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• W2974987885 endingPage "866" @default.
• W2974987885 startingPage "841" @default.
• W2974987885 abstract "Abstract The pH/ T duality of acidic pH and temperature ( T ) action for the growth of grass shoots was examined in order to derive the phenomenological equation of wall properties for living plants. By considering non-meristematic growth as a dynamic series of state transitions (STs) in the extending primary wall, the critical exponents were identified, which exhibit a singular behaviour at a critical temperature, critical pH and critical chemical potential ( μ ) in the form of four power laws: $$f_{pi } left( tau right) propto left| tau right|^{beta - 1}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi>π</mml:mi></mml:msub><mml:mfenced><mml:mi>τ</mml:mi></mml:mfenced><mml:mo>∝</mml:mo><mml:msup><mml:mfenced><mml:mi>τ</mml:mi></mml:mfenced><mml:mrow><mml:mi>β</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math> , $$f_{tau } (pi ) propto left| pi right|^{1 - alpha }$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mi>τ</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>π</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>∝</mml:mo><mml:msup><mml:mfenced><mml:mi>π</mml:mi></mml:mfenced><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mi>α</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math> , $$g_{mu } (tau ) propto left| tau right|^{ - 2 - alpha + 2beta }$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mi>μ</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>τ</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>∝</mml:mo><mml:msup><mml:mfenced><mml:mi>τ</mml:mi></mml:mfenced><mml:mrow><mml:mo>-</mml:mo><mml:mn>2</mml:mn><mml:mo>-</mml:mo><mml:mi>α</mml:mi><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:mi>β</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math> and $$g_{tau } (mu ) propto left| mu right|^{2 - alpha }$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mi>τ</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>μ</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>∝</mml:mo><mml:msup><mml:mfenced><mml:mi>μ</mml:mi></mml:mfenced><mml:mrow><mml:mn>2</mml:mn><mml:mo>-</mml:mo><mml:mi>α</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math> . The indices α and β are constants, while π and τ represent a reduced pH and reduced temperature, respectively. The convexity relation α + β ≥ 2 for practical pH-based analysis and β ≡ 2 “mean-field” value in microscopic ( μ ) representation were derived. In this scenario, the magnitude that is decisive is the chemical potential of the H + ions, which force subsequent STs and growth. Furthermore, observation that the growth rate is generally proportional to the product of the Euler beta functions of T and pH, allowed to determine the hidden content of the Lockhart constant Ф . It turned out that the pH-dependent time evolution equation explains either the monotonic growth or periodic extension that is usually observed—like the one detected in pollen tubes—in a unified account." @default.
• W2974987885 created "2019-10-03" @default.
• W2974987885 creator A5085155291 @default.
• W2974987885 date "2019-09-23" @default.
• W2974987885 modified "2023-09-30" @default.
• W2974987885 title "Chemical Potential-Induced Wall State Transitions in Plant Cell Growth" @default.
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