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Dimensional Analysis of Expansive Growth of Cells with Walls

Joseph KE Ortega

Expansive growth is central to development, morphogenesis, and sensory responses of algal, fungal and plant cells. These walled cells generate turgor pressure by absorbing water. The turgor pressure produces irreversible (plastic) and reversible (elastic) deformations in a wall whose mechanical properties are regulated biochemically. These biophysical processes (water uptake and wall deformation) are described by established interrelated biophysical equations, the augmented growth equations. Dimensional analysis is used to make the Augmented Growth Equations dimensionless, producing dimensionless coefficients. The dimensionless coefficients are interpreted as ratios of biophysical processes. The utility of the dimensionless augmented growth equations and the dimensionless coefficients are explored. It is found that one dimensionless coefficient may provide insight into the wall chemistry used by different cells to regulate their wall mechanical properties. Different magnitudes of the dimensionless coefficient for algal, fungal, and plant cells suggests that different molecular mechanisms are used to regulate their wall mechanical properties.