Effective diffusion rates and cross-correlation analysis of "acid growth" data

Abstract

We investigated the growth–temperature relationship in plants using a quantitative perspective of a recently derived growth functional. We showed that auxin-induced growth is achieved by the diffusion rate, which is almost constant or slowly ascending in temperature, while the diffusion rate of fusicoccin (FC)-induced growth increases monotonically with temperature for the entire temperature range (0–45) °C, although for some concentrations of indole-3-acetic acid (IAA), “super-diffusion” takes place for unperturbed growth. We also calculated the cross-correlations and the derivative of cross-correlations for elongation growth (rate) and pH as a function of time delay (lag) parameterised by temperature for artificial pond water (APW) control conditions (endogenous growth) and exogenous IAA and FC that were introduced into the medium. Dimensionality analysis revealed that discontinuities in the cross-correlation derivative corresponded to H+ ion kinetics, which attained definite numerical values that were approximately proportional to the (logarithm of) proton secretion rates (or relative buffer acidification). Furthermore, three types of experiments were compared: for abraded coleoptiles, coleoptile segments and intact growing seedlings. From the cross-correlation analysis, it was found that the timing of IAA and FC-induced proton secretion and growth matched well. Unambiguous results concerning the canvas constituting acid growth hypothesis were obtained by cross- and auto-correlation analysis: (1) for abraded coleoptiles, because of the lowering of the cuticle potential barrier, auxin-induced cell wall pH decreased simultaneously with the change in growth rate; no advancement or retardation of pH (proton efflux rate) or growth rate took place, (2) exogenous protons were able to substitute for auxin thus causing wall loosening and growth, (3) although the underlying molecular mechanisms differ vastly, a potent stimulator of proton secretion, the fungal toxin FC, promoted growth that was similar to auxin, although of an elevated intensity; as for auxin—no advancement or retardation took place.