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

Question

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.

Answer 1

Hi Ali A.,

No, sorry, you don't need a chemistry expert. More math and physiology.

You are starting to surf the interface between distribution processes of drugs in the body as rates (usually, exponential approaches to steady-state, and compartments), and the math of equilibria (concentrations, not rates!). Looks like you are just starting to get into this? -- anyway, there's lots of details that you will appreciate later -- but for right now, consider:

1) how does the injected bolus spread into the volume of blood?, and

2) how promptly does the unbound agent become removed (liver or kidney removal, usually)?.

If the free agent is essentially removed on a single pass through the kidneys, say, that must affect how much you need to inject to label your tumor cells quantitatively!

But, even assuming that complete equilibrium is achieved before substantial removal of unbound agent (a reasonable assumption), there are no data given on the sensitivity of the detection mechanism. That's essential for detecting the cells at all, in Task 1;

Also, the statement of "essentially removed in 5 minutes" is inadequate, since Task 1 (time cells remain labeled) depends on both that detail and on k(off).

Also, Task 2 requires apparently independently a volume and concentration of injected agent -- those aren't logically independent!; a more important variable might be the period over which the bolus is to be injected.

Some of this info you could obtain by checking the given primary source?, and maybe the rest of it from a standard pharmacology textbook, such as Goodman and Gilman?

Hope this steers you in a profitable direction,

-- Cheers, -- Mr. d.