Anatomical basis for an apparent paradox concerning conduction velocities of two identified axons in Aplysia.

Larger axons usually have faster conduction velocities, lower thresholds, and larger extracellular action potentials than smaller axons. However, it has been shown that the largest fiber, R2, in the right pleurovisceral connective of the marine mollusc, Aplysia, has a higher threshold and a slower conduction velocity than does the smaller axon of cell RI, even though the amplitude of R2's spike is larger than R1's spike. One explanation of this apparent parodox is that the two axons have different "intrinsic membrane and axoplasmic constants" (Goldman, L. (1961), J. Cell Comp. Physiol. 57: 185-191). However, the deep infolding of R2's axonal membrane suggested that differences in the shape of the two axons might also account for the paradox. Accordingly, we measured the conduction velocities of the two axons and then examined the same axons in the electron microscope in order to measure their volumes and surface areas. Our morphological observations indicate that the extensive infolding of surface membrane causes R2 to have a smaller volume to surface area ratio than R1. Thus, since conduction velocity is proportional to the square root of the volume to surface area ratio (Hodgkin, A.L. (1954), J. Physiol. 125: 221-224), it is predictable that the smaller axon would have a faster conduction velocity. The results suggest that the paradoxical conduction velocities can be explained largely as resulting from differences in the shapes of the two axons. However, certain discrepancies between the measured and the predicted values suggest that other factors are contributing as well.     

The velocity of conduction in nerve fiber and its electric characteristics

The theory developed in this paper shows that the propagation of spike potential along a nerve fiber and the conduction of an electric wave along an inert inorganic conductor follow a common quantitative relationship. This result gives further support to the belief that propagation of excitation is an electrical process. The basic idea of the theory is derived from the consideration that velocity has, by its mathematical definition, a local meaning; conduction in a nerve is completely determined by the local characteristics of the latter, as well as those of the wave. The final formula derived does not make use of any other field of science beyond the fundamental principles of electricity. It gives the conduction velocity in terms of the electric characteristics of the fiber and of the duration of the spike potential. The formula is in agreement with the known dependence of the conduction velocity on various parameters characterizing the axon. The computed velocity agrees with the measured ones on the squid giant axon, crab nerve axon, frog muscle fiber and Nitella cell. The membrane inductance appears as a velocity controling agent which prevents also a possible distortion of the spike potential during conduction. The structural meaning of the electric characteristics of the axon membrane is discussed from the viewpoint of the diffusion theory. A formula for the velocity of spread of the electrotonus is also derived.     

Nerve conduction theory: Some mathematical consequences of Bernstein's model

The generally accepted permeability theory of nerve conduction is presented in mathematical form. The resulting velocity formula is found to agree well with data on squid giant axon, but predicts velocities considerably too high in the case ofNitella. The dependence of velocity on fiber diameter is discussed for both medullated and non-medullated nerve, it being shown theoretically that velocity is proportional to the square root of diameter for non-medullated and to the diameter for medullated nerve. The equations relating the shape of the action spike to the observed permeability changes are given but are not solved.     

Computation of Impulse Conduction in Myelinated Fibers; Theoretical Basis of the Velocity-Diameter Relation

For myelinated fibers, it is experimentally well established that spike conduction velocity is proportional to fiber diameter. However no really satisfactory theoretical treatment has been proposed. To treat this problem a theoretical axon was described consisting of lengths of passive leaky cable (internode) regularly interrupted by short isopotential patches of excitable membrane (node). The nodal membrane was assumed to obey the Frankenhaeuser-Huxley equations. The explicit diameter dependencies of the various parameters were incorporated into the equations. The fiber diameter to axon diameter ratio was taken to be constant, and the internode length was taken to be proportional to the fiber diameter. Both these conditions reflect the situation that exists in real, experimental fibers. Dimensional analysis shows that these anatomical conditions are equivalent to Rushton's (1951) assumption of corresponding states. Hence, conduction velocity will be proportional to fiber diameter, in complete agreement with the experimental findings. Digital computer solutions of these equations were made in order to compute a set of actual velocities. Computations made with constant internode length or constant myelin thickness (i.e., nonconstant fiber diameter to axon diameter ratio) did not show linearity of the velocity-diameter relation.     

Preface

The physiological function of the axon is to conduct short all-or-none action potentials from their site of initiation (usually the cell body) to the synapse. To ensure this function, both passive and active biophysical properties of the axons are tuned very precisely, especially the voltage-dependent ionic conductances to sodium and potassium. Under normal conditions, axons are not spontaneously active. Minor modifications of their ionic micro-environment or slight changes in the membrane properties are however sufficient to induce rhythmical activity and modify the time course of the action potentials. These modifications can be induced by a variety of pharmacological agents. Some typical examples taken from original studies on invertebrate preparations are illustrated. The experiments were carried out on two axonal preparations: the giant axon of the squid Loligo forbesi and the giant axon of the cockroach Periplaneta americana. The axons were ‘space-clamped’ and studied under both current-clamp and voltage-clamp conditions. Voltage-clamp experiments were used to dissect out the mechanisms underlying repetitive activity and to extract the relevant parameters. These parameters were then used to rebuild the observed effects using an extended version of the Hodgkin and Huxley (1952, J Physiol (Lond) 117, 500–544) formulation. One easy way to get repetitive firing in both preparations is to reduce potassium conductance. The effect of 4-aminopyridine on squid axon is illustrated here. The experimental results, including the occurrence of bursts of activity, can be described by adding a time- and voltage-dependent block of the potassium channels to the original Hodgkin and Huxley (1952, J Physiol (Lond) 117, 500–544) model. Repetitive spike activity and plateau action potentials are also produced when the depolarising effect of the voltage-dependent potassium current is counterbalanced by a maintained inward sodium current. This maintained sodium current can be due to several different mechanisms. This will be illustrated by five structurally unrelated molecules: two scorpion toxins, two insecticide molecules and one sea anemone toxin. One toxin purified from the venom of the scorpion Buthotus judaïcus (insect toxin 1) exerts its effects by shifting the sodium activation curve towards more hyperpolarized potentials. Another toxin purified from the venom of another scorption Androctonus australis (mammal toxin 1) modifies a significant proportion of normal (fast) sodium channels into slowly activating and inactivating sodium channels. The main effect of the insecticide DDT is to maintain sodium channels in the ‘open’ configuration. Another insecticide molecule known to induce repetitive activity, S-bioallethrin, activates voltage-dependent sodium channels with slow activation and inactivation kinetics. The sea anemone toxin anthopleurin A, purified from the venom of Anthopleura xanthogrammica, delays inactivation of the sodium current without changing its activation kinetics. These examples show that minor modifications of the properties of the nerve membrane are sufficient to alter nerve function. These deleterious effects will be amplified at the synapse through dramatic changes in transmitter release and will lead eventually to disastrous alterations of brain function.     

Oscillation and Repetitive Firing in Squid Axons : Comparison of experiments with computations

Space-clamped squid axons treated with low calcium and computed Hodgkin-Huxley (HH) axons were stimulated by steps of superthreshold current from 101 to 400% of the rheobasic value over a temperature range of 5–27°C. The natural frequency of sustained repetitive firing of real and computed axons depended weakly upon stimulus intensity and strongly upon temperature, with a Q₁₀ of 2.7 (experimental) and 2.6 (computed). For real axons, but not the computed axon, the intervals between the first two spikes were shorter than between subsequent spikes. Constant spike frequencies from 75 Hz at low intensities and temperatures to 330 Hz at high intensities and temperatures were soon achieved. Subthreshold and superthreshold responses were sometimes intermixed in a train of responses from a real axon responding to a constant step of current, but not predicted by HH. The time interval following a spike was always longer than that following a subthreshold oscillation in slightly decalcified real axons, as Huxley and FitzHugh also found for computed axons. There was a bias toward spikes at the beginning of the train and toward subthreshold responses later on. Some repeated patterns were found, every second, third, or fourth response being a spike. Neither the HH equations nor the computed or experimental threshold behaviors show a critical temperature to support a membrane phase transition.     

Relative Conduction Velocities of Small Myelinated and Non-myelinated Fibres in the Central Nervous System

IN peripheral nerve, most axons with diameters of less than 1 µm do not have myelin sheaths, while most fibres more than 1 µm in diameter are myelinated^1,2. In the central nervous system, axons as small as 0.2 µm in diameter may be myelinated^2–5. In his paper on the effects of myelin on conduction velocity, Rushton⁶ concluded that 1 µm is the “critical diameter” above which “myelin increases conduction velocity” and below which “conduction is faster without myelination”. This conclusion is referred to widely (see, for example, refs. 7–9). In this communication we demonstrate that the analysis leading to this conclusion is based on morphological data¹⁰ which do not apply either to central or to peripheral fibres, so that myelinated fibres considerably smaller than 1 µm might be expected to conduct more rapidly than non-myelinated fibres of similar size.     

A model of motor and sensory axon activation in the median nerve using surface electrical stimulation

Surface electrical stimulation has the potential to be a powerful and non-invasive treatment for a variety of medical conditions but currently it is difficult to obtain consistent evoked responses. A viable clinical system must be able to adapt to variations in individuals to produce repeatable results. To more fully study the effect of these variations without performing exhaustive testing on human subjects, a system of computer models was created to predict motor and sensory axon activation in the median nerve due to surface electrical stimulation at the elbow. An anatomically-based finite element model of the arm was built to accurately predict voltages resulting from surface electrical stimulation. In addition, two axon models were developed based on previously published models to incorporate physiological differences between sensory and motor axons. This resulted in axon models that could reproduce experimental results for conduction velocity, strength-duration curves and activation threshold. Differences in experimentally obtained action potential shape between the motor and sensory axons were reflected in the models. The models predicted a lower threshold for sensory axons than motor axons of the same diameter, allowing a range of sensory axons to be activated before any motor axons. This system of models will be a useful tool for development of surface electrical stimulation as a method to target specific neural functions.     

Spontaneous firing and myelination of very small axons

In this article the question of what evolutionary factors guided acquisition of myelin in the nervous system is addressed. The conclusion that conduction velocity of action potentials along the axon has been the only motive force needs reformulation, as other factors may have played a central role as well. In particular, protection against firing of spontaneous action potentials which may result from the simultaneous opening of only few (less than 10) sodium channels at the nodes of small (less than 1 micron diameter) myelinated axons, may have greatly contributed to discouraging myelination of axons smaller than 1 micron.     

Conduction velocities and fiber diameters in a cutaneous nerve of the pigeon

Summary The characteristics of fibers of a cutaneous nerve supplying the wing skin of the pigeon have been investigated with electrophysiological and electron microscopic techniques.Recordings of the compound action potential showed four distinct peaks with conduction velocities of about 30 m/s, 12 m/s, 4 m/s and 0.5 m/s.From electron micrographs both fiber diameters and thickness of myelin sheath were assessed and used as criteria for segregating various fiber populations. Altogether four groups could be discerned: large thickly myelinated fibers, small thickly myelinated fibers, small thinly myelinated fibers, and unmyelinated or C-fibers. The subdivision of the thickly myelinated fibers into two populations is evidenced mainly by corresponding peaks in the compound action potential. The thinly myelinated fibers with a mean diameter of 2 m contributed about 90% of all myelinated fibers in this nerve.When comparing fiber dimensions and conduction velocities of this avian nerve with those of mammalian cutaneous nerves, the lower CV's of avian nerve fibers can be explained by smaller diameters and thinner myelin sheaths.The results of this investigation are a prerequisite for latency considerations in central somatosensory pathways in birds.Abbreviations CAP compound action potential - CV conduction velocity - D fiber diameter - d axon diameter - g ratio d/D - m thickness of myelin sheath     

Propagation of action potentials in squid giant axons. Repetitive firing at regions of membrane inhomogeneities

Effects of reduction in potassium conductance on impulse conduction were studied in squid giant axons. Internal perfusion of axons with tetraethylammonium (TEA) ions reduces G K and causes the duration of action potential to be increased up to 300 ms. This prolongation of action potentials does not change their conduction velocity. The shape of these propagating action potentials is similar to membrane action potentials in TEA. Axons with regions of differing membrane potassium conductances are obtained by perfusing the axon trunk and one of its two main branches with TEA after the second branch has been filled with normal perfusing solution. Although the latter is initially free of TEA, this ion diffuses in slowly. Up until a large amount of TEA has diffused into the second branch, action potentials in the two branches have very different durations. During this period, membrane regions with prolonged action potentials are a source of depolarizing current for the other, and repetitive activity may be initiated at transitional regions. After a single stimulus in either axon region, interactions between action potentials of different durations usually led to rebound, or a short burst, of action potentials. Complex interactions between two axon regions whose action potentials have different durations resembles electric activity recorded during some cardiac arrhythmias.     

Impulse Propagation at the Septal and Commissural Junctions of Crayfish Lateral Giant Axons

Transmission across the septal junctions of the segmented giant axons of crayfish is accounted for quantitatively by a simple equivalent circuit. The septal membranes are passive, resistive components and transmission is ephaptic, by the electrotonic spread of the action current of the pre-septal spike. The electrotonic spread appears as a septal potential, considerably smaller than the pre-septal spike, but usually still large enough to initiate a new spike in the post-septal segments. The septal membranes do not exhibit rectification, at least over a range of ± 25 mv polarization and this accounts for their capacity for bidirectional transmission. The commissural branches, which are put forth by each lateral axon, make functional connections between the two axons. Transmission across these junctions can also be bidirectional and is probably also ephaptic. Under various conditions, the ladder-like network of cross-connections formed by the commissural junctions can give rise to circus propagation of impulses from one axon to the other. This can give rise to reverberatory activity of both axons at frequencies as high as 400/sec.     

Composition of the antennal nerve of Homarus americanus at different points along the flagellum

The antennal flagellum nerve of Homarus americanus was investigated as to structure, number and size of axons, and propagation velocity. Frequency distributions of axon diameters, evaluated at four equidistant levels on the flagellum, ranged with continuity between 0.25 and 14.7 µm, with maximum at 0.5-1.5 µm. Axons 0.5-1.5 µm in diameter were more abundant at the distal level, indicating sensory specialization near the tip. The total axon numbers increased from about 9000 at the distal level to about 45 000 at the base. Axons of different size followed different patterns of increase in number from tip to base; these patterns were examined in relation to structural features of the flagellum, and to hypotheses of association with known or unidentified receptors. Propagation velocities were distributed with continuity, in the range between 3.39 and 0.24 m/s; velocity-diameter correspondences were outlined.     

Seasonal variation in conduction velocity of action potentials in squid giant axons

To determine whether the electrical properties of the squid giant axon are seasonally acclimated, action potentials, recorded at different temperatures, were compared between giant axons isolated from Loligo pealei caught in May, from relatively cold waters (approximately 10 degrees-12 degrees C), and in August, from relatively warm waters (approximately 20 degrees C). Parameters relating to the duration of the action potential (e.g., maximum rate of rise, maximum rate of fall, and duration at half-peak) did not change seasonally. The relationship between conduction velocity and temperature remained constant between seasons as well, in spite of the fact that May axons were significantly larger than August axons. When normalized to the fiber diameter, mean May conduction velocities were 83% of the August values at all temperatures tested, and analysis of the rise time of the action potential foot suggested that a change in the axoplasmic resistivity was responsible for this difference. Direct measurements of axoplasmic resistance further supported this hypothesis. Thus seasonal changes in the giant axon's size and resistivity are not consistent with compensatory thermal acclimation, but instead serve to maintain a constant relationship between conduction velocity and temperature.     

The corpus callosum in primates: processing speed of axons and the evolution of hemispheric asymmetry

Interhemispheric communication may be constrained as brain size increases because of transmission delays in action potentials over the length of axons. Although one might expect larger brains to have progressively thicker axons to compensate, spatial packing is a limiting factor. Axon size distributions within the primate corpus callosum (CC) may provide insights into how these demands affect conduction velocity. We used electron microscopy to explore phylogenetic variation in myelinated axon density and diameter of the CC from 14 different anthropoid primate species, including humans. The majority of axons were less than 1 µm in diameter across all species, indicating that conduction velocity for most interhemispheric communication is relatively constant regardless of brain size. The largest axons within the upper 95th percentile scaled with a progressively higher exponent than the median axons towards the posterior region of the CC. While brain mass among the primates in our analysis varied by 97-fold, estimates of the fastest cross-brain conduction times, as conveyed by axons at the 95th percentile, varied within a relatively narrow range between 3 and 9 ms across species, whereas cross-brain conduction times for the median axon diameters differed more substantially between 11 and 38 ms. Nonetheless, for both size classes of axons, an increase in diameter does not entirely compensate for the delay in interhemispheric transmission time that accompanies larger brain size. Such biophysical constraints on the processing speed of axons conveyed by the CC may play an important role in the evolution of hemispheric asymmetry.     

Neuregulin-1 type III determines the ensheathment fate of axons

The signals that determine whether axons are ensheathed or myelinated by Schwann cells have long been elusive. We now report that threshold levels of neuregulin-1 (NRG1) type III on axons determine their ensheathment fate. Ensheathed axons express low levels whereas myelinated fibers express high levels of NRG1 type III. Sensory neurons from NRG1 type III deficient mice are poorly ensheathed and fail to myelinate; lentiviral-mediated expression of NRG1 type III rescues these defects. Expression also converts the normally unmyelinated axons of sympathetic neurons to myelination. Nerve fibers of mice haploinsufficient for NRG1 type III are disproportionately unmyelinated, aberrantly ensheathed, and hypomyelinated, with reduced conduction velocities. Type III is the sole NRG1 isoform retained at the axon surface and activates PI 3-kinase, which is required for Schwann cell myelination. These results indicate that levels of NRG1 type III, independent of axon diameter, provide a key instructive signal that determines the ensheathment fate of axons.     

The function of the proximal synapses of the squid stellate ganglion

In the oxygenated excised squid (Loligo pealii) stellate ganglion preparation one can produce excitation of the stellar giant axons by stimulating the second largest (accessory fiber, Young, 1939) or other smaller preganglionic giant axons. Impulse transmission is believed to occur at the proximal synapses of the stellar giant axons rather than the distal (giant) synapses which are excited by the largest giant preaxon. Proximal synaptic transmission is more readily depressed by hypoxia and can be fatigued independently of, and with fewer impulses than, the giant synapses. Intracellular recording from the last stellar axon at its inflection in the ganglion reveals both proximal and distal excitatory postsynaptic potentials EPSP's). The synaptic delay, temporal form of the EPSP, and depolarization for spike initiation were similar for both synapses. If the proximal EPSP occurs shortly after excitation by the giant synapse it reduces the undershoot and adds to the falling phase of the spike. If it occurs later it can produce a second spike. Parallel results were obtained when the proximal EPSP's arrived earlier than the EPSP of the giant synapse. In fatigued preparations it was possible to sum distal and proximal or two proximal EPSP's and achieve spike excitation.     

Neocortical Axon Arbors Trade-off Material and Conduction Delay Conservation

The brain contains a complex network of axons rapidly communicating information between billions of synaptically connected neurons. The morphology of individual axons, therefore, defines the course of information flow within the brain. More than a century ago, Ramón y Cajal proposed that conservation laws to save material (wire) length and limit conduction delay regulate the design of individual axon arbors in cerebral cortex. Yet the spatial and temporal communication costs of single neocortical axons remain undefined. Here, using reconstructions of in vivo labelled excitatory spiny cell and inhibitory basket cell intracortical axons combined with a variety of graph optimization algorithms, we empirically investigated Cajal''s conservation laws in cerebral cortex for whole three-dimensional (3D) axon arbors, to our knowledge the first study of its kind. We found intracortical axons were significantly longer than optimal. The temporal cost of cortical axons was also suboptimal though far superior to wire-minimized arbors. We discovered that cortical axon branching appears to promote a low temporal dispersion of axonal latencies and a tight relationship between cortical distance and axonal latency. In addition, inhibitory basket cell axonal latencies may occur within a much narrower temporal window than excitatory spiny cell axons, which may help boost signal detection. Thus, to optimize neuronal network communication we find that a modest excess of axonal wire is traded-off to enhance arbor temporal economy and precision. Our results offer insight into the principles of brain organization and communication in and development of grey matter, where temporal precision is a crucial prerequisite for coincidence detection, synchronization and rapid network oscillations.     

Rapid conduction and the evolution of giant axons and myelinated fibers

Nervous systems have evolved two basic mechanisms for increasing the conduction speed of the electrical impulse. The first is through axon gigantism: using axons several times larger in diameter than the norm for other large axons, as for example in the well-known case of the squid giant axon. The second is through encasing axons in helical or concentrically wrapped multilamellar sheets of insulating plasma membrane--the myelin sheath. Each mechanism, alone or in combination, is employed in nervous systems of many taxa, both vertebrate and invertebrate. Myelin is a unique way to increase conduction speeds along axons of relatively small caliber. It seems to have arisen independently in evolution several times in vertebrates, annelids and crustacea. Myelinated nerves, regardless of their source, have in common a multilamellar membrane wrapping, and long myelinated segments interspersed with 'nodal' loci where the myelin terminates and the nerve impulse propagates along the axon by 'saltatory' conduction. For all of the differences in detail among the morphologies and biochemistries of the sheath in the different myelinated animal classes, the function is remarkably universal.     

Transfer of molecules from glia to axon in the squid may be mediated by glial vesicles

Although the transfer of glial proteins into the squid giant axon is well documented, the mechanism of the transfer remains unknown. We examined the possibility that the transfer involved membrane-bound vesicles, by taking advantage of the fact that the fluorescent compound, 3,6-acridinediamine, N,N,N,',N'-tetramethylmonohydride [acridine orange (AO)], rapidly and selectively stains vesicular structures in glial cells surrounding the giant axon. We labeled cleaned axons (1–3 cm long) by incubation for 1 min in filtered seawater (FSW) containing AO. Because the AO was concentrated in glial vesicular organelles, these fluoresced bright orange when the axon was examined by epifluorescence microscopy. To look for vesicle transfer, axoplasm was extruded from such AO-treated axons at various times after labeling. During the initial 15 min, an increasing number of fluorescent vesicles were observed. No further increases were observed between 15 and 60 min post AO. The transfer of the fluorescent vesicles into the axoplasm seemed to be energy dependent, as it was inhibited in axons treated with 2 mM KCN. These results suggest that a special mode of exchange exists between the adaxonal glia and the axon, perhaps involving phagocytosis by the axon of small portions of the glial cells.