Proteome adaptations under contrasting soil phosphate regimes of Rhizophagus irregularis engaged in a common mycorrhizal network

•The ERM of R. irregularis was grown between poplar and sorghum under Pi limitation or not.•Shotgun proteomic and qRT-PCR approaches shed light on the ERM adaptive mechanisms to Pi availability.•Lipids are used as the main C source for fungal development in low-Pi condition.•Pi mobilization and N catabolism are stimulated in low-Pi condition.