NERVE ANSWERS
4) Sequences which make sense
Although it is sometimes not very hard to arrange a sequence of steps in logical order, what is difficult is avoiding errors in the correct use of scientific language. The following sentences contain various errors in describing experiments on stimulating and recording from nerves. What are they?
1.
Stimuli were applied to the nerve with an inter-stimulus delay of 5 msec.
2.
The inter-stimulus was 5 msec.
3.
The criteria used was a response bigger than 1 mV.
4.
The phenomena investigated was the response to increasing stimulation.
5.
The data shows that there was a big increase in response.
6.
Less fibres were active during the relative refractory period.
7.
The conduction velocity is the time taken to travel from A to B.
8.
The latency is the time it takes for the stimulus artifact to illicit a response.
9.
The conduction velocity is proportional to the latency.
10.
The distance traveled by the stimulus was determined by the length of the nerve.
Explanations of errors:
1.
It is better to use the term inter-stimulus “interval” rather than “delay”, as this clearly describes the time between the applications of successive stimuli to the nerve, whereas “delay” refers to the time which elapses after a single stimulus until the next one is applied; it also is used to refer to the elapsed time between a stimulus artifact and the beginning of the compound action potential.
2.
The word “interval” is missing after “inter-stimulus”.
3.
“Criteria” is plural and refers to more than one criterion, so needs a plural verb
“were”; however as only one criterion is mentioned the sentence should read
“The criterion used was a response bigger than 1 mV”.
4.
A similar error is often made with the word “phenomena” which is the plural of “phenomenon”, so it is necessary to write “The phenomenon investigated was…” or “The phenomena investigated were
……”.
5.
“Data” is also plural, this time of the word “datum” (sorry, but that’s the difference between Latin and Greek!), so “ data show
….”.
6.
“Less” is used for amounts, “fewer” for numbers
.
7.
A velocity cannot be a time, since it has units of distance divided by time.
8.
“Latency” is another word for “delay”, as mentioned in 1. The stimulus artifact doesn’t even “elicit” a response which would be quite “illicit” for it to do, given that it is itself a response! The stimulus elicits the response.
9.
The conduction velocity is able to be read off as the slope of the line expressing the relationship between distance and latency, which are proportional to each other if the line goes through the origin .
10.
The stimulus didn’t travel anywhere, the action potential did, and what the length of the nerve determined was how long it took for the potential to reach recording electrodes at the other end.

Extra notes
When answering some of the questions on nerve activity, the concepts below may be relevant. Consider the relationships between physical structure and different aspects of physiological function, including any relevant mathematical equations.
1. Structural variation in nerve fibre populations
Nerves are composed of nerve fibres or axons, which not only subserve different functions such as motor or sensory (touch, pressure, temperature) but also have different structures . The most important structural parameters with respect to their functioning are the diameter and the presence or absence of myelin . These variables determine a number of their electrical characteristics, which in turn determine how the fibre responds to a stimulus by generating local and propagated potentials. Three important properties relating to this are discussed below – threshold for excitation, conduction velocity of action potentials, and refractory periods. This section also addresses the issue of how the responses of nerves are built up from the responses of their individual contributing fibres.
2. Correlation of structure with electrical properties
A simple electrical model of a nerve fibre consists of resistances for membrane and cytoplasmic current flow and a capacitance for membrane storage of charge. When the resting potential is temporarily changed in the direction of becoming less negative i.e. depolarization, the voltage difference between the depolarized and resting sections of the fibre drives a current round the resulting circuit, the magnitude of which depends on the total resistance in the membrane plus cytoplasm. The fraction of this voltage which drops across each resistor is proportional to its contribution to the total resistance (see Extra notes on Resistances).
Both the diameter and the myelination of a fibre impact on these electrical properties. a) Diameter
An increased diameter results in a decreased longitudinal resistance
(inversely proportional to cross-sectional area) and also membrane resistance
(inversely proportional to surface area). However the longitudinal decrease is greater than the trans-membrane, so more of the voltage drop occurs across the membrane and less along the fibre length. There is also an increase in the membrane capacitance , since this is proportional to area. b) Myelin
Myelination produces an increase in membrane resistance and a decrease in capacitance . c) Time and space constants
These changes then impact on two important constants – the time constant and the space constant. Each of these is a measure of the ease of achieving a particular outcome - either the time needed to change the membrane voltage by a certain fraction or the distance for which the membrane voltage is maintained above a certain fraction. Both increased diameter and myelination result in a smaller time constant and a bigger space constant.

The net result of this is that large fibres reach threshold quicker and the electrotonic potentials travel further than in small fibres. These have obvious implications for the speed of propagation of the action potential along these fibres
(see 6. Conduction velocity).
The implications for spread along myelinated fibres are more complicated because the myelin is interrupted periodically by non-myelinated areas known as nodes of Ranvier . Hence the comparison of properties includes different sections of the same fibre, as well as different fibres. The increased membrane resistance and decreased capacitance due to myelin means that reaching threshold will be more difficult than in an unmyelinated region; the converse of this is that little current will leak out where myelin is present. In addition, at the nodes there is an approximately
50-80-fold increase in the number of voltage-gated Na channels compared to internodal regions, while totally unmyelinated axons have a maximum of a tenth of the number of these Na channels that are present at the nodes.
The increased space constant due to myelin increasing membrane resistance means that current is effectively forced to exit the cytoplasm at the nodes only.
Because of the distances between these depolarized regions, this makes for much faster spread, a phenomenon called saltatory conduction ( see 6.). The shorter time constant is less relevant here because the threshold in the inter-nodal regions is significantly raised due to the paucity of voltage-gated Na channels and the simultaneous increase in membrane capacitance necessitating a much larger current flow to produce a given depolarisation.

m x
c x
m
x
x
x
x
m
c
m
c
m
3. Threshold for excitation
The main determinant of the threshold for excitation is the ease with which a given stimulus is able to produce the necessary depolarization of the membrane potential from its resting value to the value at which flow of positive charge inward initiates the Hodgkin cycle of increased Na conductance leading to further depolarization in an irreversible manner. The threshold is thus dependent on the degree to which a membrane is depolarized, which in turn will vary with the fractional voltage change which occurs here compared to along the length of the fibre.
Since larger diameter fibres have lower internal resistances , more current will flow and more of the voltage drop will happen across the membrane, yielding a lower threshold of stimulus voltage necessary to reach a particular membrane voltage and trigger the Hodgkin cycle.
4. Population code
When explaining the shape of the stimulus-response curve, it is necessary to refer to the different thresholds of fibres of different sizes making up the sciatic nerve.
Sub-threshold stimuli, giving no AP, are too weak to bring any fibres to their threshold. At the threshold stimulus, when there is a tiny response, the most sensitive fibres of lowest threshold have been activated. As the stimulus strength increases more and more fibres, of progressively increasing threshold, are recruited, until all the fibres are contributing to the CAP with a maximal stimulus, and the curve reaches a plateau for supra-maximal stimuli.
This section also refers to the distinction between the frequency code and the population code. It is the population code which is exemplified in the stimulusresponse curve, and even if the fibres were increasing their frequency of firing with increasing stimulus strengths (i.e. the frequency code was also operating), the method of recording did not display this.

5. Shape of CAP
(see Concept Map)
The amplitude of the CAP is not physiologically significant, as it is not an absolute measure of any particular event of physiological significance as say the blood pressure is, and varies with the recording conditions. However it gives an indication of the amount of activity in a particular group of nerve fibres, so that relative changes reflect variations in the number of contributing fibres.
As the CAP is an envelope of potential change over time, it reflects the addition of all the APs generated at the stimulating electrodes and travelling down fibres of different sizes and myelination, and hence having different velocities of conduction. This means that the AP in the fastest fibres reaches the recording electrodes first and hence contributes to the beginning of the CAP, the average velocity fibres contribute to the peak, and the slowest contribute to the tail. Since the duration of the CAP is longer than that of a single AP, several single ones travelling at different velocities could sum to give a wider, but not a higher, CAP. It is therefore necessary to divide the area under the curve of the CAP by that under a single AP to obtain an estimate of the number of fibres contributing.
The summation of subthreshold responses to successive stimuli which are sufficiently close together in time illustrates that only the complete membrane potential reversals which occur during an AP are picked up by the external recording electrodes, but that depolarisations are still occurring, which outlast the duration of an
AP, as charge is stored on the membrane, which acts as a capacitor.
Since local anaesthetics first affect the smallest pain fibres - which is their whole raison d’etre – they alter the shape of the CAP. Such drugs block action potential transmission by blocking voltage-gated sodium channels. Since surface area of the membrane is proportional to size, smaller fibres will have fewer channels needing blocking and hence respond to lower doses. Can you think of any other reasons for the differential responsiveness e.g. drug accessibility?
6. Conduction velocity
(see Concept Map)
The speed with which nerve axons transmit action potentials is another property which is affected by both their diameter and their myelination. There are 2 quite separate events contributing to the total time which elapses between the beginning of stimulation and the recording of a response: the time needed to depolarize the membrane to threshold, and the time it takes for the action potential to spread along the axon. Both of these are faster in larger fibres, and myelin additionally allows for a specialized form of conduction called “saltatory”, where the action potential “jumps” between nodes of Ranvier, giving a faster transmission.
• Nodes of Ranvier are only part of axon which is not myelinated
•
Cm here is much greater than in myelinated inter-nodal parts
•
Rm here is much less than in myelinated inter-nodal parts
• Na channels here are much more frequent

•
Thus threshold reached only at nodes
One reason why the velocity is slower in toad than human nerves is their lower body temperature.
7. Reduced excitability (refractory periods) of single fibres
For a very short period of time after firing an action potential nerve fibres are unable to fire again, being “refractory” to repeated stimulation. For the period when they cannot respond at all, no matter how large the stimulus size, the term
“absolute” refractory period is used, and this is followed by a period when a response can be obtained, but only with a larger stimulus than before, hence the term
“relative” refractory period .
The mechanisms which underpin this variation in excitability have been covered in your lectures. Basically they are the conductance properties of the voltagegated channels for Na and K, which undergo a cycle of availability followed by nonavailability each time an action potential occurs. The diagram and discussion below explain this.
A nerve fibre cannot fire a second AP until it is just outside its absolute refractory period, so the maximum frequency of its firing is a little less than the reciprocal of this period e.g. if the ARR is measured as 1 ms, the fibre cannot fire every ms or 1000 times per second, but slightly less frequently. Published frequencies should be obtained by referring to graphs of nerve firing rates in your textbooks, and will vary depending on the type of nerve.
As mentioned above, it is changes in sodium and potassium channel conductances which underlie absolute and relative refractoriness. The diagram below is taken from Dr. W. Phillips’ Supplementary Notes on Single Cells
Membrane potential sodium conductance potassium conductance
0 1 2
Time (ms ec)
3
Fi g. 3 Conduct ance cha nges cont ributing to t he acti on pot enti al
The sequence of events is as follows:
(i) Depolarisation of the membrane potential to threshold (see 3.) results in the opening of voltage-gated Na channels and the Na conductance rises.
(ii) Net inward flow of positive ions pushes the membrane towards the Na equilibrium potential.

(iii) As the depolarisation approaches the peak of the action potential these Na channels close and are inactivated.
(iv) There is a delayed opening of the voltage-gated K channels at this time and thus a rise in the K conductance.
(v) The Na channels became capable of re-opening as the membrane becomes less depolarized due to outward flow of K, with this process being complete approximately when the membrane potential has fallen to the threshold value.
This marks the end of the absolute refractory period, and it is now possible to depolarize to threshold for another action potential.
(vi) However, the increased K conductance eventually results in membrane hyperpolarisation, so that a greater stimulus voltage is required to bring the membrane to threshold as the net outward flow of positive ions pushes the membrane towards the K equilibrium potential.
(vii) It is therefore now in its relative refractory period.
(viii) The voltage-gated K channels close and the membrane potential returns to its resting level, as determined by the relative conductances of the K and Na leakage channels. It has now fully recovered its excitability and is no longer refractory to stimuli of the original voltage strength.
During the period of reduced responsiveness of the whole nerve , a second
AP is obtained from that fraction of the population which is not refractory. The length of both the absolute and the relative refractory periods varies between different nerve fibres, being shortest for the largest (presumably because the swing in favour of available voltage-gated Na channels over available voltage-gated K channels occurs sooner in the latter). For an individual fibre to fire an AP, it MUST be out of its absolute refractory period, but can be in its relative if the stimulus strength is increased. Accordingly, at any time when whole nerve excitability is reduced, but not zero, the contributing fibres will be partly in their relative refractory periods, partly completely beyond even this, i.e. completely recovered.

Concept maps
AMPLITUDE of CAP from
NERVE
No. of nerve fibres depolarised to threshold for AP
Threshold for depolarisation and
EC current & voltage
Spread of CAP i.e.duration
Strength of stimulus
Myelination and size distribution of nerve fibres
Spread of conduction velocities
CONDUCTION
VELOCITY in axons of NERVE
AP jumps from node to node (g
Na
)
Saltatory conduction
↑Space constant and spread
↓Time constant to threshold
Speed of chemical reactions
Myelination
( ↑Rm ↓Cm)
Size
( ↓Rm ↓↓Rc ↑Cm)
Temperature

•Faster to threshold
= smaller time constant
→ Faster spread
= √ (R m x R
• Myelin: c
) x C m
√(more x same) x less
= less i.e. depolarised faster
(than unmyelinated axons)
But no AP here as Na channels only in unmyelinated nodes
• Increased diameter d:
√(less x much less) x more
= less i.e. depolarised faster
(than smaller axons) as smaller
R c cf to R m gives larger current also means greater relative voltage drop across membrane cf to along cytoplasm to depolarise to threshold
• Further before decrease
= larger space constant
→ Faster spread
λ = √(R m
• Myelin:
/ R c
) or √(d R m
R m more so λ more
• Increased diameter d:
/4 R c
R m
(determined by surface area) drops less than R c
(determined by cross-sectional area) so λ more
Conduction Velocity = λ / τ
= √ (R m
/ R c
) / √ (R m x R c
• Alternate formula for CV
) x C m
= k/ C m x √ (d/4 x R m x R c
) i.e. apart from relative Rs, CV will be faster when d is larger and also when C m is smaller