Lattice model residue

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). 

Despite their simplicity, certainly compared to the all-atom potentials used in molecular dynamics studies, these contact energy functions enable the exploration of different interaction scenarios. This diversity is achieved by changing the heterogeneity of the sequence, by altering the number N of different types of residues that are being used. The most elementary lattice model involves only two types of monomers hydrophobic... 

This approach was later extended to off-lattice models and a more detailed description of the transfer energy of the different amino acid residues [77]. Magainin, melit-tin, and several other amphipathic peptides were simulated. In these simulations, differences in the interaction of the peptides with the lipid phase were observed. For example, magainin only showed adsorption onto the lipid and no crossing of the lipid occurred, whereas melittin crossed the lipid and formed a stable transmembrane helix. These results are in full agreement with later studies reported by other research groups presented below, involving more elaborate simulation protocols and representations of the peptides and the lipid. These examples show the potential of computer simulations even when some simplifications have to be made to make the system computationally tractable. 

The Oishi-Prausnitz model cannot be defined strictly as a lattice model. The combinatorial and residual terms in the original UNIFAC and UNIQUAC models can be derived from lattice statistics arguments similar to those used in deriving the other models discussed in this section. On the other hand, the free volume contribution to the Oishi-Prausnitz model is derived from the Flory equation of state discussed in the next section. Thus, the Oishi-Prausnitz model is a hybrid of the lattice-fluid and free volume approaches. 

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... 

Conversely, our findings suggest the need to be careful when double mutation experiments are used to probe residue pair interactions in proteins. The study of the two-dimensional square lattice model clearly demonstrates a counterexample in which cooperative effects between two residue pairs can occur even though there is no direct interaction between the two residue pairs. Therefore, results from double mutation experiments may not necessarily reflect residue pair interactions. 

Fig. 27. Resistivity p(T) (a), thermoelectric power S(T) and Lorenz number L T) (b), calculated with LNCA techniques for a sixfold degenerate Anderson lattice model in the Kondo regime (Cox and Grewe 1988). Impurity results, scaled with concentration are shown for comparison. The resistivity results exhibit the logarithmic increase with decreasing temperature and the coherence-derived decrease below T = to the residual value due to impurities, which is quadratic in the Fermi liquid regime T < T. S(T ) is positive definite for the simple model situation chosen.

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