Antidromic propagation of action potentials in branched axons: implications for the mechanisms of action of deep brain stimulation

Electrical stimulation of the central nervous system creates both orthodromically propagating action potentials, by stimulation of local cells and passing axons, and antidromically propagating action potentials, by stimulation of presynaptic axons and terminals. Our aim was to understand how antidromic action potentials navigate through complex arborizations, such as those of thalamic and basal ganglia afferents-sites of electrical activation during deep brain stimulation. We developed computational models to study the propagation of antidromic action potentials past the bifurcation in branched axons. In both unmyelinated and myelinated branched axons, when the diameters of each axon branch remained under a specific threshold (set by the antidromic geometric ratio), antidromic propagation occurred robustly; action potentials traveled both antidromically into the primary segment as well as "re-orthodromically" into the terminal secondary segment. Propagation occurred across a broad range of stimulation frequencies, axon segment geometries, and concentrations of extracellular potassium, but was strongly dependent on the geometry of the node of Ranvier at the axonal bifurcation. Thus, antidromic activation of axon terminals can, through axon collaterals, lead to widespread activation or inhibition of targets remote from the site of stimulation. These effects should be included when interpreting the results of functional imaging or evoked potential studies on the mechanisms of action of DBS.     

A quantitative study of microtubules in motor and sensory axons

The number, density and distribution of microtubules were compared in the myelinated motor and sensory axons of the spinal roots of lizard (Lacerta muralis). In both motor and sensory axons the average number and density of microtubules were found to be related to the axonal size: the average number of microtubules rose, while the microtubular density decreased with an increase in the cross-sectional area of the axon. More precisely, a linear relationship was observed between the logarithm of the microtubular density and the cross-sectional area of the axon. No significant differences in the microtubular number and density were found between motor and sensory axons of corresponding size. Microtubules were unevenly distributed throughout the cross section of both motor and sensory axons. In particular, a nonaccidental association between microtubules and mitochondria was found in both axon types.     

Synaptic potential in the motor giant axon of the crayfish

Some electrical properties of the synapses between central giant axons (presynaptic) and the motor giant axon (postsynaptic) of the crayfish abdominal nerve cord have been investigated. Postsynaptic potential change in response to presynaptic volleys contains two components: a spike potential and a synaptic potential of very long time course. Amplitude of the synaptic potential is graded according to the number of active presynaptic axons. Conductance increase in the synaptic membrane endures over most of the period of potential change, and it is this rather than the "electrical time constant" of the membrane that in large measure determines the form of the synaptic potential. Temporal summation of synaptic potential occurs during repetitive presynaptic stimulation, and after such stimulation the rate of decay of synaptic potential is greatly slowed.     

Simple models of stimulation of neurones in the brain by electric fields

The excitation of pyramidal cells in the motor cortex, produced by electric fields generated by distant electrodes or by electromagnetic induction, has been modelled. Linear, steady-state models of myelinated axons capture most of the geometrical aspects of neurone activation in electric fields. Some non-linear features can be approximated. Models with a proximal sealed-end and distal infinite axon, or of finite length, are both serviceable. Surface anodal stimulation produces hyperpolarisation of the proximal axon (closest to the anode) and depolarisation in the distal axon. The point of maximum depolarisation can be influenced by the location of the cathode (greater separation of anode and cathode causes more distal depolarisation). Axon bends can produce very localised depolarisation. Cathodal stimulation may be less effective than anodal as a result of anodal block of conduction of action potentials in the distal axon. The latencies of responses to anodal stimulation, recorded in the distal axon, will decrease as the stimulus strength is increased and the point of action potential initiation moves distally node by node. Larger jumps in latency will be produced when the point of action potential initiation moves from one axon bend to another.     

Innervation of developing intrafusal muscle fibers in the rat

The chronology of development of spindle neural elements was examined by electron microscopy in fetal and neonatal rats. The three types of intrafusal muscle fiber of spindles from the soleus muscle acquired sensory and motor innervation in the same sequence as they formed--bag2, bag1, and chain. Both the primary and secondary afferents contacted developing spindles before day 20 of gestation. Sensory endings were present on myoblasts, myotubes, and myofibers in all intrafusal bundles regardless of age. The basic features of the sensory innervation--first-order branching of the parent axon, separation of the primary and secondary sensory regions, and location of both primary and secondary endings beneath the basal lamina of the intrafusal fibers--were all established by the fourth postnatal day. Cross-terminals, sensory terminals shared by more than one intrafusal fiber, were more numerous at all developmental stages than in mature spindles. No afferents to immature spindles were supernumerary, and no sensory axons appeared to retract from terminations on intrafusal fibers. The earliest motor axons contacted spindles on the 20th day of gestation or shortly afterward. More motor axons supplied the immature spindles, and a greater number of axon terminals were visible at immature intrafusal motor endings than in adult spindles; hence, retraction of supernumerary motor axons accompanies maturation of the fusimotor system analogous to that observed during the maturation of the skeletomotor system. Motor endings were observed only on the relatively mature myofibers; intrafusal myoblasts and myotubes lacked motor innervation in all age groups. This independence of the early stages of intrafusal fiber assembly from motor innervation may reflect a special inherent myogenic potential of intrafusal myotubes or may stem from the innervation of spindles by sensory axons.     

Axon guidance and somites

The segmental arrangement of spinal nerves in higher vertebrate embryos provides a simple system in which to study the factors that influence axon pathfinding. Developing motor and sensory axons are intimately associated with surrounding tissues that direct axon guidance. We argue that two distinct guidance mechanisms, viz. contact repulsion and chemorepulsion, act simultaneously to prescribe spinal axon trajectories by ’surround-repulsion’. Motor and sensory axons grow freely within the anterior half of each mesodermal somite, because they are excluded from posterior half-somites by contact repulsion. By contrast, the dorsoventral trajectory that bipolar sensory axons of the dorsal root ganglia follow is governed by diffusible repellents originating from the notochord medially and dermamyotome laterally. Even though spinal nerve development appears to be a simple system for elucidating axon guidance mechanisms, many distinct candidate guidance molecules have been implicated and their relative contributions remain to be evaluated. Received: 28 May 1997 / Accepted: 27 June 1997     

Dynein-dynactin function and sensory axon growth during Drosophila metamorphosis: A role for retrograde motors

Mutations in the genes for components of the dynein-dynactin complex disrupt axon path finding and synaptogenesis during metamorphosis in the Drosophila central nervous system. In order to better understand the functions of this retrograde motor in nervous system assembly, we analyzed the path finding and arborization of sensory axons during metamorphosis in wild-type and mutant backgrounds. In wild-type specimens the sensory axons first reach the CNS 6-12 h after puparium formation and elaborate their terminal arborizations over the next 48 h. In Glued1 and Cytoplasmic dynein light chain mutants, proprioceptive and tactile axons arrive at the CNS on time but exhibit defects in terminal arborizations that increase in severity up to 48 h after puparium formation. The results show that axon growth occurs on schedule in these mutants but the final process of terminal branching, synaptogenesis, and stabilization of these sensory axons requires the dynein-dynactin complex. Since this complex functions as a retrograde motor, we suggest that a retrograde signal needs to be transported to the nucleus for the proper termination of some sensory neurons.     

Spinal nerve segmentation in the chick embryo: analysis of distinct axon-repulsive systems

In higher vertebrates, the segmental organization of peripheral spinal nerves is established by a repulsive mechanism whereby sensory and motor axons are excluded from the posterior half-somite. A number of candidate axon repellents have been suggested to mediate this barrier to axon growth, including Sema3A, Ephrin-B, and peanut agglutinin (PNA)-binding proteins. We have tested the candidacy of these factors in vitro by examining their contribution to the growth cone collapse-inducing activity of somite-derived protein extracts on sensory, motor, and retinal axons. We find that Sema3A is unlikely to play a role in the segmentation of sensory or motor axons and that Ephrin-B may contribute to motor but not sensory axon segmentation. We also provide evidence that the only candidate molecule(s) that induces the growth cone collapse of both sensory and motor axons binds to PNA and is not Sema3A or Ephrin-B. By grafting primary sensory, motor, and quail retinal neurons into the chick trunk in vivo, we provide further evidence that the posterior half-somite represents a universal barrier to growing axons. Taken together, these results suggest that the mechanisms of peripheral nerve segmentation should be considered in terms of repellent molecules in addition to the identified molecules.     

Identified motor terminals in Drosophila larvae show distinct differences in morphology and physiology

In Drosophila, the type I motor terminals innervating the larval ventral longitudinal muscle fibers 6 and 7 have been the most popular preparation for combining synaptic studies with genetics. We have further characterized the normal morphological and physiological properties of these motor terminals and the influence of muscle size on terminal morphology. Using dye-injection and physiological techniques, we show that the two axons supplying these terminals have different innervation patterns: axon 1 innervates only muscle fibers 6 and 7, whereas axon 2 innervates all of the ventral longitudinal muscle fibers. This difference in innervation pattern allows the two axons to be reliably identified. The terminals formed by axons 1 and 2 on muscle fibers 6 and 7 have the same number of branches; however, axon 2 terminals are approximately 30% longer than axon 1 terminals, resulting in a corresponding greater number of boutons for axon 2. The axon 1 boutons are approximately 30% wider than the axon 2 boutons. The excitatory postsynaptic potential (EPSP) produced by axon 1 is generally smaller than that produced by axon 2, although the size distributions show considerable overlap. Consistent with vertebrate studies, there is a correlation between muscle fiber size and terminal size. For a single axon, terminal area and length, the number of terminal branches, and the number of boutons are all correlated with muscle fiber size, but bouton size is not. During prolonged repetitive stimulation, axon 2 motor terminals show synaptic depression, whereas axon 1 EPSPs facilitate. The response to repetitive stimulation appears to be similar at all motor terminals of an axon.     

Anatomical coupling of sensory and motor nerve trajectory via axon tracking

It is a long-standing question how developing motor and sensory neuron projections cooperatively form?a common principal grid of peripheral nerve pathways relaying behavioral outputs and somatosensory inputs. Here, we explored this issue through targeted cell lineage and gene manipulation in mouse, combined with in?vitro live axon imaging. In the absence of motor projections, dorsal (epaxial) and ventral (hypaxial) sensory projections form in a randomized manner, while removal of EphA3/4 receptor tyrosine kinases expressed by epaxial motor axons triggers selective failure to form epaxial sensory projections. EphA3/4 act non-cell-autonomously by inducing sensory axons to track along preformed epaxial motor projections. This involves cognate ephrin-A proteins on sensory axons but is independent from EphA3/4 signaling in motor axons proper. Assembly of peripheral nerve pathways thus involves motor axon subtype-specific signals that couple sensory projections to discrete motor pathways.     

Modelling the Effects of Electrical Coupling between Unmyelinated Axons of Brainstem Neurons Controlling Rhythmic Activity

Gap junctions between fine unmyelinated axons can electrically couple groups of brain neurons to synchronise firing and contribute to rhythmic activity. To explore the distribution and significance of electrical coupling, we modelled a well analysed, small population of brainstem neurons which drive swimming in young frog tadpoles. A passive network of 30 multicompartmental neurons with unmyelinated axons was used to infer that: axon-axon gap junctions close to the soma gave the best match to experimentally measured coupling coefficients; axon diameter had a strong influence on coupling; most neurons were coupled indirectly via the axons of other neurons. When active channels were added, gap junctions could make action potential propagation along the thin axons unreliable. Increased sodium and decreased potassium channel densities in the initial axon segment improved action potential propagation. Modelling suggested that the single spike firing to step current injection observed in whole-cell recordings is not a cellular property but a dynamic consequence of shunting resulting from electrical coupling. Without electrical coupling, firing of the population during depolarising current was unsynchronised; with coupling, the population showed synchronous recruitment and rhythmic firing. When activated instead by increasing levels of modelled sensory pathway input, the population without electrical coupling was recruited incrementally to unpatterned activity. However, when coupled, the population was recruited all-or-none at threshold into a rhythmic swimming pattern: the tadpole “decided” to swim. Modelling emphasises uncertainties about fine unmyelinated axon physiology but, when informed by biological data, makes general predictions about gap junctions: locations close to the soma; relatively small numbers; many indirect connections between neurons; cause of action potential propagation failure in fine axons; misleading alteration of intrinsic firing properties. Modelling also indicates that electrical coupling within a population can synchronize recruitment of neurons and their pacemaker firing during rhythmic activity.     

Diverse mechanisms for assembly of branchiomeric nerves

The formation of branchiomeric nerves (cranial nerves V, VII, IX and X) from their sensory, motor and glial components is poorly understood. The current model for cranial nerve formation is based on the Vth nerve, in which sensory afferents are formed first and must enter the hindbrain in order for the motor efferents to exit. Using transgenic zebrafish lines to discriminate between motor neurons, sensory neurons and peripheral glia, we show that this model does not apply to the remaining three branchiomeric nerves. For these nerves, the motor efferents form prior to the sensory afferents, and their pathfinding show no dependence on sensory axons, as ablation of cranial sensory neurons by ngn1 knockdown had no effect. In contrast, the sensory limbs of the IXth and Xth nerves (but not the Vth or VIIth) were misrouted in gli1 mutants, which lack hindbrain bmn, suggesting that the motor efferents are crucial for appropriate sensory axon projection in some branchiomeric nerves. For all four nerves, peripheral glia were the intermediate component added and had a critical role in nerve integrity but not in axon guidance, as foxd3 null mutants lacking peripheral glia exhibited defasciculation of gVII, gIX, and gX axons. The bmn efferents were unaffected in these mutants. These data demonstrate that multiple mechanisms underlie formation of the four branchiomeric nerves. For the Vth, sensory axons initiate nerve formation, for the VIIth the sensory and motor limbs are independent, and for the IXth/Xth the motor axons initiate formation. In all cases the glia are patterned by the initiating set of axons and are needed to maintain axon fasciculation. These results reveal that coordinated interactions between the three neural cell types in branchiomeric nerves differ according to their axial position.     

Differential survival of isolated portions of crayfish axons

Summary Electron microscopic studies show that transplanted segments of sensory axons of varying lengths degenerate within 7–14 days whereas transplanted segments of crustacean motor axons survive morphologically intact for 20–30 days. The middle portion of an isolated motor axon segment degenerates less rapidly than portions of the same axon located nearer the periphery or nearer the ventral nerve cord. One week after transplantation, glial cells appear to phagocytize sensory axons whereas glial cells around motor axons appear to hypertrophy and to have more rough endoplasmic reticulum. After three weeks, motor axons also appear to be phagocytized by glial cells.These data suggest that the glia surrounding isolated motor axons can change from a supportive to a destructive function, whereas glial cells surrounding severed sensory axons primarily have a destructive function. These and other data also indicate that crustacean motor axons receive significant trophic inputs from their own perikaryon, from post-synaptic contacts, and from adjacent glial cells. The possibility that adjacent healthy cells may supply metabolically deficient cells with needed substances could be a significant adaptive advantage for the evolution of multicellular organisms.Supported in part by an NIH grant (NS-1186101) to Dr. BittnerThe authors wish to thank Mr. Martis Ballinger and Mr. Robert Riess for their valuable assistance in all stages of this research     

Axonal degeneration within the tympanal nerve of Schistocerca gregaria

This study describes time course and ultrastructural changes during axonal degeneration of different neurones within the tympanal nerve of the locust Schistocerca gregaria. The tympanal nerve innervates the tergit and pleurit of the first abdominal segment and contains the axons of both sensory and motor neurones. The majority of axons (approx. 97%) belong to several types of sensory neurones: mechano- and chemosensitive hair sensilla, multipolar neurones, campaniform sensilla and sensory cells of a scolopidial organ, the auditory organ. Axons of campaniform sensilla, of auditory sensory cells and of motor neurones are wrapped by glial cell processes. In contrast, the very small and numerous axons (diameter <1 microm) of multipolar neurones and hair sensilla are not separated individually by glia sheets. Distal parts of sensory and motor axons show different reactions to axotomy: 1 week after separation from their somata, distal parts of motor axons are invaded by glial cell processes. This results in fascicles of small axon bundles. In contrast, distal parts of most sensory axons degenerate rapidly after being lesioned. The time to onset of degeneration depends on distance from the lesion site and on the type of sensory neurone. In axons of auditory sensory neurones, ultrastructural signs of degeneration can be found as soon as 2 days after lesion. After complete lysis of distal parts of axons, glial cell processes invade the space formerly occupied by sensory axons. The rapid degeneration of distal auditory axon parts allows it to be excluded that they provide a structure that leads regenerating axons to their targets. Proximal parts of severed axons do not degenerate.     

Eph:ephrin-B1 forward signaling controls fasciculation of sensory and motor axons

Axon fasciculation is one of the processes controlling topographic innervation during embryonic development. While axon guidance steers extending axons in the accurate direction, axon fasciculation allows sets of co-extending axons to grow in tight bundles. The Eph:ephrin family has been involved both in axon guidance and fasciculation, yet it remains unclear how these two distinct types of responses are elicited. Herein we have characterized the role of ephrin-B1, a member of the ephrinB family in sensory and motor innervation of the limb. We show that ephrin-B1 is expressed in sensory axons and in the limb bud mesenchyme while EphB2 is expressed in motor and sensory axons. Loss of ephrin-B1 had no impact on the accurate dorso-ventral innervation of the limb by motor axons, yet EfnB1 mutants exhibited decreased fasciculation of peripheral motor and sensory nerves. Using tissue-specific excision of EfnB1 and in vitro experiments, we demonstrate that ephrin-B1 controls fasciculation of axons via a surround repulsion mechanism involving growth cone collapse of EphB2-expressing axons. Altogether, our results highlight the complex role of Eph:ephrin signaling in the development of the sensory-motor circuit innervating the limb.     

Responses of Retinal Ganglion Cells to Extracellular Electrical Stimulation,from Single Cell to Population: Model-Based Analysis

Retinal ganglion cells (RGCs), which survive in large numbers following neurodegenerative diseases, could be stimulated with extracellular electric pulses to elicit artificial percepts. How do the RGCs respond to electrical stimulation at the sub-cellular level under different stimulus configurations, and how does this influence the whole-cell response? At the population level, why have experiments yielded conflicting evidence regarding the extent of passing axon activation? We addressed these questions through simulations of morphologically and biophysically detailed computational RGC models on high performance computing clusters. We conducted the analyses on both large-field RGCs and small-field midget RGCs. The latter neurons are unique to primates. We found that at the single cell level the electric potential gradient in conjunction with neuronal element excitability, rather than the electrode center location per se, determined the response threshold and latency. In addition, stimulus positioning strongly influenced the location of RGC response initiation and subsequent activity propagation through the cellular structure. These findings were robust with respect to inhomogeneous tissue resistivity perpendicular to the electrode plane. At the population level, RGC cellular structures gave rise to low threshold hotspots, which limited axonal and multi-cell activation with threshold stimuli. Finally, due to variations in neuronal element excitability over space, following supra-threshold stimulation some locations favored localized activation of multiple cells, while others favored axonal activation of cells over extended space.     

The Nodes of Ranvier: Molecular Assembly and Maintenance

Action potential (AP) propagation in myelinated nerves requires clustered voltage gated sodium and potassium channels. These channels must be specifically localized to nodes of Ranvier where the AP is regenerated. Several mechanisms have evolved to facilitate and ensure the correct assembly and stabilization of these essential axonal domains. This review highlights the current understanding of the axon intrinsic and glial extrinsic mechanisms that control the formation and maintenance of the nodes of Ranvier in both the peripheral nervous system (PNS) and central nervous system (CNS).Axons conduct electrical signals, called action potentials (APs), among neurons in a circuit in response to sensory input, and between motor neurons and muscles. In mammals and other vertebrates, many axons are myelinated. Myelin, made by Schwann cells and oligodendrocytes in the peripheral nervous system (PNS) and central nervous system (CNS), respectively, is a multilamellar sheet of glial membrane that wraps around axons to increase transmembrane resistance and decrease membrane capacitance. Although myelin is traditionally viewed as a passive contributor to nervous system function, it is now recognized that myelinating glia also play many active roles including regulation of axon diameter, axonal energy metabolism, and the clustering of ion channels at gaps in the myelin sheath called nodes of Ranvier. Together, the active and passive properties conferred on axons by myelin, result in axons with high AP conduction velocities, low metabolic demands, and reduced space requirements as compared with unmyelinated axons. Thus, myelin and the clustering of ion channels in axons permitted the evolution of the complex nervous systems found in vertebrates. This review highlights the current understanding of the axonal intrinsic and glial extrinsic mechanisms that control the formation and maintenance of the nodes of Ranvier in both the PNS and CNS.     

Computation of action potential propagation and presynaptic bouton activation in terminal arborizations of different geometries.

Action potential propagation in axons with bifurcations involving short collaterals with synaptic boutons has been simulated using SPICE, a general purpose electrical circuit simulation program. The large electrical load of the boutons may lead to propagation failure at otherwise uncritical geometric ratios. Because the action potential gradually fails while approaching the branch point, the electrotonic spread of the failing action potential cannot depolarize the terminal boutons above an assumed threshold of 20 mV (Vrest = 0 mV) for the presynaptic calcium inflow, and therefore fails to evoke transmitter release even for boutons attached at short collaterals. For even shorter collaterals the terminal boutons can again be activated by the spread of passive current reflected at the sealed end of the bouton which increases the membrane potential above firing threshold. The action potential is then propagated in anterograde fashion into the main axon and may activate the terminal bouton on the other collateral. Differential activation of the synaptic boutons can be observed without repetitive activation of the main axon and with the assumption of uniform membrane properties. Axon enlargements above a critical size at branch points can increase the safety factor for propagation significantly and may serve a double function: they can act both as presynaptic boutons and as boosters, facilitating invasion of the action potential into the terminal arborizations. The architecture of the terminal arborizations has a profound effect on the activation pattern of synapses, suggesting that terminal arborizations not only distribute neural information to postsynaptic cells but may also be able to process neural information presynaptically.     

Netrin-3 protein is localized to the axons of motor, sensory, and sympathetic neurons

The netrin family of axon guidance cues has been shown to play a pivotal role in the guidance of a variety of axon projections during embryonic development, both in the vertebrate and invertebrate. While the guidance potential of netrin-1 has been examined in depth in many regions of the developing mouse brain very little information is available on the expression and activity of netrin-3. Here we show that the netrin-3 protein is present on motor neurons and subpopulations of neurons within sensory and sympathetic ganglia. Moreover, significant levels of netrin-3 protein were found to be associated with the axons projecting from these neurons suggesting a role for netrin-3 in axon pathfinding and fasciculation within the peripheral nervous system.