Protein folding lattice models

C2.5.3.4 EXPLORING THE PROTEIN FOLDING MECHANISM USING THE LATTICE MODEL... 

Abstract. A smooth empirical potential is constructed for use in off-lattice protein folding studies. Our potential is a function of the amino acid labels and of the distances between the Ca atoms of a protein. The potential is a sum of smooth surface potential terms that model solvent interactions and of pair potentials that are functions of a distance, with a smooth cutoff at 12 Angstrom. Techniques include the use of a fully automatic and reliable estimator for smooth densities, of cluster analysis to group together amino acid pairs with similar distance distributions, and of quadratic progrmnming to find appropriate weights with which the various terms enter the total potential. For nine small test proteins, the new potential has local minima within 1.3-4.7A of the PDB geometry, with one exception that has an error of S.SA. 

Sali A, E Shakhnovich and M Karplus 1994b. PCinetics of Protein Folding. A Lattice Model Study of Requirements for Folding to the Native State, journal of Molecular Biology 235 1614-1636. 

Simplified models for proteins are being used to predict their stmcture and the folding process. One is the lattice model where proteins are represented as self-avoiding flexible chains on lattices, and the lattice sites are occupied by the different residues (29). When only hydrophobic interactions are considered and the residues are either hydrophobic or hydrophilic, simulations have shown that, as in proteins, the stmctures with optimum energy are compact and few in number. An additional component, hydrogen bonding, has to be invoked to obtain stmctures similar to the secondary stmctures observed in nature (30). 

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. 

To conclude, although the models used in lattice simulations are very simplified, the results provide general information on possible protein folding scenarios, albeit not on the detailed behavior of specific proteins, which would require more complex models and more accurate potentials. The contribution made by these simulations is that they enable an analysis of the structures, energetics, and dynamics of folding reactions at a level of detail not accessible to experiment. 

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 Kolinski, J Skolmck. Monte Carlo simulations of protein folding. I. Lattice model and interaction scheme. Pi-otem 18 338-352, 1994. 

A Sail, El Shakhnovich, M Karplus. Kinetics of protein folding A lattice model study of the requirements for folding to the native state. J Mol Biol 235 1614-1636, 1994. 

Hermans, Jr., J., Lohr, D. and Ferro, D. Treatment of the Folding and Unfolding of Protein Molecules in Solution According to a Lattic Model. Vol. 9, pp. 229-283. 

A step closer toward realism is taken by off-lattice models in which the backbone is specified in some detail, while side chains, if they are represented at all, are taken to be single, unified spheres [44-50]. One indication that this approach is too simplistic was given in [51], which proved that for a backbone representation in which only Ca carbons were modeled, no contact potential could stabilize the native conformation of a single protein against its nonnative ( decoy ) conformations. However, Irback and co-workers were able to fold real protein sequences, albeit short ones, using a detailed backbone representation, with coarse-grained side chains modeled as spheres [49, 52-54]. 

Although their medium-resolution model was successful for a-helical proteins, folding P-hairpin structures have been difficult. In general, many off-lattice approaches have been tested, and although definitive proof does not exist in most cases, there appears to be a growing consensus that such off-lattice models are not sufficient. 

Mirny, L., and Shakhnovich, E. (2001). Protein folding theory From lattice to all-atom models. Annu. Rev. Biophys. Biomolec. Strud. 30, 361-396. 

Thirumalai, D., and Klimov, D. K. (1999). Deciphering the timescales and mechanisms of protein folding using minimal off-lattice models. Curr. Opin. Struct. Biol. 9, 197-207. 

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