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Fractional-order differential equations are prevalent in many scientific fields; hence, their study has seen a renaissance in recent years. The fascinating realm of fractional calculus is explored in this research study, with particular emphasis on the Harry Dym equation. To solve this problem, we use the Laplace Residual Power Series Method (LRPSM) and introduce the New Iterative Method (NIM). Both the mathematical complexity of the Harry Dym problem and the viability of the Caputo operator in this setting are investigated in our work. We go beyond the limitations of traditional mathematical methods to provide novel insights into the results of fractional-order differential equations via careful analysis and cutting-edge procedures. In this paper, we combine theory and practice to provide a novel perspective to the results of high-order fractional differential equations. Our efforts pay off by expanding our knowledge of mathematics and revealing the latent potential of the Harry Dym equation. This study expands researchers’ and mathematicians’ perspectives, bringing in a new and exciting period of progress in the field of fractional calculus.

Direct oxidation of methane (DOM) into high-value C2+ products using molecular oxygen (O 2 ) is essential for the sustainable production of clean energy and bulk chemicals, but is still challenging due to the difficult C-H activation and uncontrollable C-C coupling process. Herein, we design and construct the Fe-(μ-O)-Zn dual-atom sites by supporting Fe and Zn atoms on ZSM-5 (Fe 1 -Zn 1 /ZSM-5), which achieves the DOM by O 2 to acetic acid under ambient temperature and pressure. The Fe-(μ-O)-Zn dual-atom sites yield an acetic acid productivity of 3006 μmol•g cat −1 •h −1 with 86.8% selectivity (total C2+ products selectivity of 93.0%) for at least 20 hours at 25 o C and atmospheric pressure. The mutual electronic modulation between Fe and Zn shifts the d -band center of Fe 3 d in Fe-(μ-O)-Zn dual-atom sites upwards, which promotes the formation and stabilization of highly reactive Fe=O species through O 2 photodissociation and thereby enhances the C-H bond activation of CH 4 . The Fe-(μ-O)-Zn dual-atom reaction sites (spatial distance of 2.7 Å) boost the C-C coupling of key CH 3 and HCHO intermediate species, which steadily produce acetic acid and other C2+ oxygenates. This work would broaden the avenue towards the sustainable conversion of methane to value-added C2+ products under ambient temperature and pressure. Direct methane oxidation to C2+ with O 2 is impeded by tough C–H activation and uncontrolled coupling. Here, Fe-(μ-O)-Zn dual-atom sites on ZSM-5 enable efficient photocatalytic acetic acid production at ambient temperature and pressure.

The thermodynamic Cucker–Smale model (TCS model) describes dynamic consistency caused by different temperatures between multi-agent particles. This paper studies the flocking behaviors of the TCS model with multiplicative white noise under hierarchical leadership. First, we introduce the corresponding model of two particles. Then, by using mathematical induction and considering the properties of differential functions, it is proved that, under certain conditions, the group can achieve flocking. Finally, we verify the conclusion through numerical simulation results. Similarly, this paper studies the above model with perturbation functions.

Direct oxidation of methane (DOM) into high-value C2+ products using molecular oxygen (O ) is essential for the sustainable production of clean energy and bulk chemicals, but is still challenging due to the difficult C-H activation and uncontrollable C-C coupling process. Herein, we design and construct the Fe-(μ-O)-Zn dual-atom sites by supporting Fe and Zn atoms on ZSM-5 (Fe -Zn /ZSM-5), which achieves the DOM by O to acetic acid under ambient temperature and pressure. The Fe-(μ-O)-Zn dual-atom sites yield an acetic acid productivity of 3006 μmol•g •h with 86.8% selectivity (total C2+ products selectivity of 93.0%) for at least 20 hours at 25 C and atmospheric pressure. The mutual electronic modulation between Fe and Zn shifts the d-band center of Fe 3d in Fe-(μ-O)-Zn dual-atom sites upwards, which promotes the formation and stabilization of highly reactive Fe=O species through O photodissociation and thereby enhances the C-H bond activation of CH . The Fe-(μ-O)-Zn dual-atom reaction sites (spatial distance of 2.7 Å) boost the C-C coupling of key CH and HCHO intermediate species, which steadily produce acetic acid and other C2+ oxygenates. This work would broaden the avenue towards the sustainable conversion of methane to value-added C2+ products under ambient temperature and pressure.

● Soil pH was the key factor influencing the phoD -harboring bacterial networks. ● Identification of a cluster positively linked to ALP activity and plant P uptake. ● Low soil pH resulted in a severe loss of phoD -harboring bacterial core cluster. Fertilization treatments profoundly influence the bacterial communities associated with soil organic phosphorus (P) mineralization and alkaline phosphatase (ALP) activity. However, the relationships among the phoD-harboring bacterial communities associated with soil organic P mineralization, soil ALP activity, and plant P uptake under long-term fertilization remain unexplored. This study investigated these associations at the wheat rapid growth stage in a 40-year fertilization experiment. NPK fertilization led to a significant decrease in the diversity of phoD-harboring bacteria, which could be partially mitigated by the addition of organic materials. Soil pH emerged as the key factor influencing the structure and diversity of the phoD-harboring bacterial community. Furthermore, fertilizations involving manure additions resulted in more stable and cooperative phoD-harboring bacterial co-occurrence networks, compared to NPK fertilization. A functional phoD-harboring bacterial cluster, comprising genera Nostoc, Bradyrhizobium, and Pseudomonas, was identified, showing a positive association with soil ALP activity and plant P uptake. In summary, our study highlights the significant role of the identified core cluster of phoD-harboring bacteria in maintaining soil ALP activity and promoting plant P uptake, in decades of fertilization. Moreover, this study inferred a list of phoD-harboring bacterial genera from the core cluster, with established links to both plant P uptake and soil organic P mineralization. These findings offer valuable insights for sustainable agricultural practices.

The NLR family apoptosis inhibitory proteins (NAIPs) bind conserved bacterial ligands, such as the bacterial rod protein PrgJ, and recruit NLR family CARD-containing protein 4 (NLRC4) as the inflammasome adapter to activate innate immunity. We found that the PrgJ-NAIP2-NLRC4 inflammasome is assembled into multisubunit disk-like structures through a unidirectional adenosine triphosphatase polymerization, primed with a single PrgJ-activated NAIP2 per disk. Cryo–electron microscopy (cryo-EM) reconstruction at subnanometer resolution revealed a ∼90° hinge rotation accompanying NLRC4 activation. Unlike in the related heptameric Apaf-1 apoptosome, in which each subunit needs to be conformationally activated by its ligand before assembly, a single PrgJ-activated NAIP2 initiates NLRC4 polymerization in a domino-like reaction to promote the disk assembly. These insights reveal the mechanism of signal amplification in NAIP-NLRC4 inflammasomes.

The CARD-only protein INCA inhibits inflammasome assembly by capping caspase-1 CARD oligomers and preventing their further polymerization. Inflammasomes are cytosolic caspase-1-activation complexes that sense intrinsic and extrinsic danger signals, and trigger inflammatory responses and pyroptotic cell death. Homotypic interactions among Pyrin domains and caspase recruitment domains (CARDs) in inflammasome-complex components mediate oligomerization into filamentous assemblies. Several cytosolic proteins consisting of only interaction domains exert inhibitory effects on inflammasome assembly. In this study, we determined the structure of the human caspase-1 CARD domain (caspase-1 CARD ) filament by cryo-electron microscopy and investigated the biophysical properties of two caspase-1-like CARD-only proteins: human inhibitor of CARD (INCA or CARD17) and ICEBERG (CARD18). Our results reveal that INCA caps caspase-1 filaments, thereby exerting potent inhibition with low-nanomolar K i on caspase-1 CARD polymerization in vitro and inflammasome activation in cells. Whereas caspase-1 CARD uses six complementary surfaces of three types for filament assembly, INCA is defective in two of the six interfaces and thus terminates the caspase-1 filament.

Synthetic microbial communities (SynComs) are microbial consortia with defined taxonomic and functional traits, so that the combination elicits a predictable response under defined conditions. SynComs are artificially designed to enable inter‐species metabolic interactions, metabolic division of labor, and ecological interactions that can elicit phenotypes like colonization stability and environmental adaptation. As an applied tool, SynComs have been deployed in diverse contexts, including agriculture, industry, and environmental ecology. This systematic review explores the processes used to construct SynComs, the mechanisms of metabolic interaction between members, and a review of the different ways that SynComs have been applied. We also explore the challenges for SynCom development and application, and future research directions that could overcome these challenges. SynComs are a powerful tool in our arsenal of applied technologies, but research and application are still nascent. While advances have been made, more research is needed to ensure SynCom technologies do not threaten global ecological security. SynCom technology represents a versatile platform for the controlled manipulation of microbial systems, enabling targeted modification of ecological and physiological processes. This emerging field marks a transition from descriptive biology toward a predictive and engineering‐driven framework for understanding and shaping living systems.

Inflammasomes are cytosolic caspase-1 activation complexes that sense intrinsic and extrinsic danger signals to trigger inflammatory responses and pyroptotic cell death. Homotypic interactions by Pyrin domains (PYD) and caspase recruitment domains (CARD) in inflammasome component proteins mediate oligomerization into filamentous assemblies. Several cytosolic proteins consisting of only the interaction domains exert inhibitory effects on inflammasome assembly. In this study, we determined the structure of human caspase-1CARD filament by cryo-electron microscopy and investigated the biophysical properties of two caspase-1-like CARD-only proteins, human inhibitor of CARD (INCA or CARD17) and ICEBERG (or CARD18). Our results reveal the surprising finding that INCA caps caspase-1 filament, thereby exerting potent inhibition with low nanomolar Ki on caspase-1CARD polymerization in vitro and inflammasome activation in cells. While caspase-1CARD uses six complementary surfaces of three types for filament assembly, INCA is defective in two of the six interfaces to terminate caspase-1 filament.