1. Estimate the flux (mg/cm^2/s) by diffusion of a hydrophobic anti-cancer drug through a lipid bilayer membrane.(Assume the diffusion coefficient for steroid in the lipid bilayer is 2x10-6 cm2 /s, and that the concentration is 2 ng/mL on the outside of the membrane and 0 on the inside)

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Asked Sep 18, 2019
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1. Estimate the flux (mg/cm^2/s) by diffusion of a hydrophobic anti-cancer drug through a lipid bilayer membrane.

(Assume the diffusion coefficient for steroid in the lipid bilayer is 2x10-6 cm2 /s, and that the concentration is 2 ng/mL on the outside of the membrane and 0 on the inside)

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Expert Answer

Step 1

Given:

Diffusion coefficient for steroid in the lipid bilayer is 2x10-6 cm2 /s

Concentration is 2 ng/mL on the outside of the membrane.

We need to Estimate the flux in mg/cm2/s

Flux is the number of particles which pass through a unit area in a unit of time.

Step 2

If we consider steady state configuration,

J = -D dc/dx 

J  =  flux of atoms (atoms/(m2 s))

D – diffusivity or diffusion coefficient, m2/s

dC/dx – concentration gradient, atoms/m4.

Lipid bilayer size is considered as 3 nm as we assumed steady state configuration

Step 3

Calculate dC/dx :

            dC/dx = 2 ng/mL/ 3 nm

1 ng/mL = 10-6 mg/cm3 and 3 nm = 3 X 10-7cm

So,

            dC/dx = 2 ng/mL X 10-6 mg/cm3  / 3 nm X 10-7cm

                       = 2 X 10-6 / 3 X 10-7

                       = 20 /3 = 6.66 mg/cm4

 J = -D.dc/dx = - 2x10-6 cm2 /s  X  6.66 mg/cm4

    = -13.32 X 10-6mg/s-cm2 

...

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