# Cooperative Binding of Proteins to DNA

### Cooperative Binding of Proteins to DNA

We have just spent much time studying the cooperative binding of oxygen to hemoglobin. Cooperativity seemed to require conformational changes in a multimeric protein. Is it possible to get cooperative binding of ligands without conformational changes? In a recent book by Ptashne and Gann (Genes and Signals, Cold Spring Harbor Press, 2002), it is argued that you can and through a very simple mechanism.

It must be clear that to activate gene transcription, several transcription factor proteins must assemble at the promoter before RNA polymerase can transcribe a gene. There are multiple DNA-protein and protein-protein contacts. To simplify this discussion, consider the case of two proteins, A and B, that must bind to the DNA and to each other for transcription to occur.

Figure: two proteins, A and B

The binding of each protein alone is characterized by a characteristic $$K_d$$, $$k_{on}$$, and $$k_{off}$$. What happens to $$k_{on}$$ and $$k_{off}$$ for protein B, for example, when A is already bound? You can imagine that $$k_{on}$$ does not change much, but what about $$k_{off}$$ after the protein is interacting both with its DNA site and with protein A? If B did dissociate from its DNA site, it would still be held in close approximation to that site because of its interaction with the bound protein A. Its effective concentration goes up and you should readily image that it would rebind very quickly to its DNA site. The net effect would be that it's apparent $$k_{off}$$ would decrease, which would increase its apparent binding affinity and decrease its apparent $$K_d$$. Remember that

$K_d = \dfrac{ k_{off}}{k_{on}}$.

Hence prior binding of A would lead to cooperative binding of protein B.