Optimizing mitochondrial maintenance in extended neuronal projections

Abstract

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.

Fig 1. Schematic of quantitative models for mitochondrial maintenance in long neuronal projections.

(a) Mitochondria are produced at the soma at rate k_p, move processively with velocity v, and can stop at one of n discrete sites with high metabolic demand. Mitochondrial health degrades continuously with rate k_d. Gray box represents the modeled linear domain of length L. (b) Two models for mitochondrial exchange at demand sites. In the CoG model, stationary mitochondria re-enter the motile population with rate k_w while passing motile mitochondria stop with probability p_s. Stopping and restarting rates are independent of mitochondrial health; on average, however, restarting mitochondria will be less healthy than when they first stopped at the site, due to degradation in the stationary state. In the SS model, transient fusion events occur with probability p_f each time a motile mitochondrion passes a permanently stationary one [53].

Fig 2. Comparison of mean-field and discrete stochastic models.

(a) Snapshot of stochastic simulation of the CoG model, with M = 100. (b) Steady-state solution for mitochondrial health in the CoG model (Eq 2). Solid curves show linear density of mitochondrial health in anterograde (blue) and retrograde (magenta) mitochondria, normalized by total number of mitochondria in the domain. Yellow circles show total health at each of the discrete demand sites (dashed black lines), normalized by the total number of mitochondria per region. Shaded regions show corresponding quantities from discrete stochastic simulations (mean ± standard deviation) with M = 1500 mitochondria in the domain. Parameters used in (a) and (b): n = 5, p_s = 0.4, f_s = 0.5, k_d L/v = 0.6. Corresponding results for the SS model are provided in S1 Fig.

Fig 3. Comparison of mitochondrial maintenance models for matched parameter values.

(a) Steady-state normalized mitochondrial health averaged over all demand regions is computed with the CoG model (solid lines) and the SS model (dashed lines) as a function of the fraction of stopped mitochondria (f_s) for three different values of the effective protein stopping probability ${\widehat{p}}_s$. (b) Corresponding plots of the normalized health in the most distal demand site, for both models. All values are computed with M = 1500, ${\widehat{k}}_d=0.06$, and n = 30.

Fig 4. Mitochondrial health as a function of key dimensionless parameters.

Solid curves show normalized average health over all demand sites; dashed curves show normalized health at the most distal site. The number of demand sites is set to n = 30 (blue) or n = 100 (magenta). For each fraction of stationary mitochondria the fusion probability is adjusted to give a fixed number of stopping events for an individual protein traversing the domain: (a) N_s = 2 and (b) N_s = 20. All values shown are for the SS model, with M = 1600 and ${\widehat{k}}_d=0.06$. Results for different values of M are provided in S2 Fig.

Fig 5. Optimizing mitochondrial health through variation of transport parameters.

(a-b) Average health across all demand regions as a function of fraction of stopped mitochondria (f_s) and number of stopping events (N_s), for two dimensionless decay rates (${\widehat{k}}_d$). (c-d) Mitochondrial health at the most distal demand site, for two different decay rates. (e-f) Values of the f_s and N_s parameters that correspond to maximum average health (blue curves) or last region health (yellow curves). Optimal parameters are plotted as a function of the decay rate. Results shown were computed for the CoG model.

Fig 6. Mitochondrial health in the presence of local translation.

(a) Average health across all demand regions as a function of fraction of stopped mitochondria (f_s) and number of stopping events (N_s), for high decay rate (${\widehat{k}}_d$) and local translation level α = 10%. Markers show the optimal parameter values with (red asterisk) and without (blue circle) local translation. (b) Corresponding mitochondrial health at the most distal demand site. (c) Enhancement of health levels at each demand site in the presence (H_i,t) versus absence (H_i) of local translation, for one set of transport parameters, (f_s = 0.5, N_s = 0.4), two decay rates ${\widehat{k}}_d$, and three different local translation levels (α).

Fig 7. Variability of mitochondrial health in different maintenance models.

Plotted is the standard deviation in health per region (σ_H) divided by its average value ($\overline{\langle H\rangle }$), across 1000 iterations of stochastic simulations. Results are shown for 300 (blue), 500 (magenta), and 1500 (yellow) average mitochondria in the domain. Solid lines correspond to simulations of the CoG model and dashed lines to the SS model. All simulations used parameters ${\widehat{k}}_d=0.6$, n = 10, N_s = 2. Corresponding plots are provided in S3 Fig to show the effect of lower decay rates (S3 Fig) and of random stationary mitochondria distribution in the SS model (S3 Fig).

Fig 8. Effect of mitophagy, at fixed production rate k_p.

(a) The total number of mitochondria in the domain (yellow) and the number of stationary mitochondria (blue) are plotted as a function of the mitophagy threshold, for both the CoG model (solid lines) and the SS model (dashed lines). Mitochondria quantities are normalized by the steady-state number of mitochondria in the absence of mitophagy. (b) Mitochondrial health for the CoG model, averaged over all demand sites, plotted as a function of mitophagy threshold and number of stopping events N_s. (c) Health at most distal demand site, for the CoG model. (d-e) Analogous plots of average health and distal site health for the SS model. All plots assume mitochondrial production rate does not change with increased mitophagy, and correspond to fraction of mitochondria stopped f_s(ϕ = 0) = 0.53 in the absence of mitophagy.

Fig 9. Effect of mitophagy when total mitochondrial number is limited.

(a) Fraction of mitochondria in the stationary state as a function of increasing mitophagy threshold, for the CoG model (solid line) and the SS model (dashed line), with parameters set such that f_s = 0.53 at ϕ = 0. (b) Mitochondrial health, normalized by the total number of mitochondria per site, averaged over all demand sites, for the CoG model. (c) Normalized mitochondrial health at most distal demand site, for the CoG model. (d-e) Analogous plots of normalized average health and distal site health for the SS model. Normalizing by total mitochondrial number is equivalent to a system where the total mitochondrial content is held fixed with the onset of mitophagy (S4 Fig).

Fig 10. Optimal performance of mitochondrial maintenance models in presence of mitophagy.

(a) For each mitophagy threshold ϕ, the parameters f_s, N_s are optimized to give the maximum normalized average health: 〈H〉. The resulting normalized average health (blue) and normalized last region health (yellow) are plotted for the CoG model (solid) and SS model (dashed). (b) Analogous plots, with parameters adjusted to maximize the normalized last region health ${\widehat{H}}_n$ for each mitophagy threshold. All health levels are normalized by total mitochondrial content per region (M/n), corresponding to a system where the total amount of mitochondrial material is limited. Error bars show standard error of the mean from 10 replicates. Fixed parameters are ${\widehat{k}}_d=0.6$, M = 300, n = 10. A corresponding plot of optimized health for low decay rate ${\widehat{k}}_d$ is provided in S5 Fig.