Rugen-1, -2, and -3 are a series of proteins in which a short polypeptide linker connects two polypeptides, each comprising the three zinc fingers of Zif268. (See the diagrams below.) As shown in the following table, the three-finger Zif268 peptide binds DNA with a dissociation constant of 1 nM. The table also shows the dissociation constants for the six-finger proteins binding to DNA and the sequences of their respective polypeptide linkers.
Protein Linker Sequence Kd

Zif268 n/a 1 nM (10-9 M)

Rugen-1 GGSGGSGGSGG 1 pM (10-12 M)

Rugen-2 GGSGGSGG 1 fM (10-15 M)

Rugen-3 GGSGG 1 nM (10-9 M)

a. Explain the difference in Kd values for Rugen-1 and Zif268. Base your argument on entropy and cooperativity.

b. Propose an explanation for the difference in Kd values for Rugen-1, Rugen-2, and Rugen-3. In your answer, address whether ∆H and/or ∆S is likely to differ among these processes.

c. The diagram on the next page depicts the binding of Rugen-2 to DNA as a two-step process. Given the data in the table above, provide the expected values for the three equilibrium constants. Include proper units. Describe the binding event that each equilibrium constant represents.

d. Calculate the effective concentration for binding of a Zif268 moiety in Rugen-2 when the other Zif268 moiety is already bound to DNA. Remember that the effective concentration is the ratio d. Calculate the effective concentration for binding of a Zif268 moiety in Rugen-2 when the other Zif268 moiety is already bound to DNA. Remember that the effective concentration is the ratio of the equilibrium dissociation constant for a bimolecular reaction to the equilibrium constant for a corresponding unimolecular reaction. Show your work and include the proper units. In addition, predict whether Rugen-3 would exhibit a higher or lower effective concentration.