I have a 5 cm x 5 cm square petri dish that has cells adhered to the bottom. The cells are spherical with a diameter of 30 μm and are packed in a perfect square array. The cell membranes have receptors embedded in them, there are 100,000 receptors per cell and each receptor is spherical with a diameter of 4 nm and are embedded in the membrane.
a) How many cells are on the plate?
b) What fraction of the cell surface is occupied by receptors versus normal phospholipids?
c) If the cell culture media in the dish is 1 cm deep and I have a ligand in the media at a concentration of 1 μM and the Kd for the receptor-ligand interaction is 10 μM, what proportion of the ligands in solution are bound to receptors?