Figure 5:

Continuum modeling of CM tubule formation reveals a snapthrough instability mediated by both lipid and ATP synthase generated curvatures.

(A) Schematic depiction of yeast CM tubules containing a modeled neck force (f_c) induced by Mgm1p and MICOS complexes, a deviatoric curvature imposed by ATP synthase at tubule ridges (D₀), and a spontaneous curvature along the entire membrane imposed by asymmetric distribution of CL across the IMM (C₀). (Right) TEM image showing typical yeast CM tubules in a single mitochondrion. Scale bars, 100 nm. The average tubule length (140.3±87.9nm) and diameter (19.4±4.7nm) of 15 cristae tubules were analyzed from tomograms of n=3 SFA2 mitochondria.

(B) Changes in deviatory and spontaneous curvatures modulates tubule morphology. Panels i-ix show shapes of the membranes from simulations of the continuum model. For these simulations, the bending modulus of the membrane was maintained at 15 k_B T and the tension was set at 0.01 pN/nm. The total membrane area was set to 5.65 × 10⁵ nm² and the coated area was 1.413 × 10⁴ nm² The values of C₀ and D₀ were varied as shown and f_c was set to 8 pN/nm at the base of the coat.

(C) CM tubule formation shows a snap-through behavior. (i) Length of the tube as a function of C₀ and D₀ for the same values of bending modulus, tension, and areas as shown in (B). The white region shows the transition from the short to the long tube. The color bar shows the length of the tube in nm. Line graphs in (ii) show the length of the tube as a function of C₀ for D₀ fixed at 0.0175 nm⁻¹ and line graphs in (iii) show the length of the tube as a function of D₀ for C₀ fixed at 0.0225 nm⁻¹ for three different values of к. In both these graphs, the abrupt change in length is indicative of a snapthrough instability.