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The regulation of biological functions is achieved through the modulation of biochemical reaction network dynamics. The diversity of cell states and the transitions between them have been interpreted as bifurcations in these dynamics. However, due to the complexity of networks and limited knowledge of reaction kinetics, bifurcation behaviors in biological systems remain largely underexplored. To address this, we developed a mathematical method, Structural Bifurcation Analysis (SBA), which decomposes the system into substructures and determines important aspects of bifurcation behaviors—such as substructures responsible for bifurcation conditions, bifurcation-inducing parameters, and bifurcating variables—solely from network topology. We establish a direct relationship between SBA and classical bifurcation analysis, enabling the study of systems even in the presence of conserved quantities. Additionally, we provide a step-by-step bifurcation analysis for general use. We applied our method to the macrophage M1/M2 polarization system. Our analysis reveals that the network structure strongly constrains possible patterns of polarization. We also clarify the dependency of the M1/M2 balance on gene expression levels and predict the emergence of intermediate polarization patterns under gene deletions, including SOCS3, which are experimentally testable.

Abrupt changes in system states and dynamical behaviors are often observed in natural systems; such phenomena, named regime shifts, are explained as transitions between alternative steady states (more generally, attractors). Various methods have been proposed to detect regime shifts from time series data, but a generic detection method with theoretical linkage to underlying dynamics is lacking. Here, we provide a novel method named Nested-Library Analysis (NLA) to retrospectively detect regime shifts using empirical dynamic modeling (EDM) rooted in theory of attractor reconstruction. Specifically, NLA determines the time of regime shift as the cutting point at which sequential reduction of the library set (i.e., the time series data used to reconstruct the attractor for forecasting) optimizes the forecast skill of EDM. We illustrate this method on a chaotic model of which changing parameters present a critical transition. Our analysis shows that NLA detects the change point in the model system and outperforms existing approaches based on statistical characteristics. In addition, NLA empirically detected a real-world regime shift event revealing an abrupt change of Pacific Decadal Oscillation index around the mid-1970s. Importantly, our method can be easily generalized to various systems because NLA is equation-free and requires only a single time series.

Soil salinity is a main abiotic stress in agriculture worldwide. The Na+/H+ antiporters (NHXs) play pivotal roles in intracellular Na+ excretion and vacuolar Na+ compartmentalization, which are important for plant salt stress resistance (SSR). However, few systematic analyses of NHXs has been reported in allotetraploid rapeseed so far. Here, a total of 18 full-length NHX homologs, representing seven subgroups (NHX1-NHX8 without NHX5), were identified in the rapeseed genome (AnAnCnCn). Number variations of BnaNHXs might indicate their significantly differential roles in the regulation of rapeseed SSR. BnaNHXs were phylogenetically divided into three evolutionary clades, and the members in the same subgroups had similar physiochemical characteristics, gene/protein structures, and conserved Na+ transport motifs. Darwin´s evolutionary pressure analysis suggested that BnaNHXs suffered from strong purifying selection. The cis-element analysis revealed the differential transcriptional regulation of NHXs between the model Arabidopsis and B. napus. Differential expression of BnaNHXs under salt stress, different nitrogen forms (ammonium and nitrate), and low phosphate indicated their potential involvement in the regulation of rapeseed SSR. Global landscapes of BnaNHXs will give an integrated understanding of their family evolution and molecular features, which will provide elite gene resources for the genetic improvement of plant SSR through regulating the NHX-mediated Na+ transport.

Background Plants worldwide are often stressed by low Fe availability around the world, especially in aerobic soils. Therefore, the plant growth, seed yield, and quality of crop species are severely inhibited under Fe deficiency. Fe metabolism in plants is controlled by a series of complex transport, storage, and regulatory mechanisms in cells. Allohexaploid wheat ( Triticum aestivum L.) is a staple upland crop species that is highly sensitive to low Fe stresses. Although some studies have been previously conducted on the responses of wheat plants to Fe deficiency, the key mechanisms underlying adaptive responses are still unclear in wheat due to its large and complex genome. Results Transmission electron microscopy showed that the chloroplast structure was severely damaged under Fe deficiency. Paraffin sectioning revealed that the division rates of meristematic cells were reduced, and the sizes of elongated cells were diminished. ICP-MS-assisted ionmics analysis showed that low-Fe stress significantly limited the absorption of nutrients, including N, P, K, Ca, Mg, Fe, Mn, Cu, Zn, and B nutrients. High-throughput transcriptome sequencing identified 378 and 2,619 genome-wide differentially expressed genes (DEGs) were identified in the shoots and roots between high-Fe and low-Fe conditions, respectively. These DEGs were mainly involved in the Fe chelator biosynthesis, ion transport, photosynthesis, amino acid metabolism, and protein synthesis. Gene coexpression network diagrams indicated that TaIRT1b-4A , TaNAS2-6D , TaNAS1a-6A , TaNAS1-6B, and TaNAAT1b-1D might function as key regulators in the adaptive responses of wheat plants to Fe deficiency. Conclusions These results might help us fully understand the morpho-physiological and molecular responses of wheat plants to low-Fe stress, and provide elite genetic resources for the genetic modification of efficient Fe use.

Background Nitrogen (N), referred to as a “life element”, is a macronutrient essential for optimal plant growth and yield production. Amino acid (AA) permease ( AAP ) genes play pivotal roles in root import, long-distance translocation, remobilization of organic amide-N from source organs to sinks, and other environmental stress responses. However, few systematic analyses of AAPs have been reported in Brassica napus so far. Results In this study, we identified a total of 34 full-length AAP genes representing eight subgroups ( AAP1–8 ) from the allotetraploid rapeseed genome (A n A n C n C n , 2 n  = 4 x  = 38). Great differences in the homolog number among the BnaAAP subgroups might indicate their significant differential roles in the growth and development of rapeseed plants. The BnaAAPs were phylogenetically divided into three evolutionary clades, and the members in the same subgroups had similar physiochemical characteristics, gene/protein structures, and conserved AA transport motifs. Darwin’s evolutionary analysis suggested that BnaAAPs were subjected to strong purifying selection pressure. Cis -element analysis showed potential differential transcriptional regulation of AAPs between the model Arabidopsis and B. napus . Differential expression of BnaAAPs under nitrate limitation, ammonium excess, phosphate shortage, boron deficiency, cadmium toxicity, and salt stress conditions indicated their potential involvement in diverse nutrient stress responses. Conclusions The genome-wide identification of BnaAAPs will provide a comprehensive insight into their family evolution and AAP-mediated AA transport under diverse abiotic stresses. The molecular characterization of core AAPs can provide elite gene resources and contribute to the genetic improvement of crop stress resistance through the modulation of AA transport.

Background B-box ( BBX ) genes play important roles in plant growth regulation and responses to abiotic stresses. The plant growth and yield production of allotetraploid rapeseed is usually hindered by diverse nutrient stresses. However, no systematic analysis of Brassicaceae BBXs and the roles of BBXs in the regulation of nutrient stress responses have not been identified and characterized previously. Results In this study, a total of 536 BBXs were identified from nine brassicaceae species, including 32 AtBBXs , 66 BnaBBXs , 41 BoBBXs , 43 BrBBXs , 26 CrBBXs , 81 CsBBXs , 52 BnBBXs , 93 BjBBXs , and 102 BcBBXs . Syntenic analysis showed that great differences in the gene number of Brassicaceae BBXs might be caused by genome duplication. The BBXs were respectively divided into five subclasses according to their phylogenetic relationships and conserved domains, indicating their diversified functions. Promoter cis -element analysis showed that BBXs probably participated in diverse stress responses. Protein-protein interactions between BnaBBXs indicated their functions in flower induction. The expression profiles of BnaBBXs were investigated in rapeseed plants under boron deficiency, boron toxicity, nitrate limitation, phosphate shortage, potassium starvation, ammonium excess, cadmium toxicity, and salt stress conditions using RNA-seq data. The results showed that different BnaBBXs showed differential transcriptional responses to nutrient stresses, and some of them were simultaneously responsive to diverse nutrient stresses. Conclusions Taken together, the findings investigated in this study provided rich resources for studying Brassicaceae BBX gene family and enriched potential clues in the genetic improvement of crop stress resistance.

Background Soil salinization has become a global problem restricting the seed yield and quality of crops, including wheat ( Triticum aestivum L.). Salinity significantly alters plant morphology and severely disrupts physiological homeostasis. Salt tolerance of wheat has been widely studied whereas core ion transporters responsive to salt stress remain elusive. Results In this study, the wheat seedlings were subjected to salinity toxicity for morpho-physiological and transcriptomic analysis of wheat salt tolerance. There was a inversely proportional relationship between salt concentrations and morpho-physiological parameters. Under the condition of 100 mM NaCl, the H 2 O 2 , O 2 − , MDA content and membrane permeability were significantly increased whereas the chlorophyll content was markedly decreased. Under salt stress, a larger proportion of Na + was partitioned in the roots than in the shoots, which had a lower Na + /K + ratio and proline content. Salt stress also obviously affected the homeostasis of other cations. Genome-wide transcriptomic analysis showed that a total of 2,807 and 5,570 differentially expressed genes (DEGs) were identified in the shoots and roots, respectively. Functionality analysis showed that these DEGs were mainly enriched in the KEGG pathways related to carbon metabolism, phenylalanine, and amino acid biosynthesis, and were primarily enriched in the GO terms involving proline metabolism and redox processes. The Na + transporter genes were upregulated under salt stress, which repressed the gene expression of the K + transporters. Salt stress also significantly elevated the expression of the genes involved in osmoregulation substances biosynthesis, and obviously affected the expression profiling of other cation transporters. Co-expression network analysis identified TaNHX6-D5 / TaNHX4-B7 and TaP5CS2-B3 potentially as core members regulating wheat salt tolerance. Conclusions These results might help us fully understand the morpho-physiological and molecular responses of wheat seedlings to salt stress, and provide elite genetic resources for the genetic modification of wheat salt tolerance.

Background Oilseed rape ( B. napus L.) has great potential for phytoremediation of cadmium (Cd)-polluted soils due to its large plant biomass production and strong metal accumulation. Soil properties and the presence of other soluble compounds or ions, cause a heterogeneous distribution of Cd. Results The aim of our study was to reveal the differential responses of B. napus to different Cd abundances. Herein, we found that high Cd (50 μM) severely inhibited the growth of B. napus , which was not repressed by low Cd (0.50 μM) under hydroponic culture system. ICP-MS assays showed that the Cd 2+ concentrations in both shoots and roots under 50 μM Cd were over 10 times higher than those under 0.50 μM Cd. Under low Cd, the concentrations of only shoot Ca 2+ /Mn 2+ and root Mn 2+ were obviously changed (both reduced); under high Cd, the concentrations of most cations assayed were significantly altered in both shoots and roots except root Ca 2+ and Mg 2+ . High-throughput transcriptomic profiling revealed a total of 18,021 and 1408 differentially expressed genes under high Cd and low Cd conditions, respectively. The biological categories related to the biosynthesis of plant cell wall components and response to external stimulus were over-accumulated under low Cd, whereas the terms involving photosynthesis, nitrogen transport and response, and cellular metal ion homeostasis were highly enriched under high Cd. Differential expression of the transporters responsible for Cd uptake ( NRAMPs ), transport ( IRTs and ZIPs ), sequestration ( HMAs , ABCs , and CAXs ), and detoxification ( MTPs , PCR , MTs , and PCSs ), and some other essential nutrient transporters were investigated, and gene co-expression network analysis revealed the core members of these Cd transporters. Some Cd transporter genes, especially NRAMPs and IRTs , showed opposite responsive patterns between high Cd and low Cd conditions. Conclusions Our findings would enrich our understanding of the interaction between essential nutrients and Cd, and might also provide suitable gene resources and important implications for the genetic improvement of plant Cd accumulation and resistance through molecular engineering of these core genes under varying Cd abundances in soils.

Background Histone modification is an important epigenetic regulatory mechanism and essential for stress adaptation in plants. However, systematic analysis of histone modification genes ( HMs ) in Brassicaceae species is lacking, and their roles in response to abiotic stress have not yet been identified. Results In this study, we identified 102 AtHMs , 280 BnaHMs , 251 BcHMs , 251 BjHMs , 144 BnHMs , 155 BoHMs , 137 BrHMs , 122 CrHMs , and 356 CsHMs in nine Brassicaceae species, respectively. Their chromosomal locations, protein/gene structures, phylogenetic trees, and syntenies were determined. Specific domains were identified in several Brassicaceae HMs , indicating an association with diverse functions. Syntenic analysis showed that the expansion of Brassicaceae HMs may be due to segmental and whole-genome duplications. Nine key BnaHMs in allotetraploid rapeseed may be responsible for ammonium, salt, boron, cadmium, nitrate, and potassium stress based on co-expression network analysis. According to weighted gene co-expression network analysis (WGCNA), 12 BnaHMs were associated with stress adaptation. Among the above genes, BnaPRMT11 simultaneously responded to four different stresses based on differential expression analysis, while BnaSDG46 , BnaHDT10 , and BnaHDA1 participated in five stresses. BnaSDG46 was also involved in four different stresses based on WGCNA, while BnaSDG10 and BnaJMJ58 were differentially expressed in response to six different stresses. In summary, six candidate genes for stress resistance ( BnaPRMT11 , BnaSDG46 , BnaSDG10 , BnaJMJ58 , BnaHDT10 , and BnaHDA1 ) were identified. Conclusions Taken together, these findings help clarify the biological roles of Brassicaceae HMs . The identified candidate genes provide an important reference for the potential development of stress-tolerant oilseed plants.

Background Salinity severely inhibit crop growth, yield, and quality worldwide. Allotetraploid rapeseed ( Brassica napus L.), a major glycophyte oil crop, is susceptible to salinity. Understanding the physiological and molecular strategies of rapeseed salinity resistance is a promising and cost-effective strategy for developing highly resistant cultivars. Results First, early leaf senescence was identified and root system growth was inhibited in rapeseed plants under severe salinity conditions. Electron microscopic analysis revealed that 200 mM NaCl induced fewer leaf trichomes and stoma, cell plasmolysis, and chloroplast degradation. Primary and secondary metabolite assays showed that salinity led to an obviously increased anthocyanin, osmoregulatory substances, abscisic acid, jasmonic acid, pectin, cellulose, reactive oxygen species, and antioxidant activity, and resulted in markedly decreased photosynthetic pigments, indoleacetic acid, cytokinin, gibberellin, and lignin. ICP-MS assisted ionomics showed that salinity significantly constrained the absorption of essential elements, including the nitrogen, phosphorus, potassium, calcium, magnesium, iron, mangnese, copper, zinc, and boron nutrients, and induced the increase in the sodium/potassium ratio. Genome-wide transcriptomics revealed that the differentially expressed genes were involved mainly in photosynthesis, stimulus response, hormone signal biosynthesis/transduction, and nutrient transport under salinity. Conclusions The high-resolution salt-responsive gene expression profiling helped the efficient characterization of central members regulating plant salinity resistance. These findings might enhance integrated comprehensive understanding of the morpho-physiologic and molecular responses to salinity and provide elite genetic resources for the genetic modification of salinity-resistant crop species.