Divergent association between pain intensity and resting-state fMRI-based brain entropy in different age groups.

Pain is a multidimensional subjective experience sustained by multiple brain regions involved in different aspects of pain experience. We used brain entropy (BEN) estimated from resting-state fMRI (rsfMRI) data to investigate the neural correlates of pain experience. BEN was estimated from rs-fMRI data provided by two datasets with different age range: the Human Connectome Project-Young Adult (HCP-YA) and the Human Connectome project-Aging (HCP-A) datasets. Retrospective assessment of experienced pain intensity was retrieved from both datasets. No main effect of pain intensity was observed. The interaction between pain and age, however, was related to increased BEN in several pain-related brain regions, reflecting greater variability of spontaneous brain activity. Dividing the sample into a young adult group (YG) and a middle age-aging group (MAG) resulted in two divergent patterns of pain-BEN association: In the YG, pain intensity was related to reduced BEN in brain regions involved in the sensory processing of pain; in the MAG, pain was associated with increased BEN in areas related to both sensory and cognitive aspects of pain experience.

Synthesis and characterization of TiNbZrMo medium-entropy bio-composites: Microstructure, mechanical properties, and in vitro degradation.

This study reports the synthesis and characterization of hydroxyapatite (HA)-based bio-composites reinforced with varying amounts (by weight, 1-15 wt.%) of bio-medium entropy alloy (BioMEA) for load-bearing implant applications. BioMEA powders consisting of Ti, Nb, Zr, and Mo were mechanically alloyed for 100 h and subsequently added to HA using powder metallurgy techniques. To show the effect of BioMEA, the microstructure, density, and mechanical tests have been conducted and the synthesized BioMEA was characterized by scanning electron microscope (SEM), x-ray diffractometer (XRD), and Fourier-transform infrared spectroscopy (FTIR) analysis. In addition, in vitro degradation behavior and bioactivity analyses of bio-composites have been conducted. XRD analysis revealed the formation of BioMEA after 20 h of mechanical alloying. The highest density value of 2.47 g/cm3 was found in 15 wt.% BioMEA-reinforced bio-composite. The addition of BioMEA reinforcement led to a significant increase in hardness and tensile strength values, with the highest values observed at 15 wt.% reinforcement. Compression tests demonstrated a significant increase in compressive strength and deformation capability of the bio-composites with the highest values observed at 15 wt.% BioMEA addition. The highest toughness of 7.68 kJ/m2 was measured in 10 wt.% MEA-reinforced bio-composites. The produced bio-composite materials have an elastic modulus between 3.5-5.5 GPa, which may provide a solution to the stress shielding problems caused by the high elastic modulus of metallic implant materials. The most severe degradation occurred in 15 wt.% MEA-reinforced bio-composites, and the effect of degradation caused a decrease in Ca and an increase in Ti-Ni-Zr-Mo in all bio-composites. These findings suggest that HA/BioMEA bio-composites have the potential to be developed as advanced biomaterials with moderate mechanical and biological properties for load-bearing implant applications.

The quality and complexity of pairwise maximum entropy models for large cortical populations.

We investigate the ability of the pairwise maximum entropy (PME) model to describe the spiking activity of large populations of neurons recorded from the visual, auditory, motor, and somatosensory cortices. To quantify this performance, we use (1) Kullback-Leibler (KL) divergences, (2) the extent to which the pairwise model predicts third-order correlations, and (3) its ability to predict the probability that multiple neurons are simultaneously active. We compare these with the performance of a model with independent neurons and study the relationship between the different performance measures, while varying the population size, mean firing rate of the chosen population, and the bin size used for binarizing the data. We confirm the previously reported excellent performance of the PME model for small population sizes N < 20. But we also find that larger mean firing rates and bin sizes generally decreases performance. The performance for larger populations were generally not as good. For large populations, pairwise models may be good in terms of predicting third-order correlations and the probability of multiple neurons being active, but still significantly worse than small populations in terms of their improvement over the independent model in KL-divergence. We show that these results are independent of the cortical area and of whether approximate methods or Boltzmann learning are used for inferring the pairwise couplings. We compared the scaling of the inferred couplings with N and find it to be well explained by the Sherrington-Kirkpatrick (SK) model, whose strong coupling regime shows a complex phase with many metastable states. We find that, up to the maximum population size studied here, the fitted PME model remains outside its complex phase. However, the standard deviation of the couplings compared to their mean increases, and the model gets closer to the boundary of the complex phase as the population size grows.

Classification of motor imagery using chaotic entropy based on sub-band EEG source localization.

Objective.Electroencephalography (EEG) has been widely used in motor imagery (MI) research by virtue of its high temporal resolution and low cost, but its low spatial resolution is still a major criticism. The EEG source localization (ESL) algorithm effectively improves the spatial resolution of the signal by inverting the scalp EEG to extrapolate the cortical source signal, thus enhancing the classification accuracy.Approach.To address the problem of poor spatial resolution of EEG signals, this paper proposed a sub-band source chaotic entropy feature extraction method based on sub-band ESL. Firstly, the preprocessed EEG signals were filtered into 8 sub-bands. Each sub-band signal was source localized respectively to reveal the activation patterns of specific frequency bands of the EEG signals and the activities of specific brain regions in the MI task. Then, approximate entropy, fuzzy entropy and permutation entropy were extracted from the source signal as features to quantify the complexity and randomness of the signal. Finally, the classification of different MI tasks was achieved using support vector machine.Main result.The proposed method was validated on two MI public datasets (brain-computer interface (BCI) competition III IVa, BCI competition IV 2a) and the results showed that the classification accuracies were higher than the existing methods.Significance.The spatial resolution of the signal was improved by sub-band EEG localization in the paper, which provided a new idea for EEG MI research.

Loop-extruders alter bacterial chromosome topology to direct entropic forces for segregation.

Entropic forces have been argued to drive bacterial chromosome segregation during replication. In many bacterial species, however, specifically evolved mechanisms, such as loop-extruding SMC complexes and the ParABS origin segregation system, contribute to or are even required for chromosome segregation, suggesting that entropic forces alone may be insufficient. The interplay between and the relative contributions of these segregation mechanisms remain unclear. Here, we develop a biophysical model showing that purely entropic forces actually inhibit bacterial chromosome segregation until late replication stages. By contrast, our model reveals that loop-extruders loaded at the origins of replication, as observed in many bacterial species, alter the effective topology of the chromosome, thereby redirecting and enhancing entropic forces to enable accurate chromosome segregation during replication. We confirm our model predictions with polymer simulations: purely entropic forces do not allow for concurrent replication and segregation, whereas entropic forces steered by specifically loaded loop-extruders lead to robust, global chromosome segregation during replication. Finally, we show how loop-extruders can complement locally acting origin separation mechanisms, such as the ParABS system. Together, our results illustrate how changes in the geometry and topology of the polymer, induced by DNA-replication and loop-extrusion, impact the organization and segregation of bacterial chromosomes.

From field soil sampling to watershed model: Upscaling by integrating information entropy and interpolation method.

Soil property data plays a crucial role in watershed hydrology and non-point source (H/NPS) modeling, but how to improve modeling accuracy with affordable soil samplings and the effects of sampling information on H/NPS modeling remains to be further explored. In this study, the number of sampling points and soil properties were optimized by the information entropy and the spatial interpolation method. Then the sampled properties were parameterized and the effects of different parameterization schemes on H/NPS modeling were tested using the Soil and Water Assessment Tool (SWAT). The results indicated that the required sampling points increased successively for soil bulk density (SOL_BD), soil saturated hydraulic conductivity (SOL_K) and soil available water capacity (SOL_AWC). Compared to the traditional database (Harmonized world soil database), the NSE and R2 performance by new scheme increased by 22.8% and 10.5%, respectively. The entropy-based optimization reduced the sampling points by 13.2%, indicating a more cost-effective scheme. Compared to hydrological simulation, sampled properties showed greater effects on NPS modeling, especially for nitrogen. This proposed method/framework can be generalized to other watersheds by upscaling field soil sampling information to the watershed scale, thus improving H/NPS simulation.

Upgraded and Light-Up Biosensing Platform: Entropy-Driven Catalysis Circuit Manipulates the Configuration Transformation of Novel DNA Silver Nanoclusters on the Graphene Oxide Surface.

To tackle the predicament of the traditional turn-off mechanism, exploring an activated turn-on system remains an intriguing and crucial objective in biosensing fields. Herein, a dark DNA Ag nanocluster (NC) with hairpin-structured DNA containing a six-base cytosine loop (6C loop) as a template is atypically synthesized. Intriguingly, the dark DNA Ag NCs can be lit to display strong red-emission nanoclusters. Building upon these exciting findings, an unprecedented and upgraded turn-on biosensing system [entropy-driven catalysis circuit (EDCC)-Ag NCs/graphene oxide (GO)] has been created, which employs an EDCC to precisely manipulate the conformational transition of DNA Ag NCs on the GO surface from adsorption to desorption. Benefiting from the effective quenching of GO and signal amplification capability of the EDCC, the newly developed EDCC-Ag NCs/GO biosensing system displays a high signal-to-background (S/B) ratio (26-fold) and sensitivity (limit of detection as low as 0.4 pM). Meanwhile, it has good specificity, excellent stability, and reliability in both buffer and biological samples. To the best of our knowledge, it is the first example that adopts an EDCC to precisely modulate the configuration transformation of DNA Ag NCs on the GO surface to obtain a biosensor with low background, strong fluorescence, high contrast, and sensitivity. This exciting finding may provide a new route to fabricate a novel turn-on biosensor based on hairpin-templated DNA Ag NCs in the optical imaging and bioanalytical fields.

Integrated information decomposition unveils major structural traits of in silico and in vitro neuronal networks.

The properties of complex networked systems arise from the interplay between the dynamics of their elements and the underlying topology. Thus, to understand their behavior, it is crucial to convene as much information as possible about their topological organization. However, in large systems, such as neuronal networks, the reconstruction of such topology is usually carried out from the information encoded in the dynamics on the network, such as spike train time series, and by measuring the transfer entropy between system elements. The topological information recovered by these methods does not necessarily capture the connectivity layout, but rather the causal flow of information between elements. New theoretical frameworks, such as Integrated Information Decomposition (Φ-ID), allow one to explore the modes in which information can flow between parts of a system, opening a rich landscape of interactions between network topology, dynamics, and information. Here, we apply Φ-ID on in silico and in vitro data to decompose the usual transfer entropy measure into different modes of information transfer, namely, synergistic, redundant, or unique. We demonstrate that the unique information transfer is the most relevant measure to uncover structural topological details from network activity data, while redundant information only introduces residual information for this application. Although the retrieved network connectivity is still functional, it captures more details of the underlying structural topology by avoiding to take into account emergent high-order interactions and information redundancy between elements, which are important for the functional behavior, but mask the detection of direct simple interactions between elements constituted by the structural network topology.

Sensitive fluorescence assay of chloramphenicol coupled with two-level isothermal amplification using a self-powered catalyzed hairpin assembly and entropy-driven circuit.

Two levels of nucleic acids-based isothermal amplification normally require a long reaction time due to the low concentration of catalyst, which limits its practical application. A sensitive fluorescence assay of chloramphenicol (CAP) was developed coupled with two-level isothermal amplification using a self-powered catalyzed hairpin assembly (CHA) and entropy-driven circuit (EDC). CAP can bind with its aptamer to open its closed structure. The opened hairpin can initiate self-powered CHA and EDC. The product of CHA can circularly catalyze the CHA with increasing concentration. In principle, the product of CHA plays the role of catalyst and increases with the progression of the reaction. Compared with the normal two levels of amplification, the amplification efficiency of our strategy is much higher due to the self-powered reaction by the CHA product. Thus, the reaction time is shortened to 110 min in this strategy. Moreover, the detection limit for CAP can achieve 0.1 pM and shows promising prospects for practical application.

Exploring UMAP in hybrid models of entropy-based and representativeness sampling for active learning in biomedical segmentation.

In this work, we study various hybrid models of entropy-based and representativeness sampling techniques in the context of active learning in medical segmentation, in particular examining the role of UMAP (Uniform Manifold Approximation and Projection) as a technique for capturing representativeness. Although UMAP has been shown viable as a general purpose dimension reduction method in diverse areas, its role in deep learning-based medical segmentation has yet been extensively explored. Using the cardiac and prostate datasets in the Medical Segmentation Decathlon for validation, we found that a novel hybrid combination of Entropy-UMAP sampling technique achieved a statistically significant Dice score advantage over the random baseline (3.2% for cardiac, 4.5% for prostate), and attained the highest Dice coefficient among the spectrum of 10 distinct active learning methodologies we examined. This provides preliminary evidence that there is an interesting synergy between entropy-based and UMAP methods when the former precedes the latter in a hybrid model of active learning.

A fluorescent aptasensor for enzyme-free and sensitive detection of kanamycin based on entropy-driven strand displacement reaction.

BACKGROUND: Kanamycin is an antibiotic that can easily cause adverse side effects if used improperly. Due to the extremely low concentrations of kanamycin in food, quantitative detection of kanamycin becomes a challenge. As one of the DNA self-assembly strategies, entropy-driven strand displacement reaction (EDSDR) does not require enzymes or hairpins to participate in the reaction, which greatly reduces the instability of detection results. Therefore, it is a very beneficial attempt to construct a highly sensitive and specific fluorescence detection method based on EDSDR that can detect kanamycin easily and quickly while ensuring that the results are effective and stable. RESULTS: We created an enzyme-free fluorescent aptamer sensor with high specificity and sensitivity for detecting kanamycin in milk by taking advantage of EDSDR and the high specific binding between the target and its aptamer. The specific binding can result in the release of the promoter chain, which then sets off the pre-planned EDSDR cycle. Fluorescent label modification on DNA combined with the fluorescence quenching-recovery mechanism gives the sensor impressive fluorescence response capabilities. The research results showed that within the concentration range of 0.1 nM-50 nM, there was a good relationship between the fluorescence intensity of the solution and the concentration of kanamycin. Specificity experiments and actual sample detection experiments confirmed that the biosensor could achieve highly sensitive and specific detection of trace amounts of kanamycin in food, with a detection limit of 0.053 nM (S/N = 3). SIGNIFICANCE: To our knowledge, this is the first strategy to combine EDSDR with fluorescence to detect kanamycin in food. Accurate results can be obtained in as little as 90 min with no enzymes or hairpins involved in the reaction. Furthermore, our enzyme-free biosensing method is straightforward, highly sensitive, and extremely specific. It has many possible applications, including monitoring antibiotic residues and food safety.

Quantitative entropy-enthalpy compensation in intraprotein interactions from model compound data.

Many small globular proteins exist in only two states-the physiologically relevant folded state and an inactive unfolded state. The active state is stabilized by numerous weak attractive contacts, including hydrogen bonds, other polar interactions, and the hydrophobic effect. Knowledge of these interactions is key to understanding the fundamental equilibrium thermodynamics of protein folding and stability. We focus on one such interaction, that between amide and aromatic groups. We provide a statistically convincing case for quantitative, linear entropy-enthalpy compensation in forming aromatic-amide interactions using published model compound transfer-free energy data.

Spatio-temporal evolution of sports tourism industry integration: A empirical analysis of Xinjiang in China.

Since the issuance of the "Guiding Opinions on Vigorously Developing Sports Tourism" in 2016, the integration of sports and tourism has become a strategy in regional economic development. It creates new economic growth points, enhances local images, and promotes cultural communication. In the context of the "Tourism Makes Xinjiang Thrive" strategy, quantitatively investigating the integration of the sports and tourism industries helps people to better understand their interaction which can serve as the valuable input in policy-making for the comprehensive development of a region. This paper uses entropy weight method, stochastic frontier analysis and coupling coordination model to quantitatively analyze the effect of sports tourism industry integration in Xinjiang from the perspective of integration path. Meanwhile, the Dagum Gini coefficient and nuclear density estimation were used to analyze the regional differences and dynamic evolution of industrial integration quality. The result shows that (1) The sports and tourism integration quality in Xinjiang has not reached the optimal goal of complete integration. In the process of mutual industrial promotion, tourism promotes a higher degree of integration with the sports industry. (2) The industrial integration quality shows a phenomenon of "imbalance and inadequacy" among the regions. The regions with high quality of industrial integration were Urumqi, Ili, Kashgar, Altay and Changji, which have rich sports tourism resources. (3) The overall spatial difference in the quality of industrial integration presented a fluctuation downtrend. The difference between the tourism industrial belts was very significant.

Permutation entropy analysis of EEG signals for distinguishing eyes-open and eyes-closed brain states: Comparison of different approaches.

Developing reliable methodologies to decode brain state information from electroencephalogram (EEG) signals is an open challenge, crucial to implementing EEG-based brain-computer interfaces (BCIs). For example, signal processing methods that identify brain states could allow motor-impaired patients to communicate via non-invasive, EEG-based BCIs. In this work, we focus on the problem of distinguishing between the states of eyes closed (EC) and eyes open (EO), employing quantities based on permutation entropy (PE). An advantage of PE analysis is that it uses symbols (ordinal patterns) defined by the ordering of the data points (disregarding the actual values), hence providing robustness to noise and outliers due to motion artifacts. However, we show that for the analysis of multichannel EEG recordings, the performance of PE in discriminating the EO and EC states depends on the symbols' definition and how their probabilities are estimated. Here, we study the performance of PE-based features for EC/EO state classification in a dataset of N=107 subjects with one-minute 64-channel EEG recordings in each state. We analyze features obtained from patterns encoding temporal or spatial information, and we compare different approaches to estimate their probabilities (by averaging over time, over channels, or by "pooling"). We find that some PE-based features provide about 75% classification accuracy, comparable to the performance of features extracted with other statistical analysis techniques. Our work highlights the limitations of PE methods in distinguishing the eyes' state, but, at the same time, it points to the possibility that subject-specific training could overcome these limitations.

Modulatory effects of low-intensity retinal ultrasound stimulation on rapid and non-rapid eye movement sleep.

Prior investigations have established that the manipulation of neural activity has the potential to influence both rapid eye movement and non-rapid eye movement sleep. Low-intensity retinal ultrasound stimulation has shown effectiveness in the modulation of neural activity. Nevertheless, the specific effects of retinal ultrasound stimulation on rapid eye movement and non-rapid eye movement sleep, as well as its potential to enhance overall sleep quality, remain to be elucidated. Here, we found that: In healthy mice, retinal ultrasound stimulation: (i) reduced total sleep time and non-rapid eye movement sleep ratio; (ii) changed relative power and sample entropy of the delta (0.5-4 Hz) in non-rapid eye movement sleep; and (iii) enhanced relative power of the theta (4-8 Hz) and reduced theta-gamma coupling strength in rapid eye movement sleep. In Alzheimer's disease mice with sleep disturbances, retinal ultrasound stimulation: (i) reduced the total sleep time; (ii) altered the relative power of the gamma band during rapid eye movement sleep; and (iii) enhanced the coupling strength of delta-gamma in non-rapid eye movement sleep and weakened the coupling strength of theta-fast gamma. The results indicate that retinal ultrasound stimulation can modulate rapid eye movement and non-rapid eye movement-related neural activity; however, it is not beneficial to the sleep quality of healthy and Alzheimer's disease mice.

How ATP suppresses the fibrillation of amyloid peptides: analysis of the free-energy contributions.

Recent experiments have revealed that adenosine triphosphate (ATP) suppresses the fibrillation of amyloid peptides - a process closely linked to neurodegenerative diseases such as Alzheimer's and Parkinson's. Apart from the adsorption of ATP onto amyloid peptides, the molecular understanding is still limited, leaving the underlying mechanism for the fibrillation suppression by ATP largely unclear, especially in regards to the molecular energetics. Here we provide an explanation at the molecular scale by quantifying the free energies using all-atom molecular dynamics simulations. We found that the changes of the free energies due to the addition of ATP lead to a significant equilibrium shift towards monomeric peptides in agreement with experiments. Despite ATP being a highly charged species, the decomposition of the free energies reveals that the van der Waals interactions with the peptide are decisive in determining the relative stabilization of the monomeric state. While the phosphate moiety exhibits strong electrostatic interactions, the compensation by the water solvent results in a minor, overall Coulomb contribution. Our quantitative analysis of the free energies identifies which intermolecular interactions are responsible for the suppression of the amyloid fibril formation by ATP and offers a promising method to analyze the roles of similarly complex cosolvents in aggregation processes.

Edge-based relative entropy as a sensitive indicator of critical transitions in biological systems.

BACKGROUND: Disease progression in biosystems is not always a steady process but is occasionally abrupt. It is important but challenging to signal critical transitions in complex biosystems. METHODS: In this study, based on the theoretical framework of dynamic network biomarkers (DNBs), we propose a model-free method, edge-based relative entropy (ERE), to identify temporal key biomolecular associations/networks that may serve as DNBs and detect early-warning signals of the drastic state transition during disease progression in complex biological systems. Specifically, by combining gene‒gene interaction (edge) information with the relative entropy, the ERE method converts gene expression values into network entropy values, quantifying the dynamic change in a biomolecular network and indicating the qualitative shift in the system state. RESULTS: The proposed method was validated using simulated data and real biological datasets of complex diseases. The applications show that for certain diseases, the ERE method helps to reveal so-called "dark genes" that are non-differentially expressed but with high ERE values and of essential importance in both gene regulation and prognosis. CONCLUSIONS: The proposed method effectively identified the critical transition states of complex diseases at the network level. Our study not only identified the critical transition states of various cancers but also provided two types of new prognostic biomarkers, positive and negative edge biomarkers, for further practical application. The method in this study therefore has great potential in personalized disease diagnosis.

Understanding the Reversible Binding of a Multichain Protein-Protein Complex through Free-Energy Calculations.

We demonstrate that the binding affinity of a multichain protein-protein complex, insulin dimer, can be accurately predicted using a streamlined route of standard binding free-energy calculations. We find that chains A and C, which do not interact directly during binding, stabilize the insulin monomer structures and reduce the binding affinity of the two monomers, therefore enabling their reversible association. Notably, we confirm that although classical methods can estimate the binding affinity of the insulin dimer, conventional molecular dynamics, enhanced sampling algorithms, and classical geometrical routes of binding free-energy calculations may not fully capture certain aspects of the role played by the noninteracting chains in the binding dynamics. Therefore, this study not only elucidates the role of noninteracting chains in the reversible binding of the insulin dimer but also offers a methodological guide for investigating the reversible binding of multichain protein-protein complexes utilizing streamlined free-energy calculations.

Constructing an evaluation model for the comprehensive level of sustainable development of provincial competitive sports in China based on DPSIR and MCDM.

This study focuses on the objective assessment of sport development in socio-economic environments, considering the challenges faced by the industry. These challenges include disparities in regional investments, limited market participation, slow progress towards sports professionalization, and insufficient technological innovations. To tackle these challenges, we suggest implementing an integrated evaluation model that follows the DPSIR (Drivers, Pressures, States, Impacts, Responses) framework and incorporates comprehensive socioeconomic indicators. Subsequently, we utilized the Entropy power method and TOPSIS (Order Preference Technique for Similarity to an Ideal Solution, TOPSIS) analysis to comprehensively assess the progress of competitive sports development in 31 provinces and cities in China. Additionally, we recommended further developments in competitive sports and proposed precise strategies for promoting its growth. The framework and methodology developed in this paper provide an objective and scientifically based set of decision-making guidelines that can be adopted by government agencies and related industries in order to create successful plans that promote the sustainable growth of competitive sport. This is expected to bolster the nation's global influence, enhance social unity, and fuel economic expansion. The findings of this study offer policymakers valuable insights regarding competitive sports and can advance the development of the sports sector in China, thus making it a crucial driver of regional socio-economic progress.