Final answer:
The fraction of protein bound to estrogen with a total ligand concentration of 3 nM and a KD of 5 nM is 0.375 or 37.5%, meaning that approximately 40% of the estrogen receptors will be occupied by estrogen.
Step-by-step explanation:
The question revolves around the concept of ligand binding to a receptor, specifically the binding of estrogen to its receptor and the calculation of the fraction of receptor that is bound by the ligand. The binding process can be quantitatively described using the dissociation constant (KD), which reflects the affinity between the ligand and its receptor. In this case, the KD value for the interaction between estrogen and its receptor is given as 5 nM, and the total concentration of estrogen is 3 nM. Using these figures, we can apply the equation for the receptor occupancy, which is the concentration of ligand divided by the sum of the KD plus the concentration of ligand (L/(KD+L)).
Applying the values to the equation, we have:
- Receptor occupancy = L/(KD+L) = 3 nM / (5 nM + 3 nM)
- Receptor occupancy = 3 nM / 8 nM = 0.375
Therefore, the fraction of the protein bound to estrogen at equilibrium is 0.375 or 37.5%. This implies that under the given conditions, almost 40% of the estrogen receptors will be occupied by estrogen.