An analytical complete model of root pressure generation: Theoretical bases for studying hydraulics of bamboo

To better understand the dynamics and functional roles of root pressure, we represent a novel and the first complete analytical model for root pressure, which can be applied to complex roots/shoots. The osmotic volume of a single root is equal to that of the vessel lumen in fine roots and adjacent apoplastic spaces. Water uptake occurs via passive osmosis and active solute uptake (Js* ${J}_{{\rm{s}}}<^>{* }$, osmol s-1), resulting in the osmolyte concentration Cr (mol center dot kg-1 of water) at a fixed osmotic volume. Solute loss occurs via two passive processes: radial diffusion of solute Km (Cr- Csoil) from fine roots to soil, where Km is the diffusional constant and Csoil is the soil-solute concentration, and the mass flow of solute and water into the plant from the fine roots. The proposed model predicts the quadratic function of root pressure (Pr), Pr2+bPr+c=0 ${P}_{{\rm{r}}}<^>{2}+b{P}_{{\rm{r}}}+c=0$, where b and c are the functions of plant hydraulic resistance, soil water potential, solute flux and gravitational potential. The model demonstrates the root pressure-mediated distribution of water through the hydraulic architecture of a 6.8-m-tall bamboo shoot. This model provides a theoretical basis to test the functional roles of root pressure in shaping the hydraulic architecture and refilling potential xylem embolisms. An analytical solution for root pressure is derived and illustrated by applying it to the measured hydraulic architecture of a 7-m bamboo shoot.