Combined Allosteric Responses Explain the Bifurcation in Non-Linear Dynamics of 15N Root Fluxes Under Nutritional Steady-State Conditions for Nitrate

Abstract

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 ${}^{15}\mathrm{NO}_3^{-}$ 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 ${}^{15}\mathrm{NO}_3^{-}$ uptake rate (v_in ) was explained by the combined cooperative properties between the v_app (N uptake, storage and assimilation rate) and v_out (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_in and v_out 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_app and v_out 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.

Keywords: N translocation; analysis of non-linear dynamic systems; ion transport kinetics; irreversible thermodynamics; nitrate uptake.