Hydrophobic-polar Research Articles

Investigation of the three-dimensional lattice HP protein folding model using a genetic algorithm

An approach to the hydrophobic-polar (HP) protein folding model was developed using a genetic algorithm (GA) to find the optimal structures on a 3D cubic lattice. A modification was introduced to the scoring system of the original model to improve the model's capacity to generate more natural-like structures. The modification was based on the assumption that it may be preferable for a hydrophobic monomer to have a polar neighbor than to be in direct contact with the polar solvent. The compactness and the segregation criteria were used to compare structures created by the original HP model and by the modified one. An islands' algorithm, a new selection scheme and multiple-points crossover were used to improve the performance of the algorithm. Ten sequences, seven with length 27 and three with length 64 were analyzed. Our results suggest that the modified model has a greater tendency to form globular structures. This might be preferable, since the original HP model does not take into account the positioning of long polar segments. The algorithm was implemented in the form of a program with a graphical user interface that might have a didactical potential in the study of GA and on the understanding of hydrophobic core formation.

Preferential adsorption of hydrophobic-polar model proteins on patterned surfaces.

We study the adsorption of a single hydrophobic-polar (HP) model protein under the influence of a flat but specially designed surface. A folded HP model protein is brought to the surface with a designed pattern consisting of certain attractive and repulsive sites for the different monomers (amino acids). In contrast to the deformation of a random sequence that is continuous, deformation of any protein-like sequences is unlikely and an energy gap is associated with it. The surface with a certain wavelength of pattern attracts a certain type of folded structure preferentially and the free energy of the combined system is reduced. The model presented here represents a minimal theoretical model for protein recognition.

Randomness, Structural Uniqueness, Modularity and Neutral Evolution in Sequence Space of Model Proteins

The genotype-phenotype map for short chains of a protein-like hetero-polymer model has been characterised [9, 12]. Hydrophobic-Polar (HP) sequences on a square lattice, their structures and partition functions have been exhaustively enumerated and analysed. Homologous sequences folding uniquely into the same structure are interconnected by point mutations. These

Geometry selects highly designable structures

By enumerating all sequences of length 20, we study the designability of structures in a two-dimensional hydrophobic-polar (HP) lattice model in a wide range of intermonomer interaction parameters. We find that although the histogram of designability depends on interaction parameters, the set of highly designable structures is invariant. So in the HP lattice model the high designability should be a purely geometrical feature. Our results suggest two geometrical properties for highly designable structures; they have the maximum number of contacts and a unique neighborhood vector representation. Also we show that the contribution of perfectly stable sequences in the designability of structures plays a major role in making them highly designable.

How are model protein structures distributed in sequence space?

The figure-to-structure maps for all uniquely folding sequences of short hydrophobic polar (HP) model proteins on a square lattice is analyzed to investigate aspects considered relevant to evolution. By ranking structures by their frequencies, few very frequent and many rare structures are found. The distribution can be empirically described by a generalized Zipf's law. All structures are relatively compact, yet the most compact ones are rare. Most sequences falling to the same structure belong to "neutral nets." These graphs in sequence space are connected by point mutations and centered around prototype sequences, which tolerate the largest number (up to 55%) of neutral mutations. Profiles have been derived from these homologous sequences. Frequent structures conserve hydrophobic cores only while rare ones are sensitive to surface mutations as well. Shape space covering, i.e., the ability to transform any structure into most others with few point mutations, is very unlikely. It is concluded that many characteristic features of the sequence-to-structure map of real proteins, such as the dominance of few folds, can be explained by the simple HP model. In analogy to protein families, nets are dense and well separated in sequence space. Potential implications in better understanding the evolution of proteins and applications to improving database searches are discussed.

Perturbations of the denatured state ensemble: modeling their effects on protein stability and folding kinetics.

By considering the denatured state of a protein as an ensemble of conformations with varying numbers of sequence-specific interactions, the effects on stability, folding kinetics, and aggregation of perturbing these interactions can be predicted from changes in the molecular partition function. From general considerations, the following conclusions are drawn: (1) A perturbation that enhances a native interaction in denatured state conformations always increases the stability of the native state. (2) A perturbation that promotes a non-native interaction in the denatured state always decreases the stability of the native state. (3) A change in the denatured state ensemble can alter the kinetics of aggregation and folding. (4) The loss (or increase) in stability accompanying two mutations, each of which lowers (or raises) the free energy of the denatured state, will be less than the sum of the effects of the single mutations, except in cases where both mutations affect the same set of partially folded conformations. By modeling the denatured state as the ensemble of all non-native conformations of hydrophobic-polar (HP) chains configured on a square lattice, it can be shown that the stabilization obtained from enhancement of native interactions derives in large measure from the avoidance of non-native interactions in the D state. In addition, the kinetic effects of fixing single native contacts in the denatured state or imposing linear gradients in the HH contact probabilities are found, for some sequences, to significantly enhance the efficiency of folding by a simple hydrophobic zippering algorithm. Again, the dominant mechanism appears to be avoidance of non-native interactions. These results suggest stabilization of native interactions and imposition of gradients in the stability of local structure are two plausible mechanisms involving the denatured state that could play a role in the evolution of protein folding and stability.

Protein core assembly processes

How does a protein or HP (hydrophobic/polar) copolymer find its globally optimal (native) state without a globally exhaustive search? This is the Levinthal paradox. We consider three routes by which a copolymer might assemble a compact conformation with a maximum number of hydrophobic (HH) contacts: (i) the exhaustive search (ES) process, which assures the global optimum; (ii) a ‘‘maximum entropy string’’ (MES), a series of stepwise decisions each of which explores conformational space exhaustively for given prior contacts; and (iii) a ‘‘T-local string,’’ or ‘‘hydrophobic zippers’’ (HZ) process, which makes HH contacts opportunistically based on prior contacts. Using a two-dimensional HP short-chain lattice model, for which the partition function is exactly enumerable, we find that for many HP sequences, T-local strings lead to the globally optimal conformation, offering a resolution to the Levinthal paradox.