Conduction of nerve impulses

This chapter is vaguely relevant to the aims of Section K1(iv) from the 2017 CICM Primary Syllabus, which expects the exam candidate to "explain the basic electro-physiology of neural tissue, including conduction of nerve impulses and synaptic function". This subject matter has only come up once, as part of Question 3(p.2) from the first paper of 2009, which was only passed by 30% of the trainees. Fortunately, this was one of the older questions, and the college comments were quite informative regarding what the examiners' expectations were. The headings of this chapter were based on the main points mentioned in this answer.

If one has the right kind of library, A.G Brown's "Nerve Cells and Nervous Systems" (2001) is excellent, even if you can only get a hold of the action potential chapter. Specifically, everything from page 27 onwards is pure gold. Alternatively, the free article by Bean (2007) is very good, even though it is clearly written for somebody already immersed in the deep lore of neurophysiology.

Physiological basis of the resting membrane potential

It would seem pointless to restate a large amount of material already covered in the chapter on the mechanisms responsible for the cell resting membrane potential, and in excellent peer-reviewed papers such as Wright (2004) . Instead, one can summarise this subject as follows:

• The resting membrane potential (RMP) is the voltage (charge) difference between the intracellular and extracellular fluid, when the cell is at rest (i.e not depolarised by an action potential).
• Mechanisms responsible for the resting membrane potential include:
  • Chemical gradients generated by active transport pumps: the concentration of ions are significantly different between the intracellular and extracellular fluid, eg. the ratio of potassium ions is 35:1.
  • Selective membrane permeability: the cell membrane is selectively ion-permeable, specifically it is much more permeable to potassium ions
  • Electrical gradients are generated because potassium leak (via K_2P channels) from the intracellular fluid creates a negative intracellular charge. This charge attracts potassium ions back into the cell and thus opposes the chemical gradient.
  • Electrochemical equilibrium develops when electrical and chemical forces are in balance for each specific ion species, and this is described by the Nernst equation.
  • The Nernst potential for each ion is the transmembrane potential difference generated when that ion is at electrochemical equilibrium.
  • The total membrane resting potential for all important ion species is described by the Goldman-Hodgkin-Katz equation, which takes into account the different membrane permeabilities for each ion. 

These Nernst potentials for all the important species, as well as the total RMP they generate, can all can be plotted on the same graph.

These upper and lower limits demonstrate the "boundary conditions" of the membrane, i.e. it cannot be any more positive than + 64 mV (the Nernst equilibrium potential for sodium), or more negative than -92 mV (the equilibrium potential for potassium). These numbers come from a thought experiment by Wright (2004), and will obviously vary in nature, but the point remains the same: at rest, with normal intracellular and extracellular electrolyte concentrations, the net charge of the intracellular side of the cell membrane is negative.

Magnitude of the resting membrane potential

How negative is the inside of the neuron, as compared to the outside? Most of the time, textbooks give -70 to -90 mV as the normal transmembrane resting potential for neurons, but where does it come from? Textbook authors usually either completely fail to disclose their sources or reference an older textbook, but by gradually pulling on these threads, one ultimately arrives at a huge pile of dead squid.

Most of the earliest most influential studies of neurophysiology data we have seems to have come from studies performed on the squid giant axon. It's the nerve that innervates the concentric mantle cavity muscle of a squid, used by the animal for rapid waterjet propulsion. Specifically, giant axons of the longfin inshore squid (Doryteuthis pealeii, formerly Loligo) became the default axon for neurophysiology research. This is because this particular species of squid was "most commonly found at Wood's Hole", the fishing community where J.Z. Young (1938), the pioneer of squid axon physiology, went looking for his subjects. Theoretically, any other squid would have probably been fine too, but neurobiologist are creatures of habit and the Loligo genus became embedded in their folklore for decades, such that people in the 1970s were publishing practical guides for undergrads on how to handle and prepare these animals (these "tricks of the squid trade" are still available from the Woods Hole Open Access Server). It does not hurt that this species enjoys massive abundance; the annual domestic catch in the US alone was 19,044 metric tons in 2016.

Thus, as the result of being widely available, cheap, and monstrously huge (1.5mm in diameter), squid axons ended up being used by Huxley and Hodgkin in the late 1930s-early 1940s to investigate the behaviour of ion channels. The size was important because it made it much easier to stick a microelectrode inside the axon to record the potential difference across the membrane. This is where they first recorded and described the resting membrane potential and the passage of an action potential in 1939:

 

You will note that this oscilloscope recording puts the resting membrane potential at something like 55 mV, which is different from what the textbooks usually quote. Huxley & Hodkin themselves remarked that 

"The potential difference across the membrane may be greater than this, because there may be a junction potential between the axoplasm and the sea water in the tip of the electrode. This potential cannot be estimated, because the anions inside the nerve fibre have not been identified."

One might think this is all the consequence of ersatz equipment (they are forgiven for this anyway, being Nobel-winning pioneers in the field). However, when later authors tried to fill in the blanks with better instruments, the accuracy of the estimates did not improve. The reason for this is clearly the dynamic and variable nature of RMPs in the substrate tissue. As should be abundantly clear to most normal people, the  -70 to -90 mV value quoted by textbooks should be viewed as a guess. True measured RMP will vary from species to species, from axon to axon within a species, and even along the axon of a single neuron. Moreover, that potential doesn't just sit there statically, as the neuron in vivo is constantly buffeted from all sides by gusts of local chemical and electrical activity. As an example, Li & McIlwain (1957) recorded cortical resting potentials in the range of -1 to -91 mV in their guinea pig model, and those were just inert brain slices in a nutrient goo. The best guess for what is happening in the living human brain probably comes from work like Crochet & Petersen (2006), who worked on collecting action potential data from intact mammalian neurons. A representative 20-second recording is reproduced below, showing the activity of a barrel cortex neuron from an awake mouse.

Ionic basis of the action potential

The nerve action potential does not have such well-defined phases as the cardiac action potential, but there are certainly predictable elements in its shape, and it is punctuated by ionic events which will be familiar to the person who had just studied cardiac or muscle physiology. In this sense, the resting membrane potential of the neurons represents "Phase 4". 

Threshold potential

As a neuron is stimulated (for example, through neurotransmission or by the arrival of an action potential from elsewhere), the resting membrane potential is disturbed. At a certain point, the membrane potential reaches a critical value which causes voltage-gated sodium channels to open and produce a depolarisation of the membrane.

The specific membrane potential at which this happens is the threshold potential, occasionally referred to as the spike threshold, and it is highly variable between cells and even over the timeframe of seconds within the same cell. From this, it should follow that - like with the resting membrane potential - the only real interest a person should have in the Exact Number of millivolts is for the purpose of labelling their graph in the exam. Sure, among the official textbooks of the CICM syllabus there is a bit of disagreement, but ultimately it appears that -55 mV is the correct value to regurgitate:

• Kam & Power (p. 7 of the 3rd ed., 2015) give -55 mV
• Guyton & Hall (p.69 of the 13th ed., 2016) give -65 mV
• Ganong (p.86 of the 23rd ed., 2010) give -55 mV

The essential take-home message here is that memorising numeric values is pointless, and that to grasp the concept is by far the more important achievement. That concept is that there is a threshold potential, usually about 10-15 mV less negative than the resting membrane potential, and at this potential, the voltage-gated sodium channels all suddenly open.  Different kinds of sodium channels have different threshold potentials and may be distributed in different locations around a neuron, giving rise to the observed variability in threshold potential. For example, it appears to be advantageous to have a bunch of low-threshold channels available in their greatest density at the "AP trigger zone", a specialised highly sensitive area at the distal portion of the axon initial segment (Katz et al, 2018).

The voltage-gated sodium channels respond to the change in transmembrane potential by undergoing a conformational change that opens the pore through which sodium can move. Beyond describing their function in this simplistic way, nothing additional can be said that would make any sense. According to a recent opinion by a group of authorities (Lenaeus et al, 2017), the molecular innards of the voltage-gated channels "remain uncertain due to the size and complexity of eukaryotic Na_v channels, which are >200 kDa, contain 24 transmembrane segments, and remain resistant to detailed structural analysis". Helpfully, there are also at least nine subtypes (Nav1.1 - Nav1.9), most of which are expressed variably all around the CNS, and which have some subtle differences in their function, sodium flux capacity, and threshold. With no clear end to the topic of sodium channels, it would probably be better to just drop a reference here for further detailed reading (Wang et al, 2017, in case anybody is interested) and move on. 

"All-or-nothing" effect

Sometimes referred to as the "all-or-none" effect, this refers to the finding that 

"Once an action potential has been elicited at any point on the membrane of a normal fiber, the depolarization process travels over the entire membrane if conditions are right, but it does not travel at all if conditions are not right. This principle is called the all-or-nothing principle"

- Ganong, p.69 of the 23rd ed, 2010

Talking abut conditions being "right" or "not right" does not sound very scientific, and even though Ganong is the official CICM exam preparation resource, one might be tempted to look for a better definition. For example, this:

"The stimulus either (if it is subthreshold) fails to set up an impulse, or (if it is threshold or above) sets up a full-sized impulse."

- Nerve and Muscle, Keynes & Aidley, p.17 of the 2011 edition

Or, after Henry Pickering Bowditch (1871), who first discovered this phenomenon in cardiac muscle,

"An unserem Object bewirkt der Inductionsstrom entweder eine Zucking oder er vermag dieses nicht"

which can be loosely translated as "it either fully twitches, or it doesn't". In short, this principle describes the observation that in nerves (and various other excitable tissues) the "strength" of a response (however you decide to measure the magnitude of it) will not be proportional to the stimulus. A feeble stimulus or a potent stimulus will have exactly the same effect: if the threshold potential is achieved, each will produce an identical action potential response. On the other hand, if the stimulus is "subthreshold", and is unable to achieve the necessary 10-15 mV positive change in transmembrane potential, there will be no action potential of any sort. This sort of response is the exact opposite of a graded response, where the magnitude of response has some relationship (eg. is proportional) to the magnitude of the stimulus.  If one ever needed to represent this in the form of some sort of diagram, this would be the most recognisable form of it:

That is not to say that nerve transmission is completely binary.  Of course the "response" itself may vary quite dramatically in its magnitude, depending on things like the number of nerve fibres recruited and the rate of their firing. In this way, all-or-none conduction can still be used to communicate the "gradedness" of a stimulus, or to produce different grades of response. However, taken individually, an isolated nerve fibre will produce a stereotyped response to any sufficient stimulus.

Depolarisation of the neuron membrane

Like the fast voltage-gated sodium channels of the myocardium, which snap open like a gunshot, the sodium channels of the nervous system depolarise rather rapidly, particularly where there is some sort of motor or sensory information to be conducted. Other neurons are somewhat more sluggish. It is actually important to remember that neurons all differ in their functional characteristics, and therefore should all be expected to have differently shaped action potentials. Bean (2007) produces a whole array of different recordings from about seven different authors to illustrate this fact. That diagram is already good, but for some internally upsetting reason the author has presumed to upstage the artists of the Nature Publishing Group by plotting exactly the same action potentials on the same set of coordinates.

In many respects, there are similarities between all excitable tissues, but there are also differences. For example, the transmembrane sodium concentration gradient of neurons is a bit different. Intracellular sodium is said to be around 9mmol/L in working myocytes, but is 30 mmol/L in mature spinal neurons, and up to 60mmol/L in developing ones (Lindsly et al, 2017). There are also numerous variants of sodium channels, and their expression on the surface of the specific membrane you are measuring is obviously going to influence the behaviour of the action potential. In short, it would be unexpected for all of them to depolarise in exactly the same way.

Anyway: with the opening of some voltage-gated channels, the transmembrane potential becomes more positive, which has the effect of opening even more voltage-gated channels, which means the early stages of depolarisation have a ski-slope hyperbolic appearance, as the rate of voltage change climbs steeply following a stimulus. If you plot the rate of voltage change (dV/dt) against transmembrane potential, you can clearly see this relationship as a steady linear increase. Here's a vandalised diagram from Bean (2007) to illustrate:

In summary: a suprathreshold stimulus opens sodium channels, and more sodium channels keep opening as the membrane becomes more positive, bringing about a substantial and accelerating inward sodium current. This is the first major step in the nerve action potential.

Repolarisation

The sodium current, if allowed to run things on its own terms,  would rapidly put the membrane at the potential difference equivalent to the Nernst potential for sodium, which would be something like +52 mV. And it would stay there. Clearly this does not happen. The action potential is called a "spike" because it is a fleeting momentary event; all the sodium entry stops quite quickly, the membrane never reaches the sodium Nernst potential, and is rapidly restored to its original resting potential. This happens because of two main factors:

• Voltage gated sodium channels do not remain open for long- they slam shut at the peak of the of the action potential, and enter an absolute refractory period which ends well into the undershoot period. Thus, no further inward sodium current can occur; no additional positive charge can enter the cell.
• Voltage-sensitive potassium channels open and allow potassium to leave the cell, which pushes the membrane potential into a more negative territory (i.e. this is positive charge leaving the cell).

Then, given enough time, Na⁺/K⁺ ATPase will dutifully pack all of the potassium back into the neuron, and dutifully extrude all of the sodium, so that the cycle can occur again.

When this is discussed in textbooks, they usually limit the discourse to covering only sodium and potassium movements, mainly because those are the main electrolyte species acting in the squid axon, and that's what Hodkin & Huxley (1952) were experimenting on when they created their famous diagram. Stripped of all the charm that comes with scientific accuracy and axis labels, that current diagram looks like this:

There are, of course, numerous other ion channels and ion currents active during the neuronal action potential (of which the most important is probably calcium), but for the time being, the most important matter to internalise is that an outward potassium current mediates much of the repolarisation in neuronal action potentials. 

"Undershoot" or afterhyperpolarisation

The concept of "undershoot", just as the concept of "overshoot", is bizarre because it implies that the membrane ion channels are aiming for some kind of goal and just aren't quite accurate enough to hit it. In neurophysiology this term usually describes the post-spike negative dip in transmembrane potential, which transiently falls below the normal resting membrane potential. "Afterhyperpolarisation" is much more accurate, if less mellifluous, term to describe this phenomenon. Without going into excessive detail, it appears that this happens because of persistent calcium-activated potassium channel activity, which are opened by the intracellular influx of calcium during the action potential (Shah & Haylett, 2000).

Apart from being a weirdly named thing that you need to remember for exam purposes, afterhyperpolarisation has a specific physiological role to play. It is a feedback mechanism which shapes the frequency of neuronal firing, bringing it under regulatory control by means of manipulating intracellular calcium (Sah & Faber, 2002). For example, one important role for it is in the management of "pacemaker" neurons where it influences the rate of spontaneous depolarisation (eg. in the neurons of the suprachiasmatic nucleus).

Propagation of the "nerve impulse"

One often comes across the phrase "impulse" when referring to the movement of an action potential along an excitable membrane. The use of this term is ubiquitous (as in "the nerve impulse") and is even found in the CICM syllabus document. It is a borrowed name misused in neurobiology, much to the scoffing of physicists ("lol, J =∫Fdt"), and probably represents a persistent anachronistic metaphor from the days when people like Ludimar Hermann (1899) were trying to explain nerve conduction by likening it to electrical signals in an insulated telegraph cable. Most serious publications seem to use it interchangeably with the term "action potential", but some authors do try to make a distinction between the two. Brown (2001), for example,  remarks that "it is well worth differentiating between the action potential and the nerve impulse" and makes a series of disparaging allusions based on neurocentric exclusionism ("many types of living cells can generate action potentials, for example oocytes, some gland cells and even some plant cells"), implying that action potentials propagating along nerves are somehow special. To be fair, they are pretty special, in the sense that the Xenopus egg doesn't really do anything interesting with its depolarised membrane, whereas your neurons can fashion thoughts into art (or art criticism). In short, some of the people who write textbooks about neurophysiology seem to hold that the action potential is the ionic mechanism underlying the nerve impulse, and the nerve impulse is the directional propagation of an action potential along a membrane, which is a distinct function of excitable tissues expected of coordinated activity.

Anyway: the nerve impulse. You can think of its propagation as a ripple in a pond, except the pond surface is wrapped around an axon. The action potential propagates in one direction, because the refractory periods of the sodium channels make it impossible to re-depolarise tissue that has recently depolarised already. In this fashion, the site of maximum positive transmembrane potential moves down the nerve fibre.  The actual spike itself is very short-lived, but the rate of conduction is relatively quick, which means that a fairly long segment of the nerve fibre could be depolarised.  In a slow nerve fibre with a conduction velocity of 2 metres per second, an action potential with a duration of 2 milliseconds would occupy about 4 mm of nerve. In fast fibres (eg. squid giant axon), the conduction velocity is up to 70 m/s, and a 1msec action potential would occupy about 70mm of the axon's length. Which brings us handily to the next section:

Factors that affect the velocity of axonal conduction

Several characteristics play a role in determining whether a fibre will conduct an action potential quickly or slowly. In order of importance: 

• Myelination: probably the most important element
• Thickness of the fibre (axon diameter) - next most important element
• Properties of the membrane: capacitance and resistance
• Properties of the extra-axonal environment (eg. electrolyte derangement)

This order of importance is somewhat counterproductive to actually understanding how these factors work, but fortunately a logical progression of ideas presents itself. 

Properties of the membrane: As the membrane depolarises, a local circuit is created (flow of ions is current). This local electrical field depolarises the membrane ahead of the action potential, thereby propagating the action potential.  This definitely plays a major role: if a short segment of an axon is anaesthetised with a sodium channel blocker, the impulse will still be conducted so long as the local circuit is powerful enough. Hodgkin (1937) disabled 3-5mm lengths of frog nerve by local cooling and found that an impulse could "skip" across that region (this is their diagram from the original paper):

Obviously, this ability will depend on the magnitude of the current and the electrical properties of the membrane: specifically, its capacitance and its axial resistance.

• Capacitance is the ability of the membrane to store charge; the greater the capacitance the more charge needs to be displaced by the local circuit and therefore the greater the current required in that local circuit. In short, for faster conduction, you want a low-capacitance membrane that carries barely any charge.
• Axial resistance is the resistance to ion flow along the axon, measured between two flat cut ends of the axon. It is a measure of the resistivity of the axoplasm, i.e. axonal cytoplasm, and is normally approximately in the realms of 100 Ω.cm. Ion flow requires substrate to flow through, and therefore more axoplasm usually means better conduction.

Thickness of the fibre: Capacitance varies directly with axon diameter (per unit length of axon), i.e. thicker axon means more membrane means more capacitance. But directly is the operative word. In contrast, axial resistance varies inversely with the square of diameter, i.e. it drops dramatically with relatively small increases in axon thickness. The result of these relationships is a marked improvement in conduction velocity with increasing axon thickness. In this fashion, very small unmyelinated axons end up having a conduction rate as low as 0.1m/s, whereas huge fat axons (eg. aforementioned squid axons) can conduct at over 70m/s, which is probably some sort of land speed record for unmyelinated axons.

Myelination is the trick mammals use to overcome the natural size limit for single axon size (2mm, by squid experience). Wrapping an axon in a nice myelin-rich Schwann cell results in a marked decrease in membrane capacitance, with a predictable improvement in the speed of conduction. Additionally, it permits saltatory conduction:

• Most of an axon is covered in a myelin sheath, and not much AP propagation occurs over the myelinated length
• Instead the sodium channels are concentrated at the unmyelinated regions between myelin segments, called nodes of Ranvier
• The action potential can propagate from one node to another (by means of local circuits) 
• The distance between nodes varies; the nodes are closer together along smaller axons (every 0.2mm), as these axons cannot generate large currents and their local circuits are therefore weaker. Large axons have larger internodal distances (~ 2mm). According to Brown (2001), the ratio of axon diameter to internodal distance is about 100, i.e. an axon 10μm thick will have an internodal distance of about 1mm. 

The effect of these factors on overall nerve conduction is startling. Here, a table stolen almost verbatim from Brown (2001) lists common classifications of nerve fibres according to their diameter, myelination, impulse conduction velocity and bodily purpose:

Classification of Peripheral Nerve Fibres,
organised by a focus on conduction velocity

Erlanger & Gasser classification
	Diameter (μm)	Velocity (m/s)	Myelinated?	Purpose/role
Aα	8-20	48-120	Yes	Muscle efferents
Aβ	5-14	30-84	Yes	Cutaneous mechanoreceptors
Aχ	2-8	12-48	Yes	Intrafusal muscle efferents
Aδ	1-5	6-30	Yes	Cutaneous pain (modality-specific)  and muscle afferents
B	<1-3	3-15	Sometimes	Autonomic preganglionic efferents
C	~1	<2	No	Pain afferents (polymodal); Preganglionic sympathetic efferents
Lloyd classification
Ia	12-20	72-120	Yes	Muscle spindle primary afferents
Ib	12-20	72-120	Yes	Golgi tendon organ afferents
II	4-12	24-72	Yes	Muscle spindle secondary afferents
III	1-5	6-12	Sometimes	Muscle nociceptive afferents
IV	~1	<2	No	Preganglionic sympathetic efferents

Figures of 100 or 120 m/s are usually quoted from these data to describe the "fastest" neurons as if they hold some kind of Olympic record, but in fact we vertebrates have nothing to be proud of, as the fastest nerve fibres in the animal kingdom belong to the penaeid shrimp. These are also myelinated, just with a special extracellular space between the axon and the myelin, and are capable of achieving transmission speeds of around 200 m/s.

The effect of prevailing conditions on nerve conduction

As it depends on transmembrane electrochemical gradients, it would be logical to expect the delicate choreography of the action potential to be upset by extracellular electrolyte weirdness, and indeed it is. Several electrolyte abnormalities present a major problem for nerve conduction, as they do for cardiac conduction and muscle contraction. Notable examples include:

Hyponatremia: That sodium concentration gradient there is what drives the rapid depolarisation of a neuron. It would be a shame if anything were to happen to it. With a lower driving gradient, one might expect the sodium current to be weaker, and the rate of voltage change to be lower. It is hard to say whether this contributes much to the CNS features of hyponatremia, but it certainly seems to slow peripheral nerve conduction.  Vandergheynst et al (2016) demonstrated that the correction of relatively mild hyponatremia from 121 mmol/L  to 135 mmol/L produced a 14.3% improvement in nerve conduction velocity.

Hypocalcemia decreases the amplitude of the action potential of peripheral nerves, whereas nerve conduction velocity appears unchanged. The effect can be quite profound. Zaidi et al (2018) reported a case of a patient who looked like Guillain-Barre syndrome with weakness and areflexia. The culprit was hyperparathyroidism; symptoms were completely corrected by calcium replacement.

 Hypermagnesemia decreases the nerve conduction velocity.  Fleming et al (1972) explored this in groups of dialysis-dependent patients who were being dialysed with magnesium-rich and magnesium-free dialysate fluid. The high-magnesium group clearly had nerve conduction defects, which were completely reversed by using the other dialysate.

Acidosis alters the flow of sodium through voltage-gated sodium channels (Ghovanloo et al, 2018). It is not clear what this does in the brain, but it cannot be benign. 

Temperature: Predictably, nerve conduction does not work very well during hypothermia, in the same way as nothing works very well during hypothermia.  When Stecker & Baylor (2009) chilled some rat sciatic nerves to 16ºC, they found that the amplitude of the action potentials decreased by about 50%., and nerve conduction speed decreased by about 2.8 m/s for every degree below 37. After extended periods at 10ºC, action potentials were abolished completely.