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Crowding effects critically impact the self-organization of densely packed cellular assemblies, such as biofilms, solid tumors, and developing tissues. When cells grow and divide, they push each other apart, remodeling the structure and extent of the population's range. Recent work has shown that crowding has a strong impact on the strength of natural selection. However, the impact of crowding on neutral processes, which controls the fate of new variants as long as they are rare, remains unclear. Here, we quantify the genetic diversity of expanding microbial colonies and uncover signatures of crowding in the site frequency spectrum. By combining Luria-Delbrück fluctuation tests, lineage tracing in a novel microfluidic incubator, cell-based simulations, and theoretical modeling, we find that the majority of mutations arise behind the expanding frontier, giving rise to clones that are mechanically "pushed out" of the growing region by the proliferating cells in front. These excluded-volume interactions result in a clone-size distribution that solely depends on where the mutation first arose relative to the front and is characterized by a simple power law for low-frequency clones. Our model predicts that the distribution depends on a single parameter-the characteristic growth layer thickness-and hence allows estimation of the mutation rate in a variety of crowded cellular populations. Combined with previous studies on high-frequency mutations, our finding provides a unified picture of the genetic diversity in expanding populations over the whole frequency range and suggests a practical method to assess growth dynamics by sequencing populations across spatial scales.
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Biofilmes , Gastrópodes , Animais , Microfluídica , Mutação , Taxa de MutaçãoRESUMO
Cell size and cell count are adaptively regulated and intimately linked to growth and function. Yet, despite their widespread relevance, the relation between cell size and count has never been formally examined over the whole human body. Here, we compile a comprehensive dataset of cell size and count over all major cell types, with data drawn from >1,500 published sources. We consider the body of a representative male (70 kg), which allows further estimates of a female (60 kg) and 10-y-old child (32 kg). We build a hierarchical interface for the cellular organization of the body, giving easy access to data, methods, and sources (https://humancelltreemap.mis.mpg.de/). In total, we estimate total body counts of ≈36 trillion cells in the male, ≈28 trillion in the female, and ≈17 trillion in the child. These data reveal a surprising inverse relation between cell size and count, implying a trade-off between these variables, such that all cells within a given logarithmic size class contribute an equal fraction to the body's total cellular biomass. We also find that the coefficient of variation is approximately independent of mean cell size, implying the existence of cell-size regulation across cell types. Our data serve to establish a holistic quantitative framework for the cells of the human body, and highlight large-scale patterns in cell biology.
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Contagem de Células , Criança , Humanos , Feminino , Masculino , Biomassa , Tamanho Celular , Correlação de DadosRESUMO
The prediction of optical properties dominated by light scattering in particulate media composed of high-concentration and polydisperse particles is greatly important in various optical applications. However, the accuracy and efficiency of light propagation simulations are still limited by the huge computational burden and complex interactions between dense and polydisperse particles. Here, we proposed a new optimization strategy that can effectively and accurately predict optical properties based on Monte Carlo simulation with particle size and dependent scattering corrections. Both the scattering parameters of particles and the experimental reflectance spectrum are fully examined for verification. Furthermore, using the weighted solar reflectance of particulate media as a representative optical property, both numerical simulations and experiments confirm the superiority and universality of the proposed optimization approach in a variety of materials systems. Moreover, our work can guide the design of particulate media with specific optical features insightfully and will be applicable in many fields involving multiparticle scattering.
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The development of pure-blue perovskite light-emitting diodes (PeLEDs) faces challenges of spectral stability and low external quantum efficiency (EQE) due to phase separation in mixed halide compositions. Perovskite quantum dots (QDs) with strong confinement effects are promising alternatives to achieve high-quality pure-blue PeLEDs, yet their performance is often hindered by the poor size distribution and high trap density. A strategy combining thermodynamic control with a polishing-driven ligand exchange process to produce high-quality QDs is developed. The strongly-confined pure-blue (≈470 nm) CsPbBr3 QDs exhibit narrow size distribution (12% dispersion) and are achieved in Br-rich ion environment based on growth thermodynamic control. Subsequent polishing-driven ligand exchange process removes imperfect surface sites and replaces initial long-chain organic ligands with short-chain benzene ligands. The resulting QDs exhibit high photoluminescence quantum yield (PLQY) to near-unity. The resulting PeLEDs exhibit a pure-blue electroluminescence (EL) emission at 472 nm with narrow full-width at half-maximum (FWHM) of 25 nm, achieving a maximum EQE of 10.7% and a bright maximum luminance of 7697 cd m-2. The pure-blue PeLEDs show ultrahigh spectral stability under high voltage, a low roll-off of EQE, and an operational half-lifetime (T50) of 127 min at an initial luminance of 103 cd m-2 under continuous operation.
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Despite the high potential for reducing carbon emissions and contributing to the future of energy utilization, polymer electrolyte membrane fuel cells (PEMFCs) face challenges such as high costs and sluggish oxygen transport in cathode catalyst layers (CCLs). In this study, the impact of pore size distribution on bulk oxygen transport behavior is explored by introducing nano calcium carbonate of varying particle sizes for pore-forming. Physicochemical characterizations for are employed to examine the electrode structure, while in situ electrochemical measurements are used to scrutinize bulk oxygen transport resistance, effective oxygen diffusivity ( D O 2 eff $D_{{{\mathrm{O}}}_2}^{{\mathrm{eff}}}$ ) and fuel cell performance. Additionally, the CCLs are constructed with aid of Lattice Boltzmann method (LBM) simulations and D O 2 eff $D_{{{\mathrm{O}}}_2}^{{\mathrm{eff}}}$ for CCLs with different pore size distribution are calculated. The findings reveal that D O 2 eff $D_{{{\mathrm{O}}}_2}^{{\mathrm{eff}}}$ initially increases and then decreases as the most probable pore size increases. A "sphere-pipe" model is proposed to describe practical bulk oxygen transport in CCLs, highlighting the significant role of not only the pore size of secondary pores but also the number of primary pores in bulk oxygen transport.
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Data are presented demonstrating that absorbance detection can be used during high-speed sedimentation velocity analytical ultracentrifugation (hs-SV-AUC) experiments to characterize the size distribution of adeno-associated virus (AAV) drug products accurately. Advantages and limitations of being able to use this detector in this specific type of SV-AUC experiment are discussed.
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Dependovirus , Ultracentrifugação , Dependovirus/genética , Dependovirus/isolamento & purificação , Ultracentrifugação/métodos , HumanosRESUMO
Simulated SV-AUC data for an adeno-associated virus (AAV) sample consisting of four components having closely spaced sedimentation coefficients were used to develop a high-speed protocol that optimized the size distribution analysis resolution. The resulting high speed (45K rpm) SV-AUC (hs-SV-AUC) protocol poses several experimental challenges: 1) the need for rapid data acquisition, 2) increased potential for optical artifacts from steep and fast moving boundaries and 3) the increased potential for convection. To overcome these challenges the protocol uses interference detection at low temperatures and data that are confined to a limited radial-time window. In addition to providing higher resolution AAV SV-AUC data and very short run times (<20 min after temperature equilibration), the need to match the sample and reference solvent composition and meniscus positions is relaxed making interference detection as simple to employ as absorbance detection. Finally, experimental data comparing hs-SV-AUC (at 45K rpm) with standard low-speed (15K rpm) SV-AUC on the same AAV sample demonstrate the size distribution resolution improvement. These experiments also validate the use of a radial-time window and show how quickly data can be acquired using the hs-SV-AUC protocol.
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Temperatura Baixa , Dependovirus , Dependovirus/genética , Área Sob a Curva , Ultracentrifugação/métodos , TemperaturaRESUMO
Fat cells, called adipocytes, are designed to regulate energy homeostasis by storing energy in the form of lipids. Adipocyte size distribution is assumed to play a role in the development of obesity-related diseases. These cells that do not have a characteristic size, indeed a bimodal size distribution is observed in adipose tissue. We propose a model based on a partial differential equation to describe adipocyte size distribution. The model includes a description of the lipid fluxes and the cell size fluctuations and using a formulation of a stationary solution fast computation of bimodal distribution is achieved. We investigate the parameter identifiability and estimate parameter values with CMA-ES algorithm. We first validate the procedure on synthetic data, then we estimate parameter values with experimental data of 32 rats. We discuss the estimated parameter values and their variability within the population, as well as the relation between estimated values and their biological significance. Finally, a sensitivity analysis is performed to specify the influence of parameters on cell size distribution and explain the differences between the model and the measurements. The proposed framework enables the characterization of adipocyte size distribution with four parameters and can be easily adapted to measurements of cell size distribution in different health conditions.
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Modelos Biológicos , Modelos Teóricos , Ratos , Animais , Adipócitos , Tecido Adiposo , Tamanho CelularRESUMO
Because microstructure plays an important role in the mechanical properties of structural materials, developing the capability to quantify microstructures rapidly is important to enabling high-throughput screening of structural materials. Electron backscatter diffraction (EBSD) is a common method for studying microstructures and extracting information such as grain size distributions (GSDs), but is not particularly fast and thus could be a bottleneck in high-throughput systems. One approach to accelerating EBSD is to reduce the number of points that must be scanned. In this work, we describe an iterative method for reducing the number of scan points needed to measure GSDs using incremental low-discrepancy sampling, including on-the-fly grain size calculations and a convergence test for the resulting GSD based on the Kolmogorov-Smirnov test. We demonstrate this method on five real EBSD maps collected from magnesium AZ31B specimens and compare the effectiveness of sampling according to two different low discrepancy sequences, the Sobol and R2 sequences, and random sampling. We find that R2 sampling is able to produce GSDs that are statistically very similar to the GSDs of the full density grids using, on average, only 52% of the total scan points. For EBSD maps that contained monodisperse GSDs and over 1000 grains, R2 sampling only required an average of 39% of the total EBSD points.
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PURPOSE: A comparative assessment was performed to evaluate the potential of particle sizing by an ensemble based conventional dynamic light scattering (DLS) technique and an emerging technology based on tunable resistive pulse sensing (TRPS) using particle by particle approach by evaluating three different types of vaccine formulations representing three case studies and showing the limitation of each technique, instrument variability, sensitivity, and the resolution in mixed population. METHODS: Three types of in-house vaccine formulations- a protein antigen, an outer membrane vesicle and viral particles were simultaneously evaluated by TRPS based Exoid and two DLS instruments-Zetatrac and Zetasizer for particle size distribution, aggregates, and resolution of polydisperse species. RESULTS: The data from first case study show the risk of possible size overestimation and size averaging in polydisperse samples in DLS measurements which can be addressed by the TRPS analysis. It also shows how TRPS may be utilized only to large size antigens due to its limited size range. The second case study highlights the difference in the sensitivities of two DLS instruments working on the same principle. The third case study show that how TRPS can better resolve the large aggregate species compare to DLS in polydisperse samples. CONCLUSION: This analysis shows that TRPS can be used as an orthogonal technique in addition to conventional DLS based methods for more precise and in-depth characterization. Both techniques are efficient in size characterization and produce comparable results, however the choice will depend on the type of formulation and size range to be evaluated.
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Difusão Dinâmica da Luz , Tamanho da Partícula , Vacinas , Difusão Dinâmica da Luz/métodos , Vacinas/química , Composição de Medicamentos/métodosRESUMO
PURPOSE: This study is focused on monitoring process parameters and quality attributes of aluminum phosphate (AlPO4) using multiple in-line probes incorporated into an industrial-scale adjuvant suspension manufacturing unit. METHODS: The manufacturing of aluminum adjuvant suspension was monitored at manufacturing scale using conductivity, turbidity, infrared, and particle sizing and count probes to follow the continuous evolution of particle formation and size distribution, and the reaction kinetics during the synthesis of AlPO4. RESULTS: The data showed that AlPO4 forms large particles at the early stages of mixing, followed by a decrease in size and then stabilization towards the later stages of mixing and pH adjustment. The results provided a complementary view of process events and assisted in optimizing several parameters, e.g., flow rate of reactants AlCl3 and Na3PO4 solutions, mixing rate, pH, and conductivity of AlPO4, as well as adjuvant quality attribute such as particle size, thus streamlining and shortening the process development stage. CONCLUSION: The results of this study showed the usefulness of the in-line probes to automate continuous assessment of AlPO4 batch-to-batch consistency during in-house adjuvant production at the industrial scale.
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Adjuvantes Imunológicos , Compostos de Alumínio , Fosfatos , Tamanho da Partícula , Tecnologia Farmacêutica/métodosRESUMO
Environmental RNA (eRNA) analysis is conventionally expected to infer physiological information about organisms within their ecosystems, whereas environmental DNA (eDNA) analysis only infers their presence and abundance. Despite the promise of eRNA application, basic research on eRNA characteristics and dynamics is limited. The present study conducted aquarium experiments using zebrafish (Danio rerio) to estimate the particle size distribution (PSD) of eRNA in order to better understand the persistence state of eRNA particles. Rearing water samples were sequentially filtered using different pore-size filters, and the resulting size-fractioned mitochondrial cytochrome b (CytB) eDNA and eRNA data were modeled with the Weibull complementary cumulative distribution function (CCDF) to estimate the parameters characterizing the PSDs. It was revealed that the scale parameter (α) was significantly higher (i.e., the mean particle size was larger) for eRNA than eDNA, while the shape parameter (ß) was not significantly different between them. This result supports the hypothesis that most eRNA particles are likely in a protected, intra-cellular state, which mitigates eRNA degradation in water. Moreover, these findings also imply the heterogeneous dispersion of eRNA relative to eDNA and suggest an efficient method of eRNA collection using a larger pore-size filter. Further studies on the characteristics and dynamics of eRNA particles should be pursued in the future.
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DNA Ambiental , Perciformes , Animais , Peixe-Zebra/genética , Citocromos b/genética , Ecossistema , RNA , Tamanho da Partícula , ÁguaRESUMO
Modeling of microplastic (MP) transport in the aquatic environment is complicated by the diverse properties of the plastic particles. Traditional modeling methods such as Lagrangian particle tracking and Eulerian discrete class (DC) methods have limitations as they are not best placed to account for the diverse characteristics of individual particles, namely, size, density, and shape, which are crucial for determining the transport of MPs. In this work, we address the issue of particle size diversity by using the population balance equations (PBE) method. In addition to the advection-diffusion terms, the PBE transport equation involves a deposition sink term. Seven size classes of MPs are modeled in the DC method, which is compared to the PBE method. The evolution of particle size distribution is compared between the two methods using a simplified test case of a schematized estuary with tidal forcing and river discharge. This work successfully demonstrates the applicability and appropriateness of the PBE model in modeling the transport of MPs to track the dynamic and complete size distribution at a reduced computational cost in comparison to the DC model. With the PBE method, it is possible to address other diversities of the MPs such as the shape and density.
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Microplásticos , Tamanho da Partícula , Poluentes Químicos da Água , Modelos Teóricos , Monitoramento Ambiental/métodos , Rios/químicaRESUMO
Concerns about civil aviation's air quality and environmental impacts have led to recent regulations on nonvolatile particulate matter (nvPM) mass and number emissions. Although these regulations do not mandate measuring particle size distribution (PSD), understanding PSDs is vital for assessing the environmental impacts of aviation nvPM. This study introduces a comprehensive data set detailing PSD characteristics of 42 engines across 19 turbofan types, ranging from unregulated small business jets to regulated large commercial aircraft. Emission tests were independently performed by using the European and Swiss reference nvPM sampling and measurement systems with parallel PSD measurements. The geometric mean diameter (GMD) at the engine exit strongly correlated with the nvPM number-to-mass ratio (N/M) and thrust, varying from 7 to 52 nm. The engine-exit geometric standard deviation ranged from 1.7 to 2.5 (mean of 2.05). The study proposes empirical correlations to predict GMD from N/M data of emissions-certified engines. These predictions are expected to be effective for conventional rich-burn engines and might be extended to novel combustor technologies if additional data become available. The findings support the refinement of emission models and help in assessing the aviation non-CO2 climate and air quality impacts.
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Tamanho da Partícula , Material Particulado , Material Particulado/análise , Emissões de Veículos , Monitoramento Ambiental/métodos , Aviação , Poluentes Atmosféricos/análise , Poluição do Ar , Aeronaves , Meio AmbienteRESUMO
Floating microplastics are susceptible to sunlight-driven photodegradation, which can convert plastic carbon to dissolved organic carbon (DOC) and can facilitate microplastic fragmentation by mechanical forces. To understand the photochemical fate of sub-millimeter buoyant plastics, â¼0.6 mm polypropylene microplastics were photodegraded while tracking plastic mass, carbon, and particle size distributions. Plastic mass loss and carbon loss followed linear kinetics. At most time points DOC accumulation accounted for under 50% of the total plastic carbon lost. DOC accumulation followed sigmoidal kinetics, not the exponential kinetics previously reported for shorter irradiations. Thus, we suggest that estimates of plastic lifespan based on exponential DOC accumulation are inaccurate. Instead, linear plastic-C mass and plastic mass loss kinetics should be used, and these methods result in longer estimates of photochemical lifetimes for plastics in surface waters. Scanning electron microscopy revealed that photoirradiation produced two distinct patterns of cracking on the particles. However, size distribution analyses indicated that fragmentation was minimal. Instead, the initial population of microplastics shrank in size during irradiations, indicating photoirradiation in tranquil waters (i.e., without mechanical forcing) dissolved sub-millimeter plastics without fragmentation.
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Microplásticos , Poluentes Químicos da Água , Polipropilenos/análise , Plásticos/análise , Poluentes Químicos da Água/análise , Luz Solar , Carbono , Monitoramento AmbientalRESUMO
In recent years, the use of lipid nanoparticles (LNPs) for delivery of messenger RNA (mRNA)-based therapies has gained substantial attention in the field of drug development. In such an application, multiple LNP attributes have to be carefully characterized to ensure product safety and quality, whereas accurate and efficient characterization of these complex mRNA-LNP formulations remains a challenging endeavor. Here, we present the development and application of an online separation and characterization platform designed for the isolation and in-depth analysis of mRNAs and mRNA-loaded LNPs. Our asymmetrical flow field-flow fractionation with a multi-detector (MD-AF4) method has demonstrated exceptional resolution between mRNA-LNPs and mRNAs, delivering excellent recoveries (over 70%) for both analytes and exceptional repeatability. Notably, this platform allows for comprehensive and multi-attribute LNP characterization, including online particle sizing, morphology characterization, and determination of encapsulation efficiency, all within a single injection. Furthermore, real-time online sizing by synchronizing multi-angle light scattering (MALS) and dynamic light scattering (DLS) presented higher resolution over traditional batch-mode DLS, particularly in differentiating heterogeneous samples with a low abundance of large-sized particles. Additionally, our method proves to be a valuable tool for monitoring LNP stability under varying stress conditions. Our work introduces a robust and versatile analytical platform using MD-AF4 that not only efficiently provides multi-attribute characterizations of mRNA-LNPs but also holds promise in advancing studies related to formulation screening, quality control, and stability assessment in the evolving field of nanoparticle delivery systems for mRNAs.
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Fracionamento por Campo e Fluxo , Lipídeos , Nanopartículas , RNA Mensageiro , RNA Mensageiro/isolamento & purificação , RNA Mensageiro/genética , RNA Mensageiro/análise , Fracionamento por Campo e Fluxo/métodos , Nanopartículas/química , Lipídeos/química , Tamanho da Partícula , LipossomosRESUMO
Diesel vehicle exhaust is one of the major contributors to ultrafine particles (UFPs) in urban areas in China. However, there is still a lack of knowledge about UFPs emission characteristics from current in-use diesel vehicles. This study has carried out an on-road test of 10 in-use Light-duty Diesel Trucks (LDDTs) with different emission control standards in China using a self-established portable measurement system based on the Electronic Low-pressure Impactor (ELPI) and characterized the ultrafine particle number (PN) concentration, particle size distribution and metal element contents. The results revealed a significant reduction of 93.37% in the average PN0.1 emission factor of LDDTs from China IV to China VI. Notably, LDDTs compliant with the China VI vehicle emission control standard exhibited the lowest PN0.1 and PM0.1 emission factors, measuring 4.991×1014 #/km and 0.627 g/km, respectively. By taking into account emissions under real driving conditions, we found that the PN emission rates grow with the increase of the Vehicle Specific Power (VSP). The cold-start phase had higher PN emissions than the hot-start phase, with 8590, 1890, 477, and 22 times higher than those of the ambient air (1.18×105 #/cm3), respectively. The installation of Diesel Particulate Filter (DPF) can decrease UFPs by more than 99.8%, while the PN emission factor during the DPF regeneration stage (1.85×1016 #/km) increased by 5 orders of magnitude that of the DPF normal works (7.51×1011 #/km). Metal element contents analysis shows that Fe, Ca, Al and Mg are the dominant elements in UFPs of LDDT exhaust gas, but the element of Ni is slightly increasing in a China VI, possibly due to the new automotive engine exhaust manifolds being made of Ni instead of cast iron for the purpose of having more high-temperature resistance. Our study demonstrates the importance of monitoring and routine maintenance of exhaust after-treatment systems.
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In the aftermath of the Fukushima Daiichi Nuclear Power Plant accident, a pioneering large-scale decontamination project was initiated, aiming to enable the return of evacuees. This project, the first of its kind in human history, involved the transportation of soils collected during decontamination to interim storage facilities. Before recycling or disposal, these soils undergo processes like volume reduction. However, there's a need for innovative methods to reduce volume effectively and treat secondary wastes more efficiently. The current study explores the impact of a dispersant, sodium hexametaphosphate (SHMP), on the behavior of radiocesium (r-Cs: 137Cs) dynamics in different size fractions of radioactively contaminated soils from Fukushima. The solid-phase speciation analysis of Fukushima soils validated that at least 50% of the 137Cs or other minerals are associated with difficult-to-extract soil phases. Nonetheless, the low 137Cs/133Cs ratio in corresponding soil phases implies a slower r-Cs fixation mechanism. The wet-sieving of r-Cs contaminated soil fraction, < 2 mm, with SHMP, resulted in different soil subfractions (2000-212, 212-53, and < 53 µm). Following SHMP treatment, dispersion of > 92% of 137Cs associated with < 212 µm soil size fractions was observed. The migration of 137Cs towards smaller soil size fractions can be attributed to either SHMP-induced cation exchange or the formation of polyvalent complexes involving SHMP and soil minerals. The condensation of 137Cs in < 212 µm, as induced by SHMP, enabled the subsequent reuse of the larger soil fraction (> 212 µm), which was less contaminated. This study provides a new perspective on the effects of dispersants and contributes to a better understanding of the complex interactions among organic carbon, 137Cs, monovalent and polyvalent cations, and soil functional groups concerning the volume reduction of soils contaminated with r-Cs.
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Radioisótopos de Césio , Acidente Nuclear de Fukushima , Poluentes Radioativos do Solo , Radioisótopos de Césio/análise , Poluentes Radioativos do Solo/análise , Solo/química , Monitoramento de Radiação/métodos , Descontaminação/métodos , JapãoRESUMO
Anaerobic digestion of phenolic wastewater by anaerobic membrane bioreactor (AnMBR) has revealed increasing attractiveness, but the application of AnMBRs for treating high-strength phenolic wastewater faces challenges related to elevated phenol stress and membrane fouling. In this study, the coupling of AnMBR and polyaluminum chloride (PAC) was developed for efficient treatment of high-strength phenolic wastewater. The system achieved robust removal efficiencies of phenol (99%) and quinoline (98%) at a gradual increase of phenol concentration from 1000 to 5000 mg/L and a constant quinoline concentration of 100 mg/L. The dosing of PAC could effectively control the membrane fouling rate with the transmembrane pressure (TMP) increasing rate as low as 0.17 kPa/d. The robust performances were mainly attributed to the favorable retention of functional microbes through membrane interception, while pulse cross flow buffered against phenol stress and facilitated cake layer removal. Meanwhile, the enriched core functional microbes, such as Syntrophorhabdus, Syntrophus, Mesotoga and Methanolinea, played a crucial role in further reduction of phenol stress. Notably, the significant presence of biomacromolecule degrader, such as Levilinea, contributed to membrane fouling mitigation through extracellular polymer degradation. Moreover, the enlargement of particle size distribution (PSD) by PAC was expected to mitigate membrane fouling. This study provided a promising avenue for sustainable treatment of high-strength phenolic wastewater.
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Reatores Biológicos , Membranas Artificiais , Eliminação de Resíduos Líquidos , Águas Residuárias , Águas Residuárias/química , Eliminação de Resíduos Líquidos/métodos , Anaerobiose , Hidróxido de Alumínio/química , Fenóis/análise , Poluentes Químicos da Água/análiseRESUMO
Human pluripotent stem cells (hPSCs) hold promise for regenerative medicine to replace essential cells that die or become dysfunctional. In some cases, these cells can be used to form clusters whose size distribution affects the growth dynamics. We develop models to predict cluster size distributions of hPSCs based on several plausible hypotheses, including (0) exponential growth, (1) surface growth, (2) Logistic growth, and (3) Gompertz growth. We use experimental data to investigate these models. A partial differential equation for the dynamics of the cluster size distribution is used to fit parameters (rates of growth, mortality, etc.). A comparison of the models using their mean squared error and the Akaike Information criterion suggests that Models 1 (surface growth) or 2 (Logistic growth) best describe the data.