Evolution of pre-myelinate rapid conduction

[some of this material has been included in an article by Ann Castelfranco and Daniel Hartline, "Evolution of rapid nerve conduction" for Brain Research 2015.]
[original post: 2015-07-25]

Rapid conduction in nerve

The pinnacle of speed in rapid nerve impulse conduction is clearly reached by large myelinated nerve fibers. Wrapped in multiple layers of condensed membrane and some conducting at speeds over 200 m s-1, the morphological as well as the physiological differences between myelinated and non-myelinated nerve fibers could hardly be greater. Figure 1 illustrates this with electron micrographs of fibers from the same nerve trunk (the antennular nerve) in an amyelinate (A) and a myelinate (B) species of calanoid copepod. But why and how myelinate species diverged from amyelinate kin, some possibly as recently as 270 million years ago (Bradford-Grieve 2002), to evolve such an elaborate structure is less clear. Ancestral species had to go from amyelinate Point A (Figure 1A, Labidocera) to myelinate Point B (Figure 1B, Bestiolina) without degrading function. The "why" and the "how" of this will be explored below. We first examine the "ultimate" causes for evolution of rapid signaling -- the selective advantages that can be deduced from examining extant cases of rapid conduction.

Figure 1. Images by: (A) Jenn Kong; (B) Caroline Wilson

Why care about conduction velocity?

The ultimate cause of an evolutionary advance is the adaptive value or advantage of the evolved trait. It is usually taken for granted that conduction speed in the nervous system has adaptive value, and the faster the better. This is supported by several specific potential advantages it could have, any one or more of which might provide the selective force driving the evolution of higher speeds: 1) Timely reaction to predatory attack is perhaps the most often-cited and obvious advantage (e.g. Wine and Krasne, 1972). The sooner an organism can recognize the signs of such an attack, the more likely it will be able to take effective evasive measures. 2) More rapid conduction decreases reaction times in launching predatory strikes when opportunity arises suddenly and/or precise timing of an attack is critical (Zalc and Colman, 2000). 3) Greater speed can serve to better synchronize contraction of a distributed muscle sheet, all regions of which must contract at the same time to be effective (e.g. in cephalopod mantle: Pumphrey and Young, 1938). 4) It improves precision in temporal discrimination, since it reduces the impact of natural variations in the rate of conduction (Hartline, 2008; Wang et al., 2008). 5) Speed allows timely integration of information from spatially-dispersed sensors and better coordination of dispersed muscles. It thus allows evolution of more complex sophisticated nervous systems. 6) It permits evolution of larger body sizes, since faster speeds are needed to keep in timely communication with increasingly distant parts. [For discussion of limitations on speed, including "Bullock's Paradox", see "The Need for Speed."]

Proximate issues in the evolution of rapid conduction

Granted the value of rapid signal conduction, it is less obvious how the mechanisms for it came to evolve and be fine-tuned over the eons of geologic time. The millisecond reaction times of some organisms, and conduction velocities of over 100 meters per second in myelinated axons, had humble beginnings. Life forms have had to set a myriad of novelties in place without adversely affecting organismal fitness -- indeed enhancing it at each step. The evolutionary trajectory culminating in such speeds thus depends strongly on the "nuts and bolts" made available through evolution for the "physical plant." However, the evolved novelties are constraining within a given line, as they are for other evolutionary trajectories. They commit each independent line to a separate path. The comparison between lines is then revealing of both basic design principles and likely evolutionary pathways. These paths lead from improvements over chemical communication speeds through the invention of electrical signaling, to channels with integrated voltage sensors for impulse generation, then to core-conductor axons capable of reaching more distant points, and optimized for speed. At this point the paths diverge as the different forms of the complex insulation of myelin are added. The first several innovations appeared before the rise of the Bilateria. Myelin, on the other hand, has arisen independently in four different groups since the bilaterian radiation. In what follows, we will take up this sequence of innovations as a rough guide to a logical trajectory followed in the evolution of rapid conduction.

Non-regenerative mechanisms

Chemical signaling by diffusion

Starting with the very small, the size of single-celled organisms allows slower communication modalities to suffice, and these appear to have been the first to evolve. In the Bacteria, Archaea and unicellular Eukaryota, communication is often by chemical diffusion and reaction, as in the control of flagellar movement (Blair, 2003) and turning responses in chemotactic or phototactic bacteria (Zusman et al., 2007) and motile algae (Jékely, 2009). While the speed of diffusional communication in cells of bacterial size (μm) involves timescales of milliseconds for key small signaling molecules such as calcium, this timescale lengthens with the square of distance, which is a rapidly-increasing disadvantage as cells enlarge. Diffusion-dependent signaling still remains an important modality in "higher" organisms, as in the spread of calcium waves in astrocytes (Table I; see below), at synapses and in parasynaptic (retrograde) transmission (Fitzsimons and Poo, 1995), but the key to diffusional speed is employing small molecules over short distances. The need to circumvent this diffusional constraint as an organism evolves toward larger and more complex morphologies is likely to have provided the evolutionary impetus for the early emergence of faster conduction mechanisms.

Faster signaling by chemical transport

One way chemical communication can be speeded is through special adaptations for transporting the signal (or effector) molecules. This includes "advective" bulk transport of the fluid in which the chemical signal is embedded, as in cyclosis (cytoplasmic streaming) in certain plant cells and unicellular organisms, and carrier-based transport as in axonal transport in animals with nervous systems (Fitzsimons and Poo, 1995) and circulatory-system-based communication using hormones. The relative effectiveness of transport vs diffusional chemical conduction can be represented by the "Péclet number," Pe = Tdiffusion/Ttransport = UL/D, where U is the transportation velocity, L is the size of the communication dimension (e.g. cell length) and D is Fick's diffusion coefficient (Verchot-Lubicz and Goldstein, 2010). Pe ~ 1 is the dividing line between diffusion-dominated and transport-dominated signaling. With D for small molecules ~10-6 cm2 s-1 (100 m2 s-1) and intracellular transport processes reaching up to 100 m s-1 (Table I), diffusion can dominate in organisms below ~1 m (bacterial size). However, for even small molecules traveling at the slow rates of axonal transport (1 m s-1 when in motion: Roy et al., 2007) over distances of centimeters, Pe is much greater than 1, and transport becomes by comparison a "rapid conduction" modality (e.g. Mignot et al 2007).

Voltage-based passive signaling

Using the time-scale measure suggested above (§1.3), transport-based communication even as high as 100 m s-1 will only suffice for organisms that travel well under this rate, such as many protozoans (cyclosis is not found in prokaryotes, although other transport processes are: Zusman et al., 2007). A faster communication means is needed for larger organisms. This speed barrier was broken by the invention of voltage-based signaling. Voltage perturbations, even passively ("electrotonically") conducted, spread much more rapidly along cell membranes than chemical diffusion or transport (Table I). Various protozoans have achieved this by employing membrane-localized electrical signaling in the control of their locomotion. In the 100-200 m-long protozoan ciliate, Paramecium, a mechanical stimulus applied posteriorly activates a non-regenerative hyperpolarizing potassium current with a concomitant speeding of the forward propulsion by the cilia (Naitoh and Eckert, 1973; review: Martinac et al., 2006). The use of electrical signaling enhances the protozoan's capability for responding rapidly and correctly along its whole elongate ciliated body to predatory attack from behind. While electrical signals are intrinsically fast-conducting, they are also intrinsically slowed by the capacitance of the lipid membranes upon which they depend for the separation of charge needed to sustain a voltage signal. They also lack the richness that chemical signaling offers. For evolution to optimize an electrical modality of signaling, it must adjust the parameter controlling timing and response speed in passive membrane, i.e. the membrane time constant. Reducing membrane resistance shortens this time constant. However, the ability to conduct voltage signals over distance in an elongate cell depends on the length constant, which is also shortened by reducing membrane resistance resulting in greater spatial attenuation of the signal. The interaction between the two is subject to evolutionary mediation, and these same parameters are important in controlling the speed of conduction in myelinated nerves. Although typically slower than action potentials, passive conduction of non-spiking electrical signals is nevertheless retained in key roles even in nervous systems with well-developed spike-generating properties. The "all-or-none" nature of conventional spikes has the disadvantage of requiring intensity to be encoded in spike timing (e.g. frequency), which provides only intermittent rather than continuous information transfer. Passive graded signal conduction in electrotonically short processes, as for example in many dendritic trees, permits continuous but still timely spatial and temporal integration of local information prior to the spike generation used for long-distance communication. Vertebrate photoreceptors, bipolar and horizontal cells operate over short distances without spikes entirely, and even long-distance voltage-based signaling can be achieved without spikes, in neurons with elevated membrane resistance (Mirolli, 1979; Table I).

Regenerative voltage-based mechanisms

As cells evolve more elongated forms, electrical communication between increasingly distant points becomes difficult with passive electrical processes, owing to electrotonic decrement. Surmounting this impediment, while also assuring timely communication of the information that a critical (threshold) level of input has been reached, are likely selective forces that promoted the evolution of regenerative signaling. This solution was based on coupling a voltage sensor to an ion channel. The coupling came in two forms, a "graded" form in which a voltage perturbation of extrinsic origin was augmented by intrinsic mechanisms without being self-sustaining, and a self-sustaining action potential, typically of an "all-or-none" character. As an early example, also from Paramecium, the same mechanical stimulus that elicits a non- (or weakly) regenerative voltage signal when applied to the posterior end, when applied to the anterior end, elicits a regenerative (albeit not all-or-none) calcium action potential in the cilia, which causes ciliary reversal (Eckert et al., 1972; Naitoh et al., 1972; review: Eckert and Brehm, 1979). This enables the protozoan to respond within milliseconds by rapid backing away from collisions with objects in a manner again coordinated along its entire body. Calcium diffusion by itself from end to end of this 100 m organism would take ~10 seconds, and transport-based signaling ~1 second. Although most reported regenerative spike-producing mechanisms depend on depolarizing (positive-going) membrane mechanisms, hyperpolarization-activated regenerative hyperpolarization can be produced in Paramecium in a potassium-free medium (Eckert and Brehm, 1979), in Necturus inner segments amplifying the negative-going primary receptor potential (Werblin, 1975) and mediating rapid relaxation in Ascaris oesophageal muscle (delCastillo and Morales, 1967) among others (Grundfest, 1961).

Signal conduction in multicellular organisms

With the arrival of the key evolutionary leap of multicellularity, the need arose to coordinate activity among multiple individual cells by extending impulse conduction to intercellular communication. The most widely-used solution has been the evolution of special channels directly bridging between adjacent cells. Such a bridge probably evolved initially to pass small signaling molecules of different kinds. Throughout much of the animal kingdom such bridges are provided by gap junctions, which are broadly produced by the pannexin family of proteins (also connexins in chordates and plasmodesmata in plants) (White et al., 1995). Such systems evolved in basal metazoans (Mackie, 1965) and, with a few notable exceptions, are nearly ubiquitous between cells in physical contact, whether or not dependent on electrical signaling. Gap junctions in vertebrate brain have recently come into focus as the means by which waves of ATP-activated calcium entry into astrocytic networks spread. While still only partially understood, these slowly-propagating waves are limited by the central role played by chemical diffusion (Table I; e.g. Charles, 1998; Stout et al., 2002). However, the same gap junctions enable communication through the flow of ionic current and hence electrical signals. In such a role, these become "electrotonic connections" or "electrical synapses" according to the time-scale of signals being passed. Gap-junction-mediated spread of electrical signals among epithelial cells has been identified as the modality for producing coordinated swimming behavior in certain basal metazoans including ctenophores (Satterlie and Case, 1978) and jellyfish (Mackie, 1965, Mackie and Passano, 1968; review: Mackie, 2004). Electrically-mediated excitation in epithelia of various jellyfish spreads at 0.15 - 0.55 m s-1; that among heart muscle cells in a range between 0.05 to 4 m s-1 (Table I).

Impulse conduction in plants

Strange as it may seem to those focused on animal nervous systems, it has long been known that motor activity in plants is accompanied by electrical signals. These signals are now known to mediate the activity. Galvanometric responses from stimulated Venus fly traps were described by Burdon-Sanderson (1873), including their activation by electrical stimulation. More recently, it has become increasingly clear that other higher plants also use propagating all-or-none ionic-current-based electrical signals to mediate key physiological processes, not restricted to rapid movements as in the fly trap or Mimosa (review: Fromm and Lautner, 2007). These tend to be prolonged (seconds) and slowly propagating (cm per second: see Table I), but have all the basic features of nerve action potentials including a specialized conducting system in the phloem, as a plant equivalent of a nerve trunk. Nevertheless, since plants cannot pick up their roots and run to escape predators, nor do most have the capabilities for rapid motor behavior like the whomping willow (Rowling 1998), the selective forces for more rapid conduction appear not yet to have produced the more rapid impulse conduction speeds found in animals (albeit some reports of surprisingly rapid conduction have appeared recently). What we learn from examining the plant situation is that as in animals, voltage-dependent mechanisms modifying the conductance state of ion channels in conjunction with an electrical conducting system situated in elongate cells with specialized "electricity-friendly" connections to other cells seem to be the design features utilized to best effect in long-distance rapid (as plants go) signal conduction.

Speeding voltage-based regenerative processes

Certain green algae with elongate cells provide added insight into rapid conduction principles. These are among the more basal organisms to have employed the voltage-regenerative modality of conduction to communicate over their length (e.g. Findlay, 1959). For producing the inward currents of regenerative impulses, neuroscientists are used to thinking in terms solely of Na+ and Ca2+, both cations, as charge carriers, with voltage-gated cation-selective channels as their conduits. However, the stonewort alga Nitella (Figure 2 from Wikipedia) (and the related Chara) respond to predator-induced injury with action potentials that communicate the injury and coordinate the response: halting protoplasmic streaming to minimize damaging cytoplasmic loss (Wayne, 1993). The main depolarizing inward current sustaining this action potential is provided not by Na+ or Ca2+ entry but by Cl- exit through chloride/anion-selective channels. The signal propagates at rates comparable to those for calcium spikes in cnidarian epithelia and axons (Table I). Thus at some level, choice of ionic species has little intrinsic impact on impulse speed. The ubiquity of calcium channels as charge carriers in many cells may be largely owed to the role for calcium established early in evolutionary history as a diffusion-conducted messenger within cells. Voltage changes originally produced as a byproduct of receptor or stimulus-based selective calcium permeability may have facilitated evolution of faster voltage-gated processes. Nor is there an intrinsic necessity for voltage signals to be depolarizing (positive-going), as the regenerative hyperpolarizations in Paramecium, Ascaris, and vertebrate rods illustrate. The few cases of regenerative hyperpolarization that have been investigated identify potassium ions as the primary charge carrier (delCastillo and Morales, 1967; Eckert and Brehm, 1979; Werblin, 1975,). While a few voltage-based signals involve conductance decreases e.g. vertebrate photoreceptors, Werblin 1975), the lengthening of overall membrane time constant makes this an unlikely mode for the most rapid communication. Further investigation of se issues would be informative.

Molecular substrates

Accompanying the evolutionary changes in the morphological and physiological traits that underlie more rapid conduction is of course much molecular evolution, most of which we will not deal with here. However the evolution, diversification, and activation mechanisms of inward current channel proteins are particularly relevant to speed issues. In a departure from the "standard" molecular channel model, the chloride channels of Nitella do not themselves contain a voltage sensor. Conduction requires a two-step process: depolarization gates the entry of calcium ions from extracellular (or tonoplast) sources, which ions in turn activate the chloride channels internally (Wayne 1994). This two-step process slows it (Castelfranco, 1988). However, a two-step process was once considered possible for the rapid conduction of nerve impulses through local acetylcholine release followed by short-distance diffusion and receptor binding before the current picture emerged (Nachmanson, 1961; Ritchie, 1967). Single-step activation of voltage acting on a voltage sensor that is intrinsic to the channel protein is potentially more rapid. However, that in itself is not sufficient to assure the fastest channel kinetics. When expressed in mammalian cell lines, the bacterial sodium channel, which contains such a sensor, is much slower to activate than eukaryote sodium channels (NaV; Ren et al., 2001). Further, the closely-related (some have suggested ancestral to NaV) calcium channels for all of their diversity in the service of a variety of functions, are slow compared with NaVs. It has been suggested that this ability to utilize rapidly-conducting electrical signals, in particular the voltage-sensitive variety, arose during evolution from a non-voltage-sensitive ancestral ion-channel molecule consisting of two trans-membrane segments (S5 and S6) connected by an ion-selective pore-lining "p-loop." To this was then added a voltage-sensor complex consisting of four more trans-membrane segments (S1-S4) (Moran et al., 2015). This strategy has been retained (or convergently evolved) and elaborated upon (as with the joining of four such subunits to form calcium and sodium-selective channels) to produce the principal voltage-gated channels of more rapidly-conducting metazoan nerve.

Origins of the nervous system

The multicellular cell-to-cell "bucket brigade" approach to signal conduction tends to be slow as it leads to circuitries with high access resistances and capacitances (e.g. Lieberman et al., 1973). While this organization provides notable exceptions in the multicellular lateral giant axons of decapods (Payton et al., 1969) and the medial giants of earthworms (Oesterle and Barth, 1981) , electrical synapses still produce a synaptic delay. While such delays may be acceptable or inevitable for some communication, especially local, timely signaling to remote parts requires the invention of long-distance pathways along which electrical impulses can travel unimpeded by junctional delays. This doubtless contributes to the remarkable early evolutionary innovation of a long thin filiform cell specialized for communication: a "neuron."

Metazoan electrical communication

Surviving examples of the neuronal communication system that arose early on are found in ctenophores and cnidarians. Their nervous system includes regenerative impulses capable of traveling long distance through interconnected networks of axons from sites of input to effector organs (Satterlie, 2015). The communication is, however, generally slower than in nerve fibers of more advanced groups (Figure 3, starred points). Part of the explanation for this appears to be the inheritance from protist ancestors of relatively slow voltage-gated channels. The particularly slow ones are permeable to calcium rather than sodium, but even axons with sodium-gated channels fall below the curve for more advanced groups in conduction speed for a given diameter (Meech and Mackie, 1993). Indeed, the employment of calcium as a charge carrier in long-distance axonal conduction is rare, even among cnidarians. Sodium is by far the dominant charge carrier in rapidly-conducted metazoan action potentials, probably in part, at least, due to its adaptability to more rapid gating (see discussion in Meech, 2004). Nevertheless, the early evolution of a voltage-gated calcium channel molecule is a major advance in communication, since it has allowed linking of four previously separate subunits into a single molecule capable of forming a channel on its own, the different portions of which can be tailored to different functions, such as inactivation, within the same molecule (Moran et al., 2015).

Figure 3: Conduction velocity for nerve fibers vs fiber diameter. Lines indicate general relations over a range of diameters, many taken from Bullock and Horridge (1965) but adjusted to a standard temperature of 20 C using a Q10 of 1.8 (Chapman and Pankhurst 1967) and an internal and external ionic conductivity of a squid axon (35.4 Ω cm). Thus vplot = vmeas = 1.8(20-T)/10(35.4/Raxoplasm) where T is the temperature in degrees C for the measured velocity vmeas and Raxoplasm is the specific resistance of the axoplasm, if available, or the extracellular medium if otherwise. Specific labeled points or lines from the following sources: Squid: Hartline & Young 1936 cited in Pumphrey and Young (1938); Earthworm: Eccles, Granit & Young (1932); Penaeus and Macrobrachium: Kusano (1966). Crayfish: Govind and Lang (1976); Hydromedusa: Mackie and Meech (1985).

Cables for rapid propagation of regenerative signals

Theoretical considerations: the Huxley function

In 1855, Lord Kelvin develpped the mathematical description of the way electric current flows in a "core conductor" consisting of a cylindrical insulator separating two conducting media, an inner "core" conductor and an external surrounding one. The same equivalent electrical circuit and mathematics apply to nerve fibers, both unmyelinate (Figure 4A) and myelinated (Figire 4B).

Figure 4. Core-conductor circuitry of (A) an unmyelinated fiber and (B) a myelinated fiber. Arrows indicate the current flow for impulses generated in the membrane patch labeled "1". Current of the rapidly-rising voltage upstroke predominantly flows out through capacitances of adjacent membrane, "2" , which provides accessible paths in unmyelinated fibers (A), but which carry little of the current in myelinated axons because of the lowered capacitance of the internode. The current is instead directed farther down the fiber to charge the capacitance of the next node, "3" .

Its application to passive signal spread in axons by Rushton (1951) and others was followed by the seminal research of Hodgkin and Huxley (1952) on the biophysics of action potential propagation along such cables. It is with these advances that additional factors affecting conduction speed became apparent. Huxley (1959) analyzed solutions of the Hodgkin-Huxley (HH) equations as a general case of a wave traveling along a uniform cable at constant velocity and showed that the velocity can be represented as the product of two factors dependent on the 5 basic parameters describing the active cable:

(1) ν = α½f(β), for α = k d /(R C) and β = γ/(k C),

where k is a scaling parameter for the rate constants of the active channels, d is the diameter of the axon, R is the specific resistance of axoplasm, C is the specific membrane capacitance of the axon, and ? is a scaling parameter for the conductance density of the active channels. The "Huxley function", f(β), is a unitless empirically-determined function, which is plotted, normalized to squid axon parameters (indicated by the subscript "0"), in Figure 5A (see caption for details). Multiplying f(β) by α½, for any set of values of the 5 parameters yields a predicted velocity for that set. Three such (normalized) plots are superimposed in Figure 5B: varying the activation rate constant factor (k0: broken line), varying the membrane capacitance factor (C0; dotted line) and varying peak channel conductance factor (γ0: solid line). Note that the latter line coincides with the f(β) line, since conductance does not contribute to γ. Thus the analysis predicts a maximum of f(β) = 1.16 for γ = 6.5, which gives a peak in the velocity vs conductance relation (Figure 5B). Hodgkin (1975) and others have recognized that the sodium channel density in the squid giant axon may have evolved to maximize conduction velocity. However, the maximum for the Huxley function predicts a channel density much greater than that actually observed (Figure 5; Castelfranco and Hartline, 2015), and even carefully refined models of the squid action potential including voltage-dependent gating currents predict an optimal sodium channel density significantly larger than the densities observed in nature (Sangrey et al., 2004). Crotty et al. (2006) addressed this problem and proposed that when the metabolic cost of conduction velocity was taken into account, the squid channel densities indeed minimized the metabolic cost of an impulse for a given velocity and axon diameter. Thus the adaptive pressure for faster conduction is countered by adaptive pressures from other sources, and the balance among these competing influences must be quantitatively accounted for in modeling the evolution of rapid conduction.

Figure 5: Huxley function. (A) Plot of f(β) vs γ normalized to parameters for a Hodgkin-Huxley squid axon. A maximum occurs at β = 6.5. (B) Plots of of predicted conduction velocity (ν normalized to squid value of 12.3 m s-1 at 6.3 degrees C) as functions of three of the cable parameters, specific capacitance (C0 normalized to squid values of 1 μF cm2), channel rate constants, k0 (relative to squid at 6.3 degrees Ceslius) and channel density, γ0 (relative to squid).

Enhancing cable conduction: Rate kinetics

In addition to optimizing channel densities, another way to increase conduction speed is to speed the kinetics of the active channels. The Huxley formulation shows, and model runs and experimental manipulations confirm, that conduction velocity of the squid axon can be increased by increasing the rate constants (principally the opening rate for sodium; increasing temperature is one way to increase channel rate kinetics uniformly). However, the increase in speed obtained is only modest, as the f(β) curve is nearly flat for axons with squid parameters, so conduction speed only increases with the square root of the rate-constant factor.

Enhancing cable conduction: ri-based mechanisms

Basal metazoans invented a third mechanism for speeding communication, exploiting the fact that a lowered internal core resistance, ri, of an axon enhances the electrotonic spread of current and hence increases the velocity of nerve impulses. Two strategies have evolved over time for doing this: increasing the inner diameter of the axon core and decreasing the specific resistance of the electrolyte contained in that core.

Axon diameter

Enlarging axon diameter operates on the fact that internal axial resistance decreases rapidly as the square of diameter. For unmyelinated fibers, impulse propagation velocity increases with diameter, usually with close to a square root dependence (Pumphrey and Young, 1938; Figure 3; but for deviations, see e.g. Hoffmeister et al., 1991; Govind and Lang, 1976). In terms of evolution, this should be a relatively easy route, since the mechanisms for increasing axonal diameter already exist for the developmental program. The principle is taken to an extreme in the evolution of "giant axons" several times larger than other large axons in a nervous system. Such giant axons occur throughout the Metazoa, often associated with escape or other rapid reactions in organisms possessing them. Unmyelinated giant-fiber-mediated escape systems of Hydrozoa, Reptantia (crayfish) and Oligochaeta (earthworms) have already been mentioned. Those of polychaetes have been extensively reviewed by Nicol (1948), mediating among tube worms the dramatically-fast withdrawal of gills and retreat to cover. Among insects the collection of giant fibers in the ventral nerve cord have been shown to underlie the rapid directional response of a cockroach to air puffs, as would be produced by a predatory attack (Camhi and Tom, 1978). Figure 6 shows an example of such a "giant" fiber in a predatory caterpillar, an inchworm relative, to illustrate the size differential in such rapidly-conducting axons. The best-known of the cases is undoubtedly the giant axon in the mantle nerve of squid, brought to light by J. Z. Young (1936) and made famous by Hodgkin and Huxley (1952) among others, which mediates the escape jetting of that organism (adaptive, perhaps, as much for its synchronization of muscle contraction as for its quick reaction: Pumphrey and Young, 1938). The Mauthner-cells mediating fast-starts in amyelinate lampreys provide a classic vertebrate example (Rovainen, 1967). Thus while basal metazoans were the first to invent "giant" axons (e.g. Satterlie, 2015), these axons remain a recurrent feature of rapid-response circuitry throughout the animal kingdom.

Figure 6. Giant fiber from the ventral nerve cord of a carnivorous caterpillar, Eupithecia orichloris. The caterpillar, a member of the geometrid family (inch worms), when contacted on posteriorly-located hairs by a small insect, launches a rapid attack with the anteriorly-located grasping appendages, possibly mediated by this fiber. Scale bar: 2 μm. Image by J. Kong,

Speeding communication by enlarging core-conductor (axon) size has implications for long-distance communication in organisms against the backdrop of an evolutionary trend toward larger body size (also relevant to developmental changes). Because of its square root dependence, scaling of conduction speed with axon dimensions is allometric, obeying a power function with an allometric coefficient (exponent) less than 1.0 (negative allometry). Thus, if a neuron in which it takes a certain time for an impulse to propagate its length doubles in size in all dimensions with growth or evolution, it will take 2½ times or ~40% longer for impulses to reach the terminals. This means that if an organism doesn't increase the relative size of its axons (and as it turns out, other neuron metrics) as it evolves to larger size, it is increasingly sluggish in its ability to communicate with its distant parts. One solution is "isoelectrotonic" growth, in which unmyelinated axon diameters increase as the square of the growth in length, as has been documented in cricket (Olsen et al., 1996), but such growth in a vertebrate would lead to unmanageably large heads (and swelled heads in people!). If the "need for speed" only increases as the 2/3 power of body length (§1.4), the shortfall only increases as the 1/3 power of length, but this is still disadvantageous. Two ways around this impediment have evolved:

Increased conductivity of the core

An additional method for reducing ri, is to provide the core conductor with more highly-conducting medium. This has been the case for marine invertebrates, which, in order to maintain body fluids isotonic with the surrounding sea water, maintain a high axoplasmic ionic strength giving a specific resistance of 35 Ω cm (Hodgkin and Huxley 1952) or above. With much lower ionic strengths in vertebrates and non-marine invertebrates, axoplasmic specific resistances are typically 3-fold higher, so a marine invertebrate axon of a given size can conduct almost twice as fast (a correction for this has been made in the plots of Figure 3). This principle has been carried even further by penaeid shrimp, in which the heavy myelin sheath forms a tube surrounding a large extracellular space (Xu and Terakawa, 1999; Figure 7). Instead of axoplasm, much of the interior of the tube is filled with fluid having conductivity close to that of sea water (23 ? cm: Kusano, 1966) as the core conductor, which in turn is predicted to increase conduction speed by 25% above that of squid axons of comparable diameter.

Figure 7: Extracellular space (ex) enclosed in a myelin-lined (my) tube including a much reduced axon (ax) from a penaeid shrimp (Litopenaeus vannamei). Transmission electron micrograph of a cross-section of the ventral nerve cord by Monica Orcine.

In principle, altering the external medium could have a similar effect on conduction, either by altering its conductivity or especially by increasing the electromotive driving force (EMF) on the inward current carriers (e.g. Katz, 1947; Hardy 1973). While such a mechanism is utilized to amplify mechanoreceptive signals in the ear (Ochs 1965), we are unaware of examples of its being used to specifically speed nerve impulse conduction. However, in a related phenomenon, the specialized perineurium of insects provides their nervous system with an assured supply of the necessary sodium ions required for reliable conduction speeds in the face of highly variable and potentially disruptive ionic compositions of hemolymph (Treherne and Schofield, 1981).


Summary of principles

Table I is still under construction - apologies for its absence!


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This material has been assembled and presented as a public service by Dan Hartline, Bekesy Laboratory of Neurobiology, Pacific Biosciences Research Center, University of Hawaii at Manoa (danh at hawaii.edu). Opinions expressed here are those of the author and do not represent the position or policies of the University or any funding agency.
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