## Saturday, January 16, 2010

### When Mechanistic Models Explain (Part 3): Evaluating Models

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 at an article by Craver entitled "When Mechanistic Models Explain". Part one covered some distinctions between explanatory models and non-explanatory models. Part Two considered the example of the Hodgkin-Huxley model of the action potential and how it transitioned from being a how-possibly (non-explanatory) model to a how-actually explanatory model.

In this part, I will set-out Craver's evaluative criteria for mechanistic models. The criteria help to distinguish good explanatory models from bad non-explanatory ones. In deriving these criteria, we consider four questions:
1. Does the model cover all the relevant phenomena it purports to explain?
2. Does the model identify all the entities/parts involved in producing the target phenomenon?
3. Does the model identify the activities involved in producing the target phenomenon?
4. Does the model successfully organise the entities and activities?
Before looking at each of these questions in more detail, it is worth refreshing our memories about the nature of a scientific model. A model takes a target phenomenon (T) and represents it in some algorithm or function (S). S can then be implemented in a physical system, computer program, mathematical equation, box-and-arrow diagram or whatever.

(1) Does the model cover the target phenomenon?
The Hodgkin-Huxley model (S) is a mathematical model of the action potential (T). The action potential is the sudden change in membrane potential in a neuron. It is a multi-faceted phenomenon. It involves the sudden increase in potential, followed by a rapid decrease and recovery period. The first test of a successful model is whether it captures all facets of T.

The second test is whether the model can describe the inhibiting conditions of T. In other words, if we know that action potentials can be prevented or inhibited (e.g. by applying tetrodoxin, which blocks the flow of sodium ions through the ion channel), then our model should be able to account for these inhibiting conditions.

The third test is whether the model can identify the modulating conditions of T. In other words, the model should be able to tell us whether an alteration in certain variables will affect T. So in the case of the action potential, we want our model to tell us if variations in the density of ion channels or the diameter of the cell have an effect on it.

The fourth test is whether the model covers what happens in non-standard conditions. For instance, most laboratory experiments occur in non-standard conditions, the difference between these and standard conditions should be covered by the model.

The fifth test is trickier. One thing that distinguishes a how-possibly model from a how-actually model is that the latter will account for byproducts in the mechanism being modeled. So for example when sodium ion channels are opened there is a slight movement of positive charge to the outside of the cell, this is quickly counteracted by the flow of the positively-charged sodium ions into the cell. The slight movement of positive charge to the outside would not be an essential part of a how-possibly model of the action potential because it is an irrelevant blip. However, it would be an essential part of a how-actually model. More recent models of the action potential cover this blip. It turns out it is caused by a particular component of the ion-channel (the alpha helix, discussed here).

(2) Does the model identify the entities/parts responsible for the phenomenon?
Mechanistic models explain phenomena in terms of entities and activities. A key part to a successful mechanistic explanations is the correct identification of entities. By "correct" is meant actually existent not fictional.

The line between a fictional entity and one that actually exists is indistinct. For instance, one could argue that Mendelian genetics started out with fictional entities (genes), but that this definitely changed through repeated experimentation, manipulation and confirmation of Mendel's model. Despite the blurry lines, we can be confident that the entities actually exist if:
• They constitute a stable cluster of properties: for instance, ion channels were originally fictional, but over time it became possible to sequence their structure and work out how they reacted when in the presence of certain chemical agonists and antagonists. Thus ion channels were found to have a stable cluster of properties.
• They are robust: they can be identified with different techniques and devices. For instance, ion channels can be identified through pharmacological manipulations, X-ray crystallography, and electron microscopy.
• They can be used to intervene in other processes: for instance sodium ion channels can be manipulated so as to open potassium ion channels.
• They are plausible in the circumstances being investigated: this criterion varies from case-to-case. In the case of the action potential, any proposed entities should be plausible given background knowledge about the construction of nerve cells.
• They are relevant to the target phenomenon: in other words, when modeling the action potential we should not include entities that are present in the cell but clearly have no role in changing membrane potential. Examples might include: DNA, RNA, and microtubules.

(3) Does the model identify the relevant activities?
As mentioned above, a mechanistic explanation is built out of entities and activities. The activities are the things that the entities do (e.g. sodium ions diffuse down concentration gradients). It is possible to identify fallacious activities. For example, one could observe that the rooster always crows before the sun rises. But it would be a mistake to think that crowing was what brought about the sun rise. Mistaken causal inferences of this sort are everywhere (astrology, homeopathy etc.).

So how do we know if we have correctly identified the activities? Craver proposes one criterion that can help answer this question: the manipulability criterion. If we propose an activity linking two variables (e.g. roosters and sunrises) then it must be the case that manipulating one of these variables manipulates the other. Thus, silencing the rooster should -- if it were a correctly identified activity -- stop the sunrise. Of course it doesn't, so this is a bad mechanistic model.

(4) Does the model correctly organise the entities and activities?
The final crucial criterion for a good mechanistic model is its organisation. In other words, the model must have the correct spatial and temporal organisation of the entities and activities identified. It cannot be the case that taking out one entity and relocating it produces the same phenomenon.

There is quite a bit to take in here. In the interests of cognitive perspicuity, the following diagram summarises the criteria we need for evaluating mechanisms.