## Using formal logic in biology

The 2012 Noble Prize in physiology or medicine went to John Gurdon and Shinya Yamanaka for turning mature cells into stem cells. Yamanaka shook the world just six years ago in a Cell paper (it can be obtained here) that showed how to reprogram adult fibroblast cells into pluripotent stem cells (iPS cells) by simply inducing four genes – Oct3/4, Sox2, c-Myc, and Klf4.  Although he may not frame it this way, Yamanaka arrived at these four genes by applying a simple theorem of formal logic, which is that a set of AND conditions is equivalent to negations of OR conditions.  For example, the statement A AND B  is True is the same as Not A OR Not B is False.  In formal logic notation you would write $A \wedge B = \neg(\neg A \vee \neg B)$.  The problem then is given that we have about 20,000 genes, what subset of them will turn an adult cell into an embryonic-like stem cell. Yamanaka first chose 24 genes that are known to be expressed in stem cells and inserted them into an adult cell. He found that this made the cell pluripotent. He then wanted to find a smaller subset that would do the same. This is where knowing a little formal logic goes a long way. There are $2^{24}$ possible subsets that can be made out of 24 genes so trying all combinations is impossible. What he did instead was to run 24 experiments where each gene is removed in turn and then checked to see which cells were not viable. These would be the necessary genes for pluripotency.  He found that  pluripotent stem cells never arose when either Oct3/4, Sox2, c-Myc or Klf4 were missing. Hence, a pluripotent cell needed all four genes and when he induced them, it worked. It was a positively brilliant idea and although I have spoken out against the Nobel Prize (see here), this one is surely deserved.