Mβ2 mediates phagocytosis of complement-opsonized objects, adhesion to the extracellular matrix, and transendothelial migration of leukocytes. However, the mechanistic aspects of αMβ2 signaling upon ligand binding are unclear. Here, we present the first atomic structure of the human αMβ2 headpiece fragment in complex with the nanobody (Nb) hCD11bNb1 at a resolution of 3.2 Å. We show that the receptor headpiece adopts the closed conformation expected to exhibit low ligand affinity. The crystal structure indicates that in the R77H αM variant, associated with systemic lupus erythematosus, the modified allosteric relationship between ligand binding and integrin outside–inside signaling is due to subtle conformational effects transmitted over a distance of 40 Å. Furthermore, we found the Nb binds to the αI domain of the αM subunit in an Mg2+-independent manner with low nanomolar affinity. Biochemical and biophysical experiments with purified proteins demonstrated that the Nb acts as a competitive inhibitor through steric hindrance exerted on the thioester domain of complement component iC3b attempting to bind the αM subunit. Surprisingly, we show that the Nb stimulates the interaction of cell-bound αMβ2 with iC3b, suggesting that it may represent a novel high-affinity proteinaceous αMβ2-specific agonist. Taken together, our data suggest that the iC3b–αMβ2 complex may be more dynamic than predicted from the crystal structure of the core complex. We propose a model based on the conformational spectrum of the receptor to reconcile these observations regarding the functional consequences of hCD11bNb1 binding to αMβ2.The integrin receptor α Mβ2, also known as complement receptor 3, CD11b/CD18, and macrophage-1 antigen (Mac-1), participates in all three types of interactions. The noncovalently associated subunits αM (CD11b) and β2 (CD18) consist of a large N-terminal ectodomain, a single transmembrane helix, and a C-terminal cytoplasmic tail  and αxβ2  form the foundation for the mechanistic understanding of β2-integrins (A). αMβ2 contains a von Willebrand factor type A domain, known as the αI domain, in the α-chain   , 7. The Mβ2 is phagocytosis of complement-opsonized cells and immune complexes. Proteolytic cleavage of component 3 (C3) by convertases deposits the opsonin C3b on the activator (B). The C3b has a short half-life and is quickly converted to iC3b . In the low-affinity bent-closed state, the ectodomain conformation positions the αI close to the plasma membrane with the HP in the ligand-binding inactive conformation. In the intermediary extended-closed conformation, the integrin extends, leading to the αI domain pointing away from the plasma membrane, but the HP remains in the closed conformation. In the high-affinity extended-open state, the β2 hybrid domain is swung away from the αM thigh domain opening the HP for ligand binding.One primary function attributed to αctivator B. The C3 to iC3b  and evend weaker , 11. αMβeostasis , 14, 15.us floor . Externaus floor A. In the2 subunit, the βI domain is structurally homologous to the αI domain but contains two additional regulatory metal ion–binding sites  from the αM subunit located at the C-terminal region of the α7 helix of αI. Its interaction with the βI domain exerts a pull on the helix, which forces the αI domain into the open conformation during inside–out signaling. Conversely, movement of the α7 helix induced by ligand binding to the αI domain induces Glu320 coordination of the βI domain MIDAS Mg2+ and shifts the βI domain into the open conformation. Crystal structures indicate that the transition to the open conformation of the βI domain translates into a 60° swing out of the β2 hybrid domain that moves the plexin–semaphorin–integrin (PSI) domain by 70 Å  hCD11bNb1 obtained by crystallography. The receptor adopts the closed conformation with low ligand affinity. The Nb binds to the αI domain in the αM subunit in an Mg2+-independent manner, and biophysical experiments as well as a structural comparison suggest that it acts as a competitive inhibitor of iC3b binding. In assays with cell-bound αMβ2, however, the Nb stimulates interaction with iC3b. We propose a model that integrates the entire conformational spectrum of the receptor and the dynamic properties of ligand–αMβ2 complexes to reconcile these observations.Here, we present the first atomic structure of the αMβ2 HP could enable its structure determination and, at the same time, lead to identification of novel modulators of the αMβ2–ligand interactions. We selected Nbs against recombinant human αI domain using a phage library generated from a Llama immunized with the αMβ2 HP. To favor the selection of Nbs with potential for interfering with the interaction between αI domain and C3d, we performed competitive elution with recombinant C3d. This elution strategy yielded the Nb hCD11bNb1, which we cloned into a bacterial expression vector, expressed, and purified.Nbs are single domain antibodies of typically 120 residues derived from the variable domain of heavy chain–only antibodies present in members of the Camelidae family. In addition to their potential for modulating the function of their antigen, Nbs often facilitate structure determination of challenging targets . Hence, 2+. The complex eluted markedly earlier than the two separate components, and SDS-PAGE analysis confirmed the presence of both components in the early peak fractions (C). Next, we investigated the effect of hCD11bNb1 on the interaction between the αI domain and C3d in the presence of Mg2+. After having confirmed that the αI domain and C3d form a complex stable during SEC analysis and eluting at 10.6 ml (D and D).We validated the interaction of hCD11bNb1 with the αI domain by size-exclusion chromatography (SEC) in the absence of Mgractions C. Next,  10.6 ml D and S1,ml D and D.Mβ2 interaction using biolayer interferometry (BLI). We loaded His-tagged hCD11bNb1 on sensors coated with a His5-specific antibody and transferred the sensors into a solution containing either recombinant αMβ2 HP or the αI domain (E–G). Data analysis with a 1:1 binding model revealed that the Nb binds with a low nanomolar affinity to both the αMβ2 HP and the αI domain (G). Overall, our SEC and biophysical experiments demonstrated that hCD11bNb1 binds with nanomolar affinity to the αI domain and compete with the C3d ligand, the latter a prior expectation considering the selection strategy.We next measured the binding kinetics for the hCD11bNb1–αI domain , E–G. DaI domain G. OveralMβ2 HP alone and its complex with C3d or iC3b, we failed to obtain useful crystals or nonaggregated particles on cryo-EM grids; in the latter case, most likely because of the effects of the air–water interface . We also identified electron density that could be manually fitted with a model of the Nb bound to its epitope in the αI domain. The electron density calculated from the resulting model and noncorrected diffraction data was of low quality in the receptor proximal part of the thigh domain, the PSI and I-EGF1, and at C-terminal pole of the Nb irrespective of the used dataset. Data were therefore scaled anisotropically with the STARANISO server  . Using the anisotropy-corrected data, we refined the complex structure to an Rfree value of 0.295  , which lf 1.14 Å , A–C. Usof 0.295 . Figure M and the βI domain in the β2 subunit, with a buried surface area of 3650 Å2. Superposition of the αMβ2 onto structures of αLβ2 and αXβ2 revealed that the β-propeller and the βI domains interact in an almost identical manner across the three β2 receptors (A). The orientation of the thigh domain relative to the β-propeller is also quite similar in αxβ2 and αMβ2 (B). In the αM β-propeller, two calcium ions organize coordinating loop regions that together with the first residue of αM forms the interface with the thigh domain (B). In contrast, the metal ion–binding sites in both the αI and βI domains are empty, and the internal ligand region at the C-terminal end of the αI α7 helix is not interacting with the βI MIDAS site (C). This is an important notion, as ligand binding to the αI domain induces movement of the α7 helix. In turn, αM Glu320 may coordinate the metal ion within the βI MIDAS site and induce the ligand-bound open conformation of the βI domain that propagates into the extended-open conformation of αMβ2 (A). For this reason, the region around Glu320 is known as the internal ligand (B). The overall conformation of the αMβ2 HP is closed with the hybrid, PSI, and I-EGF1 domain in the β2 subunit located toward the αM thigh domain, in contrast to the open conformation of the β2 subunit known from a structure of ligand-bound αIIβ3 integrin (D). Within the β2 subunit, the arrangement of the four domains in the closed conformation of αMβ2 is also highly similar to those observed for αXβ2 and αLβ2 (C).The two subunits associate through an extensive intermolecular interface formed between the β-propeller in αeceptors A. The orand αMβ2 B. In theh domain B. In conDAS site C. This i of αMβ2 A. For thl ligand B. The ovintegrin D. Withinand αLβ2 C.Figure M subunit β-propeller predisposes the carrier for systemic lupus erythematosus (SLE) , ICAM-2, and DC-SIGN (dendritic cell–specific intercellular adhesion molecule-3-grabbing nonintegrin). Furthermore, R77H monocytes stimulated with a Toll-like receptor 7/8 agonist exhibit a significantly smaller decrease in cytokine secretion upon binding of iC3b-opsonized red blood cells compared with WT monocytes  . The R77ignaling , 27. Howing . The side chain of Arg61 only appears to interact with the nearby loop Gly111–Pro118 by nonspecific van der Waals interactions. The arginine side chain does not engage in specific hydrogen bonds or electrostatic interactions that could directly explain the altered allosteric coupling in αMβ2 containing the R77H variant. In our crystal structure, Arg61 is located ∼40 Å from both the α7 helix in the αI domain and the MIDAS site in the βI domain. Hence, a direct interaction of Arg61 with residues in the αM–β2 interface involved in the allosteric coupling between ligand binding and transition to the extended-open conformation cannot explain the observed functional defects. Furthermore, based on the structure of the closed-bent conformation αXβ2  is exposed on the edge of the αropeller F. The siion αXβ2 , we alsoF) changes conformation and dynamic properties because of perturbation of van der Waal interactions formed by Arg61. Alternatively, a histidine side chain at position 61 may engage in hydrogen bonds with the 111 to 118 loop. In support of an altered conformation of the 111 to 118 loop, we notice that in αX with a glycine residue corresponding to αM Arg61, the equivalent loop adopts a different conformation and is not in contact with the region containing the glycine. An altered conformation of the 111 to 118 loop could propagate and influence the dynamic properties of the N-terminal linkage between the β-propeller domain and the αI domain in residues 123 to 129. Alternatively, such conformational changes could propagate to αM residues located at the interface to the βI domain such as the loop region Thr96–Thr101. Transmission of force is crucially dependent on a stable αM–β2 interface; even a small perturbation may give rise to the observed abnormal outside–in signaling in the R77H αM variant.However, a possible consequence of a histidine at position 61 is that the neighboring 111 to 118 loop F changesXβ2 and αLβ2 revealed that the α-subunit β-propeller and the βI domain form a platform above which the αI domain has considerable freedom to orientate in response to crystal packing and the βI coordination state of the αM internal ligand region . When comparing our αMβ2 structure to αXβ2 and αLβ2, where the internal ligand region is not contacting the β2 MIDAS, the αI domain is rotated by 125° and 42°, respectively (E). The αMβ2-specific orientation of the αI domain may well be a result of crystal packing, since the αI-hCD11bNb1 part of the complex firmly contacts three symmetry-related complexes (D). Supporting this, there are no specific interaction between the N-terminal linker region (αM residues 123–131) and the platform. At the C-terminal linker region (residues 321–328), only a putative hydrogen bond between Thr322 and a sugar residue from the glycan attached to Asn375 appears to be specific for the αMβ2 structure.Prior structures of αd region , 4. Conf by 180° E. When cectively E. The αMomplexes D. Suppor2+ ion although it was available during crystallization. Also, the electron density suggests that the main-chain conformation of residues Asp242–Glu244 may not be fixed. As this region differ between the open and closed forms of the αI domain (A). Hence, the Nb does not appear to depend on a particular MIDAS conformation, and SEC analysis confirms that its binding to the αI domain is Mg2+ independent (C and D). This is also consistent with that the conformation of the epitope described later does not differ significantly in structures representing the open and closed states of the αI domain.The αI domain has no clear density for a MgI domain , the conI domain A. Hence,ependent , C and DM Phe302–Glu320 region is in a helical conformation  meaning that this region adopts the closed conformation that prevents Glu320 from interacting with the βI MIDAS. Since hCD11bNb1 and the α7 helix are located oppositely on the αI domain (A) and the Nb apparently does not induce a specific conformation of the αI MIDAS, the Nb is unlikely to influence the conformation of the α7 helix significantly. Its closed conformation is more likely to be a result of the crystal packing that favors the overall closed conformation of the β2 subunit in the βI domain incompatible with binding of the αM internal ligand region. In summary, both the αI domain α7 helix and the overall conformation of the αMβ2 HP signify the closed conformation; however, this appears not to be a consequence of the Nb. In solution, the αMβ2 HP contains a mixture of the open and closed conformations . Furthermore, known structures of the αI domain and our own 1.14 Å-resolution structure of hCD11bNb1 itself (A) considerably facilitated modeling of the intermolecular interface. The buried surface area of the interface is 1330 Å2, which is low, but not unusual, when compared with most other Nb–antigen complexes (C and D). Extensive burial of hydrophobic side chains at the Nb–antigen interface plays a prominent role in our complexes of Nbs with complement C3b, C4b, and C1q (D). The epitope of the Nb comprises two distinct regions in the αI domain. First, Nb complementarity-determining regions (CDRs) 1 and 3 recognize αI residues Pro201–Leu206 with hydrogen bonds and van der Waals interactions (C and S2D). Second, αI residues in the region Glu179–His183 encompassing β-strand C interact with hCD11bNb1 CDR1 and CDR2 through van der Waals interactions and hydrogen bonds (D and S2D).The quality of the electron density for the Nb–αI interface is overall good considering the resolution and data anisotropy D. Furthe1 itself A consideomplexes . The intomplexes , C and D and C1q , 30, 31  and C1q D. The epractions C and S2Den bonds D and S2DE and F). Specifically, the Nb CDR3 residues 103 to 107 are predicted to exert steric hindrance on C3d residues Ala1214–Lys1217 in a loop region at the end of a C3d α-helix. Since the thioester domain of iC3b is expected to bind αMβ2 in the same manner . In the presence of hCD11bNb1, the signal decreased to 32 to 55% of the signal obtained in the absence of the Nb (B and C), demonstrating that the Nb acts as an inhibitor of iC3b for binding to the αMβ2 HP.To test the prediction that hCD11bNb1 acts as a competitive inhibitor for the αf the Nb A. In thef the Nb , B and CMβ2 HP observed in the crystal structure, we mutated Nb residues in direct contact with the receptor  or in the vicinity (Ile29 and Phe32) likely to support the conformation of the directly interacting residues. We next coupled biotinylated WT hCD11bNb1 to streptavidin-coated BLI sensors and carried out a competition assay where variants of hCD11bNb1 were present in the fluid phase in 10-fold molar excess to the αMβ2 HP. As expected, the presence of the parental hCD11bNb1 in the fluid phase reduced the binding to approximately 22% of the signal obtained with the αMβ2 HP only (D). The Ile29Ala variant competed almost as well as the parental Nb, whereas the remaining variants more or less lost the ability to inhibit binding of the αMβ2 HP to the immobilized hCD11bNb1 (D). Overall, our experiments with mutated Nb variants validated the paratope–epitope interaction deduced from the crystal structure.To validate the interface between hCD11bNb1 and the α HP only D. The IlCD11bNb1 D. OveralMβ2, we investigated whether the Nb could bind to the recombinant αI domain from the murine αM subunit. If hCD11bNb1 also modulates the activity of murine αMβ2, it may be an attractive reagent for in vivo murine models of pathogenesis where the receptor plays a role as discussed later. We charged anti-His BLI sensors with His-tagged hCD11bNb1 and compared the binding of the recombinant murine αI domain to the human αI domain. While we observed a strong signal for the human domain, the murine αI domain bound much weaker (E), and the data could not be fitted to obtain rate constants or the KD value. To understand why the Nb binds the murine αI domain much weaker, we constructed a homology model of the murine domain. Inspection of this model suggested two reasons for our observations. First, a lysine in mouse αI substitutes for Thr203 in the human αI domain. This is likely to lead to steric hindrance when the Nb binds to the murine domain. Second, L206 in the human αI domain making contact with CDR3 of the Nb is replaced by the polar N222 in murine αM, which may also decrease affinity. In conclusion, our biophysical experiments agreed with the predictions made from the crystal structure of the complex and demonstrated that hCD11bNb1 is unlikely to modulate the activity of murine αMβ2.Since hCD11bNb1 appeared to modulate the function of αh weaker E, and thMβ2 HP leading to release of iC3b or acted as a partial antagonist in a mechanism distinct from the competitive inhibition suggested by our structural analysis. Since neither BLI nor SPR reveal the oligomerization state of the fluid phase analyte, we took advantage of mass photometry . Titration of the αMβ2 HP–iC3b complex with increasing amounts of hCD11bNb1 leads to dissociation of the complex (D–F). At 10-fold molar excess, complex dissociation appeared to be complete (F). Overall, our mass photometry data supported that hCD11bNb1 acts as a competitive inhibitor of iC3b binding to the αMβ2 HP.To obtain more insight in the mechanism of inhibition, we investigated whether hCD11bNb1 induced aggregation of the αotometry  to studyd values . As expe αMβ2 HP , B and C complex , D–F. Atcomplete F. OveralMβ2 receptor on cells. The binding of the iC3b ligand to αMβ2 was evaluated in two types of cell-based assays. The first assay was based on the binding of fluorescent-labeled iC3b (iC3b∗) incubated with K562 cells that express αMβ2. Here, the long incubation time permitted the reaction to reach equilibrium (A) or with Mn2+ added to activate ligand binding (B). In this assay, the influence of hCD11bNb1 showed a dose-dependent increase of ∗iC3b both under conditions with and without integrin activation (C and D). Importantly, an unrelated control Nb did not increase the binding quantitatively. When this binding was normalized to the signal with no hCD11bNb1 (E and F), it became clear that the observed increase in iC3b∗ binding was independent of integrin activation: in both cases, the stimulation was approximately twofold higher in the presence of hCD11bNb1. Especially for nonactivating conditions (E), the binding signal followed the hCD11bNb1 concentration with lower signal for a concentration of 1 μg/ml (∼75 nM) compared with 5 or 10 μg/ml, which showed signs of saturation.We next asked whether the competition between the Nb and iC3b observed in binding experiments with isolated components and rationalized by structural comparison could be translated to the full αilibrium , and theilibrium A or with binding B. In thitivation , C and DCD11bNb1 , E and Fnditions E, the biMβ2 mimicking physiological conditions, where sheer stress acts similarly . As a control, we tested αXβ2-expressing K562 cells, which also bind iC3b in the centrifugation assay. In this case, the hCD11bNb1 had no influence on the cell adhesion, consistent with the absence of the αM chain (I and J). Overall, the cell-based assays demonstrated that hCD11bNb1, through its binding to the αI domain, can both stimulate the interaction of αMβ2 with fluid phase monovalent iC3b as well as the multivalent interaction between αMβ2-presenting cells and an iC3b-coated surface. Hence, with the receptor presented on the cell surface, hCD11bNb1 acted as new protein-based αMβ2-specific agonist that promotes interaction with iC3b.Our second cell-based assay involved force exerted through centrifugation of V-shaped microtiter wells coated with iC3b. In this way, adherent cells transmit a force load onto the ligand-bound αimilarly . Adhesio to 100g , G and HαM chain , I and JMβ2 HP and the isolated αI domain in solution-based assays. In this case, the apparent affinity (KD) of hCD11bNb1 was 1 to 6 nM. By contrast, the cell-expressed αMβ2 responded to hCD11bNb1 by increased iC3b∗ binding. One of the major differences between the fluid phase assays with pure components and those involving the cell-expressed αMβ2 was the presence of the cell membrane in the latter experiments. Adair et al. . This membrane proximity may contribute to the unexpected effect of the Nb on cell-bound αMβ2. Binding of the Nb possibly promotes a transition to a more extended conformation (A and 6K). If this influence of the Nb affects a rate-limiting step with respect to presenting a high-affinity binding site for iC3b, it may explain the agonist behavior of the Nb. This would also agree with the somewhat higher dosage requirement for inducing the agonistic effect  compared with expectations from the formal affinity of hCD11bNb1 for isolated HP (KD ∼1 nM). In the solution-based protein interaction assays with our αMβ2 HP, this putative membrane-dependent unbending effect on αMβ2 conformation is, of course, not a factor. Here, hCD11bNb1 may either be neutral or act as a weak stabilizer of the αMI closed conformation, which together with steric hindrance exerted on the C3d or the iC3b thioester domain explains the observed blocking of iC3b and C3d binding. Nevertheless, if induction of αMβ2 unbending accounts for the agonistic effect of hCD11bNb1, it is surprising that the effect also manifests itself in the presence of Mn2+, which conformationally activates integrins. However, in agreement with our proposal, the influence of the Mn2+ is mainly through binding to a metal-binding site adjacent to the βI MIDAS, and occupation of this site with Mn2+ may not lead to a fully extended integrin unless high concentrations of ligand are present as was noted for αLβ2 . The discrepancy between this prediction and the cell-based assay suggests that iC3b binding to the receptor is more dynamic than apparent from our crystal structure of the C3d–αI core complex , a small molecule that stimulates leukocyte αMβ2 interaction with ICAM-1 and iC3b-presenting cells . Animaldes iC3b , with ICLama glama was immunized with the αMβ2 HP by Capralogics , and the peripheral blood lymphocytes were isolated from a blood sample. The RNA was purified from these lymphocytes and used to prepare a complementary DNA library. The region corresponding to the variable domain of heavy-chain only antibodies were cloned into a phagemid vector by PCR, and phage display was used to select Nbs specific toward the αI domain of αMβ2. Escherichia coli TG1 cells harboring the phagemid vectors were coinfected with the VCMS13 helper phages and grown for 16 h at 30 °C to generate Nb-presenting phages. Meanwhile, one well in a microtiter plate was coated with 1 μg of αMβ2 αI domain in 100 μl PBS and 3 mM MgCl2. The well of the microtiter plate was subsequently blocked by addition of PBS and 3 mM MgCl2 supplemented with 2% (w/w) bovine serum albumin (BSA). Next, 3 × 1012 Nb-presenting M13 phages were added to the well, and the plate was incubated for 1 h at room temperature to allow binding of phages to the αI domain. Next, the well was washed 15 times in PBS, 3 mM MgCl2, 0.1% Tween-20, and 15 times in PBS and 3 mM MgCl2 to remove unbound phages. The αI domain–binding phages were liberated through competitive elution by addition of a 100-fold molar excess, to αMβ2 αI domain, of recombinant C3d in PBS and 3 mM MgCl2. The eluted phages were amplified in the ER2748/TG1 strain E. coli and provided the basis for the second round of selection, performed similarly, however only using 0.1 μg αMβ2 αI domain for coating. ELISA was used to identify Nbs binding the αMβ2 αI domain. To this end, an ELISA plate was coated with 100 μl of 0.1 μg/ml αMβ2 αI domain in PBS and 3 mM MgCl2. Meanwhile, in a 96-well format, single phage–infected colonies were inoculated LB and grown at 37 °C for 6 h followed by induction of Nb expression by addition of isopropyl β-d-1-thiogalactopyranoside to a final concentration of 0.8 mM. The cells were grown for 16 h at 30 °C, then pelleted, and the Nb-enriched supernatant was transferred to the ELISA plate. The plate was incubated for 1 h followed by six washes in PBS, 3 mM MgCl2, and 0.1% Tween-20. Then, 1:10,000 diluted E-tag-horseradish peroxidase antibody (Bethyl) was added, and the plate was incubated for 1 h. The plate was washed and developed using 3,3′,5,5′-tetramethylbenzidine, until a clear signal was obtained. About 1 M HCl was added to stop further development, and the absorbance at 450 nm was measured. Unique Nbs were identified by sequencing and subsequently cloned into the bacterial expression vector pET-22b(+).The hCD11bNb1 Nb was selected as previously described . BrieflyMβ2 HP was produced as previously described . The protein was subsequently applied to a 1 ml StrepTactin column  yielding pure αMβ2 HP. The affinity tags and coiled coil domains were removed by addition of the 3C protease, and a final polishing step was performed using SEC into 20 mM Hepes (pH 7.5), 150 mM NaCl, 5 mM MgCl2, and 1 mM CaCl2. Recombinant αI domain was purified as described , and 150 mM NaCl. The mix was incubated for 30 min on ice and then applied to a 24 ml Superdex 75 increase  column equilibrated in 20 mM Hepes (pH 7.5) and 150 mM NaCl. For analysis of the inhibition, 170 μg αI domain and an equimolar amount of C3d were incubated for >5 min on ice in the presence or the absence of a twofold molar excess of hCD11bNb1 in a reaction buffer containing 20 mM Hepes (pH 7.5), 150 mM NaCl, and 2 mM MgCl2. The mix was next applied to a 24 ml Superdex 75 increase column equilibrated in 20 mM Hepes (pH 7.5), 150 mM NaCl, and 2 mM MgCl2.For analysis of hCD11bNb1: α4 and 0.1 M Bis–Tris (pH 6.5). The crystals were soaked in reservoir solution supplemented with 30% glycerol before being flash frozen in liquid nitrogen. The data were collected at BioMAX (MAX IV) at 100 K and processed with XDS , 150 mM NaCl, 5 mM MgCl2, and 1 mM CaCl2 was mixed with a 1.5-fold molar excess of hCD11bNb1 to a final complex concentration of 9 mg/ml. Crystals were grown at 19 °C by vapor diffusion in sitting drops made by mixing the complex in a 1:1 ratio with reservoir containing 1.25 M sodium malonate, 76 mM Hepes (pH 8.0), 24 mM Hepes (pH 6.5), and 0.5% Jeffamine ED2001 (pH 7.0). The crystals were soaked in a saturated sodium malonate solution before being flash frozen in liquid nitrogen. The data were collected at BioMAX at 100 K and processed with XDS (Xβ2 (Protein Data Bank [PDB] entry: 4NEH) and βI domain of αLβ2 (PDB entry: 5E6S) in Phaser  were first washed for 2 min, followed by a 5 min loading step where hCD11bNb1 at 5 μg/ml was loaded on the sensors. Subsequently, the sensors were washed for 30 s and then baselined for 2 min. Association to αMβ2 HP  was followed for 3 min, followed by a 5 min dissociation step. The binding assay with the αMβ2 αI domain was performed in the same manner, except that the association was followed for 300 s, and that the concentrations used were 25, 12.5, 6.25, 3.135, 1.6, 0.8, and 0 nM. All experiments were performed in triplicates. The 0 nM measurements were subtracted from all data series before fitting to a 1:1 Langmuir binding model. The association was modeled as: R(t) = Rmax([αMβ2]/([αMβ2] + KD)(1−exp(−t·(kon·[αMβ2] − koff))), KD = kon/koff, and the dissociation was modeled as a first-order exponential decay, R(t) = R(300)·exp(−koff(t − 300 s)).All BLI experiments were performed on an Octet Red96 (ForteBio) at 30 °C and shaking at 1000 rpm. The running and wash buffer is 20 mM Hepes (pH 7.5), 150 mM NaCl, 5 mM MgClMβ2 binding, the streptavidin biosensors (ForteBio) were first washed for 2 min in running buffer supplemented with 1 mg/ml BSA, before biotinylated avi-tagged hCD11bNb1 at 5 μg/ml were loaded on the sensors for 5 min. The sensors were then washed for 2 min in running buffer supplemented with 1 mg/ml BSA, before being baselined for 2 min. Thereafter, association between 20 nM αMβ2 HP alone or 20 nM αMβ2 HP preincubated with 10-fold molar excess of hCD11bNb1 mutants I29A, N30A, F32A, F54A, N101A, or WT hCD11bNb1 was followed for 5 min. Subsequently, the dissociation was followed for 5 min.For the competition assay assessing the ability of different hCD11bNb1 mutants to compete with WT hCD11bNb1 for αMβ2 αI, anti–penta-HIS sensors were washed for 5 min in 20 mM Hepes (pH 7.5) and 150 mM NaCl. The hCD11bNb1 at 5 μg/ml was loaded onto the sensors, followed by a 2 min wash step and a 2 min baselined step. The association of hCD11bNb1 to murine αI  or 50 nM human αI was followed for 5 min followed by a 5 min dissociation step. The 0 nM measurement was subtracted from all data series. This experiment was performed in duplicates.For analysis of the interaction between hCD11bNb1 and murine α2, and 1 mM CaCl2. Streptavidin was immobilized on a CMD500M chip  to 200 response units. Next, biotinylated iC3b was injected on one flow cell in excess, saturating the chip surface. For competition experiment, αMβ2 at 1.25 to 100 nM was injected in either the presence or the absence of a 1.5-fold molar excess of hCD11bNb1. Upon the competition experiment, 50 mM EDTA, 1 M NaCl, and 100 mM Hepes (pH 7.5) were injected over the chip to regenerate the surface.The SPR experiment was performed on a Biacore T200  instrument as described . The sysTWO; Refeyn Ltd) (Mβ2 HP and iC3b were diluted immediately prior to measurements in 20 mM Hepes (pH 7.5), 150 mM NaCl, 5 mM MgCl2, and 1 mM CaCl2 to a concentration of 10 nM. For 1:1 complex formation, αMβ2 HP and iC3b were mixed in a 1:1 M ratio, whereas αMβ2 HP and hCD11bNb1 were mixed in a 1:10 M ratio. The influence of hCD11bNb1 on αMβ2 HP–iC3b complex formation was measured using molar ratios of hCD11bNb1 to αMβ2 HP . The recorded videos were analyzed using DiscoverMP  to quantify protein-binding events. The molecular weight was obtained by contrast comparison with known mass standard calibrants measured on the same day.The measurements were performed on glass coverslips and recorded on a mass photometer (MPeyn Ltd)  for 60 tMβ2 was investigated by use of K562 cells with a recombinant expression of αMβ2, or, as a control, αXβ2. For binding under conditions approaching equilibrium, αMβ2/K562 cells were cultured and treated with fluorescence-conjugated iC3b as described (2+ and 1 mM Mg2+ or as further supplemented with 1 mM Mn2+ to activate integrin ligand binding. Following 45 min of incubation with 10 μg/ml Alexa Fluor 488-conjugated (iC3b∗) together with 0, 1, 5, or 10 μg/ml of either hCD11bNb1 or an unrelated control (Ctrl) Nb specific for complement C4 called Nb10 (M ICRF44 (The binding of iC3b by cell-expressed αescribed . BrieflyMβ2/K562 or αXβ2/K562 cells was tested in a centrifugation-based assay described earlier (2+ and Mg2+ or with a further addition of 1 mM Mn2+ to activate integrin ligand binding. Nbs were added in concentrations of 0, 1, 5, or 10 μg/ml for either buffer condition. Following incubation for 10 min at 37 °C, the cells were centrifuged at 10g for 5 min and read in a fluorescence plate reader. The centrifugation and plate reading were repeated at 30g, 50g, and 100g.To investigate the influence of hCD11bNb1 under cell adhesion with a mimetic of the shear stress–influencing cells under physiological conditions, adhesion of α earlier . BrieflyMβ2 complex and hCD11bNb1 are available at the PDB as entries 7P2D and 7NP9.Coordinates and structure factor for the hCD11bNb–αThis article contains The authors declare that they have no conflicts of interest with the contents of this article.


The purpose of this paper is to evaluate the nutritional, phytochemical, rheological, technological, and sensory properties of wheat flour dough and bread under a replacement of lupin flour at level 10, 20, and 30%. In this sense, the proximate composition, fatty acids profile, the content in total polyphenols content (TPC), antioxidant activity (AA), and flavonoids content (TFC) of lupin; wheat and flour composites; and the bread obtained from them were determined. The rheological properties of the dough using the Mixolab system were also evaluated. The results showed an improvement in the nutritional properties of bread with addition of lupin in the composite flour, especially in terms of proteins, lipids, and mineral substances and a significant increases of functional attributes, such as TPC, TFC, and AA, which recorded the highest values in the bread with 30% lupin flour . The decrease of lupin bread volume compared to wheat bread ranged between 0.69–7.37%, porosity between 6.92–35.26%, elasticity between 63–70%, and H/D between 3.17–19.05%. The rheological profile of the dough obtained with lupin flours indicates a moderate stability and proper kneading behavior. The sensory analysis was also performed in order to identify the consumer’s acceptability regarding this type of bread. According to a 5-point hedonic scale, the most highly appreciated was the bread with 10% lupin flour, which obtained mean scores of 4.73 for general acceptability as compared with control bread (4.43). Lupinus spp.) is a legume used as a raw material in food and feed production. Its many nutritional and health-promoting benefits have increased its popularity and consumption in recent years [Lupin , Poland (261.5 metric kilotons), and Russia (103.8 metric kilotons) [Of the more than 200 species, in addition to all wild varieties, there are species cultivated for human consumption, others as ornamental plants, and most as animal feed. The progress of genetics in the twentieth century has contributed to the complete domestication of lupin species by hybridizing those with weak alkaloids and those with soft seeds, giving rise to new varieties that are sweet and more suitable for human consumption .Lupinus albus, white lupin; Lupinus luteus, yellow lupin; Lupinus angustifolius, blue lupin) are used in food, especially in the Mediterranean area. Over the last 20 years, researchers have looked to use lupin as a substitute for soybeans in vegetable production, with Australia  and Germany (EU level) being in first place. In these countries, lupin and soybeans are grown alternately [Certain varieties of lupin . In terms of nutritional benefits, lupin seeds are an alternative to soy, as they are non-genetically modified organisms. Especially in this second direction of exploitation, namely in healthy food, sweet lupin can be a solution to increase income for owners of small areas that are dedicated to organic farming .L. luteus to 18.9 g/100 g dw in L. mutabilis. Lupin is rich in in protein (up to 39%), with a protein content four times higher than in wheat grains. It also has one of the highest fiber concentrations (32%) and contains a very small content of starch. Lupin does not contain cholesterol [The proximate composition of raw lupin depends by genetic and agronomical factors, and the composition of lupin can be affected by water stress; e.g., lipid content was reduced by half in conditions of water stress . The lipLupin is processed into various forms, as it is included in bread (which gives it a very pleasant taste) and various pastries but also in meat, sausages, and drinks, and its use is expected to increase significantly in the coming years as resources become more limited. Lupin berries contain proteins that can be used to produce meat and dairy substitutes, as they are suitable for all requirements for use by vegetarians and more.Lupin flour might be integrated in bread formula in different forms: dehulled or hulled flour, hydrolysates or protein isolates, germinated or fermented flour, and as single- or multi-pulses blends . The addAlthough the literature  suggestsLupinus albus. Wheat flour (WF) type 550 was purchased from Auchan supermarket in Timisoara, Romania. Based on the literature studies [Lupin organic flour (LF) produced by Dried Fruits Suppliers was purchased from VitaMix40 shop in Timisoara, Romania, and was obtained from the sweet lupin seeds variety  studies  and our  studies ,17,18,19The proximate composition was determined in accordance with guideline of the Association of Official Analytical Chemists AOAC 2000) standard method [00 standaBy summing up the caloric intake produced by the individual nutrients , the energy value of the products was determined taking into account the following correlations: 1 g lipids = 9 kcal, 1 g carbohydrates = 4 kcal, and 1 g proteins = 4 kcal.From each sample, 1 g was weighed and placed in containers lids over which 10 mL of 70% ethanol  was added. The containers were closed and shaken for 30 min using the hot plate shaker . After stirring, the extracts were filtered through a Whatman filter paper .The total phenolic content (TPC) of flour composites and breads with different percentages of lupin flour was analyzed according to the modified Folin–Ciocâlteu method . The resThe method presented by  was usedcontrol and Asample are the absorbance values of the control and the tested samples, respectively.In order to determine the antioxidant activity of flour composites and bread, the method described by Ciulca et al. (2021)  was usedThe assay of macro and microelements content both for flour composites and bread was carried out by atomic absorption spectroscopy (AAS) using Varian 220 FAA equipment after calcination of the samples. Briefly, 3 g of each sample were burned using calcination furnace , at a temperature of 650 °C. The white ash obtained was dissolved in HCl 20% and further used to determine macro- and microelements. For calibration curve, a mix standard solution (ICP Multi Element Standard solution IV CertiPUR) was used. The minimum detection limits (MDL) for analyzed elements were 0.02 ppm for Mg and K; 0.06 ppm for Fe, Cu, Zn, and Mn; and 0.03 ppm for Ca. The results were expressed in ppm. All determinations were made in triplicate .Fatty acid profile was determined after derivatization as fatty acid methyl esters (FAME) according the method described by Posta et al. (2022) .Fatty acids were identified based on the NIST 05 spectrum library using peak area normalization method by relating the peak area corresponding to a given compound to the total area of all peaks. All the analyses were conducted in three replicates. Saturated fatty acids (SFA) were calculated based on the sum of C4:0–C24:0, monounsaturated fatty acids (MUFA) were calculated as sum of C16:1–C22:1, and polyunsaturated fatty acids (PUFA) were calculated as sum of C18:2, C18:3, and C20:4. Unsaturated fatty acids (UFA) were calculated as sum of MUFA and PUFA.On the basis of the identified fatty acids, the atherogenic index (AI) and the thrombogenic index (TI) were calculated using the following equations :AI = [C1The quality parameters such as moisture content, acidity, volume, porosity, springiness (elasticity of core), and the height/diameter ratio were determined according with SR 91:2007 . The resRheological and sensory properties are of major importance in the acceptability of a novel food product by consumers. The rheological properties of wheat and lupin flours and also of flour mixes flours were analyzed using Chopin Mixolab test  using the “Chopin+” protocol . A quantity of 50 g of sample was placed into the Mixolab bowl and mixed. After mixing the solid part, the necessary water was added by the equipment to obtain an optimal consistency. During the tests, the running parameters of the Mixolab equipment are: -80 rpm mixing rate;-First plateau: time 8 min, temperature 30 °C, gradient 4 °C/min;-Second plateau: 7 min, temperature 90 °C, gradient 4 °C/min;-Third plateau 50 °C, 5 min .The parameters evaluated from the Mixolab profile were: water absorption; dough development time; stability (mixing resistance of dough); maximum torque during mixing (C1); weakening of the protein (C2), which appears due to mechanical stress as the temperature rises; rate of starch gelatinization (C3); minimum torque during the heating period (C4); and torque after cooling at 50 °C (C5). Other parameters determined by Mixolab were protein-weakening speed under heating effect ; starch-gelatinization speed (beta slope); enzyme-degradation speed (gamma slope); cooking stability (C4/C3); and starch retrogradation at cooling stage (C5–C4), which represents the shelf-life of the final products .Bread samples WBL10, WBL20, and WBL30 were evaluated by a panel consisting in 44 untrained assessors  between the ages of 19 and 52, non-smokers, ad without known cases of food allergies. The slices of bread, with the crust, were presented (1 cm thick) on cardboard plates, encoded in double-digit characters, and served in random order under normal lighting conditions and at room temperature. To evaluate the consumer’s acceptance, a five-point hedonic scale was used [Panelists were asked to evaluate the sensory attributes of the samples, including appearance, color, texture, flavor, taste, and general acceptability based on their liking degree. The ranges of score and acceptability level were as follows: 1.00–1.49 = not acceptable (NA); 1.50–2.49 = slightly acceptable (SA); 2.50–3.49 = moderately acceptable (MA); 3.50–4.49 = acceptable (A); and 4.50–5.00 = highly acceptable (HA) . t-test  using Microsoft Excel 365. Differences were considered significant when p-values < 0.05. All determinations were made twice or in triplicate depending on the method, as is presented in each subchapter of materials and methods, and the results are reported as mean values ± standard deviation (SD). Differences between means were analyzed with a one-way ANOVA, followed by multiple comparison analysis using the The results presented in It is observed that there are significant differences in the protein, lipid, and mineral content of lupin flour (LF) and wheat flour (WF) that are reflected in the proximate composition of mixed flours (WFL). LF, like other legumes, is characterized by a significant protein intake (30.95%) compared to WF (12%), lipid content (12.42% LF and 0.32% WF), and macro- and microelements intake (3.67% LF compared to 0.66% WF), which recommends LF as a functional matrix in baking. The moisture level of the samples falls within the same range of values, without significant differences recorded for the flour composites. The carbohydrate content was lower in the LF sample (45.7988%) compared to WF (80.105%), contributing to the decrease of the carbohydrate content of flour composites even with a minimal addition of LF in WF.The increase in protein fraction by addition of LF in WF varies between 14.67–52.92% in flour composites and between 13.10–58.75% in composite breads, respectively. In the same way, the lipid content increased between 418.75–1156.25% in flour composites reported with the initial content in WF and between 170.59–185.29% in bread composites compared with white wheat bread.The bread composites variants (WLB) are distinguished by a protein, lipid, and mineral content superior to the control bread, and these hardly increased with the proportion of LF added to the WF. Significant differences in protein content are noted in the case of the addition of 10 to 30% LF in bread composition. The lipid content is tripled by the substitution of WF with 10–30% LF, but there are no significant differences in the case of composite bread variants (WFL10–WFL30 and WBL10). The mineral substances in the bread obtained with flour composites increase with the addition of LF, with significant differences compared to the control bread being registered in the case of the addition of 20 and 30% LF. However, the carbohydrate content is significantly lower in the case of bread with flour composites.Lupin flour is widely used in various foods in bakery and confectionery products, protein concentrates, and other industrial products due to its nutritional quality and its high functional properties ,32. The Our study aimed to obtain three prototypes of functional bread with the addition of 10%, 20%, and 30% lupin flour. The comparative analysis was carried out to explain the impact of different proportions of LP added to the WF on the proximate composition of breads. The bread samples studied had humidity content between 32.86% and 37.92%. Similar results were reported by Wandersleben et al. (2018)  for lupiVegetable proteins are increasingly sought after lately due to their content in essential amino acids, which are especially important for a balanced diet. Since WF is low in protein , LF suppIn addition to a significant increase in protein content, bread with the addition of LF provides a significant intake of lipids. There was an increase from 0.34% in the case of the WB samples: 0.92% for WB1, 0.94% for WB2, and 0.97% for WB3.A trend of increasing lipid content for bread with the addition of LF was also reported by Previtali et al. (2014)  and simiOur results show that the ash content in the samples of lupin flour bread slightly increased from 0.74% for WB to 0.77% for WB1, 1.15% for WB2, and 1.34% for WB3. This increase is due to the relatively high content of mineral substances in lupin flour (3.67%). Similar results were mentioned by Wandersleben et al. (2018) , who repThe carbohydrate content recorded was 52.34% for WB, the values decreasing with the increase in the proportion of lupin flour as follows: 52.21% for WBL10, 51.73% for WBL20, and 51.44% for WBL30. A lower carbohydrate content in lupin bread was also reported by Wandersleben et al. (2018)  in theirAnother advantage of adding LF to bread is to increase the energy value from 243.23 kcal/100 g for WB to 251.99 kcal/100 g for WBL10, 250.13 kcal/100 g for WBL20, and 242.48 kcal/100 g for WBL30 without increasing the carbohydrate content. The same trend was reported in the case of fortification of bread with hemp flour .Phytochemical profiles of lupin flour composites and bread  are presented in the The obtained results shown that the content of total polyphenols (TPC) increased with the level of LF added in the composite samples. The TPC content is more than double in LF compared to WF, with significant differences regarding this parameter being recorded between the flour composites and breads.The recorded increases in flour composites compared to the WF varied between 5.58–58.99% for TPC, between 15.48–56.99% for TFC, and between 32.88–55.47% for AA. The same pattern was highlighted when wheat bread was fortified with LF. The increases of functional parameters in the bread composites compared with WB were 35.86–140.64% for TPC, 33.02–166.04% for TFC, and 15.60–79.03% for AA.It is also worth noting that the TPC content in bread samples is lower than the TPC content in flour composites. Thus, in the case of flour samples, it can be seen that the highest TPC content was found in WFL30 (85.41 ± 1.94 mg GAE/100 g sample), while the lowest value was recorded for the WF control sample (53.72 ± 0.38 mg GAE/100 g). In the case of bread samples, the highest TPC content was found in WBL30 (76.50 ± 0.70 mg GAE/100 g sample), while the lowest value was recorded for the WB control sample (31.79 ± 0.58 mg GAE/100 g). The total flavonoid content (TFC) showed the same pattern as the TPC profile. Hence, the TFC was maximal in the LF and minimal in the WF. Furthermore, the TFC recorded in the bread samples was lower than the TFC recorded in the flour samples. Thus, in the case of flour composites, the TFC was within the limits of 4.65 ± 0.07 mg QE/100 g and 12.36 ± 0.11 mg QE/100 g, with the highest value being found in LF, while the lowest value was recorded for the WF control sample. In the case of flour mixtures, the TFC content increased in a statistically significant way with addition of the LF content due to the high content of flavonoids in lupin flour.In the case of bread samples, the TFC content varied within 3.21 ± 0.06 in WB and 8.54 ± 0.19 mg QE/100 g in WBL30. Similar with the TPC profile, the TFC decreased in the case of bread samples compared to the flour samples from which they were prepared. Statistically significant differences were recorded within the TFC content of bread samples with a different percentage of lupin.The same trend measured for TPC and TFC was maintained in the antioxidant activity (AA) profile. In the case of flour samples, the AA values were within 52.98 ± 0.24% and 93.37 ± 1.53%. The highest value was recorded for LF (93.37 ± 1.53%) and the lowest value for WF (52.98 ± 0.24%). In the case of flour composites, the AA increased with the percentage of LF added and is correlated with the high AA of LF (data not shown). Statistically significant differences were detected within all composite and non-flour composites.In the case of bread samples, the AA was within the limits of 30.71 ± 3.82 and 54.98 ± 1.21%, the highest value being measured for WBL and the lowest value for the WB control sample. As TPC and TFC profiles, the AA decreased in bread samples compared to the flour samples from which they were prepared.Lupin flour is a good source of polyphenols, and this is due to the high content of polyphenols reported in lupin seeds . SeveralDalaram (2017)  reportedThe TPC content of analyzed breads with different levels of LF varies between 43.19 and 76.49 mg GAE/100 g. The study regarding the improvement of functional cake formulation with fermented lupin powders highlighted that the TPC decreased by addition of LF and varies between 220–264 mg GAE/100 g in cakes depending on the content of LF. The same author reported a TPC content in fermented lupin powder of 298 mg GAE/100 g . The higThe TFC varies in flour composites between 46.50–73.03 μg/g and between 42.70–85.41 μg/g in composite breads. Results in the same range of values were reported by other authors: 12.40–16.60 μg/g  and 108.The processing of lupin seeds influences the phytochemical profile. During debittering, the content of tocopherols and bound flavonoids slightly increased, while free phenolics and bound phenolic acids decreased by 76.2% and 50.1%, respectively. The extrusion of lupin seeds slightly increased TPC, but the spray-drying process diminished TPC .In Magnesium (Mg) is the most abundant macroelement in the analyzed samples and varies between 124.67 ± 5.66 mg/kg in WB and 783.33 ± 14.14 mg/kg in LF. Statistically significant differences were found both in terms of Mg content in lupin, wheat, and flour composites but also in the bread obtained.Magnesium is a mineral that plays an essential role in the optimal functioning of the body. More than 600 enzymatic reactions depend on it, including energy metabolism and protein synthesis. Magnesium is needed for calcium and potassium ion transport, muscle contraction and relaxation, neurotransmitter release, protein biosynthesis, cellular energy production, mitochondrial function, cell membrane stabilization, transmembrane ion flow, genome stability, bone development, and glucose homeostasis. The National Institutes of Health recommends that the daily magnesium intake of the healthy population be over 400 mg for men and over 310 mg for women depending on age.Our results show that the addition of LF (Mg content 78.3 mg/100 g) in the flour composites and breads leads to the enhancing of Mg content, with the maximal content of Mg being recorded in the WFL30 and WBL30 samples. Similar results were reported by other authors regarding the content of Mg in LF: 33.93 mg/100 g , 82.61 mThe calcium content (Ca) in the WFL10 (226.00 ± 6.36 mg/kg) and WFL20 (244.64 ± 5.65 mg/kg) composite flour samples did not show significant differences from WF (225.33 ± 6.60 mg/kg). The LF recorded the highest Ca content (290.00 ± 7.07 mg/kg) without significant differences related to WFL30 sample (287.67 ± 6.48 mg/kg). WB content was 129.00 ± 4.24 mg/kg, lower than the WBL that recorded values between 262.00 ± 5.66 mg/kg (WBL10) and 533.00 ± 10.61 mg/kg (WBL30).Calcium plays an essential role in the human body, ensuring the normal functioning of the osteoarticular system, bone density, and the functioning of muscle and nerve cells. A vital macro-element for humans, calcium is found in many foods, but its fixation in bones also depends on the presence of other vitamins and minerals.Our results regarding the Ca content in flour composites and breads are in agreement with previous studies that reported 37.69 and 38.15 mg Ca/100 g lupin flour depending on the flour type . AdditioPotassium content (K) in flour composites varied in the range 70.32 ± 1.41 mg/kg and 165.33 ± 5.66 mg/kg and increased with LF addition. Significant differences were observed between WB (162.33 ± 4.24 mg/kg) and composite breads, but no significant statistical differences were recorded between WBL10/WBL30.Potassium is an essential element for the balance of electrolytes and body fluids. It is also the third most present mineral in the body and is needed for the functioning of many organs, including the heart, kidneys, brain, and muscle tissue. The content of K in LF was found by Aslan et al. (2019)  to be 53The debittering process influences the content of K in LF. Therefore, K in bitter LF was found to be 980.55 mg/100 g, while in debittered LF, it was 23.15 and 27.82 mg/100 g depending of the process type . In breaThe first studies on the importance of the presence of zinc in the diet appeared after the 1960s, when, in 1961, the clinical deficiency of zinc was described for people with a poor diet in products containing this mineral. An adult needs a maximum of 3 g of zinc daily. Over 60% of this amount is used to mineralize the bones that support the skeleton, 30% is used for the bones in the joints, and the remaining 10% is used in the metabolism of the liver and the structure of the epidermis. The Zn content in our samples was 1.78 mg/100 g for LF and 1.20 mg/100 g for WF. The addition of LF increased the content of Zn until 1.4 mg/100 g in bread with 30% FL. Similar results were obtained by other authors: 0.94 mg/100 g in LF and 1.16 mg/100 g in bread with 20%FL  and 1.29The copper (Cu) content determined in the analyzed flour samples was in the range of 3.21 ± 0.21 mg/kg and 3.46 ± 0.09 mg/kg and in the bread samples was in the range of 0.60 ± 0.01 mg/kg and 1.67 ± 0.06 mg/kg.Copper is an essential microelement for the body; along with iron, it plays an important role in the formation of red blood cells and in maintaining the health of blood vessels, nerves, bones, and the immune system. Literature studies reported 0.23–0.71 mg/100 g Cu in LF , which iThe copper level in the LF was found to be 3.46 ± 0.09 mg/kg but was not detectable in WF. The supplementation of WF with LF increased the content of Cu both in flour composites and breads.Between analyzed microelements, manganese (Mn) recorded the highest level in LF (136.74 ± 4.99 mg/kg), while WF content was only 0.25 ± 0.001 mg/kg. The addition of LF in composite flour increase the level of Mn in bread, reaching the highest level in WBL30 (117.37 ± 6.55 mg/kg) compared to 2.95 ± 0.15 mg/kg in WB.Manganese is a trace element that forms part of mitochondrial enzymes and also activates many enzymes. Thus, manganese plays an essential role in lipid and carbohydrate metabolism, bone tissue formation, and reproductive processes. A high content of Mn was found in the sample of LF analyzed in our study (13.60 mg/100 g) and low content in WF (0.25 mg/100 g). The addition of LF in bread enhanced the Mn content until the 11.70 mg/100 g level for the WBL30 sample. Further, 10.56 mg Mn/100 g was detected in cake obtained with 30% LF  and 12.4The highest level of iron (Fe) was recorded in LF (22.00 ± 1.41 mg/kg) compared with WF (0.51 ± 0.01 mg/kg). In composite bread, the level of Fe varied between 124.67 ± 5.66 mg/kg in WB and 403.00 ± 10.32 mg/kg in WBL30, with significant statistical differences between samples.Iron is an essential mineral for the proper functioning of the body and for maintaining long-term health. According to statistics, about 20% of women, 50% of pregnant women, and 3% of men lack iron in the body, and deficiency leads to severe diseases, the most common being anemia. The level of Fe in analyzed samples varies between 2.09 mg/100 g in LF and 1.482 mg/100 g in WBL30. Similar values were reported in LF (6.12 mg/100 g), in bread with 20% LF (2.65 mg/100 g) , betweenZinc (Zn) is the element that was found in higher quantities in WF (23.35 ± 0.50 mg/kg) compared with LF (12.79 ± 0.18 mg/kg).Flour composites nickel (Ni) and chromium (Cr) is minor elements found in WF and LF, and their changes in the flour composites and breads do not influence the mineral composition. The fatty acid composition, SFA, and the UFA (monounsaturated MUFA plus PUFA) content for composite lupin flours and breads are reported in From the analysis of the data obtained, LF has a lower proportion of saturated fatty acids (SFA), with a value of 32.92%, the predominance being palmitic acid (C16:0) (21.38%) and stearic acid (C18:0) (5.50%). The higher content is found in monounsaturated fatty acids (MUFA) (48.03%), predominantly being oleic acid C18:1n9 (40.58%), oleic (C18:1n7) (2.16%), and eicosenoic acid (C20:1n9) (3.52%). As for the polyunsaturated fatty acids (PUFA), they are found in a proportion of 18.95%, the most significant proportions belonging to linoleic acid (C18:2n6) (18.64%). In contrast, for WB, a higher content of SFA was recorded at 36.68%, the most predominant also being palmitic acid C16:0 (22.44%) and stearic C18:0 (12.20%). The proportion of MUFA in WB was significantly lower at 19.44%, predominantly being oleic acid C18:1n9 (17.14%) and eicosenoic acid (C20:1n9) (1.63%), but the proportion of PUFA was much higher (42.50%), and for WB, the predominant proportion was that of linoleic acid (C18:2n6) (40.92%). In terms of flour mixtures, the proportion of SFA is inversely proportional to the LF content, at 39.08% for WFL10 and 37.01% for WFL30. In contrast, the proportion of UFA is directly proportional to the LF content, namely 61.22% for WFL10 and 62.08% for WFL30.As regards the bread samples, it can be noted that the samples containing LF had a lower content of saturated fatty acids compared to the control sample (64.40%), with this content being inversely proportional to the proportion of added LF (37.07% for WBL10 and 36.20% for WBL30 versus 40.49% for WB). Regarding the content of unsaturated fatty acids, their proportion increases with the increase in the content of added LF (62.92% for WBL10 and 63.43% for WBL30 compared to 59.36% for WB). This is due to the low content of SFA (32.95%) in lupin and the high content of MUFA  compared to WB, which recorded a SFA content of 38.68% and MUFA content of 19.44%. Lupin has an interesting unsaturated fatty acid (FA) profile mainly consisting of oleic and linoleic acids and ratios between fatty acids, which confer upon it specific functionalities. Unsaturated fatty acids (UFAs) are essential nutrients, and the n-3/n-6 polyunsaturated fatty acids (PUFA) ratio is considered very important with respect to human and animal nutrition.The similar composition of fatty acids in lupin flour with those detected in our study was also reported by Uauy et al. (1995) , who ideFatty acids composition plays an important role in control of cardiovascular diseases. To evaluate the different effects of the fatty acids, two indices, atherogenic index (AI) and thrombogenic index (TI), were developed in order to characterize the atherogenic and thrombogenic potential of food based on total saturated fatty acids (SFA) or on the polyunsaturated/saturated fatty acids ratio (PUFA/SFA) ,58,59. LThe AI and TI values presented in the Similar values were reported by Chiofalo et al. (2012)  regardinAfter baking, the volume, porosity, elasticity, height/diameter ratio (H/D), acidity, and humidity were determined for all samples according to SR 91:2007 . The expAnalyzing the data obtained, it can be pointed out that the volume, porosity, elasticity, and H/D index were higher in the case of the control sample than composite bread sample with different proportions of lupin flour; however, the products were not excessively flattened . The dec3/100 g) and H/D ratio (0.632) compared to the samples with LF, which registered lower values regarding these parameters.The control sample  registered the highest values in terms of volume  and an elastic core, and when it is pressed, it returns to it initial shape with 70% elasticity, and the H/D ratio is 0.613. Analyzing the porosity, it was found that in the case of the addition of lupin flour in a proportion of 10%, the appearance of the pores is maintained. Bread with 10% lupin flour (WBL10) is well-leavened with a volume of 431 cmThe data showed that by adding LF, the bread H/D ratio decreases, the control sample shows a 0.632 ratio, and the samples with the three proportions of lupin flour recorded an H/D ratio between 0.51 (WBL30) and 0.61 (WBL10) . For valThe data show that the volume and H/D ratio of all samples with the addition of LF were lower than that of the control sample (WB), but the porosity was more pronounced and uniform, the elasticity was better in the sample with 10% lupin flour (WFL10.), and the crust showed a more developed coloration due to the Maillard compounds formed during baking.From the data presented in The compact layers in the core, also known as “bacon layers”, look like a hard, non-porous, sticky mass. The layers appear in the form of horizontal stripes (WBL20) and can have different sizes. Compact layers appear in the center of the core because some of the water vapor formed in the peripheral areas suddenly enters the center due to the high temperature of the oven.Another defect that is observed in the case of bread with the addition of lupin flour is the cracks in the crust and its irregular appearance .The cracks may be on the surface of the shell or appear laterally. In all cases, they are formed due to the exit of fermentation gases from the dough, namely:-When the flours come from sprouted grains or contain too little gluten; the bread crust is less elastic; and the fermentation gases, not meeting sufficient resistance to pressure, come out of the dough and form cracks on the surface of the bread;-When the dough has an increased action of proteolytic enzymes, the resistance of gluten decreases, and the fermentation gases form a large number of small cracks, which greatly degrade the appearance of the bread .The primary parameters  of the mIn The results presented in Water absorption index (WAI) depends on the quantity and quality of the flour components . Higher index provides a higher water absorption capacity. The absorption index is 2 for WF, 7 for WFL10, and increases to 8 with the addition of LF in the bread recipe. Similar values for wheat flour (WAI = 1) were reported by Antanas et al. (2013) [. (2013) , who higMixing index (MI). This index gives information on the behavior of the flour when it is kneaded at 30 °C and expresses the dough’s stability and softness. When this index increases, the dough becomes more stable at kneading. Our results are in line with previous study [us study , namely Gluten+ index (GI) measures the behavior of gluten during the heating of the dough. The higher the index, the more resistant the gluten is to the conditions of the technological process. Gluten resistance is maximum in WFL10 (5) and decreases with the addition of LF in the flour composites. WF has a lower index than WFL10. Similar results were obtained for flour composites from WF and triticale and rye flour [ye flour . Viscosity index (VI). The increase in viscosity during this phase is due to both the amylase activity and the quality of the starch. The higher the index, the higher it is the viscosity of the dough during the heat treatment. The viscosity of the dough is high for WF and decreases with the addition of LF in all analyzed samples (until index 1 for WFL30), which are values that give good dough-processing conditions. A previous study pointed out that the addition of 20% triticale flour in wheat flour decrease the VI from 7 (WF) to 6 in flour composites [mposites . Amylolysis index (AmI). This index depends on the resistance of the dough to diastatic activity. The higher the index, the lower is the amylase activity. Amylase activity is maximal (8) in WF, while for WFL10, there is an index of 7, and for 20 and 30% LF in the composite dough, the AI is 6. WFL30 is distinguished by an increased amylase activity compared to other samples. The same value (7 for AmI) was reported for wheat flour, and a decrease of this index in flour composites is based on rye and triticale flours [e flours .Retrogradation index (RI). Downgrade is due to the behavior of starch during cooling . The higher the index, the shorter the expiration dates. RI for WF is 8 and decreases to 6 with the addition of LF in composite bread. This indicator provides valuable information on the shelf life of lupin bread, which can be kept longer without impairing physico-chemical indices, which gives it economic sustainability.According to the Mixolab profile, five different stages regarding the dough torque depending on the time are presented in the diagrams . The iniThe second stage of the Mixolab profile represents the first stage of heating and corresponds to protein weakening. The combined effect of mechanical stress and temperature induced a decrease in C2 torque, which is the minimum value of torque produced by the passage of dough subjected to mechanical and thermal constraints . CompareIn the third stage, starch gelatinization occurs. Heating the dough induces the swelling of the starch particles, and the viscosity of the dough increases. Cooking stage describes starch behavior and is characterized by following parameters: (i) maximum torque produced during the heating stage (C3); (ii) C4 calculated as a ratio of the torque after the holding time at 90 °C and the maximum torque during heating period; (iii) gelatinization rate (β); and (iv) cooking stability rate (γ) .Torque point C3 expresses the viscosity of the dough on heating. The increase of this parameter highlights the increase of the viscosity of the dough. C4 and β value indicate the content of alpha-amylase in the flour, with the increase of this enzyme producing the increase of the two mentioned parameters . The obtIn the fourth stage of Mixolab profile, the temperature is constantly maintained. During this phase, the dough suffers the double action of mixing and enzymatic attack, observed by a decrease of consistency.The dough cooling (the fifth stage) leads to starch retrogradation, and the stiffness of the cooked dough increases. C5 represents the difference between the torque produced after cooling at 50 °C and heating period. C5 varies between 3.29–2.30, which is at the maximum in case of WF and minimum in WFL30.Evaluation of consumers’ acceptability of lupin bread samples was carried out using sensory evaluation by a panel of 44 assessors  with the help of a five-point hedonic scale. The most highly appreciated was the WBL10 sample with 10% lupin flour, which obtained mean scores of 4.55 for taste and 4.52 for color and 4.73 for general acceptability, , fallingThe control sample (with wheat flour) was rated with scores similar to the WFL10 sample, scoring on a scale between 4.5 and 5, i.e., highly acceptable (HA), for taste and texture and between 3.5 and 4. 49, i.e., acceptable (A), for appearance, color, flavor, and general acceptability. The lowest rates were obtained by WFL30 sample, with 30% lupin substitution registering values between 2.50 and 3.49 (moderately acceptable) for taste and acceptable (3.5 and 4.49) for all other attributes . The resThe addition of different proportions of lupin flour exhibited a substantial effect on the sensory properties of bread samples. The sensory scores for the color of the bread increased once with the incorporation of lupin flour (up to 20% lupin substitution). A light-yellow color given by the natural pigments present in lupin flour was well-appreciated by the evaluators compared to the whitish color of the control sample.The global evaluation from the nutritional, phytochemical, sensory, and rheological point of view of the flour composites fortified with lupin and the bread obtained showed that lupin flour can represent a valid vegetal source in baking for a sustainable economy. The nutritional and functional attributes of wheat bread were enhanced using 10–30% lupin flour, but significant shortening of rheological properties, i.e., dough stability, may cause technological issues. The consumers’ acceptability regarding this type of bread indicated that the most highly appreciated was the bread with 10 % lupin flour, but the bread with the addition of 20–30% lupin flour also obtained good scores on certain sensory parameters. Our study aims to strengthen the attempt at widening the assorted range of vegetal matrices for use in baking in order to find alternative solutions to cereal flour.


Elliptic boundary value problems which are posed on a random domain can be mapped to a fixed, nominal domain. The randomness is thus transferred to the diffusion matrix and the loading. While this domain mapping method is quite efficient for theory and practice, since only a single domain discretisation is needed, it also requires the knowledge of the domain mapping. However, in certain applications, the random domain is only described by its random boundary, while the quantity of interest is defined on a fixed, deterministic subdomain. In this setting, it thus becomes necessary to compute a random domain mapping on the whole domain, such that the domain mapping is the identity on the fixed subdomain and maps the boundary of the chosen fixed, nominal domain on to the random boundary. To overcome the necessity of computing such a mapping, we therefore couple the finite element method on the fixed subdomain with the boundary element method on the random boundary. We verify on one hand the regularity of the solution with respect to the random domain mapping required for many multilevel quadrature methods, such as the multilevel quasi-Monte Carlo quadrature using Halton points, the multilevel sparse anisotropic Gauss–Legendre and Clenshaw–Curtis quadratures and multilevel interlaced polynomial lattice rules. On the other hand, we derive the coupling formulation and show by numerical results that the approach is feasible. Many practical problems in science and engineering lead to elliptic boundary value problems for an unknown function. Their numerical treatment by e.g. finite difference or finite element methods is in general well understood provided that the input parameters are given exactly. This, however, is often not the case in practical applications.If a statistical description of the input data is available, one can mathematically describe data and solutions as random fields and aim at the computation of corresponding deterministic statistics of the unknown random solution. The present article is dedicated to the treatment of uncertainties in the description of the computational domain. Applications are, besides traditional engineering, for example uncertain domains which are derived from inverse methods such as tomography. In recent years, this situation has become of growing interest: In  the so-cApart from the domain mapping method, other methods of describing and solving boundary value problems on random domains have also been considered; by the necessity of being domain mapping free, they can only be directly posed and solved on realisations of the random domain or its boundary. In  for examdered in , where iA further alternative approach based on shape calculus is considered in , 31 for random domain mappingreference domain D. Thus, the randomness is transferred to the diffusion matrix and the loading of the boundary value problemIn this article, we are going to focus on the domain mapping method. Given enough spatial regularity of the random domain mapping, we first prove that the solution is analytically dependent on the random domain mapping also in the mentclass2pt{minimlly from . Therefot}P, cf. .Indeed, when the random domain mapping is given in a parametric formmixed derivatives of Given that these estimates hold for all finitely supported multi-indices with a sufficiently fast decaying see e.g. , 28, 43 see e.g. , 21, yiesee e.g. , 11. In mixed smoothness between the smoothness in the integration variables and the spatial smoothness, see e.g. [When one wants to consider the multilevel versions of the previously mentioned quadratures, one is considering a sparse grid combination technique of the quadrature methods and the spatial discretisation. This requires see e.g. , 19, 27,deterministic subdomain, B, which almost surely is a subset of the domain realisations, where However, while the random domain mapping approach is mathematically natural, it is not necessarily the setting that is directly encountered in practical applications. This mainly stems from the fact that the random domain mapping does not only describe the random domains themselves but also includes a specific point correspondence between the domain realisations. In applications often only a description of the random boundary might be known, however in such cases the quantity of interestdary. In , the autdary. In –16, to eB and treat the rest of the domain by a boundary element method. This is also advantageous, since large domain deformations on coarse discretisations can be handled more easily, as we do not need to mesh the random part of the domain but only its boundary. Moreover, such an approach may also be useful when computing on an unbounded domain.To overcome the necessity of computing such a random domain mapping in this setting, we propose to compute the quantity of interest by performing the calculations on the realisations of the random domains. However, in our setting, care then must be taken that the discretisation chosen is regular enough to ensure that the spatially discretised problems inherit sufficient regularity with respect to their dependence on the boundary description, such that the multilevel quadrature method stays viable. Therefore, we choose to sidestep the generation of a mesh on the random part of the domain First, we extend results regarding the regularity of the domain mapping method for elliptic partial differential equations on random domains from , 28 to aSecond, we propose and discuss using a coupling of the finite element method and the boundary element method as the spatial discretisation in a multilevel quadrature method. This yields an efficient method that only requires a domain mapping to exist, but does neither need to know it nor need to compute it. Thus, it is very applicable to practical problems, where only knowledge of a random boundary description is available, for example, from nondestructive measurements.The rest of this article is organised as follows. Section The contribution of this article is thus twofold:Before we complete the mathematical setting of our model problem, we will introduce the notations used throughout the rest of the article. Especially, for the regularity considerations in Sect. We use For multi-indices Subsequently, we will always equip Let ace, see , which cc can be bounded by a multiple of d, independently of parameters which c and d may depend on. Obviously, For a given Banach space reference domain with boundary D is a bounded and convex domain with Lipschitz continuous boundary—and random domain mapping. Moreover, we require that, for uniformity conditionhold-all domaindeterministic subdomainB that satisfies Let While, by definition, we know that D to For The fact that D instead of considering it on the actual domain realisations Now, since for ow, with  this leaentclass1pt{minimaFrom here on, we assume that the spatial variable see e.g. . We now The random variables We assume that the Therefore, we now can restrict Note that while we restrict ourselves to the stated model problem here to simplify the analysis, the regularity result can be extended. For example, it is not necessary that }y as in , as longentclass1pt{minimaOur aim is to consider quantities of interest that are of the form example .To prove the analyticity of the mapping lts from  to arrivlts from  and usesIn the following subsection we will derive the bounds on the derivatives of the diffusion coefficient and the loading piece by piece by using addition, multiplication and composition of functions with bounds of the formwill use , Lemma 8r non-vanishing multi-indices Let For convenience, we introduce the following notation for this proof: For a multi-index r non-empty blocks. The cardinality is thus also given by the expressionr non-empty blocks, which yields the desired assertionNow, as the expressionWe will use this combinatorial lemma to give the following boundmple, in , which wmentclass2pt{minimmentclass2pt{minimTo provide regularity estimates for the diffusion coefficient mentclass2pt{minimWe have for all By definition we have that s.Next, we supply bounds on the derivatives of the mappings The mapping We start with the mappingsn, using , Lemma 3r-th Fréchet derivative of Next, we consider the mapping can use , Lemma 4r-th Fréchet derivative of k from 1 to r. Now, since we can bound the determinant of a matrix by the product of the norms of its columns, i.e.Finally, we consider the mapping can use , Lemma 4Finally, the use of , Lemma 3s is infinitely Fréchet differentiable withThe mapping We start with the mappingn, using , Lemma 4Moreover, as shown in the previous proof we also have thate use of , Lemma 3Now, these results enable us to show the following regularity estimates for the diffusion coefficient We know for all Because n employ , Lemma 8mentclass2pt{minimThis proves the assertion for D is convex and bounded, or from [D is of class D, It follows from [The unique solution Moreover, this higher spatial regularity also carries over to the derivates The derivatives of the solution B, which describe our random domain, compare Fig. While the results in the previous subsections are valid for general random domain mappings, we will now restrict them according to the remarks made in the introduction. That is, we assume for the rest of the article that we are given a random boundary description, mentclass2pt{minimWe will assume that there is a random domain mapping mentclass2pt{minimB but without needing a mesh on So, to be able to use multilevel quadrature to compute the quantity of interest efficiently, we consider a formulation here, that enables us to compute the Galerkin solution mentclasspt{minima example , 23, and example .D is assumed to be fixed. Of course, when applying a sampling method for  surface mesh, coming for example from some computer assisted design system, which is perturbed by moving control points or mesh vertices, then this immeadiately supplies triangulations on all sampled boundaries.Since the variational formulation is stable without further restrictions, the discretisation is along the lines of . We firs example . Indeed,B and of the surface triangulation of h. For the FEM part, we consider continuous, piecewise linear ansatz functions We define the maximum diameter of all elements of the triangulation of For sake of simplicity in representation, we set Then, introducing the system matricesBy applying standard error estimates for the Galerkin scheme and possibly also the Aubin–Nitsche trick, see for example [10h.We denote the solution of  by \docuB and of uniform triangulations of the boundary B and a given coarse triangulation of the boundary B and To arrive at an efficient solver for the linear system  of equatr system  of equatThe complexity is governed by the BEM part since the boundary element matrices are densely populated. Following , 26, we The crucial idea of the multilevel quadrature to compute the quantity of interest  is to coIf, for example, we assume that there is an , we use , Lemma 7, we use , to see Similarily, if we assume that there is a As these quadrature method examples use For the spatial approximation, we shall use the hierarchy of triangulations introduced in Subsect. xpansion , we may ion, cf. , it is kion, cf. , 27, 37 see e.g. , 43. Esp compare . The quasee e.g. . That ismentclass2pt{minimBy choosing the accuracy of the quadrature in accordance with stead of , the appentclass1pt{minimaccuracy,  must be D to be the ellipse with semi-axis 0.7 and 0.5. We represent its boundary by In our numerical example, we consider the reference domain entclass1pt{minimaB, based on Zlámal’s curved finite elements [B and the boundary elements yielding the discretisations of level 1 to 10, with mesh size L. Since the exact solution is unknown, we use the quantity of interest computed on level The coarse triangulation of elements , consistnce, see  for exammentclasspt{minimaThe computational costs of these choices are shown in Fig. given by , seems te points  there isgiven by , is alsoAs it is seen in Fig. We provided regularity estimates of the solution to elliptic problems on random domains which allow for the application of many multilevel quadrature methods. In order to avoid the need to compute either a random domain mapping or to generate meshes for every domain sample, we couple finite elements with boundary elements. It has been shown by numerical experiments that this approach is indeed able to exploit the additional regularity we have in the underlying problem without causing numerical problems on too coarse grids.