Figure 1.
The structure of mitochondrial membraneous compartments.
(A) Membrane surface rendering of mitochondrial tomogram. Cristae (yellow), inner boundary membrane (light blue) and outer membrane (dark blue) are shown from different perspectives. Image courtesy of Terrence G. Frey (San Diego St. Univ.). (B) Computational model of the inner mitochondrial membrane applied in this study. Blue: inner boundary membrane; red and green: two examplary cristae. In both (A) and (B) lamellar compartments (central cristae parts) are connected to the inner boundary membrane through a number of tubular compartments of variable lengths but of uniform diameter.
Figure 2.
Lattice architecture of lamellar cristae.
Tracers are positioned at nodes of the triangular lattice. Red: Inner boundary membrane, violet: Crista junction, blue: Tubular crista subcompartment, turquoise: Crista main body.
Figure 3.
Examplary cristae configurations.
(A) tubular; (B)–(D) lamellar.
Figure 4.
Diffusion in the inner membrane having tubular cristae.
Relative diffusivities projected on the long mitochondrial axis for different tubular cristae configurations. Red: fully permeable junctions (p = (1,1)), green: fully impermeable junctions (p = (0,0)). (A) For indicated cristae lengths L (in units of mitochondrial radius Rm = 200 nm). Cristae junction radius a = 14 nm and density σ = 126 cristae per µm of mitochondrial length. (B) For indicated cristae junction radii, (in units of a = 14 nm), L = 0.8Rm, σ = 126, p = (1,1). (C) For indicated cristae densities, a = 14 nm, L = 0.8Rm, p = (1,1).
Figure 5.
Diffusion in the inner membrane having lamellar cristae.
(A) Relative diffusivities projected on the long mitochondrial axis for mitochondria having lamellar cristae with varying geometry as indicated by the radius of the lamellae expressed as a fraction of mitochondrial radius (Rm = 200 nm) and 3 junctions per crista. Cristae junction radius a = 14 nm, density σ = 42 cristae per µm of mitochondrial length, fully permeable junctions. (B) Blue dots: same as (A), but for the number of junctions increasing with lamella radii from 1 to 6. This condition reflects the proposition [13] that lamellar cristae may have formed via fusion of a number of tubular ones For comparison, the projected diffusivities of two tubular geometries are shown as red circles. For tubular cristae, length L = (2.10Rm, 2.18Rm) and density σ = 126 were chosen to give the same cristae surface area and number of junctions as in the case of corresponding lamellar cristae.
Figure 6.
Limiting values of projected diffusivities: comparison of the MC results to the area scaling theory.
Long-term (open markers) and short-term (filled markers) limiting values for tubular (circles) and lamellar (squares) cristae topologies obtained from fits to the Monte Carlo simulations (Figs. 4, 5) for different cristae sizes (i.e. cristae length in the case of tubular topology, lamellae diameter in the case of lamellar one), fully permeable junctions and a = 14 nm. Other paramemters are as in Fig. 4A and Fig. 5A. Statistical errors (40 configurations) are in the range from ±0.001 to ±0.004. The same variables computed according to the area scaling model (Eqs. 4, 5) are shown as lines.
Figure 7.
Relative projected diffusivities for tubular cristae of the same membrane area.
Ratios of junction radius a to crista length L are as indicated. Cristae density σ = 126 cristae per µm of mitochondrial length, fully permeable junctions.
Figure 8.
Time dependence of the projected diffusivities.
Comparison of MC results for tubular cristae geometry (dots) to the theoretical model, Eq. 8, (red lines) for two examplary membrane configurations. Cristae density σ = 126 cristae per micrometer, fully permeable junctions. Definition of the transition time for alternative models of transient anomalous diffusion is illustrated with black lines.
Figure 9.
Probability distribution of escape times from tubular cristae.
Cristae have radius a = 14 nm and lengths as indicated in the legend (in units of mitochondrial radius Rm = 200 nm). Power law t−3/2 (magenta) is shown for comparison. Insert: Average time spent inside a crista versus cristae length (circles), linear fit (line).