Problem 2. To turn on a signaling pathway of interest, a ligand binds its cognat

Question

Problem 2. To turn on a signaling pathway of interest, a ligand binds its cognate receptor and the complex turns on downstream pathways. However, the ligand also might turn on off-target pathways by binding other off-target receptors. The KD of the ligand with cognate receptor is 1nM, and two off-target receptors each have KD = 10nM, and all receptors are present at 50nM each. Assuming signaling is proportional to ligand-receptor complex concentration, and that we can’t have off-target signaling exceed 10% of their respective maximums, what is the optimal total ligand concentration to most activate the signaling pathway of interest (hint: think about the tradeoff between fractional occupancy and specificity factor)?

Explanation / Answer

Fractional occupancy since cannot be greater than 0.1 for off target receptors

F.O=B/R= Lf/Lf+Kd

B= bound ligand and receptor

Lf = free ligand concentration

0.1=Lf/Lf+10

Lf=1.11nM

B=R×0.1

50×0.1=5 nM

Total ligand concentration = B+Lf=6.1 nF

Fractioonal occupancy for cognate receptor must be 1 for most activate it

B of cognate = 1×50= 50nM

Total ligand concentration must be 56.1nM

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