2015/05/02 by Mariusz Pietruszka, Mariusz A. Pietruszka, Pietruszka, Mariusz A.
Agricultural and Biological Sciences · Biochemistry, Genetics and Molecular Biology · #Photosynthetic Processes and Mechanisms #Plant Molecular Biology Research #Plant Reproductive Biology #q-bio.CB
paper · pdf · doi:10.48550/arxiv.1505.00327
50 pages, 10 figures
arxiv created 2017/07/27 · arxiv updated 2017/07/28
We examined the pH/T (or μ/T) duality of acidic pH and temperature (T) for the growth of grass shoots in order to determine the equation of state (EoS) for living plants. By considering non-meristematic growth as a dynamic series of 'state transitions' (STs) in the extending primary wall, we identified the critical (read: optimum) exponents for this phenomenon, which exhibit a singular behaviour at a critical temperature, critical pH and critical chemical potential (μ) in the form of four power laws: F(τ)π∝|τ|β-1, F(π)τ∝|π|1-α, G(τ)μ∝|τ|-2-α+2β and G(μ)τ∝|μ|2-α. The power-law exponents α and β are numbers, which are independent of pH (or μ) and T that are known as critical exponents, while π and τ represent a reduced pH and reduced temperature, respectively. Various 'scaling' predictions were obtained - a convexity relation α+ β≥ 2 for practical pH-based analysis and a β≡ 2 identity in microscopic representation. In the presented scenario, the magnitude that is decisive is the chemical potential of H+ ions (protons), enforcing subsequent STs and growth. The EoS span areas of the biological, physical, chemical and Earth sciences cross the borders with the language (adapted formalism) of phase transitions.