A stochastic model that explains axonal organelle pileups induced by a reduction of molecular motors

Why slow axonal transport is bidirectional - can axonal transport of tau protein rely only on motor-driven anterograde transport?

Slow axonal transport (SAT) moves multiple proteins from the soma, where they are synthesized, to the axon terminal. Due to the great lengths of axons, SAT almost exclusively relies on active transport, which is driven by molecular motors. The puzzling feature of slow axonal transport is its bidirectionality. Although the net direction of SAT is anterograde, from the soma to the terminal, experiments show that it also contains a retrograde component. One of the proteins transported by SAT is the microtubule-associated protein tau. To better understand why the retrograde component in tau transport is needed, we used the perturbation technique to analyze how the full tau SAT model can be simplified for the specific case when retrograde motor-driven transport and diffusion-driven transport of tau are negligible and tau is driven only by anterograde (kinesin) motors. The solution of the simplified equations shows that without retrograde transport the tau concentration along the axon length stays almost uniform (decreases very slightly), which is inconsistent with the experimenal tau concentration at the outlet boundary (at the axon tip). Thus kinesin-driven transport alone is not enough to explain the empirically observed distribution of tau, and the retrograde motor-driven component in SAT is needed.

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.

How neurons maintain their axons long-term: an integrated view of axon biology and pathology

Axons are processes of neurons, up to a metre long, that form the essential biological cables wiring nervous systems. They must survive, often far away from their cell bodies and up to a century in humans. This requires self-sufficient cell biology including structural proteins, organelles, and membrane trafficking, metabolic, signalling, translational, chaperone, and degradation machinery-all maintaining the homeostasis of energy, lipids, proteins, and signalling networks including reactive oxygen species and calcium. Axon maintenance also involves specialised cytoskeleton including the cortical actin-spectrin corset, and bundles of microtubules that provide the highways for motor-driven transport of components and organelles for virtually all the above-mentioned processes. Here, we aim to provide a conceptual overview of key aspects of axon biology and physiology, and the homeostatic networks they form. This homeostasis can be derailed, causing axonopathies through processes of ageing, trauma, poisoning, inflammation or genetic mutations. To illustrate which malfunctions of organelles or cell biological processes can lead to axonopathies, we focus on axonopathy-linked subcellular defects caused by genetic mutations. Based on these descriptions and backed up by our comprehensive data mining of genes linked to neural disorders, we describe the 'dependency cycle of local axon homeostasis' as an integrative model to explain why very different causes can trigger very similar axonopathies, providing new ideas that can drive the quest for strategies able to battle these devastating diseases.

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.

Accumulation of PSA-NCAM marks nascent neurodegeneration in the dorsal hippocampus after neonatal hypoxic-ischemic brain injury in mice

Neonatal hypoxia-ischemia (nHI) disrupts hippocampal GABAergic development leading to memory deficits in mice. Polysialic-acid neural-cell adhesion molecule (PSA-NCAM) developmentally declines to trigger GABAergic maturation. We hypothesized that nHI changes PSA-NCAM abundance and cellular distribution, impairing GABAergic development, and marking nascent neurodegeneration. Cell degeneration, atrophy, and PSA-NCAM immunoreactivity (IR) were measured in CA1 of nHI-injured C57BL6 mice related to: (i) cellular subtype markers; (ii) GAD65/67 and synatophysin (SYP), pre-synaptic markers; (iii) phospho-Ser³⁹⁶Tau, cytoskeletal marker; and (iv) GAP43, axonalregeneration marker. PSA-NCAM IR was minimal in CA1 of shams at P11. After nHI, PSA-NCAM IR was increased in injured pyramidal cells (PCs), minimal in parvalbumin (PV)⁺INs, and absent in glia. PSA-NCAM IR correlated with injury severity and became prominent in perikaryal cytoplasm at P18. GAD65/67 and SYP IRs only weakly related to PSA-NCAM after nHI. Injured phospho-Ser³⁹⁶Tau⁺ PCs and PV⁺INs variably co-expressed PSA-NCAM at P40. While PCs with cytoplasmic marginalized PSA-NCAM had increased perisomatic GAP43, those with perikaryal cytoplasmic PSA-NCAM had minimal GAP43. PSA-NCAM increased in serum of nHI-injured mice. Increased PSA-NCAM is likely a generic acute response to nHI brain injury. PSA-NCAM aberrant cellular localization may aggravate neuronal degeneration. The significance of PSA-NCAM as a biomarker of recovery from nHI and nascent neurodegeneration needs further study.

Modelling the motion of organelles in an elongated cell via the coordination of heterogeneous drift-diffusion and long-range transport

 Cellular distribution of organelles in living cells is achieved via a variety of transport mechanisms, including directed motion, mediated by molecular motors along microtubules (MTs), and diffusion which is predominantly heterogeneous in space. In this paper, we introduce a model for particle transport in elongated cells that couples poleward drift, long-range bidirectional transport and diffusion with spatial heterogeneity in a three-dimensional space. Using stochastic simulations and analysis of a related population model, we find parameter regions where the three-dimensional model can be reduced to a coupled one-dimensional model or even a one-dimensional scalar model. We explore the efficiency with which individual model components can overcome drift towards one of the cell poles to reach an approximately even distribution. In particular, we find that if lateral movement is well mixed, then increasing the binding ability of particles to MTs is an efficient way to overcome a poleward drift, whereas if lateral motion is not well mixed, then increasing the axial diffusivity away from MTs becomes an efficient way to overcome the poleward drift. Our three-dimensional model provides a new tool that will help to understand the mechanisms by which eukaryotic cells organize their organelles in an elongated cell, and in particular when the one-dimensional models are applicable.

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.

A mechanism for neurofilament transport acceleration through nodes of Ranvier

Neurofilaments are abundant space-filling cytoskeletal polymers in axons that are transported along microtubule tracks. Neurofilament transport is accelerated at nodes of Ranvier, where axons are locally constricted. Strikingly, these constrictions are accompanied by sharp decreases in neurofilament number, no decreases in microtubule number, and increases in the packing density of these polymers, which collectively bring nodal neurofilaments closer to their microtubule tracks. We hypothesize that this leads to an increase in the proportion of time that the filaments spend moving and that this can explain the local acceleration. To test this, we developed a stochastic model of neurofilament transport that tracks their number, kinetic state, and proximity to nearby microtubules in space and time. The model assumes that the probability of a neurofilament moving is dependent on its distance from the nearest available microtubule track. Taking into account experimentally reported numbers and densities for neurofilaments and microtubules in nodes and internodes, we show that the model is sufficient to explain the local acceleration of neurofilaments within nodes of Ranvier. This suggests that proximity to microtubule tracks may be a key regulator of neurofilament transport in axons, which has implications for the mechanism of neurofilament accumulation in development and disease.

Crowd Control: Effects of Physical Crowding on Cargo Movement in Healthy and Diseased Neurons

High concentration of cytoskeletal filaments, organelles, and proteins along with the space constraints due to the axon's narrow geometry lead inevitably to intracellular physical crowding along the axon of a neuron. Local cargo movement is essential for maintaining steady cargo transport in the axon, and this may be impeded by physical crowding. Molecular motors that mediate active transport share movement mechanisms that allow them to bypass physical crowding present on microtubule tracks. Many neurodegenerative diseases, irrespective of how they are initiated, show increased physical crowding owing to the greater number of stalled organelles and structural changes associated with the cytoskeleton. Increased physical crowding may be a significant factor in slowing cargo transport to synapses, contributing to disease progression and culminating in the dying back of the neuronal process. This review explores the idea that physical crowding can impede cargo movement along the neuronal process. We examine the sources of physical crowding and strategies used by molecular motors that might enable cargo to circumvent physically crowded locations. Finally, we describe sub-cellular changes in neurodegenerative diseases that may alter physical crowding and discuss the implications of such changes on cargo movement.