Question

The surface of a solid sphere is covered by a monolayer of receptors for a ligand. When the ligands diffuse to the surface of the sphere, they are captured instantaneously by the receptors. The ligand diffusion coefficient is 5.2*10-9m2/s. Assume the bulk concentration far away from the sphere is constant of 6.6 nM and the sphere radius is 9.8 μm. (a) Find the ligand concentration C at the location of r=4.9 μm at steady state, where r is the distance to the surface of the sphere. Please enter the numerical value with a unit of nM.

Answer 1

Answer:

The ligand concentration C is 0.274 nM

Explanation:

According to the image, the bulk concentration is inversely proportional to the radius, thus:

$B=\frac{B_{\alpha }r^{2} }{\alpha }$

Where

Bα = 6.6 nM

r = 14.7 um = 1.47x10⁻⁵m

$B=\frac{6.6*(1.47x10^{-5})^{2} }{5.2x10^{-9} } =0.274nM$