In a recent comparison of selected mRNA and protein abundances in human liver, a correlation of only 0.48 was observed between the two. Clearly, protein levels form an important part of the internal state of a cell.
In addition to mRNA and protein levels, one could imagine measuring a number of other parameters, including cell volume, growth rate, methylation states of DNA, phosphorylation state of proteins, localization of proteins and mRNA within the cell, ion levels, etc. One class of data which could be very useful is metabolite and nutrient levels.
For example, constraining the genes to be regulated by no more than 7 other genes will drastically simplify the number of regulatory interactions we need to consider.
Constraining the model by using a priori information about what is biologically known or plausible is probably the most important weapon we have to fight the Curse of Dimensionality! How precisely to include this information into the inference process is the true art of modeling.
http://www.cs.unm.edu/~patrik/networks/datareq.html
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