Site-specific labelling of native peptides and proteins: chemical and enzymatic strategies

• Antonio Angelastro,
• Jonathan Bargh,
• Subhajit Guria,
• Victor Laserna and
• Louis Luk

Beilstein J. Org. Chem. 2026, 22, 857–881, doi:10.3762/bjoc.22.67

• product can be reacted with hydroxylamine-containing payloads to afford oxime-linked conjugates (Scheme 3c) [29][30]. Additionally, dibromomaleimides 8 [31][32] and dibromopyridazinediones 9 (Scheme 3d) [33] bearing payloads at the N-position can rebridge cysteines through an addition–elimination

• mechanism. These reagents have been extensively explored for protein conjugates, especially as ADCs [34]. Similarly, divinylpyrimidines 10 [35] and arylenedipropiolonitriles 11 [36] have also been investigated for analogous purposes but via a conjugate addition mechanism (Scheme 3e). Exploiting the unique

• oxidation state of phosphorous, diethynylphosphonites 12 also utilize conjugate addition to provide a versatile three-point conjugation platform [37]. Related technologies have been adapted to link multiple disulfide residues simultaneously. Using bis-dibromopyridazinediones bis-9 [38] or bis/tetra

The trans-influence in gold chemistry from a catalytic perspective

• Manfred Bochmann

Beilstein J. Org. Chem. 2026, 22, 838–856, doi:10.3762/bjoc.22.66

• ^C^N complex 12 (H trans to C) is stable in THF solution at −20 °C but decomposes at room temperature. This instability of 12 may in part also be due to the tendency of the pyridine arm to dissociate; for example, on addition of LiHBEt3 the pyridine is displaced to give the dihydrido complex Li[(N–C

• into M–H or M–C are a mainstay of homogeneous catalysis. Alkyne insertion by a migratory insertion process leads to cis-addition. By contrast, insertions of alkyne into Au–H bonds result in anti (trans)-addition products, which cannot readily be explained by the conventional migratory pathway. To the

• complexes of type 8 can react with acetylenes slowly, in a possibly light-induced radical reaction [49]. The addition of radical initiators such as azobis(isobutyronitrile) (AIBN) reduced the reaction times from days to minutes, with quantitative and completely stereoselective formation of Z-vinyl gold

Unsymmetrical sulfoxides with sterically hindered catechol fragment: synthesis, structure, electrochemical properties, and antiradical activity

• Daria A. Burmistrova,
• Vasiliy A. Fokin,
• Oleg P. Demidov,
• Mikhail A. Kiskin,
• Maxim V. Arsenyev,
• Andrey I. Poddel’sky,
• Nadezhda T. Berberova and
• Ivan V. Smolyaninov

Beilstein J. Org. Chem. 2026, 22, 828–837, doi:10.3762/bjoc.22.65

• , and antibacterial agents [6][7][8]. However, the practical utility of such type of compounds extends beyond biomedical applications. For instance, Michael addition reactions between dithiols and phenolic compounds yield cross-linked, colorless polymer films with universal adhesion and high stability

• ). Addition of the target catechols to a DPPH radical solution leads to a decrease in absorbance at the 517 nm maximum. The antiradical activities of CatH2-S-R and CatH2-SO-R were evaluated through the determination of IC50 and the time to reach the steady-state equilibrium (TEC50) values, together with the

Total synthesis of the capsular polysaccharide repeating unit towards the development of a glycoconjugate vaccine against Klebsiella pneumoniae ST512

• Shuo Zhang,
• Ondřej Daněk and
• Peter H. Seeberger

Beilstein J. Org. Chem. 2026, 22, 821–827, doi:10.3762/bjoc.22.64

• repeating unit {3)-[α-ʟ-Rhap-(1→4)]-α-ᴅ-GalpA-(1→2)-α-ʟ-Rhap-(1→2)-α-ʟ-Rhap-(1→2)-α-ʟ-Rhap-(1→3)-β-ᴅ-Galp-(1→}n (Figure 1) [13]. The chemical synthesis of this molecule is challenging due to the stereoselective formation of the 1,2-cis glycosidic linkage on the galacturonic acid core. In addition, the

Synthesis and structural elucidation of a novel bis-spirooxindole from isatin and ethylenediamine

• Irene Moreno-Gutiérrez,
• Josefa L. López-Martínez,
• Sonia Berenguel-Gómez,
• Irene Torres-García,
• Duane Choquesillo-Lazarte,
• Manuel Muñoz-Dorado,
• Miriam Álvarez-Corral and
• Ignacio Rodríguez-García

Beilstein J. Org. Chem. 2026, 22, 813–820, doi:10.3762/bjoc.22.63

• single-crystal X-ray diffraction. In addition, the isolated diiminoisatin can be independently reduced to the same bis-spirooxindole. These results broaden the scope of isatin–diamine condensations and demonstrate their potential to generate structurally complex spirooxindole architectures under simple

• NaBH4 or by the ethylenediamine acting as a hydride donor. In addition, if the formation of 28 by addition of the enol of 27 to the imine were reversible (and the reduction step irreversible), then the more stable, dipole-opposed C2-symmetric structure for 28 should be dominant, thus explaining the

Knoevenagel condensation of 4,5- and 1,8-diazafluorenes

• Darya S. Cheshkina,
• Christina S. Becker,
• Alina A. Sonina and
• Maxim S. Kazantsev

Beilstein J. Org. Chem. 2026, 22, 803–812, doi:10.3762/bjoc.22.62

• cases when the condensation product precipitated from the reaction mixture (see note d in Table 1), i.e., when the reaction became irreversible. The proposed mechanism for the condensation reaction in the presence of ammonium acetate is shown in Scheme 2 [25]. Accordingly, the addition of diazafluorene

• ). Contrary, both the neutral (2) and protonated (2A’) forms of 1,8-diazafluorene were identified in both solvents (see Supporting Information File 1, Figure S2) with relatively high ratio (2 to 2A’ = 1:0.4 in CD3OD and 1:0.9 in CD3COOD). This equilibrium was reached immediately after the addition of the acid

• the protonation and subsequent addition of a nucleophile (H2O) an intramolecular rearrangement facilitated by the proximity of a neighboring nitrogen atom (in position 1 or 8) occurred (see Scheme 3). Elimination of the aldehyde leads to the formation of 1,8-diazafluorene (2), which can be oxidized

Synthetic study of vic-bromination of diarylacetylenes, easy purification and separation

• Akane Togo,
• Hiyono Suzuki,
• Yuto Akai,
• Makoto Matsumoto,
• Yoshinori Suzuma,
• Hidehiko Kodama and
• Kouichi Matsumoto

Beilstein J. Org. Chem. 2026, 22, 795–802, doi:10.3762/bjoc.22.61

• -osaka, Osaka 577-0056, Japan 10.3762/bjoc.22.61 Abstract E-Selective bromination for diphenylacetylene was established by using the combination of NBS and FeBr3 in CH2Cl2. In addition, easy purification and separation from the crude product were found. When the crude product was treated with heptane

• ; Introduction The addition reaction of bromine to diphenylacetylene is one of basic reactions and is recognized as important, because resulting 1,2-dibromo-1,2-diphenylethylene can serve as a precursor for various molecular transformations in organic synthesis [1][2]. This reaction seems to be simple, but some

• synthesis. In addition, we have found an easy purification and separation method of E and Z isomers of the crude product by using heptane. The method utilizes the difference in solubility of E and Z isomers. Because of this technique, the purification, separation, and scale-up were easy to perform. In this

Halogenated azobenzene acrylates: from efficient solution photoswitching to stable solid-state photochromic materials

• Martina Vachtlová,
• Michaela Fecková,
• Vítězslav Zima,
• Jan Podlesný,
• Milan Klikar,
• Oldřich Pytela,
• Patrik Pařík,
• Jakub Opršal,
• Eliška Juhaňáková,
• Veronika Chrtová and
• Filip Bureš

Beilstein J. Org. Chem. 2026, 22, 782–794, doi:10.3762/bjoc.22.60

• agreement with literature data showing that anisole- and methoxyarene-type systems typically undergo an initial oxidation of the alkoxyaryl unit [29][30][31]. In addition, possible oxidation involving the aryl halide moiety generally requires a more positive potential [28]. Taken together, these data

Design, synthesis, and biological evaluation of FXR/ASK1 dual-target modulators

• Xi Zhang,
• Jingyan Wang,
• Ziqiang Zhao,
• Caiyi Wang,
• Zenghui Ye,
• Wei-Yuan Ma,
• Jian-Xing Xu and
• Fengzhi Zhang

Beilstein J. Org. Chem. 2026, 22, 771–781, doi:10.3762/bjoc.22.59

• -luciferase reporter assay in CHO cells cultured for 24 hours following addition of GW4064 and test compounds. Compared to the control group, **p < 0.01 and ns indicate no significant difference, with control; DMSO serving as the control group. ASK1 inhibition of all compounds. Results of the ADP-Glo™ kinase

Preparation of 3-(alkylamino)imidazo[1,2-a]pyridine-2-carbaldehydes via Kornblum oxidation and unexpected ring-opening reactions of the corresponding alcohols under oxidative conditions

• Sandile J. Mkhize,
• Memory Zimuwandeyi,
• Manuel A. Fernandes,
• Amanda L. Rousseau and
• Moira L. Bode

Beilstein J. Org. Chem. 2026, 22, 763–770, doi:10.3762/bjoc.22.58

• esters, had been obtained from 2-aminopyridines 9a–d while no reaction was observed for 2-aminopyridine 9e (Scheme 1). We reasoned that at the relatively small scale of the reaction (≈350 mg aminopyridine) and because a period of 30 min stirring of all reactants had been allowed prior to addition of the

• taken place before addition of the other reagents. Increasing the amount of acid catalyst to 0.2 equiv significantly increased the yield of the ester products 13, although the yields were still modest (Table 1). A further increase to 0.3 equiv of acid catalyst did not lead to further yield improvement

Synthesis and biological evaluation of new brassinosteroid analogs with C-22 benzoate function

• María Núñez,
• Camila Escobar,
• Mario Párraga,
• Mauricio Soto,
• Luis Espinoza-Catalán,
• Katy Díaz and
• Andrés F. Olea

Beilstein J. Org. Chem. 2026, 22, 753–762, doi:10.3762/bjoc.22.57

• in Table 2. The data indicate that derivatives with a OH group at C-3 (TE analogs) are much more active than derivatives with a carbonyl group in this position (3-DT analogs). However, the addition of another OH group at C-2 (CAT analogs) increases the activity of analogs substituted with p-methyl

• complex mixture of proteins. In addition, it is possible to quantify their expression by using suitable primary and secondary antibodies to visualize it. It has been established that the dephosphorylated forms of BZR1 and BES1, and their concomitant accumulation in the nucleus, control the activity in the

• . However, it seems that on the signaling cascade this structural effect is lost, and the outcome do not follow the initial pattern. It is known that plant cells can synthesize most hormones and, therefore their regulation is decentralized. In addition, each hormone modulates its own synthesis, degradation

Rongalite addition to dienones: diastereoselectivity in cyclic sulfone synthesis; stereochemical rationalization and prospects as a general conjugate nucleophile

• Melina Goga,
• Hao Zong,
• James Franco,
• Jazmine Prana,
• Rudolph Michel,
• Antonia Muro,
• Elana Rubin,
• Janet Brenya,
• Henk Eshuis and
• Magnus W. P. Bebbington

Beilstein J. Org. Chem. 2026, 22, 742–752, doi:10.3762/bjoc.22.56

• sought confirmation of the structures of the minor and major diastereomers in our own hands. Noting that preparation of sulfides by double conjugate addition of Na2S or NaSH has been widely studied, and that the stereochemical assignments presented therein are in some cases supported by X-ray

• crystallographic studies, we prepared trans-sulfide 2 using an established protocol [23], and then oxidized it to trans-sulfone 1a (Scheme 2). This material was identical to the major product from Rongalite double conjugate addition. Additional confirmation of the structures of major and minor diastereomers 1a and

• (indicated). There is nothing to suggest from the calculations that an inherent reactivity problem prevents the initial addition of Rongalite to the enone, especially given that the singly electrophilic 2,6-dimethylbenzalacetone is known to participate in reactions with conjugate nucleophiles [25]. It is

Synthesis of heterocycles based on azomethine ylides from α-amino acids (or amines) and carbonyl compounds

• Ekaterina V. Berezhnaya,
• Alexander I. Ponyaev,
• Vitali M. Boitsov and
• Alexander V. Stepakov

Beilstein J. Org. Chem. 2026, 22, 705–741, doi:10.3762/bjoc.22.55

• yields and with high diastereoselectivity and enantioselectivity (up to 97% ee). However, α-(alkylimino)esters were less reactive, requiring longer reaction times and yielding products with slightly lower enantioselectivity (up to 81% ee). In addition to dimethyl maleate, other dipolarophiles, such as

• addition to gem-difluorostyrenes, 1,1,2-trifluorostyrenes can be used in the synthesis, which leads to the formation of 3,3,4-trifluoropyrrolidines in moderate yields and high diastereoselectivity [30]. In addition to the above, the authors demonstrated the broad applicability of this method using

• form pyrrolidine 64. Further treatment of 64 with cinnamaldehyde and N-phenylmaleimide leads to the second (3 + 2) cycloaddition adduct 65. Addition of ICl to 65 results in cyclization involving the styrene groups, which is accompanied by the formation of decahydropyrrolo[2,1,5-cd]indolizine 66. The

Anti-invasive and cytotoxic evaluation of a (+)-pinoresinol-based semisynthetic library against glioblastoma

• Chen Zhang,
• Kah Yean Lum,
• Jonathan M. White,
• Paul I. Forster,
• Nicholas Booth,
• Sunita A. Ramesh and
• Rohan A. Davis

Beilstein J. Org. Chem. 2026, 22, 691–704, doi:10.3762/bjoc.22.54

• two new pinoresinol ester derivatives 6 and 7 showed the biggest differences to the natural products owing to the addition of UV-active acyl moieties. Owing to our developing interest in identifying natural products and derivatives that are cytotoxic to human cancer cell lines and/or block invasion or

• aliquot (10 µL) of the harvested cells was counted in a haemocytometer after the addition of 10 µL of trypan blue to determine the cell count. The remaining cells were centrifuged at 1,100 rpm for 5 min. Based on the cell count, the spun cells were resuspended in the appropriate volume of complete medium

• addition of an extracellular matrix, such as Matrigel, on top of a porous membrane that allows cells to invade in response to the chemotactic gradient. The transwell assay protocol was adapted from the method outlined by Justus et al. [41]. Corning 6.5 mm transwell assay plates (24 wells) with

Synthesis of depressin, cryptomeridiol and 4-epi-cryptomeridiol enabled by a terpenoid chiral pool-producing platform

• Yao Kong,
• Tao Wang,
• Chen Wang,
• Pengcheng Zhang,
• Yuanning Liu,
• Kaibiao Wang,
• Fen Liu,
• Hongli Jia and
• Zhengren Xu

Beilstein J. Org. Chem. 2026, 22, 683–690, doi:10.3762/bjoc.22.53

• . Their complex structures and diverse skeletons have continuously inspired chemists to design novel strategies and develop new synthetic methodologies. For the synthesis of complex terpenoid natural products, in addition to those starting from simple and easily available starting materials, Nature has

• the selective late-stage functionalization. In addition, since the precursors for terpene cyclases are general no matter they are provided by the IU pathway or MVA/MEP pathways, a diversity of terpene skeletons would be easily accessible by simply integrating known or newly discovered terpene cyclases

Harnessing light energy with molecules

• Grace G. D. Han,
• Mogens Brøndsted Nielsen and
• Hermann A. Wegner

Beilstein J. Org. Chem. 2026, 22, 680–682, doi:10.3762/bjoc.22.52

• and can be potentially used at a later stage. A strong emphasis is on molecular photoswitches (photochromic molecules) that upon irradiation undergo cis/trans isomerization, intramolecular photocycloaddition, or an electrocyclic reaction. In addition, several articles describe absorption tuning by

• -workers [4], the π-system of monoaryl-substituted NBDs was synthetically extended by acetylenic bridges. In addition, Hebborn, Ihmels, and co-workers [5] show that 19F NMR spectroscopy enables unambiguous identification of mono- and bisQC intermediates in the sequential photoreactions of a fluorinated

• singlet-state photoredox catalyst in the sulfonylation/arylation of styrenes and as a triplet sensitizer in energy transfer catalysis. In addition to the photoredox contribution mentioned above, this thematic issue contains two publications on photochemical reactions beyond photoisomerizations. In the

Using generative AI to transform peptide hits into small molecule leads

• Joshua Mills and
• Yu Heng Lau

Beilstein J. Org. Chem. 2026, 22, 672–679, doi:10.3762/bjoc.22.51

• molecule candidates, providing potential alternatives to traditional computationally expensive physics-based workflows such as docking, MD, and free-energy perturbation (FEP) calculations for affinity estimation. For example, Boltz-2 features a strong emphasis on affinity prediction in addition to its core

Photoorganocatalytic trifluoromethylation of (het)arenes in green conditions

• Egor N. Boronin,
• Svetlana E. Kaurkina,
• Milena M. Svetlakova,
• Anton S. Bolshakov,
• Maxim V. Arsenyev,
• Vasilii F. Otvagin,
• Alexey Yu. Fedorov,
• Timothy Noël and
• Alexander V. Nyuchev

Beilstein J. Org. Chem. 2026, 22, 662–671, doi:10.3762/bjoc.22.50

• processes. Umemoto and Togni reagents display low atom efficiencies in addition to very high costs. Taken together, these considerations indicate that TFA and TFAA represent the most attractive choices from both ecological and economic perspectives. In the selection of solvents for photochemical

• that the addition of the electrophilic CF3 radical to the aromatic ring may differ in energetic profile between the two substrates (Scheme 5). However, DFT calculations showed that the thermodynamic parameters for both processes are comparable, indicating that other elementary steps may be responsible

• substrates are shown in Supporting Information File 1. Radical trapping reactions. Proposed mechanism. Addition of CF3 radical to benzene and TMB. Comparison of atom efficiency and prices of the CF3 sources.a Optimization of reaction conditions. Scaling-up of the trifluoromethylation of TMB. Supporting

Advantages of PROTACs in achieving selective degradation of homologous protein families

• Luxi Yang,
• Xinfei Mao,
• Jingyi Zhang,
• Jing Shu,
• Wenhai Huang,
• Xiaowu Dong,
• Yinqiao Chen and
• Mingfei Wu

Beilstein J. Org. Chem. 2026, 22, 628–661, doi:10.3762/bjoc.22.49

• , Hangzhou 310053, China College of Pharmaceutical Sciences, Zhejiang University, Hangzhou, 310058, China 10.3762/bjoc.22.49 Abstract Proteolysis-targeting chimeras (PROTACs) have emerged as a promising therapeutic modality and now represent an important addition to the toolkit of medicinal chemists

• are mainly involved in transcriptional regulation. However, the biological functions of CDK10, 11, 14–18, and 20 have not been fully elucidated [45][46]. CDKs are essential in cell proliferation, transcriptional activity, and neuronal activity [44]. In addition, disorders of these protein kinases

• and E3 ligand when designing PROTACs with high selectivity to target the degradation of CDK6. However, some studies did not support this hypothesis. When considering the influence of the linker on PROTAC selectivity, attention must be paid to the composition of the linker in addition to its length. In

Hydrogen production from formic acid catalyzed by NHC–Cu complexes

• Orlando Santoro and
• Catherine S. J. Cazin

Beilstein J. Org. Chem. 2026, 22, 620–627, doi:10.3762/bjoc.22.48

• realization of a hydrogen economy [6][7]. Amongst the various H2 sources investigated to date, formic acid (HCO2H, FA) is considered one of the most promising. Indeed, FA contains 4.4% H2, is inexpensive and is liquid under ambient conditions, thus easy to handle and transport. In addition, the CO2 generated

• ][29] and Rh [30][31] have shown to allow the selective transformation of formic acid into H2 and CO2 with high turnover frequencies (TOFs). In most cases, addition of a base (either amines or formate salts) is required to obtain high catalytic activity. Efficient systems based on inexpensive metals

• formate products. Excess H2 can be generated by dehydrogenative coupling of those species in the presence of the copper catalyst. Indeed, metal hydride systems have shown high catalytic activity in such a reaction [59][60]. In addition, the formation of products compatible with the polymerization of

Towards the targeted protein degradation of CK2: design and synthesis of CAM4066-based PROTACs

• Sophie Day-Riley,
• Sona Krajcovicova,
• Aryaman Raj Sokhal,
• Jan L. Venne,
• Paul Brear,
• Marko Hyvönen,
• Benjamin C. Whitehurst,
• Jason S. Carroll and
• David R. Spring

Beilstein J. Org. Chem. 2026, 22, 611–619, doi:10.3762/bjoc.22.47

• itself is a moderately polar molecule, and linker addition further increases polarity. Collectively, these proof-of-concept results highlight the complexity of designing bivalent molecules for CK2 degradation and underscore the need for further optimisation of warhead potency, linker length, exit vector

Computational prediction of C–H hydricities and their use in predicting the regioselectivity of electron-rich C–H functionalisation reactions

• Rasmus M. Borup,
• Nicolai Ree and
• Jan H. Jensen

Beilstein J. Org. Chem. 2026, 22, 603–610, doi:10.3762/bjoc.22.46

• -catalysed C–H carbamoylation of the cis-fused azabicyclo[4.3.0]nonane derivative 9, and Overman and Tomasi [46] reported the Cu(II) salt-catalysed addition of a N-tosyl group to the C–C double bond in compound 10 in conjunction with an H-abstraction, to form a new C–C double bond. In all three cases, the

• , 7, and 9) indicating that hydricities offer a valuable measure of reactivity in addition to BDEs for these types of reactions. Conclusion We have developed HAlator, an automated QM-based workflow for computing C–H hydricities, benchmarked against 35 experimental values in DMSO to yield an MAE of

Continuous-flow carbonyl hydrogenation under subatmospheric to atmospheric hydrogen pressure enabled by robust heterogeneous Pt–Fe catalysts

• Hiroyuki Miyamura,
• Ryosuke Kajiyama,
• Shun-ya Onozawa,
• Yoshihiro Kon and
• Shū Kobayashi

Beilstein J. Org. Chem. 2026, 22, 575–582, doi:10.3762/bjoc.22.43

• heterogeneous catalysts are used in a continuous-flow system, the catalyst included in a column allows semi-permanent use without recovery and reuse operations that are usually needed in a batch system. The integration of multiple column reactors also enables multistep continuous production. In addition, an

• conditions is adaptable to sustainable chemical synthesis, minimizing energy consumption and enabling the use of green hydrogen. In addition, the newly obtained insights regarding the relationships among the Fe/Pt ratios in the catalysts, the bimetallic structure, and the resulting catalytic performance for

Molecular tweezer–peptide conjugates disrupt the protein–protein interaction between survivin and histone H3 essential in mitosis

• Catherine Gsell,
• Philipp Rebmann,
• Karina Opara,
• Christine Beuck,
• Peter Bayer,
• David Bier,
• Ingrid R. Vetter and
• Thomas Schrader

Beilstein J. Org. Chem. 2026, 22, 557–567, doi:10.3762/bjoc.22.41

• ) Peptide tweezer conjugates 1 and 2a with triazoles linking the tweezer and H3 peptide at its C-terminus. Note that both azidopropylamine as well as azidoornithine establish almost the same distance between peptide and tweezer. In addition, they place the tweezer into the vicinity of the phosphorylated

Melifoliox B, a novel phloroglucin derivative isolated from Melicope barbigera (Rutaceae) and synthesis of new oxidation products from melifoliones A and B

• Horst Weber,
• Kim-Thao Tran-Cong,
• Bernhard Mayer,
• Guido J. Reiss,
• Iryna S. Konovalova,
• Marc S. Appelhans,
• Kenneth R. Wood and
• Claus M. Passreiter

Beilstein J. Org. Chem. 2026, 22, 535–546, doi:10.3762/bjoc.22.39

• Duesseldorf, Germany Integrative Taxonomy of Plants, Friedrich-Schiller-University Jena, 07743 Jena, Germany Senckenberg Institute for Plant Form and Function (SIP) Jena, 07743 Jena, Germany National Tropical Botanical Garden, 3530 Papalina Road, Kalaheo, HI 96741, USA 10.3762/bjoc.22.39 Abstract In addition

• isolated from a dichloromethane extract of leaves of Melicope barbigera A. Gray, a species endemic to the island of Kaua’i, Hawaiian Islands [2][3]. In addition, small amounts of two tetracyclic citrans were identified as a 30:70%-mixture of isomeric melifoliones A (1), and melifolione B (2) [1], both

• ), but the yield was less than 5% and therefore of no preparative interest. The best results to get melifolione B (2) were achieved by briefly heating 5 in a closed microwave apparatus without solvent at 130–140 °C after addition of catalytic amounts of acetic acid. By this procedure, the proportion of 2