Accessibility

There are many reasons why one wants to know the accessible surface of proteins or even individual amino acids or atoms. For example:

• A buried, unsatisfied hydrogen bond donor or acceptor is energetically not good for the folded protein. (Why?)
• Residues at the surface can be antigenic.
• Cavities (internal 'accessible' surface) are energetically not good unless 'properly' filled with something that is happy there.

So, there are enough reasons to think about accessible surfaces.

Figure 35. In this figure the outside of the black area is called the molecular surface and the line that indicates where the center of the solvent probe can be found that rolls over the surface is the accessible surface. Well, that is if it wasn't for a small problem that is shown in the next figure. This figure was obtained from biogeometry.duke.edu/software/proshape/protsurf.html.

Question 25: Take a very good look, what is the difference between the Van der Waals Surface and the Molecular Surface?

Figure 36. The red balls are atoms. The blue balls represent the solvent molecule that roles over the surface. As you can see, there is a little problem that is caused by the blue areas. Obviously, a water can get there, but there is no atom there to assign the accessibility to. These little blue areas are called the re-entrant surface.

In the literature there is some fuzz about this re-entrant surface. But in practice it doesn't matter much whether you calculate it properly or not. To see why, draw two covalently bound carbon atoms and draw their Van der Waals' radii. Now draw a water at the correct scale that 'docks' on both carbons. That illustration should explain it all.

Question 26:

1. Draw two covalently bound carbons with proper dimensions. Add one water to the plot. This water should be as close to the two carbons as is possible.
2. Repeat the drawing for two carbons that are at a distance of 3.9 Ångström.
3. Why is the existence of the re-entrant surface mainly a problem for the calculation of the molecular surface and less for the accessible surface?
4. Google the rolling sphere algorithm for accessibility calculations and summarize that algorithm in less than 20 words.