Brain development of a school-aged boy with autism spectrum condition talented in arithmetic: a case report.

Whereas autism spectrum condition is known for its social and communicative challenges, some autistic children demonstrate unusual islets of abilities including those related to mathematics, the neurobiological underpinnings of which are increasingly becoming the focus of research. Here we describe an 8-year-old autistic boy with intellectual and language challenges, yet exceptional arithmetic ability. He can perform verbal-based multiplication of three- and even four-digit numbers within 20 seconds. To gain insights into the neural basis of his talent, we investigated the gray matter in the child's brain in comparison to typical development, applying voxel-based morphometry to magnetic resonance imaging data. The case exhibited reduced gray matter volume in regions associated with arithmetic, which may suggest an accelerated development of brain regions with arithmetic compared to typically developing individuals: potentially a key factor contributing to his exceptional talent. Taken together, this case report describes an example of the neurodiversity of autism. Our research provides valuable insights into the potential neural basis of exceptional arithmetic abilities in individuals with the autism spectrum and its potential contribution to depicting the diversity and complexity of autism.

Impacts and Risk Assessments of Climate Change for the Yields of the Major Grain Crops in China, Japan, and Korea.

Climate change poses a high risk to grain yields. Maize, rice, and wheat are the three major grain crops in China, Japan, and Korea. Assessing the impacts and risks of climate on the yields of these grain cops is crucial. An economy-climate model (C-D-C model) was established to assess the impacts of climate factors on the grain yields in different crop areas. The peaks over threshold model based on the generalized Pareto distribution was used to calculate the value at risk and the expected shortfall, which can evaluate the yield risk of different crops. The impact ratio of climate change was employed to estimate the impacts of climate change under different climate scenarios. The main conclusions can be summarized as follows: the impacts of climate factors on grain yields and the risk vary widely across the different regions and crops. Compared to 1991-2020, climate change from 2021 to 2050 exerts positive impacts on rice and wheat, while the negative impacts on maize in the crop areas are significantly affected by climate factors. The impact ratios of climate change are larger in the SSP1-2.6 and the SSP5-8.5 scenarios than under the SSP2-4.5 scenario. These findings are useful for targeting grain yields in smaller study areas.

Horizontally-oriented barium titanate@polydomine/polyimide nanocomposite films for high-temperature energy storage.

High-temperature ceramics polymer dielectric nanocomposite materials have broad application prospects in energy storage. The barium titanate (BT) plays an important role as one of outstanding representative ceramics in the dielectric nanocomposite materials. However, there is little known for the effects of two-dimensional (2D) BT morphology and layout on the properties of high-temperature nanocomposite materials. Hence, 2D scale-like BT ceramic fillers were prepared from layered K0.8Li0.27Ti1.73O4 crystals as precursors using a combined solid-state and hydrothermal process. 2D scale-like BT@polydopamine (PDA) core-shell nanocomposites were prepared via coating PDA on the BT. BT@PDA/polyimide(PI) nanocomposite films were fabricated by horizontally oriented distribution of BT@PDA in the PI matrix. The BT@PDA/PI nanocomposite films exhibit a high energy density (3.34 J/cm3) and high charge-discharge efficiency (83.68 %) at 150 °C. It is currently the highest energy storage performance in the BT/PI nanocomposite films at 150 °C. The excellent properties are due to preventing upward breakdown of electrical pathways and promoting dispersion and entanglement of the electrical pathway routes. Additionally, strong electrostatic interactions between the different polymer chains (PDA and PI) restricts the movement of space charges. This work demonstrates that introducing horizontally oriented, organically shell-modified and 2D small-sized BT nanoparticles into a PI matrix is an effective method for improving energy storage performance.

Structure, Properties, Preparation, and Application of Layered Titanates.

As a typical cation-exchangeable layered compound, layered titanate has a unique open layered structure. Its excellent physical and chemical properties allow its wide use in the energy, environmental protection, electronics, biology, and other fields. This paper reviews the recent progress in the research on the structure, synthesis, properties, and application of layered titanates. Various reactivities, as well as the advantages and disadvantages, of different synthetic methods are discussed. The reaction mechanism and influencing factors of the ion exchange reaction, intercalation reaction, and exfoliation reaction are analyzed. The latest research progress on layered titanates and their modified products in the fields of photocatalysis, adsorption, electrochemistry, and other applications is summarized. Finally, the future development of layered titanate and its exfoliated product two-dimensional nanosheets is proposed.

OBMeta: a comprehensive web server to analyze and validate gut microbial features and biomarkers for obesity-associated metabolic diseases.

MOTIVATION: Gut dysbiosis is closely associated with obesity and related metabolic diseases including type 2 diabetes (T2D) and nonalcoholic fatty liver disease (NAFLD). The gut microbial features and biomarkers have been increasingly investigated in many studies, which require further validation due to the limited sample size and various confounding factors that may affect microbial compositions in a single study. So far, it lacks a comprehensive bioinformatics pipeline providing automated statistical analysis and integrating multiple independent studies for cross-validation simultaneously. RESULTS: OBMeta aims to streamline the standard metagenomics data analysis from diversity analysis, comparative analysis, and functional analysis to co-abundance network analysis. In addition, a curated database has been established with a total of 90 public research projects, covering three different phenotypes (Obesity, T2D, and NAFLD) and more than five different intervention strategies (exercise, diet, probiotics, medication, and surgery). With OBMeta, users can not only analyze their research projects but also search and match public datasets for cross-validation. Moreover, OBMeta provides cross-phenotype and cross-intervention-based advanced validation that maximally supports preliminary findings from an individual study. To summarize, OBMeta is a comprehensive web server to analyze and validate gut microbial features and biomarkers for obesity-associated metabolic diseases. AVAILABILITY AND IMPLEMENTATION: OBMeta is freely available at: http://obmeta.met-bioinformatics.cn/.

Meet the authors: Meiling Wang, Wenjing Li, and Weixing Zhao.

Molecular Cell talks to co-first authors Meiling Wang and Wenjing Li with co-corresponding author Weixing Zhao about their paper, "Crucial roles of the BRCA1-BARD1 E3 ubiquitin ligase activity in homology-directed DNA repair" (in this issue of Molecular Cell) and what motivates their scientific pursuits.

Crucial roles of the BRCA1-BARD1 E3 ubiquitin ligase activity in homology-directed DNA repair.

The tumor-suppressor breast cancer 1 (BRCA1) in complex with BRCA1-associated really interesting new gene (RING) domain 1 (BARD1) is a RING-type ubiquitin E3 ligase that modifies nucleosomal histone and other substrates. The importance of BRCA1-BARD1 E3 activity in tumor suppression remains highly controversial, mainly stemming from studying mutant ligase-deficient BRCA1-BARD1 species that we show here still retain significant ligase activity. Using full-length BRCA1-BARD1, we establish robust BRCA1-BARD1-mediated ubiquitylation with specificity, uncover multiple modes of activity modulation, and construct a truly ligase-null variant and a variant specifically impaired in targeting nucleosomal histones. Cells expressing either of these BRCA1-BARD1 separation-of-function alleles are hypersensitive to DNA-damaging agents. Furthermore, we demonstrate that BRCA1-BARD1 ligase is not only required for DNA resection during homology-directed repair (HDR) but also contributes to later stages for HDR completion. Altogether, our findings reveal crucial, previously unrecognized roles of BRCA1-BARD1 ligase activity in genome repair via HDR, settle prior controversies regarding BRCA1-BARD1 ligase functions, and catalyze new efforts to uncover substrates related to tumor suppression.

Developmental prediction modeling based on diffusion tensor imaging uncovering age-dependent heterogeneity in early childhood autistic brain.

OBJECTIVE: There has been increasing evidence for atypical white matter (WM) microstructure in autistic people, but findings have been divergent. The development of autistic people in early childhood is clouded by the concurrently rapid brain growth, which might lead to the inconsistent findings of atypical WM microstructure in autism. Here, we aimed to reveal the developmental nature of autistic children and delineate atypical WM microstructure throughout early childhood while taking developmental considerations into account. METHOD: In this study, diffusion tensor imaging was acquired from two independent cohorts, containing 91 autistic children and 100 typically developing children (TDC), aged 4-7 years. Developmental prediction modeling using support vector regression based on TDC participants was conducted to estimate the WM atypical development index of autistic children. Then, subgroups of autistic children were identified by using the k-means clustering method and were compared to each other on the basis of demographic information, WM atypical development index, and autistic trait by using two-sample t-test. Relationship of the WM atypical development index with age was estimated by using partial correlation. Furthermore, we performed threshold-free cluster enhancement-based two-sample t-test for the group comparison in WM microstructures of each subgroup of autistic children with the rematched subsets of TDC. RESULTS: We clustered autistic children into two subgroups according to WM atypical development index. The two subgroups exhibited distinct developmental stages and age-dependent diversity. WM atypical development index was found negatively associated with age. Moreover, an inverse pattern of atypical WM microstructures and different clinical manifestations in the two stages, with subgroup 1 showing overgrowth with low level of autistic traits and subgroup 2 exhibiting delayed maturation with high level of autistic traits, were revealed. CONCLUSION: This study illustrated age-dependent heterogeneity in early childhood autistic children and delineated developmental stage-specific difference that ranged from an overgrowth pattern to a delayed pattern. Trial registration This study has been registered at ClinicalTrials.gov (Identifier: NCT02807766) on June 21, 2016 ( https://clinicaltrials.gov/ct2/show/NCT02807766 ).

BRCA1/BARD1 intrinsically disordered regions facilitate chromatin recruitment and ubiquitylation.

BRCA1/BARD1 is a tumor suppressor E3 ubiquitin (Ub) ligase with roles in DNA damage repair and in transcriptional regulation. BRCA1/BARD1 RING domains interact with nucleosomes to facilitate mono-ubiquitylation of distinct residues on the C-terminal tail of histone H2A. These enzymatic domains constitute a small fraction of the heterodimer, raising the possibility of functional chromatin interactions involving other regions such as the BARD1 C-terminal domains that bind nucleosomes containing the DNA damage signal H2A K15-Ub and H4 K20me0, or portions of the expansive intrinsically disordered regions found in both subunits. Herein, we reveal novel interactions that support robust H2A ubiquitylation activity mediated through a high-affinity, intrinsically disordered DNA-binding region of BARD1. These interactions support BRCA1/BARD1 recruitment to chromatin and sites of DNA damage in cells and contribute to their survival. We also reveal distinct BRCA1/BARD1 complexes that depend on the presence of H2A K15-Ub, including a complex where a single BARD1 subunit spans adjacent nucleosome units. Our findings identify an extensive network of multivalent BARD1-nucleosome interactions that serve as a platform for BRCA1/BARD1-associated functions on chromatin.

Oriented Plate-like KNbO3 Polycrystals: Topochemical Mesocrystal Conversion and Piezoelectric and Photocatalytic Responses.

KNbO3 (KN) with a perovskite structure is an outstanding representative of lead-free piezoelectric materials, and its mesocrystals have broad application prospects in the fields of catalysis, energy storage, and conversion. However, the formation conditions of KN mesocrystals reported so far are difficult owing to their high aspect ratio and excellent preferred orientation. In this study, the solvothermal process was used successfully to prepare the flake-like potassium salt of Lindquist hexaniobate (K8Nb6O19·10H2O). Subsequently, the precursor niobate was calcined to prepare two-dimensional (2D) plate-like KN mesocrystals. The formation mechanism of the plate-like KN mesocrystals is further revealed from a paired topochemical mesocrystal conversion of K8Nb6O19·10H2O niobate. Finally, the microscopic piezoelectric and photocatalytic responses of the obtained plate-like KN mesocrystals were investigated. The high piezoelectric coefficient of plate-like KN mesocrystals implies that excellent charge separation promotes the photocatalytic performance of rhodamine B (RhB). This study provides a strategy for the efficient application of 2D oriented materials in the field of piezoelectricity and photocatalysis.

Structural insights into BCDX2 complex function in homologous recombination.

Homologous recombination (HR) fulfils a pivotal role in the repair of DNA double-strand breaks and collapsed replication forks1. HR depends on the products of several paralogues of RAD51, including the tetrameric complex of RAD51B, RAD51C, RAD51D and XRCC2 (BCDX2)2. BCDX2 functions as a mediator of nucleoprotein filament assembly by RAD51 and single-stranded DNA (ssDNA) during HR, but its mechanism remains undefined. Here we report cryogenic electron microscopy reconstructions of human BCDX2 in apo and ssDNA-bound states. The structures reveal how the amino-terminal domains of RAD51B, RAD51C and RAD51D participate in inter-subunit interactions that underpin complex formation and ssDNA-binding specificity. Single-molecule DNA curtain analysis yields insights into how BCDX2 enhances RAD51-ssDNA nucleoprotein filament assembly. Moreover, our cryogenic electron microscopy and functional analyses explain how RAD51C alterations found in patients with cancer3-6 inactivate DNA binding and the HR mediator activity of BCDX2. Our findings shed light on the role of BCDX2 in HR and provide a foundation for understanding how pathogenic alterations in BCDX2 impact genome repair.

Lysine-specific histone demethylase 1A (KDM1A/LSD1) inhibition attenuates DNA double-strand break repair and augments the efficacy of temozolomide in glioblastoma.

BACKGROUND: Efficient DNA repair in response to standard chemo and radiation therapies often contributes to glioblastoma (GBM) therapy resistance. Understanding the mechanisms of therapy resistance and identifying the drugs that enhance the therapeutic efficacy of standard therapies may extend the survival of GBM patients. In this study, we investigated the role of KDM1A/LSD1 in DNA double-strand break (DSB) repair and a combination of KDM1A inhibitor and temozolomide (TMZ) in vitro and in vivo using patient-derived glioma stem cells (GSCs). METHODS: Brain bioavailability of the KDM1A inhibitor (NCD38) was established using LS-MS/MS. The effect of a combination of KDM1A knockdown or inhibition with TMZ was studied using cell viability and self-renewal assays. Mechanistic studies were conducted using CUT&Tag-seq, RNA-seq, RT-qPCR, western blot, homologous recombination (HR) and non-homologous end joining (NHEJ) reporter, immunofluorescence, and comet assays. Orthotopic murine models were used to study efficacy in vivo. RESULTS: TCGA analysis showed KDM1A is highly expressed in TMZ-treated GBM patients. Knockdown or knockout or inhibition of KDM1A enhanced TMZ efficacy in reducing the viability and self-renewal of GSCs. Pharmacokinetic studies established that NCD38 readily crosses the blood-brain barrier. CUT&Tag-seq studies showed that KDM1A is enriched at the promoters of DNA repair genes and RNA-seq studies confirmed that KDM1A inhibition reduced their expression. Knockdown or inhibition of KDM1A attenuated HR and NHEJ-mediated DNA repair capacity and enhanced TMZ-mediated DNA damage. A combination of KDM1A knockdown or inhibition and TMZ treatment significantly enhanced the survival of tumor-bearing mice. CONCLUSIONS: Our results provide evidence that KDM1A inhibition sensitizes GBM to TMZ via attenuation of DNA DSB repair pathways.

DNA binding and RAD51 engagement by the BRCA2 C-terminus orchestrate DNA repair and replication fork preservation.

The tumor suppressor BRCA2 participates in DNA double-strand break repair by RAD51-dependent homologous recombination and protects stressed DNA replication forks from nucleolytic attack. We demonstrate that the C-terminal Recombinase Binding (CTRB) region of BRCA2, encoded by gene exon 27, harbors a DNA binding activity. CTRB alone stimulates the DNA strand exchange activity of RAD51 and permits the utilization of RPA-coated ssDNA by RAD51 for strand exchange. Moreover, CTRB functionally synergizes with the Oligonucleotide Binding fold containing DNA binding domain and BRC4 repeat of BRCA2 in RPA-RAD51 exchange on ssDNA. Importantly, we show that the DNA binding and RAD51 interaction attributes of the CTRB are crucial for homologous recombination and protection of replication forks against MRE11-mediated attrition. Our findings shed light on the role of the CTRB region in genome repair, reveal remarkable functional plasticity of BRCA2, and help explain why deletion of Brca2 exon 27 impacts upon embryonic lethality.

Carbon dioxide emission characteristics and peak trend analysis of countries along the Belt and Road.

Under the pressure of global carbon neutrality, it is necessary to study the characteristics of carbon emissions and the trend of "carbon peaking" in countries along the "Belt and Road." Because most of these countries have not yet reached their peak carbon emissions, they still have great potential for growth, and peak carbon emissions are a prerequisite for carbon neutrality. This paper divides the countries along the Belt and Road into 9 country groups according to the level of economic development and industrial structure. Based on the carbon emission panel data of countries along the "Belt and Road" from 1970 to 2018 and environmental Kuznets curve (EKC) theory, a panel model was established for each country group for research. This paper analyzes the characteristics of carbon emissions and the trend of "carbon peaking" in these countries and analyzes the economic growth and carbon emissions in combination with the Tapio decoupling model. The decoupling relationship changes on the time scale as a supplement. The results show that in the study area, some countries have completely passed the "carbon peak." The reasons for this are as follows: first, the carbon peak is achieved through industrial upgrading; second, the "carbon peak" is caused by the drastic changes in Eastern Europe and the disintegration of the Soviet Union and deindustrialization; and third, the carbon peak is caused by poverty and population growth. Most of the remaining countries have not yet achieved the carbon peak. Among them, some countries represented by the Middle East are highly coupled with their economic development and carbon emissions. Middle-income and high-industrial-dependence countries are in the transitional period in terms of the carbon peak. Low-income and medium- and high-industrial-dependence countries are currently still in the stage of barbaric development. From the research on the decoupling situation, the relationship between the economic growth of countries along the "Belt and Road" and their carbon emissions has been improving in recent decades, and it is expected that a more ideal state of decoupling will be achieved in the future.

A Pair-Electrosynthesis for Formate at Ultra-Low Voltage Via Coupling of CO2 Reduction and Formaldehyde Oxidation.

Formate can be synthesized electrochemically by CO2 reduction reaction (CO2RR) or formaldehyde oxidation reaction (FOR). The CO2RR approach suffers from kinetic-sluggish oxygen evolution reaction at the anode. To this end, an electrochemical system combining cathodic CO2RR with anodic FOR was developed, which enables the formate electrosynthesis at ultra-low voltage. Cathodic CO2RR employing the BiOCl electrode in H-cell exhibited formate Faradaic efficiency (FE) higher than 90% within a wide potential range from - 0.48 to - 1.32 VRHE. In flow cell, the current density of 100 mA cm-2 was achieved at - 0.67 VRHE. The anodic FOR using the Cu2O electrode displayed a low onset potential of - 0.13 VRHE and nearly 100% formate and H2 selectivity from 0.05 to 0.35 VRHE. The CO2RR and FOR were constructed in a flow cell through membrane electrode assembly for the electrosynthesis of formate, where the CO2RR//FOR delivered an enhanced current density of 100 mA cm-2 at 0.86 V. This work provides a promising pair-electrosynthesis of value-added chemicals with high FE and low energy consumption.

Regulation of BRCA1 stability through the tandem UBX domains of isoleucyl-tRNA synthetase 1.

Aminoacyl-tRNA synthetases (ARSs) have evolved to acquire various additional domains. These domains allow ARSs to communicate with other cellular proteins in order to promote non-translational functions. Vertebrate cytoplasmic isoleucyl-tRNA synthetases (IARS1s) have an uncharacterized unique domain, UNE-I. Here, we present the crystal structure of the chicken IARS1 UNE-I complexed with glutamyl-tRNA synthetase 1 (EARS1). UNE-I consists of tandem ubiquitin regulatory X (UBX) domains that interact with a distinct hairpin loop on EARS1 and protect its neighboring proteins in the multi-synthetase complex from degradation. Phosphomimetic mutation of the two serine residues in the hairpin loop releases IARS1 from the complex. IARS1 interacts with BRCA1 in the nucleus, regulates its stability by inhibiting ubiquitylation via the UBX domains, and controls DNA repair function.

The Protective Effect of Sulodexide on Acute Lung Injury Induced by a Murine Model of Obstructive Jaundice.

Introduction: The effect of sulodexide (SLX) on obstructive jaundice- (OJ-) induced acute lung injury (ALI) in rats was examined in this study. Methods: In this study, 48 rats were randomly assigned to one of six groups: sham, OJ, OJ+saline, OJ+SLX (0.5 mg/ml/d), OJ+SLX (1 mg/ml/d), and OJ+SLX (2 mg/ml/d). The pathological lung injury was assessed by histological analysis and lung injury grading. ELISA kits were used to evaluate the expression of IL-6, IL-1, TNF-α, and syndecan-1 (SDC-1) in bronchoalveolar lavage fluids (BALFs). Commercial assay kits were performed to evaluate malondialdehyde (MDA) production and catalase (CAT) activity in lung tissues. The apoptosis was assessed by TUNEL assay. The lung microvascular permeability was investigated using Evans blue leakage, lung wet/dry weight (W/D) ratio, and lung permeability index (LPI). SDC-1, claudin-5, ZO-1, and VE cadherin expression levels in lung tissues were measured using Western blot. Results: The OJ-induced ALI rats showed severe lung injury. The value of IL-6, IL-1ß, TNF-α, and SDC-1 in BALFs was remarkedly increased in the OJ group. MDA content, apoptotic area, apoptotic molecules, and SDC-1 level were all higher in the OJ group's lung tissues than in the sham group. CAT activity, Evans blue leakage, W/D ratio, LPI, and expression of claudin-5, ZO-1, and VE cadherin were all lower in the OJ group compared to the sham group. The degenerative alterations in lung tissue improved after 7 days of treatment with 2 mg/ml SLX. The BALFs had lower amounts of IL-6, IL-1, TNF-α, and SDC-1. The SLX therapy reduced MDA levels while restoring CAT activity. In lung tissues, SLX reduced apoptotic area and SDC-1 expression. SLX reduced lung microvascular permeability by raising the expression of Claudin-5, ZO-1, and VE-cadherin in lung tissue when compared to the OJ group. Conclusion: The results suggested that SLX attenuates OJ-induced ALI in rats by protecting the pulmonary microvascular endothelial barrier.

Rare c-KIT c.1926delA and c.1936T>G Mutations in Exon 13 Define Imatinib Resistance in Gastrointestinal Stromal Tumors and Melanoma Patients: Case Reports and Cell Experiments.

Background: Target therapies play more and more important roles in gastrointestinal stromal tumors (GISTs) and melanoma with the advancement of clinical drugs that overcome the resistance caused by gene mutations. c-KIT gene mutations account for a large portion of GIST patients, which are known to be sensitive or resistant to tyrosine kinase inhibitors. However, the role rare mutations play in drug efficacy and progression-free duration remains elusive. Methods: Two rare mutations were identified using Sanger sequencing from the GIST and melanoma cases. Cell experiments were further carried out to demonstrate their role in the imatinib resistance. Results: c-KIT c.1926delA p.K642S*FS mutation in primary and recurrent GIST patients and c-KIT c.1936T>G p.Y646D point mutation in melanoma patients in exon 13 were first demonstrated to be novel targets resistant to imatinib agent. Conclusion: c-KIT mutations c.1926delA and c.1936T>G in exon 13 are clinically significant targets that exhibit resistance to imatinib. This study provides guidance to GIST and melanoma treatments.

Impacts of Extreme Climate Events on Future Rice Yields in Global Major Rice-Producing Regions.

Under the dual impacts of climate change and COVID-19, there are great risks to the world's food security. Rice is one of the three major food crops of the world. Assessing the impact of climate change on future rice production is very important for ensuring global food security. This article divides the world's main rice-producing regions into four regions and uses a multivariate nonlinear model based on historical economic and climatic data to explore the impacts of historical extreme climatic events and economic factors on rice yield. Based on these historical models, future climatic data, and economic data under different shared socioeconomic pathways (SSPs), the yields of four major rice-producing regions of the world under different climate change scenarios (SSP126, SSP245, and SSP585) are predicted. The research results reveal that under different climate change scenarios, extreme high-temperature events (Tx90p) and extreme precipitation events (Rx5day, R99pTOT) in the four major rice-producing regions have an upward trend in the future. Extreme low-temperature events (Tn10p) have a downward trend. In the rice-producing regions of Southeast Asia and South America, extreme precipitation events will increase significantly in the future. The prediction results of this model indicate that the rice output of these four major rice-producing regions will show an upward trend in the future. Although extreme precipitation events will have a negative impact on rice production, future increases in rice planting areas, economic development, and population growth will all contribute to an increase in rice production. The increase in food demand caused by population growth also brings uncertainty to global food security. This research is helpful for further understanding climate change trends and risks to global rice-production areas in the future and provides an important reference for global rice-production planning and risk management.

In Vitro Reconstitution of BRCA1-BARD1/RAD51-Mediated Homologous DNA Pairing.

RAD51-mediated homologous recombination (HR) is a conserved mechanism for the repair of DNA double-strand breaks and the maintenance of DNA replication forks. Several breast and ovarian tumor suppressors, including BRCA1 and BARD1, have been implicated in HR since their discovery in the 1990s. However, a holistic understanding of how they participate in HR has been hampered by the immense challenge of expressing and purifying these large and unstable protein complexes for mechanistic analysis. Recently, we have overcome such a challenge for the BRCA1-BARD1 complex, allowing us to demonstrate its pivotal role in HR via the promotion of RAD51-mediated DNA strand invasion. In this chapter, we describe detailed procedures for the expression and purification of the BRCA1-BARD1 complex and in vitro assays using this tumor suppressor complex to examine its ability to promote RAD51-mediated homologous DNA pairing. This includes two distinct biochemical assays, namely, D-loop formation and synaptic complex assembly. These methods are invaluable for studying the BRCA1-BARD1 complex and its functional interplay with other factors in the HR process.