Analyzing energy landscapes for folding model proteins

Abstract

A new benchmark 20-bead HP model protein sequence (on a square lattice), which has 17 distinct but degenerate global minimum (GM) energy structures, has been studied using a genetic algorithm (GA). The relative probabilities of finding particular GM conformations are determined and related to the theoretical probability of generating these structures using a recoil growth constructor operator. It is found that for longer successful GA runs, the GM probability distribution is generally very different from the constructor probability, as other GA operators have had time to overcome any initial bias in the originally generated population of structures. Structural and metric relationships (e.g., Hamming distances) between the 17 distinct GM are investigated and used, in conjunction with data on the connectivities of the GM and the pathways that link them, to explain the GM probability distributions obtained by the GA. A comparison is made of searches where the sequence is defined in the normal (forward) and reverse directions. The ease of finding mirror image solutions are also compared. Finally, this approach is applied to rationalize the ease or difficulty of finding the GM for a number of standard benchmark HP sequences on the square lattice. It is shown that the relative probabilities of finding particular members of a set of degenerate global minima depend critically on the topography of the energy landscape in the vicinity of the GM, the connections and distances between the GM, and the nature of the operators used in the chosen search method.

A Study of Hydrophobic Effect on the Protein Folding Using Monte Carlo

“…Monte Carlo and HP model have been used to investigate the folding problem and aspect like hidrophobicity, folding pathways and chain sequence chain optimization [30,31]. In this work a bidimensional grid, monte carlo and HP model was used to study the influence of the hydrophobic residues in the chain folding.…”

“…One of the most popular models is the so-called HP model, where the hydrophobic interactions between the amino acids are considered to be the main force in the folding process [30]. In this work, we have adopted the 2D square lattice HP bead model where the H and P beads are constrained to lie on a bi-dimensional square lattice and interactions occur only between nonbonded beads that lies adjacent to each other on the lattice and they are not adjacent in the sequence.…”

“…on structural databases have been used in the simulations which are performed through a variety of methods such as molecular dynamics, monte carlo simulations, genetic algorithms, neural networks, simulated annealing to predict the secondary and tertiary structure of proteins and to optimize the conformation of macromolecules [22,23,24,25,26,27,28,29]. The work reported in this paper present the use of monte carlo and the HP model [30,31,32] to study the effect of hydrophobic residues on the folding chains. The next section presents a brief report on folding protein problem and the HP model.…”

Construction of model Hamiltonians for adiabatic quantum computation and its application to finding low-energy conformations of lattice protein models

“…In the quantum version of the problem, these configurations span a Hilbert space of dimension 2 16 . The state vectors can be written as…”

“…Still its accuracy in predicting some of the folding behaviour of real proteins has made it a useful benchmark for testing optimization algorithms such as simulated annealing [14], genetic algorithms [15][16][17][18][19], and ant colony optimization [20]. Other heuristic methods such as hydrophobic core threading [21], chain growth [22,23], contact interactions [24], and hydrophobic zippers [25] have also been considered.…”