Diffusion through many circular apertures in a planar barrier

1.

• Read Berg Links to an external site. pages 34-35.

The problem we want to understand is that of particles diffusing from a plate to a surface that is reflecting except for a regular array of disks of radius s in which particles are adsorbed. We want to compare this to the situation where the surface is all totally adsorbing as discussed by Berg.

• Go through hw3/3d_diff/box_diff.py and comment it to explain what it is doing.
• Use it to verify the solution numerically of Berg. Here we have a walker in a rectangular box with reflecting sides. Particles are emitted from the top surface and will be adsorbed if they hit a disk at the bottom. Relate this to a regular infinite array of adsorbing disks with no reflecting sides.

2

1. The above results are applicable to membrane proteins. Give examples of the kind of membrane proteins that are relevant to this process.
2. What is the total density of all membrane proteins in a typical cell (pick an organism of your choice)? What proportion of the membrane mass are membrane proteins, and what does this imply about the importance of transporters?
3. For a membrane protein family of your choice, what is the predicted spacing from the model given in Berg? What could cause the spacing to deviate from the model?