SUMMARYInorganic phosphorus (Pi) is an essential element in numerous metabolic reactions and signaling pathways, but the molecular details of these pathways remain largely unknown. In this study, metabolite profiles of maize (Zea mays L.) leaves and roots were compared between six low‐Pi‐sensitive lines and six low‐Pi‐tolerant lines under Pi‐sufficient and Pi‐deficient conditions to identify pathways and genes associated with the low‐Pi stress response. Results showed that under Pi deprivation the concentrations of nucleic acids, organic acids and sugars were increased, but that the concentrations of phosphorylated metabolites, certain amino acids, lipid metabolites and nitrogenous compounds were decreased. The levels of secondary metabolites involved in plant immune reactions, including benzoxazinoids and flavonoids, were significantly different in plants grown under Pi‐deficient conditions. Among them, the 11 most stable metabolites showed significant differences under low‐ and normal‐Pi conditions based on the coefficient of variation (CV). Isoleucine and alanine were the most stable metabolites for the identification of Pi‐sensitive and Pi‐resistant maize inbred lines. With the significant correlation between morphological traits and metabolites, five low‐Pi‐responding consensus genes associated with morphological traits and simultaneously involved in metabolic pathways were mined by combining metabolites profiles and genome‐wide association study (GWAS). The consensus genes induced by Pi deficiency in maize seedlings were also validated by reverse‐transcription quantitative polymerase chain reaction (RT‐qPCR). Moreover, these genes were further validated in a recombinant inbred line (RIL) population, in which the glucose‐6‐phosphate‐1‐epimerase encoding gene mediated yield and correlated traits to phosphorus availability. Together, our results provide a framework for understanding the metabolic processes underlying Pi‐deficient responses and give multiple insights into improving the efficiency of Pi use in maize.

Fear extinction is generally considered a form of new learning that inhibits previously acquired fear memories. Here, by tracking immediate early gene expression in vivo, we found that contextual fear extinction training evoked distinct neural ensembles in mouse retrosplenial cortex (RSC). The optogenetic reactivation of these extinction-activated neurons in the RSC was sufficient to suppress a fear response, while the reactivation of conditioning-activated neurons in the same area promoted a fear response. The generation of such an extinction-memory-related neural ensemble was associated with adult neurogenesis, as abolishing newborn neurons in the adult hippocampus via X-ray irradiation eliminated both the extinction-activated neurons in the RSC and the optogenetic-reactivation-induced suppression of contextual fear memory. Therefore, switching from fear to no fear in response to the same context is modulated by the RSC through an extinction-activated neural ensemble, the generation of which might require adult neurogenesis in the hippocampus.

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A brick is a  non-bipartite matching covered graph without non-trivial tight cuts. Bricks are building blocks of matching covered graphs. We say that an edge $e$ in a brick $G$ is $b$-invariant if $G-e$ is matching covered and a tight cut decomposition of $G-e$ contains exactly one brick. A 2-edge-connected cubic graph is essentially 4-edge-connected if it does not contain nontrivial 3-cuts. A brick $G$ is near-bipartite if it has a pair of edges $\{e_1, e_2\}$ such that $G-\{e_1,e_2\}$ is bipartite and matching covered. Kothari, de Carvalho, Lucchesi  and Little proved that each essentially 4-edge-connected cubic non-near-bipartite brick $G$, distinct from the Petersen graph, has at least $|V(G)|$ $b$-invariant edges. Moreover, they made a conjecture: every essentially 4-edge-connected cubic near-bipartite brick $G$, distinct from $K_4$, has at least $|V(G)|/2$ $b$-invariant edges. We confirm the conjecture in this paper. Furthermore, all the essentially 4-edge-connected cubic near-bipartite bricks, the numbers of $b$-invariant edges of which attain the lower bound, are presented.

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