Abstract
Experiments demonstrate that both plastic and elastic deformation of the cell wall are necessary for wall stress relaxation and expansive growth of walled cells. A biophysical equation (Augmented Growth Equation) was previously shown to accurately model the experimentally observed wall stress relaxation and expansive growth rate. Here, dimensional analysis is used to obtain a dimensionless Augmented Growth Equation with dimensionless coefficients (groups of variables, or Π parameters). It is shown that a single Π parameter controls the wall stress relaxation rate. The Π parameter represents the ratio of plastic and elastic deformation rates, and provides an explicit relationship between expansive growth rate and the wall’s mechanical properties. Values for Π are calculated for plant, algal, and fungal cells from previously reported experimental results. It is found that the Π values for each cell species are large and very different from each other. Expansive growth rates are calculated using the calculated Π values and are compared to those measured for plant and fungal cells during different growth conditions, after treatment with IAA, and in different developmental stages. The comparison shows good agreement and supports the claim that the Π parameter is central to expansive growth rate of walled cells.
Highlights
Expansive growth is defined as a permanent increase in cell volume
Dimensional analysis provides a physical interpretation for the Πpe parameter; it is the ratio of the relative volumetric plastic deformation rate of the wall and relative volumetric elastic deformation rate of the wall
The expansive growth rate of a walled cell is determined by the net water uptake rate and cell wall deformation rate
Summary
Dimensional analysis reveals that the rate of wall stress relaxation is directly related to the magnitude of a single dimensionless parameter, Πpe; see equation (5). One wonders if the magnitude of Πpe is invariant and is determined by a chemical wall loosening-hardening mechanism (chemorheology) that is fundamental to each species of cell, so that the same ratio of plastic and elastic wall deformation rates are produced for each cell species If this suggestion were correct, it would make two predictions. The Πpe parameters can be used to provide insight into similarities and differences in the ratio of plastic and elastic wall deformation rates during expansive growth of different cell species. It would be interesting and important to determine Πpe for ‘growth mutant’ cells[31] and ‘wall mutant’ cells[32], and compare their magnitudes to Πpe values obtained from wild type cells of the same species This could reveal whether the mutation produced a change in the ratio of plastic and elastic wall deformation rates.
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