Lattice models hydrophobic-polar model

To clarify the relevance of non-native intermediates in the folding of proteins dictated by the formation of disulfide bonds Camacho and Thirumalai [45] used lattice models. While these models are merely caricatures of proteins, they contain the specific effects that can be studied in microscopic detail. We used a two-dimensional lattice sequence consisting of hydrophobic (H), polar (P), and Cys (C) residues. If two C beads are near neighbors on the lattice, they can form a S-S bond with an associated energy gain of —with > 0. Thus, topological specificity is required for native S-S bond formation in this model. We have studied the folding kinetics of this model, which is perhaps the simplest model that can probe the characteristics of native and non-native disulfide bonded intermediates. 

The HP model is a coarse-grained (lattice or off-lattice) polymer model that abstracts from real polymers in two important ways (i) Instead of modeling the positions of all atoms of the polymer, it models only the backbone structure of the polymer, i.e., one position for each monomeric unit, (ii) Usually, only the hydrophobic interaction between the monomeric units is modeled, therefore the model distinguishes only two kinds of monomeric units, namely hydrophobic (H) and hydrophilic (or polar, P). 

The lattice model for ternary amphiphilic systems can now be constructed [33,36]. A binary variable 5, = 1 indicates whether a lattice site i is occupied by a polar or hydrophobic species, and a second variable /, = 1,0 indicates whether that species is part of a surfactant molecule or not. The Hamiltonian for these variables is... 

Polymer Description. A lattice model heteropolymer (129-131) provides a simple yet instructive description of a protein molecule. In general, the coarse graining is such that each segment represents a portion of the protein (ie many amino acids). In the simplest case, two t3q>es of segments are present these may be thought of as polar and hydrophobic (132-138). In other cases, a distribution... 

Since lattice models suffer from undesired effects of the underlying lattice symmetries, simple hydrophobic-polar off-lattice models were introduced. One such model is the AB model, where, for historical reasons, A symbolizes hydrophobic and B polar regions of the protein, whose conformations are modeled by polymer chains in continuum space governed by effective bending energy and van der Waals interactions [14]. These models allow for the analysis of different mutated sequences with respect to their folding... 

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. 

The simplest model for a quahtative description of protein folding is the lattice hydrophobic jolar (HP) model [12]. In this model, the continuous conformational space is reduced to discrete regular lattices and conformations of proteins are modeled as selfavoiding walks restricted to the lattice. Assuming that the hydrophobic interaction is the most essential force toward the native fold, sequences of HP proteins consist of only two types of monomers (or classes of amino acids) Amino acids with high hydrophobicity are treated as hydrophobic monomers (//), while the class of polar (or hydrophihc) residues is... 

A manifest off-lattice generalization of the HP model is the AB model (1.13), where the hydrophobic monomers are labeled A and the polar or hydrophilic ones, 5 [ 14]. The contact interaction is replaced by a distance-dependent Leimard-Jones type of potential accounting for short-range excluded volume repulsion and long-range interaction, the latter being attractive for AA and BB pairs and repulsive for AB pairs of monomers. An additional... 

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