Proteins and electrolytes can be transported into cells in two ways: either through diffusion through the plasma membrane, or facilitated diffusion through a channel. Some proteins or electrolytes can be transported through both mechanisms. We can make a simplified model of this by modeling two membranes in parallel with each other, and assuming 1D diffusion through both. Assume that protein A can be transported through the membrane in either method (i.e., direct diffusion or facilitated diffusion) (NOTE: this picture doesnât really describe the system well. Imagine the red circles can move through the membrane AND/OR through the channel). Outside of the cell, the concentration of protein A is 100 nM. Inside the cell, the concentration is 10 nM. Assume the thickness of the plasma membrane is 10 nm. The diffusion constant for direct diffusion of Protein A in the membrane is 1x10^-10 cm2 /s, and the diffusion constant for facilitated diffusion is 5x10^-10 cm2 /s. The partition coefficient Φ for Protein A in the plasma membrane is 0.01, and the partition coefficient Φ for Protein A in the channel is 0.05.
A. Assume that initially the channel is closed, so Protein A can only get into the cell via direct diffusion through the membrane. Calculate the steady-state flux of Protein A across the membrane. Assume 1-D diffusion, steady state diffusion, and no convection.
B. Assume that the channel is now open, and acting in parallel to direct diffusion. Assume 1-D diffusion through both the membrane and the channel, assume steady state diffusion, and assume no convection.
C. Determine a general expression for the effective diffusion coefficient through the system in Part B, and show how these two pathways behave like resistors in parallel.
A v v Diffusion Facilitated diffusion Passive transport
