AUTHOR=Le Deunff Erwan , Beauclair Patrick , Lecourt Julien , Deleu Carole , Malagoli Philippe 

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

JOURNAL=Frontiers in Plant Science

VOLUME=11

YEAR=2020

URL=https://www.frontiersin.org/journals/plant-science/articles/10.3389/fpls.2020.01253

DOI=10.3389/fpls.2020.01253

ISSN=1664-462X

ABSTRACT=<p>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 <sup>15</sup>N fluxes among cellular compartments of <italic>B. napus</italic> seedlings in response to a wide range of external <inline-formula><mml:math display="inline" id="im1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mmultiscripts><mml:mi>NO</mml:mi><mml:mn>3</mml:mn><mml:mo>−</mml:mo><mml:mprescripts /><mml:none /><mml:mn>15</mml:mn></mml:mmultiscripts></mml:mrow></mml:math></inline-formula> 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 <inline-formula><mml:math display="inline" id="im2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mmultiscripts><mml:mi>NO</mml:mi><mml:mn>3</mml:mn><mml:mo>−</mml:mo><mml:mprescripts /><mml:none /><mml:mn>15</mml:mn></mml:mmultiscripts></mml:mrow></mml:math></inline-formula> uptake rate (<italic>v<sub>in</sub></italic>) was explained by the combined cooperative properties between the <italic>v<sub>app</sub></italic> (N uptake, storage and assimilation rate) and <italic>v<sub>out</sub></italic> (N translocation rate) <sup>15</sup>N 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 <sup>15</sup>N flux pattern. This bifurcation in the <italic>v<sub>in</sub></italic> and <italic>v<sub>out</sub></italic><sup>15</sup>N fluxes fits better with the increase of <italic>BnNPF6.3/NRT1.1</italic> expression than <italic>BnNRT2.1</italic> nitrate transporter genes, confirming the allosteric property of the <italic>BnNPF6/NRT1.1</italic> 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 <italic>v<sub>app</sub></italic> and <italic>v<sub>out</sub></italic><sup>15</sup>N 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.</p>