I am trying to go thrgouh this question and I need someone who is chemsity expert to try to solve this problem which is related to the contrant rates
You designed a contrast agent that incorporates folate so it can bind to folate receptors. When injected intravenously (IV), this contrast agent will mark circulating tumor cells, overexpressing folate receptors. To mark these cells, you rely on folate-folate receptor interactions (see numerical data below). The plan is to inject solution of the contrast agent in humans. Upon binding to the circulating tumor cells, the contrast agent will help you to follow the distribution of the cells. Contrast agent that did not bind will clear the circulation within 5 minutes (will be removed by natural mechanism) and does not interfere.
Numerical data for folate binding to folate receptor:
Kd = 20 pM
kon = 1×106 M-1 s-1
koff = 1.3 ×10-5 s-1
Source: J Agric Food Chem 53 (2005) 5473
Task 1: Starting from injection, how long will you be able to track circulating tumor cells?
Task 2: Design the dose for IV injection (injection volume and concentration of the agent) that will ensure that at least 50% of circulating tumor cells are labelled with the contrast agent.