Spontaneous Rotational Inversion in Phycomyces

The filamentary fungus Phycomyces blakesleeanus undergoes a series of remarkable transitions during aerial growth. During what is known as the stage IV growth phase, the fungus extends while rotating in a counterclockwise manner when viewed from above (stage IVa) and then, while continuing to grow, spontaneously reverses to a clockwise rotation (stage IVb). This phase lasts for 24–48 h and is sometimes followed by yet another reversal (stage IVc) before the overall growth ends. Here, we propose a continuum mechanical model of this entire process using nonlinear, anisotropic, elasticity and show how helical anisotropy associated with the cell wall structure can induce spontaneous rotation and, under appropriate circumstances, the observed reversal of rotational handedness.

Figure 1

Left: The fungus Phycomyces blakesleeanus as drawn by Carnoy [1]. The spherical dome on top of the tube is the sporangium that contains the spores that are disseminated on completion of the life cycle. Right: The 4 stages of growth for the aerial hypha. In stage IV helical growth reversal is observed: Stage IVa exhibits right-handed growth, and stage IVb presents left-handed growth. Stage IVb continues for up to 2 days when the organisms can reach up to 10 cm in height (reproduced from Ref. 12).

Figure 2

Effect of fiber precompression on torsion $\tau$ as a function of the fiber angle $\Phi$ (the behaviors illustrated in Figs. 2, 3, 4 are all for $\mu =5$, $\zeta =1.4$ but are robust to changes in the parameter values).

Figure 3

Fiber orientation $\varphi$ in the current configuration as a function of $\Phi$, and the corresponding plot of $\tau (\Phi )$. The dashed diagonal line corresponds to $\varphi =\Phi$.

Figure 4

Dynamic of $\tau$, $\nu$, and $\Phi$ for a given material point as a function of time (${\kappa }_1=16{\mathrm{h}}^{-1}$, ${\kappa }_2=4{\mathrm{h}}^{-1}$. While this process takes place, the material point at $t=0$ starts on top of the growth zone and is convected downward (with respect to a reference frame moving with the top of the growth zone).

Figure 5

Rotational velocity (in units of radians per unit time $t_r$) of the sporangiophore as a function of time. The time $-1$ on the right side of the time axis refers to 1 h before the end of growth, i.e., the time in this simulation at which the growth zone starts to retract.