Modelling transport of layered double hydroxide nanoparticles in axons and dendrites of cortical neurons

This paper develops a model of nanoparticle transport in neurons. It is assumed that nanoparticles are transported inside endocytic vesicles by a combined effect of dynein-driven transport and diffusion. It is further assumed that in axons nanoparticles are internalised only at axon terminals, whereas in dendrites nanoparticles can enter through the entire plasma membrane. This causes differences in transport of nanoparticles in axons and dendrites; these differences are investigated in this paper. Another difference is microtubule (MT) orientation in axons and dendrites; in axons, all MTs have their plus-ends oriented towards the axon terminal; in a proximal region of a dendrite, MTs have mixed orientation, whereas in a distal dendritic region the MT orientation is similar to that in an axon. It is shown that if molecular-motor-driven transport were powered by dynein alone, such MT orientation in a dendrite would result in a region of nanoparticle accumulation located at the border between the proximal and distal dendritic regions.     

Method of modelling intracellular transport in branching neurites: application to axons and dendrites of Drosophila sensory neurons

This paper develops a method of calculating the transport of intracellular organelles in neurons with branching neurites which is based on the Smith–Simmons equations of motor-assisted transport. The method is aimed at understanding the effects of microtubule (MT) polarity orientation in branching neurites on transport of organelles at the fundamental level. The method is applied to calculating the organelle transport in axons and dendrites of Drosophila neurons, using the map of MT orientation in such neurons developed by Stone et al. (Mol Biol Cell 19:4122–4129, 2008). The proximal dendrite is assumed to branch and form two distal dendrites. Two different MT polarity arrangements in a proximal dendrite are considered, and implications of these MT arrangements on organelle transport are analysed. It is demonstrated that the MT arrangement found in Drosophila dendrites (MTs have their minus ends out in a proximal dendrite) results in much more efficient motor-driven transport than the structure with a mixed MT orientation in proximal dendrites.     

Sorting of cargos between axons and dendrites: modelling of differences in cargo transport in these two types of neurites

Explaining how intracellular cargos are sorted between axons and dendrites is important for a mechanistic understanding of what happens in many neurodegenerative disorders. A simple model of cargo sorting relies on differences in microtubule (MT) orientation between axons and dendrites: in mammalian neurons all MTs in axons have their plus ends directed outward while in proximal regions of dendrites the MT polarity is mixed. It can therefore be assumed that cargos that need to be driven into axons associate with kinesin motors while cargos that need to be driven into dendrites associate with dynein motors. This paper develops equations of cargo transport in axons and dendrites based on the above assumptions. Propagation of a pulse of radiolabelled cargos entering an axon and dendrite is simulated. The model equations are solved utilising the Laplace transform method. Differences in cargo transport between axons and dendrites are discussed.     

Transport of dendritic microtubules establishes their nonuniform polarity orientation

The immature processes that give rise to both axons and dendrites contain microtubules (MTs) that are uniformly oriented with their plus- ends distal to the cell body, and this pattern is preserved in the developing axon. In contrast, developing dendrites gradually acquire nonuniform MT polarity orientation due to the addition of a subpopulation of oppositely oriented MTs (Baas, P. W., M. M. Black, and G. A. Banker. 1989. J. Cell Biol. 109:3085-3094). In theory, these minus-end-distal MTs could be locally nucleated and assembled within the dendrite itself, or could be transported into the dendrite after their nucleation within the cell body. To distinguish between these possibilities, we exposed cultured hippocampal neurons to nanomolar levels of vinblastine after one of the immature processes had developed into the axon but before the others had become dendrites. At these levels, vinblastine acts as a kinetic stabilizer of MTs, inhibiting further assembly while not substantially depolymerizing existing MTs. This treatment did not abolish dendritic differentiation, which occurred in timely fashion over the next two to three days. The resulting dendrites were flatter and shorter than controls, but were identifiable by their ultrastructure, chemical composition, and thickened tapering morphology. The growth of these dendrites was accompanied by a diminution of MTs from the cell body, indicating a net transfer of MTs from one compartment into the other. During this time, minus-end-distal microtubules arose in the experimental dendrites, indicating that new MT assembly is not required for the acquisition of nonuniform MT polarity orientation in the dendrite. Minus-end-distal microtubules predominated in the more proximal region of experimental dendrites, indicating that most of the MTs at this stage of development are transported into the dendrite with their minus-ends leading. These observations indicate that transport of MTs from the cell body is an essential feature of dendritic development, and that this transport establishes the nonuniform polarity orientation of MTs in the dendrite.     

Rearrangement of microtubule polarity orientation during conversion of dendrites to axons in cultured pyramidal neurons

Axons and dendrites of neurons differ in the polarity orientation of their microtubules. Whereas the polarity orientation of microtubules in axons is uniform, with all plus ends distal, that in dendrites is nonuniform. The mechanisms responsible for establishment and maintenance of microtubule polarity orientation in neuronal processes remain unclear, however. We previously described a culture system in which dendrites of rat cortical neurons convert to axons. In the present study, we examined changes in microtubule polarity orientation in such dendrites. With the use of the hooking procedure and electron microscopy, we found that microtubule polarity orientation changed from nonuniform to uniform, with a plus end-distal arrangement, in dendrites that gave rise to axons during culture of neurons for 24 h. Microtubule polarity orientation remained nonuniform in dendrites that did not elongate. Axon regeneration at the dendritic tip thus triggered the disappearance of minus end-distal microtubules from dendrites. These minus end-distal microtubules also disappeared from dendrites during axon regeneration in the presence of inhibitors of actin polymerization, suggesting that actin-dependent transport of microtubules is not required for this process and implicating a previously unidentified mechanism in the establishment and maintenance of microtubule polarity orientation in neuronal processes.     

Plasticity of polarization: changing dendrites into axons in neurons integrated in neuronal circuits

Developing neurons can change axonal and dendritic fate upon axonal lesion, but it is unclear whether neurons retain such plasticity when they are synaptically interconnected. To address whether polarity is reversible in mature neurons, we cut the axon of GFP-labeled hippocampal neurons in dissociated and organotypic cultures and found that a new axon arose from a mature dendrite. The regenerative response correlated with the length of the remaining stump: proximal axotomies (<35 microm) led to the transformation of a dendrite into an axon (identity change), whereas distal cuts (>35 microm) induced axon regrowth, similar to what is seen in young neurons. Searching for a putative landmark in the distal axon that could determine axon identity, we focused on the stability of microtubules, which regulate initial neuronal polarization during early development. We found that functionally polarized neurons contain a distinctively high proportion of stable microtubules in the distal axon. Moreover, pharmacological stabilization of microtubules was sufficient to induce the formation of multiple axons out of differentiated dendrites. Our data argue that mature neurons integrated in functional networks remain flexible in their polarity and that mechanisms acting during initial axon selection can be reactivated to induce axon growth out of functionally mature dendrites.     

Microtubules have opposite orientation in axons and dendrites of Drosophila neurons

In vertebrate neurons, axons have a uniform arrangement of microtubules with plus ends distal to the cell body (plus-end-out), and dendrites have equal numbers of plus- and minus-end-out microtubules. To determine whether microtubule orientation is a conserved feature of axons and dendrites, we analyzed microtubule orientation in invertebrate neurons. Using microtubule plus end dynamics, we mapped microtubule orientation in Drosophila sensory neurons, interneurons, and motor neurons. As expected, all axonal microtubules have plus-end-out orientation. However, in proximal dendrites of all classes of neuron, approximately 90% of dendritic microtubules were oriented with minus ends distal to the cell body. This result suggests that minus-end-out, rather than mixed orientation, microtubules are the signature of the dendritic microtubule cytoskeleton. Surprisingly, our map of microtubule orientation predicts that there are no tracks for direct cargo transport between the cell body and dendrites in unipolar neurons. We confirm this prediction, and validate the completeness of our map, by imaging endosome movements in motor neurons. As predicted by our map, endosomes travel smoothly between the cell body and axon, but they cannot move directly between the cell body and dendrites.     

The transport properties of axonal microtubules establish their polarity orientation

It is well established that axonal microtubules (MTs) are uniformly oriented with their plus ends distal to the neuronal cell body (Heidemann, S. R., J. M. Landers, and M. A. Hamborg. 1981. J. Cell Biol. 91:661-665). However, the mechanisms by which these MTs achieve their uniform polarity orientation are unknown. Current models for axon growth differ with regard to the contributions of MT assembly and transport to the organization and elaboration of the axonal MT array. Do the transport properties or assembly properties of axonal MTs determine their polarity orientation? To distinguish between these possibilities, we wished to study the initiation and outgrowth of axons under conditions that would arrest MT assembly while maintaining substantial levels of preexisting polymer in the cell body that could still be transported into the axon. We found that we could accomplish this by culturing rat sympathetic neurons in the presence of nanomolar levels of vinblastine. In concentrations of the drug up to and including 100 nM, the neurons actively extend axons. The vinblastine- axons are shorter than control axons, but clearly contain MTs. To quantify the effects of the drug on MT mass, we compared the levels of polymer throughout the cell bodies and axons of neurons cultured overnight in the presence of 0, 16, and 50 nM vinblastine with the levels of MT polymer in freshly plated neurons before axon outgrowth. Without drug, the total levels of polymer increase by roughly twofold. At 16 nM vinblastine, the levels of polymer are roughly equal to the levels in freshly plated neurons, while at 50 nM, the levels of polymer are reduced by about half this amount. Thus, 16 nM vinblastine acts as a "kinetic stabilizer" of MTs, while 50 nM results in some net MT disassembly. At both drug concentrations, there is a progressive increase in the levels of MT polymer in the axons as they grow, and a corresponding depletion of polymer from the cell body. These results indicate that highly efficient mechanisms exist in the neuron to transport preassembled MTs from the cell body into the axon. These mechanisms are active even at the expense of the cell body, and even under conditions that promote some MT disassembly in the neuron. MT polarity analyses indicate that the MTs within the vinblastine-axons, like those in control axons, are uniformly plus-end-distal.(ABSTRACT TRUNCATED AT 400 WORDS)     

Dynein is required for polarized dendritic transport and uniform microtubule orientation in axons

Axons and dendrites differ in both microtubule organization and in the organelles and proteins they contain. Here we show that the microtubule motor dynein has a crucial role in polarized transport and in controlling the orientation of axonal microtubules in Drosophila melanogaster dendritic arborization (da) neurons. Changes in organelle distribution within the dendritic arbors of dynein mutant neurons correlate with a proximal shift in dendritic branch position. Dynein is also necessary for the dendrite-specific localization of Golgi outposts and the ion channel Pickpocket. Axonal microtubules are normally oriented uniformly plus-end-distal; however, without dynein, axons contain both plus- and minus-end distal microtubules. These data suggest that dynein is required for the distinguishing properties of the axon and dendrites: without dynein, dendritic organelles and proteins enter the axon and the axonal microtubules are no longer uniform in polarity.     

Focal laser stimulation of fly nociceptors activates distinct axonal and dendritic Ca2+ signals

Drosophila class IV neurons are polymodal nociceptors that detect noxious mechanical, thermal, optical, and chemical stimuli. Escape behaviors in response to attacks by parasitoid wasps are dependent on class IV cells, whose highly branched dendritic arbors form a fine meshwork that is thought to enable detection of the wasp’s needle-like ovipositor barb. To understand how mechanical stimuli trigger cellular responses, we used a focused 405-nm laser to create highly localized lesions to probe the precise position needed to evoke responses. By imaging calcium signals in dendrites, axons, and soma in response to stimuli of varying positions, intensities, and spatial profiles, we discovered that there are two distinct nociceptive pathways. Direct stimulation to dendrites (the contact pathway) produces calcium responses in axons, dendrites, and the cell body, whereas stimulation adjacent to the dendrite (the noncontact pathway) produces calcium responses in the axons only. We interpret the noncontact pathway as damage to adjacent cells releasing diffusible molecules that act on the dendrites. Axonal responses have higher sensitivities and shorter latencies. In contrast, dendritic responses have lower sensitivities and longer latencies. Stimulation of finer, distal dendrites leads to smaller responses than stimulation of coarser, proximal dendrites, as expected if the contact response depends on the geometric overlap of the laser profile and the dendrite diameter. Because the axon signals to the central nervous system to trigger escape behaviors, we propose that the density of the dendritic meshwork is high not only to enable direct contact with the ovipositor but also to enable neuronal activation via diffusing signals from damaged surrounding cells. Dendritic contact evokes responses throughout the dendritic arbor, even to regions distant and distal from the stimulus. These dendrite-wide calcium signals may facilitate hyperalgesia or cellular morphological changes after dendritic damage.     

Modeling organelle transport in branching dendrites with a variable cross-sectional area

The purpose of this paper is to develop a method for calculating organelle transport in dendrites with a non-uniform cross-sectional area that depends on the distance from the neuron soma. The model is based on modified Smith–Simmons equations governing molecular motor-assisted organelle transport. The developed method is then applied to simulating organelle transport in branching dendrites with two particular microtubule (MT) orientations reported from experiments. It is found that the rate of organelle transport toward a dendrite’s growth cone heavily depends on the MT orientation, and since there is experimental evidence that the MT orientation in a particular region of a dendrite may depend on the dendrite’s developmental stage, the obtained results suggest that a rearrangement of the MT structure may depend on the amount of organelles needed at the growth cone.     

A composite model for establishing the microtubule arrays of the neuron

Neurons generate two distinct types of processes, termed axons and dendrites, both of which rely on a highly organized array of microtubules for their growth and maintenance. Axonal microtubules are uniformly oriented with their plus ends distal to the cell body, whereas dendritic microtubules are nonuniformly oriented. In neither case are the microtubules attached to the centrosome or any detectable structure that could establish their distinct patterns of polarity orientation. Studies from our laboratory over the past few years have led us to propose the following model for the establishment of the axonal and dendritic microtubule arrays. Microtubules destined for these processes are nucleated at the centrosome within the cell body of the neuron and rapidly released. The released microtubules are then transported into developing axons and dendrites to support their growth. Early in neuronal development, the microtubules are transported with their plus ends leading into immature processes that are the common progenitors of both axons and dendrites. This sets up a uniformly plus-end-distal pattern of polarity orientation, which is preserved in the developing axon. In the case of the dendrite, the plus-end-distal microtubules are joined by another population of microtubules that are transported into these processes with their minus-ends leading. Implicit in this model is that neurons have specialized machinery for regulating the release of microtubules from the centrosome and for transporting them with great specificity.     

Modelling organelle transport after traumatic axonal injury

This paper is motivated by recent experimental research (Tang-Schomer et al. 2012) on the formation of periodic varicosities in axons after traumatic brain injury (TBI). TBI leads to the formation of undulated distortions in the axons due to their dynamic deformation. These distortions result in the breakage of some microtubules (MTs) near the peaks of undulations. The breakage is followed by catastrophic MT depolymerisation around the broken ends. Although after relaxation axons regain their straight geometry, the structure of the axon after TBI is characterised by the presence of periodic regions where the density of MTs has been decreased due to depolymerisation. We modelled organelle transport in an axon segment with such a damaged MT structure and investigated how this structure affects the distributions of organelle concentrations and fluxes. The modelling results suggest that organelles accumulate at the boundaries of the region where the density of MTs has been decreased by depolymerisation. According to the model, the presence of such damaged regions decreases the organelle flux by only about 12%. This provides evidence that axon degradation after TBI may be caused by organelle accumulation rather than by starvation due to insufficient organelle flux.     

Fine structural characteristics and synaptic connections of trigeminocerebellar projection neurons in rat trigeminal nucleus oralis

In order to classify the presynaptic terminals contacting trigeminocerebellar projection neurons (TCPNs) in rat trigeminal nucleus oralis (Vo), electron-microscopic examination of sequential thin sections made from TCPNs located in the border zone (BZ) of Vo, labeled by the retrograde transport of horseradish peroxidase, was undertaken. The use of BZ TCPNs, labeled in Golgi-like fashion so that many of their dendrites and axons were visible, allowed for the determination of the distribution of each bouton type along the soma and dendrites, as well as for the characterization of the morphology and synaptic relations of the labeled axon and its terminals. Three types of axon terminals contacting labeled BZ TCPNs have been recognized, depending upon whether they contain primarily spherical-shaped, agranular synaptic vesicles (S endings); predominantly flattened, agranular synaptic vesicles (F endings); or a population of pleomorphic-shaped, agranular synaptic vesicles (P endings). The S endings represent the majority of axon terminals contacting labeled BZ TCPNs and establish asymmetrical axosomatic and axodendritic synaptic contacts. Many S endings are situated in one of two types of synaptic glomeruli. One type of glomerulus has a large S ending at its core, whereas the other contains a small S ending. Large-S-ending glomeruli include only labeled distal dendrites of BZ TCPNs; small-S-ending glomeruli contain either a labeled soma, proximal dendrite, or distal dendritic shaft. The remaining S endings are extraglomerular, synapsing on distal dendrites. P endings are less frequently encountered and establish intermediate axosomatic and axodendritic synapses. These endings exhibit a generalized distribution along the entire somatodendritic tree. F endings make symmetrical axodendritic synapses with distal dendrites, are only found in glomeruli containing small S endings, and are the least frequently observed ending contacting labeled BZ TCPNs. The majority of axonal endings synapsing on labeled BZ TCPNs are located along distal dendrites, with only a relatively few synapsing terminals situated on proximal dendrites and somata. The axons of labeled BZ TCPNs arise from the cell body and generally give rise to a single short collateral near their points of origin. This collateral remains unbranched and generates several boutons within BZ, while the parent axon acquires a myelin sheath and, without branching further, travels dorsolaterally toward the inferior cerebellar peduncle. The collateral boutons resemble extraglomerular S endings. They contain agranular, spherical-shaped synaptic vesicles and make asymmetrical axodendritic synapses with small-diameter unlabeled dendritic shafts in the BZ neuropil.     

Gamma-tubulin distribution in the neuron: implications for the origins of neuritic microtubules

Axons and dendrites contain dense microtubule (MT) assays that are not attached to a traditional MT nucleating structure such as the centrosome. Nevertheless, the MTs within these neurites are highly organized with respect to their polarity, and consist of a regular 13-protofilament lattice, the two known characteristics of MTs nucleated at the centrosome. These observations suggest either that axonal and dendritic MTs arise at the centrosome, or that they are nucleated locally, following a redistribution of MT nucleating material from the centrosome during neuronal development. To begin distinguishing between these possibilities, we have determined the distribution of gamma-tubulin within cultured sympathetic neurons. gamma-tubulin, a newly discovered protein which is specifically localized to the pericentriolar region of nonneuronal cells (Zheng, Y., M. K. Jung, and B. R. Oakley. 1991. Cell. 65:817-823; Stearns, T., L. Evans, and M. Kirschner. 1991. Cell. 65:825-836), has been shown to play a critical role in MT nucleation in vivo (Joshi, H. C., M. J. Palacios, L. McNamara, and D. W. Cleveland. 1992. Nature (Lond.). 356:80-83). Because the gamma-tubulin content of individual cells is extremely low, we relied principally on the high degree of resolution and sensitivity afforded by immunoelectron microscopy. Our studies reveal that, like the situation in nonneuronal cells, gamma-tubulin is restricted to the pericentriolar region of the neuron. Furthermore, serial reconstruction analyses indicate that the minus ends of MTs in both axons and dendrites are free of gamma-tubulin immunoreactivity. The absence of gamma-tubulin from the axon was confirmed by immunoblot analyses of pure axonal fractions obtained from explant cultures. The observation that gamma-tubulin is restricted to the pericentriolar region of the neuron provides compelling support for the notion that MTs destined for axons and dendrites are nucleated at the centrosome, and subsequently released for translocation into these neurites.     

The Yin–Yang of Dendrite Morphology: Unity of Actin and Microtubules

Actin and microtubules (MT) are targets of numerous molecular pathways that control neurite outgrowth. To generate a neuronal protrusion, coordinated structural changes of the actin and MT cytoskeletons must occur. Neurite formation occurs when actin filaments (F-actin) are destabilized, filopodia are extended, and MTs invade filopodia. This process results in either axon or dendrite formation. Axonal branching involves interplay between F-actin and MTs, with F-actin and MTs influencing polymerization, stabilization, and maintenance of each other. Our knowledge of the mechanisms regulating development of the axon, however, far eclipses our understanding of dendritic development and branching. The two classes of neurites, while fundamentally similar in their ability to elongate and branch, dramatically differ in growth rate, orientation of polarized MT bundles, and mechanisms that initiate branching. In this review, we focus on how F-actin, MTs, and proteins that link the two cytoskeletons coordinate to specifically initiate dendritic events. Penelope C. Georges and Norell M. Hadzimichalis contributed equally.     

Quantitative analysis of microtubule transport in growing nerve processes

In neurons, tubulin is synthesized primarily in the cell body, whereas the molecular machinery for neurite extension and elaboration of microtubule (MT) array is localized to the growth cone region. This unique functional and biochemical compartmentalization of neuronal cells requires transport mechanisms for the delivery of newly synthesized tubulin and other cytoplasmic components from the cell body to the growing axon. According to the polymer transport model, tubulin is transported along the axon as a polymer. Because the majority of axonal MTs are stationary at any given moment, it has been assumed that only a small fraction of MTs translocates along the axon by saltatory movement reminiscent of the fast axonal transport. Such intermittent "stop and go" MT transport has been difficult to detect or to exclude by using direct video microscopy methods. In this study, we measured the translocation of MT plus ends in the axonal shaft by expressing GFP-EB1 in Xenopus embryo neurons in culture. Formal quantitative analysis of MT assembly/disassembly indicated that none of the MTs in the axonal shaft were rapidly transported. Our results suggest that transport of axonal MTs is not required for delivery of newly synthesized tubulin to the growing nerve processes.     

Effect of the degree of polar mismatching on traffic jam formation in fast axonal transport

This paper simulates an axon with a region of reversed microtubule (MT) polarity, and investigates how the degree of polar mismatching in this region affects the formation of organelle traps in the axon. The model is based on modified Smith–Simmons equations governing molecular-motor-assisted transport in neurons. It is established that the structure that develops as a result of a region with disoriented MTs consists of two organelle traps, the trap to the left of this region accumulates plus-end-oriented organelles and the trap to the right of this region accumulates minus-end-oriented organelles. The presence of such a structure is shown to inhibit the transport of organelles down the axon. The degree by which the transport of organelles is inhibited depends on the degree of polar mismatching of MTs in the region between MT traps. Four cases with a different degree of polar mismatching are investigated.     

Processes induced by tau expression in Sf9 cells have an axon-like microtubule organization

We have indirectly analyzed the role of tau in generating the highly organized microtubule (MT) array of the axon. Axons contain MT arrays of uniform polarity orientation, plus ends distal to the cell body (Heidemann, S. R., J. M. Landers, and M. A. Hamborg. 1981. J. Cell Biol. 91:661-673). Surprisingly, these MTs do not radiate from a single discrete nucleating structure in the cell body (Sharp, G. A., K. Weber, and M. Osborn. 1982. Eur. J. Cell Biol. 29: 97-103), but rather stop and start at multiple sites along the length of the axon (Bray, D., and M. B. Bunge. 1981. J. Neurocytol. 10:589-605). When Sf9 ovarian cells are induced to express high levels of tau protein, they develop cellular processes which are similar in appearance to axons and which contain dense arrays of MTs (Knops, J., K. S. Kosik, G. Lee, J. D. Pardee, L. Cohen-Gould, and L. McConlogue. 1991. J. Cell Biol. 114:725-734). We have analyzed the organization of MTs within these arrays, and determined it to be similar, but not identical, to the organization of MTs within the axon. The caliber, MT number, and MT density vary significantly from process to process, but on average are manyfold higher in the tau-induced processes than typically found in axons. Greater than 89% of the MTs in the processes are oriented with their plus ends distal to the cell body, and this proportion is even higher in the processes that are most similar to axons with regard to caliber, MT number, and MT density. Similar to the situation in the axon, MTs are discontinuous along the length of the tau-induced processes, and do not emanate from any observable nucleating structure in the cell body. We have also identified bundles of MTs throughout the cell bodies of the Sf9 cells induced to express tau. Similar to the MT arrays in the processes, these MT bundles are not visibly associated with any other cytological structures that might regulate their polarity orientation. Nevertheless, these bundles consist of MTs most (greater than 82%) of which have the same polarity orientation. Collectively, these results suggest that tau may play a fundamental role in generating MT organization in the axon. In particular, a key property of tau may be to bundle MTs preferentially with the same polarity orientation.     

Modeling anterograde and retrograde transport of short mobile microtubules from the site of axonal branch formation

This theoretical research is motivated by a recent model of microtubule (MT) transport put forward by Baas and Mozgova (Cytoskeleton 69:416–425, 2012). According to their model, in an axon all plus-end-distal mobile MTs move anterogradely while all minus-end-distal mobile MTs move retrogradely. Retrograde MT transport thus represents a mechanism by which minus-end-distal MTs are removed from the axon. We suggested equations that implement Baas and Mozgova’s model. We employed these equations to simulate transport of short mobile MTs from a region (such as the site of axonal branch formation) where MT severing activity results in generation of a large number of short MTs of both orientations. We obtained the exact and approximate transient solutions of these equations utilizing the Laplace transform technique. We applied the obtained solutions to calculate the average rates of anterograde and retrograde transport of short MTs.