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Most of the previous studies on classical thermalization focus on the wave-vector space, encountering limitations when extended beyond quasi-integrable regions. In this study, we propose a scheme to study the thermalization of the classical Hamiltonian chain of interacting oscillators in real space by developing a thermalization indicator proposed by Parisi [Europhys. Lett. 40, 357 (1997)0295-507510.1209/epl/i1997-00471-9], which approaches zero in the thermal state. Upon reaching the steady state characterized by the generalized Gibbs ensemble for a harmonic chain, a quench protocol is implemented to change the Hamiltonian to a nonintegrable form instantaneously, thereby preparing nonequilibrium initial states. This approach enables investigations of thermalization in real space, particularly valuable for exploring regions beyond quasi-integrability. For the FPUT-ß lattice, we observe that the thermalization time as a function of the nonintegrable strength follows a -2 scaling law in the quasi-integrable region and -1/4 in the strongly integrable region. Moreover, numerical results reveal the thermalization time is proportional to the Lyapunov time, which bridges microscopic chaotic dynamics and the macroscopic thermalization process.
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In this article, we find that impurity in a one-dimensional harmonic chain leads to spikes in the phonon transmission. Using the Langevin equations and Green's function method (LEGF), we find the underlying mechanism of spikes, which comes from the fact that the wave energy can be transferred through uniform subchains laid between impurities without loss. Both the position and magnitude of spikes can be analytically obtained. By employing these results, we provide an analytical approach to transmission in the thermodynamic limit, thereby compensating for the limitation of LEGF that are practically confined to finite system size. Finally, we determine an expression for the localization length based on LEGF, demonstrating the equivalence between mass disorder and spatial disorder in low impurity concentration.
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Hospital wastewater treatment systems (HWTSs) are a significant source and reservoir of antibiotic resistance genes (ARGs) and a crucial hub for transmitting ARGs from clinical to natural environments. However, there is a lack of research on the antibiotic resistome of clinical wastewater in HWTSs. In this study, we used metagenomics to analyze the prevalence and abundance of ARGs in five typical HWTSs. A total of 17 antibiotics from six categories were detected in the five HWTSs; ß-lactam antibiotics were found at the highest concentrations, with up to 4074.08 ng·L-1. We further found a total of 21 ARG types and 1106 subtypes of ARGs with the highest percentage of multi-drug resistance genes (evgS, msbA, arlS, and baeS). The most abundant last-resort ARGs were mcr, which were detected in 100 % of the samples. HWTSs effluent is a major pathway for the transmission of last-resort ARGs into urban wastewater networks. The removal of antibiotics, antibiotic-resistant bacteria, and ARGs from HWTSs was mainly achieved by tertiary treatment, i.e., chlorine disinfection, but antibiotics and ARGs were still present in the HWTSs effluent or even increased after treatment. Moreover, antibiotics and heavy metals (especially mercury) in hospital effluents can exert selective pressure for antibiotic resistance, even at low concentrations. Qualitative analyses based on metagenome-assembled genome analysis revealed that the putative hosts of the identified ARGs are widely distributed among Pseudomonas, Acidovorax, Flavobacterium, Polaromonas, and Arcobacter. Moreover, we further assessed the clinical availability of ARGs and found that multidrug ARGs had the highest clinical relevance values. This study provides new impulses for monitoring and removing antibiotics and ARGs in the hospital sewage treatment process.
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Antibacterianos , Purificação da Água , Águas Residuárias , Genes Bacterianos , HospitaisRESUMO
BACKGROUND AND AIMS: Use the MDRD (Modification of Diet in Renal Disease) and 2021 CKD-EPI (Chronic Kidney Disease Epidemiology Collaboration) equation void of race coefficients (CKD-EPICrea, CKD-EPICys-C, and CKD-EPICrea+Cys-C) to estimate the BV (Biological variation) of eGFR (estimated glomerular filtration rate) within 24 h in a healthy population to help explain future studies using eGFR in the context of a known BV. METHODS: Blood samples were collected from 30 healthy subjects at six time points within 24 h. Serum creatinine (S-Crea) and serum cystatin C (S-Cys-C) were measured, and the BV of eGFR was calculated. Outlier and variance homogeneity analyses were performed, followed by CV-ANOVA on trend-corrected data. RESULTS: The eGFR CVI for the four equations (MDRD, CKD-EPICrea, CKD-EPICys-C, and CKD-EPICrea+Cys-C) were 8.39% (7.50-9.51%), 3.90% (3.49-4.42%), 6.58% (5.88-7.46%), and 5.03% (4.50-5.71%), respectively. The corresponding II and RCVpos/neg values were 0.69, 0.48, 0.51, and 0.31, and (29.30%, - 22.66%), (12.69%, - 11.2 6%), (20.97%, - 17.33%), and (15.88%, - 13.70%), respectively; RCVpos /neg of eGFR was highest in the MDRD equation and lowest in the CKD-EPI Crea equation. Additionally, the RCVpos/neg values of the individual was highest in the MDRD equation and lowest in the CKD-EPICrea+Cys-C equation; they are (56.51%, - 36.11%) and (5.01%, - 4.77%), respectively. CONCLUSIONS: We present data on the 24 h BV eGFR of the 2021 CKD-EPI equations. The presence of BV has impact on the interpretation of GFR results, affecting CKD disease grading. The RCVpos/neg differences were large among the individuals. When using eGFRs based on the MDRD and CKD-EPI equations, it is necessary to combine RCVpos/neg values before interpreting the results.
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Creatinina , Cistatina C , Taxa de Filtração Glomerular , Insuficiência Renal Crônica , Humanos , Taxa de Filtração Glomerular/fisiologia , Masculino , Feminino , Cistatina C/sangue , Adulto , Creatinina/sangue , Pessoa de Meia-Idade , Insuficiência Renal Crônica/fisiopatologia , Insuficiência Renal Crônica/sangue , Voluntários Saudáveis , Adulto Jovem , IdosoRESUMO
Introduction: Internal quality control (IQC) is a core pillar of laboratory quality control strategies. Internal quality control commercial materials lack the same characteristics as patient samples and IQC contributes to the costs of laboratory testing. Patient data-based quality control (PDB-QC) may be a valuable supplement to IQC; the smaller the biological variation, the stronger the ability to detect errors. Using the potassium concentration in serum as an example study compared error detection effectiveness between PDB-QC and IQC. Materials and methods: Serum potassium concentrations were measured by using an indirect ion-selective electrode method. For the training database, 23,772 patient-generated data and 366 IQC data from April 2022 to September 2022 were used; 15,351 patient-generated data and 246 IQC data from October 2022 to January 2023 were used as the testing database. For both PDB-QC and IQC, average values and standard deviations were calculated, and z-score charts were plotted for comparison purposes. Results: Five systematic and three random errors were detected using IQC. Nine systematic errors but no random errors were detected in PDB-QC. The PDB-QC showed systematic error warnings earlier than the IQC. Conclusions: The daily average value of patient-generated data was superior to IQC in terms of the efficiency and timeliness of detecting systematic errors but inferior to IQC in detecting random errors.
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Laboratórios , Humanos , Controle de QualidadeRESUMO
Branched flows occur ubiquitously in various wave systems, when the propagating waves encounter weak correlated scattering potentials. Here we report the experimental realization of electrical tuning of the branched flow of light using a nematic liquid crystal (NLC) system. We create the physical realization of the weakly correlated disordered potentials of light via the inhomogeneous orientations of the NLC. We demonstrate that the branched flow of light can be switched on and off as well as tuned continuously through the electro-optical properties of NLC film. We further show that the branched flow can be manipulated by the polarization of the incident light due to the optical anisotropy of the NLC film. The nature of the branched flow of light is revealed via the unconventional intensity statistics and the rapid fidelity decay along the light propagation. Our study unveils an excellent platform for the tuning of the branched flow of light which creates a testbed for fundamental physics and offers a new way for steering light.
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OBJECTIVE: We evaluated the intraday changes of thyroid function biomarkers in healthy subjects to help clinicians diagnose thyroid diseases in appropriate timing. METHODS: Blood samples were collected from 31 subjects at 0:00, 4:00, 8:00, 12:00, 16:00 and 20:00 on the sampling day and analyzed for thyroid-stimulating hormone (TSH), triiodothyronine (T3), thyroxine (T4), free T3 (FT3), and free T4 (FT4). The intraday concentration changes were analyzed using Friedman's 2-way analysis of variance by ranks. RESULTS: The concentrations of TSH, T3, T4, FT3, and FT4 in males were significantly higher than those in females (Pâ <â .01). The obvious peak circadian rhythm of TSH was observed at 0:00 AM with gradual decline thereafter, whereas other biomarkers showed no rhythmic changes. CONCLUSION: Sex differences should be considered in interpreting thyroid function tests. It is important to select the sampling time according to the clinician's diagnostic needs, especially at night when TSH secretion peaks.
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Glândula Tireoide , Tri-Iodotironina , Humanos , Masculino , Feminino , Voluntários Saudáveis , Tiroxina , TireotropinaRESUMO
BACKGROUND AND AIMS: To explore the biological variation (BV) of kidney injury markers in serum and urine of healthy subjects within 24 hours to assist with interpretation of future studies using these biomarkers in the context of known BV. MATERIALS AND METHODS: Serum and urine samples were collected every 4 hours (0, 4, 8, 12, 16 and 20 hours) from 31 healthy subjects within 24 hours and serum creatinine (s-Crea), serum ß2-microglobin (s-ß2MG), serum cystatin C (s-CYSC), serum neutrophil gelatinase-associated lipoprotein (s-NGAL), urine creatinine (u-Crea), urine ß2-microglobin (u-ß2MG), urine cystatin C (u-CYSC), urine neutrophil gelatinase-associated lipoprotein (u-NGAL) were measured. Outlier and variance homogeneity analyses were performed, followed by CV-ANOVA analysis on trend-corrected data (if relevant), and analytical (CVA), within-subject (CVI), and between-subject (CVG) biological variation were calculated. RESULTS: The concentration of kidney injury markers in male was higher than that in female, except for u-CYSC and u-NGAL. There were no significant difference in serum and urine kidney injury markers concentration at different time points. Serum CVI was lower than urine CVI, serum CVG was higher than CVI, and urine CVG was lower than CVI. The individual index (II) of serum kidney injury markers was less than 0.6, while the II of urinary kidney injury markers was more than 1.0. CONCLUSIONS: This study provides new short-term BV data for kidney injury markers in healthy subjects within 24 hours, which are of great significance in explaining other AKI / CKD studies.
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Injúria Renal Aguda , Cistatina C , Biomarcadores , Creatinina , Feminino , Gelatinases , Humanos , Rim , Lipocalina-2/urina , MasculinoRESUMO
BACKGROUND: Thyroid-stimulating hormone (TSH), triiodothyronine (T3), thyroxine (T4), free T3 (FT3), and free T4 (FT4) are used to diagnose thyroid diseases and monitor treatment effects. Reliable biological variation (BV) data is required to ensure accurate clinical decisions. METHODS: Blood samples were collected from 31 healthy subjects at 00:00, 04:00, 08:00, 12:00, 16:00, and 20:00; each sample was analyzed twice for TSH, T3, T4, FT3, and FT4. After outlier exclusion, normality assessment, and variance homogeneity, sex-stratified BV, including within-subject (CVI) and between-subject (CVG), was defined using nested ANOVA. RESULTS: Concentrations of five biomarkers were significantly different between sexes. The CVI and CVG estimates were 34.54% and 34.43% for TSH, 5.89% and 14.18% for T3, 4.48% and 14.96% for T4, 5.37% and 11.23% for FT3, and 3.57% and 8.03% for FT4, respectively. The individual indexes (IIs) of all the biomarkers (except TSH) were ≤ 0.63. Males had lower CVIs and IIs than females. CONCLUSION: CVI estimates of all hormones, except TSH, were lower than those reported on the BV website, showing low IIs and differences between sexes. We provide updated data on the short-term BV of thyroid function biomarkers according to sex and complement BV data of thyroid function biomarkers.
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Glândula Tireoide , Tri-Iodotironina , Biomarcadores , Feminino , Humanos , Masculino , Valores de Referência , Tireotropina , TiroxinaRESUMO
The finite-time fluctuation theorem (FT) for the master functional, total entropy production, and medium entropy is studied in the one-dimensional Fermi-Pasta-Ulam-Tsingou-ß (FPUT-ß) chain coupled with two heat reservoirs at different temperatures. Through numerical simulations and theoretical analysis, we find that the nonequilibrium steady-state distribution of the one-dimensional FPUT-ß chain violates the time-reversal symmetry. Thus, unlike the master functional, the total entropy production fails to satisfy the fluctuation relation for finite time. Meanwhile, we discuss the range of medium entropy production which obeys the conventional steady-state fluctuation theorem (SSFT) in the infinite time limit. Furthermore, we find that the generalized SSFT for medium entropy monotonically approaches the conventional SSFT as the time interval increases, irrespective of temperature difference, anharmonicity, and system size. Interestingly, the medium entropy production rate shows a nonmonotonic variation with anharomonicity, which comes from a competition mechanism of the phonon transport. Correspondingly, the difference between the generalized SSFT and the conventional SSFT shows similar nonmonotonic behaviors.
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Heat conduction through a disordered Fermi-Pasta-Ulam-ß (DFPU-ß) chain is studied. The presence of disorder makes the heat current behave significantly different from that of the ordered Fermi-Pasta-Ulam-ß (FPU-ß) chain. Thanks to the interplay between disorder and anharmonicity, a nonmonotonic-monotonic transition occurs when the disorder strength increases. That is, a peak for the heat current emerges for weak disorder; however, monotonic increasing of the heat current shows up for strong disorder. This can be understood based on the competition between two effects of anharmonicity on phonons, namely, delocalization and phonon-phonon scattering, which is shown by the spectral decomposition of heat current.
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Based on the geometrization of dynamics and self-consistent phonon theory, we develop an analytical approach to derive the Lyapunov time, the reciprocal of the largest Lyapunov exponent, for general nonlinear lattices of coupled oscillators. The Fermi-Pasta-Ulam-Tsingou-like lattices are exemplified by using the method, which agree well with molecular dynamical simulations for the cases of quartic and sextic interactions. A universal scaling behavior of the Lyapunov time with the nonintegrability strength is observed for the quasi-integrable regime. Interestingly, the scaling exponent of the Lyapunov time is the same as the thermalization time, which indicates a proportional relationship between the two timescales. This relation illustrates how the thermalization process is related to the intrinsic chaotic property.
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BACKGROUND: Increasing epidemiological evidence suggests that diabetes may be associated with meningioma risk, but the evidence supporting this association is still inconclusive. Therefore, we performed a meta-analysis of all eligible observational studies to evaluate the potential association of diabetes with meningioma risk. METHODS: A comprehensive literature search was performed in the PubMed, Web of Science and Cochrane Library databases up to November 30, 2020. A random-effects model was applied to calculate the pooled effect size (ES) and its 95 % confidence interval (CI). RESULTS: Eight studies were included in this study. In a random-effects pooled analysis, the results showed that DM (diabetes mellitus) increased the risk of meningioma (ES 1.17, 95 % CI: 1.02-1.35, P = 0.027). In subgroup analyses, DM increased the risk of meningioma in women (ES: 1.19, 95 % CI: 1.02-1.40, P = 0.027) and men (ES: 1.53, 95 % CI: 1.25-1.88, P = 0.000). This effect was not observed in the postmenopausal group (ES: 1.18, 95 % CI: 0.64-2.18, P = 0.597). CONCLUSION: Our meta-analysis showed that DM increases the risk of meningioma, but the association was only present in some subgroups. This conclusion should be further confirmed.
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Diabetes Mellitus , Neoplasias Meníngeas , Meningioma , Diabetes Mellitus/epidemiologia , Humanos , Neoplasias Meníngeas/epidemiologia , Meningioma/epidemiologia , Estudos Observacionais como Assunto , Fatores de RiscoRESUMO
AIMS: To correlate glycated albumin (GA) and glycosylated haemoglobin (HbA1c) and establish a novel formula for estimating HbA1c from GA. METHODS: We retrospectively enrolled 20,381 cases and excluded HbA1c and GA outliers by residual analysis. HbA1c ranged from 4.0-12.0% and GA from 7.5-45%. The HbA1c range of 4.0-8.0% in both sexes was stratified into eight groups with an increase of 0.5%, and the means of GA and HbA1c were compared. HbA1c was divided into 38 groups with increments of 0.1% (range, 4.3-8.0%), and the correlation between HbA1c and GA was investigated. RESULTS: There was no significant sex-based difference between HbA1c and GA. The analysis showed that when HbA1c was 6.2% or GA was 12.28%, the linear relationship between the two parameters was not continuous. When HbA1c was <6.2% or GAâ¯<â¯12.28%, we devised the formula: HbA1câ¯=â¯1.136â¯×â¯GAâ¯-â¯7.289 (R2â¯=â¯0.824). For HbA1câ¯≥â¯6.2% or GAâ¯≥â¯12.28%, the equation was: HbA1câ¯=â¯0.252â¯×â¯GAâ¯+â¯3.163 (R2â¯=â¯0.948). CONCLUSION: A discontinuous linear relationship exists between HbA1c and GA when HbA1c is 6.2% or GA is 12.28%, although with a significant turning point. The GA value can be used to estimate the HbA1c value with the two regression equations to accurately estimate the long-term average blood glucose level of patients.
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Glicemia , Hemoglobinas Glicadas , Produtos Finais de Glicação Avançada/análise , Albumina Sérica/análise , China/epidemiologia , Feminino , Hemoglobinas Glicadas/análise , Humanos , Masculino , Estudos Retrospectivos , Albumina Sérica GlicadaRESUMO
BACKGROUND: Solid/cystic hemangioblastomas are rare, and they lack a systematic description. We clarify the epidemiology, clinical features, imaging characteristics, and surgical outcomes of sporadic solid/cystic hemangioblastomas in the cerebellum. METHODS: A total of 75 patients with sporadic hemangioblastomas from 2006 to 2018 were enrolled in this retrospective study and divided into solid (26/75), cystic (40/75), and solid/cystic (9/75) groups according to the imaging findings. All patients underwent microsurgical resection and had a definite 31 pathologic diagnosis. RESULTS: The age at diagnosis in the solid/cystic group was the highest among the 3 groups (P < 0.05). The solid/cystic group showed the shortest symptom duration (P < 0.05), which was related to obvious peritumoral brain edema (P < 0.05). The combination of computed tomography angiography and magnetic resonance imaging helped with the differential diagnosis. The solid/cystic group showed the lowest rate of gross total resection (P < 0.05) as a result of the obscure brain-tumor interface, and the guidance of intraoperative ultrasonography helped with the microsurgical procedures to a certain extent. Patients in the solid/cystic group showed greater intraoperative blood loss (P < 0.05), a lower ratio of symptom improvement (P < 0.05), and a longer mean hospital stay (P < 0.05) than did patients in the cystic group. CONCLUSIONS: Cerebellar sporadic solid/cystic hemangioblastomas are rare and usually affect elderly people. The combination of computed tomography angiography and magnetic resonance imaging may improve the preoperative diagnosis. Solid/cystic hemangioblastomas showed the lowest rate of gross total resection as a result of the obscure brain-tumor interface.
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Neoplasias Cerebelares/diagnóstico , Neoplasias Cerebelares/epidemiologia , Hemangioblastoma/diagnóstico , Hemangioblastoma/epidemiologia , Adulto , Neoplasias Cerebelares/cirurgia , Feminino , Hemangioblastoma/cirurgia , Humanos , Masculino , Pessoa de Meia-Idade , Recidiva Local de Neoplasia/epidemiologia , Recidiva Local de Neoplasia/cirurgia , Estudos Retrospectivos , Resultado do TratamentoRESUMO
We present an analytical approach for measuring the temperature of nonlinear dynamical systems in the microcanonical ensemble. Via the self-consistent phonon theory, one can analytically obtain the temperature with respect to the internal energy density in a canonical way. We show how that provides a measure of temperature in the microcanonical ensemble, under the hypothesis of ensemble equivalence. Two models, the FPU-ß and Ï^{4} lattices, are studied obtaining results consistent with those derived from time averages along trajectories in the phase space. Furthermore, our approach is corroborated by the fact that temperature obtained in terms of the average energy density after thermalization agrees with the thermostat temperature. The hypothesis is validated via examining the energy distribution for different numbers of particles in the canonical ensemble. Further, we have quantified the corresponding finite size effects. Unlike other existing methods, which require time-consuming computations, our analytical approach performance improves with the number of particles.
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Controlling the direction and magnitude of both heat and electronic currents using rectifiers has significant implications for the advancement of molecular circuit design. In order to facilitate the implementation of new transport phenomena in such molecular structures, we examine thermal and thermoelectric rectification effects that are induced by an electron transfer process that occurs across a temperature gradient between molecules. Historically, the only known heat conduction mechanism able to generate thermal rectification in purely molecular environments is phononic heat transport. Here, we show that electron transfer between molecular sites with different local temperatures can also generate a thermal rectification effect and that electron hopping through molecular bridges connecting metal leads at different temperatures gives rise to asymmetric Seebeck effects, that is, thermoelectric rectification, in molecular junctions.
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A logarithmic oscillator has been proposed to serve as a thermostat recently since it has a peculiar property of infinite heat capacity according to the virial theorem. In order to examine its feasibility in numerical simulations, a modified logarithmic potential has been applied in previous studies to eliminate the singularity at the origin. The role played by the modification has been elucidated in the present study. We argue that the virial theorem is practically violated in finite-time simulations of the modified log-oscillator illustrated by a linear dependence of kinetic temperature on energy. Furthermore, as far as a thermalized log-oscillator is concerned, our calculation based on the canonical ensemble average shows that the generalized equipartition theorem is broken if the temperature is higher than a critical temperature. Finally, we show that log-oscillators fail to serve as thermostats for their incapability of maintaining a nonequilibrium steady state even though their energy is appropriately assigned.
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Phytochemical investigation of the ethyl acetate and methanol extracts of the bark of Madagascan endemic and medicinal plant Cinnamosma fragrans led to the isolation of two drimane sesquiterpene derivatives: cinnafragroside A (1) and cinnafragrin E (2), two aromatic glycosides: 3,4,5-trimethoxyphenol 1-O-ß-d-apiofuranosyl-(1â6)-ß-d-glucopyranoside (3) and 3,4-dimethoxyphenyl-1-O-ß-d-apiofuranosyl-(1â6)-ß-d-glucopyranoside (4), together with 12 known compounds identified as: helicide (6), 1-(α-l-rhamnosyl(1â6)-ß-d-glucopyranosyloxy)-3,4,5-trimethoxybenzene (7), vanilloloside (8), cinnamadin (9), ugandensolide (10), cinnamosmolide (11), cinnamolide (12), polygodial (13), cinnamodial (14), bemadienolide (15), 4-isopropyl-6-methyl-α-tetralone (16), and capsicodendrin (17). Another new compound, 11-norcinnafragrolide-9-one (5), was obtained during chemical derivatization of capsicodendrin and gave a hint to understanding the structure required for the antiproliferative activity of 17. The structures of the new compounds were elucidated based on the interpretation of their spectroscopic data including one and two dimensional nuclear magnetic resonance (1D- and 2D-NMR) and mass spectroscopic data. All isolated compounds were evaluated against the hormone dependent breast cancer cell line MCF-7. Compound 17 exhibited the most potent activity with an IC50 value of 0.6µM. Our preliminary SAR study showed that the hydroxyl group at C-12' and the presence of conjugated carbonyl contribute to the antiproliferative activity.
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Antineoplásicos Fitogênicos/química , Antineoplásicos Fitogênicos/farmacologia , Glicosídeos/química , Glicosídeos/farmacologia , Sesquiterpenos/química , Sesquiterpenos/farmacologia , Antineoplásicos Fitogênicos/isolamento & purificação , Neoplasias da Mama/tratamento farmacológico , Proliferação de Células/efeitos dos fármacos , Feminino , Glicosídeos/isolamento & purificação , Humanos , Células MCF-7 , Magnoliopsida/química , Modelos Moleculares , Plantas Medicinais/química , Sesquiterpenos Policíclicos , Sesquiterpenos/isolamento & purificaçãoRESUMO
Through the integration of the power spectral density, we obtain temperature profiles of both multisegment harmonic and anharmonic systems, showing the presence of an anomalous negative temperature gradient inside the interfacial segment. Via investigating patterns of the power spectral density, we found that the counterintuitive phenomenon comes from the presence of interfacial localized phonon modes. Two out-band localized modes of the harmonic model, which make no contributions to local temperature due to the absence of phonon interactions, result in the concave temperature profile and overcooling effect. For the anharmonic model, thanks to the phonon-phonon interactions, the localized modes are excited and make considerable contributions to interfacial temperature, which is clearly shown by examining the temperature accumulation function. When anharmonicity is considerably large, the negative temperature gradient is absent since the localized phonon modes are fully mixed. The presence of localized modes are evidently demonstrated by the inverse participation ratio and normal mode analysis for the isolated harmonic model. The localized modes make contribution to interfacial temperature profiles of the harmonic system when they are excited in initial conditions of simulations.