Tubes marginally compact

Figure 12.2. Sketch of the maximal number of contacts that a short, compact tube can make as a function of X, the dimensionless ratio of the tube thickness to the range of the attractive interaction. When X is large compared with 1, one obtains a swollen phase. At the other extreme, when X 1, one finds a highly degenerate compact phase. The twilight zone between these two phases occurs in the vicinity of X 1 and is characterized by marginally compact structures. The figure shows typical tube conformations in each of the phases.

In the twilight zone, a tube is barely able to avail itself of the attractive interactions promoting compaction. In this region of parameter space, the forces promoting compaction just set in, and one would expect to obtain marginally compact structures that have the ability to expel the water from the interior. In addition, because the scale of the interaction strength is relatively small, one would expect a... 

In this marginally compact state, the number of candidate tube structures is somewhat limited. The ground-state structures of a short tube in the marginally compact phase subject to compaction are shown in the bottom panel of Figure 12.3 below. 

Let us make the constructive hypothesis that the extraordinary similarity between the structures adopted by short tubes in the marginally compact phase and the building blocks of protein native-state structures is not a mere coincidence. We postulate instead that the tube picture presented above is a paradigm for understanding protein structures. Quite generally, such postulates are of limited utility unless one is able to unify seemingly unrelated aspects of the problem and make new predictions amenable to experimental verification. In our case, although the tube idea is theoretical, a wealth of experimental data is already available on proteins. Before we proceed to explore the consequences of our hypothesis, we... 

The marginally compact phase in tubes occurred for a finely tuned ratio, X, around 1, of the tube thickness to the range of attractive interactions. Strikingly, for proteins, this quantity is self-tuned around this value. Steric interactions lead to a vast thinning of the phase space that protein structures can explore [37,38]. Physically, the notion of a thick chain or a tube follows directly from steric interactions in a protein one... 

The situation is somewhat reminiscent of a content-addressable memory [72], in which partial information is converted by the brain to recover the complete information. Such content-addressable memories [72], as well as the energy landscape [73] suitable for prebiotic evolution [74], have been modeled through spin glasses [75]. The energy landscape of spin glasses is also characterized by diversity and stability arising from randomness and frustration, which is quite distinct from the the physical mechanisms of short tubes in the marginally compact phase. 

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