My primary interest/background is in evolutionary psychology but I have been paying my way through school by research grants to study gene expression and regulation. I work with a researcher, Dr. Stuart Kauffman and several other people in mathematically modeling ideas behind regulation.
20-30 years ago Dr. Kauffman developed the idea that cell types emerged as steady states from random gene regulation interactions. Basically, imagine that every gene can be either "on" or "off" and to make things simple imagine every gene receives two inputs (usually other genes). These inputs are either "on" or "off" then there are a series of Boolean rules that each gene follows to decide if it stays on or off. So if its an 'or' rule the gene stays on or turns off if either input is "on".
You can model these networks, called Random Boolean Networks, using very simple computer programs. What you find is that the genes enter into cycles that repeat. Kauffman proposed that these were actually cell types. And that differentiation took a similar path to what was described above.
This was a long time ago and a lot of research has been done since. For example I am finishing up a paper now that modeled a small 3 gene circuit in a continuous differential equation to test noise. This model does not rely on the discreet states of a Boolean net and we were able to show attractor points were fairly stable to noise. Along with a couple other cool findings.
At the moment I am creating a model known as a medusa network. Where there is a "head" of genes that are regulators and the "tail" genes do not regulate at all. This is viewed as a more accurate model than every gene being a regulator. We are working on applying noise value and scale free aspects as well (scale free is the number of inputs is not defined).
These networks can also be made more accurate by examining cells and how they actually do work. For example, one Boolean network was modeled after a yeast system. Researchers identified the number of regulation genes in the yeast, and which genes they inputted into. This was used as a frame work for a Boolean model. The Boolean rules still had to be randomly generated.
We have recently hooked up with some researchers and are exploring ways of experimentally examining the "rules" behind the networks but are a long ways away from that.
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