Fig. 3.

Model of diffusion between neighboring mitochondria in the spanning cluster. The concentration profiles of were calculated from the solution of a diffusion model (31):

[1]

where c, x, and t are messenger concentration, distance, and time, respectively. When the solution of Eq. 1 is supposed to depend on a spatial parameter, z = x – vt, we obtain:

[2]

whose solution is:

[3]

The concentration gradients of between mitochondria as a function of its rate of scavenging, v, were calculated according to Eq. 3 and the following boundary conditions: c(0) = C_max, and c(∞) = 0. The higher the rate of scavenging, the steeper the gradient and the lower the concentration reaching the second mitochondrion. A maximal distance between two neighboring mitochondria of 0.5 μm was determined. The ROS threshold of 20% was obtained experimentally by image analysis (see Fig. 2 A), and the two mitochondria at the critical state are assumed to belong to the spanning cluster, i.e., they possess a level of ROS very close to the threshold. For those conditions in which ROS near Mito 2 exceeds the threshold, ROS-induced ROS release is predicted. Considering the volume of an average mammalian cell of the order of 4 × 10^–12 liters (32) and of single mitochondria, 10^–15 liters (≈500–1,000 mitochondria in a plane; e.g., see Fig. 2B), we estimate that the levels of released between neighboring mitochondria would have to be at least in the micromolar range for propagation to occur in the presence of superoxide dismutase (k_cat ≈ 1 nmol/s).