Elastocapillary Instability in Mitochondrial Fission

Mitochondria are dynamic cell organelles that constantly undergo fission and fusion events. These dynamical processes, which tightly regulate mitochondrial morphology, are essential for cell physiology. Here we propose an elastocapillary mechanical instability as a mechanism for mitochondrial fission. We experimentally induce mitochondrial fission by rupturing the cell’s plasma membrane. We present a stability analysis that successfully explains the observed fission wavelength and the role of mitochondrial morphology in the occurrence of fission events. Our results show that the laws of fluid mechanics can describe mitochondrial morphology and dynamics.

Figure 1

Sketch of the experimental setup. (1) A layer of bovine endothelial cells (represented by the undulated curve) is grown on (2) a glass-bottom dish. The dish is filled with culture medium and placed on (3) an inverted microscope. (4) A curved glass micropipette, manipulated by means of (5) a micropipette holder, is used to exert a controlled impact on the cell’s plasma membrane (indicated by the block arrow) and to rupture it. The inset represents the contact between the micropipette tip and the cell.

Figure 2

Top row: Time sequence of the morphological change of mitochondria (fluorescently labeled in black), following the micropipette-induced plasma membrane rupture that occurs at time $t=0\mathrm{s}$ and at the location indicated by the left-pointing black arrow. The scale bar measures $10\mu \mathrm{m}$. The inset shows a magnification of the mitochondrial morphological change. The black arrow in the inset follows an unstable mitochondrion, and the white arrow follows a stable one. The inset’s scale bar measures $2\mu \mathrm{m}$. Bottom row: Time sequence of the Plateau-Rayleigh instability of a water film on a glass fiber. The scale bar measures 1 mm.

Figure 3

(a) Conceptualization used in the instability calculation. A mitochondrion is represented by a long cylinder of initial radius $R_0$ with a membrane tension $\gamma$ and elastic modulus $E$, filled with a viscous fluid of viscosity $\mu$. (b) Conceptualization of the shape relaxation process.

Figure 4

(a) Stability phase diagram. Each symbol corresponds to an observed mitochondrion, characterized by its initial radius $R_0$ and its initial length $L_0$. Mitochondrial geometry is determined from the experimental images with an uncertainty of at most 15% due to diffraction blur. Blue squares indicate mitochondria that do not fission upon plasma membrane rupture, and red circles indicate mitochondria that fission into two or more subunits. The dashed line indicates the limit of the stability region predicted by the model $L_0=4.2\pi R_0$. (b) Predicted growth rate $\sigma$ for perturbations of different wave number $k$. The solid line is the result of Eq. (6) for $N_{\mathrm{EC}}=0.1$ and the dashed line for $N_{\mathrm{EC}}=1$. (c) Wavelength $\lambda$ of the observed instability, as a function of the mitochondrial initial radius $R_0$. Circles correspond to experimental measurements, and the dashed line corresponds to the model’s prediction $\lambda \approx 9.5R_0$. (d) Evolution of the mitochondrial shape as a function of the elapsed time. The figure represents the normalized time $\xi \equiv t/\tau$ versus the normalized projected area $y\equiv [(A-A_{\infty })/(A+A_{\infty })][(A_0+A_{\infty })/(A_0-A_{\infty })]$. The symbols represent the mean and the standard deviation of the measurements. (We followed 29 mitochondria belonging to three different cells.) The dashed line represents the fit of Eq. (9), with a value of the fitting parameter $\gamma /\mu =0.045\mu \mathrm{m}/\mathrm{s}$.