Expansive Growth vs. pH Reflects a Poisson Point Process of Binding/Unbinding Events in Plant Cell Walls

Abstract The paramount role of $$\mathrm{pH}$$ pH and temperature $$\left(T\right)$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">T in the expansive growth a plant coleoptile/hypocotyl non-meristematic zone or fungal cells was examined within framework underlying chemical bond statistics order to reproduce an experimental plot vs. . Here, according definition, $$\mathrm{pH}=\mathrm{pH}\left({\mu }_{{\mathrm{H}}^{+}}\left(T\right), T\right)$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">pH=pHμH+T,T is considered as function potential H + (hydronium) ions ( $${\mu }_{{\mathrm{H}}^{+}})$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">μH+) , well implicit explicit $$T$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">T derivation dependent distribution from Poisson “tethers” that bonds between microfibrils determined. probability for attachment/detachment/reattachment events tethers are connected elongation obtained. two distinct but interrelated modes growth, which known “acid growth” “auxin were distinguished analytic model, while acid hypothesis verified confirmed at semi-empirical microscopic levels first time. Moreover, further perspectives, macroscopic variables $$\left(P, V, xmlns:mml="http://www.w3.org/1998/Math/MathML">P,V,T with $$P$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">P standing turgor pressure $$V$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">V cell volume, variables, $${E}^{{\varvec{d}},{\varvec{r}}}$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">Ed,r represent binding energies detachment/reattachment expense ATP energy, }_{{\mathrm{H}}^{+}}$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">μH+ can occur simultaneously, identified. With few assumptions partly based on data it possible synthesise link microscopic, statistical explanation dynamics rheological properties wall given temperature. A description predicted importance temperature-dependent result would be supposedly applicable across scales.