Dimensionless Numbers to Analyze Expansive Growth Processes

Cells of algae, fungi, and plants have walls and exhibit expansive growth which can increase their volume by as much as 10,000 times. Expansive growth is central to their morphogenesis, development, and sensory responses to environmental stimuli. Equations describing the biophysical processes of the water uptake rate and the wall deformation rate have been derived, validated, and established. A significant amount of research provides insight into the molecular underpinnings of these processes. What is less well known are the relative magnitudes of these processes and how they compare during expansive growth and with walled cells from other species. Here, dimensionless numbers (Π parameters) are used to determine the magnitudes of the biophysical processes involved in the expansive growth rate of cells from algae (Chara corallina), fungi (Phycomyces blakesleeanus), and plants (Pisum satinis L.). It is found for all three species that the cell's capability for the water uptake rate is larger than the wall plastic deformation rate and much larger than the wall elastic deformation rate. Also, the wall plastic deformation rates of all three species are of similar magnitude as their expansive growth rate even though the stress relaxation rates of their walls are very different. It is envisioned that dimensionless numbers can assist in determining how these biophysical processes change during development, morphogenesis, sensory responses, environmental stress, climate change, and after genetic modification.