Analysis of the Dynamic and Steady-State Responses of Growth Rate and Turgor Pressure to Changes in Cell Parameters

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Abstract
The physical analysis of plant cell enlargment is extended to show the dependence of turgor pressure and growth rate under steady-state conditions on the parameters which govern cell wall extension and water transport in growing cells and tissues, and to show the dynamic responses of turgor and growth rate to instantaneous changes in one of these parameters. The analysis is based on the fact that growth requires simultaneous water uptake and irreversible wall expansion. It shows that when a growing cell is perturbed from its steady-state growth rate, it will approach the steady-state rate with exponential kinetics. The half-time of the transient adjustment depends on the biophysical parameters governing both water transport and irreversible wall expansion. When wall extensibility is small compared to hydraulic conductance, the growth rate is controlled by the yielding properties of the cell wall, while the half-time for changes in growth rate is controlled by the water transport parameters. The reverse situation occurs when hydraulic conductance is lower than wall extensibility. The analysis also shows explicitly that turgor pressure is tightly coupled with growth rate when growth is controlled by both water transport and wall yielding parameters. In growing tissue where the resistance to water flow is distributed throughout the tissue, the physical analysis is more complicated because gradients in water potential (and hence turgor pressure) are required to sustain high growth rates. However, the analysis of growth in such tissues shows that the turgor and time-course relations are similar to that in single cells. These turgor and time-course relations provide experimentally useful ways for determining (a) whether growth is limited by water uptake, and (b) whether an agent which alters the growth rate does so by affecting the water transport or wall yielding properties or both.