What are the relationships between free energy and the presence of ligands or oligos that bind with an RNA riboswitch?

Hello! I learned that when ligands bind to the RNA, they give the RNA an energy bonus (Decreases free energy) and in the case for oligos, they give the RNA an energy penalty (Increases free energy).

I think Ligands give energy bonuses because they bind with both sides of the RNA aptamer loop, making the entire structure a bit harder to unstabilize and therefore, lower free energy. But what about Oligos? How do they increase free energy?

Also, is there an equation that can tell us the relationship between free energy and the presence of ligands or oligos that bind with an RNA riboswitch? Is there one for the relationship between free energy and the folding structure of the RNA?

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I always thought that your question is one of the reasons for the labs, to better understand the switching capabilities of ligands and oligos. In the labs you can hypothesize what you think should happen and actually find out if you were correct once the results are out by designing puzzles.