ROR2 expression in TOF patients compared to healthy control individuals. Transcriptome analysis revealed diminished ROR2 expression in TOF pathological samples relative to normal tissues. Of the 2246 genes that exhibited altered expression, 886 were upregulated, while 1360 were down‐regulated. KEGG analysis and GO analysis of the differentially expressed genes indicated that these genes were significantly enriched in the Wnt signalling pathway, apoptosis and cardiac development function. Importantly, ROR2 was the only gene shared among the three pathways. Furthermore, interference with ROR2 promotes apoptosis and curtails cell proliferation in vitro. The knockdown of the ROR2 gene in AC16 cells resulted in a significant decrease in Edu‐positive cells. Flow cytometry studies indicated an increase in the percentage of cells in the S phase. In contrast, the G2/M cell cycle transition was blocked in the ROR2‐knockdown group, leading to a significant increase in apoptosis. Moreover, the CCK‐8 cell viability assay demonstrated a reduced proliferation in the ROR2‐knockdown group. Furthermore, both in vivo and in vitro data indicated that the expression of HSPA6 (Recombinant Heat Shock 70 kDa Protein6), an essential gene enriched in cardiac tissue and associated with apoptosis, was down‐regulated following ROR2 knockdown mediated by the β‐catenin/SOX3 signalling pathway. In conclusion, low expression of ROR2 plays a crucial role in the occurrence and development of TOF, which may be related to the downregulation of HSPA6 through the β‐catenin/SOX3 signalling pathway.Tetralogy of Fallot (TOF) is the highly conventional appearance of cyanotic congenital heart disease. Our study aimed to assess the involvement of receptor tyrosine kinase‐like orphan receptor 2 (ROR2) in TOF and elucidate the specific mechanism. Upon investigation of human tissue samples, we observed a decrease in  The control heart tissue was taken from six organ donors without congenital heart disease, and the tissue was located in the same location as the heart tissue of the TOF patients. The tissues were rapidly frozen in liquid nitrogen and then stored in a −80°C refrigerator. Three normal myocardial tissues and three TOF myocardial tissues were used for transcriptome sequencing, and the other three were used to validate transcriptome results and follow‐up experiments. Query Table 2.2Sprague–Dawley rats (1 week old) were obtained from the Experimental Animal Center of Xuzhou Medical University. At Week 1, SD rats were intraperitoneally injected with 4 μL of AAV9‐ROR2‐RNAi , and the control group was injected with 4 μL of AAV9CON534 (GeneChem). All animals were housed in rooms with a 12‐h diurnal cycle and had AD libitum access to food and water. The rats were followed up for 3–5 days to observe the changes in mental status, diet and physical fitness. All animals were treated in accordance with prescribed Good animal practices. The rats were euthanized 5 weeks after the virus injection. All operations were performed under the regulations of the Animal Care Center Use Committee of Xuzhou Medical University (202006w010).2.3The human cardiomyocyte derivative AC16 cell line  was divided into two groups to transfect with small interference RNA, including the control group , and targeting ROR2 . The siRNA was acquired from Genepharma. Each experiment was performed three times.2.4ROR2 knockdown AC16 cells were cultured in cell culture. After the cell fusion reached 90%, the AC16 cells and the AC16 that knocked down the ROR2 gene were digested by pancreatic enzyme, respectively, and the plates were grown from 5000 cells per well to 96‐well plates. After incubation for 0, 12, 24, 36, 48 and 72 h, 10 μL CCK8 solution (Yeasen) was added to each well, and the 96‐well plates were continuously incubated for 2 h at 37°C in a 2% CO2 incubator. A microplate reader measured the absorbance value of each well solution, and AC16 cell viability was measured by 450 nm optical filter (BioTek).CCK8, the full name of the Cell Counting Kit‐8 reagent, can be used for simple and accurate cell proliferation and toxicity analysis. Wild‐type AC16 cells and 2.5The human tissue  and Rat tissue (Control and ROR2‐KD) or human cardiomyocytes AC16 homogenate (100 μL) were placed in the reaction tube. Total RNA was extracted from tissues and cell lines with the TRIzol reagent (Solarbio) according to the manufacturer's protocol. cDNA was synthesized with the PrimeScript RT Reagent Kit (Roche). Real‐time quantitative PCR (qRT‐PCR) analyses were performed with the SYBR Green Premix Ex Taq (Takara). Primers used for PCR were synthesized by Genepharma. The sequence is as follows: Glyceraldehyde‐3‐phosphate dehydrogenase (GAPDH) Sense: 5′‐UGACCUCAACUACAUGGUUTT‐3′ and antisense: 5′‐AACCAUGUAGUUGAGGUCATT‐3′, ROR2 sense: 5′‐ATGGTTCACGACTGCGAATCC‐3′ and antisense: 5′‐ATGGTTCACGACTGCGAATCC‐3′. Each experiment was repeated three times.2.6p ≤ value 0.05, fold change ≥ 2). R3.6.3 software, including the ggplot2 and cluster profile packages, was used to perform the heat map, volcano plot, gene ontology (GO) analysis and visualization.Total RNA was extracted in the manner described in the previous section. The RNA easy micro kit  and the RNase‐Free DNase Set  were purified and sequenced. To confirm the insert size and determine the mole concentration, purified libraries were measured using a Qubit®2.0 fluorometer (Invitrogen) and validated using an Agilent 2100 bioanalyzer (Agilent Technologies). Clusters were generated by cBot using a diluted library of 10 pM and sequenced on an Illumina HiSeq 2500 platform (Illumina) using a two‐terminal sequencing model (Berry Genomics). EdgeR was used to perform the differentially expressed gene (DEG) analysis (2.76 cells per 100 μL Annexin‐V/propidium iodide (PI) staining buffer were resuspended and incubated with 1 mL HEPES buffer for 15 min. Apoptosis detection was performed by Flow cytometry . The excitation wavelength was 525 nm, and the maximum absorbance of FITC was 488 nm. The maximum absorption wavelength of the PI‐DNA complex was 535 nm, and the maximum emission wavelength was 615 nm. Each experiment was repeated three times.After 48 h transfection, cells were trypsinized (0.25%) without EDTA, collected in a flow tube and centrifuged to remove the supernatant. Cell pellets were centrifuged to remove the supernatant. Annexin‐V/fluorescein isothiocyanate (FITC) staining buffer (Shuojia Biotech) was prepared according to the manufacturer's instructions. Annexin‐v‐fits, PI and HEPES buffer from the kit were mixed in a 1:2:50 ratio. 1 × 102.8Proteins were extracted from the corresponding tissues or cells using radioimmunoprecipitation assay lysis buffer supplemented with phenylmethylsulfonyl fluoride  precooled at 4°C. The protein concentration in each sample was determined using a Bicinchoninic acid (BCA) kit (Yeasen). Equal amounts of proteins in the samples were separated by sodium dodecyl sulfide‐polyacrylamide gel electrophoresis (SDS‐PAGE) and transferred to a polyvinylidene difluoride (PVDF) membrane. Membranes were blocked with 5% BSA for 1 h at room temperature and incubated with anti‐rabbit primary antibody overnight at 4°C. The primary antibodies used were anti‐ROR2 antibody , anti‐SOX3 antibody , and anti‐β‐catenin antibody . rabbit (WL0962a), HSPA6 antibody  and β‐tubulin antibody . After incubation with the primary antibody, the cells were washed three times with TBST and incubated with a fluorescent secondary antibody for 2 h at room temperature. The membrane was then washed three times with TBST, and the resulting image was obtained using the Odyssey CLX instrument detection. The results were analysed using ImageJ software. The relative protein content was expressed as the grey value of the corresponding protein band and the grey value of Tubulin. Each experiment was repeated three times.2.9The myocardial tissue of SD rats and humans was obtained, respectively. Heart tissue was fixed in 4% paraformaldehyde for 24 h, dehydrated in gradient ethanol, embedded in paraffin and sectioned to a thickness of 4 μm. The sections were dewaxed with xylene, rehydrated with upgraded ethanol and washed three times with distilled water. After antigen repair, sections were boiled in citrate buffer for 11 min. After cooling, sections were washed in Tris buffer and incubated in bovine serum albumin (BSA) for 10 min. After antigen retrieval, the sections were incubated in the primary antibody  for 1 h at room temperature. Sections were washed in Tris buffer (pH: 7.4) and then incubated in goat anti‐rats secondary antibody  for 1 h. The samples were incubated with DAB for 10 min, rinsed with Tris buffer (pH: 7.4), counterstained with haematoxylin, rinsed with tap water, dehydrated with graded alcohol, cleared with xylene and covered with the cover sheet. The density of ROR2 was observed in coronal sections with ×400 magnification using a microscope (OlympusAX70). The results were analysed using Image J software, the corresponding OD values were read, and statistical analysis was performed. The specific operation is as follows: (1) Open the picture, Image, type, 8‐bit to convert the picture to a grayscale picture. Convert 8‐bit grayscale picture to OD value: Analyse, Calibrate, select Uncalibrate OD to calibrate; (2) Select the parameters to be measured: Select Set Measurements under ImageJ software Analyse to set the measurement parameters, select Integrated density, Area, Limit to threshold , click OK; (3) Analyse, Measure (Ctrl+M) and get the OD value.2.10n = 6) were sedated with a high dose of pentobarbital sodium (160 mg/kg) and transcardially reperfused with 0.01 M of PBS and fixed with 4% paraformaldehyde (PFA) in 0.01 M of PBS. The heart was taken and left overnight in 4% PFA, 20% and 30% sucrose solutions. These tissues were fixed in an embedding medium (OTC) and cut into 20 μm sections using a microtome . All sections were preserved in cryoprotectant until further use. The sections were rinsed in PBS (0.01 M × 5 min followed by two times), blocked with 10% normal goat serum  and incubated overnight at 4°C with specific primary antibodies: anti‐ROR2 , SOX3 antibody , β‐catenin antibody , HSPA6 antibody  and β‐tubulin . Then, the sections were rinsed in PBS (0.01 M × 5 min followed by two changes) and incubated with a conjugated secondary antibody . The sections were mounted onto slides and cover‐slipped with Vectashield . IF results were acquired on a confocal fluorescence microscope Lecia STELLARIS 5.The SD rats were euthanized 4 weeks after the AAV9 injection. Rats (2.11ROR2‐pcDNA3.1 was constructed by cloning the full‐length complementary CDS sequence of human ROR2 by Youbao Bio by adding overexpression plasmid (Unibio) and liposome transfection reagent lLIPO3000 (Thermo). The solution was replaced after 6 h, and the ROR2 overexpression efficiency was verified after 48 h.When AC16 cells reached 75% confluence, the overexpression plasmid 2.12p < 0.05 was considered statistically significant. Data with normal distribution and homogeneity of variance were compared between the two groups by unpaired t‐test. One‐way analysis of variance (anova) was used to compare data between different groups, and the post hoc Tukey test was used. Repeated measures anova with post hoc Tukey test was used to compare data at multiple time points between different groups.Data were expressed as mean ± standard deviation (SD) and analysed by GraphPad. 33.1p < 0.0001). Furthermore, the protein level was analysed by western blotting (western blot), and the quantification of western blot results showed that the ROR2 protein level was significantly higher in the control compared to the TOF . Similarly, mRNA analysis reveals a low level of ROR2 expression in the TOF compared to the control group, which was consistent with western blot results . All these results suggest that ROR2 is down‐regulated in TOF.To detect whether the ROR2 expression is altered in Tetralogy of Fallot patients: The expression of ROR2 was detected by the immunohistochemistry (IHC), and the analysis revealed that the expression of ROR2 was significantly decreased in the TOF patients compared to the control group  and TOF patients. A volcano plot analysis was performed to show the DEGs between the two samples. DEGs were screened using the following criteria: |log2(fold change)| ≥ 1 and es Table  are showes Table . Principes Table . The cores Table . This coes Table . KEGG anF Figure .3.3ROR2 (ROR2‐KD) in an appropriate environment. The normal cells showed a high proportion of the Edu‐positive cells compared to the ROR2‐KD . This indicated that after knocking down ROR2, the growth rate of cells gradually decreased. Furthermore, we observe the migration activity of cells at 24 and 48 h after cutting the cell cluster. The analysis reveals that the cell migration activity was significantly decreased in the ROR2‐KD cell compared to the control group . Moreover, ROR2‐KD and control group cell lines were performed in the transwell chambers with non‐Matrigel or Matrigel, and the cell was stained with crystal violet. The results indicated a significant reduction in the invasion and migration capability of the ROR2‐KD group . A flow cytometry study was conducted to determine whether the growth inhibitory effects of ROR2‐KD were cell cycle‐dependent. The number of arrests in each cycle phase  was measured. The analysis indicated that the percentage of the cell cycle in the S phase was elevated in the ROR2‐KD group; nevertheless, the G2/M cell cycle stagnated compared to the control group . The flow cytometry showed that ROR2‐KD cells' apoptosis significantly increased after FITC Annexin‐V and PI staining . Moreover, the RT‐qPCR results indicated that the expression of the ROR2 was decreased in the KD group  to knockdown the g Figure . In addip Figure . All the3.4ROR2. The same screening criteria further reveal the 297 genes altered in the ROR2‐KD group, of which 182 are upregulated and 115 genes are down‐regulated  and transfected with siRNA to knock down the ed Table , as showed Table . The heaed Table . In addied Table . Likewised Table . We inteed Table . GO ontoed Table . So we c3.5ROR2 downstream signalling in vivo, the animal model was established by knocking down the ROR2 using AAV9. In order to verify the successful construction of ROR2 knockdown SD rat model, the following experiments were performed. Immunofluorescence was used to detect the expression of GFP and ROR2 protein in the myocardial tissue of the normal group and the knockdown group. Compared with the control group, the expression of ROR2 in the myocardial tissue of the knockdown group was significantly reduced . B‐ultrasound was used to take pictures of the hearts of the model rats, as shown in Fig.: Compared with the control group, ROR2 gene knockdown rats had significantly increased right ventricle hypertrophy. The hearts of the two groups of experimental rats were removed to measure the radius and weight . The results showed that the weight and volume of the ROR2 knockdown heart were significantly larger than those of the control group, further confirming the potential significance of ROR2 in TOF disease. The heart tissue of the rat model was incubated with the ROR2 antibodies. The immunofluorescence images show a significantly low expression of ROR2 in the ROR2‐KD group compared to the control group . Moreover, the heart tissue was further incubated with β‐catenin, and the results indicated high expression in the control group compared to the ROR2‐KD group . The heart samples of rats incubated with SOX3 and HSPA6, and ROR2 to further describe the downstream signalling. IF images of samples reveal a significant decrease in SOX3 expression in ROR2‐KD compared to the control group . Similarly, the results indicated that HSPA6 expression was decreased in the ROR2‐KD group than in the control . These results suggest that the ROR2 regulates the HSPA6 expression.Furthermore, to study the d Figure A. The ex3.6p < 0.001). Additionally, the results show that the protein ratio of β‐catenin, SOX3 and HSPA6 was significantly decreased in the ROR2‐KD group corresponding to the control group . Similarly, in vivo, the gel images of western blot were displayed . Moreover, the quantification of western blot shows that the protein ratio of β‐catenin, SOX3 and HSPA6 was significantly decreased in the ROR2‐KD group (SD rats) corresponding to the control group , and the results were parallel with in vitro. To confirm that ROR2 regulates HSPA6 expression through β‐catenin signalling pathway, a plasmid overexpressing ROR2 was transfected into human cardiomyocytes AC16. western blot results showed that ROR2 protein expression was significantly increased after AC16 cells were infected with the overexpressed virus . Overexpression of ROR2 also increased HSPA6 protein expression compared with control . AC16 cells overexpressing ROR2 were added with a β‐catenin signalling pathway inhibitor. The addition of the inhibitor MSAB (Mce) significantly reduced HSPA6 protein expression compared with control cells, which was consistent with the effect of ROR2 knockdown . This strengthens our belief that ROR2 regulates HSPA6 expression through the β‐catenin/SOX3 signalling pathway, providing some clinical implications for treating TOF in congenital heart disease.To further confirm the hypothesis that ROR2 regulates the HSPA6 via β‐catenin and SOX3 in vivo and in vitro, we performed the western blot analysis in rat models and AC16 cells. In vitro, the gel images of western blot have been displayed Figure . The anad Figure . The wes4ROR2 deletion or downregulation may indirectly lead to right ventricular enlargement in TOF‐related symptoms. Immunohistochemical analysis of human heart tissue samples showed that the expression of ROR2 was significantly decreased in the TOF patients compared to the control group. Furthermore, western blot and RT‐qPCR results showed that the ROR2 level was significantly higher in the control compared to the TOF. These results propose that ROR2 expression is down‐regulated in TOF. In support of this study, previous researchers found that ventricular septal defects were found to be associated with ROR2‐deficient mice.Tetralogy of Fallot is one of the most common congenital heart diseases developed during embryonic development. In embryonic development, successful cell‐to‐cell coordination is required to provide appropriate direction, resulting in cell proliferation, differentiation and apoptosis.Furthermore, potential interactions between gene expression and TOF were identified in this study. Interestingly, this effect was even more pronounced, with 2246 genetic alterations reported in TOF, of which 886 were upregulated and 1360 were down‐regulated. ROR2, SOX3 and HSPA6 were among the top 17 down‐regulated genes associated with TOF patients. Similarly, in vitro, the whole genomic analysis was performed on AC16 cells, including control (non‐transfected) and transfected cell line (ROR2‐KD). The mRNA expression in the ROR2‐KD group was parallel to TOF samples. Additionally, heat maps showed a significant transcriptome alteration in the ROR2‐KD group.In vitro experiments confirmed that interference with ROR2 promoted apoptosis and curtailed cell proliferation. The transfected AC16 cell displayed low expression of the Edu and migration activity, suggesting the growth rate of cells progressively declined. Likewise, previous publications explore the role of ROR2 in cell lines, and they indicated that knockdown of the ROR2 suppresses proliferation and promotes apoptosis.This study further reports that ROR2 regulates the HSPA6 via β‐catenin and SOX3 in vivo and in vitro. In vitro studies showed that the proportion of β‐catenin, SOX3 and HSPA6 proteins was decreased in the ROR2‐KD group. Henry et al.In conclusion, this study provides evidence of impaired ROR2 function in TOF patients. Moreover, in vivo experiments demonstrated that ROR2 exerts a suppressive effect on apoptosis and promotes cell proliferation. Additionally, the study revealed an increase in the percentage of cells in the S phase and a blockage of the G2/M cell phase. In vitro experiments using the SD rat model indicated that ROR2 regulates the expression of HSPA6 through the β‐catenin/SOX3 pathway. Western blot results also confirmed the downregulation of HSPA6 protein expression via β‐catenin/SOX3 following ROR2 knockdown in both in vivo and in vitro settings. These results suggest that ROR2 plays a critical role in the development of TOF by inhibiting cell proliferation and promoting apoptosis, which is mediated by the downregulation of HSPA6 through the β‐catenin/SOX3 signalling pathway.Rui Guo: Conceptualization ; methodology ; writing – original draft ; writing – review and editing . Yiran Zhou Guo: Writing – review and editing . Qing Zhou: Writing – review and editing . Guoju Li: Formal analysis . Zhanghui Du: Formal analysis . Yefei Shi: Formal analysis . Quansheng Xing: Funding acquisition (lead); resources ; supervision ; writing – original draft ; writing – review and editing .This work was supported by grants from The National Natural Science Foundation of China (NSFC) (Grant No: 8170315 and 82071583) and the Taishan Scholarship Program.The authors declared no conflict of interest.Figures S1–S2:Click here for additional data file.Table S1:Click here for additional data file.Table S2:Click here for additional data file.Table S3:Click here for additional data file.


In the context of cancer therapy, a recently identified therapeutic target is represented by the essential subtype of RNA transcripts ‐ the long noncoding RNAs (lncRNA). While this is the case, it is especially difficult to successfully regulate the expression of this subtype in vivo, particularly due to the protection granted by the nuclear envelope of nuclear lncRNAs. This study documents the development of a nucleus‐specific RNA interference (RNAi) nanoparticle (NP) platform for the targeted regulation of the nuclear lncRNA function, in order to effectuate successful cancer therapy. An NTPA (nucleus‐targeting peptide amphiphile) and an endosomal pH‐responsive polymer make up the novel RNAi nanoplatform in development, which is capable of complexing siRNA. The nanoplatform is capable of accumulating greatly in the tumor tissues and being internalized by tumor cells, following intravenous administration. The exposed complexes of the NTPA/siRNA may conveniently escape from the endosome with the pH‐triggered NP disassociation, following which it can target the nucleus by specifically interacting with the importin α/β heterodimer. In orthotopic and subcutaneous xenograft tumor models, this would result in a notable suppression of the expression of nuclear lncNEAT2 as well as greatly impede the growth of tumors in liver cancer. We herein developed a nucleus‐specific RNAi nanoplatform for targeted regulation of nuclear lncRNA function and effective cancer therapy. This new RNAi nanoplatform could respond to the endosomal pH to expose NTPA/siRNA complexes for the nucleus‐specific siRNA delivery, leading to a significant inhibition of nuclear lncNEAT2 expression and tumor growth of liver cancer. While a vast majority of the human genome is transcribed into several lncRNAs (>50%) that are primarily situated in the cytoplasm and nucleus; a negligible portion of it (<3%) is transcribed into protein‐coding mRNAs; the lncRNAs play a significant role in the progression of various diseases, cancer being one among these. Thus, while having been identified as a novel therapeutic target for the effective treatment of cancer, the challenge in the regulation of in vivo lncRNA has been an important concern that hampers their adoption in practical approaches.With a length surpassing 200 nucleotides, long non‐coding RNAs (lncRNAs) have been identified as a novel subtype of RNAs that were previously dismissed as “transcriptional noise” or “junk DNA” due to their lack of ability to code proteins.1 Howe Small interfering RNA (siRNA) among other similar RNAi effector molecules are capable of being incorporated within RNA‐induced silencing complex (RISC), a protein complex wherein Argonaute 2 (Ago2) may cleave the double strand of siRNA, while the target genes in the activated protein complex can be bound by its antisense strand, thereby starting to destroy the target genes—this is the fundamental mechanism that the technology operates upon. Due to the ability of the activated RISC to repeatedly degrade the target genes, this form of technology has been understood to be remarkable, potent, and characteristic of a prolonged preventive effect from several days (in dividing cells) to several weeks (in non‐dividing cells). Thus, for the regulated expression of long non‐coding RNAs as well as the overall progression of cancer, RNAi technology has been utilized across several practices associated with cancer therapy. Nevertheless, due to this intervention being generally compatible with long non‐coding RNAs situated within the cytoplasm; it is challenging to efficiently control the nuclear lncRNAs, even with the RISC located in the nucleus. Within the past decade, the employment of nanoparticles (NPs) for interventions with RNA, particularly in the case of stimuli‐responsive NPs capable of responding to endogenous factors in tumor cells/tissues to facilitate the delivery of siRNA, there has been a noted efficiency in the successful silencing of gene targets in vivo. Yet, as a result of the protection granted by the nucleus envelope, there remain difficulties in silencing nuclear lncRNA expression.With the function of eliminating target genes, particularly the “undruggable” components of the human genome, technology that employs RNA interference (RNAi) has brought about a pivotal shift in the treatment of various diseases.6 Smalb‐poly(2‐(diisopropylamino)‐ethylmethacrylate) (Meo‐PEG‐b‐PDPA) as well as a nucleus‐targeting peptide amphiphile (NTPA) which, through electrostatic interaction, is capable of complexing siRNA. The novel platform exhibits the following characteristics for nucleus specific siRNA delivery, following siRNA encapsulation and intravenous administration (Scheme  (ii) a rapid NP disassociation as well as an efficient endosomal escape of siRNA/NTPA complexes (through the “proton sponge” effect) take place due to the endosomal pH‐triggered protonation of hydrophobic PDPA chains; in addition to (iii), the specific interaction with the importin α/β heterodimer leads to the endowment of the abovementioned complexes with the ability to target nuclei due to the nuclear localization signal (NLS) peptide sequence (PKKKRKV) of NTPA. As a proof‐of‐concept, we selected lncRNA nuclear enrichment autosomal transcript 2 (lncNEAT2) and examined the anticancer efficacy as well as systemic lncNEAT2 siRNA (siNEAT2) delivery through the developed nucleus‐specific nanoplatform. LncNEAT2, being a classic nuclear long non‐coding RNA, appears upregulated in different cancer types, thereby carrying the potential to promote the development of cancer by controlling the expression of different target genes such as c‐Myc, β‐catenin, and EZH2 at the transcriptional and posttranscriptional levels. According to the findings from our in vivo study, the newly developed nucleus‐specific nanoplatform was capable of delivering siNEAT2 efficiently to the nucleus and silencing the expression of lncNEAT2 expression, thereby majorly preventing the growth of tumor in liver cancer across orthotopic and xenograft tumor models.To rectify and overcome such a challenge, efforts have been made by the authors of this study toward the development of a nucleus‐specific RNAi nanoplatform for the targeted regulation of nuclear lncRNA function, which would lead to the effective treatment of cancer. The nanoplatform in question is composed of an endosomal pH‐responsive polymer, methoxyl‐poly(ethylene glycol)‐n Scheme : (i) The  and 1 nmol siNEAT2 (0.1 nmol/μl aqueous solution) with varying weight ratios was mixed with a 200 μl solution of Meo‐PEG‐b‐PDPA. The mixture was then added to deionized water (5 ml) dropwise, after vigorous stirring at 1000 rpm. So as to centrifuge and filter out the free compounds and organic solvents, the suspension was transferred to an ultrafiltration device . The validated pH responsiveness of the siNEAT2‐loaded NPs received after washing it with 3 × 5 ml PBS  solution was suspended in a PBS solution of 1 ml with a pH of 7.4. With a NTPA/siNEAT2 weight ratio of 5, 10, 20, and 30, the siNEAT2‐loaded NPs were prepared and denoted NPs5, NPs10, NPs20, and NPs30. Using the instructions outlined above, control NPs were prepared with NTPA being altered with G0‐C14, a cationic lipid‐like compound. Using dynamic light scattering , the size and zeta potential were determined according to our previous methods. Furthermore, a transmission electron microscope was used to visualize the morphology of the NPs (Tecnai G2 Spirit BioTWIN). The sample had been stained with 1% uranyl acetate, then dried under air before observing. The Cy5‐siNEAT2‐loaded NPs were prepared in adherence to the method previously mentioned, and utilized to determine the EE% of siRNA. An NP suspension with a volume of 5 μl was extracted and mixed with 20‐fold DMSO. The standard was prepared by mixing 5 μl of naked Cy5‐siNEAT2 solution (1 nmol/ml in pH 7.4 PBS solution) with 20‐fold DMSO. By employing a Synergy HT multi‐mode microplate reader , the fluorescence intensity of Cy5‐siNEAT2 was evaluated, following which the EE% of siRNA was calculated as EE% = (FINPs / FIStandard) × 100.A homogenous solution was prepared by dissolving Meo‐PEG‐ methods.19 Fur2.2As per the method previously mentioned, the NPs that load fluorescein and Dabcyl‐labeled siNEAT2 were prepared and suspended in a PBS solution of 1 ml with a pH of 7.4. The sample was incubated at 37°C after 20 U of RNase was added. A microplate reader (480 nm) with an emission data range of 480–650 nm was used to evaluate the fluorescent emission spectra at predetermined time intervals.2.3NPs loaded with Cy5‐siNEAT2 were suspended in a PBS solution of 1 ml with a pH of 7.4 before being transferred to a PBS‐solution immersed (pH 7.4/6.0) Float‐a‐lyzer G2 dialysis device  at 37°C. An amount of the NP suspension (5 μl) was extracted and mixed with 20‐fold DMSO at a predetermined interval. A microplate reader was used to determine the fluorescence intensity of Cy5‐siNEAT2.2.4A humidified atmosphere with 5 percent of carbon dioxide was ensured for the incubation of liver cancer cells, SK‐Hep1 and HepG2, in DMEM with 10% FBS at 37°C. The cell lines were free of mycoplasma contamination and were validated by short tandem repeat profiling analysis.2.5Glass bottomed dishes  were used for seeding 10,000 SK‐Hep1 cells, which were later incubated for 24 h in DMEM (2 ml) with 10% FBS. A fresh medium of 2 ml replaced the previous medium, after which Cy5‐siNEAT2‐loaded NPs/Control NPs were added to the solution. The cells were placed in incubation at different times. The endosome and the nuclei were stained by Lysotracker green  and Hoechst , respectively after the medium was removed and the items were washed thrice with PBS solution (pH 7.4). Finally, the intracellular distribution of Cy5‐siNEAT2 was observed using a ZEISS 800 CLSM.2.6Six‐well plates were used to seed 50,000 SK‐Hep1 cells, which were incubated for 24 h in DMEM (2 ml) with 10% FBS. A fresh medium of 2 ml replaced the previous medium, after which Cy5‐siNEAT2‐loaded NPs/Control NPs were added to the solution. The cells were incubated for a specific duration of 8 h. The cells were digested by trypsin, and a PARIS RNA isolation kit  was used to collect the nuclei after the medium was removed and the items were washed with PBS solution (pH 7.4). The top solution was collected after repeated freezing (in liquid nitrogen) and subsequent thawing (at room temperature). Following this, a microplate reader was used to measure the fluorescence intensity of Cy5‐siNEAT2 in the nuclei.2.7Six‐well plates were used to seed 50,000 SK‐Hep1/HepG2 cells, which were incubated for 24 h in DMEM (2 ml) with 10% FBS. Following the placement of the medium with a fresh medium, the siNEAT2‐loaded NPs, Control NPs/lipofectamine 3000 (Lipo3k)/siNEAT2 complexes were added. The cells were washed with PBS solution (pH 7.4) after 24 h of incubation, after which they were incubated once again for 48 h in a fresh medium. Eventually, after trypsinizing the cells, Trizol was used to extract the total RNA from the cells. qRT‐PCR was used to evaluate the expression of lncNEAT2. Lysis buffer, which was supplemented with phenylmethanesulfonyl fluoride and protease inhibitor cocktail, was used to extract the total protein. Western blot was used to examine the expression of the c‐Myc protein. Cells were treated with the siPVT/siNEAT1‐loaded NPs to silence lncPVT1 and lncNEAT1. For qRT‐PCR analysis, the total RNA was extracted as well.2.8Six‐well plates were used to seed 50,000 SK‐Hep1 cells (per well), which were incubated for 24 h in DMEM (2 ml) with 10% FBS. After replacing the medium with a fresh one, NPs20, Control NPs/Lipo3k/siNEAT2 complexes were added at a siRNA dose of 30 nM. Following an incubation period of 24 h, PBS solution (pH 7.4) was used to wash the cells. Then, the cells were incubated further for 48 more hours in a fresh medium. After the cells were digested by trypsin, they were collected for the detection of annexin V and Propidium Iodide (PI) . A DXP11 Flow Cytometry Analyzer was used to perform the apoptosis analysis.2.9Six‐well plates were used to seed 20,000 Sk‐Hep1 cells , which were incubated for 24 h in DMEM (2 ml) with 10% FBS. This step was followed by treatment of the cells with siNEAT2‐loaded NPs, Control NPs, or Lipo3k/siNEAT2 complexes at a siRNA dose of 30 nM for 24 h. A fresh medium replaced the previous medium after the cells were washed with PBS solution with a pH of 7.4. The cells were then incubated further. AlamarBlue assay was used to measure the cytotoxicity at predetermined intervals, followed by the removal of the measurement agent. Then, the cells were incubated for a longer time to observe the formation of the colony.2.10For the purpose of the study, nude mice and healthy female BALB/c normal mice aged around 4 or 5 weeks were purchased from the Sun Yat‐Sen University Experimental Animal Center. The protocol approved by the Institutional Animal Care and Use Committee at Sun Yat‐Sen University was adhered to for in vivo studies documented herein (SYSU‐IACUC‐2021‐B0690).2.11n = 3) and intravenously injected with either (i) free Cy5‐siNEAT2, (ii) Control NPs, or (iii) Cy5‐siNEAT2‐loaded NPs at a siRNA dose of 1 nmol per mouse. Orbital vein blood (20 μl) was withdrawn at various predetermined intervals utilizing a tube that contained heparin. The bleeding was stopped by pressing the wound for several seconds. A microplate reader was used to determine the fluorescence intensity of Cy5‐siNEAT2 in the blood.Healthy female BALB/c mice were randomly divided into three groups ‐expressing SK‐Hep1 cells (1 × 106 cells suspended in 30 μl of PBS solution). After closing the abdominal cavity, D‐luciferin substrate was injected intraperitoneally at a dose of 150 mg/kg. An IVIS Lumina III  imaging system was used to view the growth of the tumors in the mice. Bioluminescence imaging was used to evaluate the mean radiance of tumor sites.Subcutaneous injection with 200 mL of SK‐Hep1 cell suspension (DMEM:Matrigel in a 1:1 volume ratio) with a density of 1 × 102.13n = 3), with each given an intravenous injection of either (i) free Cy5‐siNEAT2, (ii) Control NPs, or (iii) Cy5‐siNEAT2‐loaded NPs at a siRNA dose of 1 nmol per mouse. Following 24 h after the time of injection, In vivo imaging system  was used to image the mice, following which organs and tumors were harvested and imaged. Image‐J was used to quantify the fluorescence intensity of each tissue; this measurement was used to assess the accumulation of Cy5‐siNEAT2 in the organs and tumors imaged.Mice that carried SK‐Hep1 subcutaneous tumors were divided randomly into three groups (2.14n = 5), with each given an intravenous injection (once every 2 days) of either (i) PBS, (ii) naked siNEAT2 (1 nmol siRNA dose for each mouse), (iii) Control NPs (1 nmol siRNA dose for each mouse), (iv) NPs loaded scrambled siRNA (1 nmol siRNA dose for each mouse), or (v) siNEAT2‐loaded NPs (1 nmol siRNA dose for each mouse). Four consecutive injections were administered to the mice, following which the growth of the tumor was monitored once every 2 days using a caliper to evaluate perpendicular diameters. The tumor volume was calculated as follows:W and L are the shortest and longest diameters, respectively.Mice that carried SK‐Hep1 subcutaneous tumors were divided randomly into five groups (2.15n = 5), with each group being given an intravenous injection (once every 2 days) of either (i) PBS, (ii) naked siNEAT2 (1 nmol siRNA dose for each mouse), (iii) Control NPs (1 nmol siRNA dose for each mouse), (iv) NPs loaded scrambled siRNA (1 nmol siRNA dose for each mouse), or (v) siNEAT2‐loaded NPs (1 nmol siRNA dose for each mouse). Four consecutive injections were administered to all the mice. A bioluminescence imaging system was used to measure the growth of the tumor during the first week and at the end of the second week. All tumors were collected and sectioned at the end of the experiment for histological analysis.Mice that carried SK‐Hep1 orthotopic tumors were divided randomly into five groups . Given this data, the siNEAT2‐loaded NPs were prepared using the method of self‐assembly nanoprecipitation by mixing the DMF solution carrying Meo‐PEG‐b‐PDPA and NTPA  are majorly distributed in the cytoplasm. Only a small amount of encapsulated siNEAT2 is capable of entering the nuclei in this case  was encapsulated in the NPs20. This was followed by its incubation with SK‐Hep1. As illustrated by Figure ” effect,14 thee Figure . This hae Figure 3,B. In ce Figure ,[19]e Figure 3,B. These Figure , indicat2 Figure 3,B. Thes2 Figure , which w3.3 Based on the siNEAT2 dose which determines the differential silencing efficacy, all siNEAT2‐loaded NPs were capable of down‐regulating the expression of lncNEAT2 . As one may observe in Figure  additionally, 12 h after the injection, over 10% of injected NPs persist in the blood. Equipped with such a property, the NPs20 can greatly accumulate in the tumor tissues following intravenous injection into the SK‐Hep1 subcutaneous tumor‐bearing mice  . Following the administering of four consecutive injections, tumor growth was shown to have been inhibited significantly, with a less than threefold increase in the size of the tumor (from ∼79 to ∼226 mm3) within 20 days  Figure . Upon ob) Figure , the NPs) Figure . Subsequs Figure . In comp0 Figure , in termn = 3), it was possible for us to establish an orthotopic liver cancer model to further evaluate the anticancer effect of NPs20. Using bioluminescence imaging, the average radiance of tumor tissues supported the monitoring of tumor growth  to sufficiently measure the potential in vivo side effects that correspond with it. The level of cytokines (Figure In subcutaneous and orthotopic tumor models, the administering of NPs20 was found to not affect mouse weight Figure , suggests Figure  and bloos Figure  was founs Figure . Altoget4A nucleus‐specific RNAi nanoplatform was developed herein for the targeted regulation of nuclear lncRNA function, which is bound to support and provide effective cancer therapy. Long blood circulation and high accumulation in tumor tissues are two primary properties associated with this newly developed RNAi nanoplatform. Following internalization by tumor cells, the protonation of pH‐responsive PDPA polymer in the endosome was capable of inducing rapid NP disassociation and efficient endosomal escape of exposed NTPA/siRNA complexes. This allowed for the subsequent targeting of the nucleus by leveraging the specific interaction between the NLS peptide sequence of NTPA and importin α/β heterodimer, which achieves nuclear siRNA transport. Altogether, this leads to the efficient suppression of nuclear lncNEAT2 expression and significant inhibition of tumor growth in liver cancer. The nucleus‐specific RNAi nanoplatform could be used as an effective tool to regulate the function of various nuclear lncRNAs for cancer therapy.The authors declare no conflict of interest.Additional supporting information can be found online in the Supporting Information section at the end of this articleClick here for additional data file.


A new fingerprinting methodology is presented for phase discrimination in complex solid solutions near the morphotropic phase boundary. 1/3Nb2/3)O3–PbTiO3], PIN–PMN–PT [Pb(In1/2Nb1/2)O3–Pb(Mg1/3Nb2/3)O3–PbTiO3] and PZT [PbO3], using diffuse multiple scattering and Kossel line diffraction techniques. The method exploits the splitting of triple line intersections from special coplanar reflections combined with logical constraints to generate a splitting fingerprint for robust crystallographic phase determination and discrimination.A novel methodology is presented for identifying and distinguishing between structural phases in multi-phasic systems, such as piezoelectric materials like PMN–PT [Pb(Mg Initially, two phases were present under low stress, indicated by the split lines in Fig. 3The [011] poled PIN–PMN–PT, 12 × 4 × 4 mm, sample was placed in a multifunctional stress–strain system (Model ES1500 by Electrosciences Ltd) and mounted on a Newport kappa-geometry diffractometer on the I16 beamline (Collins 3.a)].DMS can be described by an extension of the multiple scattering (MS) geometry. A geometrical representation of the MS condition is conveniently described using Ewald construction  and the three unique settings for the monoclinic system [Fig. 5d)]. The low-stress phases can be explained by the green and blue columns (columns 1 and 4), indicating that both phases are rhombohedral, or two domains of the same phase. Following the same logic, the splitting pattern for the high-stress phase matches the yellow column (column 1), indicating that it is monoclinic. Once the phases have been identified, the lines can be assigned to their respective phases and used to refine the lattice parameters to a precision of 5 × 10−5Å (Lonsdale, 1947et al., 2021Fig. 54.We have demonstrated a new methodology for discriminating between phases in complex solid solutions. A splitting fingerprint over multiple triplets can be generated. This reduces the phase identification to the simple task of using a lookup table. The technique has been developed for DMS but is applicable to Kossel lines (Kossel, 1935


III complex [Cu(CF3)4]1−, in which the metal center tries to populate its formally unoccupied 3dx2‐y2 orbital via σ‐bonding, leading to a reduced d10 CuI description. However, Au L3‐edge X‐ray absorption spectroscopy reveals excitation into the d‐orbital of the AuIII species is still possible, showing that a genuine d10 configuration is not achieved. We also find an increased electron‐sharing nature of the σ‐bonds in the AuI species, relative to their AgI and CuI analogues, due to the low‐lying 6s orbital. We propose that gold +I and +III complexes form similar bonds with substrates, owing primarily to participation of the 5dx2‐y2 or 6s orbital, respectively, in bonding, indicating why AuI and AuIII complexes often have similar reactivity.Several gold +I and +III complexes are investigated computationally and spectroscopically, focusing on the d‐configuration and physical oxidation state of the metal center. Density functional theory calculations reveal the non‐negligible electron‐sharing covalent character of the metal‐to‐ligand σ‐bonding framework. The bonding of gold(III) is shown to be isoelectronic to the formal Cu Through the interplay of X‐ray spectroscopy and computational analysis, we show that gold +I and +III complexes, despite their physically distinct electronic structures, tend to activate substrates to similar extents. We focus in particular on the role of electron‐sharing covalency of the metal‐ligand bonds and provide an explanation for the often‐similar reactivities observed for gold complexes in these physical oxidation states. OSs) is becoming more relevant,The field of gold catalysis initially emphasized the use of gold(I) and gold(III) species by creatively exploiting their Lewis acidic properties and π‐activation ability e.g. to functionalize unsaturated substrates.OS of an atom in a molecule as the “charge after ionic approximation of its bonds”,OSs play in reactivity may therefore guide future developments. On this quest, we may gain insight and inspiration from other coinage metals. Isoelectronic to gold(III), the electronic structure of formal d8 copper(III) complexes, such as [Cu(CF3)4]1−, has been the subject of much debate.3)4]1− as containing a d10 copper(I) center.10 copper(I),β valence‐to‐core X‐ray emission spectroscopy) has provided “strong evidence for the presence of a low‐spin d8 CuIII” center in [Cu(CF3)4]1−.3)4]1− and found, using an Intrinsic Bond Orbital (IBO) analysis10 configuration is never obtained. We concluded that the tension between the intrinsic d8 configuration of copper(III) and the summed (bonding+non‐bonding) d‐electron populations can be resolved by labelling this bonding scenario as a quasi‐d10 configuration of the metal.10 copper(I) complexes such as [Cu(CF3)2]1−, whose 3d‐orbitals are fully occupied.IUPAC fairly recently defined the Pivoting back to gold, we may therefore ask:10 configuration an appropriate description of formal gold(III) complexes?is a quasi‐dhow different are the spectroscopic signatures of typical gold(I) and gold(III) complexes?do (a) and (b) carry implications for the roles of gold(I) vs. gold(III) in catalysis?3‐edge X‐ray Absorption Near Edge Spectroscopy (XANES). Au L3‐edge XANES has been previously applied to study gold clustersIn this work we investigate the electronic structure of a series of formal gold(I) and gold(III) complexes Scheme , addressThe Intrinsic Electronic Structure of Gold(III), Identifying a Quasi‐d10Configuration: We may gain immediate insight into the electronic structure of a typical gold(III) complex via examination of the Intrinsic Bonding Orbitals (IBOs)IIICl complex (1) , well localized onto the gold center (q(Au)δ‐IBO >1.96), i.e., we can identify an intrinsic d8 configuration IBO with Au 5dx2‐y2 character (see Table S1). We can judge the degree of electron sharing in the metal‐ligand σ‐bonding framework via inspection of the IBO partial charge distributions. For an ideal electron‐sharing bond (a non‐polar bond), we would expect one electron's worth of density ascribable to the metal, i.e., an IBO with metal partial charge M(1.00). The IBO of an ideal dative bond (polarized towards the ligand) would have a metal charge approaching zero, M(0.00). Where do the σ‐bonds of the formal gold(III) complex (1) lie on this bonding spectrum? Gold's partial charge in each of the σ‐IBOs, q(Au)σ‐IBO, lies around 0.5 (0.39–0.56), i.e., approximately halfway between the idealized dative and electron‐sharing scenarios. The total amount of electron density gold recovers through σ‐bonding, obtained by summing over these four bonds (Σq(Au)σ‐IBO) is 1.97e. These two electrons worth of density are in addition to the intrinsic d8 configuration, and we may thus describe this bonding scenario as a quasi‐d10 configuration at the metal center. This is isoelectronic to the formal copper(III) complex [Cu(CF3)4]1−,3)4]1− and other (trifluoromethylated) gold(III) complexes.(1–5) e.g. the individual metal IBO partial charges, q(Au)σ‐IBO, do change somewhat, but their sums, Σq(Au)σ‐IBO, and total d‐electron counts do so to a much lesser degree, indicating a similar cumulative amount of electron‐sharing in their σ‐bonding frameworks (Table phenyl bond in the C^N^C pincer ligand in (1) is slightly more electron‐sharing, as compared to the Au−Npyridine bond its N^N^N analogue (3). This effect is compensated by an increase in the dative character of the Au−Cl bond in (1).For the other formal gold(III) compounds –5 e.g. tEint) is simply the difference between the energies of the molecule and the fragments (eq. 1). The essence of EDA is that ΔEint is split up, or decomposed, into chemically interpretable contributions: the quasiclassical electrostatic interaction energy, ΔEelstat; the Pauli exchange repulsion, ΔEPauli; and the orbital mixing term, ΔEorb (eq. 2). The orbital mixing term  is the most relevant to the present purpose as it measures how much the orbitals of the fragments change (mix) upon molecular formation and can therefore be used to judge the suitability of a chosen fragmentation scheme. A smaller ΔEorb means less energetic gain due to orbital mixing, i.e., the chosen fragment states are more similar to the relaxed molecule.Like IBO analysis, Energy Decomposition Analysis (EDA)(1–7) into two fragments: the metal (Aun+) and the ligand(s) (Ln−). The electronic configuration of the metal fragment was varied from d8 to d10 by changing its charge  and enforcing local symmetry (see Supporting Information for further details). Splitting the formal gold(III) complex (1) into (5d10 Au+ & L−) fragments is found to be most favorable, as its ΔEorb is smaller than both the (5d9 Au2+ & L2−) and (5d8Au3+ & L3−) fragmentations by several hundred kcal mol−1  reveals that fragmenting to a 5d10 metal center is most favorable in every case  compounds (1–5). This finding is contrasted by e.g., nucleophilic gold complexes, which have effective 5d106s1 configurations, as identified by comparative EDA at the same level of theory.To perform comparative EDA, we chose to fragment the compounds rge n=1, , 3 and erge n=1, , 3 and e metal Aun+ and tClassical d10Gold(I): The IBOs of a typical gold(I) complex, the N‐heterocyclic carbene (NHC) gold(I) chloride complex NHC−Au−Cl (6) . The ΔEorb from the EDA of the formal gold(I) complexes (6) and (7) , seen in the IBO analysis, can be further probed by including [Xe]4f145d106s1 fragment states in the EDA. Notably, the ΔEorb of the [Xe]4f145d106s1 fragment states of (6) and (7)  indicates they are in relatively close competition with the [Xe]4f145d106s0 configuration .(6) (NHC−Ag−Cl and NHC−Cu−Cl), indicate diminished participation of the valence s‐orbital in the metal‐ligand σ‐bonding.) Figure , reveal n Figure a, suppors Figure b, which Spectroscopic Signatures of d10Gold(I) vs. Quasi‐d10Gold(III): Now that the quasi‐d10 description for gold(III) complexes has been established based on our computational analysis above, we may ask whether we can observe excitation into the d‐orbital manifold. To address this question, we applied Au L3‐edge X‐ray Absorption Near Edge Spectroscopy (XANES). The so‐called whiteline absorption feature of a Au L3‐edge XANES spectrum (ca. 11 915–11 924 eV) formally corresponds to the 2p→5d transition.10). In the case of molecular compounds, such as (1)–(7), these final states can either be fully localized on the metal or hybridized in covalent bonds with the ligands, depending on the nature of the metal‐ligand bonding.(6) and (7) –(4) all show similarly strong whiteline absorptions. The L3‐edge peak heights of the tetrahaloaurate salts (5 a) and (5 b) are somewhat anomalous as they are significantly lower than those of the gold(III) complexes, although the whiteline absorption features are still clearly visible (see Supporting Information for further details). The formal gold(III) complexes (1)–(4) exhibit remarkably similar absorption patterns, further demonstrating a unity in their electronic structures. The formal gold(I) complexes (6) and (7) are equally similar to each other. While no simple relationship was found between the edge position and the metal's OS (Table S1), the spectroscopic fingerprints of gold(I) and gold(III) complexes are clearly distinct. Specifically, strong whiteline absorptions are seen for all the gold(III) complexes, due to metal‐localized final 5d10 states. This reflects the incomplete occupation of the 5d‐orbitals in their  ground state, clearly demonstrating that d10 is not an adequate description for gold(III) complexes. For the gold(I) complexes, with their initial 5d10 states, no such excitation is possible and thus no whiteline is observed. This interpretation of Au L3‐edge absorption data is consistent with previously reported high‐energy‐resolution fluorescence‐detected XAS of Au/Al2O3,The XANES spectra of the two gold(I) complexes (1)–(4) all have intrinsic d8 configurations. Despite this, they most easily fragmented into Au d10 centers in the EDA, due to the electron‐sharing covalent contributions to the metal‐ligand σ‐bonds, i.e., quasi‐d10 configurations were identified. From the pronounced whiteline absorption features in Au XANES data of these gold(III) complexes, we can conclude that excitation into the valence d‐space is indeed still possible, further justifying the distinction between quasi‐ and classical‐d10 configurations. Although the number of complexes studied here is modest, we believe the chosen complexes are representative of typical gold(I) and gold(III) systems. For example, replacing the amide moieties in (2) with carboxylate groups in AuIIICl leads to a very similar picture , albeit one with slightly more classical (dative) metal‐ligand bonding, indicating that our findings can equally be transferred to complexes featuring oxygen‐based ligands. While these results clearly demonstrate the unsuitability of the classical‐d10 description for the formal gold(III) complexes studied here, the quasi‐d10 label is still recommended to indicate the heighted electron‐sharing nature of their metal‐ligand bonding. This is contrasted by gold complexes with more classical dative bonds e.g., fluorido gold complexes,8 character.The computational data (see above) showed that the gold(III) centers in The Role of Gold(I) vs. Gold(III) in Catalysis: In 2004, Straub reflected on the fact that both gold(I) and gold(III) had been suggested as the active species in several gold‐catalyzed reactions.OS. Jones et al. came to similar conclusions that same year, when examining C−H bond activation reactions.N‐propargyl tryptophans or tryptamines,OS formalism is supposed to summarize chemical behavior, the similarity of gold(I) and gold(III) catalysis is quite remarkable and may lead to differing explanations. For example, gold‐catalyzed reactions, where gold acts electrophilically as a Lewis acid /gold(III) couples),1−.Through analysis of computational and spectroscopic data, the electronic structures of several representative gold(I) and gold(III) complexes are probed. Our results support classical dThe authors declare no conflict of interest.1As a service to our authors and readers, this journal provides supporting information supplied by the authors. Such materials are peer reviewed and may be re‐organized for online delivery, but are not copy‐edited or typeset. Technical support issues arising from supporting information (other than missing files) should be addressed to the authors.Supporting InformationClick here for additional data file.Supporting InformationClick here for additional data file.


With the increased brilliance at the European Research Facility–Extremely Brilliant Source (ESRF–EBS), a beam-induced reduction of non-stochiometric iron oxide nanoparticles  to magnetite was observed in a mixture of ethanol and water with low ethanol concentration. in situ studies with unprecedented time resolution. While radiation damage is commonly associated with degradation of organic matter such as ionic liquids or polymers in the synchrotron beam, this study clearly shows that highly brilliant X-ray beams readily induce structural changes and beam damage in inorganic matter, too. Here, the reduction of Fe3+ to Fe2+ in iron oxide nanoparticles by radicals in the brilliant ESRF–EBS beam, not observed before the upgrade, is reported. Radicals are created due to radiolysis of an EtOH–H2O mixture with low EtOH concentration (∼6 vol%). In light of extended irradiation times during insitu experiments in, for example, battery and catalysis research, beam-induced redox chemistry needs to be understood for proper interpretation of insitu data.The storage ring upgrade of the European Synchrotron Radiation Facility makes ESRF–EBS the most brilliant high-energy fourth-generation light source, enabling  Both beamlines are equipped with a PILATUS3 X CdTe 2M detector . For data processing and treatment, we used the following: for masking Fit2D and for calibration pyFAI-calib2 , for pair distribution function (PDF) processing PDFgetX3  data IgorPro by WaveMetrics.Total scattering measurements were performed at ID15-A at ESRF before the EBS upgrade and at ID31 at ESRF after the EBS upgrade, for IONPs in EtOH–H2.1.10 to 1 × 1011 photons s−1 (see Section S2 of the supporting information). Ten scans of 25 s each were taken on every sample resulting in a total radiation dose of ∼195–390 kGy . NIST chromium(III) oxide standard was used for distance calibration and determination of instrumental resolution .Data were taken with an energy of 68 keV (0.1823 Å) and a beam size of about 120 µm × 120 µm  at ID15A before the upgrade. The photon flux on the samples was estimated to be 5 × 102.2.14 photons s−1. Ten scans of 6 s each were taken on every sample resulting in a total radiation dose of ∼40000 kGy . NIST cerium(IV) oxide standard was used for distance calibration and determination of instrumental resolution .Data were taken with an energy of 65 keV (0.1907 Å) and a beam size of about 100 µm × 300 µm  at ID31 after the upgrade. The photon flux on the samples was 1 × 103.2O mixture with low EtOH concentration (6 vol%) at ESRF–EBS, we observed shifts of the Bragg peaks over the total time of exposure of 60 s, whereby the biggest shift was observed between the first and second scan between 6 and 12 s. Initially, the IONPs feature an inverse spinel structure with a composition close to maghemite (see Section S3 of the supporting information). Fig. 1a) shows the diffraction pattern of such an IONP dispersion in the Q-range of 1–5 Å−1 in comparison with that of water. The diffraction patterns are similar, yet the first sharp diffraction peak (FSDP) of the dispersion is broadened and slightly shifted to lower Q-values due to the low amount of EtOH . The Bragg peaks of the IONPs are visible on top of the broad diffraction from the solvent. In Fig. 1b) the ten scans taken successively at ID31 after the EBS upgrade are shown in the Q-range of the (333) and (440) Bragg reflexes between 3.7 and 4.5 Å−1, for one exemplary dispersion of IONPs in EtOH–H2O mixture with low EtOH concentration (ID31-1-EtOH–H2O). Evidently, both peaks shift to lower Q-values after the first scan. This becomes even clearer in the inset which shows the (440) Bragg reflex for scan 1, 3 and 10 only, corrected for the water background. The Bragg peaks of the same IONPs dispersed in solely water (ID31-1-H2O) did not shift – see Fig. 1c). Further, we compared these data with data of samples prepared the same way taken at ID15-A ESRF before the EBS upgrade, thus with lower photon flux per irradiated volume, and consequently resulting in lower total radiation dose despite the smaller beam size and longer exposure time (cf. Section S2 of the supporting information). In this case, too, no peak shift of the IONP Bragg peaks over time could be observed – see Fig. 1d) (shown for ID15-A-1-EtOH–H2O).Performing total scattering on IONPs of 7 and 15 nm in diameter, dispersed in an EtOH–H2O mixtures after the upgrade (case 1) and its lack in only H2O after the upgrade (case 2) and the lack in EtOH–H2O mixtures before the upgrade (case 3), for several samples each. In order to quantify the shift and make sure it is bigger than the uncertainty in instrumental resolution, three scans  of two samples of each of the three cases were investigated in more detail. For those scans a Gaussian function was fitted to the (440) reflex in I(Q) data (see Section S5 of the supporting information). Since a shift to lower Q-values is associated with a lattice expansion, this lattice expansion was also confirmed and quantified by PDF fits on the differential-PDFs  (see Section S6 of the supporting information). The results of both evaluations are listed in Table 1We proved the reproducibility of the shift of Bragg peaks in EtOH–Het al., 2012et al., 1969et al., 2012et al., 2016et al., 2016et al., 2012et al., 2016et al., 20123+containing) IONPs are reduced to magnetite. Magnetite crystallizes in the inverse spinel structure, with O2− anions forming a cubic close packing, Fe3+ ions occupying the tetrahedral sites and a 1:1 mixture of Fe2+ and Fe3+ ions on the octahedral sites  all of the initial one-third of Fe2+ was oxidized to Fe3+, and thus the number of vacancies is maximal. These vacancies can either be randomly distributed on the octahedral sites or vacancy ordering can exist, lowering the symmetry of the structure  in our experiments has been higher than the total radiation doses reported in studies which aimed at synthesizing inorganic nanoparticles via radiolysis by deliberate exposure of metal ion precursor solutions to strong ionizing radiation  scans.When water is irradiated with ionizing radiation, like radioactive nuclei, beams of charged particles and X-rays with a photon energy >100 eV, radiolysis of water takes place  composition to magnetite in the highly brilliant synchrotron beam at ID31, ESRF–EBS. This is, to our knowledge, the first showcase of beam-induced damage in inorganic solids after the ESRF upgrade. Given its nature in redox chemistry and evolving radicals in solution, we expect this study to be highly relevant to a range of fields including in situ studies in catalysis and energy applications such as fuel cell or battery research. Time-dependent sample-specific changes need to be questioned in light of possibly radiolysis-induced redox chemistry.In summary, we have observed beam-induced structural changes in iron oxide nanoparticles created by radiolysis during total scattering experiments on nanoparticle dispersions in an EtOH–H5.supporting information: Bondaz et al. (2020et al. (2004et al. (2020et al. (2011et al. (2019The following references, not cited in the main body of the paper, have been cited in the  al. 2020; Caruntu al. 2004; Cooper  al. 2020; Greaves al. 2020; Qu et a al. 2011; Thomä e al. 2019.10.1107/S1600577522011523/fv5157sup1.pdfSections S1 to S6, including Tables S1 to S5 and Figures S1 to S4. DOI:


R2 used for linear models. Such a measure has long been sought to achieve ‘comparability’ of different empirical models across multiple samples addressing similar social questions. To this end, we propose a novel R2 measure for probit models using the notion of surrogacy – simulating a continuous variable S as a surrogate of the original discrete response . The proposed R2 is the proportion of the variance of the surrogate response explained by explanatory variables through a linear model, and we call it a surrogate R2. This paper shows both theoretically and numerically that the surrogate R2 approximates the OLS R2 based on the latent continuous variable, preserves the interpretation of explained variation, and maintains monotonicity between nested models. As no other pseudo R2, McKelvey and Zavoina's and McFadden's included, can meet all the three criteria simultaneously, our measure fills this crucial void in probit model inference.Probit models are used extensively for inferential purposes in the social sciences as discrete data are prevalent in a vast body of social studies. Among many accompanying model inference problems, a critical question remains unsettled: how to develop a goodness‐of‐fit measure that resembles the ordinary least square (OLS)  Probit models are used widely in social research to make inference as binary and ordinal outcomes are common in economic, political, behavioural, and psychological studies. Broadly speaking, there are three basic inference problems that need to be solved in probit analysis: (i) Which variables are significant for explanatory analysis? (ii) Which variables should be included for predictive analysis? (iii) Given the variables selected in (i) or (ii) and a candidate model, how well does the model fit the data? Problems (i) and (ii) can be tackled using the likelihood ratio test (hypothesis testing) and the Akaike (AIC) or Bayesian (BIC) information criteria (variable selection), respectively. However, the hypothesis testing or variable selection solutions do not address problem (iii): how well does the selected model fit the data?R2 is one of the key inference outcomes empirical researchers rely on in model assessment. It indicates the overall explanatory power of a model. Let us consider a situation where a few candidate models are selected using different criteria . Often these models are comparable and which model is the ‘best’ depends on the evaluation criterion domain experts would like to adopt. The choice of the final model may not be a purely statistical issue when it comes down to only a few candidate models as the difference between them may not be significant. What domain experts are more interested in knowing is what is the explanatory power of these similar models, for example, at the 7% level or 70% level. As the power being 7% or 70% will give completely different insights into the subject matter, it is imperative to have a sensible goodness‐of‐fit measure for probit analysis. For example, if previous studies give R2 values all around 70% while the current study yields an R2 of 20%, special attention needs to be paid to the design and quality of the study itself.A solution for problem (iii), such as an overall goodness‐of‐fit measure, is critical in empirical research. When linear models are employed, for instance, the ordinary least squares (OLS) R2, we have seen unceasing efforts to develop an analogous notion for generalized linear models where the response variable is binary or ordinal . We simulate 50,000 observations from the probit model for a binary responseβ=β0β1β2Τ=2,−1,0.7Τ, X1∼U−3,3, X2=X11X1≤−0.2+2.8−X11X1>−0.2 such that X2∼U−3,3, and the correlation ρX1,X2≈.70. We calculate the R2 measures for the full model which includes both X1 and X2 and a reduced model which contains X1 only. Displayed in Table ROLS2, McKelvey and Zavoina's RMZ2, and our surrogate RS2. The unobservable ROLS2 serves as the benchmark in the comparison. When both of the explanatory variables are included, the three R2 measures are close to each other (=.61). If we drop X2 from the model, both ROLS2 and RS2 naturally fall to a smaller value of .31. A shocking observation is that McKelvey and Zavoina's RMZ2 moves in a different direction: it increases by a sizeable margin and becomes .76. It approximates the OLS (C2) It preserves the interpretation of explained variation.(C3) It maintains monotonicity between nested models.R2 measures satisfy criteria (C1)–(C3) simultaneously. For example, McKelvey and Zavoina's RMZ2 does not guarantee that criteria (C1) and (C3) are met, as demonstrated in our counterexample. There is another broad class of pseudo‐R2 measures developed based on the ratio of likelihoods; see McFadden's  and (C2) (see our discussion on their merits in other aspects).No existing pseudo‐Fadden's  R2, forR2. The general idea is to simulate a continuous variable and use it as a surrogate for the original discrete response. This novel way of analysing discrete data has been proved useful in solving some previously unsolvable problems; see, for example, Liu and Zhang –(C3). It is therefore the only goodness‐of‐fit measure that resembles the OLS R2, has the explained‐variation interpretation, and maintains monotonicity between nested models. This property is achieved by generating a common surrogate response from the full model and using it for calculating R2 values for all smaller models.In this paper we propose a new notion of the goodness‐of‐fit measure for probit models. We call it a surrogate nd Zhang , Liu et nd Zhang , Cheng end Zhang , and R pnd Zhang  and Li end Zhang . This paY has J categories 1,2,…,J, with the order 1<2<⋯<J. Given a set of explanatory variables, the full model is−∞<α1<⋯<αJ=+∞ and some of the coefficients can be zero. The generic symbol Xl can represent a single variable X of interest, a high‐order term of X , or an interaction term between X and another variable. It is well known that model (1) can be expressed equivalently through a latent variable:Y can be viewed as a censored outcome followingZ in such a way that its model contains an intercept term α1, and as a result, the cutpoints to obtain Y are α1+α1α2+α1…αJ−1+α1. This mathematical manoeuvre is solely for the purpose of facilitating the calculation of our R2. As such, the model for the surrogate variable defined later will also have an intercept term, and there is no need to force it to be zero when implementing our method in statistical software.Suppose a binary or ordinal variable nd Zhang  and Liu nd Zhang , we haveS has the following properties. (i) S follows the same distribution as the latent variable Z. (ii) Both S and Z yield the same discrete outcome Y, that is, αj−1+α1<Z≤αj+α1⇔Y=j⇔αj−1+α1<S≤αj+α1foranyj. (iii) S is observable, whereas Z is not. These properties provide the theoretical grounds for the use of S as a surrogate response in our analysis and inference, in lieu of the original discrete response Y. This idea will prove useful in developing a new way to measure the goodness of fit of probit models.For discrete data analysis the surrogate idea is to simulate a continuous response variable and use it as a surrogate of the original discrete response. See Liu and Zhang  and Liu e denote the surrogate residual variable: e=S−ES  as a surrogate goodness‐of‐fit measure for the original probit model (1). For notational clarity, we writeX1…Xq is a subset of X1…Xp, then RS2X1…Xq is calculated using the same surrogate response S generated from the full model (1).Let R2 defined as such inherits the interpretation of explained variation, and it therefore satisfies criterion (C2) set out in the introduction. It is the proportion of the variance of the surrogate response S that can be explained by the covariates. Here, we have used the simulated continuous variable S to substitute the original discrete data Y. Such a substitution is a statistical tactic that can help achieve a close approximation to the OLS R2 based on the latent variable, which will be demonstrated in the sections that follow. Furthermore, ‘mapping’ the variability of the ordinal data onto a continuous scale, which is the same scale as the latent variable, also permits the ‘comparability’ among different models and samples as discussed in the introduction. It allows domain experts to compare the goodness‐of‐fit measure of a probit model with that of a linear model, if both samples address the same subject matter. The comparability is in fact part of the motivation of seeking an R2 measure for probit models that resembles the OLS R2 in social studies.The surrogate R2 approximates the OLS R2 and maintains the monotonicity between nested models. It therefore meets the other two criteria (C1) and (C3) set out in the introduction.In the next section, we will show theoretically that the surrogate RS2 and the OLS R2, we review some well‐known results when a sample z=z1,…,zn′ of the latent Z can be observed. Let 1n×1=1…1’, xl=xl1,…,xln′, X=x1x2…xp, x¯ be the 1×p vector of column means of X, and X0=X−1x¯. The z‐sample‐based least squares estimates arez^=1α^1z+Xβ^z. R2 can be expressed as the ratio of the regression sum of squares (SSR) and the total sum of squares (SST):Vx=ℒ1x1…xp, and PVx is the projection to Vx. It is known that the following results hold: (i) β^z∼NβX0’X0−1; (ii) ∥PVx⊥z∥2∼χn−p−12; and (iii) β^z and ∥PVx⊥z∥2 are independent  β^s∼NβX0’X0−1; (ii') ∥PVx⊥s∥2∼χn−p−12; and (iii') β^s and ∥PVx⊥s∥2 are independent.Using a sample of the surrogate response z‐based inference and (i')‐(iii') for s‐based inference, we can immediately establish the following result.Proposition 1Given a fixed design matrixXwith a fixed sample sizen, the surrogateRS2follows the same distribution asROLS2.In view of results (i)–(iii) for n→∞, it is known that, in probability, β^z→β, β^s→β, ∥PVx⊥z∥2/n−p−1→1, and ∥PVx⊥s∥2/n−p−1→1. Let Qx,n=X0′X0/n−1 and assume Qx=limn→∞Qx,n exists. Then both RS2 and ROLS2 converge in probability toX, the matrix Qx,n converges to ∑x=CovX, the variance–covariance matrix of X, under some weak conditions. Thus, we immediately have the following result, which states that RS2 and ROLS2 approaches the same limiting value.Proposition 2Xl are random, then both RS2 and ROLS2 converge to β′∑xββ′∑xβ+1 in probability, where ∑x is the variance–covariance matrix of X.If the explanatory variables As the sample size RS2 resembles the OLS R2 in the sense that, probabilistically, the former behaves in the same way as the latter. In light of these results, we illustrate in Figure R2 measures. The diagram advocates the use of the surrogate R2 to measure the goodness of fit of probit models as we observe that (i) the discrete data of Y are ‘sandwiched’ by continuous data of Z and S; and (ii) the z‐based and s‐based R2 measures are the ‘same’ in the sense that they follow the same distribution, at least asymptotically. The sandwich rule may suggest we use either ROLS2 or RS2 as a measure of how well the model fits the data. As the former is not available to us in practice, our only choice is to use RS2.Propositions R2 is equal to the square of the correlation coefficient between the actual and fitted values of the response variable. There is also a one‐to‐one correspondence between ROLS2 and the F statistic. In what follows we will show that similar results can be established for our surrogate RS2.Proposition 3The surrogateRS2≡rss^2, wherer⋅⋅is the sample Pearson correlation coefficient ands^=1α^1s+Xβ^s.. It is known that for linear models, the OLS s−1s¯=s−s^+s^−1s¯ and s−s^⊥s^−1s¯. The sample Pearson correlation coefficient between s and s^ isRS2 to the F statistic, we defineFS should follow an F distribution with p and n−p−1 degrees of freedom, if the regression coefficients in the probit model (1) satisfy that β1=⋯=βp=0. As a simple algebraic derivation yieldsF statistic and RS2.Proposition 4F statistic). The surrogate R‐squared has a one‐to‐one correspondence to theFstatistic through. The purpose of presenting Propositions S be generated using a full model in (1); and (ii) this surrogate response be used to calculate RS2 for all smaller models. We offer detailed discussions on this point in the last section.To guarantee monotonicity, we require that (i) a common surrogate response RS2 depend on the regression coefficients β in the full model (1), which is used to generate the surrogate response S. As long as the estimates of the β s are consistent, the distributional statements in this section still hold, albeit in an approximate sense. The closeness of the approximation will be evaluated in the simulation study in Section The exact distributions of R2 measure relies on the simulated surrogate response S. It should be acknowledged that any one‐time simulation‐based statistic carries another layer of uncertainty. To reduce this uncertainty to the extent that the simulation has little impact on decision‐making, we can consider performing multiple sampling as suggested by Liu et al.  to the bootstrap sample Sb* conditional on yb*xb*β^b* and obtain a size‐n sample sb*;Simulate a surrogate response sb*xb* and calculate its OLS R2 measure. This value is denoted by RSb*2.Fit a linear regression model to the bootstrap data Step 1: To obtain the End For loop.CI1−α=qα/2q1−α/2,Step 2: The interval measure is qν is the νth quantile of the bootstrap copies RS1*2…RSB*2.where Our proposed u et al. . For exau et al. , we use bth bootstrap sample yb*Xb*, which produces the bth copy of our surrogate RSb*2. This procedure is repeated B times, resulting in a set of bootstrap copies RS1*2…RSB*2. In step 2, the α/2 and 1−α/2 quantiles of this bootstrap set are extracted to form a 1001−α% confidence interval. We use B=2000 in our numerical implementation following the suggestion made by Efron and Tibshirani  and varying degrees of correlations . We compare our surrogate RSβ^2 and RSβ2, where the surrogate response S is generated conditional on an estimate β^ and the true value of β, respectively; the OLS R2 which serves as the benchmark; McKelvey and Zavoina's RMZ2; and McFadden's RMcF2  for reference.Simulation studies are conducted to numerically examine the point and interval Setting 1 (p=10 with mild correlations). We simulate an ordinal outcome from the probit model (1). Specifically, we set α1α2=1,2.9 such that Y has three categories. Among p=10 explanatory variables, five have non‐zero coefficients {β1,…,β5} = {.8, .7, .6, .6, .5} and the rest have zero coefficients. The explanatory variables follow a multivariate normal distribution with marginals Xl∼N0,1 and Cor = .2. The setting is illustrated below with the true signals shaded.R2 measures for the models with different sets of explanatory variables. The numeric values are arithmetic averages over 2000 simulation repetitions. For the full model containing all Xs, we observe that RSβ2 is very close to ROLS2=.799, even when the sample size is merely 200. If implemented with the estimated parameters, the resulting RSβ^2=.815 remains close to ROLS2. The numerical difference between the two decreases further, being <1%, as the sample size increases to n=500.Table R2 measures . We see a slight reduction in both RSβ^2 and ROLS2. This is consistent with our expectation as the variables X6,…,X10 are not associated with Y. When true signals are removed from the model . This simulation setting is similar to the previous one except that the set of explanatory variables is larger (p=20) and the correlations between certain variables are much stronger . Specifically, we set α1=1.2,α2=3.6, and the coefficients {β1, β3, β4, β11,…,β20} = {.8, .6, .4, .5, …, .5}. The structure of this setting is illustrated below.R2s are compared in Table RSβ^2 remain close to those of ROLS2 in all the models considered, including the full model, the models excluding a single or all non‐signals, and the models excluding a single or several true signals. Once again, we observe that RMZ2 approximates ROLS2 well and that RMcF2 is consistently smaller.The four Setting 3 (p=4 with a strong correlation). To show the advantage of our surrogate RS2 over McKelvey and Zavoina's RMZ2, we consider a setting similar to the seting of the counterexample in the introduction. The only difference is that we included two additional variables X3 and X4, both of which are independent of Y. This simulation setting is illustrated below.RMZ2. When n=1000, its value is .629 for the full mode, and it increases to .759 for a smaller model that does not contain X2. As a result, it is twice as large as the value of ROLS2. Such a notable increase is misleading in the practice of goodness‐of‐fit evaluation, and the disparity between RMZ2 and ROLS2 challenges the claim that the former is a good approximation to the latter. In contrast, Table RSβ^2 maintains monotonicity between nested models, and its values remain close to those of ROLS2. In short, it is the only goodness‐of‐fit measure that stays numerically close to ROLS2 across the models considered here.The results in Table R2 measures. Presented in Table 95% confidence intervals as well as the actual probabilities of those intervals containing the limit of the OLS R2. We do not include RMcF2 as its limit is in theory different from that of the OLS R2 (see our discussion in Section n=1000). More importantly, in setting 3, which is similar to the counterexample in the introduction, the non‐monotonicity issue of McKelvey and Zavoina's RMZ2 causes it to break down when X2 is excluded from the model. In this case, the bold numbers in the last column of Table ROLS2, which is .309.In what follows, we examine the performance of the interval R2. In contrast, the surrogate R2 is consistently close to the OLS R2, and its associated interval achieves a reasonable coverage probability  across all the models and settings considered when the sample size is moderately large . In Appendix R2 maintains monotonicity between nested models whereas McKelvey and Zavoina's R2 does not.To summarize, the non‐monotonicity seen in Table RS2 in an actual model building procedure for a wine tasting preference data set. We stress that the focus is not on what criteria to select variables but on how to measure the goodness of fit of each candidate model considered in the entire model building process, and how to quantify and compare the contribution of each variable to the final model in terms of the explanatory power.We illustrate the utility of the proposed surrogate n = 4898) of vinho verde wine from the North of Portugal. The outcome of interest preference is a rating score with ordinal values between 0 and 10. The observed ratings are 3 (20 observations), 4 (163), 5 (1457), 6 (2198), 7 (880), 8 (175), and 9 (5), while other ratings are not present in the data set. The physicochemical properties examined in their study include acidity, sugar, dioxide, pH, and others  will be used to evaluate the goodness of fit of a series of reduced models in the entire modelling process. We summarize in Table In the wine industry, it is of critical importance to understand how physicochemical properties may influence human tasting preference. To this end, Cortez et al.  analysedons), 4 13, 5 (145ons), 4 13, 5 (1453), 5 145, 6 . This negligible reduction suggests that these three variables contribute little to explaining the variability of the tasting preference. It is worth noting that RMZ2 nevertheless becomes slightly larger (.3188) than its initial value (.3186) for the full model. This real data result confirms our discovery ‐ RMZ2 cannot guarantee the monotonicity between nested models – and exemplifies the need for an R2 measure that does maintain the monotonicity.Step 1: Decide which variables to keep in the presence of multicollinearity. The variable density is highly correlated with residual.sugar and alcohol, with correlations of .84 and −.78, respectively. To decide which variables to remove, we fit two reduced models: one without density and the other without {residual.sugar, alcohol}. We see a small reduction of R2 in the former model (3.40%) yet a much greater reduction in the latter (49.21%). Therefore, we decide to remove density as a remedy to avoid multicollinearity.Step 2: Rank the remaining variables based on their contribution to R2. We drop the remaining variables one at a time and examine the reduction in R2. The top three variables are alcohol (77.42%), volatile.acidity (20.32%), and residual.sugar (5.81%). The ranking seen in Table R2‐based ranking is that it allows the interpretation in terms of the explained variance, with the aid of the notion of the surrogate response. As a result, practitioners can read Table the response were continuous and the model were linear. They can decide, based on their domain knowledge and specific needs, whether or not to further trim the model. For instance, the variable pH, sitting at the bottom of Table .32% to the R2 value.Step 3:  alcohol 7.42%, voR2 measure in this real data analysis. First, as a result of its similarity to ROLS2 (C1) and its monotonicity (C3), the surrogate R2 measure can guide the entire model building and trimming process in the same way as the OLS R2 is used for linear models. Second, as it can be interpreted as the degree of the explained variation (C2), the surrogate R2 allows us to evaluate the contribution of a single variable (or a group of variables) to explaining the total variability. Third, as our method maps the variability of the ordinal data  onto the continuous scale of the latent outcome, it enables domain researchers to compare R2 values across different samples and models. To elaborate on the last point, it is well known that wine experts traditionally use a 100‐point scoring system to rate wines, and numeric scores  are often seen in retail or wholesale stores such as Kroger and Costco. Other online marketplaces or smartphone apps, such as Vivino, invite users to rate wines using a five‐star system, which gives numeric scores . As our surrogate R2 enables comparability across different samples and models, we can use the surrogate R2 value obtained here, which is 32%, to benchmark the OLS R2 values when analysing wine data sets from Kroger, Costco, or Vivino.To conclude this section, we summarize the utility of our surrogate R2 to measure the goodness of fit of a given probit model. As the explained proportion of the variance of the surrogate response, it is conceptually simple and computationally straightforward. We have justified both theoretically and numerically that the surrogate R2 approximates the OLS R2 if the latent continuous outcome can be observed. It solves the serious non‐monotonicity issue observed in McKelvey and Zavoina's RMZ2. To conclude, our surrogate R2 is the only one known so far that meets all three crucial criteria (C1)–(C3) discussed in the introduction. It therefore makes it legitimate to compare R2 values of different empirical models across multiple samples, regardless of whether the response type is continuous, binary, or ordinal. An R package SurrogateRsq will be made available to facilitate the numerical implementation in practice.In this paper we have proposed a new We conclude with further discussions on the implementation of our method.R2 values of several probit models, nested or non‐nested, trained for the same data set. In order to use our method, data analysts should initiate a proper full model, possibly using domain knowledge as well as statistical tools such as variable selection and model diagnostics. This full model should be used to generate a single surrogate response S that will be used across the board to calculate surrogate R2 values for any smaller model. To consider an illustrative example, if X1 and X2 are deemed potentially ‘important’ and it is found to be necessary to include the square of X1, we should set the full model as (F) Y∼1+X1+X2+X12 and use it to generate a surrogate response S. This response should be used to calculate surrogate R2 values for smaller models such as (A) Y∼1+X1, (B) Y∼1+X1+X12, or (C) Y∼1+X1+X2. To make this clearer, data analysts should not use models (A), (B), and (C) to separately generate three surrogate responses and calculate their corresponding R2 values. This method is flawed. It will yield a measure similar to McKelvey and Zavoina's R2, and thus it cannot achieve monotonicity and maintain a good approximation to the OLS R2.In practice, data analysts may need to compare R2 for a group of models. In fact, it is seen in linear regression analysis, where a single continuous response is readily available – so there is no need to simulate it – and this common response is used to calculate R2 for any smaller models. Monotonicity is simply a mathematical result of having a common Y. Following the same line of thought, our method seeks a common continuous ‘Y’ for a group of smaller probit models by simulating it from the full probit model. It is this similarity that allows us to establish the theoretical and numerical results presented in this paper.It is not a strong requirement to have a common (surrogate) response for the purpose of calculating and comparing R2 depends on the specification of the full model. If domain researchers have acquired data of new explanatory variables and decided to add some of them to the full model, the proposed procedure needs to be rerun to adjust our R2. The dependence on the full model is not necessarily a weakness as long as we acknowledge that inference is always made conditional on the variables available to us. As for conditional inference, the result certainly depends on what is conditioned . When new variables become available, conditional inference should be updated and the result may not remain the same. From the perspective of conditional inference, it may be an advantage of our surrogate method not always maintainingR2X1…XpX1…XpXp+1 is the R2 of the model containing X1…Xp when the set of variables X1…XpXp+1 is available.The surrogate R2 when the continuous data of Z are missing and we only observe whether or not Z is located in an interval? Through the lens of missing‐data inference, we would not expect an inference outcome, such as R2, to remain the same regardless of how much information is given: a smaller set of variables X1…Xp or a larger set X1…XpXp+1. In fact, once a larger set of information becomes available. we should rerun the analysis as a more accurate inference may be achieved with the addition of a new variable Xp+1. In fact, R2X1…XpX1…XpXp+1 can be viewed as an update of R2X1…XpX1…Xp with the added new information contained in the variable Xp+1. This update may correct McKelvey and Zavoina's method when the non‐monotonicity is an issue. This point is seen in our simulation and real‐data studies.To explain the reason, we restate this discrete data question in the missing‐data framework: how can we uncover the underlying OLS R2 that is asymptotically equivalent to the surrogate R2 and corrects McKelvey and Zavoina's R2 for reduced models. Suppose a full model is identified with X0 being the centered design matrix as stated in Section Xr be a submatrix containing the columns of X0 that correspond to the selected variables. An asymptotic version of our surrogate R2 isβ^ is the same coefficient estimate trained from the full model. When applied to the full model itself , RS,asym2=β^′X0′X0β^/β^′X0′X0β^+n=RMZ2. This result verifies again that for the full model, our surrogate R2 is asymptotically equivalent to McKelvey and Zavoina's R2 .Step 2. Use model diagnostic tools, such as those in Liu and Zhang , to adjuR2 for the full model, which value can be used to compare with R2 obtained from other empirical samples and models on the same subject matter; (ii) calculate R2 values for any other smaller models so as to facilitate model comparison for the present sample and project; (iii) gauge the R2 contribution of each individual variable to the overall explanatory power so as to understand its importance to the subject issue. Points (i)–(iii) are illustrated in our real data analysis, which exemplifies that the role of R2 measure cannot be substituted by variable selection or model diagnostics.Step 3. Initiate a full model based on steps 1–2 and simulate a surrogate response. Use this surrogate response to: (i) calculate R2 examines the uncertainty reduction using the ratio between the explained variance and the total variance of the response variable. Our proposed surrogate R2 aims to approximate it when probit models are applied to discrete data. However, variance is not the only measure of uncertainty, and Shannon entropy is clearly an alternative. Note that McFadden's R2 is the ratio of two likelihood functions which approach the conditional (on X) and unconditional entropies when the sample size increases. It is therefore another reasonable R2 measure to use in practice. As it only relies on likelihood functions, the merit of McFadden's R2 lies in its applicability to a wide range of regression models, including the probit models considered in this paper. But for probit models specifically, our surrogate R2 is shown to be analogous to the OLS R2, which is a property needed in empirical analysis to achieve comparability between different models and studies. The idea can be naturally extended to other latent variable models, such as logistic regression models. Our preliminary investigation has shown that the R2 defined in a similar way for logistic models also meets criteria (C1)–(C3). In the context of bankruptcy studies, it allows us to compare financial markets in different countries. The research results will be reported elsewhere. As a closing remark, we point out that a further development of the notion of R2 for general models without any latent variable structure is of much greater interest.The OLS All authors declare no conflict of interest.Appendix S1.Click here for additional data file.