Optimizing mitochondrial maintenance in extended neuronal projections

Neurons rely on localized mitochondria to fulfill spatially heterogeneous metabolic demands. Mitochondrial aging occurs on timescales shorter than the neuronal lifespan, necessitating transport of fresh material from the soma. Maintaining an optimal distribution of healthy mitochondria requires an interplay between a stationary pool localized to sites of high metabolic demand and a motile pool capable of delivering new material. Interchange between these pools can occur via transient fusion / fission events or by halting and restarting entire mitochondria. Our quantitative model of neuronal mitostasis identifies key parameters that govern steady-state mitochondrial health at discrete locations. Very infrequent exchange between stationary and motile pools optimizes this system. Exchange via transient fusion allows for robust maintenance, which can be further improved by selective recycling through mitophagy. These results provide a framework for quantifying how perturbations in organelle transport and interactions affect mitochondrial homeostasis in neurons, a key aspect underlying many neurodegenerative disorders.


Generalization to Branched Axons
Zoomed-in schematic of a demand site at a branching junction. Demand site is located at position x i , with S = 5 stationary mitochondria shown (blue). The health of the j th mitochondrion is given by H i,j , and the motile health leaving and entering on each side of the region is labeled. In our simplified model, the demand site is assumed to be infinitely narrow, and x ± i refers to the positions in the domain immediately after and before the demand site.
Throughout this work we focus on the interplay between mitochondrial transport, interchange, and aging, assuming a linear geometry to minimize the geometric complexity. However, in vivo axons have a tree-like branched structure, with mitochondrial localization observed at the branching points [1]. In this section we present a generalization of the 'Space Station' model for a simple symmetric tree structure with stationary mitochondria localized at the branching points.
We assume that each branching junction splits into g = 2 identical downstream branches of equal length. The "demand sites" are placed immediately upstream of each branch point, with an equal number of mitochondria (S) situated at each site. The model geometry is sketched in Fig ??. The symmetry of the system allows us to define a coordinate system 0 ≤ x ≤ L, with 0 corresponding to the soma and L to the distal tips. The motile mitochondria health distribution H ± i (x) gives the health density at position x in any one of the corresponding branches. As before, we define H i,j to be the health of the j th mitochondrion at demand site (junction) i. The quantity H + i,j gives the anterograde-moving health density in the infinitesimally small space between mitochondrion j and j + 1 at site i; similarly, H − i,j gives the retrograde-moving health density between mitochondrion j − 1 and j. With these definitions, the branched system obeys Equations 13 after replacing the general mitochondrial density ρ with a branch-dependent density ρ i , defined by Here ρ 1 is the motile mitochondria density in the initial branch arising from the soma, and this density splits evenly at each junction point to give the downstream density ρ i between junction i − 1 and i.
In addition to Eq. 13,the boundary conditions that complete the branched system are: Eq. S2a indicates that the anterograde health density leaving each junction (H + i,S ) splits into g equal branches. Similarly, Eq. S2b defines the retrograde density entering the junction (H − i,S+1 ) as the sum of retrograde densities from g branches.
The branched model with a tree of depth m has a total of n = 2 m − 1 demand sites, with each motile mitochondrion passing m of those sites on its way down the axon. When comparing to the linear model, we compare systems with the same total number of mitochondria M servicing the same number of demand sites n, and with the same distance L from soma to distal tip. It should be noted that the average linear density of motile mitochondria is lower in the branched model because the same total number M is spread out over a larger total branch length [L tot = (2 (m+1) − 1)L/(m + 1)]. The primary model parameters (decay rate k d , fraction of stopped mitochondria f s , and average number of stopping events for each protein N s ) are defined to be conceptually analogous to the linear model. As before, we have k d = k d L/v and f s = nS/M . Because each mitochondrion traverses only one branch at each level of the tree, the number of stopping events is given by N s = 2 p s m.
The steady-state mitochondrial health at the demand sites in a tree of depth 4-level and 8-level tree are plotted in Fig ??. The overall value of both average and distal mitochondrial health is somewhat decreased, presumably as a result of the lower density of motile mitochondria servicing the more distal branches. Interestingly, increasing the depth of the branching tree (while keeping a constant length L) only slightly lowers mitochondrial health, despite the fact that the distal density of motile mitochondria decreases exponentially. This result further confirms the observation that the primary relevant parameters are fraction of mitochondria stopped (f s ) and number of stopping events N s rather than the absolute number of demand sites or density of motile mitochondria. Furthermore, we note that the optimal values of f s and N s are largely unchanged in the branched system when compared to the linear geometry (Fig. 5). We therefore conclude that our main results, which rely on a linear axonal geometry, are more generally applicable.
A number of questions remain regarding mitochondrial maintenance in a branching geometry. Namely, the potential effect of redistributing stationary mitochondria at different depths along the tree, the consequences of asymmetric tree geometries, the effect of bidirectional motion into multiple branches, and the role of autophagy in tree-like structures, may further elucidate the optimal strategies for mitostasis in realistic axonal geometries. These more in-depth explorations serve as a promising jumping-off point for future expansion of the model described in this manuscript.