A Mechanical Cusp Catastrophe Imposes a Universal Developmental Constraint on the Shapes of Tip-Growing Cells

Abstract

Understanding the mechanistic basis for morphological diversity is a central problem in biology. Here, I examine the evolutionary and mechanical basis for the diversity of cell morphologies in tip-growing organisms from across the tree of life. To investigate the factors that give rise to this diversity, I measured the spatial dependence of the cell-wall expansion rate for three species that spanned phylogeny (one plant, one fungal, and one protistan species) and shape space. I found that a single constitutive mechanical model relating the mechanical stresses in the wall to the expansion rates could explain the expansion-rate profiles from each species, which allowed us to calculate the spatial dependence of the mechanical extensibility (inverse viscosity) of the cell wall. We found that the extensibility profiles, in turn, could be fit well with a simple two-parameter empirical function. This function, in combination with the mechanical model, provided a basis that spanned a broad “morphospace” for tip-growing organisms that I described computationally, and which moreover could account for the shapes of a broad diversity of tip-growing organisms. However, the experimentally observed shapes were restricted to a narrow region of this morphospace. Using computational analysis, I discovered that natural cell morphologies are bounded by a shape instability that had hallmarks of a cusp bifurcation, and which separated fast-growing, thin cells from slow-growing, wide cells. That is, our analysis revealed a universal developmental constraint on cell shape provided by the interplay of natural selection for fast cell growth and the physical mechanism of cell growth.