Reticular chemistry of covalent organic frameworks (COFs) deals with the linking of discrete organic molecular building units into extended structures adopting various topologies by strong covalent bonds. The past decade has witnessed a rapid development of COF chemistry in terms of both structural diversity and applications. From the structural perspective, irrespective of our subject of concern with regard to COFs, it is inevitable to take into account the structural aspects of COFs in all dimensions from 1D ribbons to 3D frameworks, for which understanding the concepts of reticular chemistry, based mainly on ‘reticular design’, will seemingly lead to unlimited ways of exploring the exquisiteness of this advanced class of porous, extended, and crystalline materials. A comprehensive discussion and understanding of reticular design, therefore, is of paramount importance so that everyone willing to research on COFs can interpret well and chemically correlate the geometrical structures of this subset of reticular materials and their practical applications. This article lies at the heart of using the conceptual basis of reticular chemistry for designing, modeling, and determination of novel infinite and crystalline structures. Especially, the structure determinations are described by means of chronological advances of discoveries and development of COFs whereby their crystal structures are elucidated by modeling through the topological approach, 3D electron diffraction, single-crystal X-ray diffraction, and powder X-ray diffraction techniques. This article describes the conceptual basis of rational design in COF chemistry and comprehensively discusses the crystal structure determination of COFs using the topological approach, X-ray diffraction, and 3D electron diffraction. Being extended frameworks linked by strong covalent bonds, COFs are expected to be more stable than their MOF counterparts whose structures are based on metal–oxide links de links . Such st2–4 ‘reticular design’ has been an oft-discussed topic and it inevitably turns out to be a unique concept for designing and engineering COF structures. Particularly, this concept includes rational design of new structures, novel topologies, isoreticular expansion, and post-synthetic modification (PSM).7 These aspects are crucial for diversifying the structure library of COFs and further relatively impacting on the chemistry and applications of COFs. In other words, the rich chemistry of COFs relies much on the understanding of reticular design which in turns leads to the best correlation between the crystal structures of COFs and their performances in practical applications to ‘benefit’ the world—the final destination of chemists. Therefore, it is so important that we comprehensively discuss the concept of reticular design on the conceptual basis of reticular chemistry in practice so that (emerging) scholars can capture the big picture of using this idea for designing structures of reticular materials.Due to the exponential growth of reticular chemistry, especially in COFs over the past decade,Concerning the interplay between COF structures and their chemistry and applications, it is imperative to summarize the conceptual basis and practical guidance of applying reticular chemistry in designing reticular structures and crystallography in COFs. Particularly, this article aims to (1) generally summarize COF chemistry and its advancements, (2) comprehensively discuss the conceptual basis of reticular chemistry for the rational design of new reticular materials, mainly focusing on COFs but which can also be applied to other crystalline materials, and (3) tutorially describe the process and methods of solving the crystal structures of COFs using a variety of techniques. The last objective is largely based on using the topological approach in reticular chemistry to model structures and employing X-ray diffraction  and electron diffraction (ED) techniques to determine COF structures.This article will educate (emerging) scholars on three main lessons: the chemistry of COFs, fundamentals of rational design based on reticular chemistry, and structure determinations from the basics of modeling to advanced techniques.2.9 The first porous organic compound reported was Dianin's compound in 1914. This compound intermolecularly formed hydrogen bonds, thus affording empty space for the chemistry of host–guest interaction.10 The Dianin compound was called an “organic zeolitic sorbent”. The hydrogen bonds, however, limit 3D structures, weaken the architectural robustness of compounds, and hinder applications related to sorption, separation, and catalysis due to the fragile linkages and backbones.11 To circumvent this problem, the fragile hydrogen bonds need to be replaced by strong covalent or coordinative bonds which help rigidly extend the structural frameworks that adopt appealing topological aspects—these cannot be achieved in such materials based on weak bonds.Inorganic porous materials, zeolites, discovered in the eighteenth century, have been largely used as commercial catalysts and adsorbents.3O3 six-membered ring) and boronic-ester-based (BO2C2 five-membered ring) COFs, termed COF-1 and COF-5,12 respectively. It is worth noting that COF-1 and COF-5 are the first two exemplars whose structures were reticulated from discrete molecules into covalently extended 2D frameworks, adopting permanent porosity and controllable pore sizes. This pioneering work has inspired other studies for developing porous and crystalline COFs with multiple linkages, diverse topologies, and functionallities.At this juncture, Yaghi and co-workers inventively developed highly crystalline boroxine- . Unlike other amorphous materials , COFs crystallize from various organic SBUs by co-condensation, self-condensation, or ring-closing reaction and most importantly, COF structures can be determined by X-ray diffraction (XRD), thus allowing the structural optimization at the molecular level.14 The crystallinity of COFs relies much on the dynamically reversible bonds being capable of self-correcting the errors that occur during synthetic processes which can be varied and controlled. Especially, COFs with high crystallinity have minimal defects making them attractive in many studies ranging from atomic to macroscopic level-based devices. This feature, the well-defined structure and high crystallinity, distinguishes COFs from amorphous polymers in many applications related to the foundational understanding of molecular interaction, structure tailoring, PSM, and synergic effects.15In reticular chemistry, porosity, along with the density of active sites, is a critical factor dictating applications in gas storage, separation, catalytic transformation, and many more. The porosity of COFs is attributed to the cages/pores, formed by reticulating organic SBUs into extended structures; COFs exhibit permanent porosity ranging from hundreds to thousands m12 boronic ester,12 imine,16 borosilicate,17 spiroborate,18 triazine,19 azine,20 imide,21 squaraine,22 hydrazone,23 urea,24 and olefin25) and irreversible  links. Additionally, linkages formed by nucleophilic aromatic substitution (SNAr), by virtue of the dynamic and self-correcting nature, generate extended structures with large surface area and high chemical stability.32 Exploring COFs made up of such stable linkages is essential for practical applications.30,31In terms of structural constituents, COF structures are based on linkages inherited from organic chemistry including reversible  replacing the reversible linkages with irreversible ones33 , and/or (3) postsynthetically modifying linkages (linkage conversion).34As mentioned above, the reversible-link chemistry permits self-correction during the synthetic process, hence, enhancing the crystallinity which is an important factor determining the optimized porosity and minimizing defects. Such COFs based on reversible links, however, suffer from hydrophilic reversibility which makes them unstable under harsh conditions  and limits their practical applications. This issue can be circumvented by (1) engineering the internal structure of COFs,35The stability of COFs is determined by how long the frameworks can exist under the tested conditions which depends mainly on the strength of linkages creating the MOF structures. Owing to the covalent bond nature, the COF stability is expected to exceed that of the MOF counterparts. Particularly, COFs based on robust covalent bonds such as β-ketoenamine, amide, and benzoxazole are strongly water-stable as well as acid/base resistant. It is worth noting that the improvement of chemical stability in COF chemistry has sparked the most attention in which COFs with new bond-formation have been pursued recently. Apart from the strength of linkages, other factors including the void space of the structure, hydrophobic functionalities, intramolecular conjugation, and/or structural accessibility might contribute to the structural rigidity and stability of COFs.3.36 since the use of SXRD for the structural determination and visualization of crystalline materials. This definition of topology or structure type uses the concepts of vertices and edges where the atoms, considered as vertices, are linked together by chemical bonds (edges) to generate periodic and infinitive graphs. In other words, topology considers all symmetry operations under the graph theory . Chemists use topology as the specific fingerprint to (1) differentiate structures constructed from similar shapes of SBUs and (2) rationally design crystalline materials.37,38 Particularly, databases , ToposPro, or Systre)37,39 were developed to categorize the vast number of networks in chemistry. In particular, Yaghi and co-workers developed the use of topological symbols consisting of three-letter symbols, lowercase and bold, in the early 2000s, which are widely used in the reticular chemistry community.39Topologies or nets were first described by Wellse.g., natural tiling, dual, face) can be found in detail in RCSR, is targeted. Second, based on the detailed information of the topological structure from RCSR, the kinds of vertices and edges are identified. As a result, the geometrical shape of building units akin to the chemical building blocks used for constructing COFs will be realized and appropriately selected. Finally, such chemical equivalents are chemically reticulated into the extended COF structures. This conceptual basis works well with an array of highly symmetric topologies and dictates the formation of targeted structures, allowing structural design in a rational manner.The rational design of COF structures in light of the basic concept of reticular chemistry is described as follows. First, a specific topology, whose connectivity of vertices and edges and topological information (hcb) topology12 and the second one is COF-102 and COF-108,40 the first reported 3D COFs with ctn and bor topology, respectively. Indeed, the hcb network consists of one kind of vertex which are triangles tethered by linear building units.In order to exemplify this basic concept of reticular design, we discuss two examples: the first example is COF-5 with a honeycomb  and tetra(4-hydroxyborylphenyl)methane  into [(HHTP)4(TBPM)3]boronic ester (COF-108) through a co-condensation reaction that formed boronic ester linkages, similar to COF-5. In another reaction, the self-condensation of TBPM units led to the formation of COF-102 adopting the ctn topology with boroxine linkages.Deconstructing the topology  leads totopology . Particuetc. into extended frameworks?” The answer is: there are many ways. Nevertheless, there are some topologies that can mostly be targeted. Such topologies fall under the umbrella of ‘reticular synthesis’. To this end, one kind of link  must be used. Interestingly, this leads to the next question which is “how many such topologies?” The answer is “there are not many possibilities and they are the main targets that reticular chemistry is dealing with using reticular design”.One may ask “how can we know the exact topology formed when combining two SBUs?” Indeed, we were asked this question by our colleagues and students; we also believe that this question will be frequently asked by emerging scholars working on reticular chemistry. In order to comprehensively discuss this question, it is worth paraphrasing it from the original form to “what are the ways of reticulating organic SBUs based on triangles, squares, tetrahedra, triangular prisms, 41 For example, the chemistry of imine-linked COFs was pervasive and drastically explored since the first report of COF-300 (ref. dia) topology whereby the amine-functionalized tetrahedral units, tetra(p-aminophenyl)methane (TAPM), connect together through linear benzene-1,4-dialdehyde (BDA) linkers (dia-c5). It is accepted that the interpenetration maximizes the stability of the resultant material and its crystallinity.The basic concept of reticular chemistry has been largely employed and COF chemists indeed have reported notable achievements.300 ref.  with a d linkers . Multipldia network.42 Triangular linkers link the tetrahedral SBUs to form ctn or bor40,43 where the formation of ctn or bor depends mainly on the geometrical hindrance of the triangles.From the topological perspective, if we start using the specific linker based on the tetrahedral geometry, there are several ways to reticulate them into 3D frameworks using 2-, 3-, 4-, to 6-, or even 8-coordinate SBUs . Particularly, linear linkers connect the tetrahedral building units to generate a dia or lon44 will be generated; if 4-c + 4-c is the tetrahedral SBU + square SBU, pts45 or pth will be formed. Indeed, an extended 2-fold interpenetrated structure of 3D-Py-COF adopting the pts network was first reported by Wang and co-workers using the combination of the tetrahedral building unit of tetra(p-aminophenyl)methane (TAPM) and square-planar unit of 1,3,6,8-tetrakis(4-formylphenyl)pyrene (TFPPy).45 Unfortunately, neither COFs based on pth nor other novel topologies that are reticulated from 4-c  and 6-c  or 4-c and 8-c (cube) have been reported. Very recently, the approach of using 6-c SBUs for novel 3D COF synthesis has been achieved to some extent. Particularly, Cooper and coworkers reported the synthesis of the acs topology COF based on triangle prism (6-c) and linear (2-c) building units.46 Later, this 6-c SBU was linked by 3-c and 4-c to form ceq47 and stp48 topologies, respectively.Increasing points of extension of SBUs to 4 (4-c + 4-c) leads to two topological possibilities to obtain different kinds of structures. If 4-c + 4-c is tetrahedral SBU + another tetrahedral SBU, 49 of organic SBUs mostly requires tedious synthetic procedures.The chemistry of 3D COFs still provides many opportunities to those who are willing to take challenges because increasing the valencydia, lon) whose structures were built with one kind of vertex and binodal  where the structures were composed of two kinds of vertices. To increase the complexity of 3D COF chemistry, Feng and co-workers reported a 3D anionic cyclodextrin-based COF (CD-COF) with a trinodal network of rra.50 Particularly, a six-membered ring of γ-CD simplified by -c and trimethyl borate (B(OMe)3) were co-condensed to generate the trinodal -c rra network. This strategy showcased the fact that increasing the complexity in COFs opens a new pathway for overcoming the challenges of 3D COF synthesis. To this end and to apply suitable methods for directing the connectivity in combining triangles and squares to create COFs with 3D topologies, we have recently reported the conformational design that relies on modifying the dihedral angles,51 between 74 and 90°, by introducing methyl groups to the central phenyl ring of the triangular SBU which thereby selectively generate the 3D COFs based on the fjh topology. Interestingly, the linker lacking conformational design only reacts with square-planar SBUs to form amorphous products. This work relying on the predesigned SBUs paves the way for the designed synthesis of novel 3D COFs by modifying the geometrical structures of starting materials. Very recently, by using a similar strategy, Sun and Wang et al. reported topology control in 3D COFs.52 In particular, by tuning the geometry of building units using steric hindrance, 3D COFs including 5-fold interpenetrated pts (methoxy was introduced on the square unit) and 2-fold interpenetrated ljh (phenyl was substituted on the square unit) were obtained.All the aforementioned 3D networks of COFs are uninodal . Regarding the selective crystallization of specific topologies, geometrical conformation of SBUs is the most effective method to rely on, as recently proven by a few examples (fjh and ljh). Last but not least, frustrated chemistry provides a powerful strategy to achieve cutting-edge designs for synthesizing COFs bearing unique structural topologies (ribbon-like net and defective tth53). It is beyond doubt that comprehensive understanding of topology is imperative for the designed synthesis of novel COFs with a variety of structure types and is a key factor for the success of COF chemistry. The structural designs and discoveries of COFs having diverse topologies are based on three main concepts: geometry of linking units, geometrical constraints, and frustrated chemistry. In terms of targeted nets constructed through the conceptual basis of reticular chemistry, building-unit geometry plays an essential role, as presented early in this section  which hinders the elucidation of their crystal structures by both ED and XRD techniques.44 To date, solving the crystal structures of COFs is one of the major challenges faced by scientists working on reticular chemistry. This section, therefore, aims to (1) overview fundamentals of the structural elucidation in COFs, (2) highlight the recent achievements on this topic, and (3) educate (emerging) scholars on how to determine the crystal structures of COFs.Determining the single-crystal structures of crystalline compounds elucidates the interplay between the chemical structures and their physicochemical properties, and therefore their applicability. Especially, in the reticular chemistry of COFs, structural determination is the most important and key factor to explain and further cast light on COFs' outstanding behaviors in various applications .4.1.12,40 Indeed, the modeling of COFs lies in the conceptual basis of reticular chemistry whereby the reticulation of various SBUs into extended structures is predictable. The structural modeling proceeds through a heuristic approach including searching for possibilities, eliminating results, and matching possible models. At the end, the possible model structures are refined using the Pawley or Le Bail method. It is worth noting that this modeling process acting as a standard for reporting COF structures was put forth over a decade ago and is still applicable to many cases in which the crystallinity of COFs cannot be improved due to the crystallization challenge.It is worth clarifying that the COF crystallography has been relying on the structural modeling for a long time starting from the discovery of 2D and 3D COFs by Yaghi and colleagues.40 is described using the following steps (bor (boracite), ctn (cubic-C3N4), mhq-z, pto (Pt3O4), and tbo (twisted boracite). The suitable topologies are bor for COF-102, COF-103, and COF-105 and ctn for COF-108 whose structures comprise tetrahedra and triangles while the latter three structure types  are constructed from squares and triangles. The last step is the structural modeling and the PXRD refinement of the structural models against the experimental PXRD patterns. As mentioned above, Pawley and Le Bail fittings are often used. This heuristic process will be able to accurately predict the most preferred structures formed by various kinds of SBUs without considering linkages or structural features including pore size, empty space, density, and surface area. Additionally, this top-down approach plays an essential role in discovering new COF structures. Especially, this works well with the targets of reticular chemistry—structures resulting from linking one kind of vertex and one kind of edge.46To comprehend the detailed process of the heuristic approach using reticular design, the structural modeling of the first 3D COFs ng steps . The TBP56 but not the others (Pawley or Le Bail). Many scholars misuse, even misunderstand, these terminologies. Pawley and Le Bail refinements do not provide the structural coordination information except for the convergence of the unit cell parameters. Therefore, it is mandatory to corroborate the models by additional characterizations that show the stoichiometric ratio of linkers, linkage formation, pore size distribution, theory of surface area (if applicable), elemental compositions and ratios, and as many as possible from this list. In this context, we would like to direct the readers to the critical review of standard practices in reticular chemistry reported by Yaghi and colleagues.2Albeit powerful and irreplaceable, the heuristic method remains challenging and has limitations: it is most applicable to high symmetric SBUs and the results suggest only reported topologies. This means scientists will have to play around with the modeling with enormous efforts to simulate the structures and go through the trial and error process. Moreover, this method falls short of predicting the novel topologies of COF structures which must be first determined by the XRD or ED technique. The final drawback of the heuristic approach is structural refinement. Let us be clear at this point: a model structure can only be validated by Rietveld refinement4.2.57 Unlike X-rays or neutrons used in diffraction to study structures of materials, electron diffraction is based on charged particles that interact with crystalline materials through Coulomb forces.58 That is the reason why both positively charged atomic nucleus and negatively charged electrons are influenced by the incident electron beam, thereby resulting in strong scattering of electrons which was not considered for the application of structural determination of crystalline materials until 2007 when semi-automated techniques for ED-data collection were apparently developed.59Electron diffraction was first reported in 1927 by Thomson and Reid.60The advances of ED lie at the heart of two main factors: first, the possibility to collect electron diffraction data of samples that crystallize in the size of nanometers, an order of magnitude smaller than crystals that are used for single-crystal analysis using either a laboratory diffractometer or synchrotron irradiation; second, diffraction and imaging data can be combined in ED measurements which permit the correlation between 3D reciprocal space and direct method for phase identification and structural solution similar to that of SXRD analysis.60,61 To date, ED techniques applied for COF structure determinations include two common methods for collecting data: rotation electron diffraction (RED) and continuous rotation electron diffraction (cRED). Zhou and Huang at Stockholm University and Terasaki and Ma at ShanghaiTech University are widely known for their expertise in solving crystal structures of reticular materials using the ED techniques.ED measurements require expertise in handling the sample, setting up experiments, and data acquisition. The past decade has witnessed the rapid development of programs for reconstruction and virtualization of reflections collected by ED into a 3D reciprocal space. Details of the historical development of ED have been recently discussed in the literature.62 composed of tetra(4-anilyl)methane (TAM) and 4,4′-biphenyldialdehyde (BPDA). The combination of these units, based on reticular chemistry, would generate a structure with the diamond (dia) topology. COF-320 was measured using RED at both 298 and 89 K, wherein the latter temperature reduced the structural damage by the electron beam. Data collection for COF-320 was carried out best at 89 K using the following procedure: the COF was tilted in the range of −34.19–38.33° with a step width of 0.20°. The total measured time was 21 m; 396 ED frames were obtained which corresponded to 570 unique reflections after the reciprocal reconstruction. COF-320 can be measured with a resolution of up to 1.5 Å. Simulated annealing was applied to locate the positions of TAM and BPDA building units. Subsequently, the crystal structure of COF-320 was refined against the RED data to reveal a 9-fold interpenetration of the dia-based framework. At 298 K, only central C atoms of TAM building blocks were located. Therefore, modeling was built and then refined against the PXRD pattern to finally lead to a similar structure to COF-320 solved at 89 K, except for disordered N atoms.The first achievement in solving the single-crystal structure of COFs was COF-320 62 compos63 whose structure consists of woven building units (copper(i)-bisphenanthroline tetrafluoroborate, Cu(PDB)2(BF4)) linked by linear amino-functionalized linkers (benzidine (BZ)) (i) atoms was located by Fourier analysis of HRTEM images, thus allowing the structure of COF-505-Cu to be modeled. The Pawley method was used again to refine the unit cell parameters of COF-505-Cu.It is apparent that nanometer-sized crystals (a few hundreds) are possibly suitable for ED measurements with a short collection time. The resolution of ED measurements, however, is still low and it is not efficient to fully solve the crystal structures of COFs without other aided methods such as high-resolution transmission electron microscopy (HRTEM), modeling, and Rietveld refinement (the latter two methods will be discussed in Section 4.4). This is proven in the case of COF-505-Cune (BZ)) . Particuca. 1 μm) and diffracted at much higher resolution (0.9–1.0 Å).64 In this work, for the first time, the crystal structures of three isoreticular COFs, based on the combination of TPB-functionalized aldehyde (square unit) and TAPM , could be fully resolved by cRED. The high-resolution of these 3D pts COFs was probably attributed to the high level of interpenetration (5-fold). At the same time, Zhang and Ma et al. published a study using the cryo-EDT technique to solve the crystal structure of COF-300 crystallizing with submicrometer sizes.65 More importantly, the structural dynamics observed when molecular guests ) are incorporated in the pores of COF-300 could be fully determined and revealed at the atomic level with a resolution of 1.1 Å.Unlike COF-505-Cu, a series of 3D-TPB-COF-X  could be synthesized with a larger crystal size . Secondly, the resolution of ED in such measurements is still quite low. Therefore, it is mandatory to combine ED with other supporting characterizations69  to determine COF structures. At this point, combining the aforementioned methods and structural solution by PXRD (see Section 4.4) is worth pursuing. To this end, the COF must be crystallized with a crystallinity as high as possible so that the overlapping problem of the PXRD pattern can be minimized.Although the ED technique has been rapidly developed over the past decade and contributes to solving many crystal structures of nanometer-sized crystals including MOFs and COFs,4.3.44 Particularly, single crystals of COF-300, a hydrated form of COF-300, COF-303, LZU-79, and LZU-111 can be grown as large as 10–100 μm, ideally suited for SXRD measurements using a laboratory diffractometer. The idea of this work lies in the use of nucleophilic aniline as a modulator to first react with the aldehyde starting material to form the model compound which will then be substituted by the ditopic amino-functionalized linker through linker exchange to finally generate the extended framework . At this point, it should be noted that COF chemists are still facing a great challenge with the limitation of COF crystallization, and new chemistry with impactful solutions is highly needed to open the avenue for diversifying COF chemistry.These studies, however, draw our attention to another issue which is the generalizability—the modulator approach up to this point works well only for 3D imine-linked COFs.4.4.ab initio structure solution.69Due to the thermodynamics of organic reactions forming COFs whereby the covalent bonds are stronger than the metal–oxide bonds in MOFs, the bonding association and dissociation in COFs are more unfavorable than in the MOF counterparts, and therefore suffer from kinetic hindrance. As a consequence, COFs usually crystallize in the form of micro-crystalline products, instead of single crystals, and hence are not applicable to the SXRD analysis. The ED analysis has been proven to be useful for determining COF structures when COFs crystallize in micron particle size; this technique, however, suffers from a limitation which is low resolution thereby leading to the failure of the The tendency to obtain microcrystalline COFs along with the low resolution of ED data makes the structural elucidation tedious and laborious, or even impossible in many cases.i.e., the simulated PXRD patterns are different from the experimental one). That also means how we solve a new COF structure using PXRD data. This section seeks to provide guidance on how we elucidate a new COF structure by its PXRD pattern—this useful but sophisticated technique can also be applied to other crystalline materials.The question is what should we do if the structural models following Section 4.1 do not match with the experimental results 79 containing a large number of nonhydrogen atoms (69 atoms in the asymmetric unit); the method relies on using a textured sample and extraction of high intensity of XRD data from synchrotron radiation.Solving the crystal structures using PXRD data dates historically back to the early 1990s.Fhkl| structure modulus corresponding to the structural phases . This is a key factor that determines the success in powder solution by the direct method in step (3) (ab initio solution). The higher the crystallinity, the greater the opportunity in structure determinations.L: Lorentz factor, ρ: polarization factor, K: a constant for a given crystal in an experiment.In principle, the structure determination by PXRD goes through three steps: (1) indexing of the PXRD pattern, (2) integration of intensity, (3) structure solution, and (4) refining the structure by Rietveld refinement and only by this refinement. Particularly, powder-pattern indexing executed through standalone programs suggests the possible unit cell and lattice parameters. In the second step, calculation of integrated intensities of diffraction peaks of the powder pattern provides the experimental |l phases . The elel phases . In the ab initio method for determining structures of reticular materials was successfully accomplished for a family of Zr-based MOFs  in 2008.80 Indeed, UiO-66  with high crystallinity showed diffraction peaks up to 100° 2θ (CuKα) corresponding to a resolution of ca. 1 Å. The crystal structure of UiO-66 was solved by the direct method implemented in the EXPO program; the steps of indexing, intensity extraction, and Rietveld refinement were carried out using the TOPAS program from Bruker. Especially, the Rietveld refinement factors including Rp and Rwp converge at very low values (0.016 for Rp and 0.022 for Rwp) demonstrating the high agreement between the structural model and the experimental one. A similar method was used for elucidating the crystal structure of an exemplified Ti-based MOF, MIL-125.81It is worth discussing the achievements of structure determinations by PXRD in MOFs—the foundational background for early accomplishments in solving the crystal structure of COFs using PXRD. Particularly, the 82 The authors were able to synthesize scalable COF-300 with high crystallinity. Interestingly, COF-300 exhibited structural dynamics which contracted upon taking up water molecules (6% reduction of unit cell volume). Additionally, upon inclusion of tetrahydrofuran (THF), the cell volume of COF-300 increased by 50%. The contraction and expansion were observed along with the changes of PXRD patterns and solved by Rietveld refinement with a very low reliability factor. This dynamic behavior of COF-300 was corroborated by water and THF uptake measurements, showing different steps in the adsorption isotherms.82 This work underlines the fundamental understanding of crystal structures of dynamic COFs which can be used for many applications relying on the flexible frameworks.Rietveld refinement using high-resolution synchrotron PXRD patterns will effectively be applied to determine the crystal structures of crystalline materials. This technique allows us to refine the crystal structure at the atomic level even revealing the structural dynamics and host–guest interaction. Particularly, Zhang and co-workers reported the guest-dependent dynamics in COF-300 variants whose crystal structures were determined by synchrotron PXRD patterns.83 which is applied to solve MOF structures reported by Yaghi and co-workers in 2012 .Another method for structure determinations by PXRD is the charge-flipping method in 2012 .84 This 49 However, as specified in Section 3 and well observed in MOF chemistry, novel topologies can be formed even when ‘usual’ geometrical structures of SBUs were employed . And if this is the case, without high crystallinity, it is likely impossible to solve the crystal structures. Especially, we were able to apply the charge-flipping method to solve the crystal structures of COF-432 .432 ref.  and COF-432 ref.  whose st70In the case of COF-432, the powder-pattern indexing resulted in unit cell parameters identical to the results from the ED data. In fact, the ED did not provide much information for COF-432 due to the low-resolution data. The electron density map (EDM) of COF-432, however, showed the fragments of 1,1,2,2-tetrakis(4-aminophenyl)ethene (ETTA) but not 1,3,5-triformylbenzene (TFB) building units. Such an EDM analysis suggested the locations of ETTA entities, thus reasonably allowing structure modeling of the material. It should be mentioned that we, unfortunately, could not perform the Rietveld refinement for COF-432 due to the fact that COF-432 may contain mobile molecular guests and defects which result in the deviation between the simulated PXRD pattern and the experimental one in terms of the relative intensity, as observed in the first few peaks.p-formylphenyl)pyrene  and tris(4-aminophenyl)amine  thus generating a frustrated backbone. The EDM of COF-76 clearly indicates the high conjugation systems of square units (TFPPy) locating in parallel ribbons; the TFPPy entities between two ribbons in one layer are arranged in a zigzag manner , the COF-76 structure was refined with the Rietveld method leading to reasonable residual values of reliability profile factors   . These ti.e., low electron density). At this juncture, it is imperative to first obtain COFs with the highest crystallinity, and second to combine the structure determinations by PXRD with additional characterizations to validate the models, as presented comprehensively in the COF-432 case study. Nevertheless, it does not rule out the fact that the charge-flipping method, along with ED analysis, will be a powerful technique to aid the structure solution of COFs.It should be noted that using PXRD to solve the crystal structures of crystalline materials in general and COFs in particular is facing great challenges because of the (1) low crystallinity of COFs, (2) peak overlapping issues, and (3) absence of heavy atoms  can be effectively used to elucidate COFs' crystal structures, which will be invaluable to study further applications of COFs. It should be noted that although the COF community has achieved some important results , COF chemistry needs an impactful revolution for crystallinity enhancement. Future research in COF chemistry—a young research field—may focus on enhancing crystal sizes, crystallinity, and discovering more novel topologies, which should be developed in parallel with the practical applications.This article aims to provide as much knowledge of reticular design and crystallography in COF chemistry as possible and therefore it undoubtedly casts light on further understanding of the principle design, synthesis, and applications of COFs. We have deeply tapped into the reticular design of COFs to comprehensively overview the concept of reticular chemistry. Particularly, we have discussed (1) the design of COFs in rational ways that focus largely on the topological deconstruction, and (2) the method of modeling possible structures of targeted COFs, and highlighted the achievements of using this method to create novel topologies in 3D COFs. In order to educate (emerging) scholars on how the structures of COFs can be determined, we have finally presented the fundamentals and applications of 3D ED, SXRD, and PXRD techniques in solving the COF crystal structures. Particularly, the crystal structure determination of COFs starts with structural models which can be simply obtained by simulation using the foundational understanding of reticular chemistry. The simulation of COF structures works well with simple building units and those COF systems based on high symmetry. The models are subsequently corroborated and validated by further characterizations including Fourier-transform infrared spectroscopy, nuclear magnetic resonance spectroscopy, elemental analysis, thermogravimetric analysis, NFrom the structural perspective, COFs with new topologies in many cases are formed serendipitously and do not follow the conceptual basis of reticular chemistry. This means ones who are willing to take risk and are curious about the novel chemistry of COFs will be looking forward more to such nature-reveals-itself products. Therefore, overcoming the crystallization limitation and comprehending structural determinations in COFs must be considered so that the chemistry of COFs would be diversified similar to their MOF counterparts.H. L. N. designed and directed the project and wrote the manuscript.There are no conflicts to declare.


Herein, an exact and efficient analytic solution for an unperturbed satellite relative motion was developed using a direct geometrical approach. The derivation of the relative motion geometrically interpreted the projected Keplerian orbits of the satellites on a sphere  using the solutions of full-sky spherical triangles. The results were basic and computationally faster than the vector and plane geometry solutions owing to the advantages of the full-sky spherical geometry. Accordingly, the validity of the proposed solution was evaluated by comparing it with other analytic relative motion theories in terms of modeling accuracy and efficiency. The modeling accuracy showed an equivalent performance with Vadali’s nonlinear unit sphere approach, which is essentially equal to the Yan–Alfriend nonlinear theory. Moreover, the efficiency was demonstrated by the lowest computational cost compared with other models. In conclusion, the proposed modeling approach illustrates a compact and efficient closed-form solution for satellite relative motion dynamics. The reference satellite orbit was assumed to be circular, and the relative orbit coordinates were small compared with the reference orbit radius; hence, the resulting equation of motion was linearized. Lawden2 found an improved form for the relative motion, including reference orbit eccentricity. Carter3 later extended Lawden’s solution. Subsequently, Kechichian4 developed the exact formulation for a general elliptic orbit to analyze the relative motion in the presence of J2 potential and atmospheric drag. However, the resulting equations were required to use numerical integration over time. Sedwick et al.6 applied the J2 potential forcing function to the right-hand side of Hill’s equations. Schweighart followed these equations and found analytic solutions. Melton7 later developed an approximate solution, thereby expanding the state transition matrix in powers of eccentricity with a time-explicit representation.The dynamic models of the satellite relative motion are diverse and the developed solutions have paid attention to the performance of the dynamic model, such as computational complexity, accuracy, types of perturbations, and model assumptions. The main focus of these dynamic models has been on the study of formation flying and rendezvous and docking maneuvers of satellites. For these applications, the satellite relative motion theories began with the equations of motion derived by Clohessy and Wiltshire8, who compared and evaluated various relative motion theories: Hill’s equations, the Gim–Alfriend state transition matrix9, the small-eccentricity state transition matrix8, the non-J2 state transition matrix8, the unit sphere approach (USA)10, and the Alfriend–Yan nonlinear method11. Their evaluation of the results showed that the USA and the Yan–Alfriend nonlinear method present the highest accuracy for all eccentricities and relative orbit sizes. The USA was proposed by Vadali, who achieved the exact analytic expression in terms of differential orbital elements for relative motion problems. Alfriend and Yan applied the geometrical method to the nonlinear relative motion. The method was employed in long-term prediction of mean orbital elements, including nonlinear J2 effects, and in transforming Hill’s frame. Most of the abovementioned relative motion theories have been developed using the formation flying concept for station keeping.Accordingly, numerous theories of satellite relative motion have been added to the literature in the last decades. A brief survey was published by Alfriend and Yan12. This comparative study provided an extensive overview of the currently available literature and assessed the newly developed relative motion solutions, adding to the comparisons of Alfriend and Yan: the curvilinear Hill–Clohessy–Wiltshire (HCW) model13, the quadratic Volterra model14, GAMSTM15, KGDSTM16, and the Biria–Russell Vinti method17. The goal of this paper is to study several key features of the dynamics models paying attention to dynamical state representations, model assumptions, types of perturbations, accuracy, and computational complexity. Finally, several meaningful comparative results are presented.Recently, a comprehensive survey and assessment of satellite relative motion dynamics models was conducted by Joshua Sullivan18.In previous works, the analyst was forced into analytic approaches using vector terms rather than spherical geometry because of the singularity problem. However, these problems have been eliminated by solutions of full-sky triangles and plugged into computer programming languages for many years. This study aims to develop a solution for relative motion dynamics by direct geometrical interpretation using the advantages of full-sky spherical geometry solutions. Spherical geometry now makes computer implementation quite simple, and this has been discussed in Ref.To derive the equations of motion, the approach geometrically interprets the projected base and the target satellite Keplerian orbits on a sphere  with the spherical trigonometry solutions. The resulting equations are expressed as azimuth and elevation angles with their derivatives representing the relative angular position and velocity of the target satellite with respect to the base satellite. Subsequently, the azimuth and elevation angles are then transformed into the associated rectangular coordinates for the relative position and velocity vectors in the base satellite centered frame. The proposed solution is validated by modeling accuracy and efficiency compared with those of the exact analytic dynamic models of the satellite relative motion theories.19. The six orbital element sets are as follows:We project a Keplerian orbit on a celestial sphere using spherical coordinates. The Keplerian orbit is commonly specified by the classical orbital elements for state representations in spacea, and the eccentricity, e, listed as the first two elements above describe the orbit size and shape, respectively, while Ω, i, and ω define the orbit plane orientation. The final classical orbital element is the true anomaly, ν, which determines the object’s current angular position relative to the perigee. Figure , i, ω, and ν, which are angle-related orbit elements that describe the Keplerian orbit from the center of the Earth.The semi-major axis, r, of the object determine the spherical coordinate system in space. The radial distance, r, is written as follows in terms of ν:A spherical coordinate system in space can be used to represent the Keplerian orbit projected on a sphere. In Fig. If we represent the position of the object in the rectangular coordinate system, the spherical coordinate system is transformed by the following relations:In this section, we geometrically derive the relative position and the velocity vectors of a target satellite relative to the base satellite. The subscript B denotes the base satellite while subscript T denotes the target satellite.The Keplerian orbits of the two satellites are projected on a sphere for geometrical interpretation, as seen in Fig. In spherical geometry, intersection points always exist between great circle arcs on the sphere if they do not have the same inclinations.T, with respect to the base satellite, B, is given by the azimuth angle, α, and the elevation angle, δ. Angle α is perpendicular to angle δ through point H.The relative position of the target satellite, We introduce the argument of latitudes for the transformation between the classical orbital elements and the angular positions on the sphere. The argument of latitudes, α and δ for the target satellite relative to the base satellite in terms of the angle-related orbit elements Ω, i, ω, and ν. The general solutions for spherical triangles are given in Ref.18. The spherical triangle We first derive Applying the law of cosines for angles to the spherical triangle Dividing Eqs.  by 9) a a9) and To compute Using the law of cosine for angles, we also obtainDividing Eqs.  by 12)  12) resuNow we consider the spherical triangles on the surface of the sphere with ∆Ω = 0. In this case, we construct a celestial sphere having the pole δ is derived from the spherical triangle The elevation angle δ is obtained byThus, angle α is found by applying the law of cosines for sides twice to the spherical triangle The azimuth angle andSubstituting rom Eqs.  into The relative velocity vector s of Eq. :26\documThe relative equations of motion [Eqs.  and 26)26)] are 10, which nonlinearly maps orbital elements to the relative position and velocity in the same manner as GROM. The two solutions consisted of trigonometric functions as orbital element terms. Table The resulting solutions, we collectively call herein as geometrical relative orbit modeling (GROM), are obtained by the direct geometrical method using full-sky spherical geometry. GROM has the following explicit advantages: first, the angular values 20, and the USA. The USA has been evaluated to have the lowest index in terms of accuracy of satellite relative motion equivalent to the Yan–Alfriend nonlinear method10.We first evaluate the modeling accuracy to determine the validity of the GROM solution. To evaluate the modeling accuracy, three relative motion theories are introduced: Hill’s equation8. In Eq.  running on an 8th Intel Core i5 8265U (3.4 GHz) with 8 GB memory. The CPU time comparison of each solution is clearly implementation-dependent on the researcher. To fairly evaluate the comparison of solutions, each solution was coded efficiently, and a simple least squares linear regression and method was applied for a more robust comparison. Generally, the relationship between iterations, 013b runnIteration and CPU time are evaluated by the following linear model:m value and the least squares method is used to calculate the slope of the best fit line. Table m∗, normalized with respect to the value of GROM. GROM is nearly 7% and 25% more efficient than USA and CTBP, respectively.The computational cost of each solution is compared by the slope ω, and mean anomaly, M. The time-explicit representations of the first-order 10:A numerical example was used to study the effect of the satellite relative motion under the influence of p = a(1 − e2), We use the following values in the time-explicit orbit elements: The numerical simulation coded to iterate the solutions at each time step runs over a period of 20 days using the orbit elements for the base satellite shown in Table .8729 km and 0.0041 km/s over 20 days, respectively. However, each of the analytic solution results in different CPU times; thus, the GROM solution is approximately Table Herein, we developed an analytic solution for the unperturbed satellite relative motion using a direct geometrical approach on a sphere. The derivation of this geometrical approach is straightforward, and the resulting solutions provide a complete analytic form for relative motion dynamics with the full-sky solutions covering the range of 0°–360°. The accuracy of the proposed GROM solution equals that of the exact relative motion theories of CTBP and USA. In particular, in terms of the modeling efficiency, GROM is approximately 7% and 25% more efficient than USA and CTBP, respectively. Consequently, using full-sky spherical geometry, the proposed GROM approach facilitates simpler equations of motion and higher computational speed compared with the other methods.Supplementary Information.


Vertebrate kidneys contribute to homeostasis by regulating electrolyte, acid-base balance, removing toxic metabolites from blood, and preventing protein loss into the urine. Glomerular podocytes constitute the blood-urine barrier, and podocyte slit-diaphragm (SD), a modified tight junction, contributes to the glomerular permselectivity. Nephrin, KIRREL1, podocin, CD2AP, and TRPC6 are crucial members of the SD that interact with each other and contribute to the SD’s structural and functional integrity. This study analyzed the distribution of these five essential SD proteins across the organisms for which the genome sequence is available. We found a diverse distribution of nephrin and KIRREL1 ranging from nematodes to higher vertebrates, whereas podocin, CD2AP, and TRPC6 are restricted to the vertebrates. Among invertebrates, nephrin and its orthologs consist of more immunoglobulin-3 domains, whereas in the vertebrates, CD80-like C2-set domains are predominant. In the case of KIRREL1 and its orthologs, more Ig domains were observed in invertebrates than vertebrates. Src Homology-3 (SH3) domain of CD2AP and SPFH domain of podocin are highly conserved among vertebrates. TRPC6 and its orthologs had conserved ankyrin repeats, TRP, and ion transport domains, except Chondrichthyes and Echinodermata, which do not possess the ankyrin repeats. Intrinsically unstructured regions (IURs) are conserved across the SD orthologs, suggesting IURs importance in the protein complexes that constitute the slit-diaphragm. For the first time, a study reports the evolutionary insights of vertebrate SD proteins and their invertebrate orthologs. The vertebrate kidneys regulate the body’s homeostasis by maintaining fluid and acid-base balance and remove toxic metabolic byproducts. Nephron, the vertebrate kidney’s functional unit, consists of the glomerulus and the tubule. The former ensures ultrafiltration of plasma, and the latter participates in selective absorption of the glomerular filtrate . Thus, tThe SD develops initially as a tight junction during the comma and S-shape stages of glomerular development . EventuaNPHS1 gene, is a critical component of the SD that bridges the distance between interdigitating foot-processes. Mutations in nephrin are in Finnish-type NS patients. Nephrin has a long extracellular domain containing immunoglobulin (Ig)-like modules and a cytoplasmic fibronectin type-3 (FN-3) domain . In. In17]. The human CD2AP consists of three Src Homology-3 (SH3) domains . Pfam anSD proteins exist as large complexes via homo- and heterophilic interactions, and these interactions are predicted to be mediated by IURs ,6,16. SiPan troglodytes , wherein IURs were observed in only the Ig3 domain , IURs were observed in the ion transport protein domain. Further in Chondrichthyes, only C-terminal IURs were observed Click here for additional data file.S2 TableA predicted threshold value of ≥0.5 for residue indicates it be intrinsically unstructured.(XLSX)Click here for additional data file.


Significant correlations (p < 0.05) were found between proximate composition, dough rheological characteristics, and bread quality for the wheat–amaranth composite flours. The results of this study are an important basis for the development of innovative wheat–amaranth bread recipes.The objective of this investigation was to evaluate the effects generated by amaranth flour (AF)—of different particle sizes (PS) added to white wheat flour from 0% to 20%—on the proximate composition, dough rheological behavior, and bread technological parameters. The reduction of particle size led to an increased hydration capacity of the wheat–amaranth composite flour, while bulk density decreased. Increasing the amount of AF and decreasing the PS led to a significant increase in protein, lipids, and ash contents, while the moisture and carbohydrates of the composite flour decreased. Increasing AF addition led to an increase in dough tenacity and a decrease in dough extensibility, while the PS had an irregular trend. The large particle size, at 15% and 20% levels of AF in wheat flour, increased significantly ( Unrefined flour-based products demand new raw materials to improve bread’s nutritional quality. Recently, consumers have become more aware of the importance of food quality . A good To the best of our knowledge, no studies have been conducted to compare the effect of amaranth flour at different addition levels and particle sizes on wheat dough rheological properties by using the Alveograph device and on bread quality characteristics.This research aims to study the influence of amaranth at three different particle sizes  in wheat flour of 650 type for bread making at five levels  of substitution on Alveograph dough rheological properties, dough texture, and bread quality related to the physicochemical characteristics. The relationships between the proximate composition of wheat-amaranth composite flours, dough rheological properties, and bread features were also analyzed by using the principal component analysis method. The amaranth grains were purchased from S.C. SOLARIS PLANT S.R.L. . According to the standard analysis methods, amaranth seeds indicated the following characteristics: moisture content (14%), determined by a gravimetric method (ICC 110/1); the fat content (8.00%), determined by extraction with ether through the Soxhlet method , Italy) (ICC 104/1); protein content (17.00%), which was measured with a rapid Kjeldahl apparatus using digestion followed by steam distillation , Italy) and the values were expressed as percent protein (N × 5.53) (ICC 105/2); and ash content (3.00%) was determined in a muffle by incineration at 900 °C (ICC 106/1), as a percentage of the dried substances and total carbohydrates content 58.00%, calculated by difference {100- (moisture+fat+protein+ash)} . Refined wheat flour of 650 type acquired from a local company, S.C. Mopan S.A. , was used in this study as control and was analyzed through the same analytical procedures previously described for the following characteristics: moisture (14.00%), protein (12.60%), fat (1.40%), ash (0.65%). The wet gluten content (30.00%) of wheat flour was determined manually according to methods stated in the ICC method 106/1, falling number index (312 s) through ICC 107/1, and gluten deformation index (6.00 mm) by the Romanian standard method SR 90:2007, respectively. Sodium chloride  and dry yeast  were also used in the breadmaking.Amaranth seeds were ground with laboratory machinery  and sieved with a Retsch Vibratory Sieve Shaker AS 200 basic  for 30 min, at 70 Hz amplitude, in order to obtain the amaranth flour particle size > 500 μm. The amaranth flour (AF) particle sizes were coded as integral amaranth flour, AI (before sieving), large, AL , medium, AM  and small, AS (<180 μm), and stored in air-tight zip-lock pouches for further analysis.Amaranth flours  were analyzed according to the ICC methods as previously described: moisture content (110/1), protein content (105/2), fat content (104/1), and ash content (105/1), while total carbohydrate content was determined by difference .L*), the intensity of green (negative) or red (positive) (a*), and intensity of blue (negative) or yellow (positive) (b*) were determined with a CR-700 colorimeter . Each parameter was measured in triplicate.The color parameters of integral amaranth flour (AI) and each particle size  in terms of lightness (Water absorption capacity (WAC), water retention capacity (WRC), and swelling capacity (SC) of the amaranth flour particle sizes were determined by procedures reported previously by Coțovanu and Mironeasa . The watWheat flour was mixed with amaranth flour at different addition levels  and particle sizes  for 30 min in a Yucebas Y21 machine  in order to obtain the wheat–amaranth composite flour . The sample without amaranth flour addition was considered as the control.The composite flours formulated were analyzed according to the ICC methods as previously described: moisture content (110/1), protein content (105/2), fat content (104/1), and ash content (105/1), while total carbohydrate content was determined by difference .L*, a*, and b* were determined with a CR-700 colorimeter . Each parameter was measured in triplicate.The color parameters of composite flours, Saccharomyces cerevisiae type yeast (3 g/100 g) were used in the bread-making recipe. The water amount was calculated based on the water absorption capacity of the flour tested on the Mixolab . The bread dough was prepared using an indirect method. A half amount of composite flour and total amount of yeast and water were mixed to form the sourdough which was fermented at 30 ± 2 °C and 85% relative humidity (RH) for 2 h in a fermenting chamber . After this time, fermented sourdough and the remaining portion of the composite flour with salt were kneaded in a professional mixer for 10 min  and then the dough was fermented at 30 ± 2 °C and 85% relative humidity (RH) for 1 h in the same fermenting chamber. When the dough fermentation was complete, each dough sample was divided into 400 g, molded, and transferred into aluminum trays (size about 10 × 10 × 10 cm) for 1 h (30 ± 2 °C and 85% RH) in the fermenting chamber for the final fermentation of sugars. Then, the bread was baked at 220 ± 5 °C for 25 min in an oven . After baking, the bread was subjected to analysis after cooling for 2 h.Composite flour (300 g), salt (1.8 g/100 g), and 2O); dough extensibility, L (mm); index of swelling, G; dough strength, W (10−4 J); and curve configuration ratio, P/L.The rheological behavior of composite flour dough was analyzed using a Chopin Alveograph NG-97  with the standard procedure AACC 54-30 . Under this test, the dough is stretched during the biaxial extension stage until rupture and the recorded normal force gives information about dough firmness and extensibility. The main alveographic parameters registered were: dough tenacity, P , the samples were prepared as for breadmaking, and 50 g of the fermented dough was weighed and tested with a TVT-6700 texture analyzer . A 35 mm diameter cylindrical probe was used in a double-compression test to compress the samples up to 50% of the original height at a test speed of 5.0 mm/s, trigger force of 20 g, and the interval time between two compressions was 12 s, according to the method used by Mironeasa et al. . Hardnes3/g) and it was calculated based on the loaf volume (cm3) and mass (g). Porosity (%) was determined by using Equation (1). A 45.50 diameter and 60 mm height cylinder obtained from the middle of the bread was weighed, and its volume was measured. For the bread elasticity measurements, the cylinder was weighed, pressed for 1 min until half of the cylinder height was achieved, then the force was removed and the bread sample was left to recover for 1 min, and the final height was measured. Elasticity (%) was given by the difference between the initial and final height [V is the crumb cylinder volume (cm3), m is the crumb cylinder weight in (g), and ρ is the crumb density in (g/cm3).The bread samples were analyzed according to the Romanian standard procedure SR 91:2007, and the following parameters were determined: loaf and specific volume, porosity, elasticity, crumb, and crust color. The specific volume was measured by the rapeseed displacement method  were also determined using a CR-700 colorimeter . All analyses were performed three times.Crust and crumb color parameters  of bread was determined with a TVT-6700 texture analyzer , in accordance with the method described by Iuga et al. . A 25 mmSoftware SPSS 25.0   was used for statistical analysis of the data. Statistically significant differences for functional properties of amaranth flour particle sizes were determined by one-way ANOVA. A two-way ANOVA with Tukey’s test at 95% confidence level was also applied to test significant differences for the other parameters. A principal component analysis (PCA) was applied to observe the relationships between the wheat–amaranth flour proximate composition, dough and bread characteristics, and to visualize similarities or dissimilarities between them.p < 0.05) differences between particle sizes, which decreased with the reduction of the particle size. It can be observed that there are no differences regarding the moisture content of integral amaranth flour (AI) and large particle size (AL). The higher shear force that occurs during grinding affects the small and medium particle sizes especially, which can explain the variation in moisture content. The protein content of amaranth flour ranged between 9.22–29.35% and presented significant differences (p < 0.05) between all the samples. The highest protein content was found in the amaranth small particle size (29.35%), followed by the medium particle size (25.33%). Comparing the integral amaranth flour and the large particle size, there are significant differences, a fact that can be explained by the localization of protein in the germ of the seed (65%) [The values of the chemical composition of the large (AL), medium (AM), and small (AS) amaranth particle sizes compared with the integral amaranth flour (AI) are shown in ed 65%) ,5. The h% ,5. Thep < 0.05) different between all samples. The results are in line with those previously obtained by some authors [The fat content of the amaranth flours, integral, and particle sizes varied between 7.11–8.09% and were significantly  was observed between samples as in the case of the protein content. The small and medium particle sizes presented the highest contents of ash, probably due to the high content of minerals, the ash content being closely related to the morphological structure of amaranth seed. High levels of K, P, Ca, Mg, Na, and Fe can provide health benefits for preventing osteopenia and osteoporosis disease [Regarding the ash content of amaranth flours, which ranged between 1.05–4.45%, the same significant difference  differences between samples. It was observed that AI had a higher carbohydrate content (71.13%), the result being in line with other authors’ reports [The carbohydrate content of the studied amaranth flours varied greatly from 49.73 to 71.13% and presented significant  between samples. However, particle AS presented the highest WAC, which may be directly correlated with higher protein and ash content of the smaller particle size and indirectly correlated with the fat content of this particle, while AI had the smallest WAC and the lowest content of protein and ash. Data results were in agreement with those reported by Olawoye and Gbadamosi [p < 0.05) between the small particle (AS) and the other particle sizes (AM and AL) and AI. The AS presented the highest WRC (5.33%) which can probably be explained by amaranth seed morphology, which presented high ash and protein content and a low content of fats. It is known that the ability of flour to associate with water, at room temperature, depends mainly on proteins [p < 0.05) among all particle sizes and integral amaranth flour (p < 0.05) between them. The hydration capacities of wheat flour, regarding the value of water absorption capacity, water retention capacity, and swelling capacity, presented the following values: 1.72 (%), 4.74 (g/g), and 4.90 (mL/g), while bulk density was 0.52 (g/mL).The results for the functional properties of amaranth flours are presented in badamosi  and Shevbadamosi  for amarst WRC 5.% which cth flour , with thL*) did not show significant differences between integral amaranth flour and the large and medium particle sizes, whereas the small particle size was brighter. The a* values presented statistical (p < 0.05) differences only between AI and the large particle size (AL), and the medium and small one , while b* values did not present significant (p < 0.05) difference between the samples. This non-significant effect could be explained by the cream color of the amaranth flour which shows similarity with that of the integral wheat flour. The color parameters of basic materials may not always be the only ones responsible for the final food color. During the thermal process, the food products are exposed to biochemical reactions that may alter color properties, especially Maillard reactions and the caramelization process.The measure of food color is a quality parameter when new ingredients are added. Color parameters of integral amaranth flour (AI), large (AL), medium (AM), and small (AS) particle sizes are presented in p < 0.001) effect on all the physicochemical properties and color parameters of the formulated samples.The impact of different addition levels and particle size of AF on the physicochemical value of the wheat-amaranth composite flours used in this research is shown in p < 0.001) lower moisture contents than the control sample  influenced by the amount and particle size of AF added and showed an increase with the addition level compared with the control (The fat content of wheat-amaranth composite flours was significantly ( control . The higp < 0.001) increased in every sample, and was observed to be a rising trend for both factors—addition level and particle size—compared with the control. This increase in ash content with an increase in the AF amount and particle size can be related to the high content of ash from amaranth whole grain because in whole grains bran contains higher mineral contents than endosperm [Ash content significantly  different and decreased when supplementation of wheat flour with AF increased and particle size decreased. The addition of AF to the wheat flour significantly (p < 0.001) affected the carbohydrates content  of the composite flours (p < 0.05) varied significantly with the addition level and particle size of AF added to the wheat flour (L*) for all samples when the addition level increased and the samples were therefore characterized by a lighter color. The a* values presented a statistically (p < 0.001) difference between samples, and it can be observed in a* values increased when AF level and particle size increased. The b* value did not show a similar trend, but in general, the values increased with the amount of AF added and decreased with particle size reduction. The yellow color could be attributed to the presence of carotenoid pigments. These results are in line with those found by Sanz-Penella et al. [The color parameters  effects on dough rheological parameters.Dough alveographic results are shown in Replacing the gluten network from wheat flour with amaranth flour to develop improved bakery products is a challenge for grain technologists. The alveograph test simulated dough transformation during processing  providing useful information for processors. For breadmaking operations, it is important to establish the extensibility of dough, which represents the most unique property of wheat dough for obtaining the characteristic structure and volume of the baked products . High exp < 0.001) significant (For dough tenacity (P), all factors, level of AF addition, type of particle size, and their interaction are statistically (nificant . P was fp < 0.001) the dough extensibility index (L), and a decrease in dough extensibility (L) was observed when the AF amount and particle size increased, compared with the control dough, which may be explained by the gluten dilution effect. The findings that L decreased as the AF addition level and particle size increased are in accordance with data from the literature [p < 0.001) with the reduction of particle size. A small particle size in dough absorbs water easier, due to the larger specific surface area of amaranth starch [p < 0.001) difference for AF addition level, type of particle size, and interaction between them. p ≤ 0.001) significant results for AF addition level and type of particle size on W of wheat-amaranth composite flour dough. An increase in AF in the composite flour is linked to a decrease in dough strength. A decrease in W when gluten content of the composite flours decreased was also observed and reported by other authors [terature  and withterature ,46. In th starch , and fach starch . There w authors .p < 0.001) effect on the P/L. The P/L ratio evaluated the concordance between dough tenacity and extensibility and played a key role in the technological process of leavened products [p < 0.001) the P/L ratio, while the particle size increased the P/L ratio in an irregular order.As shown in products . The resTexture analysis of dough is very important in the development and production of bread products. The intermediate product dough quality can be an indicator of the final product sensorial characteristics. The rheology and machinability of dough enrichments with non-gluten flours will be affected and will influence the final baked product. The hardness, which is a positive character in products with low moisture content, showed higher values in dough containing AF compared with the control. Adhesiveness, which is the force required to remove food from any surface with which it has contact with, presented lower values compared with the control . All par3 and from 2.53 to 1.83 cm3/g, respectively, as the amaranth flour amount increased  on bread technological parameters. According to these results, bread with higher amounts of all AF particle sizes presented lower specific volume, compared with the control. This negative effect could be due to the poor baking quality of the flour. The globular proteins (11S and 9P) diluted the gluten network and decreased the alfa amylase activity which decreased maltose availability for yeast in the proofing process. A higher bread volume was observed for bread samples with large and medium particle sizes, compared with the bread with small particle sizes. Bread with medium particles at addition levels of 5% and 10%, and also bread with particles large at 5% (AL_5), showed higher values for specific volume than the control bread. These results are according to those obtained by Ayo [p < 0.001) by the addition of AF, particle size, and their interaction. The changes in crumb porosity may be related to its springiness and partly impacted the rating of crust and crumb appearance. When the AF addition level increased, the porosity of bread decreased significantly, while the AF particle size impacted the decrease in bread porosity in an irregular trend, as follows: AM, AL, and AS. The addition of AF, type of particle size, and the interaction between them, significantly affected (p < 0.001) bread elasticity. A regular trend was observed in the addition level of AF on bread elasticity, which decreased when the amount of AF increased (p < 0.001) compared with the control, and could be explained due to the weakening of the gluten network which leads to a decrease in volume, porosity, and elasticity in the formulations with 20%.AF particle size, addition levels, and their interaction caused significant changes  darker compared with the control bread.The color parameters of the crust and crumb were presented in p < 0.001) decrease in the crust lightness (L*). This was due to the high protein content in AF, which brought about the Maillard browning during baking. This effect may also be due to the darker color of the AF particle size, and especially the medium and large fractions compared with wheat flour. The crust a* values ranged between positive values (red hue), increasing significantly (p < 0.001) when the proportion of AF increased and particle size decreased. The yellowness value (b*) of the crust was significantly increased (p < 0.001) when the level of AF increased, and PS decreased, compared with the control, especially in formulations substituted with 15% and 20% of amaranth flour. These results are similar to the previous results of Rosell et al. [p < 0.001) affected by the AF addition level, the type of particle size, and the interaction between them. Bread crumb samples showed a tendency to decrease in terms of lightness (L*) when the AF addition level increased, and also when the AF particle size decreased. These results indicated darker crumbs in composite flours bread compared with the control. This phenomenon can be explained by the direct correlation between the chemical composition of AF, due to the increase in protein content with lysine residues and reduced sugar content [a* values ranged between negative values (green hue), increasing significantly (p < 0.001) when the proportion of AF increased and particle size decreased. The yellowness value (b*) increased significantly (p < 0.001) when the level of AF increased, and particle size decreased, compared with the control, especially in formulations with 15% and 20% of amaranth flour.Increasing the amaranth flour in the composite flours bread and decreasing AF particle size resulted in a significant  was used to highlight the influence of AF addition level and particle size on wheat-amaranth composite flour, dough, and bread analyzed variables. The two principal components explained 76.57% of the total variance (PC1 = 60.96% and PC2 = 15.60%). The PC1 was associated with composite flour moisture, lipids, ash, carbohydrates, dough alveographic parameters , dough textural parameters , and bread technological properties , while PC2 was associated with composite flour protein and bread firmness and gumminess. A high opposition between protein and carbohydrates, dough adhesiveness, and dough hardness, P and L alveograph parameters, P/L ratio and bread volume, bread cohesiveness, and bread firmness was observed.Regarding bread samples, p ≤ 0.05) relationship between wheat–amaranth composite flour, dough, and bread features. By applying Pearson’s correlation analysis for proximate composition, rheological, and technological parameters, a series of correlation coefficients were found (0.56 < r > 0.99).Multivariate correlation analysis provides information on the significant (p > 0.0001 were obtained for lipids with moisture (r = −0.65) and G (r = 0.86), protein with ash (r = 0.95) and carbohydrates (r = −0.98), and ash with carbohydrates (r = −0.97), which can be explained by the high nutritional components of amaranth flour and its addition in wheat flour directly increasing these values. Similar observations on relationships within the chemical composition of wheat flour and alveographic dough parameters were reported by Codină and Mironeasa [Significant positive correlations were obtained between moisture and alveographic parameters L (r = 0.83), G (r = 0.86), and W (r = 0.76), but were negative with dough tenacity, P r = −0.61). Significant correlations at . Signifiironeasa .p < 0.05 was obtained between dough tenacity and dough hardness (r = 0.56), dough extensibility (L) and dough adhesiveness (r = 0.81), and dough cohesiveness (r = 0.69), but a negative correlation with dough hardness (r = −0.70) was observed. P/L ratio showed a strong positive correlation with dough hardness , but a negative relationship, p < 0.05, with dough adhesiveness (r = −0.78), bread elasticity (r = −0.76), porosity (r = −0.62), and volume (r = −0.62). Bread volume was positively correlated with cohesiveness (r = 0.76), and bread porosity (r = 0.99) and elasticity , but a negative relation was observed with bread gumminess  and dough hardness (r = −0.82), while bread gumminess was strongly correlated with dough springiness , hardness (r = 0.71), and negatively with dough adhesiveness (r = −0.82). Similar results between dough textural properties and bread volume and texture properties were found by Martínez-Anaya [A positive correlation at ez-Anaya  and Miroez-Anaya .Amaranth flour fractionated on large, medium, and small particle sizes showed variation in moisture, protein, lipids, ash, and carbohydrates content. The partial replacement of wheat flour with medium and small amaranth flour particle sizes increased the amounts of protein with the increase in the addition levels of amaranth, due to the contribution in chemical constituents of these particles. Lipids and ash increased in composite flour for all addition levels and particle sizes, whereas carbohydrate content followed a reverse trend. The lowest content of carbohydrates was found in composite flour with 20% small particle size amaranth flour. A decrease in lightness (L*) for all the composite flours was obtained when the addition level increased, the lowest value was found for the small particle size at 20% addition level. Small particle size presented the highest water absorption capacity (3.08%), water retention capacity (5.33%), and swelling capacity (6.60%). The dough tenacity increased significantly for all the particle sizes with the increase in amaranth flour addition level over 5%, while dough extensibility decreased. The increase in AF level in the composite flour led to a decrease in the index of swelling and dough strength depending on the particle size, whereas the P/L ratio increased following an irregular trend. Besides the nutritional enrichment in protein, lipids, and ash contents at any addition level, the wheat–amaranth composite flour up to 10% addition level provided the best properties in baking quality  at any particle size. The medium particle sizes at an addition level of up to 10% produced bread with a lower hardness than the control.The separation of different particle sizes of amaranth flour led to different fractions rich in nutritional substances which can be used separately in the development of added-value food products. The evaluation of the combined effect of amaranth flour particle size and addition level on the composition of wheat flour, dough rheology, and bread quality offer valuable information on the processes for the development of new enriched nutritional products.


Sambucus nigra L. Three designs of sponge cakes with 5, 10, and 15% content of flour of Sambucus nigra L. corrected up to 100% with whole-grain oat flour were studied. Their characteristics were compared with sponge cakes of 100% wheat flour/control. The obtained new products were characterized by reduced carbohydrates, increased content of dietary fiber, and preserved volume compared to the control. The physicochemical parameters of sponge cake and marshmallows with different concentrations of dry flowers of Sambucus nigra L. included in them differed from the control with lower water absorption, pH, and moisture, while having a higher relative mass and ash content and retaining the original size. Pathogenic microorganisms such as Escherichia coli, Salmonella sp., and Staphylococcus aureus, and common coliforms were not detected in the control and experimental samples when determining the microbiological parameters. Therefore, the developed formulations are an excellent alternative to wheat flour, significantly improving some nutritional characteristics such as smell, taste, dietary fiber, and lower carbohydrate content.The present study aims to develop recipe compositions and technology for producing sponge cakes from wholemeal flour, partially replaced with a functional plant component dry blossom flour of  Sambucus nigra L. is one of the most common plant species in Europe [Sambucus nigra L., along with anthocyanins, glucosides, and flavonoids, protects the cell membranes from the changes caused by the free radicals [Sambucus nigra L. have perspiring, expectorating, anti-inflammatory [n Europe ,2,3,4. In Europe . Sambuciradicals . These cradicals . The ethammatory ,9,10, anammatory , and theammatory .Some of the modern tendencies in nutrition include decreasing the intake of lipids, change in the traditional technologies, and creation of new prescriptions with optimal biological and energetic values in the production of pastry. Sponge cakes are the most commonly used in the making of bakery products, as they have great porosity and can take up to 60% of sugar syrup with different concentrations without losing their elasticity. Their humidity is about 36–38%, and the baking temperature is around 170–240 °C for the time of 10–75 min, depending on the thickness of the cake’s layers ,14. The Sambucus nigra L./elderberry/and the evaluation of their physical and chemical properties, as well as their sensory properties.The inclusion of plant parts as a food supplement benefits the antioxidant and anti-inflammatory defenses of the organism  and provSambucus nigra L. dry blossom flour . The results are presented in Physicochemical parameters of pandispan blends were determined according to the formulations and technologies developed with A summary assessment of the sensory analysis performed by all the tasters is presented in Sambucus nigra L. flour.The textural characteristics of the samples are presented in The photo of the investigated samples is presented in the Sambucus nigra L. blossom flour are presented in The results obtained from the chemical composition and energy value of the sponge cake layers with Sambucus nigra L. are good sources of biocompounds, and are therefore suitable in the development of functional foods. Sambucus nigra L. dry blossom flour has a low protein content and no fat. The presence of ascorbic acid confirms that the blossom of Sambucus nigra L. has functional health potential. Wholemeal oat flour has a higher protein, fat, dietary fiber, and mineral content than wheat flour. The fat content of wholegrain oat flour is the highest.The analyzed wholegrain oat flour and dried blossom flour of Sambucus nigra L. blossom flour and oats resulted in an increase in the relative mass from 0.72 ± 0.03 to 0.81 ± 0.01 of the new product.The addition of 3) was similar in value to that of the sponge cake with the addition of elderberry flour.The volume of the sponge cake layer control  lowered the pH of the product compared to the control. This is probably caused by the lower pH of Sambucus nigra L. flour (5.32) than pH of control (5.58). The blends with functional components contained more minerals, leading to an increase of the ash content, with the blend with 15% elderberry flour having 2.98 times more ash content than the control. Weight losses after baking are calculated according to Hathorn et al. [Sambucus nigra L. weight losses are up to 11.7%.The control has the highest moisture percentage, and the ash content is inversely related to moisture. The water absorption capacity of the elderberry flour products was lower compared to the control (333 ± 8 g) and decreased with increasing concentration of the functional component. The addition of n et al. . For conMoisture content, textural parameters , fat content, carbohydrate content, color parameters a* and b*, lightness (L), and color difference ∆E are important characteristics in the quality control of the sponge cake layers.Sambucus nigra L. Therefore, 15% dried elderberry blossom flour had the greatest darkening compared to the control. High values of b (yellow component) and values of a > 2 (red component) indicate a significantly bright and intense orange–brown color [Sambucus nigra L. it remains practically the same. There was an increase in color difference only for the center of the sponge cake blotch with 15% dry flower meal of Sambucus nigra L. , albeit faint residual aftertaste was detectable. The control sponge cake and the one with 5% added Sambucus nigra L. blossom flour had the lowest residual aftertaste values.The intensity of the sweet taste of the Sambucus nigra L. dry blossom flour increased, the hardness of the samples increased linearly relative to that of the control. The increase in hardness is probably associated with lower moisture content; similar information has been reported by [Sambucus nigra L.As the concentration of orted by . Elasticorted by . The resSambucus nigra L. flour did not affect the pore size, but increased the hardness (15% flour) by two to three times compared to the control, and the tenderness increased.As can be seen from the results obtained, increasing the concentration of Sambucus nigra L. blossom flour indicates that it has functional potential and can be labeled ‘high in dietary fibers’ [The high percentage of dietary fibers in the product with 15%  fibers’ . This hi fibers’ , in addiBacillus cereus; regardless of the heat treatment, the spores can survive and subsequently overgrow and cause spoilage of the finished products. The toxins formed to make the food dangerous to human health. The intake of such foods causes nutritional diseases. Therefore, the experimental samples with the addition of Sambucus nigra L. flour were tested for the presence of Bacillus cereus. In the determination of the microbiological indicator molds and yeasts, the presence of Bacillus cereus was not detected, but only the presence of mold fungi in the control and the samples with 10 and 15% dried Sambucus nigra L. blossom flour, with the number of spores of microscopic fungi ranging from 10 to 20 cfu/g. The results obtained indicate that the prepared samples and the control meet the requirements of the standard, according to which the amount of spores of microscopic mold fungi is up to 100 cfu/g. For the 5% sample, no mold fungi or yeasts were detected.The microbiological parameters of the samples were investigated, since the plant raw materials can be contaminated with spore-forming bacteria, including the human pathogen Regression linear models were established, taking into account the content of elderflower flour on the qualities of the cupcakes at a significance level of 0.01 .In order to produce sponge cake dough, the following materials were provided by some of the big retail chains in Bulgaria: wheat flour “Extra” (type 500)—manufactured by “Sofia MEL” JSC, Sofia, hen eggs, sugar ; and wholegrain oat flour—manufactured by “Ecosem Bulgaria” Ltd., Stambolovo village.Sambucus nigra L. were collected during the period of intense flowering (May–July), depending on the altitude of the region [The blossoms of e region . The ideSambucus nigra L. are from locations in the Western Rhodopes: town of Velingrad, Golyam Beglik Dam, Karatepe-Sutka locality (Bulgaria) with geographical coordinates 35TKG5111032486, Lat. 41. 80444, Lon. 24. 159444, located at 1271 m above sea level. Blossoms of Sambucus nigra L. were dried in a thin layer, in the shade, being turned periodically to a constant mass of the sample. Dry samples were ground to a fraction size of 1–2 mm.The blossoms of Sambucus nigra L. blossom flour and oat flour. The exact recipe compositions of the control and the newly developed blends are given in Recipe compositions were developed—(1) control–sponge cake; (2) sponge cake blends with partial replacement of wheat flour with 5%, 10%, and 15% In further interpretations we will use the following designations: Option 1—with 5% elderberry flour + 25% wholemeal oat flour; Option 2—with 10% elderberry flour + 50% wholemeal oat flour; Option 3—with 15% elderberry flour + 85% wholemeal oat.The active acidity of the dough and the middle part of the cake layer were according to AACC 02-52 (27), pH meter . The temperature of the dough—(20 ± 0.5) °C.Moisture content  was determined by standards for regulation for taking samples, determination of dry material, moisture, ash and ash alkalinity ,34. EachThe relative mass of the sponge dough was calculated according to AACC method 10–95 .The total ash content for the sponge cake layer was determined by firing in a muffle furnace  at 700 °C to constant mass . DetermiThe amount of total carbohydrates was determined spectrophotometrically by the phenol-sulfuric acid method measuring absorbance at 490 nm . DetermiThe energy value was determined per 100 g of product in accordance with Regulation No. 23 of the Ministry of Health of 2001 on the conditions and requirements for the presentation of nutritional information in the labeling of foodstuffs. The energy value of the marshes was calculated by applying d’Atwater’s energy coefficients to the major nutrients. Accordingly, for 1 g protein = 17 kJ , 1 g digestible carbohydrate (without dietary fiber) = 17 kJ , 1 g fat = 37 kJ , and 1 g dietary fiber = 8 kJ .Sambucus nigra L. Microbiology is made according to ,41,42,43Measurement of the color of the peel and the sponge cake middle parts were made using a quality technical colorimeter PCE-CSM 5, PCE Instruments UK Ltd . The indicators are reported by the CIELab system . In the The color tone and the color tone angle were determined according to dependencies, respectively:L0, a0, and b0 are the color parameters of the control sample.The total color difference (ΔE) was calculated from Equation (3), where All measurements were taken at room temperature with the experiment repeated five times.Sambucus nigra L. were measured with a texture analyzer  using special software. A Teflon press (40 mm diameter) was used to obtain textural parameters such as hardness, elasticity, and brittleness under double compression. The test was carried out on pieces of pandishpan in the shape of a truncated cone. The textural properties of sponge layer cakes with 5, 10, and 15% dry blossoms of The parameters of the analysis are as follows: Pre-test speed 5 mm/s; test speed 0.25 mm/s; and 10-s delay between the first and second compression. The measurements were performed three times each, and the average values are presented as a result.The middle part of the baked sponge cake layers was observed with an Olympus SZ 61 stereomicroscope, Olympus ltd., Tokio, Japan, operating in the bright field with reflected light at 70× objective and 8× eyepiece magnification. The photos were taken with a 5Mp× Wi-fi camera.A descriptive sensory profiling test  was used2 was determined.All parameters studied were determined after three to five repetitions. Data from all studies were processed to obtain the mean and standard deviation (SD). The linear dependencies between the studied parameters were obtained by the least squares method. The coefficient of determination Rp < 0.01.IBM SPSS software was used in the statistical analyses at the significance level Kendall’s method—the sensory analysis data of pandichpan blots were processed using Kendall’s concordance method  to check the agreement in the rankings of the trained tasters in the sensory analysis with respect to the samples studied .Sambucus nigra L. included in them differ from the control with lower water absorption, pH, and moisture, while having a higher relative mass and ash content and retaining the original size.The physicochemical parameters of sponge cake and marshmallows with different concentrations of dry flowers of Chemical composition—minimal reduction of the amount of protein and carbohydrate content decreases by up to 10%, up to 1.5 times increase dietary fibers, and slightly increases fat.Sambucus nigra L. flour does not change the microbiological parameters and taste of the products.It also preserves the excellent appearance of the products. The use of Therefore, the developed formulations are an excellent alternative to wheat flour, significantly improving some nutritional characteristics such as smell, taste, dietary fiber, and lower carbohydrate content.