Friday, January 15, 2010

When Mechanistic Models Explain (Part 2): The Hodgkin-Huxley Model

This post is part of my series on the work of the philosopher Carl Craver. The series deals with the nature of neuroscientific explanations. For an index, see here.

I am currently looking an article by Craver entitled "When Mechanistic Models Explain". In part one, I introduced the concept of a scientific model and differentiated between models that explain and those that do not.

In this part, I will cover the Hodgkin-Huxley model for the action potential. The goal is to show how this model went from being non-explanatory to explanatory.

(1) What is an Action Potential?
A neuron is a cell. Like most cells it has a lipid bilayer membrane. This membrane is semi-permeable: most of the time it keeps what is inside the cell distinct from what is outside the cell, but it does occasionally allow materials to cross the membrane.

In its resting state, the membrane of the neuron separates electrically-charged ions (primarily Ca, K and Na ions) in such a way that the inside of the neuron is negatively-charged when compared to the outside. This difference in charge known as the resting potential of the membrane (roughly -70mV).

When the neuron is stimulated, there is a dramatic change in the distribution of charge. The membrane becomes highly-permeable to positively-charged ions (K, Na), which enter the cell resulting in a sudden increase in membrane potential (up to +35mV). If a certain threshold is reached, this process continues down the length of the neuron. This constitutes the electrical component of neuron-to-neuron communication (there is a chemical component too).

The sudden change in membrane potential (from -70mV to +35mV) is known as the action potential. With appropriate equipment, one can insert an electrode into a neuron and record the action potential. The data from the recording can be graphed as follows.

The graph shows the sudden rise in membrane potential, followed by a sharp decline and a recovery (or refractory) period.

(2) The Hodgkin-Huxley Model
Recall from part 1, that a scientific model is something that takes a target phenomenon (T) and represents it as an algorithm or function (S). S can be implemented in a physical system, computer program, mathematical equation and so on.

The Hogkin-Huxley model takes the action potential as its target phenomenon and represents it in a mathematical equation. This is illustrated below.

I'm not a huge math person but I think it is relatively easy to get the gist of this equation. It is showing that the total amount of current crossing the membrane is made up of four separate currents (capacitative, potassium, sodium and leakage). These currents are in turn dependent on a number of different variables. The overall equation is derived from certain laws of electricity. In particular, Coulomb's law and Ohm's law.

The question now is whether the model is explanatory or non-explanatory. Interestingly, Hodgkin and Huxley thought it was non-explanatory. They saw it as a how-possibly model. That is, as a model that showed how the changes in membrane potential that were observed could possibly come about. They did not think it accurately represented what took place in the neuron.

They were perhaps slightly unfair on themselves. They were aware that sodium, potassium and other ions crossed the membrane, and they included this in their model. However, in doing so they noted that the ability of these ions to cross the membrane was dependent on three factors (m, n and h in the equation). What these factors were was a mystery.

What Hodgkin and Huxley lacked was an understanding of ion channels. These are assemblages of protein that are embedded in the membrane of the cell. Under certain conditions, they open pores in the membrane (details here) through which ions can pass. The different proteins that make up these channels are the mysterious factors that were unaccounted for by Hodgkin and Huxley.

Experimental work on the structure of these channels, and on the conditions in which they open, was what allowed the Hodgkin-Huxley model to shift from being a how-possibly (non-explanatory) model to a how-actually (explanatory) model.

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