The paramount role of \(\mathrm{pH}\) and temperature \(\left(T\right)\) 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, \(\mathrm{pH}=\mathrm{pH}\left({\mu }_{{\mathrm{H}}^{+}}\left(T\right), T\right)\) 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 \(\left(P, V, T\right)\) 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.

在框架内检查了\(\mathrm{pH}\)和温度\(\left(T\right)\)在植物胚芽鞘/下胚轴非分生区或植物和真菌细胞的膨胀生长中的重要作用的基础化学键统计数据，以重现生长与\(\mathrm{pH}\)的实验图。这里，根据定义，\(\mathrm{pH}=\mathrm{pH}\left({\mu }_{{\mathrm{H}}^{+}}\left(T\right), T \right)\)被认为是 H ⁺（水合氢）离子化学势的函数（\({\mu }_{{\mathrm{H}}^{+}})\)，以及\(T\)的隐式和显式函数。\(\mathrm{pH}\)的推导和\(T\)依赖的膨胀生长分布从重现微纤维之间化学键的“系绳”的泊松统计中确定。获得连接到伸长区中的微纤维的系绳的附着/分离/重新附着事件的概率分布。在分析模型中区分了两种不同但相互关联的膨胀生长模式，即“酸生长”和“生长素生长”，而酸生长假说在半经验和微观水平上得到了验证和证实。第一次。此外，进一步的观点，其中宏观变量\(\left(P, V, T\right)\)与\(P\)代表膨胀压力和\(V\)代表细胞体积，以及微观变量\({E}^{{\varvec{d}},{\varvec{r}}}\)，它们代表以ATP能量为代价的脱离/再附着事件的结合能，和\({\mu }_{{\mathrm{H}}^{+}}\)可以同时发生，被确定。通过一些部分基于实验数据的假设，可以在给定\(\mathrm{pH}\)和温度。预测\(\mathrm{pH}\)重要性的统计描述H ⁺离子在导致生长的微观事件中的温度依赖性化学势可能适用于跨尺度。