Se-methylselenocysteine inhibits the progression of non-small cell lung cancer via ROS-mediated NF-κB signaling pathway.

Se-methylselenocysteine (MSC) is recognized for its potential in cancer prevention, yet the specific effects and underlying processes it initiates within non-small cell lung cancer (NSCLC) remain to be fully delineated. Employing a comprehensive array of assays, including CCK-8, colony formation, flow cytometry, MitoSOX Red staining, wound healing, transwell, and TUNEL staining, we evaluated MSC's effects on A549 and 95D cell lines. Our investigation extended to the ROS-mediated NF-κB signaling pathway, utilizing Western blot analysis, P65 overexpression, and the application of IκB-α inhibitor (BAY11-7082) or N-acetyl-cysteine (NAC) to elucidate MSC's mechanism of action. In vivo studies involving subcutaneous xenografts in mice further confirmed MSC's inhibitory effect on tumor growth. Our findings indicated that MSC inhibited the proliferation of A549 and 95D cells, arresting cell cycle G0/G1 phase and reducing migration and invasion, while also inducing apoptosis and increasing intracellular ROS levels. This was accompanied by modulation of key proteins, including the upregulation of p21, p53, E-cadherin, Bax, cleaved caspase-3, cleaved-PARP, and downregulation of CDK4, SOD2, GPX-1. MSC was found to inhibit the NF-κB pathway, as evidenced by decreased levels of P-P65 and P-IκBα. Notably, overexpression of P65 and modulation of ROS levels with NAC could attenuate MSC's effects on cellular proliferation and metastasis. Moreover, MSC significantly curtailed tumor growth in vivo and disrupted the NF-κB signaling pathway. In conclusion, our research demonstrates that MSC exhibits anticancer effects against NSCLC by modulating the ROS/NF-κB signaling pathway, suggesting its potential as a therapeutic agent in NSCLC treatment.

Hypofractionated radiotherapy for refractory or relapsed aggressive B-cell lymphoma in the rituximab era.

BACKGROUND: Radiotherapy (RT) is an effective and available local treatment for patients with refractory or relapsed (R/R) aggressive B-cell lymphomas. However, the value of hypofractionated RT in this setting has not been confirmed. METHODS: We retrospectively analyzed patients with R/R aggressive B-cell lymphoma who received hypofractionated RT between January 2020 and August 2022 at a single institution. The objective response rate (ORR), overall survival (OS), progression-free survival (PFS) and acute side effects were analyzed. RESULTS: A total of 30 patients were included. The median dose for residual disease was 36 Gy, at a dose per fraction of 2.3-5 Gy. After RT, the ORR and complete response (CR) rates were 90% and 80%, respectively. With a median follow-up of 10 months (range, 2-27 months), 10 patients (33.3%) experienced disease progression and three died. The 1-year OS and PFS rates for all patients were 81.8% and 66.3%, respectively. The majority (8/10) of post-RT progressions involved out-of-field relapses. Patients with relapsed diseases, no response to systemic therapy, multiple lesions at the time of RT, and no response to RT were associated with out-of-field relapses. PFS was associated with response to RT (P = 0.001) and numbers of residual sites (P < 0.001). No serious non-hematological adverse effects (≥ grade 3) associated with RT were reported. CONCLUSION: These data suggest that hypofractionated RT was effective and tolerable for patients with R/R aggressive B-cell lymphoma, especially for those that exhibited localized residual disease.

Preoperative contrast-enhanced CT-based radiomics nomogram for differentiating benign and malignant primary retroperitoneal tumors.

OBJECTIVES: This study evaluated the ability of a preoperative contrast-enhanced CT (CECT)-based radiomics nomogram to differentiate benign and malignant primary retroperitoneal tumors (PRT). METHODS: Images and data from 340 patients with pathologically confirmed PRT were randomly placed into training (n = 239) and validation sets (n = 101). Two radiologists independently analyzed all CT images and made measurements. Key characteristics were identified through least absolute shrinkage selection combined with four machine-learning classifiers (support vector machine, generalized linear model, random forest, and artificial neural network back propagation) to create a radiomics signature. Demographic data and CECT characteristics were analyzed to formulate a clinico-radiological model. Independent clinical variables were merged with the best-performing radiomics signature to develop a radiomics nomogram. The discrimination capacity and clinical value of three models were quantified by the area under the receiver operating characteristics (AUC), accuracy, and decision curve analysis. RESULTS: The radiomics nomogram was able to consistently differentiate between benign and malignant PRT in the training and validation datasets, with AUCs of 0.923 and 0.907, respectively. Decision curve analysis manifested that the nomogram achieved higher clinical net benefits than did separate use of the radiomics signature and clinico-radiological model. CONCLUSIONS: The preoperative nomogram is valuable for differentiating between benign and malignant PRT; it can also aid in treatment planning. KEY POINTS: • A noninvasive and accurate preoperative determination of benign and malignant PRT is crucial to identifying suitable treatments and predicting disease prognosis. • Associating the radiomics signature with clinical factors facilitates differentiation of malignant from benign PRT with improved diagnostic efficacy (AUC) and accuracy from 0.772 to 0.907 and from 0.723 to 0.842, respectively, compared with the clinico-radiological model alone. • For some PRT with anatomically special locations and when biopsy is extremely difficult and risky, a radiomics nomogram may provide a promising preoperative alternative for distinguishing benignity and malignancy.

Palladium-catalyzed decarboxylative α-allylation of thiazolidinones and azlactones with sulfonamido-substituted acyclic allylic carbonates.

A palladium-catalyzed decarboxylative α-allylation of thiazolidinones and azlactones with aza-π-allylpalladium zwitterionic intermediates, in situ generated from sulfonamido-substituted allylic carbonates, is successfully developed. This method allows the formation of a series of structurally diverse 5-alkylated thiazolidinones and 2-piperidones under mild conditions in moderate to high yields (up to 99% yield).

Pseudo-equilibrium equations for calcium phosphate precipitation with multi-unit particles.

The chemistry underlying bone mineral formation in vertebrates is the reaction of calcium phosphate precipitation. In a near-neutral solution, an amorphous phase and hydroxyapatite nanoparticles appear successively, and the reaction system containing either of the two kinds of precipitates is in a non-equilibrium state. Here, we propose a pseudo-equilibrium approach to the solution chemistry of the precipitation reactions. We employed two series of reaction systems, collected samples at various stages, and analyzed the solution chemistry data on the basis of a simplified model of reaction. We derived two types of pseudo-equilibrium equations from the two series, respectively. These equations reveal the existence of multiple structural units in a precipitate particle and correlate the ionic product with the surface proportion per structural unit (m). The surface proportion, in turn, is related to the whole particle through a particle-surface equation. Notably, the two types of pseudo-equilibrium constants have the common expression of "Kd = ionic product" if the number of the structural units (u) is large enough. Together, these findings have revealed some aspects of the non-equilibrium thermodynamics of precipitation reactions, indicating the solution chemistry route to the equilibrium state. The concept of the multi-unit particle may shed new light on the study of precipitation reactions of other slightly soluble electrolytes. And the relationship between the ionic product and the surface proportion of a structural unit is not only fundamental in chemistry, but may also apply to non-equilibrium systems in nature and biology, such as marine sedimentation, human vascular calcification, and bone mineral metabolism.

The value of routine bone marrow examination in patients with extranodal NK/T-cell lymphoma staged with PET/CT.

BACKGROUND: Limited evidence supports the omission of routine bone marrow (BM) examination (biopsy and aspiration) in patients with nasal-type extranodal NK/T-cell lymphoma (ENKTCL). This study was aimed at assessing whether BM examination provides valuable information for positron emission tomography/computed tomography (PET/CT)-based staging in this patient population. PATIENTS AND METHODS: Patients newly diagnosed with ENKTCL who underwent initial staging with both PET/CT and BM examination between 2013 and 2020 were retrospectively identified in two Chinese institutions. Overall, 742 patients were included; the BM examination was positive in 67 patients. RESULTS: Compared with BM biopsy alone, the combination of BM biopsy and aspiration assessment did not afford any additional diagnostic value. No patient with a positive BM biopsy was found to have early-stage disease by PET/CT. BM biopsy or PET/CT led to upstaging from stage III to IV as a result of BM involvement in 21 patients. In 135 patients with distant organ involvement, BM involvement was associated with worse overall survival (OS) and progression-free survival (PFS) compared with the corresponding durations in patients without BM involvement (2-year OS: 35.9% vs. 60.4%, p < .001; PFS: 26% vs. 40.7%, p = .003). No difference in survival was noted between groups judged positive based on PET/CT and BM biopsy. CONCLUSION: Compared with aspiration, BM biopsy led to the detection of more BM lesions. Baseline PET/CT can be safely used to exclude BM involvement in early-stage disease. Overall, routine BM examination affords diagnostic or prognostic value over PET/CT in patients with advanced-stage nasal-type ENKTCL.

Correlation between vitamin D metabolites and rheumatoid arthritis with osteoporosis by ultra-high-performance liquid chromatography-tandem mass spectrometry (UPLC-MS/MS).

INTRODUCTION: Our aim is to study the correlation between vitamin D metabolites and osteoporosis in rheumatoid arthritis (RA) by ultra-high-performance liquid chromatography-tandem mass spectrometry (UPLC-MS/MS). At the same time, other influencing factors and serum biomarkers of osteoporosis in patients with RA were studied. MATERIALS AND METHODS: Patients with RA admitted from January 2020 to December 2020 were selected at our hospital. The subjects were divided into the normal bone mineral density (BMD), osteopenia, and osteoporosis groups. The differences of vitamin D (VD) metabolites among groups were compared. The Pearson correlation coefficient was used to analyze the relationship between BMD and various parameters. The relationship between BMD and influencing factors was studied by a multiple linear regression equation. RESULTS: A total of 287 patients with RA were included. RA patients with 25-hydroxy vitamin D [25(OH)D] deficiency accounted for 43.63% and 25(OH)D insufficient levels accounted for 31.37%. There were 31 cases (10.80%) in the normal BMD group, 161 cases (56.10%) in the osteopenia group, and 95 cases (33.10%) in the osteoporosis group. The BMD of L1-4 (T- score) was negatively correlated with age (P < 0.05), course of disease (P < 0.05), and erythrocyte sedimentation rate (ESR) (P < 0.05), and positively correlated with 25(OH)D3 (P < 0.05). The multiple linear regression model results showed that age and 25(OH)D3 were independent predictors of BMD; this explained 22.11% of the total variation. CONCLUSIONS: VD deficiency and insufficient are common in RA patients. RA patients can be appropriately supplemented with VD. VD3 may be a better choice.

Performance exploration and microbial dynamics of urine diverting composting toilets in rural China.

The ongoing "toilet revolution" in China provides new opportunities to improve the rural living environment and sanitation, and the introduction of new sanitation facilities such as urine diverting composting toilets (UDCTs) is conducive to the effective treatment and resource utilization of feces. This study revealed the degradation performance and microbial community dynamics of UDCTs and clarified the influence mechanism of fecal volume in aerobic composting treatment. The results showed that UDCTs could effectively decompose human feces, with an organic matter degradation rate of 25%⁓30%. The temperature, water content, NH4+-N and nutrient accumulation were higher in the high fecal volume treatment than in the low fecal volume treatment. Bacterial community composition and structure in UDCTs varied with composting stage and fecal volume. The diversity and richness of bacterial community in compost were changed with different fecal volumes, but the dominant groups were similar. Redundancy analysis (RDA) showed that nitrogen and organic carbon were the main drivers of bacterial community changes during composting. Highly nutritious and non-phytotoxic compost products were suitable for agronomic uses. Based on these results, UDCTs can be an effective way to solve the problem of fecal pollution in rural areas, and fecal dosage is a potential influencing factor in the operation and maintenance of composting systems.

LncRNA TUG1 exhibits pro-fibrosis activity in hypertrophic scar through TAK1/YAP/TAZ pathway via miR-27b-3p.

Hypertrophic Scar (HS) is a complicated fibrotic disease. In addition, its pathogenesis is still to be further explored. Long non-coding RNAs (lncRNAs) have been proved to be participated in multiple diseases, including HS. However, the role of lncRNA TUG1 in HS remains unclear. The expression level of RNA and protein in cells were detected by q-PCR and western blot, respectively. MTT assay was performed to test the cell proliferation. Cell migration was detected by transwell assay. Cell apoptosis was measured by flow cytometry. Dual luciferase report assay and RNA pull down were used to verify the relationship between TUG1, miR-27b-3p and TAK1.TUG1 and TAK1 were upregulated in HS, while miR-27b-3p was downregulated. Knockdown of TUG1 significantly suppressed the proliferation and migration and induced the apoptosis of HS fibroblasts (HSF). In addition, silencing of TUG1 notably inhibited the extracellular matrix (ECM) biosynthesis in HSF. Overexpression of miR-27b-3p has the same effect on HS as that of TUG1 knockdown. Meanwhile, TUG1 could sponge miR-27b-3p, and TAK1 was the direct target of miR-27b-3p. Furthermore, knockdown of TUG1 significantly suppressed the fibrosis in HS via miR-27b-3p/TAK1/YAP/TAZ axis mediation. LncRNA TUG1 promotes the fibrosis in HS via sponging miR-27b-3p and then activates TAK1/YAP/TAZ pathway, which may serve as a potential target for treatment of HS.

Structure of HIV-1 reverse transcriptase cleaving RNA in an RNA/DNA hybrid.

HIV-1 reverse transcriptase (RT) contains both DNA polymerase and RNase H activities to convert the viral genomic RNA to dsDNA in infected host cells. Here we report the 2.65-Å resolution structure of HIV-1 RT engaging in cleaving RNA in an RNA/DNA hybrid. A preferred substrate sequence is absolutely required to enable the RNA/DNA hybrid to adopt the distorted conformation needed to interact properly with the RNase H active site in RT. Substituting two nucleotides 4 bp upstream from the cleavage site results in scissile-phosphate displacement by 4 Å. We also have determined the structure of HIV-1 RT complexed with an RNase H-resistant polypurine tract sequence, which adopts a rigid structure and is accommodated outside of the nuclease active site. Based on this newly gained structural information and a virtual drug screen, we have identified an inhibitor specific for the viral RNase H but not for its cellular homologs.

An Efficient and Accurate Iris Recognition Algorithm Based on a Novel Condensed 2-ch Deep Convolutional Neural Network.

Recently, deep learning approaches, especially convolutional neural networks (CNNs), have attracted extensive attention in iris recognition. Though CNN-based approaches realize automatic feature extraction and achieve outstanding performance, they usually require more training samples and higher computational complexity than the classic methods. This work focuses on training a novel condensed 2-channel (2-ch) CNN with few training samples for efficient and accurate iris identification and verification. A multi-branch CNN with three well-designed online augmentation schemes and radial attention layers is first proposed as a high-performance basic iris classifier. Then, both branch pruning and channel pruning are achieved by analyzing the weight distribution of the model. Finally, fast finetuning is optionally applied, which can significantly improve the performance of the pruned CNN while alleviating the computational burden. In addition, we further investigate the encoding ability of 2-ch CNN and propose an efficient iris recognition scheme suitable for large database application scenarios. Moreover, the gradient-based analysis results indicate that the proposed algorithm is robust to various image contaminations. We comprehensively evaluated our algorithm on three publicly available iris databases for which the results proved satisfactory for real-time iris recognition.

A Micron-Sized Laser Photothermal Effect Evaluation System and Method.

The photothermal effects of lasers have played an important role in both medical laser applications and the development of cochlear implants with optical stimulation. However, there are few methods to evaluate the thermal effect of micron-sized laser spots interacting with other tissues. Here, we present a multi-wavelength micro-scale laser thermal effect measuring system that has high temporal, spatial and temperature resolutions, and can quantitatively realize evaluations in real time. In this system, with accurate 3D positioning and flexible pulsed laser parameter adjustments, groups of temperature changes are systematically measured when the micron-sized laser spots from six kinds of wavelengths individually irradiate the Pd/Cr thermocouple junction area, and reference data of laser spot thermal effects are obtained. This work develops a stable, reliable and universal tool for quantitatively exploring the thermal effect of micron-sized lasers, and provides basic reference data for research on light-stimulated neuron excitement in the future.

Study on Extraction Process of Root of Henry Wood Betony Polysaccharides and Their Antitumor Activity against S180.

We optimized the hot water extraction of polysaccharides from the root of Henry wood betony (RHWPs) using a uniform test and explored their anti-tumor activities in vitro and in vivo. The optimal extraction conditions were as follows: 40 min extraction time, liquid/solid ratio 30 mL/g, 100 min soaking time, two extraction cycles, 100% ethanol concentration, and extraction temperature of 80 °C. The molecular weight distribution of RHWPs with MWs was 228,600 g/mol and 5001 g/mol. The IR spectrum further indicated that RHWPs are acidic polysaccharides containing pyranose and furan rings. The main monosaccharides found in RHWPs were mannose, ribose, l-rhamnose monohydrate, glucuronic acid, galacturonic acid, glucose, galactose, xylose, arabinose, and fucose. RHWPs inhibited the proliferation of S180 tumor cells and induced apoptosis in vitro. Oral administration of RHWPs to tumor-bearing mice significantly inhibited the growth of the S180 xenografts, accelerated apoptosis in tumor cells, and expanded the necrotic regions. Furthermore, RHWPs also markedly increased the levels of TNF-α, IFN-γ, and IL-2 in the sera of tumor-bearing mice, and activated immune cells such as lymphocytes, NK cells, and macrophages, thereby inducing tumor cell apoptosis. Taken together, RHWPs are a promising anti-tumor agent that ought to be explored further.

Correction to: Protein-bound calcium phosphate in uremic rat serum: a quantitative study.

In the original article, few equations and units were published incorrectly.

Protein-bound calcium phosphate in uremic rat serum: a quantitative study.

Protein-bound calcium (prCa) constitutes about 40% of serum total calcium, in which albumin is the most dominant protein. Given the chemical interaction between calcium and phosphate (Pi), the increased serum Pi in chronic kidney disease may cause changes in the composition and structure of the prCa fraction. Here, we report the phosphate binding on the protein-bound calcium in uremic rat serum. Using adenine-fed rats as a uremic model, we separated the calcium and phosphate fractions in rat serum by ultrafiltration, and found that the level of protein-bound phosphate (prPi) in the uremic serum was markedly higher than in control. The elevated prPi level was comparable to the prCa level, consistent with the presence of protein-bound calcium phosphate pr(Ca)j-m(CaPi)m. We then confirmed its presence by ex vivo X-ray absorption near-edge structure spectroscopy, revealing the discrete state of the calcium phosphate clusters associated with protein. Finally, in a quantitative investigation using Ca- and Pi-boosted serum, we discovered the threshold concentration for the Pi binding on prCa, and determined the binding constant. The threshold, while preventing Pi from binding to prCa in normal condition, allows the reaction to take place in hyperphosphatemia conditions. The protein-bound calcium phosphate could act as a link between the metabolism of serum proteins and the homeostasis of phosphate and calcium, and it deserves further investigation whether the molar ratio of (prPi/prCa)⋅100% may serve as a serum index of the vascular calcification status in chronic kidney disease.

Association of SOX11 Polymorphisms in distal 3'UTR with Susceptibility for Schizophrenia.

BACKGROUND: Diverse and circumstantial evidence suggests that schizophrenia is a neurodevelopmental disorder. Genes contributing to neurodevelopment may be potential candidates for schizophrenia. The human SOX11 gene is a member of the developmentally essential SOX (Sry-related HMG box) transcription factor gene family and mapped to chromosome 2p, a potential candidate region for schizophrenia. METHODS: Our previous genome-wide association study (GWAS) implicated an involvement of SOX11 with schizophrenia in a Chinese Han population. To further investigate the association between SOX11 polymorphisms and schizophrenia, we performed an independent replication case-control association study in a sample including 768 cases and 1348 controls. RESULTS: After Bonferroni correction, four SNPs in SOX11 distal 3'UTR significantly associated with schizophrenia in the allele frequencies: rs16864067 (allelic P = .0022), rs12478711 (allelic P = .0009), rs2564045 (allelic P = .0027), and rs2252087 (allelic P = .0025). The haplotype analysis of the selected SNPs showed different haplotype frequencies for two blocks (rs4371338-rs7596062-rs16864067-rs12478711 and rs2564045-rs2252087-rs2564055-rs1366733) between cases and controls. Further luciferase assay and electrophoretic mobility shift assay (EMSA) revealed the schizophrenia-associated SOX11 SNPs may influence SOX11 gene expression, and the risk and non-risk alleles may have different affinity to certain transcription factors and can recruit divergent factors. CONCLUSIONS: Our results suggest SOX11 as a susceptibility gene for schizophrenia, and SOX11 polymorphisms and haplotypes in the distal 3'UTR of the gene might modulate transcriptional activity by serving as cis-regulatory elements and recruiting transcriptional activators or repressors. Also, these SNPs may potentiate as diagnostic markers for the disease.

Co-Culture of Adipose-Derived Stem Cells and Chondrocytes With Transforming Growth Factor-Beta 3 Promotes Chondrogenic Differentiation.

Tissue engineering cartilage is a promising strategy to reconstruct the craniofacial cartilaginous defects. It demands plenty of chondrocytes to generate human-sized craniofacial frameworks. Partly replacement of chondrocytes by adipose-derived stem cells (ADSCs) can be an alternative strategy.The study aimed at evaluating the chondrogenic outcome of ADSCs and chondrocytes in direct co-culture with transforming growth factor-beta (TGF-ß3). Porcine ADSCs and chondrocytes were obtained from abdominal wall and external ears. Four groups: ADSCs or chondrocytes monocultured in medium added with TGF-ß3; ADSCs and ACs co-cultured with or without TGF-ß3. Cell growth rate was performed to evaluate the cell proliferation. Morphological, histologic and real-time polymerase chain reaction analysis were performed to characterize the chondrogenic outcome of pellets. ADSCs had favorable multi-lineage differentiation potential. Further, when ADSCs were co-cultured with chondrocytes in medium added with TGF-ß3, the cell proliferation was promoted and the chondrogenic differentiation of ADSCs was enhanced. We demonstrate that pellet co-culture of ADSCs and chondrocyte with TGF-ß3 could construct high quantity cartilages. It suggests that this strategy might be useful in future cartilage repair.

Ex vivo detection of calcium phosphate and calcium carbonate in rat blood serum.

The total calcium (tCa) in blood serum comprises free Ca2+ ions (fCa), protein-bound calcium (prCa), and complexed calcium by small anions (cCa). The cCa fraction, in addition to fCa, has been indicated to have some physiological activity. However, there is little evidence for the structure of its constituents. Here we report an ex vivo detection of the cCa constituents by synchrotron X-ray absorption near-edge structure spectroscopy. We collected the data directly on rat blood serum and, by making use of the reference samples, derived a spectrum that exhibits the features of cCa constituents. Among the features are those of the complexes of calcium phosphate and calcium carbonate. The detected complexes in the cCa fraction are mainly Ca(η2-HPO4)(H2O)4 and Ca(η1-HCO3)(H2O)5+, in which HPO42- and HCO3- serve as bidentate and unidentate ligands, respectively. The remained H2O molecules on the coordination sphere of Ca2+ enable these complexes to behave partially like aquated Ca2+ ions in protein-binding. Besides, as the dominant part of prCa, albumin-bound calcium (albCa) exhibits a spectrum that closely resembles that of fCa, indicating weak interactions between the protein carboxyl groups and calcium. The weak-bound cCa and albCa, along with fCa and the relevant anions, compose a local chemical system that could play a role in maintaining the calcium level in blood.

Long-term consequences of stopping HBIG and/or nucleotide analogues in liver transplant recipients administered hepatitis B vaccination to prevent HBV reinfection.

BACKGROUND: The long-term administration of nucleotide analogues (NAs) and hepatitis B immune globulin (HBIG) comprises standard prophylaxis for patients with hepatitis B virus (HBV)-related liver diseases to prevent HBV reinfection after liver transplantation (LT). However, prolonging the prophylaxis strategy involves safety issues, such as the development of escape mutations and/or emerging resistant strains, and is also associated with high costs; further, it remains unclear how long prophylactic treatment should be continued. METHOD: Liver transplantation recipients responding to hepatitis B vaccination due to HBV-related liver diseases were retrospectively analysed after stopping HBIG and/or NAs, administered to prevent HBV reinfection, after long-term follow-up. The safety and effectiveness of the strategy were then evaluated for these responders. RESULT: Seventy-eight responders were enrolled. All responders discontinued HBIG, among which 36 stopped both HBIG and NAs. During follow-up, four recipients experienced HBV reinfection, which was associated with HBV escape mutations, after the withdrawal of both HBIG and NAs. No death or graft loss occurred in recipients during the follow-up period. CONCLUSION: A careful withdrawal of HBIG and/or NAs is feasible and safe for responders to hepatitis B vaccination receiving transplants for HBV-related liver diseases.

Pseudo-equilibrium equation of calcium phosphate precipitation from aqueous solution.

An X-ray amorphous phase is frequently present at the early stage of calcium phosphate crystallization, and the relevant solution chemistry is essential for understanding the mechanism of reaction. Here, we report a quantitative study of a series of reaction systems at pseudo-equilibrium states. We determined the composition of solutions and the quantities of the precipitate samples, and characterized the long- and short-range order of the precipitate using X-ray diffraction and synchrotron X-ray absorption near-edge structure spectroscopy, respectively. We found that, in a particle with multiple structural units, only a fraction of the units was able to reach pseudo-equilibrium with the solution composition, which represents the average number of surficial clusters per unit. These findings enabled us to propose a general form of the equilibrium constant equation. The equation fits the pseudo-equilibrium data well, and it converts to the "solubility product (Ksp)" and the conventional "reaction quotient" in two limit cases, respectively. Further, using a cube model, we derived a "particle equation" that reveals the connection between the particle structure and the form of equilibrium constant equation. The dependency of the form of pseudo-equilibrium equation on the structure and size of the precipitate reveals a fundamental relation in chemistry, and its applicability remains to be examined in other reaction systems, such as those involving nanocrystals and porous materials.