Computer simulation of fungal morphogenesis and the mathematical basis for hyphal (tip) growth

Summary

A novel mathematical model is proposed to explain how a tubular shape (e.g., a fungal hypha) is generated by a tip-growing cell. The model derived from a computer simulation of morphogenesis assumes that: i) the cell surface expands from materials discharged by wall-destined vesicles, ii) vesicles are released from a postulated vesicle supply center (VSC), iii) vesicles move from the VSC to the surface in any random direction. The position and movement of the VSC become the critical determinant of morphogenesis: a stationary VSC releases vesicles that reach the cell surface in about equal numbers in all directions, and the cell grows as a sphere. Any displacement of the VSC from its original central position distorts the spherical shape. A sustained linear displacement of the VSC generates the typical cylindroid shape of fungal hyphae. The model yields the equation

$$y = x\cot \frac{{V \cdot x}}{N}$$

which defines both the shape and size (diameter) of a hypha by two parameters, to which physiological significance can be ascribed:N, the amount of wall-destined vesicles released from the VSC per unit time;V, the rate of linear displacement of the VSC. There is a remarkable coincidence between the position of the VSC in the model and the position of the Spitzenkörper in real hyphae. The model affords a simple mechanism to generate a tubular shape from a tip-growing cell; it obviates the need to postulate specific targets for vesicles on the apical cell surface or to invoke gradients in the properties of the apical wall. Other common morphogenetic transitions of fungi and other organisms can be simulated with the same basic model.