Facilitated Diffusion

Facilitated diffusion is a type of diffusion in which the molecules move from the regions of higher concentration to the region of lower concentration assisted by a carrier molecule. It is a selective process, only allowing specific molecules to pass the gradient. In the below figure, we have a liver compartment that is separated into blood and liver compartments with a facilitated transporter for compound A. Note that this is a one-way transport.

For the derivation of the flux equation for facilitated diffusion, we take the following equation:

\[F = \frac{V_{max}*[S_o]}{K_m}\]

where,

\(V_{max}\):

Maximum Velocity

\(S_{o}\):

Substrate Concentration

\(K_{m}\):

Affinity of how much substrate concentration needed to reach \(V_{max}\)

The flux derivations for the above example would be:

\[\begin{split}\begin{align*} V_{1} \frac{dA_1}{dt} &= - \frac{V_{max}*A_{1}}{k_m + A_1} \\ V_{2} \frac{dA_2}{dt} &= \frac{V_{max}*A_{1}}{k_m + A_1} \\ \end{align*}\end{split}\]