## 2 Results
### Gene Ontology and Interaction Network Analysis of EhFPS  
Studies of _FPS_ genes in various latex-producing plants have hypothesized that these genes are involved in a wide range of biological processes. GO enrichment analysis was conducted to investigate the functional roles of _FPS_ genes in _E. hirta_; a gene ontology (GO) enrichment analysis was conducted (Figure 7A). The results revealed that eight genes were enriched in 18 GO terms (Table S1), all of which were categorized under biological processes. The top five significantly enriched terms were isoprenoid metabolic process (GO:0006720), isoprenoid biosynthetic process (GO:0008299), cellular lipid metabolic process (GO:0044255), lipid biosynthetic process (GO:0008610), and lipid metabolic process (GO:0006629). These findings suggest that _EhFPS_ genes are likely to be involved in the synthesis and metabolism of isoprenoid compounds, as well as in lipid biosynthesis and metabolism. Overall, these results highlight the critical roles of _FPS_ genes in the key physiological functions of _E. hirta_, including growth, development, stress adaptation, and maintenance of the cell membrane structure. Figure 6: Phylogenetic tree of gene members of the FPS family in seven species. Squares of different colors represent _FPS_ genes of different species. The five different subfamilies were distinguished by yellow and green bands. Figure 7: The gene ontology enrichment (GO) analysis and protein–protein interactions (PPI) of _EhEPS_ genes. (**A**) GO analysis. The 20 enrichments with the highest scores were selected for display. The horizontal coordinate represents the gene ratio, and the circle represents the number of genes. (**B**) Protein interaction network of _E. hirta_ genes mapped to _Arabidopsis_ genes. The circle size indicates the number of interaction partners, with larger circles representing more extensive interaction networks. The protein-regulatory network of _A. thaliana_ has been systematically studied as a model plant. FPS proteins were located in homologues of _A. thaliana_, and the interaction networks and their interaction networks with other proteins were deduced (Table S2). Farnesyl pyrophosphate synthases (FPS1 and FPS2) are key enzymes in the isoprene biosynthesis pathway in _A. thaliana_. They catalyze the condensation of isoprene pyrophosphate (FPP) from isoprene IPP and dimethylallyl pyrophosphate (DMAPP), which are direct precursors of isoprene compounds, such as carotenoids, sterols, and sesquiterpenes. In the protein-protein interaction (PPI) network maps constructed with FPS1 and FPS2, the protein showed extensive connections with multiple proteins, including upstream and downstream key enzymes, indicating that the FPS protein is not only the main producer of FPP, an intermediate product of the isoprene pathway, but the regulatory hub of the metabolic network. Among the proteins involved, HMGS, IPP2, and ISPH serve as upstream regulators of FPS, which utilizes IPP and DAMPP as substrates to directly influence metabolic flow in a manner dependent on HMGS and IPP2. Conversely, SQS1, SQS2, DPS, and PSY1 were identified as direct downstream proteins of FPS. The close association between FPS, SQS1, and SQS2 highlights their collaborative role in the sterol biosynthesis pathway. Specifically, SQS1 catalyzes the conversion of farnesyl pyrophosphate (FPP) to squalene, an intermediate product in the sterol biosynthesis pathway, and a precursor for the synthesis of gas triterpenes. Farnesyl pyrophosphate synthase (FPS) and lycopene synthase (PSY1) are critical components of carotenoid biosynthesis. FPS facilitates the transformation of isopentene pyrophosphate (IPP) and dimethylallyl pyrophosphate (DMAPP) into farnesyl pyrophosphate (FPP), whereas PSY1 employs FPP as a substrate to catalyze the synthesis of lycopene. In summary, the FPS family proteins serve as the central hub of isoprene metabolism.