Figure 1. Illustration of hierarchical order with sub-divided triangles.
Thus, in the example above, we have a large triangle ABC. ABC is in turn made up of four smaller triangles, ADF, DBE, DEF, and EFC. Triangle DBE is in turn made up of four smaller triangles - DGI, GBH, GHI and HIE.
A similar example is shown below, except that we are hierarchically dis-assembling a house.
Figure 2. Illustration of hierarchical order in a building.
Analysis of protein structures by Crippen and Rose has shown them to be organized as a structural hierarchy that can be decomposed in a stepwise fashion into domains and smaller units. It is also well known, that small units of structure such as alpha helices, beta strands, beta turns and omega loops occur repeatedly in very many protein structures, which can pack together efficiently to produce higher order structures.
Figure 3. Cartoon of AZURIN. Helices are in red, beta sheet in green, beta turns in cyan and omega loops in blue.
Several experiments have shown that short stable segments of alpha-helices and beta-turns can be realized in water. These findings suggest that at least some segments can adopt well defined structures in isolation.
Taken in conjunction, these observations suggest a simple mechanism of protein folding. Segments of a chain initially partition into a limited set of conformations. Subsets of these populations can then associate into large modules, some of which are stabilized and some are not. Further iterative elaboration of these modules eventually leads to the compact tertiary structure of the protein.
Figure4. Illustration of the folding by hierarchic condensation model for protein folding. The first stage is the formation of preferentially populated states for segments of the chain, which then associate to form larger modules in an iterative fashion, until the folded tertiary structure is formed.
Based on a published algorithm it was shown that protein structures could be domains, which are further divisable into sub-domains, leading to a hierarchic molecular architecture. An example of the domains for high potential iron protein is shown below.
Figure 5. Domains in high potential iron protein. This protein contains 85 residues. The top most frame shows the entire protein as a cpk model ( in blue). The second frame shows that the protein is made up of two domains, residues 1 to 41 (in red) and 42 to 85 (in green). The domain from 1-41 can be further sub-divided into 1-20 and 21-41, while the domain from 42-85 is made up of sub-domains 42-61 and 62-85(last frame).