Tumor necrosis factoralpha TNF is a proinflammatory cytokine

Tumor necrosis factor-alpha (TNF) is a pro-inflammatory cytokine that plays a critical role in many diseases, including plaque psoriasis, which is characterized by activation and aggregation of T-cells at the dermis. Let the ligand L be TNF and the receptor R be the TNF receptor on a T-cell. Under normal conditions, there is roughly an equal amount of total receptor RT and total ligand LT concentration ~0.1 nM. If the KD is 50 pM, what is the concentration of bound receptors RL? [Do not assume the ligand is in excess.] What would you have calculated the concentration of RL to be if you had assumed the ligand was in excess?

Solution

1a RL=(L*R)/Kd Kd in nM=0.05nM

=(0.1*0.1)/0.05 =0.2nM

1 b RL= (L*Rt)/(L+Kd) convert Kd in nM=0.05 nM

(0.1*0.1)/(0.1+0.05)=0.06nM