. Among all the materials investigated, the algae-graphene composite exhibited the most favorable properties, demonstrating a specific capacitance of 192 F g They have the potential to bridge the gap between conventional capacitors and batteries, offering a unique combination of energy and power delivery for various applications, including portable electronics, electric vehicles, and renewable energy systems5. The performance of supercapacitors relies heavily on the properties of the electrode materials2. Carbon-based materials have been widely explored as electrode materials for supercapacitors due to their high surface area, good electrical conductivity, and excellent electrochemical stability10. Traditional carbon sources, such as activated carbon, have been extensively utilized12. However, there is growing interest in developing sustainable and cost-effective electrode materials derived from natural compounds16. Pyrolysis, a thermal decomposition process in the absence of oxygen, has emerged as a promising method for synthesizing carbon-based materials from natural precursors. Pyrolyzed materials exhibit unique structural and electrochemical properties, making them attractive options for supercapacitor applications18. The use of natural compounds as precursors offers several advantages, including abundant availability, low cost, and environmental friendliness19.Supercapacitors, also known as electrochemical capacitors or ultracapacitors, have gained significant attention as promising energy storage devices due to their high power density, fast charge–discharge rates, and long cycle life compared to traditional batteries20 demonstrated that pyrolyzed rice husks exhibited a specific capacitance of 278 F g−1 in a potassium hydroxide electrolyte, highlighting the impressive electrochemical performance achievable with bio-waste materials. Furthermore, Lv and colleagues21 explored the pyrolysis of chitosan, resulting in carbon-based materials with a specific capacitance of 306.4 F g−1 in 6 M KOH electrolyte, thus emphasizing the versatility of natural polymers for supercapacitor applications. Additionally, the work of Yi et al.22 on the pyrolysis of lignin-based materials showed a specific capacitance of 133 F g−1, demonstrating the viability of lignocellulosic biomass as a renewable electrode precursor. These examples underscore the burgeoning interest in sustainable and environmentally friendly electrode materials derived from readily available natural sources. The continuous investigation into the electrochemical behavior and properties of these materials promises to propel energy storage technology to new heights, with potential applications spanning a wide range of industries.Our study is situated within the context of the latest advancements in pyrolyzing diverse natural sources to serve as supercapacitor electrodes. Recent research has witnessed significant strides in this domain, showcasing the remarkable potential of materials derived from natural compounds. For instance, studies by Liu et al.In this study, the synthesis and characterization of supercapacitor materials derived from pyrolyzed natural compounds was conducted. Specifically, four compounds were investigated: lysine with methylcellulose, lysine with methylcellulose-graphene composite, algae, and algae-graphene composite. Lysine, an essential amino acid, and methylcellulose, a biodegradable polymer, have shown potential in various applications due to their unique physicochemical properties. Algae, on the other hand, are abundant and renewable biomass resources that have gained attention for their potential use in energy storage systems. The incorporation of graphene, a two-dimensional carbon material with exceptional electrical conductivity and mechanical strength, offers the opportunity to enhance the performance of the resulting supercapacitor materials. Additionally, comprehensive studies utilizing solid-state physics techniques will be conducted alongside the electrochemical investigations. These investigations will provide valuable insights into the structural and morphological properties of the pyrolyzed natural compounds and their composites. Techniques such as scanning electron microscopy (SEM), Raman spectroscopy, X-ray photoelectron spectroscopy (XPS), nitrogen adsorption at a low temperature, and elementary analysis will be employed to characterize the crystalline structure, surface morphology, and nanoscale features of the materials. These complementary studies will offer a comprehensive understanding of the relationship between the structural properties and the electrochemical performance of the synthesized materials, facilitating the design and optimization of advanced supercapacitor materials. This study aims to investigate the electrochemical properties of these pyrolyzed natural compounds and evaluate their potential as electrode materials for supercapacitors. By analyzing the specific capacitance and cyclic stability of the synthesized materials, we strive to gain insights into the performance enhancements achieved by incorporating graphene and utilizing different natural precursors.SEM images provide crucial insights into the size, shape, and internal structure of materials. In this study, SEM analysis was utilized to characterize the morphology of the composite materials, and the results are presented in Fig. 24. The disorder-induced band resulting from vacancies or dislocations in the graphene layer and at its edge (D-band), the band associated with graphene in graphite (G-band), and the band related to the graphene layer (2D-band) observed in the Raman spectra . The ratio of 2D to G band intensities for ML, MLG, A, and AG is 0.31, 0.40, 0.30, and 0.36, respectively. This I2D/IG intensity ratio is less than 1, indicating the presence of a few graphene layers.Raman spectroscopy is a leading method used to characterize carbon materials2 g−1 and 2,478 m2 g−1, respectively. The total pore volume determined at maximum p/po for the samples with the highest SBET is 1.82 cm3 g−1 and 1.11 cm3 g−1 for samples ML and A, respectively. The physical morphology of the two samples synthesized with graphene was decreased to 1,184 m2 g−1 and 1,518 m2 g−1 for MLG and AG, respectively. However, this SBET for MLG and AG is still very high, and the total pore volume was 0.99 cm3 g−1 and 0.75 cm3 g−1, respectively. The shape of the obtained nitrogen adsorption isotherms  with a small hysteresis loop at a relative pressure of 0.4–1.0. The large surface area and significant share of micropore size (less than 2 nm) visible on pore size distribution curves  method. The ML and A samples exhibited the highest specific surface areas when nitrogen-doped carbons obtained from methylcellulose with lysine or algae were used as substrates, with BET values of 2,049 mThe elemental composition of samples ML, MLG, A, and AG, with or without the participation of commercial graphene, was determined using an elemental combustion analysis. Similar levels of carbon values were obtained for ML (78.10% by weight) and A (80.87% by weight) samples, but the highest carbon content was characterized by samples whose synthesis used graphene MLG (90.38% by weight) and AG (84.14% by weight). The addition of commercial graphene during the synthesis contributed to obtaining a material with a carbon content higher by 4 or 16% compared to the material where commercial graphene was introduced mechanically before the carbonization process. The nitrogen content of lysine and algae as good nitrogen-doped carbon precursors is very high after high-temperature treatment, at 4.71% by weight and 3.75% by weight for ML and A, respectively. On the other hand, the nitrogen content decreased for samples with graphene to 1.79% and 1.39% by weight for MLG and AG, respectively. For all analyzed samples, the hydrogen content reaches low values from 0.94 to 1.06% by weight. The percentages of elements obtained by elemental analysis are shown in Table To confirm the chemical state of the atoms present on the surface of the materials obtained, X-ray photoelectron spectroscopy analysis was performed. The low-resolution broad-band spectra for MLG and AG hybrid materials are shown in the energy range from 0 to 1,200 eV Fig. a,b.Figur2) occurring at a bond energy of 284.3 eV are present in the studied structure. The energy band at 285.0 eV indicates the presence of a C–C bond (sp3). C–O–C and/or C–OH type bonds are also present in the obtained materials, which was confirmed by a band at a binding energy of 285.9 eV. The band at energies equal to 286.8 eV corresponds to C=O and/or O–C–O bonds, and at energy 288.0 eV is characteristic of O–C=O-type bonds. In addition, the band at energies equal to 289.7 eV and 292.1 eV can be attributed to shake-up excitation from sp2-type carbon. The XPS spectrum for the tested samples in the N1s region , methylcellulose with lysine-graphene composite (MLG), algae (A), and algae-graphene composite (AG). The CV curves for each sample were recorded within a voltage window of − 0.1 V to + 0.8 V  and galvanostatic charge–discharge (GDC) experiments. A three-electrode system was employed, comprising an Ag/AgCl/3 M KCl reference electrode, the obtained carbon-based materials as the working electrode, and a Pt mesh counter electrode. The electrochemical measurements were carried out using a 0.2 M KBET)36. Traditional supercapacitor research has sought to maximize surface area to achieve higher capacitance. However, the diminishing returns associated with this approach have become evident as the theoretical maximum limit for surface area utilization seems to have been reached35. The discovery that materials with graphene additives exhibit improved capacitance, even with a smaller surface area, challenges the notion that surface area is the sole driver of enhanced performance. Other factors, such as the conductivity and structural characteristics introduced by graphene, may contribute to the increased electrochemical capacitance36. The exceptional electrical conductivity of graphene facilitates efficient charge transfer and electron transport within the electrode, enabling a higher capacitive response. Additionally, the unique structural properties of graphene, such as its two-dimensional layered structure and large aspect ratio, may create favorable conditions for ion diffusion and accessibility to active sites, thereby enhancing the charge storage capability38. Therefore, the race for achieving the highest surface area is no longer the sole priority in supercapacitor research. It has become increasingly evident that, besides specific surface area, other factors play a crucial role in determining the capacitance of supercapacitor materials. These factors include the distribution of pore sizes within the material and, equally importantly, the nature of the electrolyte used. The latter consideration is particularly significant, as it involves matching the size of the ions in the electrolyte to the pore size within the material. In this context, optimizing the pore size distribution has gained prominence because it influences ion transport and accessibility to the electrode's surface. A well-balanced pore structure can facilitate efficient ion diffusion, leading to enhanced capacitance and improved charge–discharge performance. Furthermore, the choice of electrolyte plays a pivotal role in dictating the supercapacitor's overall performance. The ion size in the electrolyte should ideally align with the pore size distribution within the electrode material. This alignment ensures that ions can readily access and interact with the available surface area, maximizing the electrochemical capacitance. In essence, achieving high capacitance in supercapacitors is not solely about increasing the surface area; it also involves optimizing pore size distribution and carefully selecting an electrolyte that matches the pore size characteristics, creating an effective synergy between these factors for superior energy storage capabilities. Thus, the incorporation of graphene has opened up new avenues for improving electrochemical performance, demonstrating that factors beyond surface area can significantly influence the capacitance of electrode materials. Moreover, among the investigated materials, the highest capacitance after 100 charge–discharge cycles was observed for the material containing pyrolyzed algae with graphene  resulted in a reduction in resistance. This finding underscores the positive impact of graphene on enhancing charge transfer kinetics within the electrode–electrolyte interface, which is valuable for improving the overall performance of supercapacitors. This specific combination exhibited exceptional electrochemical performance, highlighting the synergistic effects between pyrolyzed algae and graphene in terms of charge storage. In each case, an increase in capacitance was observed with successive cycles, indicating a progressive improvement in the electrochemical performance of the materials. However, to gain a deeper understanding of this phenomenon, materials containing graphene were chosen for subsequent studies.This absence of a semicircle indicates a relatively small charge transfer resistance, which can be attributed to the porous structure of the materials40.To assess the long-term repeatability of the observed phenomenon and to determine if the capacitance value continues to increase over an extended period, electrochemical measurements were conducted over 1,000 charge–discharge cycles. The results are depicted in Fig. −1 for MLG and AG, respectively. These curves provide insights into the charge storage and discharge behavior of the supercapacitor electrodes over a long cycling period. In the two-electrode configuration, it is observed that there is no significant increase in capacitance with successive cycles, as previously observed in the three-electrode setup. However, it is worth noting that there is still an increase in capacitance throughout the cycling test, especially up to approximately 500 cycles.To evaluate the stability of symmetric supercapacitors based on the materials with methylcellulose-graphene composite and algae-graphene composite, multiple charge–discharge cycles were conducted in a two-electrode configuration. The supercapacitors underwent an extensive cycling test of 10,000 cycles to assess their long-term stability and performance. Figure The absence of a pronounced capacitance increase in the two-electrode configuration can be attributed to several factors. Firstly, the closer proximity between the two electrodes in this setup may result in a limited diffusion of ions and a reduced accessibility of active sites, thus inhibiting the full utilization of the electrode materials' capacitance. Moreover, a vacuum sealer is commonly used during the fabrication of prototype supercapacitors, which likely leads to a quicker impregnation of the carbon electrodes with the electrolyte. This accelerated impregnation may result in a faster initial capacitance increase during the early cycles.Despite the absence of a continuous capacitance increase, the observed retention of capacitance up to around 10,000 cycles indicates the stability and durability of the MLG and AG materials in the symmetric supercapacitor configuration. This capacitance retention suggests that the materials can still provide reliable and sustainable energy storage performance over several cycles.−1. The combination of algae and graphene in the composite material seems synergistic, leading to an enhanced capacitance compared to the other studied materials. The presence of graphene contributes to improved electrical conductivity, facilitating efficient charge transfer and higher charge storage capacity. Meanwhile, the unique properties of algae, such as its high surface area and porosity, likely provide additional active sites for electrochemical reactions, further enhancing the capacitance43. For comparative analysis, three representative charge–discharge cycles are presented: the first cycle, the cycle at which the maximum electrochemical capacity was achieved, and the final cycle. These cycles offer insights into the electrochemical behavior and performance of the studied materials over the course of the testing  material exhibited the highest capacitance, reaching a maximum value of 241 F gsee Fig.  inset. I−1. To determine the charge transfer process mechanism, current density (j) versus potential (v) plots  plots  and the cheap and widely available two hard templates K2CO3 and CaCO3. Carbon materials from natural sources were synthesized in two series. In the first series, natural carbon sources methylcellulose and lysine were used, along with a hard CaCO3 template in a weight ratio of 1:1:1. In the next step, a solution of K2CO3 at a concentration of 11% m/v was prepared and added to the mixture, which was then mixed mechanically and intensively until a homogeneous mass was obtained. In the second series, 100 mL of K2CO3 solution (concentration of 11% m/v) was added to 5 g of green algae and stirred until a homogeneous solution was obtained. In both series, the resulting mass was allowed to dry at 100 °C to evaporate water. The samples were then pyrolyzed at 800 °C for 1 h, with a heating rate of 10 °C min−1 in a nitrogen flow. After the pyrolysis process, the final product was treated with concentrated hydrochloric acid to remove residual carbonates. The samples were then washed with water and dried in an electric dryer. The second series was based on the use of the green algae, Chlorella vurgalis. The synthesis steps were analogous to the first series, and the mass ratio of the compounds was also the same. Commercial graphene nanoplatelets (G) with a specific surface area of 750 m2 g−1 and electrical conductivity of approximately 1,400 S cm−1  were added to both series to improve the conductive properties at a mass ratio of 0.2 to the carbon material. The samples in the first series were marked as ML and MLG, where M was designed for methylcellulose and L for lysine used during the synthesis. The samples in the second series were named A and AG, where A is algae. In both series, G is commercial graphene.Carbon materials were prepared using an uncomplicated pyrolysis method using natural sources  was determined using the Brunauer–Emmett–Teller (BET) method, which calculates the surface area based on the adsorption isotherm data. Additionally, the total pore volume  and pore size distribution were determined using the Density Functional Theory (DFT) method, providing information about the porosity of the carbon materials. To analyze the elemental composition of the samples, a bulk combustion analysis was conducted to measure the carbon, nitrogen, and hydrogen contents. This analysis provides quantitative information about the relative amounts of these elements present in the carbon materials. X-ray photoelectron spectroscopy (XPS) measurements were performed using a monochromatic Al Kα excitation source operated at 1486.6 eV. The survey spectra and high-resolution spectra were collected using pass energies of 0.5 eV and 0.1 eV, respectively. The spectra were referenced to the C1s neutral carbon peak at 284.8 eV, allowing for the characterization of the carbon-containing functional groups and their chemical states.Surface analysis of the samples was conducted using a scanning electron microscope (SEM) type 1430 VP at an accelerating voltage of 30 kV from LEO Electron Microscopy Ltd, England. This SEM instrument allowed for detailed examination and characterization of the surface morphology and features of the materials. Raman spectra were recorded using a Raman spectrometer  with a green laser (532 nm) as the excitation source. Raman spectroscopy allowed for the investigation of the materials' vibrational modes and molecular structure, providing insights into their chemical composition and bonding configurations. A detailed surface structure and features analysis was conducted to gain insights into the material's physical characteristics. The sorption of nitrogen was performed using an ASAP2020 Plus instrument from Micromeritics. Prior to the sorption measurements, the samples underwent a vacuum outgassing process at 200 °C for 24 h to remove any adsorbed contaminants. The specific surface area , with an Ag/AgCl (3 M KCl) reference electrode and a platinum mesh counter electrode. All electrochemical experiments were performed using a potentiostat/galvanostat (BioLogic VSP 2078) and involved cyclic voltammetry and galvanostatic charge–discharge (GCD) techniques. During the CV measurements, the potential was scanned from − 0.1 V to + 0.8 V vs. Ag/AgCl (3 M KCl) at a scan rate of 50 mV s−1. This range allowed for the investigation of the electrochemical behavior of the electrode materials. GCD tests were conducted within the same potential range, with a current density of 2.0 mA cm−2. The charge–discharge cycles provided insights into the energy storage capacity and performance of the synthesized materials. Moreover, EIS was performed for all obtained electrode materials in a frequency range between 20 kHz and 1 Hz with a voltage amplitude of 10 mV at an open circuit potential.The electrode materials were prepared by suspending 20 mg of the samples in a mixture of 0.75 mL distilled water, 0.2 mL isopropanol, and 0.05 mL of a 5% aqueous Nafion solution. The resulting suspension was sonicated in an ultrasonic bath for 60 min to ensure proper dispersion. Subsequently, the prepared mixture was deposited onto a polished surface of a glassy carbon electrode with a diameter of 1.5 mm and allowed to dry in an oven at 60 °C for a few minutes. For the electrochemical measurements, a three-electrode configuration was employed. The electrolyte used was a 0.2 M K−1 K2SO4 aqueous electrolyte, was placed between the electrodes. The GF was coated with a mixture containing the tested carbon materials (MLG and AG), which was then dried at 40 °C for 6 h. The mass loading of the carbon materials onto the GF was determined by measuring the weight difference of the electrode material before and after applying the mixture. An analytical balance, specifically the RADWAG XA 82/220.4Y PLUS with an accuracy of 0.01 mg, was utilized for this measurement. The mass loading was found to be approximately 4.27 mg cm−2 for MLG and 5.38 mg cm−2 for AG. The thickness of the layers was about 30 µm. Subsequently, the casing foil was sealed around three sides using a plastic foil welder. Finally, the entire setup was securely sealed using a vacuum packing machine . This construction process ensures the assembly of a symmetric supercapacitor with the MLG and AG materials as the electrodes. The use of flexible graphite foils provides mechanical support and flexibility to the device, whereas the fiberglass separator soaked in the electrolyte facilitates ion transportation between the electrodes while preventing direct contact. The sealing of the setup using the plastic foil welder and vacuum packing machine ensures the encapsulation and protection of the supercapacitor, maintaining its integrity and preventing moisture or air ingress. By employing these construction steps, a reliable and well-protected symmetric supercapacitor setup is achieved, allowing for further electrochemical characterization and performance evaluation of the MLG and AG materials. The galvanostatic charge and discharge tests  were performed for the symmetric supercapacitor. Charge and discharge measurements were made at a current density of 5 A g−1, with an electrochemical voltage range of 0 to 0.9 V. The specific capacitance (Csp) was calculated using the galvanostatic charge–discharge curves provided and Eq. .To construct a symmetric supercapacitor, two flexible graphite foils (GF) were combined with the obtained material electrodes. A fiberglass separator, soaked in a 0.2 mol L−1 over a polarization range of 0 to 0.9 V. A floating test was also conducted to evaluate the most promising stability for the carbon material, as detailed in reference54. The procedure involved conducting five galvanostatic charge–discharge cycles at maximum voltage after every 10 h of aging. The specific capacitance was then calculated. This series of sequences was repeated 10 times, totaling a floating time of 100 h.The charge–discharge measurements were also carried out for MLG and AG at current densities ranging from 1.0 to 10 A gThis article investigates the utilization of pyrolyzed natural compounds for supercapacitor applications, with a particular focus on the impact of graphene addition on the electrochemical performance. Four materials were studied: lysine with methylcellulose, lysine with methylcellulose-graphene composite, algae, and algae-graphene composite. The results demonstrate that incorporating graphene into the lysine-methylcellulose and algae matrices significantly improved the electrochemical properties of the resulting supercapacitor materials. Despite the graphene-infused materials having a smaller specific surface area compared to the carbon materials without graphene, they exhibited enhanced capacitance. The superior electrochemical performance observed in the graphene-enhanced materials can be attributed to several factors. Firstly, graphene, with its high electrical conductivity, facilitates efficient charge transfer and electron transport within the electrode. This results in improved capacitive behavior and enhanced energy storage capacity. Furthermore, the graphene reinforcement provides mechanical stability to the electrode materials, preventing structural degradation during repeated charge–discharge cycles. The resulting electrodes exhibit excellent cyclic stability and retain their electrochemical performance over extended operation. Thus, the findings of this study highlight the significant role of graphene in enhancing the electrochemical properties of pyrolyzed natural compound-based supercapacitor materials. Despite having a smaller specific surface area, the addition of graphene leads to improved capacitive behavior, higher specific capacitance, and excellent cyclic stability.


We implemented a semi-empirical pseudopotential (SEP) method for calculating the band structures of graphene and graphene nanoribbons. The basis functions adopted are two-dimensional plane waves multiplied by several B-spline functions along the perpendicular direction. The SEP includes both local and non-local terms, which were parametrized to fit relevant quantities obtained from the first-principles calculations based on the density-functional theory (DFT). With only a handful of parameters, we were able to reproduce the full band structure of graphene obtained by DFT with a negligible difference. Our method is simple to use and much more efficient than the DFT calculation. We then applied this SEP method to calculate the band structures of graphene nanoribbons. By adding a simple correction term to the local pseudopotentials on the edges of the nanoribbon (which mimics the effect caused by edge creation), we again obtained band structures of the armchair nanoribbon fairly close to the results obtained by DFT. Our approach allows the simulation of optical and transport properties of realistic nanodevices made of graphene nanoribbons with very little computation effort. The electronic properties of low-dimensional materials are unique due to unprecedented properties that are unparalleled by those in bulk counterparts ,2. A sciAb initio formalism such as density-functional theory (DFT)  has beenx-y plane) and Gaussian functions along a non-periodic  ,15 preseDFT is a widely used computational method for studying the electronic structure of AGNRs ,18. DFT Empirical methods, on the other hand, offer an alternative approach to studying AGNRs . These mGraphene nanoribbons (GNRs) ,23,24,25In electronics, AGNRs offer tunable bandgaps and unique edge states, making them potential candidates for high-performance transistors and logic devices . AGNRs aIn this paper, we implement a more sophisticated semi-empirical pseudopotential method (SEPM) within the planar basis to study the atomic and electronic structure of 2D systems, using graphene and armchair graphene nanoribbons as examples. The applications of the currently developed SEP include optical and transport properties of graphene and related structures such as graphene nanoribbons and various junction devices.To calculate the band structures of 2D materials in the semi-empirical pseudopotential (SEP) model, it is more efficient to adopt a planar basis. The basis consists of localized finite-element functions, i.e., B-splines  in the zThe first derivative of the B-spline of order z, and The derivative of B-splines of order κ is a linear combination of B-splines of order Throughout this paper, we work in atomic units, where energy is in units of Ry, and distance is in units of Bohr. The Hamiltonian of the system in the ultrasoft pseudopotential approach  is givenA is the surface area of the sample. The overlap matrix elements between two planar basis functions are given by the following:Here, R denotes a bulk lattice vector, and r. For charge-neutral systems, there is a counter long-range term in The local pseudopotential of the crystal is given by the following:For fitting empirical pseudopotentials of bulk materials, one adjusts the Fourier transform of the potential of ulations . To undeulations ,41,42. Worted in . The DFTorted in  were cheorted in , and theorted in  and paraorted in . The fitThe second term of Equation (14) denotes the difference Note that the chosen form of The best-fit parameters for short-range correction functions defined above are listed in the first row of Combining all above, the total local potential is given by the following:For convenience, z-axis used to define the B-spline basis. To check if the real space form of the local pseudopotential It is seen that the result obtained by SEP matches the corresponding DFT results very well. In z-dependence of the bond-charge contribution. Here, z-axis at To determine this contribution, we fit the difference of the local potential obtained by DFT and by SEP, i.e., The net local potential of graphene, The best-fit parameters The semi-empirical pseudopotential contains both local and non-local terms. The non-local pseudopotential contains angular momentum and energy-dependent terms . Incorpol (USPP) . The fitFor the second 2P orbital K;BiHere, This expression is identical to (39) except that the energy parameters put data ,16 to caz-axis. By adopting the B-spine basis along the z-axis and taking symmetric and antisymmetric combinations of these basis functions, we can decouple the eigenstates of the Hamiltonian within the symmetric and antisymmetric basis sets for any wave vector in the 2D plane. This significantly improves the speed of computation for the band structures. We found that using a direct solver for diagonalization becomes even faster than the iterative solver based on the conjugate-gradient (CG) approach [The formulas derived above can be extended to other two-dimensional materials beyond graphene, such as transition-metal dichalcogenides. Due to the inversion symmetry in graphene, all matrix elements become real. Furthermore, there is a mirror symmetry for the approach  for thisThe all-electron (AE) Bloch states of graphene are written as follows:equation  reads asWe apply the current SEP to calculate the band structure of graphene. The real-space structure of graphene can be described by a 2D unit cell with primitive lattice vectors z-axis) separately, the symmetry characteristics of the bands can be easily distinguished. Here, the even (odd) parity states are presented in green (red) color. It is noted that the red curves (with odd parity) are related to the In As shown in We consider a graphene nanoribbon with armchair edges with a width of ene. See b. Then, The Bloch states of the AGNRs superlattice can be written as linear combinations of basis functions that are products of 2D plane waves (labeled by wave vectors duced in ). For wiructures . If the Thus, we can write the Hamiltonian of the AGNR as y-axis. Thus, we can define symmetrized basis states with respect to the x-mirror as follows: In addition to the z-mirror symmetry, the AGNR also has x-mirror symmetry for any wave vector, i.e., The overlap matrix is given by the same expression above, with s-like) states with even and odd parity, respectively, under the x-mirror operation. Eigenstates of Here, we divide the basis set into four different subsets according to different symmetry types labeled by {The graphene bulk basis adopted above can describe the band folding due to the quantum confinement effect in the nanoribbon well, but it requires a large number of basis states to fully capture the effect of localized edge states. The AGNRs band structures obtained by solving Equation (43) are shown in We also performed DFT calculations of the same AGNR within the basis constructed by 2D plane waves multiplied by B-spline functions of z, as described in . The edgWe found that, as shown in The SEP band structures of the AGNR with the same relaxed atomic positions as determined by DFT but with the pseudopotential (PP) given by Equation (29) are shown in y-axis. As shown in To investigate the effect of local potential induced by the edge creation, we took the difference between the DFT (red curve) and SEP results (green curve) in z-dependence of the bond-charge contribution near the edges. We approximate the net three-dimensional local potential, including the bond-charge redistribution near the edges by a separable form:Finally, we add the edge-induced correction in the local pseudopotential, Here, After adding the correction term Many experimental studies on graphene and AGNR-related devices have been reported in the last decade ,59,60,61According to simple models that impose rigid boundary conditions on the edges of AGNRs, the band gap becomes zero when  integer ,62. Our mensions . The banculation  and alsoculation . Howeverculation . Since oculation , which pculation ,55,56,57culation . z-axis, our calculated band energies are absolute values with respect to the vacuum level. Therefore, it is meaningful to make such a comparison. For the case of 15-AGNR, the band gap obtained by the current SEPM is 0.49 eV, which is ~0.5 eV lower than the dI/dV measurements of 1.03 eV [For the case of 9-AGNR, the band gap obtained by the current SEPM is 0.68 eV, which is 0.7 eV lower than the 9-AGNR band gap measured by dI/dV measurements (~1.4 eV)  due to t 1.03 eV . For the 1.03 eV . Therefo results , which c results , in ordez-axis mirror), our SEP method can nearly reproduce all salient features of the DFT results with good accuracy. The time needed to compute the whole band structure associated with We developed a semi-empirical pseudopotential (SEP) method that is easy to implement and capable of obtaining accurate band structures for graphene and armchair-edged graphene nanoribbons. For the The SEP method with the same edge-induced correction potential given in Equation (51) is also applicable for AGNRs of sizes different from the example used here since the dimer formation on AGNR edges should not be significantly affected by the width of the interior region. Thus, the current model is suitable for modeling any size of AGNR  see b as a coThe close interplay between theoretical and experimental studies fosters a deeper understanding of AGNRs. Moreover, experimental data provide feedback to refine and improve theoretical methods. The collaboration between theorists and experimentalists allows for the identification of new phenomena and the validation of theoretical models. Together, theoretical and experimental studies offer a comprehensive perspective on AGNRs’ properties and pave the way for potential applications in nanoelectronics and beyond.