IB Biology HLNerves & SignallingPaper 1 & 2~12 min read
Nerve Impulses: Skills
A squid has an axon a thousand times fatter than one of yours, and yours still wins. Working out why is a nice bit of biology — and the IB then asks you to prove the link with a correlation coefficient.
📚 What you need to know
Two structural features change how fast an impulse travels: myelination and axon diameter.
Myelinated neurones conduct much faster than unmyelinated ones, because the insulation allows saltatory conduction.
A wider axon conducts faster because it offers less resistance to the action potential.
Squid giant axons are unmyelinated and up to 1 mm wide; human neurones are only 4–100 µm wide but are myelinated — and still faster.
Correlation is an association between two variables. Causation is one variable actually affecting the other. Correlation does not prove causation.
The correlation coefficient (r) runs from −1 to +1. Values near ±1 mean a strong linear relationship; 0 means none.
Pearson’s linear correlation needs data that is quantitative and normally distributed.
The coefficient of determination (R²) is r squared, usually given as a percentage.
What makes an impulse fast
Myelination
A myelinated neurone is wrapped in an insulating sheath with bare gaps in it. Ions cannot cross the membrane where the myelin is, so the impulse effectively jumps from one gap to the next instead of creeping along every millimetre of membrane. That is saltatory conduction, and it is the single biggest thing speeding a neurone up.
Diameter
A wider axon conducts more quickly than a narrow one. The reason is resistance: a wide tube of cytoplasm lets ions spread sideways more easily, so the local currents that trigger the next section of membrane reach further and reach it faster. Same idea as a wide pipe carrying water more easily than a straw.
Notice these are two separate variables. An exam graph will often change both at once and expect you to spot which one is doing the work. If a thin myelinated axon beats a fat unmyelinated one, myelination has to be the bigger factor.
The squid comparison
Squid have giant axons that are unmyelinated and can be up to 1 mm across. A human neurone is somewhere between 4 and 100 µm. Yet the human neurone conducts faster, because it is myelinated. Being wide helps, but insulation helps far more.
The two lines share a y-axis but not an x-axis. The squid axon is roughly seventy times wider at the right-hand edge, and still loses badly.
The trap in this graph. If you read both lines off the same scale you will conclude that a thin axon is faster than a thick one, which is nonsense. Always check whether a graph has been given two different x-axes before you compare the lines.
Correlation and causation
Say you measure lots of neurones and find that wider ones conduct faster. Have you shown that width causes speed? Not yet.
Correlation is an association or relationship between two variables — they change together.
Causation is when one variable actually influences the other.
A correlation does not necessarily mean a causal relationship. Something else could be affecting both.
For our two variables, there may be a correlation between diameter and speed, and between myelination and speed. Whether either is causal needs an experiment where you change one thing and control the rest.
Reading a scatter graph
Plot both variables as a scatter graph first — it shows you whether the relationship looks linear before you do any maths.
Positive correlation: as A increases, B increases.
Negative correlation: as A increases, B decreases.
Perfect correlation means every point sits exactly on a straight line, giving r of exactly 1 or −1.
No correlation gives r of 0.
The sign of r tells you the direction of the relationship. The size of r tells you how tightly the points hug a straight line. Neither tells you why.
Pearson’s linear correlation
Pearson’s linear correlation is a statistical test that tells you whether there is a linear correlation between two variables. Your data must be:
Quantitative — real measured numbers, not categories
Step 1 — plot a scatter graph of your data and check whether a linear relationship looks likely.
Step 2 — state a null hypothesis (there is no correlation between the two variables).
Step 3 — work out r using the equation.
If r comes out close to 1 or −1, there is a strong linear correlation and the null hypothesis can be rejected.
The coefficient of determination
Square r and you get R², the coefficient of determination, usually written as a percentage. It tells you how well one variable predicts the other.
R² close to 1 (100%) — strong correlation, and you can predict the dependent variable accurately from the independent variable. The null hypothesis can be rejected.
R² close to 0 — no correlation, and the dependent variable cannot be predicted.
🧠
r versus R²
r has a sign and tells you the direction. R² is always positive and tells you the strength as a percentage. Squaring throws the direction away, which is why you quote both.
Worked examples
WE 1
Calculate a correlation coefficient
Five myelinated axons were measured. Diameters (x, µm): 2, 4, 6, 8, 10. Conduction velocities (y, m s−1): 14, 25, 42, 51, 68. Calculate r and R², and comment. (4 marks)
Step 1: get the five sums
n = 5, Σx = 30, Σy = 200, Σxy = 1468, Σx² = 220, Σy² = 9810
Step 2: top of the fraction
(5 × 1468) − (30 × 200) = 7340 − 6000 = 1340Step 3: bottom of the fraction
(5 × 220) − 30² = 200 and (5 × 9810) − 200² = 9050, so √(200 × 9050) = √1810000 = 1345.4Step 4: divide, then square
r = 1340 ÷ 1345.4 = 0.996 and R² = 0.996² = 0.992
r = +1.00 (2 s.f.), R² = 99% — a very strong positive correlation, so reject the null hypothesiswrite out the five sums before touching the formula. Nearly every lost mark here is an arithmetic slip, not a method error
WE 2
Interpret a comparison between two species
A squid giant axon of diameter 800 µm conducts at 29 m s−1. A mammalian axon of diameter 11 µm conducts at 90 m s−1. Explain this difference. (3 marks)
Step 1: note the contradiction
The squid axon is roughly 70 times wider but conducts at less than a third of the speed, so diameter cannot be the main factor here.
Step 2: identify the other variable
The mammalian axon is myelinated; the squid giant axon is not.
Step 3: explain the mechanism
Myelin insulates the axon so depolarisation only happens at the nodes of Ranvier, and the impulse jumps between them by saltatory conduction instead of travelling along every part of the membrane.
Myelination outweighs diameteruse the numbers from the stem in your answer — "70 times wider yet 3 times slower" earns the comparison mark
💡 Exam tips
You are given the Pearson formula in the exam, so learn the method, not the equation.
Set your working out as a table of x, y, xy, x², y² and total each column. It is much harder to go wrong.
State the null hypothesis explicitly, then say whether you reject it. Both are marking points.
If asked whether one thing causes another, say correlation does not prove causation and suggest a controlled experiment.
Quote r to 2 or 3 significant figures and R² as a percentage.
Learn the two headline numbers: squid axon up to 1 mm, human neurone 4–100 µm.
⚠ Common mistakes
Reading a double-axis graph off one scale. Check the axis a line belongs to before comparing.
Saying a strong correlation proves causation. It never does on its own.
Confusing r with R². R² is r squared and has no sign.
Using Pearson on non-normal or non-numerical data. The conditions are part of the answer.
Forgetting that a negative r can still be strong. r of −0.95 is a strong relationship.
Writing that a thicker axon has more resistance. It has less, which is why it is faster.
Up next: Synapses — what happens when the impulse reaches the end of the axon and runs out of neurone.
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