Semiempirical and Polymer Models

It is possible to create simplified models that avoid atomic detail and instead rely on a more schematic residue-based view. A great deal is known from polymer theory about the behavior of these simplified models. Models can be constructed with a minimal amount of information and tested to see if they exhibit the behavior of actual proteins. If they do, then fundamental questions can be raised about protein stability. These include the relative importance of various constraints and intramolecular interactions. In this way, qualitative insights into protein conformation and folding can be gained. Because these models are simplified, many of the terms in the potential function do not correspond directly to actual energies, but instead are parameterized empirically to produce observed properties of interest. Skolnick and Kolinski have recently reviewed these topics.  

One way of limiting the conformational space available to a protein is to confine a model polypeptide to a lattice. In doing so, unrealistic distortions are imposed on protein structure. However, lattice models offer the possibility to enumerate the entire conformational space available to a polymer chain. A detailed atomic picture is not typically employed with lattice models. However, a variety of lattices of increasing complexity facilitate more detailed chain representations, A trade-off exists between the detail of the models and the ability to evaluate conformational alternatives exhaustively. 

Lau and Dill have also investigated the statistical mechanics of folding for simplified protein models on two-dimensional square lattices. They explored both conformational space (the set of all possible conformations) and sequence space (the set of all possible sequences) and concluded that many sequences have stable, compact, native-like structures. Another conclusion of these studies was that sequences tended to form a single, unique structure, even with only two types of residues (hydrophobic and polar). This tendency increased with chain length. Moreover, one or two mutations in these sequences did not greatly destabilize most folded states. 

Chan and Dill investigated the formation of secondary structure as a function of polymer compactness on a cubic lattice. No hydrogen bond term was used to stabilize the formation of secondary structure. They found that 

Most lattice methods rely on an extremely simple potential function, either a two state interresidue contact energy corresponding to native/nonnative contacts, or a three state model, corresponding to hydrophobic-hydrophobic, hydrophilic-hydrophilic, and hydrophobic-hydrophilic interactions. The interaction of the twenty naturally-occurring amino acids in real proteins are obviously more complex. 

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