There is a fascinating article in the latest edition of Physics Today (February, 2014):
I was initially attracted to the article by its provocative title. Like a bee to honey, I could not resist looking at it. There are a number of reasons I enjoyed it so much; here’s a synopsis followed by a slightly more digressive discussion:
- It is interesting for its own sake about understanding how genes are expressed.
- It provides a good example of how a Bayesian model (my interpretation–not the author’s) can be expanded from simple observed probabilities to include predictions from sophisticated and mathematical models.
- It highlights the importance of modeling when doing statistical analyses.
- It provides some background for thinking about the processes that might result in differential response of cancer cells (or normal cells, for that matter) to radiation and/or chemo.
In a quick synopsis, the article describes in great detail how E coli cells can convert to using glucose or lactose for energy. The system operates as a function of several variables: presence/absence of lactose and glucose and the presence/absence of two molecules, namely Lac-repressor and CRP. The CRP increases the likelihood that RNA polymerase will bind to the lac promoter portion of the DNA; the Lac-repressor sits on the promoter portion, thereby inhibiting the RNA polymerase binding. Lac-repressor tends to be present when lactose is absent; CRP is present when glucose is absent. Binding of RNA polymerase for making the protein that digests lactose follows the basic rules:
- lactose +, glucose +, no RNA polymerase
- lactose -, glucose +, no RNA polymerase
- lactose -, glucose -, no RNA polymerase
- lactose +, glucose – , RNA polymerase can bind
That makes a nice 2×2 matrix that is easily encoded into a Bayesian network (BN). However, these are chemical reactions, not logical theses, so statistical mechanics is actually a better operational model. A little calculation might give you probabilities that are a little different from 0/1 depending on concentrations. A little more work gets you a full-blown model based on the free energies and entropies of the two states (bound/not bound). In the BN world, you can now have a much more sophisticated, quantitative, continuous model without really modifying the BN in any substantial way.
The author also does a nice job of describing how having such a model can really help form the experimental setup required and the statistical analyses that should be performed to test this model. This mirrors the discussion on the use of modeling strategies in performing appropriate statistical tests in the first chapter of “Regression Modeling Strategies” by F E Harrell (Springer, 2001).
Finally, the article also describes how other aspects of the cellular mechanism, such as transporter activity across the cell membrane, can lead to positive feedback and a switching between states. As another example of bacterial free will, the article describes how E coli can switch phenotypes between antibiotic-sensitive to resistant and vice versa. These interactions between cellular activity and the environment bring to mind some of the issues with differences between tumor cell responses to radiation. The simple LQ model, while pretty good, might be greatly improved by including something like the antibiotic resistance mechanism described. Genetic instability might explain part of the hetergeneity of response, but so may environmental factors and cellular feedback processes.