A quantitative report on the impact of chloride on the kinetic coefficients of auxin-induced growth : a numerical contribution to the "acid growth hypothesis"

This work presents the application of several our own novel methods of analysing the kinetics of plant growth, which create, among others, a common platform for the comparison of experimental results. A relatively simple formula is used to parameterize the wide range of data that has been obtained for Zea mays L. in the literature, though it can also be used for different species. A biophysical/biochemical interpretation of the parameters was obtained from a theoretical model that is based on a modified Lockhart equation. The derived formula, which was extended for practical use in Zajdel et al. (Acta Physiol Plant 38:5, 2016), and which was implemented in the attached computer program (ibid.), allowed the data that was obtained from the growth-related problems to be parameterized in a simple way. As a working example that shows the robustness of our approach, we comment in detail on the qualitative assessments of the impact of chloride ions on auxin-induced growth. We note that calculated continuous curves (fits), which are rooted in the growth functional that was introduced by Pietruszka (J Theor Biol 315:119–127, 2012), were in a perfect agreement (R2 ~ 0.99998) with the raw experimental data that was published recently by Burdach et al. (Ann Bot 114:1023–1034, 2014). This fact justified the use of this strict technique, which allows for the determination of kinetic coefficients, to critically evaluate the results and suppositions (claims) therein. Moreover, we calculated the time-delay derivative of elongation growth—pH cross-correlations, and validated the “acid growth hypothesis” in figures by considering, amongst others, the magnitude of the H+-activity of elongation growth (per μm). An empirical constant (field strength), EH+ = Em/(log10 1/aH+ ∙ μm) = 0.157 ± 0.009 [V/mm] was obtained, where Em [mV] is the membrane potential in the perenchymal coleoptile cells of Zea mays L. When this relation is known, the membrane potential can not only be determined for intact growth, but also for different intervening substances exclusively from growth (or growth rate) and pH measurements, i.e. without performing electrophysiological measurements. However, the question of whether this constant is universal remains open