Friday, April 22, 2011

Analogy for Protein Bursts

Consider this scenario:
Imagine a store that is open for a certain time interval during the day. In that time interval, several customers rush in to the store. Each customer buys several items. If someone would record the number of items sold as a function of time, he/she would probably observe bursts (one burst = items bought by one person). The time duration for which the store is open will correspond to the number of bursts. In other words, time duration maps to frequency of bursts.

Now, consider this transcription model:
Consider this mechanistic/intuitive model explaining how proteins are produced in bursts and how the frequency of bursts are controlled by the transcription factor:

1. transcription factor binds to promoter regions and opens the region for access by the polymerase
2. the region remains "open" for some time
3. during this time interval, the polymerase may initiate transcription multiple times
4. for each mRNA that the polymerase transcribes, multiple proteins are produced

So, in summary, the transcription factor "opens" the promoter region for the polymerase. Lets assume that upregulating the transcription factor affects the time duration of the "open" promoter. The longer the time interval, the more mRNA will be produced. Each mRNA creates a burst of proteins. Therefore, upregulating transcription factor affects frequency of bursts.

Stochasticity can lead to Stability

While we think of "noise" as a destabilizing force, we actually use noise many times to lead a system to the most stable position. Consider the scenario where you want to get all the items out of a hand bag very quickly; you would hold the bag up-side-down and shake, i.e. add noise. If you just tilt the bag up-side-down, there is a risk that some of the items would get stuck in the bag. Shaking ensures that such temporary "traps" (in mathematical terms, local minima) are avoided. In a sense, this is like stochastic optimization. When all the items are on the floor, they will remain there even if you shake the floor, because that is that is the most stable position.

Perhaps stochasticity in natural systems is a means of "shaking", i.e. a means by which natural systems reach the most stable states and avoid local traps. The most stable state remains relatively stable even at the presence of noise. Consider the situation when all the items from the bag are on the floor -- even shaking the floor would not change the situation significantly. Perhaps this is the nature of the "most stable state" -- it has a wide basin and thus can easily tolerate noise.