Axonal conduction delays
|Harvey A. Swadlow and Stephen G. Waxman (2012), Scholarpedia, 7(6):1451.||doi:10.4249/scholarpedia.1451||revision #125736 [link to/cite this article]|
Axonal conduction delays refer to the time required for an action potential to travel from its initiation site near the neuronal soma to the axon terminals, where synapses are formed with other neurons, muscles or glands. Differences among axons (and their branches) in conduction delays are due to differences in axonal conduction velocity and conduction distance. Conduction delays vary greatly in the mammalian nervous system, from < 100 microseconds in very short axons to > 100 ms in very long non-myelinated central axons. Whereas minimizing conduction delays is clearly beneficial to speed-sensitive processes (reflexes, perceptual skills, escape responses), rapid conduction comes at a very high price in brain volume. In monkeys, for example, the fastest axons are ~ 20 microns in diameter and conduct at ~ 120 m/s. By contrast, the slowest axons are ~ 0.1 micron in diameter and conduct at ~ 0.3 m/s. Thus, the fastest axons occupy ~ 40,000 times the volume of the slowest axons, per unit length and conduct ~ 400 times faster. The finest non-myelinated axons also differ from myelinated axons in temperature sensitivity, resistance to anoxia, reliability of conduction, and in the metabolic costs per impulse (Faisal and Laughlin, 2007; Franz and Iggo, 1968; Wang et al., 2008) and such factors must also be considered in discussions of "optimization" of axonal characteristics for a given system (e.g., Budd et al., 2010; Cherniak, 1992; Chklovskii et al., 2002). In all but a few cases, axonal conduction delays have been measured using physiological recording methods, which have very high temporal resolution, but usually measure conduction along a limited segment of a single axon. Optical methods of measurement (e.g., Antic and Zecevic, 1995) hold great promise of visualizing impulse conduction along the complex axonal arborizations of single, or even multiple neurons. It is worth noting that the term “fiber” (or the British, fibre) is often used synonymously with the term “axon” (or to describe muscle), but also includes elongated dendritic processes such as those found in peripheral sensory nerves, which may be myelinated or non-myelinated.
Axonal conduction velocity and conduction delays
The diameter of the axon and the presence of myelin are the most powerful structural factors that control conduction velocity of mammalian axons (Waxman, 1980 for review). In the central nervous system, the smallest axons are ~ 0.1 microns in diameter. The diameter of the largest axons depends on the overall size of the brain, with very small mammals having maximal diameters considerably less than those of large mammals. Conduction velocity increases with both axon diameter, and with myelination and, in the central nervous system, the great majority axons that are > 0.3 microns in diameter are myelinated. The myelin sheath, produced by specialized glial cells, is a compacted spiral of membrane. In general, the thickness of the myelin sheath is roughly proportional to the diameter of the ensheathed axon, with the g-ratio (inner diameter of myelin sheath/outer diameter) being close to 0.6 (Waxman and Bennett 1972). The myelin is interrupted periodically by nodes of Ranvier, which are regions of high sodium channel density. These channels are needed for regeneration of the action potential. Myelin acts as an electrical insulator of high resistance and low capacitance, which increases the length constant of the axon and enables rapid saltatory conduction (Tasaki article, Scholarpedia) of impulses down the axon. Since early empirical (Gasser and Grundfest, 1939; Hursh, 1939) and theoretical ( Rushton, 1951) studies, is generally agreed that the conduction velocity of myelinated axons increase in a linear manner with increasing diameter. The situation for non-myelinated axons is less definitive. Based on theoretical arguments, assuming similarity of membrane properties and axoplasmic resistance, and in agreement with measures of large invertebrate axons, Hodgkin (1954) concluded that the conduction velocity of non-myelinated axons is proportional to the square root of axon diameter. However, measures of very fine non-myelinated axons found in the vertebrate nervous system sometimes have been interpreted as supporting linear relationships for these fibers (e.g., Hoffmeister et al., 1991. At diameters of < ~ 0.3 microns, Waxman and Bennett (1972) found the benefits of myelin to negligible (Figure 1), and few myelinated axons are found within the CNS at diameters below this value.
Myelin is often thought of as an exclusively vertebrate characteristic, but some invertebrates, including some earthworms and shrimp, have a small number of axons that are insulated with a myelin-like substance and demonstrate saltatory conduction (Xu and Terakawa, 1999). Indeed, the fastest impulse conduction recorded in any species was seen, ironically, in a shrimp (Kusano and LaVail, 1971). However, there are very few such axons in any invertebrates, most invertebrates do not utilize myelin, and when they require rapid impulse conduction it is achieved by with dramatic increases in axonal diameter. Squid, for example, have several "giant" axons of > 0.5 mm in diameter, which are used to generate a fast escape response. Of course, not many such giant axons can fit into the squid nervous system. By contrast, the vertebrate solution to this "speed" problem employs myelin, which achieves conduction velocities comparable to those seen in giant squid axons, but with axons of < 1/100th the diameter.
Other structural factors include internodal distance and, importantly, the complement of ion channels in the axonal membrane. Conduction velocity depends strongly on the rise time of the action potential which, in turn, depends on the density of sodium ion channels responsible for the onset of the action potential (Waxman, 1975, see also Renganathan et al., 2001). It can be argued that the wide scale use of myelin seen in vertebrates was crucial for the development of their complex, fast-acting nervous systems.
Dynamic influences on impulse conduction delays
Axonal conduction properties are temperature dependent (Franz and Iggo, 1968; Paintal, 1965). Although mammalian brain temperature is relatively constant (<±1 degree centigrade) under normal conditions, limb (and hand) temperature can drop considerably in cold weather and this, through effects on both nerve and muscle, can affect sensory capacities and dexterity. Some hibernating mammals can maintain core temperatures at near 0° C, which would halt any impulse conduction along axons (Paintal, 1965). Axons of cold-blooded animals show wide variations in conduction velocity associated with daily or seasonal changes in their body temperature (e.g. Rosenthal and Bezalila, 2000). Another dynamic effect is the short-term history of impulse conduction. In some mammalian central axons, increases in conduction velocity of up to 20% can follow a single prior impulse for up to 100 ms (supernormal conduction) and even larger decreases in conduction velocity can last for many seconds following bursts of prior Impulses (subnormal conduction, Aston-Jones et al., 1985; Gardner-Medwin, 1972; Swadlow, 1974a, review in Swadlow et al., 1980). Finally, although axonal conduction properties are often thought to represent a prototypical "hard-wired" cellular property, slowly progressing (1-2%/day) changes in axonal conduction velocity have been observed to occur along slowly conducting callosal axons over periods of many months (Swadlow, 1982; 1985).
Axonal conduction in the peripheral nervous system: structure-function correlations
Peripheral nerves demonstrate a wide variety of axonal types, from myelinated axons 20 microns in diameter, to very fine non-myelinated axons as small as 0.2 microns in diameter. Early work on impulse conduction along peripheral fibers by Erlanger and Gasser (for which they shared the Nobel Prize in 1942) demonstrated remarkable relationships between the conduction velocity of the axons and the type of information that was conveyed. The largest motor fibers (13-20 um, conducting at velocities of 80 -120 m/s) innervate the extrafusal fibers of the skeletal muscles, and smaller motor fibers (5-8 um, conducting at 4-24 m/s) innervate intrafusal muscle fibers. The largest sensory fibers (13-20 um) innervate muscle spindles and Golgi tendon organs (both conveying unconscious proprioceptive information), the next largest (6-12 um) convey information from mechanoreceptors in the skin, and the smallest myelinated fibers (1 – 5 um) convey information from free nerve endings in the skin, as well as pain, and cold receptors. Non-myelinated peripheral C fibers (0.2 – 1.5 um) carry information about pain and warmth.
Axonal conduction in the central nervous system: structure-function correlations
The axons of most cortical pyramidal neurons, which are the major cell type found the neocortex, branch profusely both locally, near the soma, and near distant targets of the primary axon (Callaway, 2004). As expected, axonal conduction times for the local connections, often only a few hundred microns of the soma, are short. Thus, Feldmeyer et al. (2006) found that the average latency of excitatory post synaptic potentials elicited at synapses between pyramidal neurons in layer 2/3 of juvenile rat barrel columns was only 1.1 ms, and much of this value can be attributed to the synaptic delay. However, conduction distances within the CNS can be quite long, especially in larger brains and within the spinal cord, and axonal delays can vary greatly. For example, some corticospinal neurons of monkeys generate impulses that require as little as 0.6 ms to reach the brain stem ~ 70 mm away, representing conduction velocities of up to 110 m/s. Such values are as high as any seen the peripheral nervous system. By contrast, neurons in the brain stem locus coeruleus of monkeys generate impulses that require 82 – 130 ms to reach axon terminals in the visual cortex (conduction velocities of 0.8 – 1.2 m/s). Table 1 gives values for axonal conduction times measured in a selection of long range axonal systems in the brains of rodents, rabbits, cats and monkeys (representing four mammalian orders). In these studies, values were obtained by the method of antidromic activation, whereby action potentials are initiated by electrical stimulation of the axon, and the latency of the conducted spike is recorded near the cell body. All of the measures shown in Table 1 were taken from adult subjects. Developmental changes in the composition of central and peripheral axon pathways can be considerable (e.g., Foster et al., 1982; Yates and Juraska, 2007), and it is important to control for age when comparing the properties of different axonal pathways.
Inspection of Table 1 shows that some axonal systems are nearly exclusively fast-conducting (corticospinal, corticotectal, and sensory thalamocortical axons), some systems are exclusively slowly conducting, with impulses taking many 10s of ms to reach their terminals (cortically projecting neurons of the locus coeruleus and substantia nigra), and some systems consist of a broad spectrum of axons (corpus callosum, some corticocortical populations, corticothalamic neurons of layer 6). There are many examples where a single axonal system has axons that display a very broad range of axonal conduction velocities. Importantly, conduction velocities are often related to the diversity of response properties seen in that system. For example, visual thalamocortical (LGN) axons of the cat can be classified as having x-, y-, or w-type receptive fields, each with its own distribution of conduction velocities (Cleland et al., 1976). Even more extreme variations in conduction times are seen among members of both visual and motor corticothalamic populations, in both cats and rabbits. Notably, in these populations, axonal conduction times are related to sensory or movement-related response properties and to spontaneous firing rates. Thus, cortical neurons with very slowly conducting axons lack sensory or motor related responses and have very low levels of spontaneous impulse activity. (Sirota et al., 2005; review in Swadlow, 2000).
The above review has described the brief conduction delays that are mediated by very short axons linking neighboring neurons within a cortical column (Feldmeyer et al., 2006), and much longer conduction delays that are mediated by long-distance, inter-areal connections (Table 1). There are also intermediate-length connections, mediated by axons that project up to several millimeters laterally within a cortical region.. In cat and primate visual cortex, for example, such “horizontal” axonal connections have been estimated to conduct impulses at ~ 0.3 m/s (Hirsch and Gilbert, 1991 ), and similar estimations for such connections have been obtained in rat neocortex ( 0.3 -0.44 m/s , Lohmann and Rorig, 1994; Telfeian and Connors, 2003). Such values are generally indicative of non-myelinated axons, or the very finest of myelinated axons (Figure 1). It is worth noting, however, that many axon pathways consist of a wide spectrum of diameters, and Kisvarday and Eysel (1992) reported that some of the “horizontal” synaptic connections made by pyramidal cells within cat primary visual cortex are mediated by myelinated axons as large as 1-3 microns in diameter. The conduction velocities were not measured, and axons may change diameter, and loose myelin along their course. Nevertheless, such axons would be expected to conduct (Figure 1) at velocities far exceeding the value of 0.3 m/s reported by Hirsch and Gilbert (1992).
Conduction delays and brain size
How do axon conduction velocities/delays scale with body/brain size? Conduction distances are greater in larger animals, both within the brain (because brains are larger) and in the periphery. Because of this, larger animals require larger-diameter axons than smaller animals to accomplish tasks requiring similar reaction times and speed, such as those mediating perception and action. It would be a slow-reacting tiger (or giraffe!) that possessed only mouse-sized axons, and there has been considerable discussion about compensatory axonal "design" principles. However, there does not appear to be a simple cross-the-board "scaling up" of axon diameters with increasing body size. Indeed, as pointed out by Ringo et al. (1994), such a simple scaling would result in prohibitive increases in brain size, due to increases in the mass of white matter, and this was the basis for their conjecture that hemispheric specializations could arise in the context of unavoidable increases in interhemispheric conduction delays in large brains. Interestingly, the diameter spectrum of the fine non-myelinated axons is quite constant across species. Thus, in the corpus callosum of both monkeys and rabbits, the great majority of non-myelinated axons are 0.1 – 0.3 microns in diameter (median values = 0.2 microns in both species), with a similar ratio of myelinated to non-myelinated axons (Swadlow et al., 1980). Olivares et al (2001) report a similar overall proportion of non-myelinated axons (21 – 31%) in the corpus callosum of a wide range of species (including rats, cats and horses), although regional variations may occur (Lamantia and Rakic, 1990). Studies of the corpus callosum of a wide range of mammals give somewhat conflicting results, showing that the median axon size increases either slightly or not at all with increasing brain size. There is agreement, however, that the size of the very few largest axons increases significantly with increases in brain size (Olivares et al., 2001, Wang et al., 2008), so that in all species the fastest interhemispheric conduction times are maintained at < 5 ms (Wang et al., 2008).
Conduction delays and synchrony of postsynaptic events
Different conduction delays can be used to synchronize the arrival time of converging impulses. This can result in the generation of coincident postsynaptic potentials in a postsynaptic target when presynaptic neurons fire simultaneously but convergent conduction paths differ in length (review in Waxman, 75). Such a mechanism was proposed > 70 years ago, in early studies of giant squid axons that innervate musculature of the mantel (Pumphrey and Young, 1938), where it was noted that ".. In Loligo there is a graded series of fibres with the larger in the longer nerves, and this is apparently a further device for ensuring more nearly simultaneous contraction.". A similar compensatory delay function was demonstrated in the barn owl for ipsilateral and contralateral inputs from cochlear nucleus to brainstem neurons that are sensitive to interaural time delays (Carr and Konishi, 1988). Similarly, different conduction delays in the diverging branches of a single axon can generate near-simultaneous responses in postsynaptic targets that lie at different conduction distance. Such "isochronic" delivery of spikes generated by neurons with multiple distant targets could serve to synchronize spatially separate members of functional ensembles (Chomiak et al., 2008). Isochronicity appears to be important in ensuring synchronous delivery of impulses from the inferior olivary nucleus in the brainstem to Purkinje neurons in the cerebellum, where longer branches have thicker diameters than shorter branches, indicating higher conduction velocities (Sugihara et. al., 1993; also see Budd et al., 2010).
The observed diversity in axonal conduction delays also bear on whether synchronous firing of presynaptic neuronal ensembles would enhance the activation of postsynaptic targets (Binding by Synchrony, Scholarpedia). Such ideas often assume that conduction delays are negligible, and such synchronous firing will result in synchronous arrival of impulses at postsynaptic targets. The broad spectrum of conduction times observed in many corticocortical systems indicates, however, that this is not always the case. Izhikevich (2006) has demonstrated that different conduction delays in the divergent axonal branches of a small group of presynaptic neurons could serve to activate a very large number of distinct postsynaptic ensembles, depending on the order of firing of the presynaptic neurons. The firing of the postsynaptic neurons would depend critically on the match between the spike timing in the presynaptic neurons and the axonal delays in their branches, such that only synchronously arriving inputs would generate spikes, and different spatiotemporal patterns of presynaptic activity would activate different postsynaptic ensembles. Through this mechanism, different spatiotemporal patterns of firing in the presynaptic neurons could generate time-locked "polychronic" firing patterns in groups of neurons, reminiscent of synfire braids (Bienenstock, 1995, also see Schuz and Preibl, 1996). Notably, these connections could be strengthened through mechanisms of spike-timing dependent plasticity (Izhikevich, 2006; Lubenov and Siapas, 2008; Paugam-Moisey et al., 2008). Diversity in signal transmission delays could also serve to shift oscillation dynamics and stabilize neural networks (Omi and Shinomoto, 2008).
One caveat for theoretical proposals employing long conduction delays to generate synchronous postsynaptic spiking is that very slowly conducting central axons may not "drive" postsynaptic targets using fast ionotropic postsynaptic receptors, as fast-conducting axons generally do. An important distinction has been made between neurons that synaptically "drive" their targets vs. those that "modulate" (Sherman and Guillery, 1998). Given the considerable biological costs of fast-conducting axons (above), it is reasonable to suppose that presynaptic axonal conduction delays may be matched to the requirements and time course of postsynaptic events. For example, the axons that mediate dopaminergic and noradrenergic synapses are very slowly conducting (Table 1) and these transmitters utilize metabotropic receptor mechanisms, which have time courses that are orders of magnitude greater than those seen in ionotropic synaptic transmission.
Conduction delays and disease
Axons can be affected by a host of pathological conditions, most of which cause conduction delays, temporal dispersion of impulses and, ultimately, conduction failure. This topic has been the subject of many clinical reviews (e.g., Waxman, 2005). It is well-established that demyelination, or loss of the myelin sheath, occurs in a multifocal manner, producing lesions or demyelinated plaques that affect multiple tracts within the CNS, in disorders such as multiple sclerosis (MS). Demyelination leads to a reduction of conduction velocity, and, in more severely affected fibers, block of high-frequency impulse conduction or even failure of single action potentials (McDonald 1974; Smith and Hall 1980; Waxman 1981). Slowing of impulse conduction is largely due to damage to the myelin insulation, with loss of the capacitative shield and a consequent increase in the time required for the propagating impulse to depolarize downstream portions of the membrane. Conduction block, on the other hand, is due to both loss of myelin’s capacitative shielding influence, and exposure after demyelination of previously myelinated parts of the axon membrane, which possess only low densities of sodium channels, too low to support high-frequency impulse conduction (Waxman 1982).
Importantly, patients with MS can experience remissions, in which they recover previously lost functions such as vision or the ability to walk, in the absence of substantial remyelination. Recovery of clinical functions in these instances appears to depend on molecular reorganization of chronically demyelinated axons, which acquire a higher-than-normal density of sodium channels in demyelinated (and previously sodium-channel-poor) regions (Craner et al., 2004). This molecular remodeling permits the bared, demyelinated axon membrane to support continuous impulse conduction which, as in fibers that are normally non-myelinated, occurs with a low conduction velocity (Bostock and Sears 1972; Smith and Waxman 2005).
Slowed conduction along demyelinated axons in MS can be measured clinically via the recording of “visual evoked responses,” in which the response of the visual cortex is recorded using scalp electrodes in response to a patterned of visual stimulus (Halliday et. al., 1973). Interestingly, patients can recover from episodes of optic neuritis (inflammation and demyelination) along the optic nerves, with a conduction delay of several tens of milliseconds in the visual evoked response (this reflects the decreased conduction velocity along the chronically demyelinated optic nerve axons). Visual acuity often recovers fully in these patients and, upon casual examination, they appear to have recovered fully. However, these patients often exhibit subtle abnormalities such as the Pulfrich phenomenon, in which patients perceive that a pendulum, swinging in front of them in a plane, to be swinging in a circular or elliptical trajectory, as a result of the delay in arrival of impulses from the affected eye.
Remyelination (production of new myelin) along demyelinated axons within the brain and spinal cord, occurs either by occasional endogenous myelin-forming cells (Smith et. al., 1981) or after transplantation of myelin-forming glial cells (Utzschneider et. al., 1993) and can restore near-normal impulse conduction properties to the previously demyelinated axons. This observation has heightened interest in the development of reparative therapies, using any of a variety of cell types, including stem cells, as a therapeutic approach that might restore function in people with demyelinating diseases such has multiple sclerosis.
Less is known about the physiology of conduction in smaller, more slowly conducting axons, particularly the non-myelinated axons, in the diseased nervous system, since it is easier to record the activity of the larger myelinated axons, and since many of the available clinical tools, e.g. assessment of deep tendon reflexes, measure activity in the larger fibers. Nonetheless, the existence of “small fiber neuropathies” has been increasingly recognized over the past decade, and there will undoubtedly be progress, in the future, in terms of studying the physiological concomitants of injury to small axons.
Conduction time (ms)
(range) (mean or med)
Conduction velocity (m/s)
(range) (mean or med)
6 - 8
(2.0 - 20.0) (8.3)
(0.3 – 3.5) (---)
(2.4 - 39.8) (16.5)
(0.7 – 7.5) (---)
(1.3 - 15.0) (2.7)
10 - 20
(2.0 - 32.0) (10.1)
(1.0 to 10.0) (---)
(2.6– 18.0) (7.0)
(3.0 – 23.0) (7.0)
(2.0 – 28.9) (11.0)
(0.3 – 4.6) (1.3)
(2.0 - 42.0) (13.5)
(0.5 – 8.0 ) (2.3)
(0.98 – 14.8) (3.7)
(1.5– 28.2) (6.4)
(1.4 – 8.3) (2.9)
(3.7 – 25.0) (11.1)
(2 – 12.0) (4.6)
(3.0 – 19.0) (8.0)
(0.5 – 5.0) (1.1)
(11.0 - 100.0) (---)
(0.6 – 5.2) (1.0)
(13.0 – 110.0) (70.0)
Cortico-thalamic (layer 6)
(2.0 – 42.7) (14.3)
(0.4 – 9.6 ) (---)
(2.5 – 45.0) (---)
(0.4 - 8.0) (---)
(2.0 - > 20.0) (9.5)
(0.6 – 3.1) (1.2)
(5.5 – 28.0) (14.8)
(0.3 – 9.7) (0.9)
(2.1- 67.0) (22.2)
(23.0 – 82.0) (44.0)
(82.0 – 130.0) (100.7)
(0.8 – 1.2) (1.0)
Table 1. Values for axonal conduction times and velocities for select axonal pathways in several mammalian species. Some axonal systems are very rapidly conducting, some are very slowly conducting, and some are characterized by a great diversity in axonal conduction delays.
Table references: 1 Simmons and Pearlman, 1983; 2 Swadlow, 1974a; 3 Innocenti, 1980; 4 Miller, 1975; 5 Swadlow et al., 1978; 6 Swadlow, 1990; 7 Ferraina et al., 2002; 8 Swadlow and Weyand, 1987; 9 Weyand et al., 1986; 10 Finlay et al, 1976; 11 Takahashi, 1965; 12 Evarts, 1965; 13 Ferster and Lindstrom, 1983; 14 Briggs and Usrey, 2009; 15 Swadlow and Weyand, 1985; 16 Cleland et al., 1976; 17 Faiers and Mogensen, 1976; 18 Aston-Jones et al., 1985; 19 Gariano and Groves, 1988.
Antic S and Zecevic D. Optical signals from neurons with internally applied voltage-sensitive dyes. J. Neuroscience, 15(2): 1392-1405, 1995
Aston-Jones, G., Foote, S. L., and Segal, M. Impulse conduction properties of noradrenergic locus coeruleus axons projecting to monkey cerebrocortex. Neuroscience, 15: 765-777, 1985.
Beloozerova, I. N., Sirota, M. G. and Swadlow, H. A. Activity of different classes of neurons of the motor cortex during locomotion. J. Neuroscience, 23: 1087-1097, 2003.
Bostock H, and Sears T. A. The intermodal axon membrane: electrical excitability and continuous conduction in segmental demyelination J. Physiol. 280:273-301, 1978
Bienenstock, E. A model of neocortex, Network: Computation in neural systems, 6: 179-224, 1995
Briggs, F. and Usrey, W. M. Parallel processing in the corticogeniculate pathway of the macaque monkey. Neuron, 62: 135-146, 2009.
Budd, J. M. L., Kovacs, K., Frecsko, A. S., Buzas, P., Eysel, U. T. and Kisvarday, Z. F. Neocortical axon arbors trade-off material and conduction delay conservation. Plos Comput Biol., 6: e1000711, 2010
Callaway, E. M., Cell types and local circuits in primary visual cortex of the macaque monkey. In: The Visual Neurosciences (Vol. 1), L.M. Chalupa and J. S. Werner (Editors), 68—694, 2004
Carr, C. E. and Konishi, M. Axonal delay lines for time measurement in the owl's brainstem. Proc. Natl. Acad. Sci. USA, 85, 8311-8315, 1988.
Cherniak, C. Local optimization of neuron arbors. Biol. Cybern., 66: 503-510, 1992.
Chklovskii, D. B. Schikorski, T. and Stevens, C. F. Wiring optimization in cortical circuits. Neuron, 34: 341-347, 2002.
Chomiak, T., Peters, S. and Hu, B. Functional architecture and spike timing properties of corticofugal projections from rat ventral temporal cortex. J. Neurophysiol., 100: 327-335, 100.
Cleland, B. G., Levick, W. R. Morstyn, R. and Wagner, H. G. J. Physiol. (Lond.), 255, 299-320, 1976.
Craner, M.J., Newcombe, J., Black, J.A., Hartle, C., Cuzner, M.L., Waxman, S.G. Molecular changes in neurons in MS: altered axonal expression of Nav1.2 and Nav1.6 sodium channels and Na+ /Ca2+ exchanger. Proc. Natl. Acad. Sci. 101: 8168-8173, 2004.
Evarts, E. V. Relation of discharge frequency to conduction velocity in pyramidal tract neurons. J. Neurophysiol, 28: 216-228, 1965.
Faiers, A. A. and Mogenson, G. J. Electrophysiological identification of neurons in locus coeruleus. Exp. Neurol., 53: 254-266, 1976.
Faisal, A. A., and Laughlin, S. B. Stochastic simulations on the reliability of action potential propagation in thin axons. PLOS Comp. Biology, 3: 0783-0795, 2007.
Feldmeyer, D., Lubke, J. and Sakmann, B. Efficacy and connectivity of intracolumnar pairs of layer 2/3 pyramidal cells in the barrel cortex of juvenile rats. J. Physiol., 583-602, 2006.
Ferraina, S., Pare, M., and Wurtz, R. H. Comparison of cortico-cortical and cortico-collicular signals for the generation of saccadic eye movements. J. Neurophysiol., 87: 845-858, 2002.
Ferster, D and Lindstrom, S. An intracellular analysis of geniculo-cortical connectivity in area 17 of the cat. J. Physiol. (Lond.), 342: 181-215, 1983.
Finlay, B. L., Schiller, P. H. and Volman, S. F. Quantitative studies of single-cell properties in monkey striate cortex. 1V. Corticotectal cells. J. Neurophysiol, 39, 1352-1361, 1976.
Foster, R. e., Connors, B. W. and Waxman, S. G. rat optic nerve: electrophysiological, pharmnaxological and anatomoical studies during development. Brain Res., 255: 371-386, 1982.
Franz, D. N. and Iggo, A. Conduction failure in myelinated and nonmyelinated axons at low temperatures, J. Physiol. (Lond.), 199: 319-345, 1968.
Gardner-Medwin, A. R. An extreme supernormal period in cerebellar parallel fibres, J. Physiol. (Lond.), 222: 357 – 371, 1972.
Gariano, R. F. and Groves, P. M. Burst firing induced in midbrain dopamine neurons by stimulation of the median prefrontal and anterior cingulated cortices. Brain Res., 462, 194-198, 1988.
Halliday A.M., McDonald W.I., Mushin J. Visual evoked response in diagnosis of multiple sclerosis. Br. Med. J., 4:661-664, 1973.
Hirsch, J. A. and Gilbert, C. D. Synaptic physiology of horizontal connections in the cat’s visual cortex, J. Neurosci., 11: 1800-1809, 1991.
Hoffmeister, B., Janiq, W. and Lisney, S. J. A proposed relationship between circumference and conduction velocity of unmyelinated axons from normal and regenerated cat hindlimb cutaneous nerves. Neuroscience, 42: 603-611.
Innocenti, G. M. The primary visual pathway through the corpus callosum: morphological and functional aspects in the cat. Arch. Ital. Biol., 118: 124-188, 1980. Izhikevich, E. M. Polychronization: Computation with spikes. Neural Computation, 18: 245-282, 2006
Kisvarday, Z. F. and Eysel, U. T. Cellular organization of reciprocal patchy networks in layer 111 of cat visual cortex (area 17). Neuroscience, 46: 275-286, 1992.
La Mantia, A.-S and Rakic, P. Cytological and quantitative characteristics of four cerebral commissures in the rhesus monkey. J. Comp. Neurol., 291, 520-537, 1990.
Lohmann, H. and Rorig, B. Long-range horizontal connections between supragranular pyramidal cells in the extrastriate visual cortex of the rat. J. Comp. Neurol., 344: 543-558, 1994.
Lubenov, E. V. and Siapas, A. G. Decoupling through synchrony in neuronal circuits with propagation delays. Neuron, 58: 118-131, 2008.
McDonald W.I. Pathophysiology in multiple sclerosis. Brain 97:179-96, 1974.
Miller, R. Distribution and properties of commissural and other neurons in cat sensorimotor cortex. J. Comp. Neurol., 164: 361-373, 1975.
Olivares, R., Montiel, J. and Aboitiz, F. Species differences and similarities in the fine structure of the mammalian corpus callosum. Brain, Behavior and Evolution, 57: 98-105, 2001.
Omi, T. and Shinomoto, S. Can distributed delays perfectly stabilize dynamical networks? , Phys. Review E, 77: 046214, 2008.
Paugam-Moisy, H., Martinez, R. and Bengio, S. Delay learning and polychronization for reservoir computing. Neurocomputing, 71: 1143-1158, 2008.
Pumphrey, R. J. and Young, J. Z. The rates of conduction of nerve fibres of various diameters in cephalopods. J. Exp. Biol, 453-466, 15: 1938.
Renganathan, M., Cummins, T.R., Waxman, S.G. Contribution of Nav1.8 sodium channels to action potential electrogenesis in DRG neurons. J. Neurophysiol., 86: 629-640, 2001.
Ringo, J. L., Doty, R. W., Dementer, S. and Simard, P. Y. Time is of the essence: a conjecture that hemispheric specialization arises from interhemispheric conduction delay. Cereb. Cortex., 4: 331-343, 1994.
Rosenthal, J. J. C., and Bezalilla, F. Seasonal variations in conduction velocity of action potentials in squid giant axons. Biol. Bull., 199: 135 – 143, 2000.
Schuz, A. and Preibl, H., Basic connectivity of the cerebral cortex and some considerations on the corpus callosum. Neuroscience and Biobehavioral Reviews, 20: 467 -470, 1996.
Sherman, S. M. and Guillery, R. W. On the actions that one nerve cell can have on another: distinguishing "drivers" from "modulators", Proc. Natl., Acad. Sci. USA, 95: 121-126, 1998.
Simmons, P. A. and Pearlman, A. L. Receptive-field properties of transcallosal visual cortical neurons in the normal and reeler mouse. J. Neurophysiol., 50: 838-848, 1983.
Sirota, M. G., Swadlow, H. A. and Beloozerova, I.N. Three channels of corticothalamic communication during locomotion. J. Neuroscience, 25: 5915 – 5925, 2005.
Smith K.J., Blakemore W.F., McDonald W.I.. The restoration of conduction by central remyelination. Brain 104:383-404, 1981.
Smith K.J., Hall S.M. Nerve conduction during peripheral demyelination and remyelination. J. Neurol. Sci. 48:201-19, 1980.
Smith, K. G. and Waxman, S. G. The Conduction Properties of Demyelinated and Remyelinated Axons 85-101. Waxman, S. G. (ed.). Multiple Sclerosis as a Neuronal Disease, Elsevier, 2005.
Sugihara I, Lang E.J., Llinas R. Uniform olivocerebellar conduction time underlies Purkinje cell complex spike synchronicity in the rat cerebellum. J. Physiol 470:243-71, 1993.
Swadlow, H. A. Systematic variations in the conduction velocity of slowly conducting axons in the rabbit corpus callosum. Experimental Neurology, 43:445-45, 1974a.
Swadlow, H. A. Properties of antidromically activated callosal neurons and neurons responsive to callosal input in rabbit binocular cortex. Experimental Neurology, 43:424-444, 1974b.
Swadlow, H. A. Impulse conduction in the mammalian brain: Physiological properties of individual axons monitored for several months. Science, 1982, 218:911-913.
Swadlow, H. A. Physiological properties of individual cerebral axons studied in vivo for as long as one year. J. Neurophysiol., 54: 1346-1362, 1985.
Swadlow, H. A. Information flow along neocortical axons. In: Time and the Brain, R. Miller (Ed.), Harwood Academic Publishers, 2000.
Swadlow, H. A. Efferent neurons and suspected interneurons in S-1 forepaw representation of the awake rabbit: Receptive fields and axonal properties. J. Neurophysiology, 63:1477-1498, 1990.
Swadlow, H. A. and Weyand, T. G. Corticogeniculate neurons, corticotectal neurons and suspected interneurons in visual cortex of the awake rabbit: Receptive field properties, axonal properties and effects of EEG arousal. J. Neurophysiology, 57:977-1001, 1987.
Swadlow, H. A. and Weyand, T. G. Receptive-field and axonal properties of neurons in the dorsal lateral geniculate nucleus of awake unparalyzed rabbits. J. Neurophysiol., 54: 168-183, 1985.
Swadlow, H. A., Waxman, s. G., and Geschwind, N. small diameter nonmyelinated axons in the primate corpus callosum. Archives of Neurology, 37:114-115, 1980
Swadlow, H. A., Kocsis, J. D., and Waxman, S. G. Modulation of impulse conduction along the axonal tree. Annual Review of Biophysics and Bioengineering, 1980, 9: 143-179.
Swadlow, H. A., Rosene, D. L., and Waxman, S. G. Characteristics of interhemispheric impulse conduction between prelunate gyri of the rhesus monkey. Exp. Brain Res., 1978, 33:455-467.
Takahashi, K., Slow and fast groups of pyramidal tract cells and t heir respective membrane properties. J. Neurophysiol., 28: 908-924, 1965.
Telfeian, A. E. and Connors, B. W. Widely integrative properties of layer 5 pyramidal cells support a role for processing of extralaminar synaptic inputs in rat neocortex. Neuroscience Letters, 343, 121-124, 2003.
Utzschneider, D.A., Thio, C., Sontheimer, H., Ritchie, J.M., Waxman, S.G. and Kocsis, J.D.: Action potential conduction and sodium channel content in the optic nerve of the myelin-deficient rat. Proc. Roy. Soc. Lond. B., 254:245-250, 1993.
Wang, S. S-H, Schulz, J. R., Burish, M. J., Harrison, K. H., Hof, P. R., Towns, L. C., Wagers, M. W. and Wyatt, K. D. Functional trade-offs in white matter axonal scaling. J. Neurosci., 28: 4047-4056, 2008.
Waxman, S. G. Integrative properties and design principles of axons. Int. Rev. Neurobiol., 1-40, 1975.
Waxman, S. G. Clinicopathological correlations in multiple sclerosis and related diseases. In: Demyelinating Diseases: Basic and Clinical Electrophysiology. Waxman, S. G. and Ritchie, J. M. (eds.), Raven Press, New York, pp. 169-182, 1981
Waxman, S. G. Current concepts in neurology: membranes, myelin and the pathophysiology of multiple sclerosis. New England Journal of Medicine 306:1529-1533, 1982.
Waxman, S. G. Axonal conduction and injury in multiple sclerosis: the role of sodium channels. Nat. Rev. Neurosci., 7: 932-941, 2006.
Waxman, S. G. Determinants of conduction velocity in myelinated nerve fibers, Muscle and Nerve, 3: 141-150, 1980.
Waxman, S. G. and Bennett, M. V. L. Relative conduction velocity of small myelinated and non-myelinated fibres in the central nervous system. Nature New Biol., 238217-219, 1972.
Waxman, S. G. and Swadlow, H. A. Ultrastructure of visual callosal axons in the rabbit. Exptl. Neurol., 53: 115-127, 1976.
Weyand, T. G., Malpeli, J. G., Lee, C., and Schwark, H. D. Cat area 17. 111. Response properties and orientation anisotropies of corticotectal cells. J. Neurophysiol., 56: 1088-1101, 1986.
Xu, K and Terakawa, S. Fenestration nodes and the wide submyelinic space form the basis for the unusually fast impulse conduction of shrimp myelinated axons. J. Exp. Biology, 202, 1979-1989, 1999.
Yates, M. A. and Juraska, J. M. Increases in size and myelination of the rat corpus callosum during adulthood are maintained into old age. Brain Res., 1142: 13-18, 2007