Snake cube

Another similarity, as well as the difference with real proteins become apparent if we compare the number of foldable sequences with the total number of possible conformations. The former number, as we have just seen, is not greater than 98,514 the latter number (conformations of the lattice 27-mer filling the 3 3 3), as we mentioned already (Section 10.10), is 103,346. The conclusion is that there are some sequences which can fold into two (or maybe even more) different conformations This is indeed similar to the story we told in Section 10.7. Of course, the analogy with proteins is limited, for instance, in proteins the number of sequences is larger than the number of possible conformations. Still, the snake cube is a great fun for someone thinking about proteins ... 

This leads us to the question are all of the possible almost 17 million sequences foldable The answer is, of course, no. For instance, if there are even two [Pg.217]

Our behavioral bioassay was designed to take advantage of the high degree of thigmotaxis displayed by the snakes and their tendency to actively explore novel environments. Snakes were tested in a clear cube-shaped Plexiglas arena, measuring 1.25m on each side. The floor of the arena was evenly divided into four quadrants with tape. Before a snake was added to the arena, a randomly chosen quadrant was treated... 

The simple circuits in the graph of the iV-cube defined by the cyclic attractors have been called snakes in the combinatorial literature. ... 

The reptation model envisages the polymer chain to be enclosed within an initial tube out of which it gradually escapes by wriggling in a snake-like manner ( reptating reptare to creep). The reptation relaxation time Tr corresponds to the time when about 70% of the chain has escaped from the initial tube. During this time, the interfacial thickness increases with time t, in proportion to f, in contrast with the relationship for Fickian diffusion. The relaxation time Tr is proportional to the cube of molecular weight. 

---