Famous First Words is a recurring LabKitty feature in which we take a look at the opening line of an historic scientific article. Sometimes I take the liberty of punching it up. Today is not one of those times
The squishy sciences tend to lag behind engineering and physics in re the embrace of mathematics, in no small part because the complexity of living things dwarfs that of an airfoil or a quark. So it was quite the coup when Alan Hodgkin and Andrew Huxley published their famous equation describing the membrane potential of a neuron -- more accurately: the membrane potential of a giant squid axon* -- which let math into neuroscience like some sneaky Trojan rabbit. To what end is not clear. Heutzutage, neural models have become so complicated you may as well be doing wetwork. Still, physicists need jobs now that there's none for them in physics, so we must tolerate their ilk living among us.
I suppose I should show you the equations before moving on to the prose, since that's the point of it all my baby dolls.
With some reasonable assumptions on membrane conductances and whatnot, we have:
Here, n, m, and h, are dimensionless quantities describing channel activation, Vm is the resulting membrane potential, I and Cm are the transmembrane current and capacitance, the three g are sodium, potassium, and leak conductances, the three other V are the corresponding reversal potentials, and the alpha and beta are rate constants. For more details, you may consult the WillyPete page I stole this from.
Alas, the equations originally appeared at the end of a series of five papers, and the opening of the final article doesn't exactly grab the reader by the buttonhole:
The squishy sciences tend to lag behind engineering and physics in re the embrace of mathematics, in no small part because the complexity of living things dwarfs that of an airfoil or a quark. So it was quite the coup when Alan Hodgkin and Andrew Huxley published their famous equation describing the membrane potential of a neuron -- more accurately: the membrane potential of a giant squid axon* -- which let math into neuroscience like some sneaky Trojan rabbit. To what end is not clear. Heutzutage, neural models have become so complicated you may as well be doing wetwork. Still, physicists need jobs now that there's none for them in physics, so we must tolerate their ilk living among us.
I suppose I should show you the equations before moving on to the prose, since that's the point of it all my baby dolls.
With some reasonable assumptions on membrane conductances and whatnot, we have:
Here, n, m, and h, are dimensionless quantities describing channel activation, Vm is the resulting membrane potential, I and Cm are the transmembrane current and capacitance, the three g are sodium, potassium, and leak conductances, the three other V are the corresponding reversal potentials, and the alpha and beta are rate constants. For more details, you may consult the WillyPete page I stole this from.
Alas, the equations originally appeared at the end of a series of five papers, and the opening of the final article doesn't exactly grab the reader by the buttonhole:
A Quantitative Description of Membrane
Current and its Application to
Conduction and Excitation in Nerve. A.L. Hodgkin and A.F. Huxley. J. Physiol. 117:500-544 (1952)
Current and its Application to
Conduction and Excitation in Nerve. A.L. Hodgkin and A.F. Huxley. J. Physiol. 117:500-544 (1952)
This article concludes a series of papers concerned with the flow of electric current through the surface membrane of a giant nerve fibre.No student of the short story, they. More impressive was that Hodgkin and Huxley actually managed to integrate the damn things, no mean feat considering that the PDP-11 wouldn't be invented for another twenty years. These days you can solve their equations on your phone. Whatever shall we do for Nobel Prizes in the future?
* Giant axon not giant squid, although I am willing to entertain the thought of Hodgkin and Huxley wrestling some Lovecraftian behemoth in their Cambridge laboratory, its horrible tentacles wriggling and flailing and dragging a screaming graduate student toward its gaping maw as they attempt to collect the necessary data to prove their model. Come to think of it, that would have made for a much more engaging introduction to the paper. Academics take note.
I love this!
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