Protein simple lattice models

DA Elmds, M Levitt. Exploring conformational space with a simple lattice model for protein structure. J Mol Biol 243 668-682, 1994. 

Because simple lattice models take no account of local directional preferences, they fail to model these important local restraints on protein structure. Instead, they rely almost entirely on long-range interactions to encode the most stable conformation(s) (Dill et al., 1995). Thus the ability of lattice models to reproduce protein-like behavior must be called into question. And though their simplicity makes them intellectually attractive, their use in teaching and modeling protein-like behavior must be qualified with a caveat that local directional preferences have been ignored. 

Lattice models have proved to be extremely useful in studies of simple, exact models and somewhat more complex models of protein-like systems. Similarly, the conformational space of a real protein could be discretized and explored in a very efficient way by various versions of Monte Carlo sampling techniques. Depending on the assumed level of discretization and model of force field, various levels of accuracy can be achieved. For example, simple lattice models of real proteins were studied by Ueda et al. 

The current understanding of the protein folding process has benefited much from studies that focus on computer simulations of simplified lattice models. These studies try to construct as simple a model as possible that will capture some of the more important properties of the real polypeptide chain. Once such a model is defined it can be explored and studied at a level of detail that is hard to achieve with more realistic (and thus more complex) atomistic models. 

Despite their contribution to the understanding of protein folding, the correspondence between lattice models and real proteins is still very limited. The first step toward making such models more realistic is to remove the lattice and study off-lattice minimalist models. Simple off-lattice models of proteins can have proteinlike shapes with well-defined sec-... 

A wide variety of energy functions have been used as part of the various GA-based protein structure prediction protocols. These range from the hydrophobic potential in the simple HP lattice model [19] to energy models such as CHARMM, based on full fledged, detailed molecular mechanics [9]. Apparently, the ease by which various energy functions can be incorporated within the framework of GAs as fitness functions encouraged researchers to modify the energy function in very creative ways to include terms that are not used with the traditional methods for protein structure prediction. 

Simple, exact models [51] consist of simple lattice polymers or heteropolymers where each amino acid in the hypothetical protein is represented by a bead occupying a single lattice point. Because of their simplicity, these models have generated considerable attention [57,58]. 

The essential features of protein lattice models were described in Section 10.3.1. Protein folding is usually studied with a seif-avoiding chain on a cubic lattice with one residue per vertex and a simple interaction model which only includes interactions between pairs of monomers that are in contact on the lattice but are not successive in the sequence. Polymers of length 27 that occupy all sites of a 3 x 3 x 3 cube are particularly popular. There are nearly... 

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