Modelling transport and mean age of dense core vesicles in large axonal arbours

Effect of mitochondrial circulation on mitochondrial age density distribution

Recent publications report that although the mitochondria population in an axon can be quickly replaced by a combination of retrograde and anterograde axonal transport (often within less than 24 hours), the axon contains much older mitochondria. This suggests that not all mitochondria that reach the soma are degraded and that some are recirculating back into the axon. To explain this, we developed a model that simulates mitochondria distribution when a portion of mitochondria that return to the soma are redirected back to the axon rather than being destroyed in somatic lysosomes. Utilizing the developed model, we studied how the percentage of returning mitochondria affects the mean age and age density distributions of mitochondria at different distances from the soma. We also investigated whether turning off the mitochondrial anchoring switch can reduce the mean age of mitochondria. For this purpose, we studied the effect of reducing the value of a parameter that characterizes the probability of mitochondria transition to the stationary (anchored) state. The reduction in mitochondria mean age observed when the anchoring probability is reduced suggests that some injured neurons may be saved if the percentage of stationary mitochondria is decreased. The replacement of possibly damaged stationary mitochondria with newly synthesized ones may restore the energy supply in an injured axon. We also performed a sensitivity study of the mean age of stationary mitochondria to the parameter that determines what portion of mitochondria re-enter the axon and the parameter that determines the probability of mitochondria transition to the stationary state. The sensitivity of the mean age of stationary mitochondria to the mitochondria stopping probability increases linearly with the number of compartments in the axon. High stopping probability in long axons can significantly increase mitochondrial age.

Simulation of a sudden drop-off in distal dense core vesicle concentration in Drosophila type II motoneuron terminals

Recent experimental observations have shown evidence of an unexpected sudden drop-off in the dense core vesicles (DCVs) content at the ends of certain types of axon endings. This article seeks to determine whether these observations may be explained without modifying the parameters characterizing the ability of distal en passant boutons to capture and accumulate DCVs. We developed a mathematical model that is based on the conservation of captured and transiting DCVs in boutons. The model consists of 77 ordinary differential equations and is solved using a standard Matlab solver. We hypothesize that the drop in DCV content in distal boutons is due to an insufficient supply of anterogradely moving DCVs coming from the soma. As anterogradely moving DCVs are captured (and eventually destroyed) in more proximal boutons on their way to the end of the terminal, the fluxes of anterogradely moving DCVs between the boutons become increasingly smaller, and the most distal boutons are left without DCVs. We tested this hypothesis by modifying the flux of DCVs entering the terminal and found that the number of most distal boutons left unfilled increases if the DCV flux entering the terminal is decreased. The number of anterogradely moving DCVs in the axon can be increased either by the release of a portion of captured DCVs into the anterograde component or by an increase of the anterograde DCV flux into the terminal. This increase could lead to having enough anterogradely moving DCVs such that they could reach the most distal bouton and then turn around by changing molecular motors that propel them. The model suggests that this could result in an increased concentration of resident DCVs in distal boutons beginning with bouton 2 (the most distal is bouton 1). This is because in distal boutons, DCVs have a larger chance to be captured from the transiting state as they pass the boutons moving anterogradely and then again as they pass the same boutons moving retrogradely.

How old are dense-core vesicles residing in en passant boutons: simulation of the mean age of dense-core vesicles in axonal arbours accounting for resident and transiting vesicle populations

In neurons, neuropeptides are synthesized in the soma and are then transported along the axon in dense-core vesicles (DCVs). DCVs are captured in varicosities located along the axon terminal called en passant boutons, which are active terminal sites that accumulate and release neurotransmitters. Recently developed experimental techniques allow for the estimation of the age of DCVs in various locations in the axon terminal. Accurate simulation of the mean age of DCVs in boutons requires the development of a model that would account for resident, transiting-anterograde and transiting-retrograde DCV populations. In this paper, such a model is developed. The model is applied to simulating DCV transport in Drosophila type II motoneurons. The model simulates DCV transport and capture in the axon terminals and makes it possible to predict the age density distribution of DCVs in en passant boutons as well as DCV mean age in boutons. The predicted prevalence of older organelles in distal boutons may explain the 'dying back' pattern of axonal degeneration observed in dopaminergic neurons in Parkinson's disease. The predicted difference of two hours between the age of older DCVs residing in distal boutons and the age of younger DCVs residing in proximal boutons is consistent with an approximate estimate of age difference deduced from experimental observations. The age density of resident DCVs is found to be bimodal, which is because DCVs are captured from two transiting states: the anterograde transiting state that contains younger DCVs and the retrograde transiting state that contains older DCVs.