In biological systems, the process by which proteins self-assemble into organized complex structures is ubiquitous1, 2. Pole-to-pole protein oscillations in the Min system ensure that the FtsZ ring, a crucial component of cell division, is placed precisely in the middle of the cell body3, 4. In response to antibiotic treatment and heat stress, some bacteria generate multiple protein foci throughout the cytoplasm5, 6. The polar localization of the secretion system, such as the type Ⅵ secretion system, is mediated by targeting proteins and potentially facilitates host-pathogen interactions7, 8. Thus, spontaneous assembly is accompanied by the formation of spatial patterns that order the intracellular environment.
To grow and colonize within the host, bacteria have evolved a mechanism for migrating towards more favorable environments. The locomotion organ (the flagellar motor) and the chemotaxis pathway play crucial roles in achieving this goal. The former provides physical drive, while the latter offers directional guidance. The initiation of cell reorientation is controlled by motor switching, which is governed by the chemotaxis two-component signaling pathway. This pathway comprises transmembrane chemoreceptors, a histidine kinase CheA, an adaptor protein CheW, a response regulator CheY, and two adaptation proteins, CheB and CheR. Receptors collaborate with CheA and CheW to form chemosensory arrays in a hexagonal pattern9, 10. Upon phosphorylation of CheY by the kinase at the array, it freely diffuses to the motor and binds to FliM, a component of the motor switch complex, to affect motor switching11–13. It is worth noting that there exists diversity among different bacterial species in the placement of flagellar motors14, whereas chemoreceptor clusters are typically found at one or both ends of the cell15. These two structural units are functionally connected. However, it remains unclear whether there is an interaction in their spatial distribution and what the specific regulatory mechanism might be.
Pseudomonas aeruginosa, a common human opportunistic pathogen, possesses four chemosensory pathways that perform distinct functions and are stimulated by signal binding to 26 chemoreceptors16. Among them, F6 pathway-related receptors that mediate chemotaxis, as well as the flagellum are localized at the same cell pole17, 18. Furthermore, the polar anchor protein FlhF has been reported to guide the flagellum to grow at the cell pole19, 20. However, the mechanism by which chemoreceptor array-related proteins aggregate and self-assemble at the cell pole is controversial. The distribution of the chemosensory arrays in the peritrichous bacterium Escherichia coli has been extensively studied and attributed to several mechanisms, including stochastic self-assembly21, 22, membrane curvature sorting23, 24, and inefficient clustering in the lateral region25. However, these mechanisms cannot explain the unipolar distribution pattern observed in P. aeruginosa. Unlike E. coli, specific genes responsible for the placement of the chemosensory array have been identified in several bacterial species. In Caulobacter crescentus, chemosensory arrays assemble at the new cell pole with the help of TipN and TipF proteins26. A tripartite ParC-ParP-CheA interaction network was reported to promote polar localization of chemosensory array in Vibrio parahaemolyticus27, 28. However, as there are no related genes in P. aeruginosa, the mechanism of its chemoreceptor array distribution remains a mystery.
Here, we combined gene editing and in vivo fluorescence imaging of flagellar filaments to directly observe the distribution of chemoreceptor arrays and flagellar motors, proposing a cooperative construction model of chemotaxis network and flagella during the entire division cycle of P. aeruginosa. The core focus of this study is to clarify the regulatory mechanism of its chemoreceptor array distribution. We found a substantial association between the assembly of the flagellar motor and the chemoreceptor array. The complete assembly of the motor serves as a partial prerequisite for the assembly of the receptor array, and its assembly site is also regulated by the polar anchor protein FlhF. Furthermore, by introducing exogenously expressed CheY protein, we found that this triggers the expression of c-di-GMP at a high level. From this, we infer that the colocalization of the chemoreceptor array and the flagellum in P. aeruginosa avoids the cross-pathway interference of signaling molecules, thus providing a guarantee for the coexistence of multiple chemosensory pathways.
Robust generation of daughter cell with both chemotaxis network and flagellar motor
CheY has been shown to colocalize with chemoreceptors29. To visualize the distribution of chemoreceptor arrays in cells, we fused the gene encoding the enhanced yellow fluorescent protein (eYFP) to the cheY gene in the P. aeruginosa chromosome (Fig. 1A). All genetic modifications were carried out at the native position on the chromosome, allowing the expression of chemotaxis proteins in precise stoichiometry from their natural promoters (Fig. 1B). The mutant strain with cheY-eyfp was able to moderately expand on soft agar plates17, proving that its chemotaxis behavior was not notably affected, so it was selected for subsequent experiments. As shown in Fig. 1C, CheY-eYFP was mainly located at the cell pole, suggesting that CheA, CheW and CheY in P. aeruginosa form a signal transduction complex that was primarily distributed at the cell pole, as described previously17. From our measurements, nearly 90% (332/372) of cells contain obvious receptor clusters, and factors such as fluorescence bleaching may have caused the loss of fluorescent spots in some cells. In addition, we observed the presence of fluorescent spots at both ends of some cells with a large aspect ratio (probably approaching cell division), indicating that the newly generated progeny cells will have a complete chemotaxis network. Next, we sought to observe the distribution of the flagella in cells simultaneously to understand the motility of future progeny.
Our recent study demonstrated the successful labeling of the flagellar filament with thiol-reactive fluorescent dye by introducing cysteine mutations into the flagellin FliC30, 31 (Fig. 1B). To avoid fluorescence interference, we utilized a dye with an excitation peak near 568 nm, considering that the excitation peak of eYFP is 513 nm, and the emission peak is 527 nm. We employed a xenon lamp as the excitation light source and switched filters to enable simultaneous fluorescence imaging of flagellar filaments and chemosensory arrays within the same cell. Remarkably, our findings revealed a surprising colocalization of chemosensory arrays and flagellar filaments at the same end of the cell body, and this colocalization was consistent, as shown in Fig. 1D. Similar to the chemoreceptor arrays, we observed the phenomenon of double flagella symbiosis in cells with a large aspect ratio, suggesting that P. aeruginosa has evolved a cell division mechanism with precise timing regulation. Before cell division, both poles of the mother cell assembled chemoreceptor arrays and flagellar motors. This ensures that daughter cells possess complete motility and chemotaxis, thereby greatly enhancing the environmental adaptability of the population.
FlhF mediates proper unipolar localization of the chemoreceptor array
Given that the physiological and physical environments of both cell poles are nearly identical, it is unlikely that the unipolar distribution of the chemoreceptor array can be attributed to passive regulatory factors. The number and distribution of flagellar motors and chemoreceptor arrays vary among different bacterial species14, 15, and the localization system for flagella has been well studied. Specifically, the FlhF-FlhG system, discovered in several monotrichous bacterial species, has been shown to control the location and number of flagella32, 33. In P. aeruginosa, a knockout of flhF leads to mis-localized flagellar assembly19, 20. Considering the consistent colocalization pattern between chemosensory arrays and flagellar motors in P. aeruginosa, we speculate that the distribution of receptor clusters is also regulated by similar molecular mechanisms.
To investigate the role of FlhF in the localization of receptor arrays, we constructed a ΔflhF strain for fluorescence observation. The results revealed that the chemoreceptor arrays no longer grow robustly at the cell pole (Fig. 2A), and the assembly positions of the flagellar motor change accordingly, colocalizing with the receptor arrays (Fig. 2B). We also quantified the proportion of individuals with obvious receptor clusters, which was more than 80% (182/221), similar to the wild-type strain. These experimental results suggest that the polar anchoring protein FlhF has a minimal impact on the assembly efficiency of P. aeruginosa’s chemosensory array, but it strictly controls its unipolar distribution. Furthermore, a consistent colocalization between the flagellar motor and chemosensory array was observed, independent of FlhF. Thus, it is crucial to determine whether there is a causal relationship in the assembly order of these two structural units.
Motor structural integrity is a prerequisite for chemoreceptor self-assembly
Cryo-electron microscopy has successfully revealed the complete flagella structure in various bacterial species. This structure includes multiple components such as the inner-membrane MS ring, the cytoplasmic C ring, and the internal protein secretion system, all of which exhibit strong similarities34. This suggests that the core structure of the flagellar motor is highly conserved. The MS ring, composed of 26 FliF proteins, forms the foundation of the flagellar structure35. In addition to serving as a mounting platform for the C ring, the MS ring also acts as a protective shell for the internal protein secretion machinery36. FliG, the main component protein of the C ring, binds directly to the cytoplasmic surface of FliF in a 1:1 ratio37. Thus, the efficient assembly of the C ring requires preassembly of the MS ring. To observe the distribution of the chemosensory array following the disruption of the C ring and MS ring, we constructed ΔfliG and ΔfliF mutants.
We performed fluorescence observation on the ΔfliG mutant, which has a disrupted flagellar motor C ring. The results showed that the proportion of ΔfliG cells with obvious chemoreceptor clusters decreased significantly compared to the wild-type cells (59.8%, 140/234), although the chemosensory arrays remained at a single cell pole. We also examined the ΔfliF mutant, which has a disrupted flagellar motor MS ring. Similar to the ΔfliG mutant, the proportion of individuals with obvious chemoreceptor clusters decreased significantly (62.5%, 202/323). Subsequently, we constructed a ΔflhFΔfliF mutant and observed that the proportion of individuals with obvious chemoreceptor clusters further decreased (50.7%, 341/672). To ascertain whether it is motor integrity rather than functionality that influences the efficiency of chemosensory array assembly, we constructed a stator mutant (ΔmotAΔmotCD). In this mutant, the motor is completely stalled while the structure remains intact. We found that the mutant performed similarly to the wild-type strain in terms of chemosensory array assembly (84.3% of individuals with obvious clusters, 204/242). The fluorescence imaging of receptor clusters for multiple mutants in this section is shown in Figure. 3A. We utilized Western blotting to measure the expression levels of CheY, which were found to be similar across the different strains (Fig. 3B). This further substantiated that the observed phenomenon is based on the structural integrity of the motor rather than the protein expression level. Additionally, we quantified the proportion of cells with receptor clusters and the absolute fluorescence intensity of individual clusters (Fig. 3C-D). Overall, our findings suggest that the polar anchor protein FlhF and the structural integrity of the motor are crucial for the formation of chemosensory arrays. The former guides them to the appropriate site, while the latter influences the assembly efficiency of the chemoreceptor complex.
Colocalization of chemosensory array and flagellar motor avoids cross-pathway interference in P. aeruginosa signal transduction
The distribution patterns of receptors associated with various signal transduction pathways in P. aeruginosa vary considerably. For instance, the biofilm formation-related receptor WspA, unlike the chemotaxis receptors discussed here, is distributed throughout the cell. This distribution is thought to enhance its sensitivity to mechanical perturbations of the cell membrane38. Previous studies speculated that the highly consistent position of chemoreceptor arrays and flagellar motors enhances bacterial chemotaxis performance28. However, a spatial separation between the chemoreceptors and flagellar motors should not significantly impact the temporal comparison in bacterial chemotaxis. The diffusion time of the phosphorylated chemotaxis regulatory protein CheY-P across the longest distance in a bacterial cell body (along the cell’s long axis) is approximately 100 ms39, 40, while the timescale for the chemotaxis temporal comparison is on the order of seconds41. Consequently, the potential significance of the colocalization of chemoreceptors and flagellar motors remains unclear.
The signal transduction pathways in E. coli are relatively simple, and the chemotaxis response regulator CheY-P affects only the regulation of motor switching11. In contrast, the intracellular signal transduction pathways in P. aeruginosa are more complex. We thus hypothesized that the co-localization of chemoreceptors and flagellar motors in P. aeruginosa ensures locally distributed CheY-P molecules, thereby eliminating the need for a high level of intracellular CheY-P and avoiding potential side effects on other signaling pathways.
To test the potential effect of an increased intracellular CheY-P level, we constructed the CheY expression plasmid cheY-pJN105, transformed it into the wild-type P. aeruginosa strain, and induced it with varying concentrations of arabinose. We observed that the higher the inducer concentration, the more pronounced the cell aggregation became in the field of view (Fig. 4A). The transition from planktonic individuals to aggregated communities is similar to biofilm formation, which is known to be accompanied by a significant increase in intracellular c-di-GMP levels.
To investigate whether a higher level of intracellular CheY-P increased the intracellular c-di-GMP level, we sought to detect the c-di-GMP level. We introduced the plasmid pCdrA-gfp into P. aeruginosa, using it as a c-di-GMP biosensor with the fluorescence intensity proportional to the c-di-GMP level42. To ensure the coexistence of the plasmids, the intracellular CheY concentration was controlled by the plasmid cheY-pME6032. We found that the average single-cell fluorescence intensity of the CheY overexpression strain was 71.8% higher than that of the wild-type strain, while the c-di-GMP level of the cheY deletion strain was 58.6% lower than that of the wild-type (Fig. 4B).
Therefore, the colocalization of chemosensory array and flagellar motor facilitates the precise regulation of cell swimming direction within the low intracellular CheY-P concentration threshold, using locally distributed CheY-P molecules. This helps to avoid the occurrence of the aforementioned cross-pathway interference.
P. aeruginosa harbors multiple signal transduction systems that regulate flagella-mediated swimming motility (Che pathway), pili-mediated interface twitching motility (Pil pathway), and biofilm formation (Wsp pathway)16. These systems allow it to thrive in various ecological niches within complex external environments. Here, employing a combination of chromosomal fluorescent protein fusion and flagellar labeling techniques in living cells, we directly observed that the chemosensory array of P. aeruginosa Che pathway and the flagellar motor share a high degree of consistency in their assembly sites. We found that the chemosensory array, comprising Che proteins, was consistently located at the cell pole where the flagellum was positioned. Based on these observations, we deduced the construction mode of the chemotactic network and flagellar motor during the entire cell growth cycle (Fig. 5A). As the cell body matures and elongates, a new flagellum grows at the opposing cell pole, accompanied by the assembly of a fresh chemosensory array. The cell then undergoes division from the middle, generating two daughter cells, each equipped with fully functional motility and chemotaxis capabilities. This ensures robust inheritance of these chemotaxis and motility-related macromolecular machines.
Based on our understanding of the regulation mechanism of flagellar position in P. aeruginosa, we constructed a ΔflhF mutant and found that the position distribution of its chemosensory array is actively regulated by FlhF-mediated molecular mechanisms, rather than being passively restricted by membrane curvature factors as seen in E. coli. A similar active regulation phenomenon was previously reported in Vibrio cholerae, with the corresponding molecular regulation mechanism detailed extensively28. The flagella and chemosensory arrays of newborn V. cholerae cells are located at the old cell pole, with the polar anchor protein HubP distributed at both cell poles. As the cell grows, HubP recruits the ParA hom*ologue ParC. Subsequently, ParC recruits ParP to assemble a new chemosensory array at the new cell pole. Upon cell division, HubP relocates to the middle of the cell, ensuring its robust presences at both poles of the daughter cells. Here, HubP recruits ParA hom*ologues including FlhG, which influence flagellar motor assembly. However, previous experiments confirmed that the cell cycle-dependent polar localization of ParC and chemotactic proteins is independent of the flagellar position regulatory protein FlhF. This suggests that the localization of flagellar motors and chemosensory arrays in V. cholerae is controlled separately through different pathways. In contrast, flagellar motors were no longer robustly distributed at the cell pole after flhF was knocked out in P. aeruginosa, whereas the assembly site of chemosensory array and flagellar motor remained remarkably consistent. This suggests that FlhF regulates the distribution patterns of both and implies an interaction between them.
We further constructed ΔfliG and ΔfliF mutants, which disrupted the assembly of the flagellar motor. Surprisingly, we observed that the assembly of chemosensory array was impaired under these conditions, with a significant decrease in the proportion of individuals exhibiting obvious Che protein fluorescent bright spots. In contrast, the chemosensory array assembly in the stator mutant (ΔmotAΔmotCD) was similar to that of the wild-type strain. This suggests that the integrity rather than functionality of the flagellar motor in P. aeruginosa is critical for the assembly of its chemosensory array, and its assembly efficiency is greatly reduced in the absence of flagellar motors. To eliminate the potential confounding effects of FlhF and flagellar motors, we constructed a ΔflhFΔfliF mutant strain. Under this condition, the proportion of individuals with obvious Che protein fluorescent bright spots dropped to ∼50%, indicating that passive regulation based on membrane curvature may still exist in P. aeruginosa, albeit to a lesser degree.
Is the remarkable consistency in the spatial distribution of these two independent structural units an unintentional outcome or a hidden mystery? By introducing a c-di-GMP monitoring system at the single-cell level, we discovered that overexpressing CheY substantially increases the intracellular c-di-GMP concentration. Previous studies generally believed that CheY-P, as a chemotactic regulatory protein, only influences flagellar motor switching. Here, we found that CheY-P, as a signaling molecule, can accomplish threshold-limited cross-pathway regulation. At low CheY-P concentrations, it is conservatively involved in motor switching regulation, as confirmed by previous studies. At high CheY-P concentrations, cell motility is suppressed, and c-di-GMP is triggered to express, though its specific mechanism needs further exploration. The intracellular environment is highly crowded43, and the proximal growth pattern shown in Fig. 5B has multiple physiological significances. On one hand, chemotaxis-related protein can precisely regulate cell motility with minimal synthesis costs. On the other hand, the chemotactic network and the flagellar motor are spatially integrated within the cell, ensuring their robust existence within the cell body and preventing mutual interference with collateral pathways.
Many bacteria possess multiple signal transduction pathways. The orderly operation of each pathway within the micrometer-scale space presents a fascinating scientific problem. Here, we utilized the well-known chemotaxis network as a starting point to shed light on this problem, providing inspiration for future in-depth understanding of related issues.
Strains and cell culture
The strains and plasmids used in this study are listed in Table 1. The Escherichia coli TOP10 strain was used for standard genetic manipulations. A single-colony isolate was grown in 3 ml of LB broth (1% Bacto tryptone, 0.5% yeast extract and 1% NaCl) overnight to saturation on a rotary shaker (250 rpm) at 37°C. An aliquot was diluted 1:100 into 10 ml of LB broth and grew to exponential phase. Appropriate antibiotics were added if necessary to prevent plasmid loss: for E. coli, 15 μg/ml Gentamicin and 25 μg/ml Tetracycline; for P. aeruginosa, 30 μg/ml Gentamicin and 50 μg/ml Tetracycline. To induce protein expression, Isopropyl β-D-1-thiogalactopyranoside (IPTG, 1.0 mM) was added to strains with pME6032-derivative vectors, and arabinose (0.005%, 0.01%, 0.05%, 0.1%) was added to strains with pJN105-derivative vectors. 2 ml of cells were harvested by centrifugation at 2000×g for 2 min, washed twice in an equal volume of motility buffer (MB) [50 mM potassium phosphate, 15 μM EDTA, 0.15 M NaCl, 5 mM Mg2+ and 10 mM lactic acid (pH 7.0)]44, and resuspended in 5 ml MB for subsequent fluorescence observation.
Construction of in-frame deletion mutants
We used polymerase chain reaction (PCR) to generate ∼1000 bp DNA fragments with upstream (Up) and downstream (Dn) sequences flanking the target gene (including flhF, fliF, motA and fliG) to be deleted. The Up and Dn DNA sequences were fused with the linearized pex18gm vector using Gibson assembly45. The resulting vectors were transformed into P. aeruginosa by electroporation, and the desired knockout mutants were obtained by double selections on gentamicin plates (LB plates with 30 µg/ml gentamicin) and sucrose plates (NaCl-free LB plates with 15% sucrose) at 37°C46.
Generation of chromosomal fusions of yfp to P. aeruginosa gene
To generate eyfp fusion at the N-terminus of cheY, we first used PCR to generate upstream and downstream DNA sequences flanking the cheY gene. A subsequent PCR reaction aimed to yield the cheY-eyfp fusion with a 3× glycine linker (GGCGGAGGA), with pVS88 serving as the source of the enhanced yellow fluorescent (eyfp). The three DNA sequences, along with the linearized vector, were fused to cheY-eyfp-pex18gm using Gibson assembly. Finally, gene replacement was used to transfer the fusion constructs into the P. aeruginosa chromosome by hom*ologous recombination.
Flagellar staining and fluorescence imaging
Flagellar filaments were labeled by following the protocol described previously47. Cells (1 ml of exponential-phase culture) were harvested by centrifugation at 2000×g for 10 min and washed twice in 1 ml MB. The final pellet was adjusted to a volume of ∼100 µl that concentrated the bacterial 10-fold. Alexa Fluor 568 maleimide (Invitrogen-Molecular Probes) was added to a final concentration of 20 μg/ml, and labeling was allowed to proceed for 30 min at room temperature with gyration at 80 rpm. Unused dye was then removed by washing the cells with MB three times, and the final pellet was resuspended in MB.
For fluorescence imaging, 50 μl of cells were added to the chamber (constructed with two double-sticky tapes, a glass slide, and a poly-L-Lysine coated coverslip), incubated for 3 min, and rinsed with 100 μl MB. The boundary of the chamber was then sealed with Apiezon vacuum grease. The chamber was placed on a Nikon Ti-E inverted fluorescence microscope with a 100× oil-immersion objective and a sCMOS camera (Primer95B, Photometrics). The flagellar filament and chemosensory array of cells were observed separately with corresponding filter-set, using a 200-ms exposure time. To quantify the fluorescence intensity of the receptor cluster, we took the intensity maximum point as the center and extract a 3×3 pixel matrix around it. The mean value of the elements in this matrix represents the final fluorescence intensity.
Western Blotting
The total protein of P. aeruginosa strain cells in each treatment group was extracted and its concentration was measured with Bicinchoninic acid (BCA Protein Quantification Kit, Yeasen Biotechnology Co., Ltd) when the cells grew to exponential phase with same reduced turbidity (OD600 between 0.9 and 1.0). The exact amount of protein was subjected to SDS-PAGE electrophoresis, then transferred to a nitrocellulose membrane, which was blocked with 50 mg/mL skim milk in TBST buffer (20 mM Tris, 150 mM NaCl [pH7.4], 0.1%Tween 20) for 1h at room temperature. Since the N-terminal sequence of EYFP is almost identical to that of GFP, a rabbit anti-GFP antibody (1:2000, Yeasen Biotechnology Co., Ltd) and a Mouse anti-β-actin antibody (1:2000, Invitrogen) were added and incubated at 4°C overnight. The nitrocellulose membrane was gently washed with TBST for 20 min, three times. Subsequently, HRP labeled goat anti-rabbit IgG (1:4000, Abcam) and rabbit anti-mouse IgG (1:4000, Abcam) were added and incubated at room temperature for 1 h. The nitrocellulose membrane was again gently washed with TBST for 20 min, three times. Then, the membrane was developed using the ECL chemiluminescence detection system (Beyotime P0018FS) and visualized with the ChemiDoc XRS+ system (Bio-Rad). Three independent experiments were conducted for reproducibility.
Monitoring c-di-GMP signal at the single-cell level
For measurements of c-di-GMP signaling, the validated reporter plasmid pCdrA-gfp, which produces green fluorescent protein (GFP) in response to an increase in c-di-GMP, was introduced into the experimental system. A 1000× diluted culture was inoculated into the apparatus described in the previous section and allowed to adhere to the surface for ∼10 min, with the slight difference that the coverslips were not coated with poly-L-Lysine to avoid interference from background fluorescence. Bacteria were imaged using a Nikon Ti-E inverted microscope, which was equipped with an EMCCD camera (DU897, iXon3, Andor Technology). We used a 100× oil-immersion objective. Bacteria were illuminated with a 488-nm laser (Sapphire 488−200 mW, Coherent), using a standard GFP filter sets in the fluorescence imaging system with an exposure time of 500 ms. To ensure the consistency of culture and observation conditions, the data of wild-type and cheY-pME6032 carried strains were collected at the same time. More than 200 independent individuals of each strain were used for data analysis.
Single-cell c-di-GMP concentration was characterized by calculating fluorescence intensity. The average fluorescence intensity of a single cell was calculated by dividing the total fluorescence intensity of a single cell by the cell volume. Bacterial were simplified to a hollow cylindrical trunk with hollow hemispherical caps at both ends. The cell volume can be calculated by taking the length of the short axis of the cell body as the diameter of the sphere and the length of the long axis as the sum of the height of the cylinder and the diameter of the sphere. The mean fluorescence intensity of the cell was obtained by subtracting the average background fluorescence intensity from the total fluorescence intensity of the cell, and then dividing by the cell volume.
J.Y. and R.Z. designed the work; Z.W., M.T. and S.F. performed the measurements with help from M.C.; Z.W and S.F analyzed the data; Z.W., J.Y. and R.Z. wrote the paper. Z.W., M.T. and S.F. contributed equally to this work.
The authors declare no competing interests.
This work was supported by National Natural Science Foundation of China Grants (11925406, 12090053, 12304241, and 12304251), a Grant from the Ministry of Science and Technology of China (2019YFA0709303), Grants from the Natural Science Foundation of Shandong Province No. ZR2023QA111 and ZR2023QC168, and a Grant from the Tai Shan Young Scholar Foundation of Shandong Province (tsqn.2024.T.M.).
