Figure 1.
A cycle of fusion, fission, and autophagy contribute to quality control of mitochondrial health.
Each mitochondrion is represented as a set of discrete health units that are in either a healthy (green) or damaged (red) state. (1) Fusion joins two (or more) mitochondria into a connected entity, though each mitochondrion is assumed to retain its original identity. Only mitochondria above a particular health threshold are permitted to fuse. (2) Fused mitochondria undergo stochastic exchange of a fixed number of health units. This exchange can lead to an asymmetry in the health of fused mitochondria, which occurs when these mitochondria undergo fission. (3) Fission separates fused mitochondria into isolated mitochondria or mitochondrial subnetworks. (4) Autophagy removes isolated mitochondria when their health is below the autophagy threshold. (5) Damage to mitochondrial health sets a health unit to the damaged state. (6) New mitochondria are produced via the cumulative effects of protein synthesis and import, and this replication event generates a copy of an existing mitochondrion that appears in the same physical neighborhood with the same number of health units as the progenitor mitochondrion. The variables representing the rates of each process () are shown next to their labels.
Figure 2.
Active transport model of mitochondrial spatial dynamics.
(A) We represent each mitochondrion as a circle with radius . (B) Each stationary mitochondrion can bind a cytoskeletal filament pointed in a random direction at rate
. (C) A mitochondrion attached to a filament moves at constant velocity
until it either unbinds at rate
or encounters another mitochondrion or the edge of the cell. (D) In the presence of fusion and fission, this model produces mitochondrial networks with structures qualitatively similar to those observed in vivo. Autophagy of unfused mitochondria with poor health (orange) is critical for the establishment of functional mitochondrial networks, by allowing the replacement of dysfunctional mitochondria with healthy mitochondria that can still undergo fusion.
Figure 3.
Maintenance of a healthy mitochondrial population requires autophagy and is enhanced by fusion and fission.
(A) In the presence of damage alone, average mitochondrial health (red) decays exponentially. The dashed lines represent the 25th and 75th percentiles of health averaged over 25 independent simulations, while the shaded region represents one standard deviation above and below the average health across the simulations. The population size (blue) remains constant. (B) With the addition of autophagy, which removes mitochondria below an autophagy threshold of (gray region), the average steady-state health initially decreases more slowly than in (A), before the decreasing number of mitochondria reduces the population density to a level that makes it impossible to maintain health. The wide range of healths near this transition point is due to the small numbers of mitochondria per cell. (C) The addition of replication rescues the population size and health to a value just above the autophagy threshold. (D) The further inclusion of fusion, for mitochondria above a fusion threshold
, and fission increases the average steady-state health of the mitochondrial population. The variability in health increases due to the stochastic nature of the asymmetric exchange of HUs during fission.
Figure 4.
Maximal average steady-state health occurs for maximal asymmetry generation through stochastic exchange and fission.
In each simulation, each mitochondrion has health units, and thus exchanging
units is equivalent to exchanging
units. For all fusion rates, the average steady-state health is maximized when 5 units (or half the total number) are exchanged during each fusion and fission event. Health reaches a plateau for all values of exchanged HUs at fusion rates of
. All fusion rates are in units of
.
Figure 5.
Mitochondrial health is maximized when the thresholds for autophagy () and fusion (
) are equal.
(A) For each , the average health (values represented by the color bar) is maximized when
has the same value (blue circles), suggesting that the mechanism for fusion selectivity shares molecular components with autophagy selectivity. (B) Distributions of health across the mitochondrial population once simulations reach a steady state for different values of
and
, highlighting the effects of unequal thresholds (ii and iii). Gray regions indicate the mitochondria that can undergo autophagy, while red regions indicate the mitochondria that can undergo fusion.
Figure 6.
Health is insensitive to density as long as fusion events are sufficiently frequent.
(A) In simulations within cells of different sizes, average steady-state health plateaus after a filling fraction of . (B) Typical network architectures at the points labeled in (A). Each mitochondrion has a radius of
in all simulations and is colored according to its health. Mitochondria above and below
and
appear in shades of green and red, respectively. (C) Histograms of the number of mitochondria in networks of different sizes. The solid lines correspond to the networks formed only by fused neighbors, while the dashed lines correspond to networks of touching mitochondria regardless of fusion state. (D) The frequency of fusion events as a function of density, showing the same transition at
filling fraction.
Figure 7.
Motion dependence of fusion alters health by rescaling the effective fusion rate.
(A) Rates of fusion were scaled down by or
if only one or neither, respectively, of the fusing mitochondria were actively being transported at the time of fusion. Transport occurs at velocity
. (B,C) Decreasing
(B) or
(C) for fixed
leads to a decrease in health. In (B),
; in (C),
. (D) Over a wide range of values of
and
, the frequency of fusion events was highly related to average health. The colors correspond to the same fusion rates specified in (B). All fusion rates are in units of
.
Figure 8.
Maximal autophagy and replication rates affect health and mitochondrial population size in distinct manners.
(A) Restricting the maximal autophagy rate causes a decrease in steady-state health with relatively little effect on population size, indicating that autophagy is critical to maintaining a healthy population. (B) In contrast, cells maintain high average health when the maximal replication rate is restricted, while the population size decreases. All damage rates are in units of .
Figure 9.
Maintenance of mitochondrial health requires a discrete health parameter.
(A) The average steady-state health of the mitochondrial population can be maintained above the autophagy threshold when the number of HUs per mitochondrion is small, but falls off rapidly to zero due to loss of mitochondria via autophagy as the total number of HUs increases toward a continuum health variable. When the rate of fusion is nonzero, cells can tolerate less discreteness in the health parameter (more HUs) due to the additional stochasticity introduced by fission and by sequestering mitochondria from autophagy while fused. (B) Histograms of the healths of mitochondria in simulations conducted with different maximum HU values and fusion rates (points labeled in (A)) show that the overall health depends on the distribution of mitochondria and this overall distribution is similar for a given average steady-state health as long as the fusion rate is nonzero.
Table 1.
Typical values of model parameters used in simulations in Fig. 3.