Modeling the Drought Response of Flows in a Fungus-Plant Symbiosis

Arbuscular mycorrhizal fungi (AMF) are symbionts that colonize the roots of most land plants and exchange resources with them. The fungi derive carbon from the plants in exchange for nutrients such as phosphorus and nitrogen. This symbiosis improves plant water status and drought resistance. Yet, the physics of the bidirectional transport of exchanged resources in the AMF filament networks (hyphae) remains unclear. Recent work has reported complex bidirectional flows driven by molecular motors in each hypha. Such flows are steady over most of the fungal colony but accelerate or even reverse in response to environmental changes. Here, we model the water exchange between AMF and a substrate with locally disturbed salinity. We write Münch-Horwitz equations for the weak permeation across the hyphal walls. Mechanosensitive aquaporin channels are modeled through a pressure-dependent wall permeability, elucidating the role of aquaporins in drought resistance. We calculate the effect of salinity perturbation on the AMF water potential and water uptake. We compare the predicted spatial flow-rate decay with bright-field microscopy measurements of flow rates in Rhizophagus irregularis in a root-organ culture disturbed by a perturbation in salt concentration in the hyphal compartment.