Exact sequence analysis for three-dimensional hydrophobic-polar lattice proteins

Abstract

We have exactly enumerated all sequences and conformations of HP proteins with chains of up to 19 monomers on the simple cubic lattice. For two variants of the hydrophobic-polar (HP) model, where only two types of monomers are distinguished, we determined and statistically analyzed designing sequences, i.e., sequences that have a non-degenerate ground state. Furthermore we were interested in characteristic thermodynamic properties of HP proteins with designing sequences. In order to be able to perform these exact studies, we applied an efficient enumeration method based on contact sets.

Thermodynamics of Protein Folding from Coarse-Grained Models’ Perspectives

“…Incorporating additional inter-residue interactions, symmetries are broken, degeneracies are smaller, and the number of designing sequences increases [14,15]. Based on the Miyazawa-Jernigan matrix [40] of inter-residue contact energies between real amino acids, an additional attractive nonzero energy contribution for contacts between H and P monomers is more realistic [4].…”

“…, 19 the total numbers S N of relevant designing sequences [41] in the HP and the MHP model. These results were obtained by exhaustive exact enumerations of the complete conformation and sequence spaces of chains with up to 19 monomers on the sc lattice [14]. Note that there are for a 19-mer more than 5 × 10 5 HP sequences and about 2×10 12 self-avoiding conformations on the sc lattice, which in total allows naively more than 10 18 possible combinations.…”

“…(14) for analyzing the conformational behavior of HP proteins in adsorption processes to different, specific solid substrates. The objective is the determination of a pseudophase diagram, which allows for the classification of conformational subphases in dependence of the external parameters temperature and solubility of the surrounding (implicit) solvent.…”

“…Therefore, sophisticated algorithms were developed to find lowest-energy states for chains of up to 136 monomers. The methods applied are based on very different algorithms, ranging from exact enumeration in two dimensions [11,12] and three dimensions on cuboid (compact) lattices [4,[13][14][15], and hydrophobic-core construction methods [16,17] over genetic algorithms [18][19][20][21][22], Monte Carlo simulations with different types of move sets [23][24][25][26], and generalized ensemble approaches [27] to Rosenbluth chaingrowth methods [28] of the 'Go with the Winners' type [29][30][31][32][33][34][35]. With some of these algorithms, thermodynamic quantities of lattice heteropolymers were studied as well [14,27,31,[34][35][36].…”

Mesoscopic Properties of Molecular Folding and Aggregation Processes

“…Such models allow a comprising analysis of both, the conformation and sequence space, e.g., by exactly enumerating all combinatorial possibilities [5]. Other important aspects in lattice model studies are the identification of lowest-energy conformations of comparatively long sequences and the characterization of the folding thermodynamics [6].…”