Theoretical Analyses of Turgor Pressure and Expansive Growth Rate of Plant Cells During Water Deficit

Expansive plant growth during water deficit is common in temperate and extreme climates. Understanding how the turgor pressure, <i>P</i>, behaves during water deficit is essential for a better understanding of expansive growth rate, <i>v</i>. Here, validated biophysical equations together with dimensional analyses are used to simulate water deficit and determine the behavior of <i>P</i> and <i>v</i>. A dimensionless number, Π_pw, helps simplify the biophysical equations and interpret the results. The magnitude of Π_pw increases as water deficit severity increases. Analyses reveal that both <i>P</i> and <i>v</i> decrease curvilinearly as Π_pw increases. Simple mathematical relationships between <i>P</i>, <i>v</i>, and Π_pw, are derived, providing a clear and quantitative understanding of how <i>P</i> and <i>v</i> change as water deficits become more severe. Additionally, it is shown how the results of these analyses can be used to assess <i>P</i> and <i>v</i> of roots growing in water deficit.