Chaos Theory Fries Your Brain

Okay, we're going to get a little hairy on you now, and go back to the chaos theme we touched on earlier. In an important review on brain ischemia published by Peter Lipton in 1999, the author postulated that the cell occupies a complex n-dimensional "cell component space," in which the n variables (or axes) are all the biochemical and biophysical attributes of the cell. No two cells are likely to occupy exactly the same coordinate position in this space, although they may be close neighbors. Under physiologic conditions, the general position (domain) of the neuron in this mathematical space is relatively stable, with minor fluctutations being brought about by synaptic activity, metabolism, growth, remodeling, etc. This domain may be viewed as a biothermodynamic well within the cell space-it takes some sort of insult to knock the cell out of its normal condition.

The ischemic insult represents a major perturbation of the cell within the cell space. If the perturbation is minor, the cell will return to its normal domain within the cell space--recovery. If, however, the perturbation (insult) is major, the cell will be knocked out of its domain. The different death phenotypes represent low energy biothermodynamic states, which may be regarded as attractors for the cell system. Depending on the cell's initial state (as defined by that cell's coordinates in the n-space), the cell will take up new coordinates within one of these attractors. Seemingly minor changes in the initial conditions can lead to vastly different outcomes. This principle of chaos theory is sometimes called The Butterfly Effect.

Figure. A Bit of Snooker. The injury can be compared to breaking a rack of billiard balls stacked in the physiologic cell component space. The various death phenotypes (pockets) are chaotic attractors. Where a particular cell ends up depends not only on the injury but a multitude of other starting conditions, any one of which can have an apparently inordinate influence on the final outcome. Stare at the cartoon a bit and realize that, if the injury is mild enough, it may not knock the cell entirely out of the physiologic (survival) space. If the injury hits a little harder, the cell may land in an apoptotic death attractor. Harder still, and the cell is more likely to land in a "necrotic" attractor. Thus, cells in the ischemic core are more classically necrotic, while cells in the penumbra look more apoptotic.