If there was a peptide that binds specifically to a folded protein, can it also bind to the same unfolded protein? Would it be logical to assume that a peptide can generally bind more strongly to unfolded proteins due to an increased number of interactions (hydrophobic, hydrophilic/charged etc)?
I would expect that a peptide binds strongly to an unfolded protein to form aggregates: if that's the case there is no surprise.
What you should ask is: does the peptide binds in the same site of the folded and unfolded protein? if that is the case, then it will be quite remarkable, but it is unlikely to be.
If there was a peptide that binds specifically to a site in folded protein, the binding of this peptide to the same unfolded protein is depending on the binding site . if the binding site changed due to unfolding the binding will be weaker .
The unfolding cause the the appearance of hydrophobic sites of the surface of protein , so if the interaction of the peptide with the protein is depending on the hydrophobic site the interaction will be stronger .
You do not say how large your peptides are or if the binding of the peptide is a specific one, binding to a binding site.
Is the protein the peptides binds to an enzyme and is the peptide meant to come off again or is it an inhibitor that binds to stop some activity?
It will depend on the balance of favorable interactions (enthalpy) versus loss in conformational entropy. For the folded protein, the loss in conformational entropy is less upon binding. But for the unfolded protein the loss in conformational entropy will be large upon binding. If the increased interactions for the unfolded protein can more than compensate the increased loss in conformational entropy then the net Gibbs free energy will be favorable resulting in tighter binding.
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