The short answer
A multiplier, a quantity and a resulting flow belong at different stages of a model. Confusing them can make a correct numerical fraction support an incorrect physical conclusion.
Evidence and original analysis
Keep three levels separate
Invented values; U denotes an arbitrary conductance unit.
| Quantity | Initial state | After m changes to 1 |
|---|---|---|
| Potassium factor / conductance | 1/16; 1U | 1/16; 1U |
| Sodium factor / conductance | 1/16; 2U | 1/2; 16U |
| Ionic currents | Not determined | Not determined |
Chronology
A timeline of the turning points
Quantitative paper
Separate capacitive and ionic current terms.
Original calculation
Invented gate values and maxima supplied.
What the selected equations describe
The paper combines a capacitance term with potassium, sodium and leak currents. Equation 26 uses conductances gฬK nโด and gฬNa mยณh; each ionic current also includes a driving-voltage factor. Earlier selected pages connect the potassium fourth power to fitted conductance changes.
These variables are model states, not a direct count of observed molecules. The paperโs modelling and physical interpretation must remain distinct from a claim that each exponent proves a unique microscopic arrangement.
Sources for this section: [1]
An invented set of factors and maxima
Use nโด and mยณh only as the selected algebraic factors. Invent n=m=h=1/2, gฬK=16U and gฬNa=32U, where U is an arbitrary conductance unit. Calculate both fractions and conductances.
Then change only m to 1, retaining n, h and both maxima. Calculate the new sodium conductance and its fold-change. Can the two ionic currents be compared numerically without any driving voltages? No voltage values are supplied.
Sources for this section: [1]
Reference answer
Initially nโด=(1/2)โด=1/16 and mยณh=(1/2)ยณ(1/2)=1/16. Multiplying by the different maxima gives gK=1U and gNa=2U. Equal normalised factors therefore do not imply equal absolute conductances.
With m=1 and h=1/2, the sodium factor becomes 1/2, giving 16U: an eightfold increase from 2U. Potassium stays 1U because its inputs have not changed.
The current comparison remains underdetermined. Each conductance must be combined with its own driving voltage; supplying a conductance is not supplying a current. The arbitrary unit U is not a historical measured parameter.
Sources for this section: [1]
A useful model is not a replication
The exercise evaluates two algebraic terms, not a complete action potential. It supplies no rate constants, time integration, membrane geometry or experimental trace. It cannot establish molecular identity or current direction, and it gives no clinical or stimulation guidance.
Sources for this section: [1]
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Quick answers
Common questions
- Do equal factors mean equal conductances?
- Not when their supplied maxima differ.
- Does an exponent count observed molecules?
- The selected formal model does not by itself establish that microscopic interpretation.
Primary and institutional sources
How this history was checked
Selected records support the historical explanation. Invented inputs and original calculations are labelled separately. This article was reviewed on 31 October 2026.