Abstract
The paramount role of mathrm{pH} and temperature left(Tright) in the expansive growth of a plant coleoptile/hypocotyl non-meristematic zone or plant and fungal cells was examined within the framework of the underlying chemical bond statistics in order to reproduce an experimental plot of growth vs. mathrm{pH}. Here, according to the definition, mathrm{pH}=mathrm{pH}left({mu }_{{mathrm{H}}^{+}}left(Tright), Tright) is considered as a function of the chemical potential of the H+ (hydronium) ions ({mu }_{{mathrm{H}}^{+}}), as well as an implicit and explicit function of T. The derivation of the mathrm{pH} and T dependent expansive growth distribution from the Poisson statistics of the “tethers” that reproduce the chemical bonds between microfibrils was determined. The probability distribution for the attachment/detachment/reattachment events of the tethers that are connected to the microfibrils in the elongation zone was obtained. The two distinct but interrelated modes of the expansive growth, which are known as “acid growth” and “auxin growth” were distinguished in the analytic model, while the acid growth hypothesis was verified and confirmed at the semi-empirical and microscopic levels for the first time. Moreover, further perspectives, in which the macroscopic variables left(P, V, Tright) with P standing for the turgor pressure and V for the cell volume, and the microscopic variables, {E}^{{varvec{d}},{varvec{r}}}, which represent the binding energies of the detachment/reattachment events at the expense of ATP energy, and {mu }_{{mathrm{H}}^{+}} can occur simultaneously, were identified. With a few assumptions that are partly based on experimental data it was possible to synthesise a link between the microscopic, explicit statistical explanation of bond dynamics and the macroscopic rheological properties of the cell wall at a given mathrm{pH} and temperature. A statistical description that predicted the importance of mathrm{pH} and temperature-dependent chemical potential of the H+ ions in microscopic events that result in growth would be supposedly applicable across scales.
Highlights
This article explores the role of pH and temperature dependence of expansive growth of plant cells using an approach of dynamic bond statistics in the cell wall
Using Eq (7) and the same set of parameters as in Fig. 2a, b, the role of the “auxin growth” that was beyond the “acid growth” was exposed, which has an interesting interpretation that is connected with the existence of the reattachment events, which can be treated as active processes, in the model
I attempted to establish the thermodynamic basis of expansive plant growth, in particular, the contribution of “acid growth” where low pH induces fast expansion and “auxin growth” where endogenous or exogenous auxin induces rapid expansion
Summary
This article explores the role of pH and temperature dependence of expansive growth of plant cells using an approach of dynamic bond statistics in the cell wall. Using Eq (7) and the same set of parameters (for clarity, here we assume probabilities pd as mainly connected with “acid”, while pr with “auxin” growth, respectively, see the comment below) as, b, the role of the “auxin growth” (either endo- or exogenous) that was beyond the “acid growth” was exposed (filled area in the plot in Fig. 2c representing auxin-enhanced H+-pumping), which has an interesting interpretation that is connected with the existence of the reattachment events, which can be treated as active processes, in the model.
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