Combined Allosteric Responses Explain the Bifurcation in Non-Linear Dynamics of ¹⁵N Root Fluxes Under Nutritional...

With regard to thermodynamics out of equilibrium, seedlings are open systems that dissipate energy towards their environment. Accordingly, under nutritional steady-state conditions, changes in external concentrations of one single ion provokes instability and reorganization in the metabolic and structure/architecture of the seedling that is more favorable to the fluxes of energy and matter. This reorganization is called a bifurcation and is described in mathematics as a non-linear dynamic system. In this study, we investigate the non-linear dynamics of ¹⁵N fluxes among cellular compartments of B. napus seedlings in response to a wide range of external $$ concentrations (from 0.05 to 20 mM): this allows to determine whether any stationary states and bifurcations could be found. The biphasic behavior of the root $$ uptake rate (v ) was explained by the combined cooperative properties between the v (N uptake, storage and assimilation rate) and v (N translocation rate) ¹⁵N fluxes that revealed a unique and stable stationary state around 0.28 mM nitrate. The disappearance of this stationary state around 0.5 mM external nitrate concentrations provokes a dramatic bifurcation in ¹⁵N flux pattern. This bifurcation in the v and v ¹⁵N fluxes fits better with the increase of BnNPF6.3/NRT1.1 expression than BnNRT2.1 nitrate transporter genes, confirming the allosteric property of the BnNPF6/NRT1.1 transporter, as reported in the literature between low and high nitrate concentrations. Moreover, several statistically significant power-law equations were found between variations in the shoots tryptophan concentrations (i.e., IAA precursor) with changes in the v and v ¹⁵N fluxes as well as a synthetic parameter of plant N status estimated from the root/shoot ratio of total free amino acids concentrations. These relationships designate IAA as one of the major biological parameters related to metabolic and structural-morphological reorganization coupled with the N and water fluxes induced by nitrate. The results seriously challenge the scientific grounds of the concept of high- and low-affinity of nitrate transporters and are therefore discussed in terms of the ecological significance and physiological implications on the basis of recent agronomic, physiological and molecular data of the literature.